Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(1009,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1680.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.t (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4148675396\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.4 | ||
Root | \(-0.854638 - 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1009 |
Dual form | 1680.2.t.j.1009.1 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.17009 | − | 0.539189i | −0.970492 | − | 0.241133i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.26180 | 0.983468 | 0.491734 | − | 0.870745i | \(-0.336363\pi\) | ||||
0.491734 | + | 0.870745i | \(0.336363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.340173i | − | 0.0943470i | −0.998887 | − | 0.0471735i | \(-0.984979\pi\) | ||
0.998887 | − | 0.0471735i | \(-0.0150214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.539189 | − | 2.17009i | 0.139218 | − | 0.560314i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.75872i | 1.39670i | 0.715759 | + | 0.698348i | \(0.246081\pi\) | ||||
−0.715759 | + | 0.698348i | \(0.753919\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.49693 | −1.49050 | −0.745249 | − | 0.666786i | \(-0.767669\pi\) | ||||
−0.745249 | + | 0.666786i | \(0.767669\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.49693i | − | 1.77173i | −0.463941 | − | 0.885866i | \(-0.653565\pi\) | ||
0.463941 | − | 0.885866i | \(-0.346435\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.41855 | + | 2.34017i | 0.883710 | + | 0.468035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.34017 | 1.49794 | 0.748970 | − | 0.662604i | \(-0.230549\pi\) | ||||
0.748970 | + | 0.662604i | \(0.230549\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.26180i | 0.567806i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.539189 | + | 2.17009i | −0.0911396 | + | 0.366812i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.15676i | − | 1.01216i | −0.862485 | − | 0.506082i | \(-0.831093\pi\) | ||
0.862485 | − | 0.506082i | \(-0.168907\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.340173 | 0.0544713 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.340173 | 0.0531261 | 0.0265630 | − | 0.999647i | \(-0.491544\pi\) | ||||
0.0265630 | + | 0.999647i | \(0.491544\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.68035i | − | 1.32374i | −0.749618 | − | 0.661870i | \(-0.769763\pi\) | ||
0.749618 | − | 0.661870i | \(-0.230237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.17009 | + | 0.539189i | 0.323497 | + | 0.0803775i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.75872 | −0.806383 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.34017i | 1.14561i | 0.819691 | + | 0.572805i | \(0.194145\pi\) | ||||
−0.819691 | + | 0.572805i | \(0.805855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.07838 | − | 1.75872i | −0.954448 | − | 0.237146i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.49693i | − | 0.860539i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.83710 | 0.890115 | 0.445057 | − | 0.895502i | \(-0.353183\pi\) | ||||
0.445057 | + | 0.895502i | \(0.353183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.3607 | 1.96674 | 0.983368 | − | 0.181627i | \(-0.0581363\pi\) | ||||
0.983368 | + | 0.181627i | \(0.0581363\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.183417 | + | 0.738205i | −0.0227501 | + | 0.0915630i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.8371i | − | 1.81264i | −0.422592 | − | 0.906320i | \(-0.638880\pi\) | ||
0.422592 | − | 0.906320i | \(-0.361120\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.49693 | 1.02291 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.9421 | 1.89198 | 0.945992 | − | 0.324190i | \(-0.105092\pi\) | ||||
0.945992 | + | 0.324190i | \(0.105092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50307i | 0.175921i | 0.996124 | + | 0.0879606i | \(0.0280350\pi\) | ||||
−0.996124 | + | 0.0879606i | \(0.971965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.34017 | + | 4.41855i | −0.270220 | + | 0.510210i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.26180i | − | 0.371716i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.68035 | 0.976615 | 0.488308 | − | 0.872672i | \(-0.337614\pi\) | ||||
0.488308 | + | 0.872672i | \(0.337614\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.83710i | 0.750469i | 0.926930 | + | 0.375235i | \(0.122438\pi\) | ||||
−0.926930 | + | 0.375235i | \(0.877562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.10504 | − | 12.4969i | 0.336789 | − | 1.35548i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.1773 | 1.60879 | 0.804394 | − | 0.594096i | \(-0.202490\pi\) | ||||
0.804394 | + | 0.594096i | \(0.202490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.340173 | −0.0356598 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.34017i | 0.864836i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.0989 | + | 3.50307i | 1.44652 | + | 0.359408i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.49693i | − | 0.659663i | −0.944040 | − | 0.329832i | \(-0.893008\pi\) | ||
0.944040 | − | 0.329832i | \(-0.106992\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.26180 | −0.327823 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.18342 | −0.217258 | −0.108629 | − | 0.994082i | \(-0.534646\pi\) | ||||
−0.108629 | + | 0.994082i | \(0.534646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.84324i | − | 0.575752i | −0.957668 | − | 0.287876i | \(-0.907051\pi\) | ||
0.957668 | − | 0.287876i | \(-0.0929491\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.17009 | − | 0.539189i | −0.211779 | − | 0.0526194i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.18342i | 0.791121i | 0.918440 | + | 0.395560i | \(0.129450\pi\) | ||||
−0.918440 | + | 0.395560i | \(0.870550\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.8371 | −1.61270 | −0.806351 | − | 0.591437i | \(-0.798561\pi\) | ||||
−0.806351 | + | 0.591437i | \(0.798561\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.15676 | 0.584373 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0205i | 1.22487i | 0.790522 | + | 0.612434i | \(0.209809\pi\) | ||||
−0.790522 | + | 0.612434i | \(0.790191\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.58145 | + | 18.4391i | −0.427222 | + | 1.71945i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.340173i | 0.0314490i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.75872 | 0.527901 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.360692 | −0.0327902 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.340173i | 0.0306724i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.32684 | − | 7.46081i | −0.744775 | − | 0.667315i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.84324i | 0.163562i | 0.996650 | + | 0.0817808i | \(0.0260607\pi\) | ||||
