Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.a (trivial) |
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: | yes |
Analytic conductor: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 17x^{6} + 37x^{5} + 105x^{4} - 117x^{3} - 238x^{2} + 42x + 90 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.92135\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.03120 | −0.461168 | −0.230584 | − | 0.973052i | \(-0.574064\pi\) | ||||
−0.230584 | + | 0.973052i | \(0.574064\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.85327 | −1.07843 | −0.539217 | − | 0.842167i | \(-0.681280\pi\) | ||||
−0.539217 | + | 0.842167i | \(0.681280\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.03120 | 0.326095 | ||||||||
\(11\) | −4.15019 | −1.25133 | −0.625665 | − | 0.780092i | \(-0.715172\pi\) | ||||
−0.625665 | + | 0.780092i | \(0.715172\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.83799 | 0.787117 | 0.393559 | − | 0.919300i | \(-0.371244\pi\) | ||||
0.393559 | + | 0.919300i | \(0.371244\pi\) | |||||||
\(14\) | 2.85327 | 0.762567 | ||||||||
\(15\) | 1.03120 | 0.266255 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.04690 | −0.469591 | −0.234795 | − | 0.972045i | \(-0.575442\pi\) | ||||
−0.234795 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(20\) | −1.03120 | −0.230584 | ||||||||
\(21\) | 2.85327 | 0.622634 | ||||||||
\(22\) | 4.15019 | 0.884824 | ||||||||
\(23\) | 7.42217 | 1.54763 | 0.773814 | − | 0.633412i | \(-0.218346\pi\) | ||||
0.773814 | + | 0.633412i | \(0.218346\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.93662 | −0.787324 | ||||||||
\(26\) | −2.83799 | −0.556576 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.85327 | −0.539217 | ||||||||
\(29\) | −9.72983 | −1.80678 | −0.903392 | − | 0.428817i | \(-0.858931\pi\) | ||||
−0.903392 | + | 0.428817i | \(0.858931\pi\) | |||||||
\(30\) | −1.03120 | −0.188271 | ||||||||
\(31\) | 8.92011 | 1.60210 | 0.801049 | − | 0.598599i | \(-0.204276\pi\) | ||||
0.801049 | + | 0.598599i | \(0.204276\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.15019 | 0.722456 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 2.94230 | 0.497339 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.78182 | −0.786126 | −0.393063 | − | 0.919511i | \(-0.628585\pi\) | ||||
−0.393063 | + | 0.919511i | \(0.628585\pi\) | |||||||
\(38\) | 2.04690 | 0.332051 | ||||||||
\(39\) | −2.83799 | −0.454442 | ||||||||
\(40\) | 1.03120 | 0.163047 | ||||||||
\(41\) | −1.47977 | −0.231101 | −0.115551 | − | 0.993302i | \(-0.536863\pi\) | ||||
−0.115551 | + | 0.993302i | \(0.536863\pi\) | |||||||
\(42\) | −2.85327 | −0.440269 | ||||||||
\(43\) | 0.900717 | 0.137358 | 0.0686790 | − | 0.997639i | \(-0.478122\pi\) | ||||
0.0686790 | + | 0.997639i | \(0.478122\pi\) | |||||||
\(44\) | −4.15019 | −0.625665 | ||||||||
\(45\) | −1.03120 | −0.153723 | ||||||||
\(46\) | −7.42217 | −1.09434 | ||||||||
\(47\) | −11.7184 | −1.70931 | −0.854655 | − | 0.519196i | \(-0.826231\pi\) | ||||
−0.854655 | + | 0.519196i | \(0.826231\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.14113 | 0.163018 | ||||||||
\(50\) | 3.93662 | 0.556722 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 2.83799 | 0.393559 | ||||||||
\(53\) | −0.396211 | −0.0544238 | −0.0272119 | − | 0.999630i | \(-0.508663\pi\) | ||||
−0.0272119 | + | 0.999630i | \(0.508663\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.27969 | 0.577073 | ||||||||
\(56\) | 2.85327 | 0.381284 | ||||||||
\(57\) | 2.04690 | 0.271118 | ||||||||
\(58\) | 9.72983 | 1.27759 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 1.03120 | 0.133128 | ||||||||
\(61\) | 5.11471 | 0.654872 | 0.327436 | − | 0.944873i | \(-0.393815\pi\) | ||||
0.327436 | + | 0.944873i | \(0.393815\pi\) | |||||||
\(62\) | −8.92011 | −1.13285 | ||||||||
\(63\) | −2.85327 | −0.359478 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.92654 | −0.362993 | ||||||||
\(66\) | −4.15019 | −0.510854 | ||||||||
\(67\) | −11.5926 | −1.41626 | −0.708130 | − | 0.706083i | \(-0.750461\pi\) | ||||
−0.708130 | + | 0.706083i | \(0.750461\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −7.42217 | −0.893524 | ||||||||
\(70\) | −2.94230 | −0.351672 | ||||||||
\(71\) | −15.8105 | −1.87636 | −0.938182 | − | 0.346144i | \(-0.887491\pi\) | ||||
−0.938182 | + | 0.346144i | \(0.887491\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −14.8648 | −1.73979 | −0.869896 | − | 0.493236i | \(-0.835814\pi\) | ||||
−0.869896 | + | 0.493236i | \(0.835814\pi\) | |||||||
\(74\) | 4.78182 | 0.555875 | ||||||||
\(75\) | 3.93662 | 0.454562 | ||||||||
\(76\) | −2.04690 | −0.234795 | ||||||||
\(77\) | 11.8416 | 1.34948 | ||||||||
\(78\) | 2.83799 | 0.321339 | ||||||||
\(79\) | 9.87378 | 1.11089 | 0.555444 | − | 0.831554i | \(-0.312548\pi\) | ||||
0.555444 | + | 0.831554i | \(0.312548\pi\) | |||||||
\(80\) | −1.03120 | −0.115292 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.47977 | 0.163413 | ||||||||
\(83\) | −4.49553 | −0.493449 | −0.246724 | − | 0.969086i | \(-0.579354\pi\) | ||||
−0.246724 | + | 0.969086i | \(0.579354\pi\) | |||||||
\(84\) | 2.85327 | 0.311317 | ||||||||
\(85\) | 1.03120 | 0.111850 | ||||||||
\(86\) | −0.900717 | −0.0971268 | ||||||||
\(87\) | 9.72983 | 1.04315 | ||||||||
\(88\) | 4.15019 | 0.442412 | ||||||||
\(89\) | 10.4285 | 1.10542 | 0.552711 | − | 0.833373i | \(-0.313594\pi\) | ||||
0.552711 | + | 0.833373i | \(0.313594\pi\) | |||||||
\(90\) | 1.03120 | 0.108698 | ||||||||
\(91\) | −8.09755 | −0.848853 | ||||||||
\(92\) | 7.42217 | 0.773814 | ||||||||
\(93\) | −8.92011 | −0.924972 | ||||||||
\(94\) | 11.7184 | 1.20866 | ||||||||
