Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [430,2,Mod(257,430)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(430, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("430.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 430 = 2 \cdot 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 430.g (of order \(4\), degree \(2\), 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: | \(3.43356728692\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 430.343 |
Dual form | 430.2.g.a.257.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/430\mathbb{Z}\right)^\times\).
\(n\) | \(87\) | \(261\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.41421 | + | 1.41421i | −0.816497 | + | 0.816497i | −0.985599 | − | 0.169102i | \(-0.945913\pi\) |
0.169102 | + | 0.985599i | \(0.445913\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.707107 | + | 2.12132i | −0.316228 | + | 0.948683i | ||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | −2.82843 | − | 2.82843i | −1.06904 | − | 1.06904i | −0.997433 | − | 0.0716124i | \(-0.977186\pi\) |
−0.0716124 | − | 0.997433i | \(-0.522814\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 2.00000 | − | 1.00000i | 0.632456 | − | 0.316228i | ||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | −1.41421 | − | 1.41421i | −0.408248 | − | 0.408248i | ||||
\(13\) | 2.00000 | + | 2.00000i | 0.554700 | + | 0.554700i | 0.927794 | − | 0.373094i | \(-0.121703\pi\) |
−0.373094 | + | 0.927794i | \(0.621703\pi\) | |||||||
\(14\) | 4.00000i | 1.06904i | ||||||||
\(15\) | −2.00000 | − | 4.00000i | −0.516398 | − | 1.03280i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 5.00000 | − | 5.00000i | 1.21268 | − | 1.21268i | 0.242536 | − | 0.970143i | \(-0.422021\pi\) |
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | 4.24264 | 0.973329 | 0.486664 | − | 0.873589i | \(-0.338214\pi\) | ||||
0.486664 | + | 0.873589i | \(0.338214\pi\) | |||||||
\(20\) | −2.12132 | − | 0.707107i | −0.474342 | − | 0.158114i | ||||
\(21\) | 8.00000 | 1.74574 | ||||||||
\(22\) | 2.82843 | + | 2.82843i | 0.603023 | + | 0.603023i | ||||
\(23\) | −5.00000 | − | 5.00000i | −1.04257 | − | 1.04257i | −0.999053 | − | 0.0435195i | \(-0.986143\pi\) |
−0.0435195 | − | 0.999053i | \(-0.513857\pi\) | |||||||
\(24\) | 2.00000i | 0.408248i | ||||||||
\(25\) | −4.00000 | − | 3.00000i | −0.800000 | − | 0.600000i | ||||
\(26\) | − | 2.82843i | − | 0.554700i | ||||||
\(27\) | −2.82843 | − | 2.82843i | −0.544331 | − | 0.544331i | ||||
\(28\) | 2.82843 | − | 2.82843i | 0.534522 | − | 0.534522i | ||||
\(29\) | 4.24264 | 0.787839 | 0.393919 | − | 0.919145i | \(-0.371119\pi\) | ||||
0.393919 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(30\) | −1.41421 | + | 4.24264i | −0.258199 | + | 0.774597i | ||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 5.65685 | − | 5.65685i | 0.984732 | − | 0.984732i | ||||
\(34\) | −7.07107 | −1.21268 | ||||||||
\(35\) | 8.00000 | − | 4.00000i | 1.35225 | − | 0.676123i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.24264 | − | 4.24264i | −0.697486 | − | 0.697486i | 0.266382 | − | 0.963868i | \(-0.414172\pi\) |
−0.963868 | + | 0.266382i | \(0.914172\pi\) | |||||||
\(38\) | −3.00000 | − | 3.00000i | −0.486664 | − | 0.486664i | ||||
\(39\) | −5.65685 | −0.905822 | ||||||||
\(40\) | 1.00000 | + | 2.00000i | 0.158114 | + | 0.316228i | ||||
\(41\) | −12.0000 | −1.87409 | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||||
−0.937043 | + | 0.349215i | \(0.886448\pi\) | |||||||
\(42\) | −5.65685 | − | 5.65685i | −0.872872 | − | 0.872872i | ||||
\(43\) | 0.535534 | − | 6.53553i | 0.0816682 | − | 0.996660i | ||||
\(44\) | − | 4.00000i | − | 0.603023i | ||||||
\(45\) | 2.12132 | + | 0.707107i | 0.316228 | + | 0.105409i | ||||
\(46\) | 7.07107i | 1.04257i | ||||||||
\(47\) | −5.00000 | + | 5.00000i | −0.729325 | + | 0.729325i | −0.970485 | − | 0.241160i | \(-0.922472\pi\) |
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(48\) | 1.41421 | − | 1.41421i | 0.204124 | − | 0.204124i | ||||
\(49\) | 9.00000i | 1.28571i | ||||||||
\(50\) | 0.707107 | + | 4.94975i | 0.100000 | + | 0.700000i | ||||
\(51\) | 14.1421i | 1.98030i | ||||||||
\(52\) | −2.00000 | + | 2.00000i | −0.277350 | + | 0.277350i | ||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | 4.00000i | 0.544331i | ||||||||
\(55\) | 2.82843 | − | 8.48528i | 0.381385 | − | 1.14416i | ||||
\(56\) | −4.00000 | −0.534522 | ||||||||
\(57\) | −6.00000 | + | 6.00000i | −0.794719 | + | 0.794719i | ||||
\(58\) | −3.00000 | − | 3.00000i | −0.393919 | − | 0.393919i | ||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 4.00000 | − | 2.00000i | 0.516398 | − | 0.258199i | ||||
\(61\) | − | 4.24264i | − | 0.543214i | −0.962408 | − | 0.271607i | \(-0.912445\pi\) | ||
0.962408 | − | 0.271607i | \(-0.0875552\pi\) | |||||||
\(62\) | −5.65685 | − | 5.65685i | −0.718421 | − | 0.718421i | ||||
\(63\) | −2.82843 | + | 2.82843i | −0.356348 | + | 0.356348i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −5.65685 | + | 2.82843i | −0.701646 | + | 0.350823i | ||||
\(66\) | −8.00000 | −0.984732 | ||||||||
\(67\) | −2.00000 | + | 2.00000i | −0.244339 | + | 0.244339i | −0.818642 | − | 0.574304i | \(-0.805273\pi\) |
0.574304 | + | 0.818642i | \(0.305273\pi\) | |||||||
\(68\) | 5.00000 | + | 5.00000i | 0.606339 | + | 0.606339i | ||||
\(69\) | 14.1421 | 1.70251 | ||||||||
\(70\) | −8.48528 | − | 2.82843i | −1.01419 | − | 0.338062i | ||||
\(71\) | − | 5.65685i | − | 0.671345i | −0.941979 | − | 0.335673i | \(-0.891036\pi\) | ||
0.941979 | − | 0.335673i | \(-0.108964\pi\) | |||||||
\(72\) | −0.707107 | − | 0.707107i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 1.41421 | − | 1.41421i | 0.165521 | − | 0.165521i | −0.619486 | − | 0.785007i | \(-0.712659\pi\) |
0.785007 | + | 0.619486i | \(0.212659\pi\) | |||||||
\(74\) | 6.00000i | 0.697486i | ||||||||
\(75\) | 9.89949 | − | 1.41421i | 1.14310 | − | 0.163299i | ||||
\(76\) | 4.24264i | 0.486664i | ||||||||
\(77\) | 11.3137 | + | 11.3137i | 1.28932 | + | 1.28932i | ||||
\(78\) | 4.00000 | + | 4.00000i | 0.452911 | + | 0.452911i | ||||
\(79\) | − | 10.0000i | − | 1.12509i | −0.826767 | − | 0.562544i | \(-0.809823\pi\) | ||
0.826767 | − | 0.562544i | \(-0.190177\pi\) | |||||||
\(80\) | 0.707107 | − | 2.12132i | 0.0790569 | − | 0.237171i | ||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | 8.48528 | + | 8.48528i | 0.937043 | + | 0.937043i | ||||
\(83\) | 6.00000 | + | 6.00000i | 0.658586 | + | 0.658586i | 0.955045 | − | 0.296460i | \(-0.0958061\pi\) |
−0.296460 | + | 0.955045i | \(0.595806\pi\) | |||||||
\(84\) | 8.00000i | 0.872872i | ||||||||
\(85\) | 7.07107 | + | 14.1421i | 0.766965 | + | 1.53393i | ||||
\(86\) | −5.00000 | + | 4.24264i | −0.539164 | + | 0.457496i | ||||
\(87\) | −6.00000 | + | 6.00000i | −0.643268 | + | 0.643268i | ||||
\(88\) | −2.82843 | + | 2.82843i | −0.301511 | + | 0.301511i | ||||
\(89\) | −14.1421 | −1.49906 | −0.749532 | − | 0.661968i | \(-0.769721\pi\) | ||||
−0.749532 | + | 0.661968i | \(0.769721\pi\) | |||||||
\(90\) | −1.00000 | − | 2.00000i | −0.105409 | − | 0.210819i | ||||
\(91\) | − | 11.3137i | − | 1.18600i | ||||||
\(92\) | 5.00000 | − | 5.00000i | 0.521286 | − | 0.521286i | ||||
\(93\) | −11.3137 | + | 11.3137i | −1.17318 | + | 1.17318i | ||||
\(94\) | 7.07107 | 0.729325 | ||||||||
\(95\) | −3.00000 | + | 9.00000i | −0.307794 | + | 0.923381i | ||||
\(96\) | −2.00000 | −0.204124 | ||||||||
\(97\) | 9.00000 | − | 9.00000i | 0.913812 | − | 0.913812i | −0.0827581 | − | 0.996570i | \(-0.526373\pi\) |
0.996570 | + | 0.0827581i | \(0.0263729\pi\) | |||||||
\(98\) | 6.36396 | − | 6.36396i | 0.642857 | − | 0.642857i | ||||
\(99\) | 4.00000i | 0.402015i | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 10.0000 | − | 10.0000i | 0.990148 | − | 0.990148i | ||||
\(103\) | −9.00000 | − | 9.00000i | −0.886796 | − | 0.886796i | 0.107418 | − | 0.994214i | \(-0.465742\pi\) |
−0.994214 | + | 0.107418i | \(0.965742\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | −5.65685 | + | 16.9706i | −0.552052 | + | 1.65616i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | + | 12.0000i | −1.16008 | + | 1.16008i | −0.175627 | + | 0.984457i | \(0.556195\pi\) |
−0.984457 | + | 0.175627i | \(0.943805\pi\) | |||||||
\(108\) | 2.82843 | − | 2.82843i | 0.272166 | − | 0.272166i | ||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | −8.00000 | + | 4.00000i | −0.762770 | + | 0.381385i | ||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | 2.82843 | + | 2.82843i | 0.267261 | + | 0.267261i | ||||
\(113\) | −7.07107 | + | 7.07107i | −0.665190 | + | 0.665190i | −0.956599 | − | 0.291409i | \(-0.905876\pi\) |
0.291409 | + | 0.956599i | \(0.405876\pi\) | |||||||
\(114\) | 8.48528 | 0.794719 | ||||||||
\(115\) | 14.1421 | − | 7.07107i | 1.31876 | − | 0.659380i | ||||
\(116\) | 4.24264i | 0.393919i | ||||||||
\(117\) | 2.00000 | − | 2.00000i | 0.184900 | − | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28.2843 | −2.59281 | ||||||||