−0.996650 | + | 0.0817808i | \(0.973939\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.68035 | 0.764262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.313511 | 0.0273916 | 0.0136958 | − | 0.999906i | \(-0.495640\pi\) | ||||
0.0136958 | + | 0.999906i | \(0.495640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.49693i | 0.563355i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.539189 | + | 2.17009i | −0.0464060 | + | 0.186771i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.18342i | − | 0.186542i | −0.995641 | − | 0.0932710i | \(-0.970268\pi\) | ||
0.995641 | − | 0.0932710i | \(-0.0297323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.02052 | −0.0865593 | −0.0432796 | − | 0.999063i | \(-0.513781\pi\) | ||||
−0.0432796 | + | 0.999063i | \(0.513781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.10957i | − | 0.0927873i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.34017 | − | 1.07838i | −0.360432 | − | 0.0895544i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.6803 | −1.20266 | −0.601330 | − | 0.799000i | \(-0.705362\pi\) | ||||
−0.601330 | + | 0.799000i | \(0.705362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.15676 | −0.175514 | −0.0877571 | − | 0.996142i | \(-0.527970\pi\) | ||||
−0.0877571 | + | 0.996142i | \(0.527970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.75872i | − | 0.465565i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.0989 | − | 4.49693i | −1.45374 | − | 0.361202i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.18342i | − | 0.493490i | −0.969080 | − | 0.246745i | \(-0.920639\pi\) | ||
0.969080 | − | 0.246745i | \(-0.0793611\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.34017 | −0.661419 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.49693 | −0.669652 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.75872 | − | 7.07838i | 0.136916 | − | 0.551051i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.47641i | − | 0.114248i | −0.998367 | − | 0.0571240i | \(-0.981807\pi\) | ||
0.998367 | − | 0.0571240i | \(-0.0181930\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8843 | 0.991099 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.49693 | 0.496833 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.75872i | − | 0.133713i | −0.997763 | − | 0.0668566i | \(-0.978703\pi\) | ||
0.997763 | − | 0.0668566i | \(-0.0212970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34017 | − | 4.41855i | 0.176900 | − | 0.334011i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.83710i | 0.513908i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.424694 | 0.0317431 | 0.0158716 | − | 0.999874i | \(-0.494948\pi\) | ||||
0.0158716 | + | 0.999874i | \(0.494948\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3668 | 0.770561 | 0.385280 | − | 0.922800i | \(-0.374105\pi\) | ||||
0.385280 | + | 0.922800i | \(0.374105\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.3607i | 1.13550i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.31965 | + | 13.3607i | −0.244066 | + | 0.982298i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.7838i | 1.37361i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7321 | 1.57248 | 0.786238 | − | 0.617923i | \(-0.212026\pi\) | ||||
0.786238 | + | 0.617923i | \(0.212026\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.36683i | − | 0.602258i | −0.953583 | − | 0.301129i | \(-0.902637\pi\) | ||
0.953583 | − | 0.301129i | \(-0.0973635\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.738205 | − | 0.183417i | −0.0528639 | − | 0.0131348i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.3340i | − | 0.950010i | −0.879983 | − | 0.475005i | \(-0.842446\pi\) | ||
0.879983 | − | 0.475005i | \(-0.157554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.49693 | 0.460555 | 0.230278 | − | 0.973125i | \(-0.426037\pi\) | ||||
0.230278 | + | 0.973125i | \(0.426037\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.8371 | 1.04653 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.00000i | − | 0.140372i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.738205 | − | 0.183417i | −0.0515585 | − | 0.0128104i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.49693i | 0.590577i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.1917 | −1.46586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.83710 | −0.470685 | −0.235343 | − | 0.971912i | \(-0.575621\pi\) | ||||
−0.235343 | + | 0.971912i | \(0.575621\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.9421i | 1.09234i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.68035 | + | 18.8371i | −0.319197 | + | 1.28468i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.34017i | − | 0.566168i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.50307 | −0.101568 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.95896 | 0.131774 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.3607i | − | 1.16256i | −0.813704 | − | 0.581279i | \(-0.802553\pi\) | ||
0.813704 | − | 0.581279i | \(-0.197447\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41855 | − | 2.34017i | −0.294570 | − | 0.156012i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.1568i | 0.674128i | 0.941482 | + | 0.337064i | \(0.109434\pi\) | ||||
−0.941482 | + | 0.337064i | \(0.890566\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.9939 | −0.990822 | −0.495411 | − | 0.868659i | \(-0.664983\pi\) | ||||
−0.495411 | + | 0.868659i | \(0.664983\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.26180 | 0.214610 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.5441i | − | 0.756280i | −0.925748 | − | 0.378140i | \(-0.876564\pi\) | ||
0.925748 | − | 0.378140i | \(-0.123436\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.68035i | 0.563849i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.8950 | −0.704736 | −0.352368 | − | 0.935861i | \(-0.614624\pi\) | ||||
−0.352368 | + | 0.935861i | \(0.614624\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.68035 | −0.430319 | −0.215159 | − | 0.976579i | \(-0.569027\pi\) | ||||
−0.215159 | + | 0.976579i | \(0.569027\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.17009 | + | 0.539189i | 0.138642 | + | 0.0344475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.21008i | 0.140624i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.83710 | −0.433284 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.1978 | −1.52735 | −0.763676 | − | 0.645600i | \(-0.776607\pi\) | ||||