\(95\) | 2.11077 | 0.216560 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 9.26422 | 0.940639 | 0.470319 | − | 0.882496i | \(-0.344139\pi\) | ||||
0.470319 | + | 0.882496i | \(0.344139\pi\) | |||||||
\(98\) | −1.14113 | −0.115271 | ||||||||
\(99\) | −4.15019 | −0.417110 | ||||||||
\(100\) | −3.93662 | −0.393662 | ||||||||
\(101\) | −18.8205 | −1.87271 | −0.936356 | − | 0.351053i | \(-0.885824\pi\) | ||||
−0.936356 | + | 0.351053i | \(0.885824\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −4.20239 | −0.414074 | −0.207037 | − | 0.978333i | \(-0.566382\pi\) | ||||
−0.207037 | + | 0.978333i | \(0.566382\pi\) | |||||||
\(104\) | −2.83799 | −0.278288 | ||||||||
\(105\) | −2.94230 | −0.287139 | ||||||||
\(106\) | 0.396211 | 0.0384834 | ||||||||
\(107\) | 5.99395 | 0.579457 | 0.289728 | − | 0.957109i | \(-0.406435\pi\) | ||||
0.289728 | + | 0.957109i | \(0.406435\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −10.3925 | −0.995417 | −0.497709 | − | 0.867344i | \(-0.665825\pi\) | ||||
−0.497709 | + | 0.867344i | \(0.665825\pi\) | |||||||
\(110\) | −4.27969 | −0.408053 | ||||||||
\(111\) | 4.78182 | 0.453870 | ||||||||
\(112\) | −2.85327 | −0.269608 | ||||||||
\(113\) | 15.8258 | 1.48877 | 0.744384 | − | 0.667752i | \(-0.232743\pi\) | ||||
0.744384 | + | 0.667752i | \(0.232743\pi\) | |||||||
\(114\) | −2.04690 | −0.191710 | ||||||||
\(115\) | −7.65376 | −0.713717 | ||||||||
\(116\) | −9.72983 | −0.903392 | ||||||||
\(117\) | 2.83799 | 0.262372 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | 2.85327 | 0.261558 | ||||||||
\(120\) | −1.03120 | −0.0941355 | ||||||||
\(121\) | 6.22411 | 0.565828 | ||||||||
\(122\) | −5.11471 | −0.463064 | ||||||||
\(123\) | 1.47977 | 0.133426 | ||||||||
\(124\) | 8.92011 | 0.801049 | ||||||||
\(125\) | 9.21547 | 0.824257 | ||||||||
\(126\) | 2.85327 | 0.254189 | ||||||||
\(127\) | −10.4413 | −0.926515 | −0.463257 | − | 0.886224i | \(-0.653319\pi\) | ||||
−0.463257 | + | 0.886224i | \(0.653319\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.900717 | −0.0793037 | ||||||||
\(130\) | 2.92654 | 0.256675 | ||||||||
\(131\) | 13.9696 | 1.22053 | 0.610264 | − | 0.792198i | \(-0.291063\pi\) | ||||
0.610264 | + | 0.792198i | \(0.291063\pi\) | |||||||
\(132\) | 4.15019 | 0.361228 | ||||||||
\(133\) | 5.84035 | 0.506423 | ||||||||
\(134\) | 11.5926 | 1.00145 | ||||||||
\(135\) | 1.03120 | 0.0887518 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −21.2201 | −1.81296 | −0.906479 | − | 0.422250i | \(-0.861240\pi\) | ||||
−0.906479 | + | 0.422250i | \(0.861240\pi\) | |||||||
\(138\) | 7.42217 | 0.631817 | ||||||||
\(139\) | 0.195248 | 0.0165607 | 0.00828037 | − | 0.999966i | \(-0.497364\pi\) | ||||
0.00828037 | + | 0.999966i | \(0.497364\pi\) | |||||||
\(140\) | 2.94230 | 0.248669 | ||||||||
\(141\) | 11.7184 | 0.986871 | ||||||||
\(142\) | 15.8105 | 1.32679 | ||||||||
\(143\) | −11.7782 | −0.984944 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.0334 | 0.833230 | ||||||||
\(146\) | 14.8648 | 1.23022 | ||||||||
\(147\) | −1.14113 | −0.0941186 | ||||||||
\(148\) | −4.78182 | −0.393063 | ||||||||
\(149\) | −14.4831 | −1.18650 | −0.593251 | − | 0.805017i | \(-0.702156\pi\) | ||||
−0.593251 | + | 0.805017i | \(0.702156\pi\) | |||||||
\(150\) | −3.93662 | −0.321424 | ||||||||
\(151\) | 23.7118 | 1.92964 | 0.964821 | − | 0.262908i | \(-0.0846814\pi\) | ||||
0.964821 | + | 0.262908i | \(0.0846814\pi\) | |||||||
\(152\) | 2.04690 | 0.166025 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −11.8416 | −0.954224 | ||||||||
\(155\) | −9.19844 | −0.738836 | ||||||||
\(156\) | −2.83799 | −0.227221 | ||||||||
\(157\) | 2.87240 | 0.229242 | 0.114621 | − | 0.993409i | \(-0.463435\pi\) | ||||
0.114621 | + | 0.993409i | \(0.463435\pi\) | |||||||
\(158\) | −9.87378 | −0.785516 | ||||||||
\(159\) | 0.396211 | 0.0314216 | ||||||||
\(160\) | 1.03120 | 0.0815237 | ||||||||
\(161\) | −21.1774 | −1.66901 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 20.9048 | 1.63739 | 0.818694 | − | 0.574229i | \(-0.194698\pi\) | ||||
0.818694 | + | 0.574229i | \(0.194698\pi\) | |||||||
\(164\) | −1.47977 | −0.115551 | ||||||||
\(165\) | −4.27969 | −0.333174 | ||||||||
\(166\) | 4.49553 | 0.348921 | ||||||||
\(167\) | 11.9527 | 0.924930 | 0.462465 | − | 0.886638i | \(-0.346965\pi\) | ||||
0.462465 | + | 0.886638i | \(0.346965\pi\) | |||||||
\(168\) | −2.85327 | −0.220134 | ||||||||
\(169\) | −4.94580 | −0.380446 | ||||||||
\(170\) | −1.03120 | −0.0790896 | ||||||||
\(171\) | −2.04690 | −0.156530 | ||||||||
\(172\) | 0.900717 | 0.0686790 | ||||||||
\(173\) | 13.3211 | 1.01278 | 0.506392 | − | 0.862303i | \(-0.330979\pi\) | ||||
0.506392 | + | 0.862303i | \(0.330979\pi\) | |||||||
\(174\) | −9.72983 | −0.737616 | ||||||||
\(175\) | 11.2322 | 0.849077 | ||||||||
\(176\) | −4.15019 | −0.312833 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −10.4285 | −0.781651 | ||||||||
\(179\) | 1.96370 | 0.146774 | 0.0733870 | − | 0.997304i | \(-0.476619\pi\) | ||||
0.0733870 | + | 0.997304i | \(0.476619\pi\) | |||||||
\(180\) | −1.03120 | −0.0768613 | ||||||||
\(181\) | 5.25021 | 0.390245 | 0.195122 | − | 0.980779i | \(-0.437490\pi\) | ||||
0.195122 | + | 0.980779i | \(0.437490\pi\) | |||||||
\(182\) | 8.09755 | 0.600230 | ||||||||
\(183\) | −5.11471 | −0.378091 | ||||||||
\(184\) | −7.42217 | −0.547169 | ||||||||
\(185\) | 4.93103 | 0.362536 | ||||||||
\(186\) | 8.92011 | 0.654054 | ||||||||
\(187\) | 4.15019 | 0.303492 | ||||||||
\(188\) | −11.7184 | −0.854655 | ||||||||
\(189\) | 2.85327 | 0.207545 | ||||||||
\(190\) | −2.11077 | −0.153131 | ||||||||
\(191\) | −12.5699 | −0.909529 | −0.454764 | − | 0.890612i | \(-0.650277\pi\) | ||||
