Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,2,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.31753163335\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.4 | ||
Root | \(1.45161 - 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.2.c.a.34.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21432i | 0.858654i | 0.903149 | + | 0.429327i | \(0.141249\pi\) | ||||
−0.903149 | + | 0.429327i | \(0.858751\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0.525428 | 0.262714 | ||||||||
\(5\) | 0.311108 | − | 2.21432i | 0.139132 | − | 0.990274i | ||||
\(6\) | 1.21432 | 0.495744 | ||||||||
\(7\) | − | 4.90321i | − | 1.85324i | −0.375999 | − | 0.926620i | \(-0.622700\pi\) | ||
0.375999 | − | 0.926620i | \(-0.377300\pi\) | |||||||
\(8\) | 3.06668i | 1.08423i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.68889 | + | 0.377784i | 0.850302 | + | 0.119466i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | − | 0.525428i | − | 0.151678i | ||||||
\(13\) | 4.14764i | 1.15035i | 0.818031 | + | 0.575175i | \(0.195066\pi\) | ||||
−0.818031 | + | 0.575175i | \(0.804934\pi\) | |||||||
\(14\) | 5.95407 | 1.59129 | ||||||||
\(15\) | −2.21432 | − | 0.311108i | −0.571735 | − | 0.0803277i | ||||
\(16\) | −2.67307 | −0.668268 | ||||||||
\(17\) | 5.33185i | 1.29316i | 0.762845 | + | 0.646582i | \(0.223802\pi\) | ||||
−0.762845 | + | 0.646582i | \(0.776198\pi\) | |||||||
\(18\) | − | 1.21432i | − | 0.286218i | ||||||
\(19\) | 5.18421 | 1.18934 | 0.594669 | − | 0.803970i | \(-0.297283\pi\) | ||||
0.594669 | + | 0.803970i | \(0.297283\pi\) | |||||||
\(20\) | 0.163465 | − | 1.16346i | 0.0365518 | − | 0.260159i | ||||
\(21\) | −4.90321 | −1.06997 | ||||||||
\(22\) | − | 1.21432i | − | 0.258894i | ||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 3.06668 | 0.625983 | ||||||||
\(25\) | −4.80642 | − | 1.37778i | −0.961285 | − | 0.275557i | ||||
\(26\) | −5.03657 | −0.987752 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 2.57628i | − | 0.486872i | ||||||
\(29\) | −1.80642 | −0.335444 | −0.167722 | − | 0.985834i | \(-0.553641\pi\) | ||||
−0.167722 | + | 0.985834i | \(0.553641\pi\) | |||||||
\(30\) | 0.377784 | − | 2.68889i | 0.0689737 | − | 0.490922i | ||||
\(31\) | 2.62222 | 0.470964 | 0.235482 | − | 0.971879i | \(-0.424333\pi\) | ||||
0.235482 | + | 0.971879i | \(0.424333\pi\) | |||||||
\(32\) | 2.88739i | 0.510423i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | −6.47457 | −1.11038 | ||||||||
\(35\) | −10.8573 | − | 1.52543i | −1.83522 | − | 0.257844i | ||||
\(36\) | −0.525428 | −0.0875713 | ||||||||
\(37\) | − | 5.80642i | − | 0.954570i | −0.878749 | − | 0.477285i | \(-0.841621\pi\) | ||
0.878749 | − | 0.477285i | \(-0.158379\pi\) | |||||||
\(38\) | 6.29529i | 1.02123i | ||||||||
\(39\) | 4.14764 | 0.664154 | ||||||||
\(40\) | 6.79060 | + | 0.954067i | 1.07369 | + | 0.150851i | ||||
\(41\) | 1.80642 | 0.282116 | 0.141058 | − | 0.990001i | \(-0.454950\pi\) | ||||
0.141058 | + | 0.990001i | \(0.454950\pi\) | |||||||
\(42\) | − | 5.95407i | − | 0.918732i | ||||||
\(43\) | 4.90321i | 0.747733i | 0.927483 | + | 0.373866i | \(0.121968\pi\) | ||||
−0.927483 | + | 0.373866i | \(0.878032\pi\) | |||||||
\(44\) | −0.525428 | −0.0792112 | ||||||||
\(45\) | −0.311108 | + | 2.21432i | −0.0463772 | + | 0.330091i | ||||
\(46\) | −4.85728 | −0.716167 | ||||||||
\(47\) | − | 7.05086i | − | 1.02847i | −0.857648 | − | 0.514236i | \(-0.828075\pi\) | ||
0.857648 | − | 0.514236i | \(-0.171925\pi\) | |||||||
\(48\) | 2.67307i | 0.385825i | ||||||||
\(49\) | −17.0415 | −2.43450 | ||||||||
\(50\) | 1.67307 | − | 5.83654i | 0.236608 | − | 0.825411i | ||||
\(51\) | 5.33185 | 0.746609 | ||||||||
\(52\) | 2.17929i | 0.302213i | ||||||||
\(53\) | − | 7.18421i | − | 0.986827i | −0.869795 | − | 0.493413i | \(-0.835749\pi\) | ||
0.869795 | − | 0.493413i | \(-0.164251\pi\) | |||||||
\(54\) | −1.21432 | −0.165248 | ||||||||
\(55\) | −0.311108 | + | 2.21432i | −0.0419498 | + | 0.298579i | ||||
\(56\) | 15.0366 | 2.00935 | ||||||||
\(57\) | − | 5.18421i | − | 0.686665i | ||||||
\(58\) | − | 2.19358i | − | 0.288031i | ||||||
\(59\) | −1.67307 | −0.217815 | −0.108908 | − | 0.994052i | \(-0.534735\pi\) | ||||
−0.108908 | + | 0.994052i | \(0.534735\pi\) | |||||||
\(60\) | −1.16346 | − | 0.163465i | −0.150203 | − | 0.0211032i | ||||
\(61\) | 0.755569 | 0.0967407 | 0.0483703 | − | 0.998829i | \(-0.484597\pi\) | ||||
0.0483703 | + | 0.998829i | \(0.484597\pi\) | |||||||
\(62\) | 3.18421i | 0.404395i | ||||||||
\(63\) | 4.90321i | 0.617747i | ||||||||
\(64\) | −8.85236 | −1.10654 | ||||||||
\(65\) | 9.18421 | + | 1.29036i | 1.13916 | + | 0.160050i | ||||
\(66\) | −1.21432 | −0.149472 | ||||||||
\(67\) | 4.85728i | 0.593411i | 0.954969 | + | 0.296706i | \(0.0958880\pi\) | ||||
−0.954969 | + | 0.296706i | \(0.904112\pi\) | |||||||
\(68\) | 2.80150i | 0.339732i | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 1.85236 | − | 13.1842i | 0.221399 | − | 1.57581i | ||||
\(71\) | 0.428639 | 0.0508701 | 0.0254351 | − | 0.999676i | \(-0.491903\pi\) | ||||
0.0254351 | + | 0.999676i | \(0.491903\pi\) | |||||||
\(72\) | − | 3.06668i | − | 0.361411i | ||||||
\(73\) | 12.7096i | 1.48755i | 0.668430 | + | 0.743775i | \(0.266967\pi\) | ||||
−0.668430 | + | 0.743775i | \(0.733033\pi\) | |||||||
\(74\) | 7.05086 | 0.819645 | ||||||||
\(75\) | −1.37778 | + | 4.80642i | −0.159093 | + | 0.554998i | ||||
\(76\) | 2.72393 | 0.312456 | ||||||||
\(77\) | 4.90321i | 0.558773i | ||||||||
\(78\) | 5.03657i | 0.570279i | ||||||||
\(79\) | 6.42864 | 0.723278 | 0.361639 | − | 0.932318i | \(-0.382217\pi\) | ||||
0.361639 | + | 0.932318i | \(0.382217\pi\) | |||||||
\(80\) | −0.831613 | + | 5.91903i | −0.0929772 | + | 0.661768i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.19358i | 0.242240i | ||||||||
\(83\) | − | 2.90321i | − | 0.318669i | −0.987225 | − | 0.159334i | \(-0.949065\pi\) | ||
0.987225 | − | 0.159334i | \(-0.0509348\pi\) | |||||||
\(84\) | −2.57628 | −0.281095 | ||||||||
\(85\) | 11.8064 | + | 1.65878i | 1.28059 | + | 0.179920i | ||||
\(86\) | −5.95407 | −0.642044 | ||||||||
\(87\) | 1.80642i | 0.193669i | ||||||||
\(88\) | − | 3.06668i | − | 0.326909i | ||||||
\(89\) | −0.622216 | −0.0659547 | −0.0329774 | − | 0.999456i | \(-0.510499\pi\) | ||||
−0.0329774 | + | 0.999456i | \(0.510499\pi\) | |||||||
\(90\) | −2.68889 | − | 0.377784i | −0.283434 | − | 0.0398220i | ||||
\(91\) | 20.3368 | 2.13187 | ||||||||
\(92\) | 2.10171i | 0.219118i | ||||||||
\(93\) | − | 2.62222i | − | 0.271911i | ||||||
\(94\) | 8.56199 | 0.883102 | ||||||||
\(95\) | 1.61285 | − | 11.4795i | 0.165475 | − | 1.17777i | ||||
\(96\) | 2.88739 | 0.294693 | ||||||||
\(97\) | 2.75557i | 0.279786i | 0.990167 | + | 0.139893i | \(0.0446758\pi\) | ||||
−0.990167 | + | 0.139893i | \(0.955324\pi\) | |||||||
\(98\) | − | 20.6938i | − | 2.09039i | ||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −2.52543 | − | 0.723926i | −0.252543 | − | 0.0723926i | ||||
\(101\) | −17.8064 | −1.77181 | −0.885903 | − | 0.463871i | \(-0.846460\pi\) | ||||
−0.885903 | + | 0.463871i | \(0.846460\pi\) | |||||||
\(102\) | 6.47457i | 0.641078i | ||||||||
\(103\) | 4.94914i | 0.487654i | 0.969819 | + | 0.243827i | \(0.0784029\pi\) | ||||
−0.969819 | + | 0.243827i | \(0.921597\pi\) | |||||||
\(104\) | −12.7195 | −1.24725 | ||||||||
\(105\) | −1.52543 | + | 10.8573i | −0.148866 | + | 1.05956i | ||||
\(106\) | 8.72393 | 0.847343 | ||||||||
\(107\) | − | 11.1985i | − | 1.08260i | −0.840830 | − | 0.541300i | \(-0.817932\pi\) | ||
0.840830 | − | 0.541300i | \(-0.182068\pi\) | |||||||
\(108\) | 0.525428i | 0.0505593i | ||||||||
\(109\) | −15.7146 | −1.50518 | −0.752591 | − | 0.658488i | \(-0.771196\pi\) | ||||
−0.752591 | + | 0.658488i | \(0.771196\pi\) | |||||||
\(110\) | −2.68889 | − | 0.377784i | −0.256376 | − | 0.0360203i | ||||
\(111\) | −5.80642 | −0.551121 | ||||||||
\(112\) | 13.1066i | 1.23846i | ||||||||
\(113\) | − | 1.76494i | − | 0.166031i | −0.996548 | − | 0.0830156i | \(-0.973545\pi\) | ||
0.996548 | − | 0.0830156i | \(-0.0264551\pi\) | |||||||
\(114\) | 6.29529 | 0.589608 | ||||||||
\(115\) | 8.85728 | + | 1.24443i | 0.825946 | + | 0.116044i | ||||
\(116\) | −0.949145 | −0.0881259 | ||||||||