\(120\) | −4.24264 | − | 1.41421i | −0.387298 | − | 0.129099i | ||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | −3.00000 | + | 3.00000i | −0.271607 | + | 0.271607i | ||||
\(123\) | 16.9706 | − | 16.9706i | 1.53018 | − | 1.53018i | ||||
\(124\) | 8.00000i | 0.718421i | ||||||||
\(125\) | 9.19239 | − | 6.36396i | 0.822192 | − | 0.569210i | ||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | −5.00000 | + | 5.00000i | −0.443678 | + | 0.443678i | −0.893246 | − | 0.449568i | \(-0.851578\pi\) |
0.449568 | + | 0.893246i | \(0.351578\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 8.48528 | + | 10.0000i | 0.747087 | + | 0.880451i | ||||
\(130\) | 6.00000 | + | 2.00000i | 0.526235 | + | 0.175412i | ||||
\(131\) | 1.41421i | 0.123560i | 0.998090 | + | 0.0617802i | \(0.0196778\pi\) | ||||
−0.998090 | + | 0.0617802i | \(0.980322\pi\) | |||||||
\(132\) | 5.65685 | + | 5.65685i | 0.492366 | + | 0.492366i | ||||
\(133\) | −12.0000 | − | 12.0000i | −1.04053 | − | 1.04053i | ||||
\(134\) | 2.82843 | 0.244339 | ||||||||
\(135\) | 8.00000 | − | 4.00000i | 0.688530 | − | 0.344265i | ||||
\(136\) | − | 7.07107i | − | 0.606339i | ||||||
\(137\) | 7.07107 | + | 7.07107i | 0.604122 | + | 0.604122i | 0.941404 | − | 0.337282i | \(-0.109507\pi\) |
−0.337282 | + | 0.941404i | \(0.609507\pi\) | |||||||
\(138\) | −10.0000 | − | 10.0000i | −0.851257 | − | 0.851257i | ||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 4.00000 | + | 8.00000i | 0.338062 | + | 0.676123i | ||||
\(141\) | − | 14.1421i | − | 1.19098i | ||||||
\(142\) | −4.00000 | + | 4.00000i | −0.335673 | + | 0.335673i | ||||
\(143\) | −8.00000 | − | 8.00000i | −0.668994 | − | 0.668994i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −3.00000 | + | 9.00000i | −0.249136 | + | 0.747409i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | −12.7279 | − | 12.7279i | −1.04978 | − | 1.04978i | ||||
\(148\) | 4.24264 | − | 4.24264i | 0.348743 | − | 0.348743i | ||||
\(149\) | −9.89949 | −0.810998 | −0.405499 | − | 0.914095i | \(-0.632902\pi\) | ||||
−0.405499 | + | 0.914095i | \(0.632902\pi\) | |||||||
\(150\) | −8.00000 | − | 6.00000i | −0.653197 | − | 0.489898i | ||||
\(151\) | 8.48528i | 0.690522i | 0.938507 | + | 0.345261i | \(0.112210\pi\) | ||||
−0.938507 | + | 0.345261i | \(0.887790\pi\) | |||||||
\(152\) | 3.00000 | − | 3.00000i | 0.243332 | − | 0.243332i | ||||
\(153\) | −5.00000 | − | 5.00000i | −0.404226 | − | 0.404226i | ||||
\(154\) | − | 16.0000i | − | 1.28932i | ||||||
\(155\) | −5.65685 | + | 16.9706i | −0.454369 | + | 1.36311i | ||||
\(156\) | − | 5.65685i | − | 0.452911i | ||||||
\(157\) | −1.41421 | − | 1.41421i | −0.112867 | − | 0.112867i | 0.648418 | − | 0.761285i | \(-0.275431\pi\) |
−0.761285 | + | 0.648418i | \(0.775431\pi\) | |||||||
\(158\) | −7.07107 | + | 7.07107i | −0.562544 | + | 0.562544i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | + | 1.00000i | −0.158114 | + | 0.0790569i | ||||
\(161\) | 28.2843i | 2.22911i | ||||||||
\(162\) | −7.77817 | − | 7.77817i | −0.611111 | − | 0.611111i | ||||
\(163\) | 2.82843 | − | 2.82843i | 0.221540 | − | 0.221540i | −0.587607 | − | 0.809146i | \(-0.699930\pi\) |
0.809146 | + | 0.587607i | \(0.199930\pi\) | |||||||
\(164\) | − | 12.0000i | − | 0.937043i | ||||||
\(165\) | 8.00000 | + | 16.0000i | 0.622799 | + | 1.24560i | ||||
\(166\) | − | 8.48528i | − | 0.658586i | ||||||
\(167\) | 11.0000 | − | 11.0000i | 0.851206 | − | 0.851206i | −0.139076 | − | 0.990282i | \(-0.544413\pi\) |
0.990282 | + | 0.139076i | \(0.0444133\pi\) | |||||||
\(168\) | 5.65685 | − | 5.65685i | 0.436436 | − | 0.436436i | ||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 5.00000 | − | 15.0000i | 0.383482 | − | 1.15045i | ||||
\(171\) | − | 4.24264i | − | 0.324443i | ||||||
\(172\) | 6.53553 | + | 0.535534i | 0.498330 | + | 0.0408341i | ||||
\(173\) | −16.0000 | − | 16.0000i | −1.21646 | − | 1.21646i | −0.968864 | − | 0.247593i | \(-0.920360\pi\) |
−0.247593 | − | 0.968864i | \(-0.579640\pi\) | |||||||
\(174\) | 8.48528 | 0.643268 | ||||||||
\(175\) | 2.82843 | + | 19.7990i | 0.213809 | + | 1.49666i | ||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.0000 | + | 10.0000i | 0.749532 | + | 0.749532i | ||||
\(179\) | −1.41421 | −0.105703 | −0.0528516 | − | 0.998602i | \(-0.516831\pi\) | ||||
−0.0528516 | + | 0.998602i | \(0.516831\pi\) | |||||||
\(180\) | −0.707107 | + | 2.12132i | −0.0527046 | + | 0.158114i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | −8.00000 | + | 8.00000i | −0.592999 | + | 0.592999i | ||||
\(183\) | 6.00000 | + | 6.00000i | 0.443533 | + | 0.443533i | ||||
\(184\) | −7.07107 | −0.521286 | ||||||||
\(185\) | 12.0000 | − | 6.00000i | 0.882258 | − | 0.441129i | ||||
\(186\) | 16.0000 | 1.17318 | ||||||||
\(187\) | −20.0000 | + | 20.0000i | −1.46254 | + | 1.46254i | ||||
\(188\) | −5.00000 | − | 5.00000i | −0.364662 | − | 0.364662i | ||||
\(189\) | 16.0000i | 1.16383i | ||||||||
\(190\) | 8.48528 | − | 4.24264i | 0.615587 | − | 0.307794i | ||||
\(191\) | − | 19.7990i | − | 1.43260i | −0.697790 | − | 0.716302i | \(-0.745833\pi\) | ||
0.697790 | − | 0.716302i | \(-0.254167\pi\) | |||||||
\(192\) | 1.41421 | + | 1.41421i | 0.102062 | + | 0.102062i | ||||
\(193\) | 11.0000 | + | 11.0000i | 0.791797 | + | 0.791797i | 0.981786 | − | 0.189989i | \(-0.0608452\pi\) |
−0.189989 | + | 0.981786i | \(0.560845\pi\) | |||||||
\(194\) | −12.7279 | −0.913812 | ||||||||
\(195\) | 4.00000 | − | 12.0000i | 0.286446 | − | 0.859338i | ||||
\(196\) | −9.00000 | −0.642857 | ||||||||
\(197\) | 2.00000 | − | 2.00000i | 0.142494 | − | 0.142494i | −0.632261 | − | 0.774755i | \(-0.717873\pi\) |
0.774755 | + | 0.632261i | \(0.217873\pi\) | |||||||
\(198\) | 2.82843 | − | 2.82843i | 0.201008 | − | 0.201008i | ||||
\(199\) | −11.3137 | −0.802008 | −0.401004 | − | 0.916076i | \(-0.631339\pi\) | ||||
−0.401004 | + | 0.916076i | \(0.631339\pi\) | |||||||
\(200\) | −4.94975 | + | 0.707107i | −0.350000 | + | 0.0500000i | ||||
\(201\) | − | 5.65685i | − | 0.399004i | ||||||
\(202\) | −1.41421 | − | 1.41421i | −0.0995037 | − | 0.0995037i | ||||
\(203\) | −12.0000 | − | 12.0000i | −0.842235 | − | 0.842235i | ||||
\(204\) | −14.1421 | −0.990148 | ||||||||
\(205\) | 8.48528 | − | 25.4558i | 0.592638 | − | 1.77791i | ||||
\(206\) | 12.7279i | 0.886796i | ||||||||
\(207\) | −5.00000 | + | 5.00000i | −0.347524 | + | 0.347524i | ||||
\(208\) | −2.00000 | − | 2.00000i | −0.138675 | − | 0.138675i | ||||
\(209\) | −16.9706 | −1.17388 | ||||||||
\(210\) | 16.0000 | − | 8.00000i | 1.10410 | − | 0.552052i | ||||
\(211\) | − | 12.7279i | − | 0.876226i | −0.898920 | − | 0.438113i | \(-0.855647\pi\) | ||
0.898920 | − | 0.438113i | \(-0.144353\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | + | 8.00000i | 0.548151 | + | 0.548151i | ||||
\(214\) | 16.9706 | 1.16008 | ||||||||
\(215\) | 13.4853 | + | 5.75736i | 0.919689 | + | 0.392649i | ||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −22.6274 | − | 22.6274i | −1.53605 | − | 1.53605i | ||||
\(218\) | −1.41421 | + | 1.41421i | −0.0957826 | + | 0.0957826i | ||||
\(219\) | 4.00000i | 0.270295i | ||||||||
\(220\) | 8.48528 | + | 2.82843i | 0.572078 | + | 0.190693i | ||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | −8.48528 | − | 8.48528i | −0.569495 | − | 0.569495i | ||||
\(223\) | −14.1421 | + | 14.1421i | −0.947027 | + | 0.947027i | −0.998666 | − | 0.0516384i | \(-0.983556\pi\) |
0.0516384 | + | 0.998666i | \(0.483556\pi\) | |||||||
\(224\) | − | 4.00000i | − | 0.267261i | ||||||
\(225\) | −3.00000 | + | 4.00000i | −0.200000 | + | 0.266667i | ||||
\(226\) | 10.0000 | 0.665190 | ||||||||
\(227\) | −14.1421 | − | 14.1421i | −0.938647 | − | 0.938647i | 0.0595772 | − | 0.998224i | \(-0.481025\pi\) |
−0.998224 | + | 0.0595772i | \(0.981025\pi\) | |||||||
\(228\) | −6.00000 | − | 6.00000i | −0.397360 | − | 0.397360i | ||||
\(229\) | − | 26.0000i | − | 1.71813i | −0.511868 | − | 0.859064i | \(-0.671046\pi\) | ||
0.511868 | − | 0.859064i | \(-0.328954\pi\) | |||||||
\(230\) | −15.0000 | − | 5.00000i | −0.989071 | − | 0.329690i | ||||
\(231\) | −32.0000 | −2.10545 | ||||||||
\(232\) | 3.00000 | − | 3.00000i | 0.196960 | − | 0.196960i | ||||
\(233\) | −9.89949 | + | 9.89949i | −0.648537 | + | 0.648537i | −0.952639 | − | 0.304102i | \(-0.901644\pi\) |
0.304102 | + | 0.952639i | \(0.401644\pi\) | |||||||
\(234\) | −2.82843 | −0.184900 | ||||||||
\(235\) | −7.07107 | − | 14.1421i | −0.461266 | − | 0.922531i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.1421 | + | 14.1421i | 0.918630 | + | 0.918630i | ||||
\(238\) | 20.0000 | + | 20.0000i | 1.29641 | + | 1.29641i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 2.00000 | + | 4.00000i | 0.129099 | + | 0.258199i | ||||
\(241\) | − | 16.9706i | − | 1.09317i | −0.837404 | − | 0.546585i | \(-0.815928\pi\) | ||
0.837404 | − | 0.546585i | \(-0.184072\pi\) | |||||||
\(242\) | −3.53553 | − | 3.53553i | −0.227273 | − | 0.227273i | ||||