−0.454764 | + | 0.890612i | \(0.650277\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 24.5408 | 1.76649 | 0.883243 | − | 0.468916i | \(-0.155355\pi\) | ||||
0.883243 | + | 0.468916i | \(0.155355\pi\) | |||||||
\(194\) | −9.26422 | −0.665132 | ||||||||
\(195\) | 2.92654 | 0.209574 | ||||||||
\(196\) | 1.14113 | 0.0815091 | ||||||||
\(197\) | −21.5354 | −1.53434 | −0.767169 | − | 0.641446i | \(-0.778335\pi\) | ||||
−0.767169 | + | 0.641446i | \(0.778335\pi\) | |||||||
\(198\) | 4.15019 | 0.294941 | ||||||||
\(199\) | 13.3601 | 0.947072 | 0.473536 | − | 0.880774i | \(-0.342977\pi\) | ||||
0.473536 | + | 0.880774i | \(0.342977\pi\) | |||||||
\(200\) | 3.93662 | 0.278361 | ||||||||
\(201\) | 11.5926 | 0.817678 | ||||||||
\(202\) | 18.8205 | 1.32421 | ||||||||
\(203\) | 27.7618 | 1.94849 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 1.52594 | 0.106576 | ||||||||
\(206\) | 4.20239 | 0.292795 | ||||||||
\(207\) | 7.42217 | 0.515876 | ||||||||
\(208\) | 2.83799 | 0.196779 | ||||||||
\(209\) | 8.49503 | 0.587614 | ||||||||
\(210\) | 2.94230 | 0.203038 | ||||||||
\(211\) | −14.2367 | −0.980097 | −0.490049 | − | 0.871695i | \(-0.663021\pi\) | ||||
−0.490049 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(212\) | −0.396211 | −0.0272119 | ||||||||
\(213\) | 15.8105 | 1.08332 | ||||||||
\(214\) | −5.99395 | −0.409738 | ||||||||
\(215\) | −0.928822 | −0.0633451 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −25.4514 | −1.72776 | ||||||||
\(218\) | 10.3925 | 0.703866 | ||||||||
\(219\) | 14.8648 | 1.00447 | ||||||||
\(220\) | 4.27969 | 0.288537 | ||||||||
\(221\) | −2.83799 | −0.190904 | ||||||||
\(222\) | −4.78182 | −0.320935 | ||||||||
\(223\) | 13.2331 | 0.886151 | 0.443075 | − | 0.896484i | \(-0.353887\pi\) | ||||
0.443075 | + | 0.896484i | \(0.353887\pi\) | |||||||
\(224\) | 2.85327 | 0.190642 | ||||||||
\(225\) | −3.93662 | −0.262441 | ||||||||
\(226\) | −15.8258 | −1.05272 | ||||||||
\(227\) | 6.46192 | 0.428893 | 0.214446 | − | 0.976736i | \(-0.431205\pi\) | ||||
0.214446 | + | 0.976736i | \(0.431205\pi\) | |||||||
\(228\) | 2.04690 | 0.135559 | ||||||||
\(229\) | 3.06685 | 0.202663 | 0.101332 | − | 0.994853i | \(-0.467690\pi\) | ||||
0.101332 | + | 0.994853i | \(0.467690\pi\) | |||||||
\(230\) | 7.65376 | 0.504674 | ||||||||
\(231\) | −11.8416 | −0.779121 | ||||||||
\(232\) | 9.72983 | 0.638794 | ||||||||
\(233\) | 8.04281 | 0.526902 | 0.263451 | − | 0.964673i | \(-0.415139\pi\) | ||||
0.263451 | + | 0.964673i | \(0.415139\pi\) | |||||||
\(234\) | −2.83799 | −0.185525 | ||||||||
\(235\) | 12.0841 | 0.788279 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −9.87378 | −0.641371 | ||||||||
\(238\) | −2.85327 | −0.184950 | ||||||||
\(239\) | −16.3115 | −1.05510 | −0.527550 | − | 0.849524i | \(-0.676889\pi\) | ||||
−0.527550 | + | 0.849524i | \(0.676889\pi\) | |||||||
\(240\) | 1.03120 | 0.0665638 | ||||||||
\(241\) | 17.8390 | 1.14911 | 0.574556 | − | 0.818465i | \(-0.305175\pi\) | ||||
0.574556 | + | 0.818465i | \(0.305175\pi\) | |||||||
\(242\) | −6.22411 | −0.400101 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.11471 | 0.327436 | ||||||||
\(245\) | −1.17673 | −0.0751788 | ||||||||
\(246\) | −1.47977 | −0.0943466 | ||||||||
\(247\) | −5.80908 | −0.369623 | ||||||||
\(248\) | −8.92011 | −0.566427 | ||||||||
\(249\) | 4.49553 | 0.284893 | ||||||||
\(250\) | −9.21547 | −0.582837 | ||||||||
\(251\) | −22.1576 | −1.39857 | −0.699286 | − | 0.714842i | \(-0.746499\pi\) | ||||
−0.699286 | + | 0.714842i | \(0.746499\pi\) | |||||||
\(252\) | −2.85327 | −0.179739 | ||||||||
\(253\) | −30.8034 | −1.93660 | ||||||||
\(254\) | 10.4413 | 0.655145 | ||||||||
\(255\) | −1.03120 | −0.0645764 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.50481 | −0.343381 | −0.171690 | − | 0.985151i | \(-0.554923\pi\) | ||||
−0.171690 | + | 0.985151i | \(0.554923\pi\) | |||||||
\(258\) | 0.900717 | 0.0560762 | ||||||||
\(259\) | 13.6438 | 0.847785 | ||||||||
\(260\) | −2.92654 | −0.181497 | ||||||||
\(261\) | −9.72983 | −0.602261 | ||||||||
\(262\) | −13.9696 | −0.863043 | ||||||||
\(263\) | 18.3990 | 1.13453 | 0.567266 | − | 0.823535i | \(-0.308001\pi\) | ||||
0.567266 | + | 0.823535i | \(0.308001\pi\) | |||||||
\(264\) | −4.15019 | −0.255427 | ||||||||
\(265\) | 0.408574 | 0.0250985 | ||||||||
\(266\) | −5.84035 | −0.358095 | ||||||||
\(267\) | −10.4285 | −0.638215 | ||||||||
\(268\) | −11.5926 | −0.708130 | ||||||||
\(269\) | −18.3949 | −1.12156 | −0.560780 | − | 0.827965i | \(-0.689499\pi\) | ||||
−0.560780 | + | 0.827965i | \(0.689499\pi\) | |||||||
\(270\) | −1.03120 | −0.0627570 | ||||||||
\(271\) | 16.0260 | 0.973507 | 0.486754 | − | 0.873539i | \(-0.338181\pi\) | ||||
0.486754 | + | 0.873539i | \(0.338181\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 8.09755 | 0.490086 | ||||||||
\(274\) | 21.2201 | 1.28196 | ||||||||
\(275\) | 16.3377 | 0.985203 | ||||||||
\(276\) | −7.42217 | −0.446762 | ||||||||
\(277\) | −13.7057 | −0.823493 | −0.411747 | − | 0.911298i | \(-0.635081\pi\) | ||||
−0.411747 | + | 0.911298i | \(0.635081\pi\) | |||||||
\(278\) | −0.195248 | −0.0117102 | ||||||||
\(279\) | 8.92011 | 0.534033 | ||||||||
\(280\) | −2.94230 | −0.175836 | ||||||||
\(281\) | −7.42920 | −0.443189 | −0.221594 | − | 0.975139i | \(-0.571126\pi\) | ||||
−0.221594 | + | 0.975139i | \(0.571126\pi\) | |||||||
\(282\) | −11.7184 | −0.697823 | ||||||||
\(283\) | −4.43689 | −0.263746 | −0.131873 | − | 0.991267i | \(-0.542099\pi\) | ||||
−0.131873 | + | 0.991267i | \(0.542099\pi\) | |||||||
\(284\) | −15.8105 | −0.938182 | ||||||||
\(285\) | −2.11077 | −0.125031 | ||||||||
\(286\) | 11.7782 | 0.696461 | ||||||||