\(117\) | − | 4.14764i | − | 0.383450i | ||||||
\(118\) | − | 2.03164i | − | 0.187028i | ||||||
\(119\) | 26.1432 | 2.39654 | ||||||||
\(120\) | 0.954067 | − | 6.79060i | 0.0870940 | − | 0.619894i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.917502i | 0.0830667i | ||||||||
\(123\) | − | 1.80642i | − | 0.162880i | ||||||
\(124\) | 1.37778 | 0.123729 | ||||||||
\(125\) | −4.54617 | + | 10.2143i | −0.406622 | + | 0.913597i | ||||
\(126\) | −5.95407 | −0.530430 | ||||||||
\(127\) | − | 18.7096i | − | 1.66021i | −0.557606 | − | 0.830106i | \(-0.688280\pi\) | ||
0.557606 | − | 0.830106i | \(-0.311720\pi\) | |||||||
\(128\) | − | 4.97481i | − | 0.439715i | ||||||
\(129\) | 4.90321 | 0.431704 | ||||||||
\(130\) | −1.56691 | + | 11.1526i | −0.137428 | + | 0.978145i | ||||
\(131\) | −1.24443 | −0.108726 | −0.0543632 | − | 0.998521i | \(-0.517313\pi\) | ||||
−0.0543632 | + | 0.998521i | \(0.517313\pi\) | |||||||
\(132\) | 0.525428i | 0.0457326i | ||||||||
\(133\) | − | 25.4193i | − | 2.20413i | ||||||
\(134\) | −5.89829 | −0.509535 | ||||||||
\(135\) | 2.21432 | + | 0.311108i | 0.190578 | + | 0.0267759i | ||||
\(136\) | −16.3511 | −1.40209 | ||||||||
\(137\) | − | 18.7971i | − | 1.60594i | −0.596019 | − | 0.802970i | \(-0.703252\pi\) | ||
0.596019 | − | 0.802970i | \(-0.296748\pi\) | |||||||
\(138\) | 4.85728i | 0.413479i | ||||||||
\(139\) | −14.0415 | −1.19098 | −0.595492 | − | 0.803361i | \(-0.703043\pi\) | ||||
−0.595492 | + | 0.803361i | \(0.703043\pi\) | |||||||
\(140\) | −5.70471 | − | 0.801502i | −0.482136 | − | 0.0677393i | ||||
\(141\) | −7.05086 | −0.593789 | ||||||||
\(142\) | 0.520505i | 0.0436798i | ||||||||
\(143\) | − | 4.14764i | − | 0.346843i | ||||||
\(144\) | 2.67307 | 0.222756 | ||||||||
\(145\) | −0.561993 | + | 4.00000i | −0.0466709 | + | 0.332182i | ||||
\(146\) | −15.4336 | −1.27729 | ||||||||
\(147\) | 17.0415i | 1.40556i | ||||||||
\(148\) | − | 3.05086i | − | 0.250779i | ||||||
\(149\) | 3.05086 | 0.249936 | 0.124968 | − | 0.992161i | \(-0.460117\pi\) | ||||
0.124968 | + | 0.992161i | \(0.460117\pi\) | |||||||
\(150\) | −5.83654 | − | 1.67307i | −0.476551 | − | 0.136606i | ||||
\(151\) | −0.326929 | −0.0266051 | −0.0133026 | − | 0.999912i | \(-0.504234\pi\) | ||||
−0.0133026 | + | 0.999912i | \(0.504234\pi\) | |||||||
\(152\) | 15.8983i | 1.28952i | ||||||||
\(153\) | − | 5.33185i | − | 0.431055i | ||||||
\(154\) | −5.95407 | −0.479792 | ||||||||
\(155\) | 0.815792 | − | 5.80642i | 0.0655260 | − | 0.466383i | ||||
\(156\) | 2.17929 | 0.174483 | ||||||||
\(157\) | 19.9081i | 1.58884i | 0.607367 | + | 0.794421i | \(0.292226\pi\) | ||||
−0.607367 | + | 0.794421i | \(0.707774\pi\) | |||||||
\(158\) | 7.80642i | 0.621046i | ||||||||
\(159\) | −7.18421 | −0.569745 | ||||||||
\(160\) | 6.39361 | + | 0.898290i | 0.505459 | + | 0.0710160i | ||||
\(161\) | 19.6128 | 1.54571 | ||||||||
\(162\) | 1.21432i | 0.0954060i | ||||||||
\(163\) | 12.1748i | 0.953607i | 0.879010 | + | 0.476804i | \(0.158205\pi\) | ||||
−0.879010 | + | 0.476804i | \(0.841795\pi\) | |||||||
\(164\) | 0.949145 | 0.0741158 | ||||||||
\(165\) | 2.21432 | + | 0.311108i | 0.172385 | + | 0.0242197i | ||||
\(166\) | 3.52543 | 0.273626 | ||||||||
\(167\) | − | 13.0049i | − | 1.00635i | −0.864184 | − | 0.503176i | \(-0.832165\pi\) | ||
0.864184 | − | 0.503176i | \(-0.167835\pi\) | |||||||
\(168\) | − | 15.0366i | − | 1.16010i | ||||||
\(169\) | −4.20294 | −0.323303 | ||||||||
\(170\) | −2.01429 | + | 14.3368i | −0.154489 | + | 1.09958i | ||||
\(171\) | −5.18421 | −0.396446 | ||||||||
\(172\) | 2.57628i | 0.196440i | ||||||||
\(173\) | 13.8938i | 1.05633i | 0.849142 | + | 0.528165i | \(0.177120\pi\) | ||||
−0.849142 | + | 0.528165i | \(0.822880\pi\) | |||||||
\(174\) | −2.19358 | −0.166295 | ||||||||
\(175\) | −6.75557 | + | 23.5669i | −0.510673 | + | 1.78149i | ||||
\(176\) | 2.67307 | 0.201490 | ||||||||
\(177\) | 1.67307i | 0.125756i | ||||||||
\(178\) | − | 0.755569i | − | 0.0566323i | ||||||
\(179\) | −12.8573 | −0.960998 | −0.480499 | − | 0.876995i | \(-0.659544\pi\) | ||||
−0.480499 | + | 0.876995i | \(0.659544\pi\) | |||||||
\(180\) | −0.163465 | + | 1.16346i | −0.0121839 | + | 0.0867195i | ||||
\(181\) | 0.917502 | 0.0681974 | 0.0340987 | − | 0.999418i | \(-0.489144\pi\) | ||||
0.0340987 | + | 0.999418i | \(0.489144\pi\) | |||||||
\(182\) | 24.6953i | 1.83054i | ||||||||
\(183\) | − | 0.755569i | − | 0.0558532i | ||||||
\(184\) | −12.2667 | −0.904314 | ||||||||
\(185\) | −12.8573 | − | 1.80642i | −0.945286 | − | 0.132811i | ||||
\(186\) | 3.18421 | 0.233477 | ||||||||
\(187\) | − | 5.33185i | − | 0.389904i | ||||||
\(188\) | − | 3.70471i | − | 0.270194i | ||||||
\(189\) | 4.90321 | 0.356656 | ||||||||
\(190\) | 13.9398 | + | 1.95851i | 1.01130 | + | 0.142085i | ||||
\(191\) | 14.3684 | 1.03966 | 0.519831 | − | 0.854269i | \(-0.325995\pi\) | ||||
0.519831 | + | 0.854269i | \(0.325995\pi\) | |||||||
\(192\) | 8.85236i | 0.638864i | ||||||||
\(193\) | − | 11.7605i | − | 0.846539i | −0.906004 | − | 0.423269i | \(-0.860882\pi\) | ||
0.906004 | − | 0.423269i | \(-0.139118\pi\) | |||||||
\(194\) | −3.34614 | −0.240239 | ||||||||
\(195\) | 1.29036 | − | 9.18421i | 0.0924049 | − | 0.657695i | ||||
\(196\) | −8.95407 | −0.639576 | ||||||||
\(197\) | 3.82071i | 0.272215i | 0.990694 | + | 0.136107i | \(0.0434592\pi\) | ||||
−0.990694 | + | 0.136107i | \(0.956541\pi\) | |||||||
\(198\) | 1.21432i | 0.0862979i | ||||||||
\(199\) | 13.7146 | 0.972199 | 0.486100 | − | 0.873903i | \(-0.338419\pi\) | ||||
0.486100 | + | 0.873903i | \(0.338419\pi\) | |||||||
\(200\) | 4.22522 | − | 14.7397i | 0.298768 | − | 1.04226i | ||||
\(201\) | 4.85728 | 0.342606 | ||||||||
\(202\) | − | 21.6227i | − | 1.52137i | ||||||
\(203\) | 8.85728i | 0.621659i | ||||||||
\(204\) | 2.80150 | 0.196144 | ||||||||
\(205\) | 0.561993 | − | 4.00000i | 0.0392513 | − | 0.279372i | ||||
\(206\) | −6.00984 | −0.418726 | ||||||||
\(207\) | − | 4.00000i | − | 0.278019i | ||||||
\(208\) | − | 11.0869i | − | 0.768741i | ||||||
\(209\) | −5.18421 | −0.358599 | ||||||||
\(210\) | −13.1842 | − | 1.85236i | −0.909797 | − | 0.127825i | ||||
\(211\) | 1.95851 | 0.134830 | 0.0674148 | − | 0.997725i | \(-0.478525\pi\) | ||||
0.0674148 | + | 0.997725i | \(0.478525\pi\) | |||||||
\(212\) | − | 3.77478i | − | 0.259253i | ||||||
\(213\) | − | 0.428639i | − | 0.0293699i | ||||||
\(214\) | 13.5986 | 0.929578 | ||||||||
\(215\) | 10.8573 | + | 1.52543i | 0.740460 | + | 0.104033i | ||||
\(216\) | −3.06668 | −0.208661 | ||||||||
\(217\) | − | 12.8573i | − | 0.872809i | ||||||
\(218\) | − | 19.0825i | − | 1.29243i | ||||||
\(219\) | 12.7096 | 0.858838 | ||||||||
\(220\) | −0.163465 | + | 1.16346i | −0.0110208 | + | 0.0784408i | ||||
\(221\) | −22.1146 | −1.48759 | ||||||||
\(222\) | − | 7.05086i | − | 0.473222i | ||||||
\(223\) | − | 26.0098i | − | 1.74175i | −0.491506 | − | 0.870874i | \(-0.663554\pi\) | ||
0.491506 | − | 0.870874i | \(-0.336446\pi\) | |||||||
\(224\) | 14.1575 | 0.945937 | ||||||||
\(225\) | 4.80642 | + | 1.37778i | 0.320428 | + | 0.0918523i | ||||
\(226\) | 2.14320 | 0.142563 | ||||||||
\(227\) | 6.34122i | 0.420882i | 0.977607 | + | 0.210441i | \(0.0674899\pi\) | ||||
−0.977607 | + | 0.210441i | \(0.932510\pi\) | |||||||
\(228\) | − | 2.72393i | − | 0.180396i | ||||||
\(229\) | 23.3274 | 1.54152 | 0.770759 | − | 0.637127i | \(-0.219877\pi\) | ||||
0.770759 | + | 0.637127i | \(0.219877\pi\) | |||||||
\(230\) | −1.51114 | + | 10.7556i | −0.0996415 | + | 0.709201i | ||||
\(231\) | 4.90321 | 0.322608 | ||||||||
\(232\) | − | 5.53972i | − | 0.363700i | ||||||
\(233\) | − | 1.42372i | − | 0.0932708i | −0.998912 | − | 0.0466354i | \(-0.985150\pi\) | ||
0.998912 | − | 0.0466354i | \(-0.0148499\pi\) | |||||||
\(234\) | 5.03657 | 0.329251 | ||||||||
\(235\) | −15.6128 | − | 2.19358i | −1.01847 | − | 0.143093i | ||||
\(236\) | −0.879077 | −0.0572231 | ||||||||
\(237\) | − | 6.42864i | − | 0.417585i | ||||||
\(238\) | 31.7462i | 2.05780i | ||||||||
\(239\) | 18.9590 | 1.22636 | 0.613178 | − | 0.789945i | \(-0.289891\pi\) | ||||
0.613178 | + | 0.789945i | \(0.289891\pi\) | |||||||
\(240\) | 5.91903 | + | 0.831613i | 0.382072 | + | 0.0536804i | ||||
\(241\) | −1.34614 | −0.0867126 | −0.0433563 | − | 0.999060i | \(-0.513805\pi\) | ||||