\(243\) | −7.07107 | + | 7.07107i | −0.453609 | + | 0.453609i | ||||
\(244\) | 4.24264 | 0.271607 | ||||||||
\(245\) | −19.0919 | − | 6.36396i | −1.21974 | − | 0.406579i | ||||
\(246\) | −24.0000 | −1.53018 | ||||||||
\(247\) | 8.48528 | + | 8.48528i | 0.539906 | + | 0.539906i | ||||
\(248\) | 5.65685 | − | 5.65685i | 0.359211 | − | 0.359211i | ||||
\(249\) | −16.9706 | −1.07547 | ||||||||
\(250\) | −11.0000 | − | 2.00000i | −0.695701 | − | 0.126491i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −2.82843 | − | 2.82843i | −0.178174 | − | 0.178174i | ||||
\(253\) | 20.0000 | + | 20.0000i | 1.25739 | + | 1.25739i | ||||
\(254\) | 7.07107 | 0.443678 | ||||||||
\(255\) | −30.0000 | − | 10.0000i | −1.87867 | − | 0.626224i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.24264 | − | 4.24264i | −0.264649 | − | 0.264649i | 0.562291 | − | 0.826940i | \(-0.309920\pi\) |
−0.826940 | + | 0.562291i | \(0.809920\pi\) | |||||||
\(258\) | 1.07107 | − | 13.0711i | 0.0666818 | − | 0.813769i | ||||
\(259\) | 24.0000i | 1.49129i | ||||||||
\(260\) | −2.82843 | − | 5.65685i | −0.175412 | − | 0.350823i | ||||
\(261\) | − | 4.24264i | − | 0.262613i | ||||||
\(262\) | 1.00000 | − | 1.00000i | 0.0617802 | − | 0.0617802i | ||||
\(263\) | 16.9706 | − | 16.9706i | 1.04645 | − | 1.04645i | 0.0475824 | − | 0.998867i | \(-0.484848\pi\) |
0.998867 | − | 0.0475824i | \(-0.0151517\pi\) | |||||||
\(264\) | − | 8.00000i | − | 0.492366i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 16.9706i | 1.04053i | ||||||||
\(267\) | 20.0000 | − | 20.0000i | 1.22398 | − | 1.22398i | ||||
\(268\) | −2.00000 | − | 2.00000i | −0.122169 | − | 0.122169i | ||||
\(269\) | − | 6.00000i | − | 0.365826i | −0.983129 | − | 0.182913i | \(-0.941447\pi\) | ||
0.983129 | − | 0.182913i | \(-0.0585527\pi\) | |||||||
\(270\) | −8.48528 | − | 2.82843i | −0.516398 | − | 0.172133i | ||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | −5.00000 | + | 5.00000i | −0.303170 | + | 0.303170i | ||||
\(273\) | 16.0000 | + | 16.0000i | 0.968364 | + | 0.968364i | ||||
\(274\) | − | 10.0000i | − | 0.604122i | ||||||
\(275\) | 16.0000 | + | 12.0000i | 0.964836 | + | 0.723627i | ||||
\(276\) | 14.1421i | 0.851257i | ||||||||
\(277\) | 5.65685 | + | 5.65685i | 0.339887 | + | 0.339887i | 0.856325 | − | 0.516437i | \(-0.172742\pi\) |
−0.516437 | + | 0.856325i | \(0.672742\pi\) | |||||||
\(278\) | 2.82843 | − | 2.82843i | 0.169638 | − | 0.169638i | ||||
\(279\) | − | 8.00000i | − | 0.478947i | ||||||
\(280\) | 2.82843 | − | 8.48528i | 0.169031 | − | 0.507093i | ||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | −10.0000 | + | 10.0000i | −0.595491 | + | 0.595491i | ||||
\(283\) | 6.00000 | + | 6.00000i | 0.356663 | + | 0.356663i | 0.862581 | − | 0.505918i | \(-0.168846\pi\) |
−0.505918 | + | 0.862581i | \(0.668846\pi\) | |||||||
\(284\) | 5.65685 | 0.335673 | ||||||||
\(285\) | −8.48528 | − | 16.9706i | −0.502625 | − | 1.00525i | ||||
\(286\) | 11.3137i | 0.668994i | ||||||||
\(287\) | 33.9411 | + | 33.9411i | 2.00348 | + | 2.00348i | ||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 33.0000i | − | 1.94118i | ||||||
\(290\) | 8.48528 | − | 4.24264i | 0.498273 | − | 0.249136i | ||||
\(291\) | 25.4558i | 1.49225i | ||||||||
\(292\) | 1.41421 | + | 1.41421i | 0.0827606 | + | 0.0827606i | ||||
\(293\) | −10.0000 | − | 10.0000i | −0.584206 | − | 0.584206i | 0.351850 | − | 0.936056i | \(-0.385553\pi\) |
−0.936056 | + | 0.351850i | \(0.885553\pi\) | |||||||
\(294\) | 18.0000i | 1.04978i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 11.3137 | + | 11.3137i | 0.656488 | + | 0.656488i | ||||
\(298\) | 7.00000 | + | 7.00000i | 0.405499 | + | 0.405499i | ||||
\(299\) | − | 20.0000i | − | 1.15663i | ||||||
\(300\) | 1.41421 | + | 9.89949i | 0.0816497 | + | 0.571548i | ||||
\(301\) | −20.0000 | + | 16.9706i | −1.15278 | + | 0.978167i | ||||
\(302\) | 6.00000 | − | 6.00000i | 0.345261 | − | 0.345261i | ||||
\(303\) | −2.82843 | + | 2.82843i | −0.162489 | + | 0.162489i | ||||
\(304\) | −4.24264 | −0.243332 | ||||||||
\(305\) | 9.00000 | + | 3.00000i | 0.515339 | + | 0.171780i | ||||
\(306\) | 7.07107i | 0.404226i | ||||||||
\(307\) | −16.0000 | + | 16.0000i | −0.913168 | + | 0.913168i | −0.996520 | − | 0.0833519i | \(-0.973437\pi\) |
0.0833519 | + | 0.996520i | \(0.473437\pi\) | |||||||
\(308\) | −11.3137 | + | 11.3137i | −0.644658 | + | 0.644658i | ||||
\(309\) | 25.4558 | 1.44813 | ||||||||
\(310\) | 16.0000 | − | 8.00000i | 0.908739 | − | 0.454369i | ||||
\(311\) | 2.00000 | 0.113410 | 0.0567048 | − | 0.998391i | \(-0.481941\pi\) | ||||
0.0567048 | + | 0.998391i | \(0.481941\pi\) | |||||||
\(312\) | −4.00000 | + | 4.00000i | −0.226455 | + | 0.226455i | ||||
\(313\) | −7.07107 | + | 7.07107i | −0.399680 | + | 0.399680i | −0.878120 | − | 0.478440i | \(-0.841202\pi\) |
0.478440 | + | 0.878120i | \(0.341202\pi\) | |||||||
\(314\) | 2.00000i | 0.112867i | ||||||||
\(315\) | −4.00000 | − | 8.00000i | −0.225374 | − | 0.450749i | ||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | 8.00000 | − | 8.00000i | 0.449325 | − | 0.449325i | −0.445805 | − | 0.895130i | \(-0.647083\pi\) |
0.895130 | + | 0.445805i | \(0.147083\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.9706 | −0.950169 | ||||||||
\(320\) | 2.12132 | + | 0.707107i | 0.118585 | + | 0.0395285i | ||||
\(321\) | − | 33.9411i | − | 1.89441i | ||||||
\(322\) | 20.0000 | − | 20.0000i | 1.11456 | − | 1.11456i | ||||
\(323\) | 21.2132 | − | 21.2132i | 1.18033 | − | 1.18033i | ||||
\(324\) | 11.0000i | 0.611111i | ||||||||
\(325\) | −2.00000 | − | 14.0000i | −0.110940 | − | 0.776580i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 2.82843 | + | 2.82843i | 0.156412 | + | 0.156412i | ||||
\(328\) | −8.48528 | + | 8.48528i | −0.468521 | + | 0.468521i | ||||
\(329\) | 28.2843 | 1.55936 | ||||||||
\(330\) | 5.65685 | − | 16.9706i | 0.311400 | − | 0.934199i | ||||
\(331\) | 26.8701i | 1.47691i | 0.674302 | + | 0.738456i | \(0.264445\pi\) | ||||
−0.674302 | + | 0.738456i | \(0.735555\pi\) | |||||||
\(332\) | −6.00000 | + | 6.00000i | −0.329293 | + | 0.329293i | ||||
\(333\) | −4.24264 | + | 4.24264i | −0.232495 | + | 0.232495i | ||||
\(334\) | −15.5563 | −0.851206 | ||||||||
\(335\) | −2.82843 | − | 5.65685i | −0.154533 | − | 0.309067i | ||||
\(336\) | −8.00000 | −0.436436 | ||||||||
\(337\) | 9.00000 | − | 9.00000i | 0.490261 | − | 0.490261i | −0.418127 | − | 0.908388i | \(-0.637313\pi\) |
0.908388 | + | 0.418127i | \(0.137313\pi\) | |||||||
\(338\) | −3.53553 | + | 3.53553i | −0.192308 | + | 0.192308i | ||||
\(339\) | − | 20.0000i | − | 1.08625i | ||||||
\(340\) | −14.1421 | + | 7.07107i | −0.766965 | + | 0.383482i | ||||
\(341\) | −32.0000 | −1.73290 | ||||||||
\(342\) | −3.00000 | + | 3.00000i | −0.162221 | + | 0.162221i | ||||
\(343\) | 5.65685 | − | 5.65685i | 0.305441 | − | 0.305441i | ||||
\(344\) | −4.24264 | − | 5.00000i | −0.228748 | − | 0.269582i | ||||
\(345\) | −10.0000 | + | 30.0000i | −0.538382 | + | 1.61515i | ||||
\(346\) | 22.6274i | 1.21646i | ||||||||
\(347\) | 8.48528 | + | 8.48528i | 0.455514 | + | 0.455514i | 0.897180 | − | 0.441666i | \(-0.145612\pi\) |
−0.441666 | + | 0.897180i | \(0.645612\pi\) | |||||||
\(348\) | −6.00000 | − | 6.00000i | −0.321634 | − | 0.321634i | ||||
\(349\) | 4.24264 | 0.227103 | 0.113552 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113552 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(350\) | 12.0000 | − | 16.0000i | 0.641427 | − | 0.855236i | ||||
\(351\) | − | 11.3137i | − | 0.603881i | ||||||
\(352\) | −2.82843 | − | 2.82843i | −0.150756 | − | 0.150756i | ||||
\(353\) | 11.0000 | + | 11.0000i | 0.585471 | + | 0.585471i | 0.936401 | − | 0.350931i | \(-0.114135\pi\) |
−0.350931 | + | 0.936401i | \(0.614135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | + | 4.00000i | 0.636894 | + | 0.212298i | ||||
\(356\) | − | 14.1421i | − | 0.749532i | ||||||
\(357\) | 40.0000 | − | 40.0000i | 2.11702 | − | 2.11702i | ||||
\(358\) | 1.00000 | + | 1.00000i | 0.0528516 | + | 0.0528516i | ||||
\(359\) | − | 14.0000i | − | 0.738892i | −0.929252 | − | 0.369446i | \(-0.879548\pi\) | ||
0.929252 | − | 0.369446i | \(-0.120452\pi\) | |||||||
\(360\) | 2.00000 | − | 1.00000i | 0.105409 | − | 0.0527046i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −4.24264 | − | 4.24264i | −0.222988 | − | 0.222988i | ||||
\(363\) | −7.07107 | + | 7.07107i | −0.371135 | + | 0.371135i | ||||
\(364\) | 11.3137 | 0.592999 | ||||||||
\(365\) | 2.00000 | + | 4.00000i | 0.104685 | + | 0.209370i | ||||
\(366\) | − | 8.48528i | − | 0.443533i | ||||||
\(367\) | 1.00000 | − | 1.00000i | 0.0521996 | − | 0.0521996i | −0.680525 | − | 0.732725i | \(-0.738248\pi\) |
0.732725 | + | 0.680525i | \(0.238248\pi\) | |||||||
\(368\) | 5.00000 | + | 5.00000i | 0.260643 | + | 0.260643i | ||||
\(369\) | 12.0000i | 0.624695i | ||||||||
\(370\) | −12.7279 | − | 4.24264i | −0.661693 | − | 0.220564i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.3137 | − | 11.3137i | −0.586588 | − | 0.586588i | ||||