\(287\) | 4.22217 | 0.249227 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −10.0334 | −0.589183 | ||||||||
\(291\) | −9.26422 | −0.543078 | ||||||||
\(292\) | −14.8648 | −0.869896 | ||||||||
\(293\) | 27.1947 | 1.58873 | 0.794365 | − | 0.607440i | \(-0.207804\pi\) | ||||
0.794365 | + | 0.607440i | \(0.207804\pi\) | |||||||
\(294\) | 1.14113 | 0.0665519 | ||||||||
\(295\) | −1.03120 | −0.0600389 | ||||||||
\(296\) | 4.78182 | 0.277938 | ||||||||
\(297\) | 4.15019 | 0.240819 | ||||||||
\(298\) | 14.4831 | 0.838984 | ||||||||
\(299\) | 21.0640 | 1.21817 | ||||||||
\(300\) | 3.93662 | 0.227281 | ||||||||
\(301\) | −2.56999 | −0.148131 | ||||||||
\(302\) | −23.7118 | −1.36446 | ||||||||
\(303\) | 18.8205 | 1.08121 | ||||||||
\(304\) | −2.04690 | −0.117398 | ||||||||
\(305\) | −5.27431 | −0.302006 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 8.18518 | 0.467153 | 0.233577 | − | 0.972338i | \(-0.424957\pi\) | ||||
0.233577 | + | 0.972338i | \(0.424957\pi\) | |||||||
\(308\) | 11.8416 | 0.674738 | ||||||||
\(309\) | 4.20239 | 0.239066 | ||||||||
\(310\) | 9.19844 | 0.522436 | ||||||||
\(311\) | 18.1124 | 1.02706 | 0.513530 | − | 0.858072i | \(-0.328338\pi\) | ||||
0.513530 | + | 0.858072i | \(0.328338\pi\) | |||||||
\(312\) | 2.83799 | 0.160670 | ||||||||
\(313\) | −22.5547 | −1.27487 | −0.637434 | − | 0.770505i | \(-0.720004\pi\) | ||||
−0.637434 | + | 0.770505i | \(0.720004\pi\) | |||||||
\(314\) | −2.87240 | −0.162099 | ||||||||
\(315\) | 2.94230 | 0.165780 | ||||||||
\(316\) | 9.87378 | 0.555444 | ||||||||
\(317\) | −13.9298 | −0.782376 | −0.391188 | − | 0.920311i | \(-0.627936\pi\) | ||||
−0.391188 | + | 0.920311i | \(0.627936\pi\) | |||||||
\(318\) | −0.396211 | −0.0222184 | ||||||||
\(319\) | 40.3807 | 2.26088 | ||||||||
\(320\) | −1.03120 | −0.0576460 | ||||||||
\(321\) | −5.99395 | −0.334550 | ||||||||
\(322\) | 21.1774 | 1.18017 | ||||||||
\(323\) | 2.04690 | 0.113893 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −11.1721 | −0.619716 | ||||||||
\(326\) | −20.9048 | −1.15781 | ||||||||
\(327\) | 10.3925 | 0.574705 | ||||||||
\(328\) | 1.47977 | 0.0817066 | ||||||||
\(329\) | 33.4358 | 1.84338 | ||||||||
\(330\) | 4.27969 | 0.235589 | ||||||||
\(331\) | 8.91532 | 0.490030 | 0.245015 | − | 0.969519i | \(-0.421207\pi\) | ||||
0.245015 | + | 0.969519i | \(0.421207\pi\) | |||||||
\(332\) | −4.49553 | −0.246724 | ||||||||
\(333\) | −4.78182 | −0.262042 | ||||||||
\(334\) | −11.9527 | −0.654024 | ||||||||
\(335\) | 11.9543 | 0.653133 | ||||||||
\(336\) | 2.85327 | 0.155658 | ||||||||
\(337\) | 18.5601 | 1.01103 | 0.505517 | − | 0.862817i | \(-0.331302\pi\) | ||||
0.505517 | + | 0.862817i | \(0.331302\pi\) | |||||||
\(338\) | 4.94580 | 0.269016 | ||||||||
\(339\) | −15.8258 | −0.859541 | ||||||||
\(340\) | 1.03120 | 0.0559248 | ||||||||
\(341\) | −37.0202 | −2.00475 | ||||||||
\(342\) | 2.04690 | 0.110684 | ||||||||
\(343\) | 16.7169 | 0.902629 | ||||||||
\(344\) | −0.900717 | −0.0485634 | ||||||||
\(345\) | 7.65376 | 0.412065 | ||||||||
\(346\) | −13.3211 | −0.716147 | ||||||||
\(347\) | 28.3802 | 1.52353 | 0.761764 | − | 0.647855i | \(-0.224334\pi\) | ||||
0.761764 | + | 0.647855i | \(0.224334\pi\) | |||||||
\(348\) | 9.72983 | 0.521573 | ||||||||
\(349\) | −0.411099 | −0.0220056 | −0.0110028 | − | 0.999939i | \(-0.503502\pi\) | ||||
−0.0110028 | + | 0.999939i | \(0.503502\pi\) | |||||||
\(350\) | −11.2322 | −0.600388 | ||||||||
\(351\) | −2.83799 | −0.151481 | ||||||||
\(352\) | 4.15019 | 0.221206 | ||||||||
\(353\) | 11.4830 | 0.611176 | 0.305588 | − | 0.952164i | \(-0.401147\pi\) | ||||
0.305588 | + | 0.952164i | \(0.401147\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 16.3038 | 0.865318 | ||||||||
\(356\) | 10.4285 | 0.552711 | ||||||||
\(357\) | −2.85327 | −0.151011 | ||||||||
\(358\) | −1.96370 | −0.103785 | ||||||||
\(359\) | 6.07107 | 0.320419 | 0.160209 | − | 0.987083i | \(-0.448783\pi\) | ||||
0.160209 | + | 0.987083i | \(0.448783\pi\) | |||||||
\(360\) | 1.03120 | 0.0543492 | ||||||||
\(361\) | −14.8102 | −0.779484 | ||||||||
\(362\) | −5.25021 | −0.275945 | ||||||||
\(363\) | −6.22411 | −0.326681 | ||||||||
\(364\) | −8.09755 | −0.424427 | ||||||||
\(365\) | 15.3286 | 0.802336 | ||||||||
\(366\) | 5.11471 | 0.267350 | ||||||||
\(367\) | 4.70200 | 0.245443 | 0.122721 | − | 0.992441i | \(-0.460838\pi\) | ||||
0.122721 | + | 0.992441i | \(0.460838\pi\) | |||||||
\(368\) | 7.42217 | 0.386907 | ||||||||
\(369\) | −1.47977 | −0.0770337 | ||||||||
\(370\) | −4.93103 | −0.256352 | ||||||||
\(371\) | 1.13050 | 0.0586924 | ||||||||
\(372\) | −8.92011 | −0.462486 | ||||||||
\(373\) | 28.6835 | 1.48517 | 0.742587 | − | 0.669749i | \(-0.233598\pi\) | ||||
0.742587 | + | 0.669749i | \(0.233598\pi\) | |||||||
\(374\) | −4.15019 | −0.214601 | ||||||||
\(375\) | −9.21547 | −0.475885 | ||||||||
\(376\) | 11.7184 | 0.604332 | ||||||||
\(377\) | −27.6132 | −1.42215 | ||||||||
\(378\) | −2.85327 | −0.146756 | ||||||||
\(379\) | −1.44882 | −0.0744207 | −0.0372103 | − | 0.999307i | \(-0.511847\pi\) | ||||
−0.0372103 | + | 0.999307i | \(0.511847\pi\) | |||||||
\(380\) | 2.11077 | 0.108280 | ||||||||
\(381\) | 10.4413 | 0.534923 | ||||||||
\(382\) | 12.5699 | 0.643134 | ||||||||
\(383\) | −24.9862 | −1.27673 | −0.638366 | − | 0.769733i | \(-0.720390\pi\) | ||||
−0.638366 | + | 0.769733i | \(0.720390\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −12.2111 | −0.622335 | ||||||||
\(386\) | −24.5408 | −1.24909 | ||||||||
\(387\) | 0.900717 | 0.0457860 | ||||||||
\(388\) | 9.26422 | 0.470319 | ||||||||
\(389\) | 22.6642 | 1.14912 | 0.574560 | − | 0.818462i | \(-0.305173\pi\) | ||||
0.574560 | + | 0.818462i | \(0.305173\pi\) | |||||||
\(390\) | −2.92654 | −0.148191 | ||||||||