−0.0433563 | + | 0.999060i | \(0.513805\pi\) | |||||||
\(242\) | 1.21432i | 0.0780594i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0.396997 | 0.0254151 | ||||||||
\(245\) | −5.30174 | + | 37.7353i | −0.338716 | + | 2.41082i | ||||
\(246\) | 2.19358 | 0.139857 | ||||||||
\(247\) | 21.5022i | 1.36816i | ||||||||
\(248\) | 8.04149i | 0.510635i | ||||||||
\(249\) | −2.90321 | −0.183984 | ||||||||
\(250\) | −12.4035 | − | 5.52051i | −0.784463 | − | 0.349147i | ||||
\(251\) | 1.08250 | 0.0683267 | 0.0341633 | − | 0.999416i | \(-0.489123\pi\) | ||||
0.0341633 | + | 0.999416i | \(0.489123\pi\) | |||||||
\(252\) | 2.57628i | 0.162291i | ||||||||
\(253\) | − | 4.00000i | − | 0.251478i | ||||||
\(254\) | 22.7195 | 1.42555 | ||||||||
\(255\) | 1.65878 | − | 11.8064i | 0.103877 | − | 0.739347i | ||||
\(256\) | −11.6637 | −0.728981 | ||||||||
\(257\) | 0.133353i | 0.00831834i | 0.999991 | + | 0.00415917i | \(0.00132391\pi\) | ||||
−0.999991 | + | 0.00415917i | \(0.998676\pi\) | |||||||
\(258\) | 5.95407i | 0.370684i | ||||||||
\(259\) | −28.4701 | −1.76905 | ||||||||
\(260\) | 4.82564 | + | 0.677993i | 0.299273 | + | 0.0420473i | ||||
\(261\) | 1.80642 | 0.111815 | ||||||||
\(262\) | − | 1.51114i | − | 0.0933584i | ||||||
\(263\) | − | 0.147643i | − | 0.00910407i | −0.999990 | − | 0.00455203i | \(-0.998551\pi\) | ||
0.999990 | − | 0.00455203i | \(-0.00144896\pi\) | |||||||
\(264\) | −3.06668 | −0.188741 | ||||||||
\(265\) | −15.9081 | − | 2.23506i | −0.977229 | − | 0.137299i | ||||
\(266\) | 30.8671 | 1.89258 | ||||||||
\(267\) | 0.622216i | 0.0380790i | ||||||||
\(268\) | 2.55215i | 0.155897i | ||||||||
\(269\) | 26.8573 | 1.63752 | 0.818759 | − | 0.574138i | \(-0.194663\pi\) | ||||
0.818759 | + | 0.574138i | \(0.194663\pi\) | |||||||
\(270\) | −0.377784 | + | 2.68889i | −0.0229912 | + | 0.163641i | ||||
\(271\) | 3.08250 | 0.187248 | 0.0936242 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936242 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(272\) | − | 14.2524i | − | 0.864180i | ||||||
\(273\) | − | 20.3368i | − | 1.23084i | ||||||
\(274\) | 22.8256 | 1.37895 | ||||||||
\(275\) | 4.80642 | + | 1.37778i | 0.289838 | + | 0.0830835i | ||||
\(276\) | 2.10171 | 0.126508 | ||||||||
\(277\) | 8.70964i | 0.523311i | 0.965161 | + | 0.261656i | \(0.0842685\pi\) | ||||
−0.965161 | + | 0.261656i | \(0.915732\pi\) | |||||||
\(278\) | − | 17.0509i | − | 1.02264i | ||||||
\(279\) | −2.62222 | −0.156988 | ||||||||
\(280\) | 4.67799 | − | 33.2958i | 0.279564 | − | 1.98980i | ||||
\(281\) | −20.3783 | −1.21567 | −0.607833 | − | 0.794065i | \(-0.707961\pi\) | ||||
−0.607833 | + | 0.794065i | \(0.707961\pi\) | |||||||
\(282\) | − | 8.56199i | − | 0.509859i | ||||||
\(283\) | − | 6.32248i | − | 0.375833i | −0.982185 | − | 0.187916i | \(-0.939827\pi\) | ||
0.982185 | − | 0.187916i | \(-0.0601734\pi\) | |||||||
\(284\) | 0.225219 | 0.0133643 | ||||||||
\(285\) | −11.4795 | − | 1.61285i | −0.679987 | − | 0.0955369i | ||||
\(286\) | 5.03657 | 0.297818 | ||||||||
\(287\) | − | 8.85728i | − | 0.522829i | ||||||
\(288\) | − | 2.88739i | − | 0.170141i | ||||||
\(289\) | −11.4286 | −0.672273 | ||||||||
\(290\) | −4.85728 | − | 0.682439i | −0.285229 | − | 0.0400742i | ||||
\(291\) | 2.75557 | 0.161534 | ||||||||
\(292\) | 6.67799i | 0.390800i | ||||||||
\(293\) | 16.6780i | 0.974339i | 0.873308 | + | 0.487169i | \(0.161971\pi\) | ||||
−0.873308 | + | 0.487169i | \(0.838029\pi\) | |||||||
\(294\) | −20.6938 | −1.20689 | ||||||||
\(295\) | −0.520505 | + | 3.70471i | −0.0303050 | + | 0.215697i | ||||
\(296\) | 17.8064 | 1.03498 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | 3.70471i | 0.214608i | ||||||||
\(299\) | −16.5906 | −0.959458 | ||||||||
\(300\) | −0.723926 | + | 2.52543i | −0.0417959 | + | 0.145806i | ||||
\(301\) | 24.0415 | 1.38573 | ||||||||
\(302\) | − | 0.396997i | − | 0.0228446i | ||||||
\(303\) | 17.8064i | 1.02295i | ||||||||
\(304\) | −13.8578 | −0.794797 | ||||||||
\(305\) | 0.235063 | − | 1.67307i | 0.0134597 | − | 0.0957998i | ||||
\(306\) | 6.47457 | 0.370127 | ||||||||
\(307\) | 9.58565i | 0.547082i | 0.961860 | + | 0.273541i | \(0.0881949\pi\) | ||||
−0.961860 | + | 0.273541i | \(0.911805\pi\) | |||||||
\(308\) | 2.57628i | 0.146797i | ||||||||
\(309\) | 4.94914 | 0.281547 | ||||||||
\(310\) | 7.05086 | + | 0.990632i | 0.400462 | + | 0.0562641i | ||||
\(311\) | 14.5303 | 0.823941 | 0.411970 | − | 0.911197i | \(-0.364841\pi\) | ||||
0.411970 | + | 0.911197i | \(0.364841\pi\) | |||||||
\(312\) | 12.7195i | 0.720099i | ||||||||
\(313\) | − | 21.0321i | − | 1.18881i | −0.804167 | − | 0.594403i | \(-0.797388\pi\) | ||
0.804167 | − | 0.594403i | \(-0.202612\pi\) | |||||||
\(314\) | −24.1748 | −1.36427 | ||||||||
\(315\) | 10.8573 | + | 1.52543i | 0.611738 | + | 0.0859481i | ||||
\(316\) | 3.37778 | 0.190015 | ||||||||
\(317\) | 0.990632i | 0.0556394i | 0.999613 | + | 0.0278197i | \(0.00885643\pi\) | ||||
−0.999613 | + | 0.0278197i | \(0.991144\pi\) | |||||||
\(318\) | − | 8.72393i | − | 0.489213i | ||||||
\(319\) | 1.80642 | 0.101140 | ||||||||
\(320\) | −2.75404 | + | 19.6019i | −0.153955 | + | 1.09578i | ||||
\(321\) | −11.1985 | −0.625039 | ||||||||
\(322\) | 23.8163i | 1.32723i | ||||||||
\(323\) | 27.6414i | 1.53801i | ||||||||
\(324\) | 0.525428 | 0.0291904 | ||||||||
\(325\) | 5.71456 | − | 19.9353i | 0.316987 | − | 1.10581i | ||||
\(326\) | −14.7841 | −0.818818 | ||||||||
\(327\) | 15.7146i | 0.869017i | ||||||||
\(328\) | 5.53972i | 0.305880i | ||||||||
\(329\) | −34.5718 | −1.90601 | ||||||||
\(330\) | −0.377784 | + | 2.68889i | −0.0207963 | + | 0.148019i | ||||
\(331\) | −17.5812 | −0.966350 | −0.483175 | − | 0.875524i | \(-0.660517\pi\) | ||||
−0.483175 | + | 0.875524i | \(0.660517\pi\) | |||||||
\(332\) | − | 1.52543i | − | 0.0837187i | ||||||
\(333\) | 5.80642i | 0.318190i | ||||||||
\(334\) | 15.7921 | 0.864107 | ||||||||
\(335\) | 10.7556 | + | 1.51114i | 0.587639 | + | 0.0825623i | ||||
\(336\) | 13.1066 | 0.715025 | ||||||||
\(337\) | 3.16992i | 0.172676i | 0.996266 | + | 0.0863382i | \(0.0275166\pi\) | ||||
−0.996266 | + | 0.0863382i | \(0.972483\pi\) | |||||||
\(338\) | − | 5.10372i | − | 0.277606i | ||||||
\(339\) | −1.76494 | −0.0958582 | ||||||||
\(340\) | 6.20342 | + | 0.871569i | 0.336428 | + | 0.0472675i | ||||
\(341\) | −2.62222 | −0.142001 | ||||||||
\(342\) | − | 6.29529i | − | 0.340410i | ||||||
\(343\) | 49.2355i | 2.65847i | ||||||||
\(344\) | −15.0366 | −0.810717 | ||||||||
\(345\) | 1.24443 | − | 8.85728i | 0.0669979 | − | 0.476860i | ||||
\(346\) | −16.8716 | −0.907021 | ||||||||
\(347\) | − | 4.97634i | − | 0.267144i | −0.991039 | − | 0.133572i | \(-0.957355\pi\) | ||
0.991039 | − | 0.133572i | \(-0.0426447\pi\) | |||||||
\(348\) | 0.949145i | 0.0508795i | ||||||||
\(349\) | −18.2034 | −0.974407 | −0.487203 | − | 0.873289i | \(-0.661983\pi\) | ||||
−0.487203 | + | 0.873289i | \(0.661983\pi\) | |||||||
\(350\) | −28.6178 | − | 8.20342i | −1.52968 | − | 0.438491i | ||||
\(351\) | −4.14764 | −0.221385 | ||||||||
\(352\) | − | 2.88739i | − | 0.153898i | ||||||
\(353\) | 22.4099i | 1.19276i | 0.802703 | + | 0.596379i | \(0.203395\pi\) | ||||
−0.802703 | + | 0.596379i | \(0.796605\pi\) | |||||||
\(354\) | −2.03164 | −0.107981 | ||||||||
\(355\) | 0.133353 | − | 0.949145i | 0.00707765 | − | 0.0503754i | ||||
\(356\) | −0.326929 | −0.0173272 | ||||||||
\(357\) | − | 26.1432i | − | 1.38364i | ||||||
\(358\) | − | 15.6128i | − | 0.825165i | ||||||
\(359\) | −21.3274 | −1.12562 | −0.562809 | − | 0.826587i | \(-0.690279\pi\) | ||||
−0.562809 | + | 0.826587i | \(0.690279\pi\) | |||||||
\(360\) | −6.79060 | − | 0.954067i | −0.357896 | − | 0.0502837i | ||||
\(361\) | 7.87601 | 0.414527 | ||||||||
\(362\) | 1.11414i | 0.0585579i | ||||||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | 10.6855 | 0.560072 | ||||||||
\(365\) | 28.1432 | + | 3.95407i | 1.47308 | + | 0.206965i | ||||
\(366\) | 0.917502 | 0.0479586 | ||||||||
\(367\) | − | 35.1338i | − | 1.83397i | −0.398921 | − | 0.916985i | \(-0.630615\pi\) | ||
0.398921 | − | 0.916985i | \(-0.369385\pi\) | |||||||
\(368\) | − | 10.6923i | − | 0.557374i | ||||||
\(369\) | −1.80642 | −0.0940387 | ||||||||