−0.763676 | + | 0.645600i | \(0.776607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 27.7152i | − | 1.74244i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.4969 | + | 3.10504i | 0.782588 | + | 0.194445i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 15.2351i | − | 0.950342i | −0.879894 | − | 0.475171i | \(-0.842386\pi\) | ||
0.879894 | − | 0.475171i | \(-0.157614\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.15676 | −0.382562 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 29.1773i | − | 1.79915i | −0.436769 | − | 0.899574i | \(-0.643877\pi\) | ||
0.436769 | − | 0.899574i | \(-0.356123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.49693 | − | 18.0989i | 0.276244 | − | 1.11181i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.1773i | 0.928834i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.13009 | 0.373758 | 0.186879 | − | 0.982383i | \(-0.440163\pi\) | ||||
0.186879 | + | 0.982383i | \(0.440163\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.7009 | −1.56122 | −0.780608 | − | 0.625021i | \(-0.785091\pi\) | ||||
−0.780608 | + | 0.625021i | \(0.785091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.340173i | − | 0.0205882i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.4124 | + | 7.63317i | 0.869101 | + | 0.460297i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.2039i | − | 0.673179i | −0.941651 | − | 0.336590i | \(-0.890726\pi\) | ||
0.941651 | − | 0.336590i | \(-0.109274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.34017 | −0.499313 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.3545 | 1.45287 | 0.726435 | − | 0.687235i | \(-0.241176\pi\) | ||||
0.726435 | + | 0.687235i | \(0.241176\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.15676i | 0.365981i | 0.983115 | + | 0.182991i | \(0.0585778\pi\) | ||||
−0.983115 | + | 0.182991i | \(0.941422\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.50307 | + | 14.0989i | −0.207504 | + | 0.835147i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.340173i | − | 0.0200798i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1629 | −0.950759 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.49693 | 0.380857 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.75872i | 0.102746i | 0.998680 | + | 0.0513729i | \(0.0163597\pi\) | ||||
−0.998680 | + | 0.0513729i | \(0.983640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.8371 | − | 3.68649i | −0.863849 | − | 0.214636i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.26180i | − | 0.189269i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.89043 | −0.167158 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.68035 | −0.500327 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.18342i | − | 0.125434i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.3340 | − | 8.28231i | −1.90870 | − | 0.474244i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 27.2039i | − | 1.55261i | −0.630357 | − | 0.776305i | \(-0.717092\pi\) | ||
0.630357 | − | 0.776305i | \(-0.282908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.84324 | 0.332411 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.8432 | 1.23862 | 0.619308 | − | 0.785148i | \(-0.287413\pi\) | ||||
0.619308 | + | 0.785148i | \(0.287413\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.3874i | 1.43498i | 0.696570 | + | 0.717489i | \(0.254709\pi\) | ||||
−0.696570 | + | 0.717489i | \(0.745291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.539189 | − | 2.17009i | 0.0303799 | − | 0.122271i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.6947i | 1.27466i | 0.770590 | + | 0.637331i | \(0.219962\pi\) | ||||
−0.770590 | + | 0.637331i | \(0.780038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.52359 | 0.365251 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.18342 | −0.456754 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 37.4140i | − | 2.08177i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.796064 | − | 1.50307i | 0.0441577 | − | 0.0833754i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 16.8371i | − | 0.931094i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.47641 | −0.301011 | −0.150505 | − | 0.988609i | \(-0.548090\pi\) | ||||
−0.150505 | + | 0.988609i | \(0.548090\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.15676i | 0.337388i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | + | 32.1978i | −0.437087 | + | 1.75915i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6742i | 0.744881i | 0.928056 | + | 0.372441i | \(0.121479\pi\) | ||||
−0.928056 | + | 0.372441i | \(0.878521\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.0205 | −0.707178 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.2039 | 1.47318 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.4391 | − | 4.58145i | −0.992726 | − | 0.246657i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.183417i | 0.00984637i | 0.999988 | + | 0.00492318i | \(0.00156710\pi\) | ||||
−0.999988 | + | 0.00492318i | \(0.998433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.67420 | 0.410791 | 0.205395 | − | 0.978679i | \(-0.434152\pi\) | ||||
0.205395 | + | 0.978679i | \(0.434152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.340173 | −0.0181571 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.4329i | 1.03431i | 0.855892 | + | 0.517155i | \(0.173009\pi\) | ||||
−0.855892 | + | 0.517155i | \(0.826991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.5958 | − | 8.59583i | −1.83616 | − | 0.456219i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.75872i | 0.304784i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.4186 | −1.34154 | −0.670770 | − | 0.741666i | \(-0.734036\pi\) | ||||
−0.670770 | + | 0.741666i | \(0.734036\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.2101 | 1.22158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 0.360692i | − | 0.0189314i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.810439 | − | 3.26180i | 0.0424203 | − | 0.170730i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.36069i | 0.488624i | 0.969697 | + | 0.244312i | \(0.0785621\pi\) | ||||
−0.969697 | + | 0.244312i | \(0.921438\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.340173 | −0.0177087 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.34017 | 0.433000 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5174i | 1.42480i | 0.701774 | + | 0.712400i | \(0.252392\pi\) | ||||
−0.701774 | + | 0.712400i | \(0.747608\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.46081 | − | 8.32684i | 0.385275 | − | 0.429996i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.680346i | − | 0.0350396i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.84324 | 0.505614 | 0.252807 | − | 0.967517i | \(-0.418646\pi\) | ||||