\(391\) | −7.42217 | −0.375355 | ||||||||
\(392\) | −1.14113 | −0.0576356 | ||||||||
\(393\) | −13.9696 | −0.704672 | ||||||||
\(394\) | 21.5354 | 1.08494 | ||||||||
\(395\) | −10.1819 | −0.512306 | ||||||||
\(396\) | −4.15019 | −0.208555 | ||||||||
\(397\) | −30.5327 | −1.53239 | −0.766196 | − | 0.642607i | \(-0.777853\pi\) | ||||
−0.766196 | + | 0.642607i | \(0.777853\pi\) | |||||||
\(398\) | −13.3601 | −0.669681 | ||||||||
\(399\) | −5.84035 | −0.292383 | ||||||||
\(400\) | −3.93662 | −0.196831 | ||||||||
\(401\) | −17.8910 | −0.893433 | −0.446717 | − | 0.894676i | \(-0.647407\pi\) | ||||
−0.446717 | + | 0.894676i | \(0.647407\pi\) | |||||||
\(402\) | −11.5926 | −0.578185 | ||||||||
\(403\) | 25.3152 | 1.26104 | ||||||||
\(404\) | −18.8205 | −0.936356 | ||||||||
\(405\) | −1.03120 | −0.0512409 | ||||||||
\(406\) | −27.7618 | −1.37779 | ||||||||
\(407\) | 19.8455 | 0.983704 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | −15.1451 | −0.748879 | −0.374439 | − | 0.927251i | \(-0.622165\pi\) | ||||
−0.374439 | + | 0.927251i | \(0.622165\pi\) | |||||||
\(410\) | −1.52594 | −0.0753609 | ||||||||
\(411\) | 21.2201 | 1.04671 | ||||||||
\(412\) | −4.20239 | −0.207037 | ||||||||
\(413\) | −2.85327 | −0.140400 | ||||||||
\(414\) | −7.42217 | −0.364780 | ||||||||
\(415\) | 4.63581 | 0.227563 | ||||||||
\(416\) | −2.83799 | −0.139144 | ||||||||
\(417\) | −0.195248 | −0.00956135 | ||||||||
\(418\) | −8.49503 | −0.415506 | ||||||||
\(419\) | −9.60013 | −0.468997 | −0.234499 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234499 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(420\) | −2.94230 | −0.143569 | ||||||||
\(421\) | −19.7712 | −0.963589 | −0.481794 | − | 0.876284i | \(-0.660015\pi\) | ||||
−0.481794 | + | 0.876284i | \(0.660015\pi\) | |||||||
\(422\) | 14.2367 | 0.693033 | ||||||||
\(423\) | −11.7184 | −0.569770 | ||||||||
\(424\) | 0.396211 | 0.0192417 | ||||||||
\(425\) | 3.93662 | 0.190954 | ||||||||
\(426\) | −15.8105 | −0.766022 | ||||||||
\(427\) | −14.5936 | −0.706236 | ||||||||
\(428\) | 5.99395 | 0.289728 | ||||||||
\(429\) | 11.7782 | 0.568658 | ||||||||
\(430\) | 0.928822 | 0.0447918 | ||||||||
\(431\) | −1.01173 | −0.0487334 | −0.0243667 | − | 0.999703i | \(-0.507757\pi\) | ||||
−0.0243667 | + | 0.999703i | \(0.507757\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 6.61470 | 0.317882 | 0.158941 | − | 0.987288i | \(-0.449192\pi\) | ||||
0.158941 | + | 0.987288i | \(0.449192\pi\) | |||||||
\(434\) | 25.4514 | 1.22171 | ||||||||
\(435\) | −10.0334 | −0.481066 | ||||||||
\(436\) | −10.3925 | −0.497709 | ||||||||
\(437\) | −15.1924 | −0.726753 | ||||||||
\(438\) | −14.8648 | −0.710267 | ||||||||
\(439\) | 2.17249 | 0.103687 | 0.0518436 | − | 0.998655i | \(-0.483490\pi\) | ||||
0.0518436 | + | 0.998655i | \(0.483490\pi\) | |||||||
\(440\) | −4.27969 | −0.204026 | ||||||||
\(441\) | 1.14113 | 0.0543394 | ||||||||
\(442\) | 2.83799 | 0.134989 | ||||||||
\(443\) | −16.4903 | −0.783479 | −0.391739 | − | 0.920076i | \(-0.628127\pi\) | ||||
−0.391739 | + | 0.920076i | \(0.628127\pi\) | |||||||
\(444\) | 4.78182 | 0.226935 | ||||||||
\(445\) | −10.7539 | −0.509785 | ||||||||
\(446\) | −13.2331 | −0.626603 | ||||||||
\(447\) | 14.4831 | 0.685027 | ||||||||
\(448\) | −2.85327 | −0.134804 | ||||||||
\(449\) | 33.2089 | 1.56722 | 0.783612 | − | 0.621250i | \(-0.213375\pi\) | ||||
0.783612 | + | 0.621250i | \(0.213375\pi\) | |||||||
\(450\) | 3.93662 | 0.185574 | ||||||||
\(451\) | 6.14133 | 0.289184 | ||||||||
\(452\) | 15.8258 | 0.744384 | ||||||||
\(453\) | −23.7118 | −1.11408 | ||||||||
\(454\) | −6.46192 | −0.303273 | ||||||||
\(455\) | 8.35021 | 0.391464 | ||||||||
\(456\) | −2.04690 | −0.0958549 | ||||||||
\(457\) | −4.22666 | −0.197715 | −0.0988574 | − | 0.995102i | \(-0.531519\pi\) | ||||
−0.0988574 | + | 0.995102i | \(0.531519\pi\) | |||||||
\(458\) | −3.06685 | −0.143305 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −7.65376 | −0.356858 | ||||||||
\(461\) | 30.0219 | 1.39826 | 0.699130 | − | 0.714994i | \(-0.253571\pi\) | ||||
0.699130 | + | 0.714994i | \(0.253571\pi\) | |||||||
\(462\) | 11.8416 | 0.550921 | ||||||||
\(463\) | 11.2614 | 0.523363 | 0.261681 | − | 0.965154i | \(-0.415723\pi\) | ||||
0.261681 | + | 0.965154i | \(0.415723\pi\) | |||||||
\(464\) | −9.72983 | −0.451696 | ||||||||
\(465\) | 9.19844 | 0.426567 | ||||||||
\(466\) | −8.04281 | −0.372576 | ||||||||
\(467\) | 21.2014 | 0.981085 | 0.490542 | − | 0.871417i | \(-0.336799\pi\) | ||||
0.490542 | + | 0.871417i | \(0.336799\pi\) | |||||||
\(468\) | 2.83799 | 0.131186 | ||||||||
\(469\) | 33.0767 | 1.52734 | ||||||||
\(470\) | −12.0841 | −0.557397 | ||||||||
\(471\) | −2.87240 | −0.132353 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −3.73815 | −0.171880 | ||||||||
\(474\) | 9.87378 | 0.453518 | ||||||||
\(475\) | 8.05787 | 0.369720 | ||||||||
\(476\) | 2.85327 | 0.130779 | ||||||||
\(477\) | −0.396211 | −0.0181413 | ||||||||
\(478\) | 16.3115 | 0.746068 | ||||||||
\(479\) | −17.0838 | −0.780579 | −0.390290 | − | 0.920692i | \(-0.627625\pi\) | ||||
−0.390290 | + | 0.920692i | \(0.627625\pi\) | |||||||
\(480\) | −1.03120 | −0.0470677 | ||||||||
\(481\) | −13.5708 | −0.618774 | ||||||||
\(482\) | −17.8390 | −0.812545 | ||||||||
\(483\) | 21.1774 | 0.963606 | ||||||||
\(484\) | 6.22411 | 0.282914 | ||||||||
\(485\) | −9.55329 | −0.433792 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 22.8872 | 1.03712 | 0.518559 | − | 0.855042i | \(-0.326469\pi\) | ||||
0.518559 | + | 0.855042i | \(0.326469\pi\) | |||||||
\(488\) | −5.11471 | −0.231532 | ||||||||
\(489\) | −20.9048 | −0.945347 | ||||||||
\(490\) | 1.17673 | 0.0531594 | ||||||||