\(370\) | 2.19358 | − | 15.6128i | 0.114039 | − | 0.811673i | ||||
\(371\) | −35.2257 | −1.82883 | ||||||||
\(372\) | − | 1.37778i | − | 0.0714348i | ||||||
\(373\) | − | 17.0049i | − | 0.880481i | −0.897880 | − | 0.440241i | \(-0.854893\pi\) | ||
0.897880 | − | 0.440241i | \(-0.145107\pi\) | |||||||
\(374\) | 6.47457 | 0.334792 | ||||||||
\(375\) | 10.2143 | + | 4.54617i | 0.527465 | + | 0.234763i | ||||
\(376\) | 21.6227 | 1.11511 | ||||||||
\(377\) | − | 7.49240i | − | 0.385878i | ||||||
\(378\) | 5.95407i | 0.306244i | ||||||||
\(379\) | −2.36842 | −0.121657 | −0.0608287 | − | 0.998148i | \(-0.519374\pi\) | ||||
−0.0608287 | + | 0.998148i | \(0.519374\pi\) | |||||||
\(380\) | 0.847435 | − | 6.03164i | 0.0434725 | − | 0.309417i | ||||
\(381\) | −18.7096 | −0.958524 | ||||||||
\(382\) | 17.4479i | 0.892710i | ||||||||
\(383\) | 1.21585i | 0.0621271i | 0.999517 | + | 0.0310635i | \(0.00988942\pi\) | ||||
−0.999517 | + | 0.0310635i | \(0.990111\pi\) | |||||||
\(384\) | −4.97481 | −0.253870 | ||||||||
\(385\) | 10.8573 | + | 1.52543i | 0.553338 | + | 0.0777430i | ||||
\(386\) | 14.2810 | 0.726884 | ||||||||
\(387\) | − | 4.90321i | − | 0.249244i | ||||||
\(388\) | 1.44785i | 0.0735035i | ||||||||
\(389\) | −2.26671 | −0.114927 | −0.0574633 | − | 0.998348i | \(-0.518301\pi\) | ||||
−0.0574633 | + | 0.998348i | \(0.518301\pi\) | |||||||
\(390\) | 11.1526 | + | 1.56691i | 0.564732 | + | 0.0793438i | ||||
\(391\) | −21.3274 | −1.07857 | ||||||||
\(392\) | − | 52.2607i | − | 2.63957i | ||||||
\(393\) | 1.24443i | 0.0627733i | ||||||||
\(394\) | −4.63957 | −0.233738 | ||||||||
\(395\) | 2.00000 | − | 14.2351i | 0.100631 | − | 0.716244i | ||||
\(396\) | 0.525428 | 0.0264037 | ||||||||
\(397\) | 18.4889i | 0.927929i | 0.885854 | + | 0.463965i | \(0.153574\pi\) | ||||
−0.885854 | + | 0.463965i | \(0.846426\pi\) | |||||||
\(398\) | 16.6539i | 0.834782i | ||||||||
\(399\) | −25.4193 | −1.27256 | ||||||||
\(400\) | 12.8479 | + | 3.68292i | 0.642396 | + | 0.184146i | ||||
\(401\) | 17.5625 | 0.877028 | 0.438514 | − | 0.898724i | \(-0.355505\pi\) | ||||
0.438514 | + | 0.898724i | \(0.355505\pi\) | |||||||
\(402\) | 5.89829i | 0.294180i | ||||||||
\(403\) | 10.8760i | 0.541773i | ||||||||
\(404\) | −9.35599 | −0.465478 | ||||||||
\(405\) | 0.311108 | − | 2.21432i | 0.0154591 | − | 0.110030i | ||||
\(406\) | −10.7556 | −0.533790 | ||||||||
\(407\) | 5.80642i | 0.287814i | ||||||||
\(408\) | 16.3511i | 0.809498i | ||||||||
\(409\) | 21.3461 | 1.05550 | 0.527749 | − | 0.849400i | \(-0.323036\pi\) | ||||
0.527749 | + | 0.849400i | \(0.323036\pi\) | |||||||
\(410\) | 4.85728 | + | 0.682439i | 0.239884 | + | 0.0337032i | ||||
\(411\) | −18.7971 | −0.927190 | ||||||||
\(412\) | 2.60042i | 0.128113i | ||||||||
\(413\) | 8.20342i | 0.403664i | ||||||||
\(414\) | 4.85728 | 0.238722 | ||||||||
\(415\) | −6.42864 | − | 0.903212i | −0.315570 | − | 0.0443369i | ||||
\(416\) | −11.9759 | −0.587165 | ||||||||
\(417\) | 14.0415i | 0.687615i | ||||||||
\(418\) | − | 6.29529i | − | 0.307913i | ||||||
\(419\) | −28.8573 | −1.40977 | −0.704885 | − | 0.709321i | \(-0.749001\pi\) | ||||
−0.704885 | + | 0.709321i | \(0.749001\pi\) | |||||||
\(420\) | −0.801502 | + | 5.70471i | −0.0391093 | + | 0.278362i | ||||
\(421\) | −35.4893 | −1.72964 | −0.864822 | − | 0.502078i | \(-0.832569\pi\) | ||||
−0.864822 | + | 0.502078i | \(0.832569\pi\) | |||||||
\(422\) | 2.37826i | 0.115772i | ||||||||
\(423\) | 7.05086i | 0.342824i | ||||||||
\(424\) | 22.0316 | 1.06995 | ||||||||
\(425\) | 7.34614 | − | 25.6271i | 0.356340 | − | 1.24310i | ||||
\(426\) | 0.520505 | 0.0252186 | ||||||||
\(427\) | − | 3.70471i | − | 0.179284i | ||||||
\(428\) | − | 5.88400i | − | 0.284414i | ||||||
\(429\) | −4.14764 | −0.200250 | ||||||||
\(430\) | −1.85236 | + | 13.1842i | −0.0893286 | + | 0.635799i | ||||
\(431\) | 9.24443 | 0.445289 | 0.222644 | − | 0.974900i | \(-0.428531\pi\) | ||||
0.222644 | + | 0.974900i | \(0.428531\pi\) | |||||||
\(432\) | − | 2.67307i | − | 0.128608i | ||||||
\(433\) | − | 6.28544i | − | 0.302059i | −0.988529 | − | 0.151030i | \(-0.951741\pi\) | ||
0.988529 | − | 0.151030i | \(-0.0482589\pi\) | |||||||
\(434\) | 15.6128 | 0.749441 | ||||||||
\(435\) | 4.00000 | + | 0.561993i | 0.191785 | + | 0.0269455i | ||||
\(436\) | −8.25686 | −0.395432 | ||||||||
\(437\) | 20.7368i | 0.991977i | ||||||||
\(438\) | 15.4336i | 0.737444i | ||||||||
\(439\) | 36.5303 | 1.74350 | 0.871749 | − | 0.489952i | \(-0.162986\pi\) | ||||
0.871749 | + | 0.489952i | \(0.162986\pi\) | |||||||
\(440\) | −6.79060 | − | 0.954067i | −0.323729 | − | 0.0454834i | ||||
\(441\) | 17.0415 | 0.811499 | ||||||||
\(442\) | − | 26.8542i | − | 1.27732i | ||||||
\(443\) | − | 38.2766i | − | 1.81857i | −0.416170 | − | 0.909287i | \(-0.636628\pi\) | ||
0.416170 | − | 0.909287i | \(-0.363372\pi\) | |||||||
\(444\) | −3.05086 | −0.144787 | ||||||||
\(445\) | −0.193576 | + | 1.37778i | −0.00917639 | + | 0.0653132i | ||||
\(446\) | 31.5843 | 1.49556 | ||||||||
\(447\) | − | 3.05086i | − | 0.144300i | ||||||
\(448\) | 43.4050i | 2.05069i | ||||||||
\(449\) | 31.8479 | 1.50300 | 0.751498 | − | 0.659735i | \(-0.229332\pi\) | ||||
0.751498 | + | 0.659735i | \(0.229332\pi\) | |||||||
\(450\) | −1.67307 | + | 5.83654i | −0.0788693 | + | 0.275137i | ||||
\(451\) | −1.80642 | −0.0850612 | ||||||||
\(452\) | − | 0.927346i | − | 0.0436187i | ||||||
\(453\) | 0.326929i | 0.0153605i | ||||||||
\(454\) | −7.70027 | −0.361391 | ||||||||
\(455\) | 6.32693 | − | 45.0321i | 0.296611 | − | 2.11114i | ||||
\(456\) | 15.8983 | 0.744506 | ||||||||
\(457\) | − | 1.39207i | − | 0.0651185i | −0.999470 | − | 0.0325592i | \(-0.989634\pi\) | ||
0.999470 | − | 0.0325592i | \(-0.0103658\pi\) | |||||||
\(458\) | 28.3269i | 1.32363i | ||||||||
\(459\) | −5.33185 | −0.248870 | ||||||||
\(460\) | 4.65386 | + | 0.653858i | 0.216987 | + | 0.0304863i | ||||
\(461\) | −7.70471 | −0.358844 | −0.179422 | − | 0.983772i | \(-0.557423\pi\) | ||||
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(462\) | 5.95407i | 0.277008i | ||||||||
\(463\) | 4.68244i | 0.217611i | 0.994063 | + | 0.108806i | \(0.0347026\pi\) | ||||
−0.994063 | + | 0.108806i | \(0.965297\pi\) | |||||||
\(464\) | 4.82870 | 0.224167 | ||||||||
\(465\) | −5.80642 | − | 0.815792i | −0.269266 | − | 0.0378314i | ||||
\(466\) | 1.72885 | 0.0800873 | ||||||||
\(467\) | − | 12.8573i | − | 0.594964i | −0.954727 | − | 0.297482i | \(-0.903853\pi\) | ||
0.954727 | − | 0.297482i | \(-0.0961468\pi\) | |||||||
\(468\) | − | 2.17929i | − | 0.100738i | ||||||
\(469\) | 23.8163 | 1.09973 | ||||||||
\(470\) | 2.66370 | − | 18.9590i | 0.122867 | − | 0.874513i | ||||
\(471\) | 19.9081 | 0.917318 | ||||||||
\(472\) | − | 5.13077i | − | 0.236163i | ||||||
\(473\) | − | 4.90321i | − | 0.225450i | ||||||
\(474\) | 7.80642 | 0.358561 | ||||||||
\(475\) | −24.9175 | − | 7.14272i | −1.14329 | − | 0.327731i | ||||
\(476\) | 13.7364 | 0.629605 | ||||||||
\(477\) | 7.18421i | 0.328942i | ||||||||
\(478\) | 23.0223i | 1.05301i | ||||||||
\(479\) | −8.38715 | −0.383219 | −0.191609 | − | 0.981471i | \(-0.561371\pi\) | ||||
−0.191609 | + | 0.981471i | \(0.561371\pi\) | |||||||
\(480\) | 0.898290 | − | 6.39361i | 0.0410011 | − | 0.291827i | ||||
\(481\) | 24.0830 | 1.09809 | ||||||||
\(482\) | − | 1.63465i | − | 0.0744561i | ||||||
\(483\) | − | 19.6128i | − | 0.892415i | ||||||
\(484\) | 0.525428 | 0.0238831 | ||||||||
\(485\) | 6.10171 | + | 0.857279i | 0.277064 | + | 0.0389270i | ||||
\(486\) | 1.21432 | 0.0550827 | ||||||||
\(487\) | − | 9.83500i | − | 0.445667i | −0.974857 | − | 0.222833i | \(-0.928469\pi\) | ||
0.974857 | − | 0.222833i | \(-0.0715306\pi\) | |||||||
\(488\) | 2.31708i | 0.104890i | ||||||||
\(489\) | 12.1748 | 0.550565 | ||||||||
\(490\) | −45.8227 | − | 6.43801i | −2.07006 | − | 0.290840i | ||||
\(491\) | −32.9403 | −1.48657 | −0.743286 | − | 0.668973i | \(-0.766734\pi\) | ||||
−0.743286 | + | 0.668973i | \(0.766734\pi\) | |||||||
\(492\) | − | 0.949145i | − | 0.0427908i | ||||||
\(493\) | − | 9.63158i | − | 0.433785i | ||||||
\(494\) | −26.1106 | −1.17477 | ||||||||
\(495\) | 0.311108 | − | 2.21432i | 0.0139833 | − | 0.0995263i | ||||
\(496\) | −7.00937 | −0.314730 | ||||||||