0.252807 | + | 0.967517i | \(0.418646\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.84324 | −0.0944323 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.8310i | 1.42210i | 0.703144 | + | 0.711048i | \(0.251779\pi\) | ||||
−0.703144 | + | 0.711048i | \(0.748221\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.75872 | + | 7.07838i | −0.0896329 | + | 0.360748i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.68035i | 0.441247i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.67420 | 0.186289 | 0.0931447 | − | 0.995653i | \(-0.470308\pi\) | ||||
0.0931447 | + | 0.995653i | \(0.470308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 48.9315 | 2.47457 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.313511i | 0.0158145i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.8371 | − | 4.68035i | −0.947797 | − | 0.235494i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.8638i | − | 1.14750i | −0.819031 | − | 0.573750i | \(-0.805488\pi\) | ||
0.819031 | − | 0.573750i | \(-0.194512\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.49693 | −0.325253 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.31965 | 0.265651 | 0.132825 | − | 0.991139i | \(-0.457595\pi\) | ||||
0.132825 | + | 0.991139i | \(0.457595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.83710i | − | 0.141326i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.17009 | − | 0.539189i | −0.107832 | − | 0.0267925i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 20.0821i | − | 0.995432i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.7275 | −1.37104 | −0.685519 | − | 0.728055i | \(-0.740425\pi\) | ||||
−0.685519 | + | 0.728055i | \(0.740425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.18342 | 0.107700 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.83710i | − | 0.336432i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.68649 | − | 14.8371i | 0.180963 | − | 0.728325i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.02052i | − | 0.0499750i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.5174 | −1.14890 | −0.574451 | − | 0.818539i | \(-0.694785\pi\) | ||||
−0.574451 | + | 0.818539i | \(0.694785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.15061 | −0.0560774 | −0.0280387 | − | 0.999607i | \(-0.508926\pi\) | ||||
−0.0280387 | + | 0.999607i | \(0.508926\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.4764 | + | 25.4452i | −0.653702 | + | 1.23427i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 15.3607i | − | 0.743356i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.10957 | 0.0535708 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.4186 | −0.839022 | −0.419511 | − | 0.907750i | \(-0.637798\pi\) | ||||
−0.419511 | + | 0.907750i | \(0.637798\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0144i | 1.25017i | 0.780556 | + | 0.625086i | \(0.214936\pi\) | ||||
−0.780556 | + | 0.625086i | \(0.785064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.07838 | − | 4.34017i | 0.0517043 | − | 0.208095i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 55.2039i | 2.64076i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.13624 | 0.245139 | 0.122570 | − | 0.992460i | \(-0.460887\pi\) | ||||
0.122570 | + | 0.992460i | \(0.460887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5380i | 0.880765i | 0.897810 | + | 0.440383i | \(0.145157\pi\) | ||||
−0.897810 | + | 0.440383i | \(0.854843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.9360 | − | 8.18342i | −1.56132 | − | 0.387931i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.6803i | − | 0.694357i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3135 | 0.486725 | 0.243362 | − | 0.969935i | \(-0.421750\pi\) | ||||
0.243362 | + | 0.969935i | \(0.421750\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.10957 | 0.0522478 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.15676i | − | 0.101333i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.738205 | + | 0.183417i | 0.0346076 | + | 0.00859874i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.36683i | 0.204272i | 0.994770 | + | 0.102136i | \(0.0325677\pi\) | ||||
−0.994770 | + | 0.102136i | \(0.967432\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.75872 | 0.268794 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.7009 | −1.56961 | −0.784803 | − | 0.619745i | \(-0.787236\pi\) | ||||
−0.784803 | + | 0.619745i | \(0.787236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.4703i | − | 0.486595i | −0.969952 | − | 0.243297i | \(-0.921771\pi\) | ||
0.969952 | − | 0.243297i | \(-0.0782291\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.49693 | − | 18.0989i | 0.208540 | − | 0.839316i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.51745i | 0.162768i | 0.996683 | + | 0.0813840i | \(0.0259340\pi\) | ||||
−0.996683 | + | 0.0813840i | \(0.974066\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.8371 | −0.685114 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.18342 | 0.284917 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 28.3135i | − | 1.30186i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.7070 | − | 15.2039i | −1.31717 | − | 0.697604i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 8.34017i | − | 0.381870i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.8432 | −0.998043 | −0.499022 | − | 0.866590i | \(-0.666307\pi\) | ||||
−0.499022 | + | 0.866590i | \(0.666307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.09436 | −0.0954947 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 8.49693i | − | 0.386624i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.50307 | + | 14.0989i | −0.159066 | + | 0.640198i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.88428i | − | 0.357271i | −0.983915 | − | 0.178635i | \(-0.942832\pi\) | ||
0.983915 | − | 0.178635i | \(-0.0571683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7731 | −0.892347 | −0.446174 | − | 0.894946i | \(-0.647214\pi\) | ||||
−0.446174 | + | 0.894946i | \(0.647214\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5174i | 0.518720i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.07838 | + | 1.75872i | 0.318149 | + | 0.0790488i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 15.9421i | − | 0.715103i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.5174 | 1.76904 | 0.884522 | − | 0.466499i | \(-0.154485\pi\) | ||||
0.884522 | + | 0.466499i | \(0.154485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.47641 | 0.0659611 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 11.2039i | − | 0.499559i | −0.968303 | − | 0.249779i | \(-0.919642\pi\) | ||