\(491\) | −13.2217 | −0.596685 | −0.298343 | − | 0.954459i | \(-0.596434\pi\) | ||||
−0.298343 | + | 0.954459i | \(0.596434\pi\) | |||||||
\(492\) | 1.47977 | 0.0667131 | ||||||||
\(493\) | 9.72983 | 0.438209 | ||||||||
\(494\) | 5.80908 | 0.261363 | ||||||||
\(495\) | 4.27969 | 0.192358 | ||||||||
\(496\) | 8.92011 | 0.400525 | ||||||||
\(497\) | 45.1116 | 2.02353 | ||||||||
\(498\) | −4.49553 | −0.201450 | ||||||||
\(499\) | 17.8300 | 0.798181 | 0.399091 | − | 0.916911i | \(-0.369326\pi\) | ||||
0.399091 | + | 0.916911i | \(0.369326\pi\) | |||||||
\(500\) | 9.21547 | 0.412128 | ||||||||
\(501\) | −11.9527 | −0.534008 | ||||||||
\(502\) | 22.1576 | 0.988940 | ||||||||
\(503\) | 10.5689 | 0.471243 | 0.235621 | − | 0.971845i | \(-0.424288\pi\) | ||||
0.235621 | + | 0.971845i | \(0.424288\pi\) | |||||||
\(504\) | 2.85327 | 0.127095 | ||||||||
\(505\) | 19.4078 | 0.863634 | ||||||||
\(506\) | 30.8034 | 1.36938 | ||||||||
\(507\) | 4.94580 | 0.219651 | ||||||||
\(508\) | −10.4413 | −0.463257 | ||||||||
\(509\) | −35.6227 | −1.57895 | −0.789473 | − | 0.613785i | \(-0.789646\pi\) | ||||
−0.789473 | + | 0.613785i | \(0.789646\pi\) | |||||||
\(510\) | 1.03120 | 0.0456624 | ||||||||
\(511\) | 42.4132 | 1.87625 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.04690 | 0.0903728 | ||||||||
\(514\) | 5.50481 | 0.242807 | ||||||||
\(515\) | 4.33352 | 0.190958 | ||||||||
\(516\) | −0.900717 | −0.0396519 | ||||||||
\(517\) | 48.6338 | 2.13891 | ||||||||
\(518\) | −13.6438 | −0.599474 | ||||||||
\(519\) | −13.3211 | −0.584731 | ||||||||
\(520\) | 2.92654 | 0.128337 | ||||||||
\(521\) | 29.8750 | 1.30885 | 0.654424 | − | 0.756128i | \(-0.272911\pi\) | ||||
0.654424 | + | 0.756128i | \(0.272911\pi\) | |||||||
\(522\) | 9.72983 | 0.425863 | ||||||||
\(523\) | 35.1099 | 1.53525 | 0.767625 | − | 0.640899i | \(-0.221438\pi\) | ||||
0.767625 | + | 0.640899i | \(0.221438\pi\) | |||||||
\(524\) | 13.9696 | 0.610264 | ||||||||
\(525\) | −11.2322 | −0.490215 | ||||||||
\(526\) | −18.3990 | −0.802235 | ||||||||
\(527\) | −8.92011 | −0.388566 | ||||||||
\(528\) | 4.15019 | 0.180614 | ||||||||
\(529\) | 32.0886 | 1.39515 | ||||||||
\(530\) | −0.408574 | −0.0177473 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 5.84035 | 0.253211 | ||||||||
\(533\) | −4.19957 | −0.181904 | ||||||||
\(534\) | 10.4285 | 0.451286 | ||||||||
\(535\) | −6.18098 | −0.267227 | ||||||||
\(536\) | 11.5926 | 0.500723 | ||||||||
\(537\) | −1.96370 | −0.0847400 | ||||||||
\(538\) | 18.3949 | 0.793063 | ||||||||
\(539\) | −4.73590 | −0.203990 | ||||||||
\(540\) | 1.03120 | 0.0443759 | ||||||||
\(541\) | 5.15896 | 0.221801 | 0.110901 | − | 0.993832i | \(-0.464627\pi\) | ||||
0.110901 | + | 0.993832i | \(0.464627\pi\) | |||||||
\(542\) | −16.0260 | −0.688374 | ||||||||
\(543\) | −5.25021 | −0.225308 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 10.7167 | 0.459055 | ||||||||
\(546\) | −8.09755 | −0.346543 | ||||||||
\(547\) | 6.05215 | 0.258771 | 0.129386 | − | 0.991594i | \(-0.458700\pi\) | ||||
0.129386 | + | 0.991594i | \(0.458700\pi\) | |||||||
\(548\) | −21.2201 | −0.906479 | ||||||||
\(549\) | 5.11471 | 0.218291 | ||||||||
\(550\) | −16.3377 | −0.696644 | ||||||||
\(551\) | 19.9160 | 0.848449 | ||||||||
\(552\) | 7.42217 | 0.315908 | ||||||||
\(553\) | −28.1725 | −1.19802 | ||||||||
\(554\) | 13.7057 | 0.582298 | ||||||||
\(555\) | −4.93103 | −0.209310 | ||||||||
\(556\) | 0.195248 | 0.00828037 | ||||||||
\(557\) | −0.641625 | −0.0271865 | −0.0135933 | − | 0.999908i | \(-0.504327\pi\) | ||||
−0.0135933 | + | 0.999908i | \(0.504327\pi\) | |||||||
\(558\) | −8.92011 | −0.377618 | ||||||||
\(559\) | 2.55623 | 0.108117 | ||||||||
\(560\) | 2.94230 | 0.124335 | ||||||||
\(561\) | −4.15019 | −0.175221 | ||||||||
\(562\) | 7.42920 | 0.313382 | ||||||||
\(563\) | 39.4104 | 1.66095 | 0.830476 | − | 0.557055i | \(-0.188069\pi\) | ||||
0.830476 | + | 0.557055i | \(0.188069\pi\) | |||||||
\(564\) | 11.7184 | 0.493435 | ||||||||
\(565\) | −16.3196 | −0.686572 | ||||||||
\(566\) | 4.43689 | 0.186496 | ||||||||
\(567\) | −2.85327 | −0.119826 | ||||||||
\(568\) | 15.8105 | 0.663395 | ||||||||
\(569\) | 34.6319 | 1.45185 | 0.725923 | − | 0.687776i | \(-0.241413\pi\) | ||||
0.725923 | + | 0.687776i | \(0.241413\pi\) | |||||||
\(570\) | 2.11077 | 0.0884104 | ||||||||
\(571\) | 29.4151 | 1.23099 | 0.615493 | − | 0.788143i | \(-0.288957\pi\) | ||||
0.615493 | + | 0.788143i | \(0.288957\pi\) | |||||||
\(572\) | −11.7782 | −0.492472 | ||||||||
\(573\) | 12.5699 | 0.525117 | ||||||||
\(574\) | −4.22217 | −0.176230 | ||||||||
\(575\) | −29.2183 | −1.21849 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.8470 | −0.951133 | −0.475566 | − | 0.879680i | \(-0.657757\pi\) | ||||
−0.475566 | + | 0.879680i | \(0.657757\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −24.5408 | −1.01988 | ||||||||
\(580\) | 10.0334 | 0.416615 | ||||||||
\(581\) | 12.8270 | 0.532152 | ||||||||
\(582\) | 9.26422 | 0.384014 | ||||||||
\(583\) | 1.64435 | 0.0681021 | ||||||||
\(584\) | 14.8648 | 0.615109 | ||||||||
\(585\) | −2.92654 | −0.120998 | ||||||||
\(586\) | −27.1947 | −1.12340 | ||||||||
\(587\) | −3.81976 | −0.157658 | −0.0788292 | − | 0.996888i | \(-0.525118\pi\) | ||||
−0.0788292 | + | 0.996888i | \(0.525118\pi\) | |||||||
\(588\) | −1.14113 | −0.0470593 | ||||||||
\(589\) | −18.2586 | −0.752331 | ||||||||
\(590\) | 1.03120 | 0.0424539 | ||||||||
\(591\) | 21.5354 | 0.885850 | ||||||||
\(592\) | −4.78182 | −0.196532 | ||||||||
\(593\) | −4.48418 | −0.184143 | −0.0920717 | − | 0.995752i | \(-0.529349\pi\) | ||||
−0.0920717 | + | 0.995752i | \(0.529349\pi\) | |||||||
\(594\) | −4.15019 | −0.170285 | ||||||||