\(497\) | − | 2.10171i | − | 0.0942746i | ||||||
\(498\) | − | 3.52543i | − | 0.157978i | ||||||
\(499\) | 1.63158 | 0.0730397 | 0.0365199 | − | 0.999333i | \(-0.488373\pi\) | ||||
0.0365199 | + | 0.999333i | \(0.488373\pi\) | |||||||
\(500\) | −2.38868 | + | 5.36689i | −0.106825 | + | 0.240014i | ||||
\(501\) | −13.0049 | −0.581017 | ||||||||
\(502\) | 1.31450i | 0.0586689i | ||||||||
\(503\) | 41.8622i | 1.86654i | 0.359171 | + | 0.933272i | \(0.383059\pi\) | ||||
−0.359171 | + | 0.933272i | \(0.616941\pi\) | |||||||
\(504\) | −15.0366 | −0.669782 | ||||||||
\(505\) | −5.53972 | + | 39.4291i | −0.246514 | + | 1.75457i | ||||
\(506\) | 4.85728 | 0.215932 | ||||||||
\(507\) | 4.20294i | 0.186659i | ||||||||
\(508\) | − | 9.83056i | − | 0.436160i | ||||||
\(509\) | 38.8573 | 1.72232 | 0.861159 | − | 0.508335i | \(-0.169739\pi\) | ||||
0.861159 | + | 0.508335i | \(0.169739\pi\) | |||||||
\(510\) | 14.3368 | + | 2.01429i | 0.634843 | + | 0.0891943i | ||||
\(511\) | 62.3180 | 2.75679 | ||||||||
\(512\) | − | 24.1131i | − | 1.06566i | ||||||
\(513\) | 5.18421i | 0.228888i | ||||||||
\(514\) | −0.161933 | −0.00714257 | ||||||||
\(515\) | 10.9590 | + | 1.53972i | 0.482911 | + | 0.0678481i | ||||
\(516\) | 2.57628 | 0.113415 | ||||||||
\(517\) | 7.05086i | 0.310096i | ||||||||
\(518\) | − | 34.5718i | − | 1.51900i | ||||||
\(519\) | 13.8938 | 0.609872 | ||||||||
\(520\) | −3.95713 | + | 28.1650i | −0.173532 | + | 1.23512i | ||||
\(521\) | 11.1111 | 0.486785 | 0.243393 | − | 0.969928i | \(-0.421740\pi\) | ||||
0.243393 | + | 0.969928i | \(0.421740\pi\) | |||||||
\(522\) | 2.19358i | 0.0960102i | ||||||||
\(523\) | 27.3002i | 1.19375i | 0.802332 | + | 0.596877i | \(0.203592\pi\) | ||||
−0.802332 | + | 0.596877i | \(0.796408\pi\) | |||||||
\(524\) | −0.653858 | −0.0285639 | ||||||||
\(525\) | 23.5669 | + | 6.75557i | 1.02854 | + | 0.294837i | ||||
\(526\) | 0.179286 | 0.00781724 | ||||||||
\(527\) | 13.9813i | 0.609033i | ||||||||
\(528\) | − | 2.67307i | − | 0.116330i | ||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 2.71408 | − | 19.3176i | 0.117892 | − | 0.839101i | ||||
\(531\) | 1.67307 | 0.0726051 | ||||||||
\(532\) | − | 13.3560i | − | 0.579055i | ||||||
\(533\) | 7.49240i | 0.324532i | ||||||||
\(534\) | −0.755569 | −0.0326967 | ||||||||
\(535\) | −24.7971 | − | 3.48394i | −1.07207 | − | 0.150624i | ||||
\(536\) | −14.8957 | −0.643396 | ||||||||
\(537\) | 12.8573i | 0.554833i | ||||||||
\(538\) | 32.6133i | 1.40606i | ||||||||
\(539\) | 17.0415 | 0.734029 | ||||||||
\(540\) | 1.16346 | + | 0.163465i | 0.0500675 | + | 0.00703440i | ||||
\(541\) | −16.1017 | −0.692267 | −0.346133 | − | 0.938185i | \(-0.612506\pi\) | ||||
−0.346133 | + | 0.938185i | \(0.612506\pi\) | |||||||
\(542\) | 3.74314i | 0.160782i | ||||||||
\(543\) | − | 0.917502i | − | 0.0393738i | ||||||
\(544\) | −15.3951 | −0.660061 | ||||||||
\(545\) | −4.88892 | + | 34.7971i | −0.209418 | + | 1.49054i | ||||
\(546\) | 24.6953 | 1.05686 | ||||||||
\(547\) | − | 40.0370i | − | 1.71186i | −0.517091 | − | 0.855930i | \(-0.672985\pi\) | ||
0.517091 | − | 0.855930i | \(-0.327015\pi\) | |||||||
\(548\) | − | 9.87649i | − | 0.421903i | ||||||
\(549\) | −0.755569 | −0.0322469 | ||||||||
\(550\) | −1.67307 | + | 5.83654i | −0.0713400 | + | 0.248871i | ||||
\(551\) | −9.36488 | −0.398957 | ||||||||
\(552\) | 12.2667i | 0.522106i | ||||||||
\(553\) | − | 31.5210i | − | 1.34041i | ||||||
\(554\) | −10.5763 | −0.449343 | ||||||||
\(555\) | −1.80642 | + | 12.8573i | −0.0766784 | + | 0.545761i | ||||
\(556\) | −7.37778 | −0.312888 | ||||||||
\(557\) | 28.2908i | 1.19872i | 0.800479 | + | 0.599361i | \(0.204578\pi\) | ||||
−0.800479 | + | 0.599361i | \(0.795422\pi\) | |||||||
\(558\) | − | 3.18421i | − | 0.134798i | ||||||
\(559\) | −20.3368 | −0.860154 | ||||||||
\(560\) | 29.0223 | + | 4.07758i | 1.22641 | + | 0.172309i | ||||
\(561\) | −5.33185 | −0.225111 | ||||||||
\(562\) | − | 24.7457i | − | 1.04384i | ||||||
\(563\) | − | 32.7926i | − | 1.38204i | −0.722834 | − | 0.691022i | \(-0.757161\pi\) | ||
0.722834 | − | 0.691022i | \(-0.242839\pi\) | |||||||
\(564\) | −3.70471 | −0.155997 | ||||||||
\(565\) | −3.90813 | − | 0.549086i | −0.164416 | − | 0.0231002i | ||||
\(566\) | 7.67752 | 0.322710 | ||||||||
\(567\) | − | 4.90321i | − | 0.205916i | ||||||
\(568\) | 1.31450i | 0.0551551i | ||||||||
\(569\) | 8.88586 | 0.372515 | 0.186257 | − | 0.982501i | \(-0.440364\pi\) | ||||
0.186257 | + | 0.982501i | \(0.440364\pi\) | |||||||
\(570\) | 1.95851 | − | 13.9398i | 0.0820331 | − | 0.583873i | ||||
\(571\) | −10.6953 | −0.447586 | −0.223793 | − | 0.974637i | \(-0.571844\pi\) | ||||
−0.223793 | + | 0.974637i | \(0.571844\pi\) | |||||||
\(572\) | − | 2.17929i | − | 0.0911205i | ||||||
\(573\) | − | 14.3684i | − | 0.600249i | ||||||
\(574\) | 10.7556 | 0.448929 | ||||||||
\(575\) | 5.51114 | − | 19.2257i | 0.229830 | − | 0.801767i | ||||
\(576\) | 8.85236 | 0.368848 | ||||||||
\(577\) | 27.1338i | 1.12960i | 0.825229 | + | 0.564798i | \(0.191046\pi\) | ||||
−0.825229 | + | 0.564798i | \(0.808954\pi\) | |||||||
\(578\) | − | 13.8780i | − | 0.577250i | ||||||
\(579\) | −11.7605 | −0.488749 | ||||||||
\(580\) | −0.295286 | + | 2.10171i | −0.0122611 | + | 0.0872688i | ||||
\(581\) | −14.2351 | −0.590570 | ||||||||
\(582\) | 3.34614i | 0.138702i | ||||||||
\(583\) | 7.18421i | 0.297540i | ||||||||
\(584\) | −38.9763 | −1.61285 | ||||||||
\(585\) | −9.18421 | − | 1.29036i | −0.379720 | − | 0.0533500i | ||||
\(586\) | −20.2524 | −0.836620 | ||||||||
\(587\) | 10.9590i | 0.452326i | 0.974089 | + | 0.226163i | \(0.0726182\pi\) | ||||
−0.974089 | + | 0.226163i | \(0.927382\pi\) | |||||||
\(588\) | 8.95407i | 0.369260i | ||||||||
\(589\) | 13.5941 | 0.560136 | ||||||||
\(590\) | −4.49871 | − | 0.632060i | −0.185209 | − | 0.0260215i | ||||
\(591\) | 3.82071 | 0.157163 | ||||||||
\(592\) | 15.5210i | 0.637908i | ||||||||
\(593\) | − | 23.7003i | − | 0.973253i | −0.873610 | − | 0.486627i | \(-0.838227\pi\) | ||
0.873610 | − | 0.486627i | \(-0.161773\pi\) | |||||||
\(594\) | 1.21432 | 0.0498241 | ||||||||
\(595\) | 8.13335 | − | 57.8894i | 0.333435 | − | 2.37323i | ||||
\(596\) | 1.60300 | 0.0656616 | ||||||||
\(597\) | − | 13.7146i | − | 0.561299i | ||||||
\(598\) | − | 20.1463i | − | 0.823842i | ||||||
\(599\) | −41.7146 | −1.70441 | −0.852205 | − | 0.523208i | \(-0.824735\pi\) | ||||
−0.852205 | + | 0.523208i | \(0.824735\pi\) | |||||||
\(600\) | −14.7397 | − | 4.22522i | −0.601748 | − | 0.172494i | ||||
\(601\) | 14.5906 | 0.595162 | 0.297581 | − | 0.954697i | \(-0.403820\pi\) | ||||
0.297581 | + | 0.954697i | \(0.403820\pi\) | |||||||
\(602\) | 29.1941i | 1.18986i | ||||||||
\(603\) | − | 4.85728i | − | 0.197804i | ||||||
\(604\) | −0.171778 | −0.00698953 | ||||||||
\(605\) | 0.311108 | − | 2.21432i | 0.0126483 | − | 0.0900249i | ||||
\(606\) | −21.6227 | −0.878362 | ||||||||
\(607\) | 19.9826i | 0.811071i | 0.914079 | + | 0.405535i | \(0.132915\pi\) | ||||
−0.914079 | + | 0.405535i | \(0.867085\pi\) | |||||||
\(608\) | 14.9688i | 0.607066i | ||||||||
\(609\) | 8.85728 | 0.358915 | ||||||||
\(610\) | 2.03164 | + | 0.285442i | 0.0822588 | + | 0.0115572i | ||||
\(611\) | 29.2444 | 1.18310 | ||||||||
\(612\) | − | 2.80150i | − | 0.113244i | ||||||
\(613\) | 19.0781i | 0.770555i | 0.922801 | + | 0.385278i | \(0.125894\pi\) | ||||
−0.922801 | + | 0.385278i | \(0.874106\pi\) | |||||||
\(614\) | −11.6400 | −0.469754 | ||||||||
\(615\) | −4.00000 | − | 0.561993i | −0.161296 | − | 0.0226617i | ||||
\(616\) | −15.0366 | −0.605840 | ||||||||
\(617\) | 39.3590i | 1.58454i | 0.610174 | + | 0.792268i | \(0.291100\pi\) | ||||
−0.610174 | + | 0.792268i | \(0.708900\pi\) | |||||||
\(618\) | 6.00984i | 0.241751i | ||||||||
\(619\) | 23.0923 | 0.928160 | 0.464080 | − | 0.885793i | \(-0.346385\pi\) | ||||
0.464080 | + | 0.885793i | \(0.346385\pi\) | |||||||
\(620\) | 0.428639 | − | 3.05086i | 0.0172146 | − | 0.122525i | ||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 17.6445i | 0.707480i | ||||||||
\(623\) | 3.05086i | 0.122230i | ||||||||
\(624\) | −11.0869 | −0.443833 | ||||||||
\(625\) | 21.2034 | + | 13.2444i | 0.848137 | + | 0.529777i | ||||
\(626\) | 25.5397 | 1.02077 | ||||||||