\(373\) | −2.82843 | + | 2.82843i | −0.146450 | + | 0.146450i | −0.776530 | − | 0.630080i | \(-0.783022\pi\) |
0.630080 | + | 0.776530i | \(0.283022\pi\) | |||||||
\(374\) | 28.2843 | 1.46254 | ||||||||
\(375\) | −4.00000 | + | 22.0000i | −0.206559 | + | 1.13608i | ||||
\(376\) | 7.07107i | 0.364662i | ||||||||
\(377\) | 8.48528 | + | 8.48528i | 0.437014 | + | 0.437014i | ||||
\(378\) | 11.3137 | − | 11.3137i | 0.581914 | − | 0.581914i | ||||
\(379\) | 28.0000i | 1.43826i | 0.694874 | + | 0.719132i | \(0.255460\pi\) | ||||
−0.694874 | + | 0.719132i | \(0.744540\pi\) | |||||||
\(380\) | −9.00000 | − | 3.00000i | −0.461690 | − | 0.153897i | ||||
\(381\) | − | 14.1421i | − | 0.724524i | ||||||
\(382\) | −14.0000 | + | 14.0000i | −0.716302 | + | 0.716302i | ||||
\(383\) | −19.7990 | + | 19.7990i | −1.01168 | + | 1.01168i | −0.0117502 | + | 0.999931i | \(0.503740\pi\) |
−0.999931 | + | 0.0117502i | \(0.996260\pi\) | |||||||
\(384\) | − | 2.00000i | − | 0.102062i | ||||||
\(385\) | −32.0000 | + | 16.0000i | −1.63087 | + | 0.815436i | ||||
\(386\) | − | 15.5563i | − | 0.791797i | ||||||
\(387\) | −6.53553 | − | 0.535534i | −0.332220 | − | 0.0272227i | ||||
\(388\) | 9.00000 | + | 9.00000i | 0.456906 | + | 0.456906i | ||||
\(389\) | 7.07107 | 0.358517 | 0.179259 | − | 0.983802i | \(-0.442630\pi\) | ||||
0.179259 | + | 0.983802i | \(0.442630\pi\) | |||||||
\(390\) | −11.3137 | + | 5.65685i | −0.572892 | + | 0.286446i | ||||
\(391\) | −50.0000 | −2.52861 | ||||||||
\(392\) | 6.36396 | + | 6.36396i | 0.321429 | + | 0.321429i | ||||
\(393\) | −2.00000 | − | 2.00000i | −0.100887 | − | 0.100887i | ||||
\(394\) | −2.82843 | −0.142494 | ||||||||
\(395\) | 21.2132 | + | 7.07107i | 1.06735 | + | 0.355784i | ||||
\(396\) | −4.00000 | −0.201008 | ||||||||
\(397\) | −20.0000 | + | 20.0000i | −1.00377 | + | 1.00377i | −0.00377836 | + | 0.999993i | \(0.501203\pi\) |
−0.999993 | + | 0.00377836i | \(0.998797\pi\) | |||||||
\(398\) | 8.00000 | + | 8.00000i | 0.401004 | + | 0.401004i | ||||
\(399\) | 33.9411 | 1.69918 | ||||||||
\(400\) | 4.00000 | + | 3.00000i | 0.200000 | + | 0.150000i | ||||
\(401\) | 16.0000 | 0.799002 | 0.399501 | − | 0.916733i | \(-0.369183\pi\) | ||||
0.399501 | + | 0.916733i | \(0.369183\pi\) | |||||||
\(402\) | −4.00000 | + | 4.00000i | −0.199502 | + | 0.199502i | ||||
\(403\) | 16.0000 | + | 16.0000i | 0.797017 | + | 0.797017i | ||||
\(404\) | 2.00000i | 0.0995037i | ||||||||
\(405\) | −7.77817 | + | 23.3345i | −0.386501 | + | 1.15950i | ||||
\(406\) | 16.9706i | 0.842235i | ||||||||
\(407\) | 16.9706 | + | 16.9706i | 0.841200 | + | 0.841200i | ||||
\(408\) | 10.0000 | + | 10.0000i | 0.495074 | + | 0.495074i | ||||
\(409\) | 31.1127 | 1.53842 | 0.769212 | − | 0.638994i | \(-0.220649\pi\) | ||||
0.769212 | + | 0.638994i | \(0.220649\pi\) | |||||||
\(410\) | −24.0000 | + | 12.0000i | −1.18528 | + | 0.592638i | ||||
\(411\) | −20.0000 | −0.986527 | ||||||||
\(412\) | 9.00000 | − | 9.00000i | 0.443398 | − | 0.443398i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.07107 | 0.347524 | ||||||||
\(415\) | −16.9706 | + | 8.48528i | −0.833052 | + | 0.416526i | ||||
\(416\) | 2.82843i | 0.138675i | ||||||||
\(417\) | −5.65685 | − | 5.65685i | −0.277017 | − | 0.277017i | ||||
\(418\) | 12.0000 | + | 12.0000i | 0.586939 | + | 0.586939i | ||||
\(419\) | −4.24264 | −0.207267 | −0.103633 | − | 0.994616i | \(-0.533047\pi\) | ||||
−0.103633 | + | 0.994616i | \(0.533047\pi\) | |||||||
\(420\) | −16.9706 | − | 5.65685i | −0.828079 | − | 0.276026i | ||||
\(421\) | 9.89949i | 0.482472i | 0.970466 | + | 0.241236i | \(0.0775528\pi\) | ||||
−0.970466 | + | 0.241236i | \(0.922447\pi\) | |||||||
\(422\) | −9.00000 | + | 9.00000i | −0.438113 | + | 0.438113i | ||||
\(423\) | 5.00000 | + | 5.00000i | 0.243108 | + | 0.243108i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −35.0000 | + | 5.00000i | −1.69775 | + | 0.242536i | ||||
\(426\) | − | 11.3137i | − | 0.548151i | ||||||
\(427\) | −12.0000 | + | 12.0000i | −0.580721 | + | 0.580721i | ||||
\(428\) | −12.0000 | − | 12.0000i | −0.580042 | − | 0.580042i | ||||
\(429\) | 22.6274 | 1.09246 | ||||||||
\(430\) | −5.46447 | − | 13.6066i | −0.263520 | − | 0.656169i | ||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 2.82843 | + | 2.82843i | 0.136083 | + | 0.136083i | ||||
\(433\) | −9.89949 | + | 9.89949i | −0.475739 | + | 0.475739i | −0.903766 | − | 0.428027i | \(-0.859209\pi\) |
0.428027 | + | 0.903766i | \(0.359209\pi\) | |||||||
\(434\) | 32.0000i | 1.53605i | ||||||||
\(435\) | −8.48528 | − | 16.9706i | −0.406838 | − | 0.813676i | ||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | −21.2132 | − | 21.2132i | −1.01477 | − | 1.01477i | ||||
\(438\) | 2.82843 | − | 2.82843i | 0.135147 | − | 0.135147i | ||||
\(439\) | 6.00000i | 0.286364i | 0.989696 | + | 0.143182i | \(0.0457335\pi\) | ||||
−0.989696 | + | 0.143182i | \(0.954267\pi\) | |||||||
\(440\) | −4.00000 | − | 8.00000i | −0.190693 | − | 0.381385i | ||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | −14.1421 | − | 14.1421i | −0.672673 | − | 0.672673i | ||||
\(443\) | 10.0000 | + | 10.0000i | 0.475114 | + | 0.475114i | 0.903565 | − | 0.428451i | \(-0.140940\pi\) |
−0.428451 | + | 0.903565i | \(0.640940\pi\) | |||||||
\(444\) | 12.0000i | 0.569495i | ||||||||
\(445\) | 10.0000 | − | 30.0000i | 0.474045 | − | 1.42214i | ||||
\(446\) | 20.0000 | 0.947027 | ||||||||
\(447\) | 14.0000 | − | 14.0000i | 0.662177 | − | 0.662177i | ||||
\(448\) | −2.82843 | + | 2.82843i | −0.133631 | + | 0.133631i | ||||
\(449\) | −36.7696 | −1.73526 | −0.867631 | − | 0.497208i | \(-0.834358\pi\) | ||||
−0.867631 | + | 0.497208i | \(0.834358\pi\) | |||||||
\(450\) | 4.94975 | − | 0.707107i | 0.233333 | − | 0.0333333i | ||||
\(451\) | 48.0000 | 2.26023 | ||||||||
\(452\) | −7.07107 | − | 7.07107i | −0.332595 | − | 0.332595i | ||||
\(453\) | −12.0000 | − | 12.0000i | −0.563809 | − | 0.563809i | ||||
\(454\) | 20.0000i | 0.938647i | ||||||||
\(455\) | 24.0000 | + | 8.00000i | 1.12514 | + | 0.375046i | ||||
\(456\) | 8.48528i | 0.397360i | ||||||||
\(457\) | 9.89949 | + | 9.89949i | 0.463079 | + | 0.463079i | 0.899663 | − | 0.436584i | \(-0.143812\pi\) |
−0.436584 | + | 0.899663i | \(0.643812\pi\) | |||||||
\(458\) | −18.3848 | + | 18.3848i | −0.859064 | + | 0.859064i | ||||
\(459\) | −28.2843 | −1.32020 | ||||||||
\(460\) | 7.07107 | + | 14.1421i | 0.329690 | + | 0.659380i | ||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 22.6274 | + | 22.6274i | 1.05272 | + | 1.05272i | ||||
\(463\) | 16.9706 | − | 16.9706i | 0.788689 | − | 0.788689i | −0.192590 | − | 0.981279i | \(-0.561689\pi\) |
0.981279 | + | 0.192590i | \(0.0616888\pi\) | |||||||
\(464\) | −4.24264 | −0.196960 | ||||||||
\(465\) | −16.0000 | − | 32.0000i | −0.741982 | − | 1.48396i | ||||
\(466\) | 14.0000 | 0.648537 | ||||||||
\(467\) | −14.1421 | − | 14.1421i | −0.654420 | − | 0.654420i | 0.299634 | − | 0.954054i | \(-0.403135\pi\) |
−0.954054 | + | 0.299634i | \(0.903135\pi\) | |||||||
\(468\) | 2.00000 | + | 2.00000i | 0.0924500 | + | 0.0924500i | ||||
\(469\) | 11.3137 | 0.522419 | ||||||||
\(470\) | −5.00000 | + | 15.0000i | −0.230633 | + | 0.691898i | ||||
\(471\) | 4.00000 | 0.184310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.14214 | + | 26.1421i | −0.0984955 | + | 1.20202i | ||||
\(474\) | − | 20.0000i | − | 0.918630i | ||||||
\(475\) | −16.9706 | − | 12.7279i | −0.778663 | − | 0.583997i | ||||
\(476\) | − | 28.2843i | − | 1.29641i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000i | 0.274147i | 0.990561 | + | 0.137073i | \(0.0437697\pi\) | ||||
−0.990561 | + | 0.137073i | \(0.956230\pi\) | |||||||
\(480\) | 1.41421 | − | 4.24264i | 0.0645497 | − | 0.193649i | ||||
\(481\) | − | 16.9706i | − | 0.773791i | ||||||
\(482\) | −12.0000 | + | 12.0000i | −0.546585 | + | 0.546585i | ||||
\(483\) | −40.0000 | − | 40.0000i | −1.82006 | − | 1.82006i | ||||
\(484\) | 5.00000i | 0.227273i | ||||||||
\(485\) | 12.7279 | + | 25.4558i | 0.577945 | + | 1.15589i | ||||
\(486\) | 10.0000 | 0.453609 | ||||||||
\(487\) | 1.00000 | − | 1.00000i | 0.0453143 | − | 0.0453143i | −0.684087 | − | 0.729401i | \(-0.739799\pi\) |
0.729401 | + | 0.684087i | \(0.239799\pi\) | |||||||
\(488\) | −3.00000 | − | 3.00000i | −0.135804 | − | 0.135804i | ||||
\(489\) | 8.00000i | 0.361773i | ||||||||
\(490\) | 9.00000 | + | 18.0000i | 0.406579 | + | 0.813157i | ||||
\(491\) | − | 1.41421i | − | 0.0638226i | −0.999491 | − | 0.0319113i | \(-0.989841\pi\) | ||
0.999491 | − | 0.0319113i | \(-0.0101594\pi\) | |||||||
\(492\) | 16.9706 | + | 16.9706i | 0.765092 | + | 0.765092i | ||||
\(493\) | 21.2132 | − | 21.2132i | 0.955395 | − | 0.955395i | ||||
\(494\) | − | 12.0000i | − | 0.539906i | ||||||
\(495\) | −8.48528 | − | 2.82843i | −0.381385 | − | 0.127128i | ||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | −16.0000 | + | 16.0000i | −0.717698 | + | 0.717698i | ||||
\(498\) | 12.0000 | + | 12.0000i | 0.537733 | + | 0.537733i | ||||