\(595\) | −2.94230 | −0.120622 | ||||||||
\(596\) | −14.4831 | −0.593251 | ||||||||
\(597\) | −13.3601 | −0.546792 | ||||||||
\(598\) | −21.0640 | −0.861373 | ||||||||
\(599\) | −21.1277 | −0.863255 | −0.431627 | − | 0.902052i | \(-0.642060\pi\) | ||||
−0.431627 | + | 0.902052i | \(0.642060\pi\) | |||||||
\(600\) | −3.93662 | −0.160712 | ||||||||
\(601\) | −11.3490 | −0.462936 | −0.231468 | − | 0.972843i | \(-0.574353\pi\) | ||||
−0.231468 | + | 0.972843i | \(0.574353\pi\) | |||||||
\(602\) | 2.56999 | 0.104745 | ||||||||
\(603\) | −11.5926 | −0.472086 | ||||||||
\(604\) | 23.7118 | 0.964821 | ||||||||
\(605\) | −6.41832 | −0.260942 | ||||||||
\(606\) | −18.8205 | −0.764531 | ||||||||
\(607\) | 39.5281 | 1.60440 | 0.802198 | − | 0.597059i | \(-0.203664\pi\) | ||||
0.802198 | + | 0.597059i | \(0.203664\pi\) | |||||||
\(608\) | 2.04690 | 0.0830127 | ||||||||
\(609\) | −27.7618 | −1.12496 | ||||||||
\(610\) | 5.27431 | 0.213550 | ||||||||
\(611\) | −33.2568 | −1.34543 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 18.5275 | 0.748317 | 0.374159 | − | 0.927365i | \(-0.377932\pi\) | ||||
0.374159 | + | 0.927365i | \(0.377932\pi\) | |||||||
\(614\) | −8.18518 | −0.330327 | ||||||||
\(615\) | −1.52594 | −0.0615319 | ||||||||
\(616\) | −11.8416 | −0.477112 | ||||||||
\(617\) | −12.8821 | −0.518614 | −0.259307 | − | 0.965795i | \(-0.583494\pi\) | ||||
−0.259307 | + | 0.965795i | \(0.583494\pi\) | |||||||
\(618\) | −4.20239 | −0.169045 | ||||||||
\(619\) | 7.43248 | 0.298737 | 0.149368 | − | 0.988782i | \(-0.452276\pi\) | ||||
0.149368 | + | 0.988782i | \(0.452276\pi\) | |||||||
\(620\) | −9.19844 | −0.369418 | ||||||||
\(621\) | −7.42217 | −0.297841 | ||||||||
\(622\) | −18.1124 | −0.726241 | ||||||||
\(623\) | −29.7553 | −1.19212 | ||||||||
\(624\) | −2.83799 | −0.113611 | ||||||||
\(625\) | 10.1801 | 0.407204 | ||||||||
\(626\) | 22.5547 | 0.901468 | ||||||||
\(627\) | −8.49503 | −0.339259 | ||||||||
\(628\) | 2.87240 | 0.114621 | ||||||||
\(629\) | 4.78182 | 0.190664 | ||||||||
\(630\) | −2.94230 | −0.117224 | ||||||||
\(631\) | 23.5434 | 0.937247 | 0.468624 | − | 0.883398i | \(-0.344750\pi\) | ||||
0.468624 | + | 0.883398i | \(0.344750\pi\) | |||||||
\(632\) | −9.87378 | −0.392758 | ||||||||
\(633\) | 14.2367 | 0.565859 | ||||||||
\(634\) | 13.9298 | 0.553223 | ||||||||
\(635\) | 10.7671 | 0.427279 | ||||||||
\(636\) | 0.396211 | 0.0157108 | ||||||||
\(637\) | 3.23851 | 0.128314 | ||||||||
\(638\) | −40.3807 | −1.59869 | ||||||||
\(639\) | −15.8105 | −0.625454 | ||||||||
\(640\) | 1.03120 | 0.0407619 | ||||||||
\(641\) | −7.93734 | −0.313506 | −0.156753 | − | 0.987638i | \(-0.550103\pi\) | ||||
−0.156753 | + | 0.987638i | \(0.550103\pi\) | |||||||
\(642\) | 5.99395 | 0.236562 | ||||||||
\(643\) | 10.7247 | 0.422941 | 0.211471 | − | 0.977384i | \(-0.432175\pi\) | ||||
0.211471 | + | 0.977384i | \(0.432175\pi\) | |||||||
\(644\) | −21.1774 | −0.834507 | ||||||||
\(645\) | 0.928822 | 0.0365723 | ||||||||
\(646\) | −2.04690 | −0.0805342 | ||||||||
\(647\) | 40.7598 | 1.60243 | 0.801216 | − | 0.598375i | \(-0.204187\pi\) | ||||
0.801216 | + | 0.598375i | \(0.204187\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −4.15019 | −0.162909 | ||||||||
\(650\) | 11.1721 | 0.438206 | ||||||||
\(651\) | 25.4514 | 0.997520 | ||||||||
\(652\) | 20.9048 | 0.818694 | ||||||||
\(653\) | 10.9227 | 0.427439 | 0.213719 | − | 0.976895i | \(-0.431442\pi\) | ||||
0.213719 | + | 0.976895i | \(0.431442\pi\) | |||||||
\(654\) | −10.3925 | −0.406377 | ||||||||
\(655\) | −14.4055 | −0.562868 | ||||||||
\(656\) | −1.47977 | −0.0577753 | ||||||||
\(657\) | −14.8648 | −0.579930 | ||||||||
\(658\) | −33.4358 | −1.30346 | ||||||||
\(659\) | −22.5972 | −0.880261 | −0.440131 | − | 0.897934i | \(-0.645068\pi\) | ||||
−0.440131 | + | 0.897934i | \(0.645068\pi\) | |||||||
\(660\) | −4.27969 | −0.166587 | ||||||||
\(661\) | −1.14472 | −0.0445245 | −0.0222622 | − | 0.999752i | \(-0.507087\pi\) | ||||
−0.0222622 | + | 0.999752i | \(0.507087\pi\) | |||||||
\(662\) | −8.91532 | −0.346504 | ||||||||
\(663\) | 2.83799 | 0.110218 | ||||||||
\(664\) | 4.49553 | 0.174461 | ||||||||
\(665\) | −6.02258 | −0.233546 | ||||||||
\(666\) | 4.78182 | 0.185292 | ||||||||
\(667\) | −72.2164 | −2.79623 | ||||||||
\(668\) | 11.9527 | 0.462465 | ||||||||
\(669\) | −13.2331 | −0.511619 | ||||||||
\(670\) | −11.9543 | −0.461835 | ||||||||
\(671\) | −21.2271 | −0.819461 | ||||||||
\(672\) | −2.85327 | −0.110067 | ||||||||
\(673\) | −12.8522 | −0.495415 | −0.247707 | − | 0.968835i | \(-0.579677\pi\) | ||||
−0.247707 | + | 0.968835i | \(0.579677\pi\) | |||||||
\(674\) | −18.5601 | −0.714908 | ||||||||
\(675\) | 3.93662 | 0.151521 | ||||||||
\(676\) | −4.94580 | −0.190223 | ||||||||
\(677\) | −34.2655 | −1.31693 | −0.658465 | − | 0.752611i | \(-0.728794\pi\) | ||||
−0.658465 | + | 0.752611i | \(0.728794\pi\) | |||||||
\(678\) | 15.8258 | 0.607787 | ||||||||
\(679\) | −26.4333 | −1.01442 | ||||||||
\(680\) | −1.03120 | −0.0395448 | ||||||||
\(681\) | −6.46192 | −0.247621 | ||||||||
\(682\) | 37.0202 | 1.41758 | ||||||||
\(683\) | 2.53827 | 0.0971242 | 0.0485621 | − | 0.998820i | \(-0.484536\pi\) | ||||
0.0485621 | + | 0.998820i | \(0.484536\pi\) | |||||||
\(684\) | −2.04690 | −0.0782652 | ||||||||
\(685\) | 21.8823 | 0.836078 | ||||||||
\(686\) | −16.7169 | −0.638255 | ||||||||
\(687\) | −3.06685 | −0.117008 | ||||||||
\(688\) | 0.900717 | 0.0343395 | ||||||||
\(689\) | −1.12444 | −0.0428379 | ||||||||
\(690\) | −7.65376 | −0.291374 | ||||||||
\(691\) | 38.5062 | 1.46485 | 0.732423 | − | 0.680850i | \(-0.238389\pi\) | ||||
0.732423 | + | 0.680850i | \(0.238389\pi\) | |||||||