0.968303 | − | 0.249779i | \(-0.0803581\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.73820 | + | 1.17727i | 0.210847 | + | 0.0523880i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.8843i | 0.572211i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.5441 | 1.04357 | 0.521787 | − | 0.853076i | \(-0.325266\pi\) | ||||
0.521787 | + | 0.853076i | \(0.325266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50307 | 0.0664920 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.49693i | 0.286846i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.15061 | + | 12.6803i | −0.138833 | + | 0.558763i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.75872 | 0.0771994 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.6537 | 1.08010 | 0.540049 | − | 0.841634i | \(-0.318406\pi\) | ||||
0.540049 | + | 0.841634i | \(0.318406\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.63931i | − | 0.115409i | −0.998334 | − | 0.0577044i | \(-0.981622\pi\) | ||
0.998334 | − | 0.0577044i | \(-0.0183781\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.41855 | + | 2.34017i | 0.192841 | + | 0.102134i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 48.0288i | 2.09217i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.1978 | −2.13903 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.83710 | −0.296705 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.115718i | − | 0.00501229i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.41241 | − | 17.7587i | 0.190765 | − | 0.767777i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.424694i | 0.0183269i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.26180 | −0.140495 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.1506 | 1.08131 | 0.540655 | − | 0.841245i | \(-0.318177\pi\) | ||||
0.540655 | + | 0.841245i | \(0.318177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3668i | 0.444883i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.5380 | + | 9.07838i | 1.56511 | + | 0.388875i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.1506i | 1.50293i | 0.659772 | + | 0.751466i | \(0.270653\pi\) | ||||
−0.659772 | + | 0.751466i | \(0.729347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.3607 | −0.655578 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.9939 | −0.553557 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.68035i | − | 0.369126i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.3607 | − | 3.31965i | −0.567130 | − | 0.140911i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3812i | 1.11781i | 0.829232 | + | 0.558904i | \(0.188778\pi\) | ||||
−0.829232 | + | 0.558904i | \(0.811222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.95282 | −0.124891 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.7838 | −0.793052 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.9939i | 0.547626i | 0.961783 | + | 0.273813i | \(0.0882849\pi\) | ||||
−0.961783 | + | 0.273813i | \(0.911715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.02052 | − | 28.2557i | 0.295355 | − | 1.18872i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.36683 | 0.266912 | 0.133456 | − | 0.991055i | \(-0.457393\pi\) | ||||
0.133456 | + | 0.991055i | \(0.457393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.63931 | −0.110452 | −0.0552258 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552258 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.7321i | 0.907870i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.8843 | − | 37.5441i | 0.829232 | − | 1.56570i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.3340i | 1.38771i | 0.720113 | + | 0.693857i | \(0.244090\pi\) | ||||
−0.720113 | + | 0.693857i | \(0.755910\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.36683 | 0.347714 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.83710 | 0.283651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.2039i | 1.12667i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.183417 | − | 0.738205i | 0.00758338 | − | 0.0305210i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.3074i | 0.714352i | 0.934037 | + | 0.357176i | \(0.116260\pi\) | ||||
−0.934037 | + | 0.357176i | \(0.883740\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −54.1855 | −2.23267 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.3340 | 0.548489 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 47.1194i | − | 1.93496i | −0.252943 | − | 0.967481i | \(-0.581398\pi\) | ||
0.252943 | − | 0.967481i | \(-0.418602\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.4969 | − | 3.10504i | −0.512324 | − | 0.127294i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.49693i | 0.265902i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.1050 | −0.535457 | −0.267729 | − | 0.963494i | \(-0.586273\pi\) | ||||
−0.267729 | + | 0.963494i | \(0.586273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.0349 | 1.18436 | 0.592179 | − | 0.805806i | \(-0.298268\pi\) | ||||
0.592179 | + | 0.805806i | \(0.298268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.8371i | 0.604213i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.782733 | + | 0.194481i | 0.0318226 | + | 0.00790678i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.9877i | − | 1.05481i | −0.849614 | − | 0.527404i | \(-0.823165\pi\) | ||
0.849614 | − | 0.527404i | \(-0.176835\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.1978i | − | 0.815781i | −0.913031 | − | 0.407891i | \(-0.866264\pi\) | ||
0.913031 | − | 0.407891i | \(-0.133736\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.183417 | − | 0.738205i | 0.00739611 | − | 0.0297673i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.8576i | 1.92668i | 0.268292 | + | 0.963338i | \(0.413541\pi\) | ||||
−0.268292 | + | 0.963338i | \(0.586459\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.3812 | −0.738803 | −0.369402 | − | 0.929270i | \(-0.620437\pi\) | ||||
−0.369402 | + | 0.929270i | \(0.620437\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.49693 | −0.340970 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 15.1773i | − | 0.608065i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | + | 20.6803i | 0.561887 | + | 0.827214i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 21.1917i | − | 0.846313i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.4551 | 1.41369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.94668 | 0.316352 | 0.158176 | − | 0.987411i | \(-0.449439\pi\) | ||||