\(499\) | 12.7279 | 0.569780 | 0.284890 | − | 0.958560i | \(-0.408043\pi\) | ||||
0.284890 | + | 0.958560i | \(0.408043\pi\) | |||||||
\(500\) | 6.36396 | + | 9.19239i | 0.284605 | + | 0.411096i | ||||
\(501\) | 31.1127i | 1.39001i | ||||||||
\(502\) | −8.48528 | − | 8.48528i | −0.378717 | − | 0.378717i | ||||
\(503\) | 5.65685 | − | 5.65685i | 0.252227 | − | 0.252227i | −0.569656 | − | 0.821883i | \(-0.692924\pi\) |
0.821883 | + | 0.569656i | \(0.192924\pi\) | |||||||
\(504\) | 4.00000i | 0.178174i | ||||||||
\(505\) | −1.41421 | + | 4.24264i | −0.0629317 | + | 0.188795i | ||||
\(506\) | − | 28.2843i | − | 1.25739i | ||||||
\(507\) | 7.07107 | + | 7.07107i | 0.314037 | + | 0.314037i | ||||
\(508\) | −5.00000 | − | 5.00000i | −0.221839 | − | 0.221839i | ||||
\(509\) | 6.00000i | 0.265945i | 0.991120 | + | 0.132973i | \(0.0424523\pi\) | ||||
−0.991120 | + | 0.132973i | \(0.957548\pi\) | |||||||
\(510\) | 14.1421 | + | 28.2843i | 0.626224 | + | 1.25245i | ||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −12.0000 | − | 12.0000i | −0.529813 | − | 0.529813i | ||||
\(514\) | 6.00000i | 0.264649i | ||||||||
\(515\) | 25.4558 | − | 12.7279i | 1.12172 | − | 0.560859i | ||||
\(516\) | −10.0000 | + | 8.48528i | −0.440225 | + | 0.373544i | ||||
\(517\) | 20.0000 | − | 20.0000i | 0.879599 | − | 0.879599i | ||||
\(518\) | 16.9706 | − | 16.9706i | 0.745644 | − | 0.745644i | ||||
\(519\) | 45.2548 | 1.98647 | ||||||||
\(520\) | −2.00000 | + | 6.00000i | −0.0877058 | + | 0.263117i | ||||
\(521\) | 19.7990i | 0.867409i | 0.901055 | + | 0.433705i | \(0.142794\pi\) | ||||
−0.901055 | + | 0.433705i | \(0.857206\pi\) | |||||||
\(522\) | −3.00000 | + | 3.00000i | −0.131306 | + | 0.131306i | ||||
\(523\) | 8.48528 | − | 8.48528i | 0.371035 | − | 0.371035i | −0.496819 | − | 0.867854i | \(-0.665499\pi\) |
0.867854 | + | 0.496819i | \(0.165499\pi\) | |||||||
\(524\) | −1.41421 | −0.0617802 | ||||||||
\(525\) | −32.0000 | − | 24.0000i | −1.39659 | − | 1.04745i | ||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 40.0000 | − | 40.0000i | 1.74243 | − | 1.74243i | ||||
\(528\) | −5.65685 | + | 5.65685i | −0.246183 | + | 0.246183i | ||||
\(529\) | 27.0000i | 1.17391i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.0000 | − | 12.0000i | 0.520266 | − | 0.520266i | ||||
\(533\) | −24.0000 | − | 24.0000i | −1.03956 | − | 1.03956i | ||||
\(534\) | −28.2843 | −1.22398 | ||||||||
\(535\) | −16.9706 | − | 33.9411i | −0.733701 | − | 1.46740i | ||||
\(536\) | 2.82843i | 0.122169i | ||||||||
\(537\) | 2.00000 | − | 2.00000i | 0.0863064 | − | 0.0863064i | ||||
\(538\) | −4.24264 | + | 4.24264i | −0.182913 | + | 0.182913i | ||||
\(539\) | − | 36.0000i | − | 1.55063i | ||||||
\(540\) | 4.00000 | + | 8.00000i | 0.172133 | + | 0.344265i | ||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | −5.65685 | − | 5.65685i | −0.242983 | − | 0.242983i | ||||
\(543\) | −8.48528 | + | 8.48528i | −0.364138 | + | 0.364138i | ||||
\(544\) | 7.07107 | 0.303170 | ||||||||
\(545\) | 4.24264 | + | 1.41421i | 0.181735 | + | 0.0605783i | ||||
\(546\) | − | 22.6274i | − | 0.968364i | ||||||
\(547\) | 16.0000 | − | 16.0000i | 0.684111 | − | 0.684111i | −0.276813 | − | 0.960924i | \(-0.589278\pi\) |
0.960924 | + | 0.276813i | \(0.0892783\pi\) | |||||||
\(548\) | −7.07107 | + | 7.07107i | −0.302061 | + | 0.302061i | ||||
\(549\) | −4.24264 | −0.181071 | ||||||||
\(550\) | −2.82843 | − | 19.7990i | −0.120605 | − | 0.844232i | ||||
\(551\) | 18.0000 | 0.766826 | ||||||||
\(552\) | 10.0000 | − | 10.0000i | 0.425628 | − | 0.425628i | ||||
\(553\) | −28.2843 | + | 28.2843i | −1.20277 | + | 1.20277i | ||||
\(554\) | − | 8.00000i | − | 0.339887i | ||||||
\(555\) | −8.48528 | + | 25.4558i | −0.360180 | + | 1.08054i | ||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | −10.0000 | + | 10.0000i | −0.423714 | + | 0.423714i | −0.886480 | − | 0.462767i | \(-0.846857\pi\) |
0.462767 | + | 0.886480i | \(0.346857\pi\) | |||||||
\(558\) | −5.65685 | + | 5.65685i | −0.239474 | + | 0.239474i | ||||
\(559\) | 14.1421 | − | 12.0000i | 0.598149 | − | 0.507546i | ||||
\(560\) | −8.00000 | + | 4.00000i | −0.338062 | + | 0.169031i | ||||
\(561\) | − | 56.5685i | − | 2.38833i | ||||||
\(562\) | −7.07107 | − | 7.07107i | −0.298275 | − | 0.298275i | ||||
\(563\) | −14.0000 | − | 14.0000i | −0.590030 | − | 0.590030i | 0.347610 | − | 0.937639i | \(-0.386993\pi\) |
−0.937639 | + | 0.347610i | \(0.886993\pi\) | |||||||
\(564\) | 14.1421 | 0.595491 | ||||||||
\(565\) | −10.0000 | − | 20.0000i | −0.420703 | − | 0.841406i | ||||
\(566\) | − | 8.48528i | − | 0.356663i | ||||||
\(567\) | −31.1127 | − | 31.1127i | −1.30661 | − | 1.30661i | ||||
\(568\) | −4.00000 | − | 4.00000i | −0.167836 | − | 0.167836i | ||||
\(569\) | 32.0000i | 1.34151i | 0.741679 | + | 0.670755i | \(0.234030\pi\) | ||||
−0.741679 | + | 0.670755i | \(0.765970\pi\) | |||||||
\(570\) | −6.00000 | + | 18.0000i | −0.251312 | + | 0.753937i | ||||
\(571\) | 7.07107i | 0.295915i | 0.988994 | + | 0.147957i | \(0.0472699\pi\) | ||||
−0.988994 | + | 0.147957i | \(0.952730\pi\) | |||||||
\(572\) | 8.00000 | − | 8.00000i | 0.334497 | − | 0.334497i | ||||
\(573\) | 28.0000 | + | 28.0000i | 1.16972 | + | 1.16972i | ||||
\(574\) | − | 48.0000i | − | 2.00348i | ||||||
\(575\) | 5.00000 | + | 35.0000i | 0.208514 | + | 1.45960i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −15.5563 | − | 15.5563i | −0.647619 | − | 0.647619i | 0.304798 | − | 0.952417i | \(-0.401411\pi\) |
−0.952417 | + | 0.304798i | \(0.901411\pi\) | |||||||
\(578\) | −23.3345 | + | 23.3345i | −0.970588 | + | 0.970588i | ||||
\(579\) | −31.1127 | −1.29300 | ||||||||
\(580\) | −9.00000 | − | 3.00000i | −0.373705 | − | 0.124568i | ||||
\(581\) | − | 33.9411i | − | 1.40812i | ||||||
\(582\) | 18.0000 | − | 18.0000i | 0.746124 | − | 0.746124i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 2.00000i | − | 0.0827606i | ||||||
\(585\) | 2.82843 | + | 5.65685i | 0.116941 | + | 0.233882i | ||||
\(586\) | 14.1421i | 0.584206i | ||||||||
\(587\) | 29.6985 | + | 29.6985i | 1.22579 | + | 1.22579i | 0.965543 | + | 0.260245i | \(0.0838034\pi\) |
0.260245 | + | 0.965543i | \(0.416197\pi\) | |||||||
\(588\) | 12.7279 | − | 12.7279i | 0.524891 | − | 0.524891i | ||||
\(589\) | 33.9411 | 1.39852 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.65685i | 0.232692i | ||||||||
\(592\) | 4.24264 | + | 4.24264i | 0.174371 | + | 0.174371i | ||||
\(593\) | −4.24264 | + | 4.24264i | −0.174224 | + | 0.174224i | −0.788833 | − | 0.614608i | \(-0.789314\pi\) |
0.614608 | + | 0.788833i | \(0.289314\pi\) | |||||||
\(594\) | − | 16.0000i | − | 0.656488i | ||||||
\(595\) | 20.0000 | − | 60.0000i | 0.819920 | − | 2.45976i | ||||
\(596\) | − | 9.89949i | − | 0.405499i | ||||||
\(597\) | 16.0000 | − | 16.0000i | 0.654836 | − | 0.654836i | ||||
\(598\) | −14.1421 | + | 14.1421i | −0.578315 | + | 0.578315i | ||||
\(599\) | − | 30.0000i | − | 1.22577i | −0.790173 | − | 0.612883i | \(-0.790010\pi\) | ||
0.790173 | − | 0.612883i | \(-0.209990\pi\) | |||||||
\(600\) | 6.00000 | − | 8.00000i | 0.244949 | − | 0.326599i | ||||
\(601\) | − | 8.48528i | − | 0.346122i | −0.984911 | − | 0.173061i | \(-0.944634\pi\) | ||
0.984911 | − | 0.173061i | \(-0.0553658\pi\) | |||||||
\(602\) | 26.1421 | + | 2.14214i | 1.06547 | + | 0.0873069i | ||||
\(603\) | 2.00000 | + | 2.00000i | 0.0814463 | + | 0.0814463i | ||||
\(604\) | −8.48528 | −0.345261 | ||||||||
\(605\) | −3.53553 | + | 10.6066i | −0.143740 | + | 0.431220i | ||||
\(606\) | 4.00000 | 0.162489 | ||||||||
\(607\) | 5.65685 | + | 5.65685i | 0.229605 | + | 0.229605i | 0.812527 | − | 0.582923i | \(-0.198091\pi\) |
−0.582923 | + | 0.812527i | \(0.698091\pi\) | |||||||
\(608\) | 3.00000 | + | 3.00000i | 0.121666 | + | 0.121666i | ||||
\(609\) | 33.9411 | 1.37536 | ||||||||
\(610\) | −4.24264 | − | 8.48528i | −0.171780 | − | 0.343559i | ||||
\(611\) | −20.0000 | −0.809113 | ||||||||
\(612\) | 5.00000 | − | 5.00000i | 0.202113 | − | 0.202113i | ||||
\(613\) | 8.00000 | + | 8.00000i | 0.323117 | + | 0.323117i | 0.849962 | − | 0.526845i | \(-0.176625\pi\) |
−0.526845 | + | 0.849962i | \(0.676625\pi\) | |||||||
\(614\) | 22.6274 | 0.913168 | ||||||||
\(615\) | 24.0000 | + | 48.0000i | 0.967773 | + | 1.93555i | ||||
\(616\) | 16.0000 | 0.644658 | ||||||||
\(617\) | −33.0000 | + | 33.0000i | −1.32853 | + | 1.32853i | −0.421877 | + | 0.906653i | \(0.638629\pi\) |
−0.906653 | + | 0.421877i | \(0.861371\pi\) | |||||||
\(618\) | −18.0000 | − | 18.0000i | −0.724066 | − | 0.724066i | ||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | −16.9706 | − | 5.65685i | −0.681554 | − | 0.227185i | ||||
\(621\) | 28.2843i | 1.13501i | ||||||||
\(622\) | −1.41421 | − | 1.41421i | −0.0567048 | − | 0.0567048i | ||||
\(623\) | 40.0000 | + | 40.0000i | 1.60257 | + | 1.60257i | ||||
\(624\) | 5.65685 | 0.226455 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | 10.0000 | 0.399680 | ||||||||
\(627\) | 24.0000 | − | 24.0000i | 0.958468 | − | 0.958468i | ||||