\(627\) | 5.18421i | 0.207037i | ||||||||
\(628\) | 10.4603i | 0.417411i | ||||||||
\(629\) | 30.9590 | 1.23442 | ||||||||
\(630\) | −1.85236 | + | 13.1842i | −0.0737997 | + | 0.525271i | ||||
\(631\) | −25.5111 | −1.01558 | −0.507791 | − | 0.861480i | \(-0.669538\pi\) | ||||
−0.507791 | + | 0.861480i | \(0.669538\pi\) | |||||||
\(632\) | 19.7146i | 0.784203i | ||||||||
\(633\) | − | 1.95851i | − | 0.0778439i | ||||||
\(634\) | −1.20294 | −0.0477750 | ||||||||
\(635\) | −41.4291 | − | 5.82071i | −1.64406 | − | 0.230988i | ||||
\(636\) | −3.77478 | −0.149680 | ||||||||
\(637\) | − | 70.6820i | − | 2.80052i | ||||||
\(638\) | 2.19358i | 0.0868445i | ||||||||
\(639\) | −0.428639 | −0.0169567 | ||||||||
\(640\) | −11.0158 | − | 1.54770i | −0.435439 | − | 0.0611783i | ||||
\(641\) | −6.25380 | −0.247010 | −0.123505 | − | 0.992344i | \(-0.539414\pi\) | ||||
−0.123505 | + | 0.992344i | \(0.539414\pi\) | |||||||
\(642\) | − | 13.5986i | − | 0.536692i | ||||||
\(643\) | 6.84743i | 0.270036i | 0.990843 | + | 0.135018i | \(0.0431093\pi\) | ||||
−0.990843 | + | 0.135018i | \(0.956891\pi\) | |||||||
\(644\) | 10.3051 | 0.406079 | ||||||||
\(645\) | 1.52543 | − | 10.8573i | 0.0600637 | − | 0.427505i | ||||
\(646\) | −33.5655 | −1.32062 | ||||||||
\(647\) | − | 20.2953i | − | 0.797890i | −0.916975 | − | 0.398945i | \(-0.869376\pi\) | ||
0.916975 | − | 0.398945i | \(-0.130624\pi\) | |||||||
\(648\) | 3.06668i | 0.120470i | ||||||||
\(649\) | 1.67307 | 0.0656738 | ||||||||
\(650\) | 24.2079 | + | 6.93930i | 0.949511 | + | 0.272182i | ||||
\(651\) | −12.8573 | −0.503916 | ||||||||
\(652\) | 6.39700i | 0.250526i | ||||||||
\(653\) | − | 10.6222i | − | 0.415679i | −0.978163 | − | 0.207840i | \(-0.933357\pi\) | ||
0.978163 | − | 0.207840i | \(-0.0666432\pi\) | |||||||
\(654\) | −19.0825 | −0.746185 | ||||||||
\(655\) | −0.387152 | + | 2.75557i | −0.0151273 | + | 0.107669i | ||||
\(656\) | −4.82870 | −0.188529 | ||||||||
\(657\) | − | 12.7096i | − | 0.495850i | ||||||
\(658\) | − | 41.9813i | − | 1.63660i | ||||||
\(659\) | −10.1017 | −0.393507 | −0.196753 | − | 0.980453i | \(-0.563040\pi\) | ||||
−0.196753 | + | 0.980453i | \(0.563040\pi\) | |||||||
\(660\) | 1.16346 | + | 0.163465i | 0.0452878 | + | 0.00636285i | ||||
\(661\) | 21.6128 | 0.840642 | 0.420321 | − | 0.907375i | \(-0.361917\pi\) | ||||
0.420321 | + | 0.907375i | \(0.361917\pi\) | |||||||
\(662\) | − | 21.3492i | − | 0.829760i | ||||||
\(663\) | 22.1146i | 0.858861i | ||||||||
\(664\) | 8.90321 | 0.345512 | ||||||||
\(665\) | −56.2864 | − | 7.90813i | −2.18269 | − | 0.306664i | ||||
\(666\) | −7.05086 | −0.273215 | ||||||||
\(667\) | − | 7.22570i | − | 0.279780i | ||||||
\(668\) | − | 6.83314i | − | 0.264382i | ||||||
\(669\) | −26.0098 | −1.00560 | ||||||||
\(670\) | −1.83500 | + | 13.0607i | −0.0708924 | + | 0.504579i | ||||
\(671\) | −0.755569 | −0.0291684 | ||||||||
\(672\) | − | 14.1575i | − | 0.546137i | ||||||
\(673\) | 10.2208i | 0.393982i | 0.980405 | + | 0.196991i | \(0.0631170\pi\) | ||||
−0.980405 | + | 0.196991i | \(0.936883\pi\) | |||||||
\(674\) | −3.84929 | −0.148269 | ||||||||
\(675\) | 1.37778 | − | 4.80642i | 0.0530309 | − | 0.184999i | ||||
\(676\) | −2.20834 | −0.0849363 | ||||||||
\(677\) | − | 13.9224i | − | 0.535082i | −0.963546 | − | 0.267541i | \(-0.913789\pi\) | ||
0.963546 | − | 0.267541i | \(-0.0862111\pi\) | |||||||
\(678\) | − | 2.14320i | − | 0.0823090i | ||||||
\(679\) | 13.5111 | 0.518510 | ||||||||
\(680\) | −5.08694 | + | 36.2065i | −0.195075 | + | 1.38846i | ||||
\(681\) | 6.34122 | 0.242996 | ||||||||
\(682\) | − | 3.18421i | − | 0.121930i | ||||||
\(683\) | − | 10.3970i | − | 0.397830i | −0.980017 | − | 0.198915i | \(-0.936258\pi\) | ||
0.980017 | − | 0.198915i | \(-0.0637418\pi\) | |||||||
\(684\) | −2.72393 | −0.104152 | ||||||||
\(685\) | −41.6227 | − | 5.84791i | −1.59032 | − | 0.223437i | ||||
\(686\) | −59.7877 | −2.28270 | ||||||||
\(687\) | − | 23.3274i | − | 0.889996i | ||||||
\(688\) | − | 13.1066i | − | 0.499686i | ||||||
\(689\) | 29.7975 | 1.13520 | ||||||||
\(690\) | 10.7556 | + | 1.51114i | 0.409458 | + | 0.0575280i | ||||
\(691\) | −0.977725 | −0.0371944 | −0.0185972 | − | 0.999827i | \(-0.505920\pi\) | ||||
−0.0185972 | + | 0.999827i | \(0.505920\pi\) | |||||||
\(692\) | 7.30021i | 0.277512i | ||||||||
\(693\) | − | 4.90321i | − | 0.186258i | ||||||
\(694\) | 6.04287 | 0.229384 | ||||||||
\(695\) | −4.36842 | + | 31.0923i | −0.165703 | + | 1.17940i | ||||
\(696\) | −5.53972 | −0.209982 | ||||||||
\(697\) | 9.63158i | 0.364822i | ||||||||
\(698\) | − | 22.1048i | − | 0.836678i | ||||||
\(699\) | −1.42372 | −0.0538499 | ||||||||
\(700\) | −3.54956 | + | 12.3827i | −0.134161 | + | 0.468022i | ||||
\(701\) | 48.9688 | 1.84953 | 0.924764 | − | 0.380542i | \(-0.124263\pi\) | ||||
0.924764 | + | 0.380542i | \(0.124263\pi\) | |||||||
\(702\) | − | 5.03657i | − | 0.190093i | ||||||
\(703\) | − | 30.1017i | − | 1.13531i | ||||||
\(704\) | 8.85236 | 0.333636 | ||||||||
\(705\) | −2.19358 | + | 15.6128i | −0.0826149 | + | 0.588014i | ||||
\(706\) | −27.2128 | −1.02417 | ||||||||
\(707\) | 87.3087i | 3.28358i | ||||||||
\(708\) | 0.879077i | 0.0330378i | ||||||||
\(709\) | 37.2672 | 1.39960 | 0.699799 | − | 0.714340i | \(-0.253273\pi\) | ||||
0.699799 | + | 0.714340i | \(0.253273\pi\) | |||||||
\(710\) | 1.15257 | + | 0.161933i | 0.0432550 | + | 0.00607725i | ||||
\(711\) | −6.42864 | −0.241093 | ||||||||
\(712\) | − | 1.90813i | − | 0.0715103i | ||||||
\(713\) | 10.4889i | 0.392811i | ||||||||
\(714\) | 31.7462 | 1.18807 | ||||||||
\(715\) | −9.18421 | − | 1.29036i | −0.343470 | − | 0.0482569i | ||||
\(716\) | −6.75557 | −0.252467 | ||||||||
\(717\) | − | 18.9590i | − | 0.708036i | ||||||
\(718\) | − | 25.8983i | − | 0.966516i | ||||||
\(719\) | −5.83500 | −0.217609 | −0.108804 | − | 0.994063i | \(-0.534702\pi\) | ||||
−0.108804 | + | 0.994063i | \(0.534702\pi\) | |||||||
\(720\) | 0.831613 | − | 5.91903i | 0.0309924 | − | 0.220589i | ||||
\(721\) | 24.2667 | 0.903739 | ||||||||
\(722\) | 9.56400i | 0.355935i | ||||||||
\(723\) | 1.34614i | 0.0500635i | ||||||||
\(724\) | 0.482081 | 0.0179164 | ||||||||
\(725\) | 8.68244 | + | 2.48886i | 0.322458 | + | 0.0924340i | ||||
\(726\) | 1.21432 | 0.0450676 | ||||||||
\(727\) | 46.8385i | 1.73715i | 0.495562 | + | 0.868573i | \(0.334962\pi\) | ||||
−0.495562 | + | 0.868573i | \(0.665038\pi\) | |||||||
\(728\) | 62.3663i | 2.31145i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −4.80150 | + | 34.1748i | −0.177712 | + | 1.26487i | ||||
\(731\) | −26.1432 | −0.966941 | ||||||||
\(732\) | − | 0.396997i | − | 0.0146734i | ||||||
\(733\) | − | 45.2083i | − | 1.66981i | −0.550395 | − | 0.834904i | \(-0.685523\pi\) | ||
0.550395 | − | 0.834904i | \(-0.314477\pi\) | |||||||
\(734\) | 42.6637 | 1.57475 | ||||||||
\(735\) | 37.7353 | + | 5.30174i | 1.39189 | + | 0.195558i | ||||
\(736\) | −11.5496 | −0.425723 | ||||||||
\(737\) | − | 4.85728i | − | 0.178920i | ||||||
\(738\) | − | 2.19358i | − | 0.0807467i | ||||||
\(739\) | −5.65433 | −0.207998 | −0.103999 | − | 0.994577i | \(-0.533164\pi\) | ||||
−0.103999 | + | 0.994577i | \(0.533164\pi\) | |||||||
\(740\) | −6.75557 | − | 0.949145i | −0.248340 | − | 0.0348913i | ||||
\(741\) | 21.5022 | 0.789905 | ||||||||
\(742\) | − | 42.7753i | − | 1.57033i | ||||||
\(743\) | 4.50622i | 0.165317i | 0.996578 | + | 0.0826585i | \(0.0263411\pi\) | ||||
−0.996578 | + | 0.0826585i | \(0.973659\pi\) | |||||||
\(744\) | 8.04149 | 0.294815 | ||||||||
\(745\) | 0.949145 | − | 6.75557i | 0.0347740 | − | 0.247505i | ||||
\(746\) | 20.6494 | 0.756029 | ||||||||
\(747\) | 2.90321i | 0.106223i | ||||||||
\(748\) | − | 2.80150i | − | 0.102433i | ||||||
\(749\) | −54.9086 | −2.00632 | ||||||||
\(750\) | −5.52051 | + | 12.4035i | −0.201580 | + | 0.452910i | ||||
\(751\) | 47.5121 | 1.73374 | 0.866870 | − | 0.498534i | \(-0.166128\pi\) | ||||
0.866870 | + | 0.498534i | \(0.166128\pi\) | |||||||
\(752\) | 18.8474i | 0.687295i | ||||||||
\(753\) | − | 1.08250i | − | 0.0394484i | ||||||
\(754\) | 9.09817 | 0.331336 | ||||||||
\(755\) | −0.101710 | + | 0.723926i | −0.00370161 | + | 0.0263464i | ||||
\(756\) | 2.57628 | 0.0936985 | ||||||||
\(757\) | 46.6637i | 1.69602i | 0.529979 | + | 0.848011i | \(0.322200\pi\) | ||||