0.158176 | + | 0.987411i | \(0.449439\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.83710i | − | 0.271750i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.993857 | − | 4.00000i | 0.0394400 | − | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.340173i | 0.0134781i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.9421 | −0.630661 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.7275 | 0.621200 | 0.310600 | − | 0.950541i | \(-0.399470\pi\) | ||||
0.310600 | + | 0.950541i | \(0.399470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.5646i | 1.75746i | 0.477322 | + | 0.878729i | \(0.341608\pi\) | ||||
−0.477322 | + | 0.878729i | \(0.658392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.8371 | − | 4.68035i | −0.741710 | − | 0.184288i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.16290i | 0.202974i | 0.994837 | + | 0.101487i | \(0.0323601\pi\) | ||||
−0.994837 | + | 0.101487i | \(0.967640\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.3012 | 0.875400 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.34017 | 0.326877 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.49079i | 0.293137i | 0.989201 | + | 0.146569i | \(0.0468229\pi\) | ||||
−0.989201 | + | 0.146569i | \(0.953177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.680346 | − | 0.169042i | −0.0265833 | − | 0.00660500i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.50307i | − | 0.0586404i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.7259 | −0.885276 | −0.442638 | − | 0.896700i | \(-0.645957\pi\) | ||||
−0.442638 | + | 0.896700i | \(0.645957\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.3258 | −0.479418 | −0.239709 | − | 0.970845i | \(-0.577052\pi\) | ||||
−0.239709 | + | 0.970845i | \(0.577052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.95896i | 0.0760798i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.50307 | − | 14.0989i | 0.135843 | − | 0.546732i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.9939i | − | 0.658005i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.3607 | 0.671203 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.1034 | 1.93422 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 25.6742i | − | 0.989668i | −0.868988 | − | 0.494834i | \(-0.835229\pi\) | ||
0.868988 | − | 0.494834i | \(-0.164771\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.34017 | − | 4.41855i | 0.0900733 | − | 0.170070i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 29.2762i | − | 1.12517i | −0.826738 | − | 0.562587i | \(-0.809806\pi\) | ||
0.826738 | − | 0.562587i | \(-0.190194\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.49693 | −0.249329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1568 | −0.389208 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 25.5441i | − | 0.977418i | −0.872447 | − | 0.488709i | \(-0.837468\pi\) | ||
0.872447 | − | 0.488709i | \(-0.162532\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.17727 | + | 4.73820i | −0.0449813 | + | 0.181037i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 14.9939i | − | 0.572051i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.83710 | 0.108085 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.3812 | −1.00359 | −0.501794 | − | 0.864987i | \(-0.667327\pi\) | ||||
−0.501794 | + | 0.864987i | \(0.667327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.26180i | 0.123905i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.21461 | + | 0.550252i | 0.0840051 | + | 0.0208723i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.95896i | 0.0742010i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5441 | 0.436638 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.6742 | −0.894162 | −0.447081 | − | 0.894493i | \(-0.647536\pi\) | ||||
−0.447081 | + | 0.894493i | \(0.647536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.0000i | 1.50863i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.18342i | 0.0821159i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.7214 | 1.52932 | 0.764662 | − | 0.644432i | \(-0.222906\pi\) | ||||
0.764662 | + | 0.644432i | \(0.222906\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.68035 | −0.325538 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 70.8659i | − | 2.65395i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.598270 | + | 2.40787i | −0.0223740 | + | 0.0900493i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 10.8950i | − | 0.406880i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.3545 | 0.833684 | 0.416842 | − | 0.908979i | \(-0.363137\pi\) | ||||
0.416842 | + | 0.908979i | \(0.363137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.84324 | −0.217614 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 6.68035i | − | 0.248445i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.83710 | + | 4.68035i | 0.328202 | + | 0.173824i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.10957i | − | 0.189504i | −0.995501 | − | 0.0947518i | \(-0.969794\pi\) | ||
0.995501 | − | 0.0947518i | \(-0.0302058\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.9877 | 1.84886 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.6475i | 1.53829i | 0.639076 | + | 0.769144i | \(0.279317\pi\) | ||||
−0.639076 | + | 0.769144i | \(0.720683\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.539189 | + | 2.17009i | −0.0198883 | + | 0.0800448i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 48.3956i | − | 1.78267i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.3135 | 1.18867 | 0.594336 | − | 0.804217i | \(-0.297415\pi\) | ||||
0.594336 | + | 0.804217i | \(0.297415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.21008 | −0.0811893 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.1711i | − | 1.10687i | −0.832892 | − | 0.553436i | \(-0.813316\pi\) | ||
0.832892 | − | 0.553436i | \(-0.186684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.8576 | + | 7.91548i | 1.16717 | + | 0.290001i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.83710i | − | 0.250156i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.18342 | 0.299016 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.1855 | 1.68533 | 0.842667 | − | 0.538436i | \(-0.180985\pi\) | ||||
0.842667 | + | 0.538436i | \(0.180985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 24.1978i | − | 0.881817i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.68035 | + | 1.16290i | 0.170335 | + | 0.0423222i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 50.5523i | − | 1.83736i | −0.395007 | − | 0.918678i | \(-0.629258\pi\) | ||
0.395007 | − | 0.918678i | \(-0.370742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.7152 | 1.00600 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.1711 | −0.441203 | −0.220602 | − | 0.975364i | \(-0.570802\pi\) | ||||