\(628\) | 1.41421 | − | 1.41421i | 0.0564333 | − | 0.0564333i | ||||
\(629\) | −42.4264 | −1.69165 | ||||||||
\(630\) | −2.82843 | + | 8.48528i | −0.112687 | + | 0.338062i | ||||
\(631\) | 8.48528i | 0.337794i | 0.985634 | + | 0.168897i | \(0.0540205\pi\) | ||||
−0.985634 | + | 0.168897i | \(0.945980\pi\) | |||||||
\(632\) | −7.07107 | − | 7.07107i | −0.281272 | − | 0.281272i | ||||
\(633\) | 18.0000 | + | 18.0000i | 0.715436 | + | 0.715436i | ||||
\(634\) | −11.3137 | −0.449325 | ||||||||
\(635\) | −7.07107 | − | 14.1421i | −0.280607 | − | 0.561214i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.0000 | + | 18.0000i | −0.713186 | + | 0.713186i | ||||
\(638\) | 12.0000 | + | 12.0000i | 0.475085 | + | 0.475085i | ||||
\(639\) | −5.65685 | −0.223782 | ||||||||
\(640\) | −1.00000 | − | 2.00000i | −0.0395285 | − | 0.0790569i | ||||
\(641\) | − | 39.5980i | − | 1.56403i | −0.623262 | − | 0.782013i | \(-0.714193\pi\) | ||
0.623262 | − | 0.782013i | \(-0.285807\pi\) | |||||||
\(642\) | −24.0000 | + | 24.0000i | −0.947204 | + | 0.947204i | ||||
\(643\) | −2.00000 | − | 2.00000i | −0.0788723 | − | 0.0788723i | 0.666570 | − | 0.745442i | \(-0.267762\pi\) |
−0.745442 | + | 0.666570i | \(0.767762\pi\) | |||||||
\(644\) | −28.2843 | −1.11456 | ||||||||
\(645\) | −27.2132 | + | 10.9289i | −1.07152 | + | 0.430326i | ||||
\(646\) | −30.0000 | −1.18033 | ||||||||
\(647\) | 5.65685 | + | 5.65685i | 0.222394 | + | 0.222394i | 0.809506 | − | 0.587112i | \(-0.199735\pi\) |
−0.587112 | + | 0.809506i | \(0.699735\pi\) | |||||||
\(648\) | 7.77817 | − | 7.77817i | 0.305556 | − | 0.305556i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −8.48528 | + | 11.3137i | −0.332820 | + | 0.443760i | ||||
\(651\) | 64.0000 | 2.50836 | ||||||||
\(652\) | 2.82843 | + | 2.82843i | 0.110770 | + | 0.110770i | ||||
\(653\) | 24.0416 | − | 24.0416i | 0.940822 | − | 0.940822i | −0.0575225 | − | 0.998344i | \(-0.518320\pi\) |
0.998344 | + | 0.0575225i | \(0.0183201\pi\) | |||||||
\(654\) | − | 4.00000i | − | 0.156412i | ||||||
\(655\) | −3.00000 | − | 1.00000i | −0.117220 | − | 0.0390732i | ||||
\(656\) | 12.0000 | 0.468521 | ||||||||
\(657\) | −1.41421 | − | 1.41421i | −0.0551737 | − | 0.0551737i | ||||
\(658\) | −20.0000 | − | 20.0000i | −0.779681 | − | 0.779681i | ||||
\(659\) | 8.00000i | 0.311636i | 0.987786 | + | 0.155818i | \(0.0498013\pi\) | ||||
−0.987786 | + | 0.155818i | \(0.950199\pi\) | |||||||
\(660\) | −16.0000 | + | 8.00000i | −0.622799 | + | 0.311400i | ||||
\(661\) | 18.0000 | 0.700119 | 0.350059 | − | 0.936727i | \(-0.386161\pi\) | ||||
0.350059 | + | 0.936727i | \(0.386161\pi\) | |||||||
\(662\) | 19.0000 | − | 19.0000i | 0.738456 | − | 0.738456i | ||||
\(663\) | −28.2843 | + | 28.2843i | −1.09847 | + | 1.09847i | ||||
\(664\) | 8.48528 | 0.329293 | ||||||||
\(665\) | 33.9411 | − | 16.9706i | 1.31618 | − | 0.658090i | ||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | −21.2132 | − | 21.2132i | −0.821379 | − | 0.821379i | ||||
\(668\) | 11.0000 | + | 11.0000i | 0.425603 | + | 0.425603i | ||||
\(669\) | − | 40.0000i | − | 1.54649i | ||||||
\(670\) | −2.00000 | + | 6.00000i | −0.0772667 | + | 0.231800i | ||||
\(671\) | 16.9706i | 0.655141i | ||||||||
\(672\) | 5.65685 | + | 5.65685i | 0.218218 | + | 0.218218i | ||||
\(673\) | −1.41421 | + | 1.41421i | −0.0545139 | + | 0.0545139i | −0.733838 | − | 0.679324i | \(-0.762273\pi\) |
0.679324 | + | 0.733838i | \(0.262273\pi\) | |||||||
\(674\) | −12.7279 | −0.490261 | ||||||||
\(675\) | 2.82843 | + | 19.7990i | 0.108866 | + | 0.762063i | ||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | −8.48528 | − | 8.48528i | −0.326116 | − | 0.326116i | 0.524992 | − | 0.851107i | \(-0.324068\pi\) |
−0.851107 | + | 0.524992i | \(0.824068\pi\) | |||||||
\(678\) | −14.1421 | + | 14.1421i | −0.543125 | + | 0.543125i | ||||
\(679\) | −50.9117 | −1.95381 | ||||||||
\(680\) | 15.0000 | + | 5.00000i | 0.575224 | + | 0.191741i | ||||
\(681\) | 40.0000 | 1.53280 | ||||||||
\(682\) | 22.6274 | + | 22.6274i | 0.866449 | + | 0.866449i | ||||
\(683\) | 26.0000 | + | 26.0000i | 0.994862 | + | 0.994862i | 0.999987 | − | 0.00512452i | \(-0.00163119\pi\) |
−0.00512452 | + | 0.999987i | \(0.501631\pi\) | |||||||
\(684\) | 4.24264 | 0.162221 | ||||||||
\(685\) | −20.0000 | + | 10.0000i | −0.764161 | + | 0.382080i | ||||
\(686\) | −8.00000 | −0.305441 | ||||||||
\(687\) | 36.7696 | + | 36.7696i | 1.40285 | + | 1.40285i | ||||
\(688\) | −0.535534 | + | 6.53553i | −0.0204170 | + | 0.249165i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 28.2843 | − | 14.1421i | 1.07676 | − | 0.538382i | ||||
\(691\) | − | 18.3848i | − | 0.699390i | −0.936864 | − | 0.349695i | \(-0.886285\pi\) | ||
0.936864 | − | 0.349695i | \(-0.113715\pi\) | |||||||
\(692\) | 16.0000 | − | 16.0000i | 0.608229 | − | 0.608229i | ||||
\(693\) | 11.3137 | − | 11.3137i | 0.429772 | − | 0.429772i | ||||
\(694\) | − | 12.0000i | − | 0.455514i | ||||||
\(695\) | −8.48528 | − | 2.82843i | −0.321865 | − | 0.107288i | ||||
\(696\) | 8.48528i | 0.321634i | ||||||||
\(697\) | −60.0000 | + | 60.0000i | −2.27266 | + | 2.27266i | ||||
\(698\) | −3.00000 | − | 3.00000i | −0.113552 | − | 0.113552i | ||||
\(699\) | − | 28.0000i | − | 1.05906i | ||||||
\(700\) | −19.7990 | + | 2.82843i | −0.748331 | + | 0.106904i | ||||
\(701\) | −2.00000 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | −8.00000 | + | 8.00000i | −0.301941 | + | 0.301941i | ||||
\(703\) | −18.0000 | − | 18.0000i | −0.678883 | − | 0.678883i | ||||
\(704\) | 4.00000i | 0.150756i | ||||||||
\(705\) | 30.0000 | + | 10.0000i | 1.12987 | + | 0.376622i | ||||
\(706\) | − | 15.5563i | − | 0.585471i | ||||||
\(707\) | −5.65685 | − | 5.65685i | −0.212748 | − | 0.212748i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 30.0000i | − | 1.12667i | −0.826227 | − | 0.563337i | \(-0.809517\pi\) | ||
0.826227 | − | 0.563337i | \(-0.190483\pi\) | |||||||
\(710\) | −5.65685 | − | 11.3137i | −0.212298 | − | 0.424596i | ||||
\(711\) | −10.0000 | −0.375029 | ||||||||
\(712\) | −10.0000 | + | 10.0000i | −0.374766 | + | 0.374766i | ||||
\(713\) | −40.0000 | − | 40.0000i | −1.49801 | − | 1.49801i | ||||
\(714\) | −56.5685 | −2.11702 | ||||||||
\(715\) | 22.6274 | − | 11.3137i | 0.846217 | − | 0.423109i | ||||
\(716\) | − | 1.41421i | − | 0.0528516i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.89949 | + | 9.89949i | −0.369446 | + | 0.369446i | ||||
\(719\) | 16.0000i | 0.596699i | 0.954457 | + | 0.298350i | \(0.0964361\pi\) | ||||
−0.954457 | + | 0.298350i | \(0.903564\pi\) | |||||||
\(720\) | −2.12132 | − | 0.707107i | −0.0790569 | − | 0.0263523i | ||||
\(721\) | 50.9117i | 1.89605i | ||||||||
\(722\) | 0.707107 | + | 0.707107i | 0.0263158 | + | 0.0263158i | ||||
\(723\) | 24.0000 | + | 24.0000i | 0.892570 | + | 0.892570i | ||||
\(724\) | 6.00000i | 0.222988i | ||||||||
\(725\) | −16.9706 | − | 12.7279i | −0.630271 | − | 0.472703i | ||||
\(726\) | 10.0000 | 0.371135 | ||||||||
\(727\) | −36.7696 | − | 36.7696i | −1.36371 | − | 1.36371i | −0.869139 | − | 0.494569i | \(-0.835326\pi\) |
−0.494569 | − | 0.869139i | \(-0.664674\pi\) | |||||||
\(728\) | −8.00000 | − | 8.00000i | −0.296500 | − | 0.296500i | ||||
\(729\) | 13.0000i | 0.481481i | ||||||||
\(730\) | 1.41421 | − | 4.24264i | 0.0523424 | − | 0.157027i | ||||
\(731\) | −30.0000 | − | 35.3553i | −1.10959 | − | 1.30766i | ||||
\(732\) | −6.00000 | + | 6.00000i | −0.221766 | + | 0.221766i | ||||
\(733\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | −1.41421 | −0.0521996 | ||||||||
\(735\) | 36.0000 | − | 18.0000i | 1.32788 | − | 0.663940i | ||||
\(736\) | − | 7.07107i | − | 0.260643i | ||||||
\(737\) | 8.00000 | − | 8.00000i | 0.294684 | − | 0.294684i | ||||
\(738\) | 8.48528 | − | 8.48528i | 0.312348 | − | 0.312348i | ||||
\(739\) | −21.2132 | −0.780340 | −0.390170 | − | 0.920743i | \(-0.627584\pi\) | ||||
−0.390170 | + | 0.920743i | \(0.627584\pi\) | |||||||
\(740\) | 6.00000 | + | 12.0000i | 0.220564 | + | 0.441129i | ||||
\(741\) | −24.0000 | −0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.65685 | − | 5.65685i | 0.207530 | − | 0.207530i | −0.595687 | − | 0.803217i | \(-0.703120\pi\) |
0.803217 | + | 0.595687i | \(0.203120\pi\) | |||||||
\(744\) | 16.0000i | 0.586588i | ||||||||
\(745\) | 7.00000 | − | 21.0000i | 0.256460 | − | 0.769380i | ||||
\(746\) | 4.00000 | 0.146450 | ||||||||
\(747\) | 6.00000 | − | 6.00000i | 0.219529 | − | 0.219529i | ||||
\(748\) | −20.0000 | − | 20.0000i | −0.731272 | − | 0.731272i | ||||
\(749\) | 67.8823 | 2.48036 | ||||||||
\(750\) | 18.3848 | − | 12.7279i | 0.671317 | − | 0.464758i | ||||
\(751\) | 11.3137i | 0.412843i | 0.978463 | + | 0.206422i | \(0.0661818\pi\) | ||||
−0.978463 | + | 0.206422i | \(0.933818\pi\) | |||||||
\(752\) | 5.00000 | − | 5.00000i | 0.182331 | − | 0.182331i | ||||
\(753\) | −16.9706 | + | 16.9706i | −0.618442 | + | 0.618442i | ||||
\(754\) | − | 12.0000i | − | 0.437014i | ||||||