−0.529979 | + | 0.848011i | \(0.677800\pi\) | |||||||
\(758\) | − | 2.87601i | − | 0.104462i | ||||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | 35.2039 | + | 4.94608i | 1.27698 | + | 0.179413i | ||||
\(761\) | 14.9304 | 0.541227 | 0.270613 | − | 0.962688i | \(-0.412773\pi\) | ||||
0.270613 | + | 0.962688i | \(0.412773\pi\) | |||||||
\(762\) | − | 22.7195i | − | 0.823040i | ||||||
\(763\) | 77.0518i | 2.78946i | ||||||||
\(764\) | 7.54956 | 0.273134 | ||||||||
\(765\) | −11.8064 | − | 1.65878i | −0.426862 | − | 0.0599733i | ||||
\(766\) | −1.47643 | −0.0533457 | ||||||||
\(767\) | − | 6.93930i | − | 0.250564i | ||||||
\(768\) | 11.6637i | 0.420878i | ||||||||
\(769\) | −38.8573 | −1.40123 | −0.700615 | − | 0.713540i | \(-0.747091\pi\) | ||||
−0.700615 | + | 0.713540i | \(0.747091\pi\) | |||||||
\(770\) | −1.85236 | + | 13.1842i | −0.0667543 | + | 0.475126i | ||||
\(771\) | 0.133353 | 0.00480259 | ||||||||
\(772\) | − | 6.17929i | − | 0.222397i | ||||||
\(773\) | − | 36.3368i | − | 1.30694i | −0.756951 | − | 0.653471i | \(-0.773312\pi\) | ||
0.756951 | − | 0.653471i | \(-0.226688\pi\) | |||||||
\(774\) | 5.95407 | 0.214015 | ||||||||
\(775\) | −12.6035 | − | 3.61285i | −0.452730 | − | 0.129777i | ||||
\(776\) | −8.45044 | −0.303353 | ||||||||
\(777\) | 28.4701i | 1.02136i | ||||||||
\(778\) | − | 2.75251i | − | 0.0986821i | ||||||
\(779\) | 9.36488 | 0.335532 | ||||||||
\(780\) | 0.677993 | − | 4.82564i | 0.0242760 | − | 0.172785i | ||||
\(781\) | −0.428639 | −0.0153379 | ||||||||
\(782\) | − | 25.8983i | − | 0.926121i | ||||||
\(783\) | − | 1.80642i | − | 0.0645563i | ||||||
\(784\) | 45.5531 | 1.62690 | ||||||||
\(785\) | 44.0830 | + | 6.19358i | 1.57339 | + | 0.221058i | ||||
\(786\) | −1.51114 | −0.0539005 | ||||||||
\(787\) | 33.5482i | 1.19586i | 0.801547 | + | 0.597932i | \(0.204011\pi\) | ||||
−0.801547 | + | 0.597932i | \(0.795989\pi\) | |||||||
\(788\) | 2.00751i | 0.0715145i | ||||||||
\(789\) | −0.147643 | −0.00525624 | ||||||||
\(790\) | 17.2859 | + | 2.42864i | 0.615005 | + | 0.0864071i | ||||
\(791\) | −8.65386 | −0.307696 | ||||||||
\(792\) | 3.06668i | 0.108970i | ||||||||
\(793\) | 3.13383i | 0.111286i | ||||||||
\(794\) | −22.4514 | −0.796770 | ||||||||
\(795\) | −2.23506 | + | 15.9081i | −0.0792695 | + | 0.564203i | ||||
\(796\) | 7.20601 | 0.255410 | ||||||||
\(797\) | 16.1334i | 0.571473i | 0.958308 | + | 0.285736i | \(0.0922382\pi\) | ||||
−0.958308 | + | 0.285736i | \(0.907762\pi\) | |||||||
\(798\) | − | 30.8671i | − | 1.09268i | ||||||
\(799\) | 37.5941 | 1.32998 | ||||||||
\(800\) | 3.97820 | − | 13.8780i | 0.140651 | − | 0.490662i | ||||
\(801\) | 0.622216 | 0.0219849 | ||||||||
\(802\) | 21.3265i | 0.753063i | ||||||||
\(803\) | − | 12.7096i | − | 0.448513i | ||||||
\(804\) | 2.55215 | 0.0900073 | ||||||||
\(805\) | 6.10171 | − | 43.4291i | 0.215057 | − | 1.53068i | ||||
\(806\) | −13.2070 | −0.465195 | ||||||||
\(807\) | − | 26.8573i | − | 0.945421i | ||||||
\(808\) | − | 54.6065i | − | 1.92105i | ||||||
\(809\) | −25.7431 | −0.905081 | −0.452540 | − | 0.891744i | \(-0.649482\pi\) | ||||
−0.452540 | + | 0.891744i | \(0.649482\pi\) | |||||||
\(810\) | 2.68889 | + | 0.377784i | 0.0944780 | + | 0.0132740i | ||||
\(811\) | 13.4509 | 0.472325 | 0.236163 | − | 0.971714i | \(-0.424110\pi\) | ||||
0.236163 | + | 0.971714i | \(0.424110\pi\) | |||||||
\(812\) | 4.65386i | 0.163318i | ||||||||
\(813\) | − | 3.08250i | − | 0.108108i | ||||||
\(814\) | −7.05086 | −0.247132 | ||||||||
\(815\) | 26.9590 | + | 3.78769i | 0.944332 | + | 0.132677i | ||||
\(816\) | −14.2524 | −0.498934 | ||||||||
\(817\) | 25.4193i | 0.889308i | ||||||||
\(818\) | 25.9210i | 0.906308i | ||||||||
\(819\) | −20.3368 | −0.710624 | ||||||||
\(820\) | 0.295286 | − | 2.10171i | 0.0103118 | − | 0.0733949i | ||||
\(821\) | 24.1748 | 0.843708 | 0.421854 | − | 0.906664i | \(-0.361380\pi\) | ||||
0.421854 | + | 0.906664i | \(0.361380\pi\) | |||||||
\(822\) | − | 22.8256i | − | 0.796135i | ||||||
\(823\) | − | 40.9117i | − | 1.42609i | −0.701118 | − | 0.713046i | \(-0.747315\pi\) | ||
0.701118 | − | 0.713046i | \(-0.252685\pi\) | |||||||
\(824\) | −15.1774 | −0.528731 | ||||||||
\(825\) | 1.37778 | − | 4.80642i | 0.0479683 | − | 0.167338i | ||||
\(826\) | −9.96158 | −0.346608 | ||||||||
\(827\) | 20.1476i | 0.700602i | 0.936637 | + | 0.350301i | \(0.113921\pi\) | ||||
−0.936637 | + | 0.350301i | \(0.886079\pi\) | |||||||
\(828\) | − | 2.10171i | − | 0.0730395i | ||||||
\(829\) | −31.4322 | −1.09168 | −0.545842 | − | 0.837888i | \(-0.683790\pi\) | ||||
−0.545842 | + | 0.837888i | \(0.683790\pi\) | |||||||
\(830\) | 1.09679 | − | 7.80642i | 0.0380701 | − | 0.270965i | ||||
\(831\) | 8.70964 | 0.302134 | ||||||||
\(832\) | − | 36.7164i | − | 1.27291i | ||||||
\(833\) | − | 90.8627i | − | 3.14821i | ||||||
\(834\) | −17.0509 | −0.590423 | ||||||||
\(835\) | −28.7971 | − | 4.04593i | −0.996563 | − | 0.140015i | ||||
\(836\) | −2.72393 | −0.0942089 | ||||||||
\(837\) | 2.62222i | 0.0906370i | ||||||||
\(838\) | − | 35.0420i | − | 1.21050i | ||||||
\(839\) | 52.8988 | 1.82627 | 0.913134 | − | 0.407659i | \(-0.133655\pi\) | ||||
0.913134 | + | 0.407659i | \(0.133655\pi\) | |||||||
\(840\) | −33.2958 | − | 4.67799i | −1.14881 | − | 0.161406i | ||||
\(841\) | −25.7368 | −0.887477 | ||||||||
\(842\) | − | 43.0954i | − | 1.48517i | ||||||
\(843\) | 20.3783i | 0.701865i | ||||||||
\(844\) | 1.02906 | 0.0354216 | ||||||||
\(845\) | −1.30757 | + | 9.30666i | −0.0449817 | + | 0.320159i | ||||
\(846\) | −8.56199 | −0.294367 | ||||||||
\(847\) | − | 4.90321i | − | 0.168476i | ||||||
\(848\) | 19.2039i | 0.659465i | ||||||||
\(849\) | −6.32248 | −0.216987 | ||||||||
\(850\) | 31.1195 | + | 8.92056i | 1.06739 | + | 0.305973i | ||||
\(851\) | 23.2257 | 0.796167 | ||||||||
\(852\) | − | 0.225219i | − | 0.00771588i | ||||||
\(853\) | − | 46.9229i | − | 1.60661i | −0.595568 | − | 0.803305i | \(-0.703073\pi\) | ||
0.595568 | − | 0.803305i | \(-0.296927\pi\) | |||||||
\(854\) | 4.49871 | 0.153943 | ||||||||
\(855\) | −1.61285 | + | 11.4795i | −0.0551582 | + | 0.392590i | ||||
\(856\) | 34.3422 | 1.17379 | ||||||||
\(857\) | 25.1481i | 0.859043i | 0.903057 | + | 0.429522i | \(0.141318\pi\) | ||||
−0.903057 | + | 0.429522i | \(0.858682\pi\) | |||||||
\(858\) | − | 5.03657i | − | 0.171945i | ||||||
\(859\) | −1.84791 | −0.0630499 | −0.0315250 | − | 0.999503i | \(-0.510036\pi\) | ||||
−0.0315250 | + | 0.999503i | \(0.510036\pi\) | |||||||
\(860\) | 5.70471 | + | 0.801502i | 0.194529 | + | 0.0273310i | ||||
\(861\) | −8.85728 | −0.301855 | ||||||||
\(862\) | 11.2257i | 0.382349i | ||||||||
\(863\) | 32.6824i | 1.11252i | 0.831007 | + | 0.556262i | \(0.187765\pi\) | ||||
−0.831007 | + | 0.556262i | \(0.812235\pi\) | |||||||
\(864\) | −2.88739 | −0.0982310 | ||||||||
\(865\) | 30.7654 | + | 4.32248i | 1.04606 | + | 0.146969i | ||||
\(866\) | 7.63254 | 0.259364 | ||||||||
\(867\) | 11.4286i | 0.388137i | ||||||||
\(868\) | − | 6.75557i | − | 0.229299i | ||||||
\(869\) | −6.42864 | −0.218077 | ||||||||
\(870\) | −0.682439 | + | 4.85728i | −0.0231368 | + | 0.164677i | ||||
\(871\) | −20.1463 | −0.682630 | ||||||||
\(872\) | − | 48.1915i | − | 1.63197i | ||||||
\(873\) | − | 2.75557i | − | 0.0932619i | ||||||
\(874\) | −25.1811 | −0.851765 | ||||||||
\(875\) | 50.0830 | + | 22.2908i | 1.69311 | + | 0.753568i | ||||
\(876\) | 6.67799 | 0.225628 | ||||||||
\(877\) | − | 49.1798i | − | 1.66068i | −0.557255 | − | 0.830341i | \(-0.688145\pi\) | ||
0.557255 | − | 0.830341i | \(-0.311855\pi\) | |||||||
\(878\) | 44.3595i | 1.49706i | ||||||||
\(879\) | 16.6780 | 0.562535 | ||||||||
\(880\) | 0.831613 | − | 5.91903i | 0.0280337 | − | 0.199531i | ||||
\(881\) | 33.8163 | 1.13930 | 0.569650 | − | 0.821888i | \(-0.307079\pi\) | ||||
0.569650 | + | 0.821888i | \(0.307079\pi\) | |||||||
\(882\) | 20.6938i | 0.696797i | ||||||||
\(883\) | 24.7368i | 0.832461i | 0.909259 | + | 0.416230i | \(0.136649\pi\) | ||||
−0.909259 | + | 0.416230i | \(0.863351\pi\) | |||||||
\(884\) | −11.6196 | −0.390810 | ||||||||
\(885\) | 3.70471 | + | 0.520505i | 0.124533 | + | 0.0174966i | ||||
\(886\) | 46.4800 | 1.56153 | ||||||||