−0.220602 | + | 0.975364i | \(0.570802\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.8371i | 0.609544i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.10504 | + | 12.4969i | −0.112263 | + | 0.451827i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.32580i | − | 0.0839797i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.36069 | −0.265433 | −0.132717 | − | 0.991154i | \(-0.542370\pi\) | ||||
−0.132717 | + | 0.991154i | \(0.542370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.2351 | 0.548680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 10.5548i | − | 0.379629i | −0.981820 | − | 0.189815i | \(-0.939211\pi\) | ||
0.981820 | − | 0.189815i | \(-0.0607887\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.8515 | + | 19.5174i | 1.32374 | + | 0.701087i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.15676i | − | 0.220872i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.21008 | −0.0791843 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.0000 | 1.86071 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.00000i | − | 0.0714742i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.33403 | + | 13.4186i | −0.118997 | + | 0.478929i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.04718i | 0.322497i | 0.986914 | + | 0.161249i | \(0.0515521\pi\) | ||||
−0.986914 | + | 0.161249i | \(0.948448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.1773 | 1.03874 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.0205 | 0.462956 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.22529i | − | 0.185556i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.0989 | + | 4.49693i | 0.641902 | + | 0.159490i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 16.9627i | − | 0.600848i | −0.953806 | − | 0.300424i | \(-0.902872\pi\) | ||
0.953806 | − | 0.300424i | \(-0.0971282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.1773 | −0.536263 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.90271i | 0.173013i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.4391 | + | 4.58145i | 0.649892 | + | 0.161475i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.13009i | 0.215790i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.9877 | −0.562098 | −0.281049 | − | 0.959693i | \(-0.590682\pi\) | ||||
−0.281049 | + | 0.959693i | \(0.590682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.39350 | 0.294736 | 0.147368 | − | 0.989082i | \(-0.452920\pi\) | ||||
0.147368 | + | 0.989082i | \(0.452920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 25.7009i | − | 0.901369i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.15676 | + | 8.68035i | −0.0755478 | + | 0.304059i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.3956i | 1.97303i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.340173 | 0.0118866 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.0288 | 1.32721 | 0.663606 | − | 0.748082i | \(-0.269025\pi\) | ||||
0.663606 | + | 0.748082i | \(0.269025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.1568i | 0.772336i | 0.922428 | + | 0.386168i | \(0.126201\pi\) | ||||
−0.922428 | + | 0.386168i | \(0.873799\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.63317 | + | 14.4124i | −0.265753 | + | 0.501776i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.8227i | 0.515437i | 0.966220 | + | 0.257718i | \(0.0829707\pi\) | ||||
−0.966220 | + | 0.257718i | \(0.917029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.9467 | −0.484388 | −0.242194 | − | 0.970228i | \(-0.577867\pi\) | ||||
−0.242194 | + | 0.970228i | \(0.577867\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2039 | 0.388660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.75872i | − | 0.199528i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.796064 | + | 3.20394i | −0.0275489 | + | 0.110877i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 8.34017i | − | 0.288279i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4764 | −0.879543 | −0.439772 | − | 0.898110i | \(-0.644941\pi\) | ||||
−0.439772 | + | 0.898110i | \(0.644941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.3545i | 0.838815i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.9600 | − | 6.94706i | −0.961853 | − | 0.238986i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.360692i | 0.0123935i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.15676 | −0.211299 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −52.3135 | −1.79328 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 58.1588i | − | 1.99132i | −0.0930604 | − | 0.995660i | \(-0.529665\pi\) | ||
0.0930604 | − | 0.995660i | \(-0.470335\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.0989 | − | 3.50307i | −0.482172 | − | 0.119803i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.9093i | − | 0.987524i | −0.869597 | − | 0.493762i | \(-0.835621\pi\) | ||
0.869597 | − | 0.493762i | \(-0.164379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.1834 | 1.71224 | 0.856118 | − | 0.516780i | \(-0.172870\pi\) | ||||
0.856118 | + | 0.516780i | \(0.172870\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.340173 | 0.0115931 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.13009i | 0.276752i | 0.990380 | + | 0.138376i | \(0.0441882\pi\) | ||||
−0.990380 | + | 0.138376i | \(0.955812\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.948284 | + | 3.81658i | −0.0322426 | + | 0.129768i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.1629i | − | 0.548921i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.3135 | 0.960470 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.04718 | −0.171017 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.49693i | 0.219888i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.46081 | + | 8.32684i | −0.252221 | + | 0.281499i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 26.8371i | − | 0.906225i | −0.891453 | − | 0.453112i | \(-0.850314\pi\) | ||
0.891453 | − | 0.453112i | \(-0.149686\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.75872 | −0.0593203 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.4846 | −1.49873 | −0.749363 | − | 0.662160i | \(-0.769640\pi\) | ||||
−0.749363 | + | 0.662160i | \(0.769640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.8781i | − | 0.702605i | −0.936262 | − | 0.351303i | \(-0.885739\pi\) | ||
0.936262 | − | 0.351303i | \(-0.114261\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.68649 | − | 14.8371i | 0.123920 | − | 0.498744i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.4079i | 0.752383i | 0.926542 | + | 0.376191i | \(0.122766\pi\) | ||||