\(755\) | −18.0000 | − | 6.00000i | −0.655087 | − | 0.218362i | ||||
\(756\) | −16.0000 | −0.581914 | ||||||||
\(757\) | −11.3137 | − | 11.3137i | −0.411204 | − | 0.411204i | 0.470954 | − | 0.882158i | \(-0.343910\pi\) |
−0.882158 | + | 0.470954i | \(0.843910\pi\) | |||||||
\(758\) | 19.7990 | − | 19.7990i | 0.719132 | − | 0.719132i | ||||
\(759\) | −56.5685 | −2.05331 | ||||||||
\(760\) | 4.24264 | + | 8.48528i | 0.153897 | + | 0.307794i | ||||
\(761\) | − | 2.82843i | − | 0.102530i | −0.998685 | − | 0.0512652i | \(-0.983675\pi\) | ||
0.998685 | − | 0.0512652i | \(-0.0163254\pi\) | |||||||
\(762\) | −10.0000 | + | 10.0000i | −0.362262 | + | 0.362262i | ||||
\(763\) | −5.65685 | + | 5.65685i | −0.204792 | + | 0.204792i | ||||
\(764\) | 19.7990 | 0.716302 | ||||||||
\(765\) | 14.1421 | − | 7.07107i | 0.511310 | − | 0.255655i | ||||
\(766\) | 28.0000 | 1.01168 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.41421 | + | 1.41421i | −0.0510310 | + | 0.0510310i | ||||
\(769\) | − | 18.0000i | − | 0.649097i | −0.945869 | − | 0.324548i | \(-0.894788\pi\) | ||
0.945869 | − | 0.324548i | \(-0.105212\pi\) | |||||||
\(770\) | 33.9411 | + | 11.3137i | 1.22315 | + | 0.407718i | ||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | −11.0000 | + | 11.0000i | −0.395899 | + | 0.395899i | ||||
\(773\) | 16.9706 | − | 16.9706i | 0.610389 | − | 0.610389i | −0.332659 | − | 0.943047i | \(-0.607946\pi\) |
0.943047 | + | 0.332659i | \(0.107946\pi\) | |||||||
\(774\) | 4.24264 | + | 5.00000i | 0.152499 | + | 0.179721i | ||||
\(775\) | −32.0000 | − | 24.0000i | −1.14947 | − | 0.862105i | ||||
\(776\) | − | 12.7279i | − | 0.456906i | ||||||
\(777\) | −33.9411 | − | 33.9411i | −1.21763 | − | 1.21763i | ||||
\(778\) | −5.00000 | − | 5.00000i | −0.179259 | − | 0.179259i | ||||
\(779\) | −50.9117 | −1.82410 | ||||||||
\(780\) | 12.0000 | + | 4.00000i | 0.429669 | + | 0.143223i | ||||
\(781\) | 22.6274i | 0.809673i | ||||||||
\(782\) | 35.3553 | + | 35.3553i | 1.26430 | + | 1.26430i | ||||
\(783\) | −12.0000 | − | 12.0000i | −0.428845 | − | 0.428845i | ||||
\(784\) | − | 9.00000i | − | 0.321429i | ||||||
\(785\) | 4.00000 | − | 2.00000i | 0.142766 | − | 0.0713831i | ||||
\(786\) | 2.82843i | 0.100887i | ||||||||
\(787\) | −20.0000 | + | 20.0000i | −0.712923 | + | 0.712923i | −0.967146 | − | 0.254223i | \(-0.918180\pi\) |
0.254223 | + | 0.967146i | \(0.418180\pi\) | |||||||
\(788\) | 2.00000 | + | 2.00000i | 0.0712470 | + | 0.0712470i | ||||
\(789\) | 48.0000i | 1.70885i | ||||||||
\(790\) | −10.0000 | − | 20.0000i | −0.355784 | − | 0.711568i | ||||
\(791\) | 40.0000 | 1.42224 | ||||||||
\(792\) | 2.82843 | + | 2.82843i | 0.100504 | + | 0.100504i | ||||
\(793\) | 8.48528 | − | 8.48528i | 0.301321 | − | 0.301321i | ||||
\(794\) | 28.2843 | 1.00377 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 11.3137i | − | 0.401004i | ||||||
\(797\) | 28.0000 | − | 28.0000i | 0.991811 | − | 0.991811i | −0.00815585 | − | 0.999967i | \(-0.502596\pi\) |
0.999967 | + | 0.00815585i | \(0.00259612\pi\) | |||||||
\(798\) | −24.0000 | − | 24.0000i | −0.849591 | − | 0.849591i | ||||
\(799\) | 50.0000i | 1.76887i | ||||||||
\(800\) | −0.707107 | − | 4.94975i | −0.0250000 | − | 0.175000i | ||||
\(801\) | 14.1421i | 0.499688i | ||||||||
\(802\) | −11.3137 | − | 11.3137i | −0.399501 | − | 0.399501i | ||||
\(803\) | −5.65685 | + | 5.65685i | −0.199626 | + | 0.199626i | ||||
\(804\) | 5.65685 | 0.199502 | ||||||||
\(805\) | −60.0000 | − | 20.0000i | −2.11472 | − | 0.704907i | ||||
\(806\) | − | 22.6274i | − | 0.797017i | ||||||
\(807\) | 8.48528 | + | 8.48528i | 0.298696 | + | 0.298696i | ||||
\(808\) | 1.41421 | − | 1.41421i | 0.0497519 | − | 0.0497519i | ||||
\(809\) | − | 4.00000i | − | 0.140633i | −0.997525 | − | 0.0703163i | \(-0.977599\pi\) | ||
0.997525 | − | 0.0703163i | \(-0.0224008\pi\) | |||||||
\(810\) | 22.0000 | − | 11.0000i | 0.773001 | − | 0.386501i | ||||
\(811\) | 29.6985i | 1.04285i | 0.853296 | + | 0.521427i | \(0.174600\pi\) | ||||
−0.853296 | + | 0.521427i | \(0.825400\pi\) | |||||||
\(812\) | 12.0000 | − | 12.0000i | 0.421117 | − | 0.421117i | ||||
\(813\) | −11.3137 | + | 11.3137i | −0.396789 | + | 0.396789i | ||||
\(814\) | − | 24.0000i | − | 0.841200i | ||||||
\(815\) | 4.00000 | + | 8.00000i | 0.140114 | + | 0.280228i | ||||
\(816\) | − | 14.1421i | − | 0.495074i | ||||||
\(817\) | 2.27208 | − | 27.7279i | 0.0794899 | − | 0.970077i | ||||
\(818\) | −22.0000 | − | 22.0000i | −0.769212 | − | 0.769212i | ||||
\(819\) | −11.3137 | −0.395333 | ||||||||
\(820\) | 25.4558 | + | 8.48528i | 0.888957 | + | 0.296319i | ||||
\(821\) | 38.0000 | 1.32621 | 0.663105 | − | 0.748527i | \(-0.269238\pi\) | ||||
0.663105 | + | 0.748527i | \(0.269238\pi\) | |||||||
\(822\) | 14.1421 | + | 14.1421i | 0.493264 | + | 0.493264i | ||||
\(823\) | 21.0000 | + | 21.0000i | 0.732014 | + | 0.732014i | 0.971018 | − | 0.239004i | \(-0.0768211\pi\) |
−0.239004 | + | 0.971018i | \(0.576821\pi\) | |||||||
\(824\) | −12.7279 | −0.443398 | ||||||||
\(825\) | −39.5980 | + | 5.65685i | −1.37862 | + | 0.196946i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.0000 | + | 26.0000i | −0.904109 | + | 0.904109i | −0.995789 | − | 0.0916799i | \(-0.970776\pi\) |
0.0916799 | + | 0.995789i | \(0.470776\pi\) | |||||||
\(828\) | −5.00000 | − | 5.00000i | −0.173762 | − | 0.173762i | ||||
\(829\) | −7.07107 | −0.245588 | −0.122794 | − | 0.992432i | \(-0.539185\pi\) | ||||
−0.122794 | + | 0.992432i | \(0.539185\pi\) | |||||||
\(830\) | 18.0000 | + | 6.00000i | 0.624789 | + | 0.208263i | ||||
\(831\) | −16.0000 | −0.555034 | ||||||||
\(832\) | 2.00000 | − | 2.00000i | 0.0693375 | − | 0.0693375i | ||||
\(833\) | 45.0000 | + | 45.0000i | 1.55916 | + | 1.55916i | ||||
\(834\) | 8.00000i | 0.277017i | ||||||||
\(835\) | 15.5563 | + | 31.1127i | 0.538350 | + | 1.07670i | ||||
\(836\) | − | 16.9706i | − | 0.586939i | ||||||
\(837\) | −22.6274 | − | 22.6274i | −0.782118 | − | 0.782118i | ||||
\(838\) | 3.00000 | + | 3.00000i | 0.103633 | + | 0.103633i | ||||
\(839\) | 53.7401 | 1.85531 | 0.927657 | − | 0.373432i | \(-0.121819\pi\) | ||||
0.927657 | + | 0.373432i | \(0.121819\pi\) | |||||||
\(840\) | 8.00000 | + | 16.0000i | 0.276026 | + | 0.552052i | ||||
\(841\) | −11.0000 | −0.379310 | ||||||||
\(842\) | 7.00000 | − | 7.00000i | 0.241236 | − | 0.241236i | ||||
\(843\) | −14.1421 | + | 14.1421i | −0.487081 | + | 0.487081i | ||||
\(844\) | 12.7279 | 0.438113 | ||||||||
\(845\) | 10.6066 | + | 3.53553i | 0.364878 | + | 0.121626i | ||||
\(846\) | − | 7.07107i | − | 0.243108i | ||||||
\(847\) | −14.1421 | − | 14.1421i | −0.485930 | − | 0.485930i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.9706 | −0.582428 | ||||||||
\(850\) | 28.2843 | + | 21.2132i | 0.970143 | + | 0.727607i | ||||
\(851\) | 42.4264i | 1.45436i | ||||||||
\(852\) | −8.00000 | + | 8.00000i | −0.274075 | + | 0.274075i | ||||
\(853\) | −4.00000 | − | 4.00000i | −0.136957 | − | 0.136957i | 0.635304 | − | 0.772262i | \(-0.280875\pi\) |
−0.772262 | + | 0.635304i | \(0.780875\pi\) | |||||||
\(854\) | 16.9706 | 0.580721 | ||||||||
\(855\) | 9.00000 | + | 3.00000i | 0.307794 | + | 0.102598i | ||||
\(856\) | 16.9706i | 0.580042i | ||||||||
\(857\) | 7.00000 | − | 7.00000i | 0.239115 | − | 0.239115i | −0.577368 | − | 0.816484i | \(-0.695920\pi\) |
0.816484 | + | 0.577368i | \(0.195920\pi\) | |||||||
\(858\) | −16.0000 | − | 16.0000i | −0.546231 | − | 0.546231i | ||||
\(859\) | 15.5563 | 0.530776 | 0.265388 | − | 0.964142i | \(-0.414500\pi\) | ||||
0.265388 | + | 0.964142i | \(0.414500\pi\) | |||||||
\(860\) | −5.75736 | + | 13.4853i | −0.196324 | + | 0.459844i | ||||
\(861\) | −96.0000 | −3.27167 | ||||||||
\(862\) | 16.9706 | + | 16.9706i | 0.578020 | + | 0.578020i | ||||
\(863\) | −33.9411 | + | 33.9411i | −1.15537 | + | 1.15537i | −0.169910 | + | 0.985460i | \(0.554348\pi\) |
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(864\) | − | 4.00000i | − | 0.136083i | ||||||
\(865\) | 45.2548 | − | 22.6274i | 1.53871 | − | 0.769355i | ||||
\(866\) | 14.0000 | 0.475739 | ||||||||
\(867\) | 46.6690 | + | 46.6690i | 1.58496 | + | 1.58496i | ||||
\(868\) | 22.6274 | − | 22.6274i | 0.768025 | − | 0.768025i | ||||
\(869\) | 40.0000i | 1.35691i | ||||||||
\(870\) | −6.00000 | + | 18.0000i | −0.203419 | + | 0.610257i | ||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | −1.41421 | − | 1.41421i | −0.0478913 | − | 0.0478913i | ||||
\(873\) | −9.00000 | − | 9.00000i | −0.304604 | − | 0.304604i | ||||
\(874\) | 30.0000i | 1.01477i | ||||||||
\(875\) | −44.0000 | − | 8.00000i | −1.48747 | − | 0.270449i | ||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | −18.0000 | + | 18.0000i | −0.607817 | + | 0.607817i | −0.942375 | − | 0.334558i | \(-0.891413\pi\) |
0.334558 | + | 0.942375i | \(0.391413\pi\) | |||||||
\(878\) | 4.24264 | − | 4.24264i | 0.143182 | − | 0.143182i | ||||
\(879\) | 28.2843 | 0.954005 | ||||||||
\(880\) | −2.82843 | + | 8.48528i | −0.0953463 | + | 0.286039i | ||||