\(887\) | − | 7.64004i | − | 0.256528i | −0.991740 | − | 0.128264i | \(-0.959060\pi\) | ||
0.991740 | − | 0.128264i | \(-0.0409404\pi\) | |||||||
\(888\) | − | 17.8064i | − | 0.597544i | ||||||
\(889\) | −91.7373 | −3.07677 | ||||||||
\(890\) | −1.67307 | − | 0.235063i | −0.0560815 | − | 0.00787934i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | − | 13.6663i | − | 0.457581i | ||||||
\(893\) | − | 36.5531i | − | 1.22320i | ||||||
\(894\) | 3.70471 | 0.123904 | ||||||||
\(895\) | −4.00000 | + | 28.4701i | −0.133705 | + | 0.951651i | ||||
\(896\) | −24.3926 | −0.814898 | ||||||||
\(897\) | 16.5906i | 0.553943i | ||||||||
\(898\) | 38.6735i | 1.29055i | ||||||||
\(899\) | −4.73683 | −0.157982 | ||||||||
\(900\) | 2.52543 | + | 0.723926i | 0.0841809 | + | 0.0241309i | ||||
\(901\) | 38.3051 | 1.27613 | ||||||||
\(902\) | − | 2.19358i | − | 0.0730381i | ||||||
\(903\) | − | 24.0415i | − | 0.800051i | ||||||
\(904\) | 5.41249 | 0.180017 | ||||||||
\(905\) | 0.285442 | − | 2.03164i | 0.00948841 | − | 0.0675341i | ||||
\(906\) | −0.396997 | −0.0131893 | ||||||||
\(907\) | 30.3970i | 1.00932i | 0.863319 | + | 0.504658i | \(0.168381\pi\) | ||||
−0.863319 | + | 0.504658i | \(0.831619\pi\) | |||||||
\(908\) | 3.33185i | 0.110571i | ||||||||
\(909\) | 17.8064 | 0.590602 | ||||||||
\(910\) | 54.6834 | + | 7.68292i | 1.81274 | + | 0.254686i | ||||
\(911\) | −45.3274 | −1.50176 | −0.750882 | − | 0.660436i | \(-0.770371\pi\) | ||||
−0.750882 | + | 0.660436i | \(0.770371\pi\) | |||||||
\(912\) | 13.8578i | 0.458876i | ||||||||
\(913\) | 2.90321i | 0.0960823i | ||||||||
\(914\) | 1.69042 | 0.0559142 | ||||||||
\(915\) | −1.67307 | − | 0.235063i | −0.0553100 | − | 0.00777095i | ||||
\(916\) | 12.2569 | 0.404978 | ||||||||
\(917\) | 6.10171i | 0.201496i | ||||||||
\(918\) | − | 6.47457i | − | 0.213693i | ||||||
\(919\) | 16.3269 | 0.538576 | 0.269288 | − | 0.963060i | \(-0.413212\pi\) | ||||
0.269288 | + | 0.963060i | \(0.413212\pi\) | |||||||
\(920\) | −3.81627 | + | 27.1624i | −0.125819 | + | 0.895518i | ||||
\(921\) | 9.58565 | 0.315858 | ||||||||
\(922\) | − | 9.35599i | − | 0.308123i | ||||||
\(923\) | 1.77784i | 0.0585184i | ||||||||
\(924\) | 2.57628 | 0.0847535 | ||||||||
\(925\) | −8.00000 | + | 27.9081i | −0.263038 | + | 0.917614i | ||||
\(926\) | −5.68598 | −0.186853 | ||||||||
\(927\) | − | 4.94914i | − | 0.162551i | ||||||
\(928\) | − | 5.21585i | − | 0.171219i | ||||||
\(929\) | 29.6128 | 0.971566 | 0.485783 | − | 0.874079i | \(-0.338535\pi\) | ||||
0.485783 | + | 0.874079i | \(0.338535\pi\) | |||||||
\(930\) | 0.990632 | − | 7.05086i | 0.0324841 | − | 0.231207i | ||||
\(931\) | −88.3466 | −2.89544 | ||||||||
\(932\) | − | 0.748060i | − | 0.0245035i | ||||||
\(933\) | − | 14.5303i | − | 0.475702i | ||||||
\(934\) | 15.6128 | 0.510868 | ||||||||
\(935\) | −11.8064 | − | 1.65878i | −0.386111 | − | 0.0542479i | ||||
\(936\) | 12.7195 | 0.415749 | ||||||||
\(937\) | − | 8.92195i | − | 0.291467i | −0.989324 | − | 0.145734i | \(-0.953446\pi\) | ||
0.989324 | − | 0.145734i | \(-0.0465543\pi\) | |||||||
\(938\) | 28.9206i | 0.944290i | ||||||||
\(939\) | −21.0321 | −0.686357 | ||||||||
\(940\) | −8.20342 | − | 1.15257i | −0.267566 | − | 0.0375925i | ||||
\(941\) | −22.2766 | −0.726195 | −0.363097 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363097 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(942\) | 24.1748i | 0.787659i | ||||||||
\(943\) | 7.22570i | 0.235301i | ||||||||
\(944\) | 4.47224 | 0.145559 | ||||||||
\(945\) | 1.52543 | − | 10.8573i | 0.0496222 | − | 0.353187i | ||||
\(946\) | 5.95407 | 0.193583 | ||||||||
\(947\) | − | 44.4612i | − | 1.44480i | −0.691477 | − | 0.722398i | \(-0.743040\pi\) | ||
0.691477 | − | 0.722398i | \(-0.256960\pi\) | |||||||
\(948\) | − | 3.37778i | − | 0.109705i | ||||||
\(949\) | −52.7150 | −1.71120 | ||||||||
\(950\) | 8.67355 | − | 30.2578i | 0.281407 | − | 0.981693i | ||||
\(951\) | 0.990632 | 0.0321234 | ||||||||
\(952\) | 80.1727i | 2.59841i | ||||||||
\(953\) | 20.5575i | 0.665924i | 0.942940 | + | 0.332962i | \(0.108048\pi\) | ||||
−0.942940 | + | 0.332962i | \(0.891952\pi\) | |||||||
\(954\) | −8.72393 | −0.282448 | ||||||||
\(955\) | 4.47013 | − | 31.8163i | 0.144650 | − | 1.02955i | ||||
\(956\) | 9.96158 | 0.322180 | ||||||||
\(957\) | − | 1.80642i | − | 0.0583934i | ||||||
\(958\) | − | 10.1847i | − | 0.329052i | ||||||
\(959\) | −92.1659 | −2.97619 | ||||||||
\(960\) | 19.6019 | + | 2.75404i | 0.632650 | + | 0.0888862i | ||||
\(961\) | −24.1240 | −0.778193 | ||||||||
\(962\) | 29.2444i | 0.942878i | ||||||||
\(963\) | 11.1985i | 0.360867i | ||||||||
\(964\) | −0.707300 | −0.0227806 | ||||||||
\(965\) | −26.0415 | − | 3.65878i | −0.838305 | − | 0.117780i | ||||
\(966\) | 23.8163 | 0.766276 | ||||||||
\(967\) | − | 27.4839i | − | 0.883824i | −0.897058 | − | 0.441912i | \(-0.854300\pi\) | ||
0.897058 | − | 0.441912i | \(-0.145700\pi\) | |||||||
\(968\) | 3.06668i | 0.0985667i | ||||||||
\(969\) | 27.6414 | 0.887971 | ||||||||
\(970\) | −1.04101 | + | 7.40943i | −0.0334248 | + | 0.237902i | ||||
\(971\) | −5.81532 | −0.186622 | −0.0933112 | − | 0.995637i | \(-0.529745\pi\) | ||||
−0.0933112 | + | 0.995637i | \(0.529745\pi\) | |||||||
\(972\) | − | 0.525428i | − | 0.0168531i | ||||||
\(973\) | 68.8484i | 2.20718i | ||||||||
\(974\) | 11.9428 | 0.382673 | ||||||||
\(975\) | −19.9353 | − | 5.71456i | −0.638442 | − | 0.183012i | ||||
\(976\) | −2.01969 | −0.0646487 | ||||||||
\(977\) | − | 48.3912i | − | 1.54817i | −0.633081 | − | 0.774085i | \(-0.718210\pi\) | ||
0.633081 | − | 0.774085i | \(-0.281790\pi\) | |||||||
\(978\) | 14.7841i | 0.472745i | ||||||||
\(979\) | 0.622216 | 0.0198861 | ||||||||
\(980\) | −2.78568 | + | 19.8272i | −0.0889853 | + | 0.633356i | ||||
\(981\) | 15.7146 | 0.501727 | ||||||||
\(982\) | − | 40.0000i | − | 1.27645i | ||||||
\(983\) | − | 49.9724i | − | 1.59387i | −0.604064 | − | 0.796936i | \(-0.706453\pi\) | ||
0.604064 | − | 0.796936i | \(-0.293547\pi\) | |||||||
\(984\) | 5.53972 | 0.176600 | ||||||||
\(985\) | 8.46028 | + | 1.18865i | 0.269567 | + | 0.0378737i | ||||
\(986\) | 11.6958 | 0.372471 | ||||||||
\(987\) | 34.5718i | 1.10043i | ||||||||
\(988\) | 11.2979i | 0.359433i | ||||||||
\(989\) | −19.6128 | −0.623652 | ||||||||
\(990\) | 2.68889 | + | 0.377784i | 0.0854586 | + | 0.0120068i | ||||
\(991\) | −7.35905 | −0.233768 | −0.116884 | − | 0.993146i | \(-0.537291\pi\) | ||||
−0.116884 | + | 0.993146i | \(0.537291\pi\) | |||||||
\(992\) | 7.57136i | 0.240391i | ||||||||
\(993\) | 17.5812i | 0.557923i | ||||||||
\(994\) | 2.55215 | 0.0809492 | ||||||||
\(995\) | 4.26671 | − | 30.3684i | 0.135264 | − | 0.962744i | ||||
\(996\) | −1.52543 | −0.0483350 | ||||||||
\(997\) | 4.33138i | 0.137176i | 0.997645 | + | 0.0685880i | \(0.0218494\pi\) | ||||
−0.997645 | + | 0.0685880i | \(0.978151\pi\) | |||||||
\(998\) | 1.98126i | 0.0627158i | ||||||||
\(999\) | 5.80642 | 0.183707 |
(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 | 165.2.c.a.34.4 | yes | 6 | |
3.2 | odd | 2 | 495.2.c.d.199.3 | 6 | |||
4.3 | odd | 2 | 2640.2.d.i.529.5 | 6 | |||
5.2 | odd | 4 | 825.2.a.n.1.1 | 3 | |||
5.3 | odd | 4 | 825.2.a.h.1.3 | 3 | |||
5.4 | even | 2 | inner | 165.2.c.a.34.3 | ✓ | 6 | |
11.10 | odd | 2 | 1815.2.c.d.364.3 | 6 | |||
15.2 | even | 4 | 2475.2.a.y.1.3 | 3 | |||
15.8 | even | 4 | 2475.2.a.be.1.1 | 3 | |||
15.14 | odd | 2 | 495.2.c.d.199.4 | 6 | |||
20.19 | odd | 2 | 2640.2.d.i.529.2 | 6 | |||
55.32 | even | 4 | 9075.2.a.cc.1.3 | 3 | |||
55.43 | even | 4 | 9075.2.a.ck.1.1 | 3 | |||
55.54 | odd | 2 | 1815.2.c.d.364.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.c.a.34.3 | ✓ | 6 | 5.4 | even | 2 | inner | |
165.2.c.a.34.4 | yes | 6 | 1.1 | even | 1 | trivial | |
495.2.c.d.199.3 | 6 | 3.2 | odd | 2 | |||
495.2.c.d.199.4 | 6 | 15.14 | odd | 2 | |||
825.2.a.h.1.3 | 3 | 5.3 | odd | 4 | |||
825.2.a.n.1.1 | 3 | 5.2 | odd | 4 | |||
1815.2.c.d.364.3 | 6 | 11.10 | odd | 2 | |||
1815.2.c.d.364.4 | 6 | 55.54 | odd | 2 | |||
2475.2.a.y.1.3 | 3 | 15.2 | even | 4 | |||
2475.2.a.be.1.1 | 3 | 15.8 | even | 4 | |||
2640.2.d.i.529.2 | 6 | 20.19 | odd | 2 | |||
2640.2.d.i.529.5 | 6 | 4.3 | odd | 2 | |||
9075.2.a.cc.1.3 | 3 | 55.32 | even | 4 | |||
9075.2.a.ck.1.1 | 3 | 55.43 | even | 4 |