−0.926542 | + | 0.376191i | \(0.877234\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.84324 | 0.0618204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.26180 | 0.109274 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.921622 | − | 0.228990i | −0.0308064 | − | 0.00765430i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 2.89043i | − | 0.0965085i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.6803 | 0.556321 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0288 | −1.60007 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 8.68035i | − | 0.288864i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.4969 | − | 5.58968i | −0.747823 | − | 0.185807i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.8781i | 0.693247i | 0.938004 | + | 0.346624i | \(0.112672\pi\) | ||||
−0.938004 | + | 0.346624i | \(0.887328\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.18342 | 0.0724194 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.52198 | −0.116688 | −0.0583442 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583442 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.3012i | 0.738063i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.28231 | − | 33.3340i | 0.273805 | − | 1.10199i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.313511i | − | 0.0103530i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.1978 | 0.402368 | 0.201184 | − | 0.979553i | \(-0.435521\pi\) | ||||
0.201184 | + | 0.979553i | \(0.435521\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.2039 | 0.896400 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 5.42309i | − | 0.178503i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.4079 | − | 27.2039i | 0.473728 | − | 0.894460i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.84324i | 0.191917i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.86376 | −0.0939570 | −0.0469785 | − | 0.998896i | \(-0.514959\pi\) | ||||
−0.0469785 | + | 0.998896i | \(0.514959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.49693 | 0.212928 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.8432i | 0.715116i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.1280 | − | 40.7624i | 0.331221 | − | 1.33307i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7480i | 0.873821i | 0.899505 | + | 0.436910i | \(0.143927\pi\) | ||||
−0.899505 | + | 0.436910i | \(0.856073\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.3874 | −0.828485 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0144 | 0.326459 | 0.163230 | − | 0.986588i | \(-0.447809\pi\) | ||||
0.163230 | + | 0.986588i | \(0.447809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.89043i | − | 0.0941252i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.17009 | + | 0.539189i | 0.0705929 | + | 0.0175398i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 47.2183i | − | 1.53439i | −0.641415 | − | 0.767194i | \(-0.721652\pi\) | ||
0.641415 | − | 0.767194i | \(-0.278348\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.511304 | 0.0165976 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.6947 | −0.735927 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14.6660i | − | 0.475077i | −0.971378 | − | 0.237539i | \(-0.923659\pi\) | ||
0.971378 | − | 0.237539i | \(-0.0763407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.1605 | − | 11.7177i | −1.52608 | − | 0.379175i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.52359i | 0.210878i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.18342 | −0.0705062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.5585 | 1.24382 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 8.18342i | − | 0.263707i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.51130 | + | 18.1568i | −0.145224 | + | 0.584487i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.3894i | 1.84552i | 0.385375 | + | 0.922760i | \(0.374072\pi\) | ||||
−0.385375 | + | 0.922760i | \(0.625928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.4140 | 1.20191 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.4017 | 0.750997 | 0.375499 | − | 0.926823i | \(-0.377471\pi\) | ||||
0.375499 | + | 0.926823i | \(0.377471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.02052i | 0.0327163i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.50307 | + | 0.796064i | 0.0481368 | + | 0.0254944i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.54411i | 0.113386i | 0.998392 | + | 0.0566931i | \(0.0180556\pi\) | ||||
−0.998392 | + | 0.0566931i | \(0.981944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.5052 | 1.58219 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.8371 | 0.537567 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.7152i | 0.373658i | 0.982392 | + | 0.186829i | \(0.0598211\pi\) | ||||
−0.982392 | + | 0.186829i | \(0.940179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.18956 | + | 28.9360i | −0.229078 | + | 0.921978i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −73.7563 | −2.34531 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.5113 | −1.79514 | −0.897570 | − | 0.440871i | \(-0.854670\pi\) | ||||
−0.897570 | + | 0.440871i | \(0.854670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.47641i | − | 0.173789i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0989 | − | 3.50307i | −0.446965 | − | 0.111055i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.9048i | 1.29547i | 0.761867 | + | 0.647734i | \(0.224283\pi\) | ||||
−0.761867 | + | 0.647734i | \(0.775717\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.15676 | −0.194791 |
(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 | 1680.2.t.j.1009.4 | 6 | ||
3.2 | odd | 2 | 5040.2.t.z.1009.6 | 6 | |||
4.3 | odd | 2 | 840.2.t.d.169.1 | ✓ | 6 | ||
5.2 | odd | 4 | 8400.2.a.dl.1.2 | 3 | |||
5.3 | odd | 4 | 8400.2.a.di.1.2 | 3 | |||
5.4 | even | 2 | inner | 1680.2.t.j.1009.1 | 6 | ||
12.11 | even | 2 | 2520.2.t.k.1009.6 | 6 | |||
15.14 | odd | 2 | 5040.2.t.z.1009.5 | 6 | |||
20.3 | even | 4 | 4200.2.a.bp.1.2 | 3 | |||
20.7 | even | 4 | 4200.2.a.bn.1.2 | 3 | |||
20.19 | odd | 2 | 840.2.t.d.169.4 | yes | 6 | ||
60.59 | even | 2 | 2520.2.t.k.1009.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.d.169.1 | ✓ | 6 | 4.3 | odd | 2 | ||
840.2.t.d.169.4 | yes | 6 | 20.19 | odd | 2 | ||
1680.2.t.j.1009.1 | 6 | 5.4 | even | 2 | inner | ||
1680.2.t.j.1009.4 | 6 | 1.1 | even | 1 | trivial | ||
2520.2.t.k.1009.5 | 6 | 60.59 | even | 2 | |||
2520.2.t.k.1009.6 | 6 | 12.11 | even | 2 | |||
4200.2.a.bn.1.2 | 3 | 20.7 | even | 4 | |||
4200.2.a.bp.1.2 | 3 | 20.3 | even | 4 | |||
5040.2.t.z.1009.5 | 6 | 15.14 | odd | 2 | |||
5040.2.t.z.1009.6 | 6 | 3.2 | odd | 2 | |||
8400.2.a.di.1.2 | 3 | 5.3 | odd | 4 | |||
8400.2.a.dl.1.2 | 3 | 5.2 | odd | 4 |