\(881\) | −24.0000 | −0.808581 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(882\) | −6.36396 | − | 6.36396i | −0.214286 | − | 0.214286i | ||||
\(883\) | −12.0000 | − | 12.0000i | −0.403832 | − | 0.403832i | 0.475749 | − | 0.879581i | \(-0.342177\pi\) |
−0.879581 | + | 0.475749i | \(0.842177\pi\) | |||||||
\(884\) | 20.0000i | 0.672673i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 14.1421i | − | 0.475114i | ||||||
\(887\) | 33.9411 | + | 33.9411i | 1.13963 | + | 1.13963i | 0.988516 | + | 0.151115i | \(0.0482865\pi\) |
0.151115 | + | 0.988516i | \(0.451714\pi\) | |||||||
\(888\) | 8.48528 | − | 8.48528i | 0.284747 | − | 0.284747i | ||||
\(889\) | 28.2843 | 0.948624 | ||||||||
\(890\) | −28.2843 | + | 14.1421i | −0.948091 | + | 0.474045i | ||||
\(891\) | −44.0000 | −1.47406 | ||||||||
\(892\) | −14.1421 | − | 14.1421i | −0.473514 | − | 0.473514i | ||||
\(893\) | −21.2132 | + | 21.2132i | −0.709873 | + | 0.709873i | ||||
\(894\) | −19.7990 | −0.662177 | ||||||||
\(895\) | 1.00000 | − | 3.00000i | 0.0334263 | − | 0.100279i | ||||
\(896\) | 4.00000 | 0.133631 | ||||||||
\(897\) | 28.2843 | + | 28.2843i | 0.944384 | + | 0.944384i | ||||
\(898\) | 26.0000 | + | 26.0000i | 0.867631 | + | 0.867631i | ||||
\(899\) | 33.9411 | 1.13200 | ||||||||
\(900\) | −4.00000 | − | 3.00000i | −0.133333 | − | 0.100000i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −33.9411 | − | 33.9411i | −1.13012 | − | 1.13012i | ||||
\(903\) | 4.28427 | − | 52.2843i | 0.142572 | − | 1.73991i | ||||
\(904\) | 10.0000i | 0.332595i | ||||||||
\(905\) | −4.24264 | + | 12.7279i | −0.141030 | + | 0.423090i | ||||
\(906\) | 16.9706i | 0.563809i | ||||||||
\(907\) | −18.0000 | + | 18.0000i | −0.597680 | + | 0.597680i | −0.939695 | − | 0.342014i | \(-0.888891\pi\) |
0.342014 | + | 0.939695i | \(0.388891\pi\) | |||||||
\(908\) | 14.1421 | − | 14.1421i | 0.469323 | − | 0.469323i | ||||
\(909\) | − | 2.00000i | − | 0.0663358i | ||||||
\(910\) | −11.3137 | − | 22.6274i | −0.375046 | − | 0.750092i | ||||
\(911\) | − | 53.7401i | − | 1.78049i | −0.455483 | − | 0.890245i | \(-0.650533\pi\) | ||
0.455483 | − | 0.890245i | \(-0.349467\pi\) | |||||||
\(912\) | 6.00000 | − | 6.00000i | 0.198680 | − | 0.198680i | ||||
\(913\) | −24.0000 | − | 24.0000i | −0.794284 | − | 0.794284i | ||||
\(914\) | − | 14.0000i | − | 0.463079i | ||||||
\(915\) | −16.9706 | + | 8.48528i | −0.561029 | + | 0.280515i | ||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 4.00000 | − | 4.00000i | 0.132092 | − | 0.132092i | ||||
\(918\) | 20.0000 | + | 20.0000i | 0.660098 | + | 0.660098i | ||||
\(919\) | − | 42.0000i | − | 1.38545i | −0.721201 | − | 0.692726i | \(-0.756409\pi\) | ||
0.721201 | − | 0.692726i | \(-0.243591\pi\) | |||||||
\(920\) | 5.00000 | − | 15.0000i | 0.164845 | − | 0.494535i | ||||
\(921\) | − | 45.2548i | − | 1.49120i | ||||||
\(922\) | 4.24264 | + | 4.24264i | 0.139724 | + | 0.139724i | ||||
\(923\) | 11.3137 | − | 11.3137i | 0.372395 | − | 0.372395i | ||||
\(924\) | − | 32.0000i | − | 1.05272i | ||||||
\(925\) | 4.24264 | + | 29.6985i | 0.139497 | + | 0.976480i | ||||
\(926\) | −24.0000 | −0.788689 | ||||||||
\(927\) | −9.00000 | + | 9.00000i | −0.295599 | + | 0.295599i | ||||
\(928\) | 3.00000 | + | 3.00000i | 0.0984798 | + | 0.0984798i | ||||
\(929\) | 2.82843 | 0.0927977 | 0.0463988 | − | 0.998923i | \(-0.485225\pi\) | ||||
0.0463988 | + | 0.998923i | \(0.485225\pi\) | |||||||
\(930\) | −11.3137 | + | 33.9411i | −0.370991 | + | 1.11297i | ||||
\(931\) | 38.1838i | 1.25142i | ||||||||
\(932\) | −9.89949 | − | 9.89949i | −0.324269 | − | 0.324269i | ||||
\(933\) | −2.82843 | + | 2.82843i | −0.0925985 | + | 0.0925985i | ||||
\(934\) | 20.0000i | 0.654420i | ||||||||
\(935\) | −28.2843 | − | 56.5685i | −0.924995 | − | 1.84999i | ||||
\(936\) | − | 2.82843i | − | 0.0924500i | ||||||
\(937\) | −15.5563 | − | 15.5563i | −0.508204 | − | 0.508204i | 0.405771 | − | 0.913975i | \(-0.367003\pi\) |
−0.913975 | + | 0.405771i | \(0.867003\pi\) | |||||||
\(938\) | −8.00000 | − | 8.00000i | −0.261209 | − | 0.261209i | ||||
\(939\) | − | 20.0000i | − | 0.652675i | ||||||
\(940\) | 14.1421 | − | 7.07107i | 0.461266 | − | 0.230633i | ||||
\(941\) | 42.0000 | 1.36916 | 0.684580 | − | 0.728937i | \(-0.259985\pi\) | ||||
0.684580 | + | 0.728937i | \(0.259985\pi\) | |||||||
\(942\) | −2.82843 | − | 2.82843i | −0.0921551 | − | 0.0921551i | ||||
\(943\) | 60.0000 | + | 60.0000i | 1.95387 | + | 1.95387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −33.9411 | − | 11.3137i | −1.10410 | − | 0.368035i | ||||
\(946\) | 20.0000 | − | 16.9706i | 0.650256 | − | 0.551761i | ||||
\(947\) | −20.0000 | + | 20.0000i | −0.649913 | + | 0.649913i | −0.952972 | − | 0.303059i | \(-0.901992\pi\) |
0.303059 | + | 0.952972i | \(0.401992\pi\) | |||||||
\(948\) | −14.1421 | + | 14.1421i | −0.459315 | + | 0.459315i | ||||
\(949\) | 5.65685 | 0.183629 | ||||||||
\(950\) | 3.00000 | + | 21.0000i | 0.0973329 | + | 0.681330i | ||||
\(951\) | 22.6274i | 0.733744i | ||||||||
\(952\) | −20.0000 | + | 20.0000i | −0.648204 | + | 0.648204i | ||||
\(953\) | 24.0416 | − | 24.0416i | 0.778785 | − | 0.778785i | −0.200839 | − | 0.979624i | \(-0.564367\pi\) |
0.979624 | + | 0.200839i | \(0.0643669\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.0000 | + | 14.0000i | 1.35909 | + | 0.453029i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.0000 | − | 24.0000i | 0.775810 | − | 0.775810i | ||||
\(958\) | 4.24264 | − | 4.24264i | 0.137073 | − | 0.137073i | ||||
\(959\) | − | 40.0000i | − | 1.29167i | ||||||
\(960\) | −4.00000 | + | 2.00000i | −0.129099 | + | 0.0645497i | ||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | −12.0000 | + | 12.0000i | −0.386896 | + | 0.386896i | ||||
\(963\) | 12.0000 | + | 12.0000i | 0.386695 | + | 0.386695i | ||||
\(964\) | 16.9706 | 0.546585 | ||||||||
\(965\) | −31.1127 | + | 15.5563i | −1.00155 | + | 0.500777i | ||||
\(966\) | 56.5685i | 1.82006i | ||||||||
\(967\) | 9.00000 | − | 9.00000i | 0.289420 | − | 0.289420i | −0.547431 | − | 0.836851i | \(-0.684394\pi\) |
0.836851 | + | 0.547431i | \(0.184394\pi\) | |||||||
\(968\) | 3.53553 | − | 3.53553i | 0.113636 | − | 0.113636i | ||||
\(969\) | 60.0000i | 1.92748i | ||||||||
\(970\) | 9.00000 | − | 27.0000i | 0.288973 | − | 0.866918i | ||||
\(971\) | 4.00000 | 0.128366 | 0.0641831 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641831 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(972\) | −7.07107 | − | 7.07107i | −0.226805 | − | 0.226805i | ||||
\(973\) | 11.3137 | − | 11.3137i | 0.362701 | − | 0.362701i | ||||
\(974\) | −1.41421 | −0.0453143 | ||||||||
\(975\) | 22.6274 | + | 16.9706i | 0.724657 | + | 0.543493i | ||||
\(976\) | 4.24264i | 0.135804i | ||||||||
\(977\) | −11.0000 | + | 11.0000i | −0.351921 | + | 0.351921i | −0.860824 | − | 0.508903i | \(-0.830051\pi\) |
0.508903 | + | 0.860824i | \(0.330051\pi\) | |||||||
\(978\) | 5.65685 | − | 5.65685i | 0.180886 | − | 0.180886i | ||||
\(979\) | 56.5685 | 1.80794 | ||||||||
\(980\) | 6.36396 | − | 19.0919i | 0.203289 | − | 0.609868i | ||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | −1.00000 | + | 1.00000i | −0.0319113 | + | 0.0319113i | ||||
\(983\) | 16.9706 | − | 16.9706i | 0.541277 | − | 0.541277i | −0.382626 | − | 0.923903i | \(-0.624980\pi\) |
0.923903 | + | 0.382626i | \(0.124980\pi\) | |||||||
\(984\) | − | 24.0000i | − | 0.765092i | ||||||
\(985\) | 2.82843 | + | 5.65685i | 0.0901212 | + | 0.180242i | ||||
\(986\) | −30.0000 | −0.955395 | ||||||||
\(987\) | −40.0000 | + | 40.0000i | −1.27321 | + | 1.27321i | ||||
\(988\) | −8.48528 | + | 8.48528i | −0.269953 | + | 0.269953i | ||||
\(989\) | −35.3553 | + | 30.0000i | −1.12423 | + | 0.953945i | ||||
\(990\) | 4.00000 | + | 8.00000i | 0.127128 | + | 0.254257i | ||||
\(991\) | − | 5.65685i | − | 0.179696i | −0.995955 | − | 0.0898479i | \(-0.971362\pi\) | ||
0.995955 | − | 0.0898479i | \(-0.0286381\pi\) | |||||||
\(992\) | 5.65685 | + | 5.65685i | 0.179605 | + | 0.179605i | ||||
\(993\) | −38.0000 | − | 38.0000i | −1.20589 | − | 1.20589i | ||||
\(994\) | 22.6274 | 0.717698 | ||||||||
\(995\) | 8.00000 | − | 24.0000i | 0.253617 | − | 0.760851i | ||||
\(996\) | − | 16.9706i | − | 0.537733i | ||||||
\(997\) | −31.1127 | − | 31.1127i | −0.985349 | − | 0.985349i | 0.0145452 | − | 0.999894i | \(-0.495370\pi\) |
−0.999894 | + | 0.0145452i | \(0.995370\pi\) | |||||||
\(998\) | −9.00000 | − | 9.00000i | −0.284890 | − | 0.284890i | ||||
\(999\) | 24.0000i | 0.759326i |
(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 | 430.2.g.a.343.1 | yes | 4 | |
5.2 | odd | 4 | inner | 430.2.g.a.257.2 | yes | 4 | |
43.42 | odd | 2 | inner | 430.2.g.a.343.2 | yes | 4 | |
215.42 | even | 4 | inner | 430.2.g.a.257.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
430.2.g.a.257.1 | ✓ | 4 | 215.42 | even | 4 | inner | |
430.2.g.a.257.2 | yes | 4 | 5.2 | odd | 4 | inner | |
430.2.g.a.343.1 | yes | 4 | 1.1 | even | 1 | trivial | |
430.2.g.a.343.2 | yes | 4 | 43.42 | odd | 2 | inner |