\(692\) | 13.3211 | 0.506392 | ||||||||
\(693\) | 11.8416 | 0.449826 | ||||||||
\(694\) | −28.3802 | −1.07730 | ||||||||
\(695\) | −0.201341 | −0.00763728 | ||||||||
\(696\) | −9.72983 | −0.368808 | ||||||||
\(697\) | 1.47977 | 0.0560502 | ||||||||
\(698\) | 0.411099 | 0.0155603 | ||||||||
\(699\) | −8.04281 | −0.304207 | ||||||||
\(700\) | 11.2322 | 0.424538 | ||||||||
\(701\) | 1.11309 | 0.0420409 | 0.0210205 | − | 0.999779i | \(-0.493308\pi\) | ||||
0.0210205 | + | 0.999779i | \(0.493308\pi\) | |||||||
\(702\) | 2.83799 | 0.107113 | ||||||||
\(703\) | 9.78791 | 0.369158 | ||||||||
\(704\) | −4.15019 | −0.156416 | ||||||||
\(705\) | −12.0841 | −0.455113 | ||||||||
\(706\) | −11.4830 | −0.432167 | ||||||||
\(707\) | 53.6999 | 2.01959 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −18.5538 | −0.696802 | −0.348401 | − | 0.937346i | \(-0.613275\pi\) | ||||
−0.348401 | + | 0.937346i | \(0.613275\pi\) | |||||||
\(710\) | −16.3038 | −0.611872 | ||||||||
\(711\) | 9.87378 | 0.370296 | ||||||||
\(712\) | −10.4285 | −0.390825 | ||||||||
\(713\) | 66.2065 | 2.47945 | ||||||||
\(714\) | 2.85327 | 0.106781 | ||||||||
\(715\) | 12.1457 | 0.454224 | ||||||||
\(716\) | 1.96370 | 0.0733870 | ||||||||
\(717\) | 16.3115 | 0.609162 | ||||||||
\(718\) | −6.07107 | −0.226570 | ||||||||
\(719\) | −4.27977 | −0.159609 | −0.0798043 | − | 0.996811i | \(-0.525430\pi\) | ||||
−0.0798043 | + | 0.996811i | \(0.525430\pi\) | |||||||
\(720\) | −1.03120 | −0.0384307 | ||||||||
\(721\) | 11.9905 | 0.446551 | ||||||||
\(722\) | 14.8102 | 0.551179 | ||||||||
\(723\) | −17.8390 | −0.663440 | ||||||||
\(724\) | 5.25021 | 0.195122 | ||||||||
\(725\) | 38.3026 | 1.42252 | ||||||||
\(726\) | 6.22411 | 0.230998 | ||||||||
\(727\) | −5.07131 | −0.188084 | −0.0940422 | − | 0.995568i | \(-0.529979\pi\) | ||||
−0.0940422 | + | 0.995568i | \(0.529979\pi\) | |||||||
\(728\) | 8.09755 | 0.300115 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.3286 | −0.567337 | ||||||||
\(731\) | −0.900717 | −0.0333142 | ||||||||
\(732\) | −5.11471 | −0.189045 | ||||||||
\(733\) | −4.89485 | −0.180795 | −0.0903976 | − | 0.995906i | \(-0.528814\pi\) | ||||
−0.0903976 | + | 0.995906i | \(0.528814\pi\) | |||||||
\(734\) | −4.70200 | −0.173554 | ||||||||
\(735\) | 1.17673 | 0.0434045 | ||||||||
\(736\) | −7.42217 | −0.273585 | ||||||||
\(737\) | 48.1115 | 1.77221 | ||||||||
\(738\) | 1.47977 | 0.0544711 | ||||||||
\(739\) | −38.3700 | −1.41146 | −0.705732 | − | 0.708479i | \(-0.749382\pi\) | ||||
−0.705732 | + | 0.708479i | \(0.749382\pi\) | |||||||
\(740\) | 4.93103 | 0.181268 | ||||||||
\(741\) | 5.80908 | 0.213402 | ||||||||
\(742\) | −1.13050 | −0.0415018 | ||||||||
\(743\) | −9.94179 | −0.364729 | −0.182364 | − | 0.983231i | \(-0.558375\pi\) | ||||
−0.182364 | + | 0.983231i | \(0.558375\pi\) | |||||||
\(744\) | 8.92011 | 0.327027 | ||||||||
\(745\) | 14.9350 | 0.547177 | ||||||||
\(746\) | −28.6835 | −1.05018 | ||||||||
\(747\) | −4.49553 | −0.164483 | ||||||||
\(748\) | 4.15019 | 0.151746 | ||||||||
\(749\) | −17.1023 | −0.624906 | ||||||||
\(750\) | 9.21547 | 0.336501 | ||||||||
\(751\) | 16.4626 | 0.600729 | 0.300365 | − | 0.953824i | \(-0.402892\pi\) | ||||
0.300365 | + | 0.953824i | \(0.402892\pi\) | |||||||
\(752\) | −11.7184 | −0.427328 | ||||||||
\(753\) | 22.1576 | 0.807466 | ||||||||
\(754\) | 27.6132 | 1.00561 | ||||||||
\(755\) | −24.4517 | −0.889889 | ||||||||
\(756\) | 2.85327 | 0.103772 | ||||||||
\(757\) | 2.38610 | 0.0867243 | 0.0433622 | − | 0.999059i | \(-0.486193\pi\) | ||||
0.0433622 | + | 0.999059i | \(0.486193\pi\) | |||||||
\(758\) | 1.44882 | 0.0526234 | ||||||||
\(759\) | 30.8034 | 1.11809 | ||||||||
\(760\) | −2.11077 | −0.0765656 | ||||||||
\(761\) | −16.0025 | −0.580091 | −0.290045 | − | 0.957013i | \(-0.593670\pi\) | ||||
−0.290045 | + | 0.957013i | \(0.593670\pi\) | |||||||
\(762\) | −10.4413 | −0.378248 | ||||||||
\(763\) | 29.6525 | 1.07349 | ||||||||
\(764\) | −12.5699 | −0.454764 | ||||||||
\(765\) | 1.03120 | 0.0372832 | ||||||||
\(766\) | 24.9862 | 0.902786 | ||||||||
\(767\) | 2.83799 | 0.102474 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 26.4893 | 0.955229 | 0.477615 | − | 0.878569i | \(-0.341502\pi\) | ||||
0.477615 | + | 0.878569i | \(0.341502\pi\) | |||||||
\(770\) | 12.2111 | 0.440057 | ||||||||
\(771\) | 5.50481 | 0.198251 | ||||||||
\(772\) | 24.5408 | 0.883243 | ||||||||
\(773\) | 46.4652 | 1.67124 | 0.835618 | − | 0.549311i | \(-0.185110\pi\) | ||||
0.835618 | + | 0.549311i | \(0.185110\pi\) | |||||||
\(774\) | −0.900717 | −0.0323756 | ||||||||
\(775\) | −35.1151 | −1.26137 | ||||||||
\(776\) | −9.26422 | −0.332566 | ||||||||
\(777\) | −13.6438 | −0.489469 | ||||||||
\(778\) | −22.6642 | −0.812551 | ||||||||
\(779\) | 3.02894 | 0.108523 | ||||||||
\(780\) | 2.92654 | 0.104787 | ||||||||
\(781\) | 65.6167 | 2.34795 | ||||||||
\(782\) | 7.42217 | 0.265416 | ||||||||
\(783\) | 9.72983 | 0.347716 | ||||||||
\(784\) | 1.14113 | 0.0407546 | ||||||||
\(785\) | −2.96202 | −0.105719 | ||||||||
\(786\) | 13.9696 | 0.498278 | ||||||||
\(787\) | 10.7835 | 0.384389 | 0.192195 | − | 0.981357i | \(-0.438439\pi\) | ||||
0.192195 | + | 0.981357i | \(0.438439\pi\) | |||||||
\(788\) | −21.5354 | −0.767169 | ||||||||
\(789\) | −18.3990 | −0.655022 | ||||||||
\(790\) | 10.1819 | 0.362255 | ||||||||
\(791\) | −45.1553 | −1.60554 | ||||||||
\(792\) | 4.15019 | 0.147471 | ||||||||
\(793\) | 14.5155 | 0.515461 | ||||||||
\(794\) | 30.5327 | 1.08356 | ||||||||
\(795\) | −0.408574 | −0.0144906 | ||||||||
\(796\) | 13.3601 | 0.473536 | ||||||||
\(797\) | −2.90504 | −0.102902 | −0.0514510 | − | 0.998676i | \(-0.516385\pi\) | ||||
−0.0514510 | + | 0.998676i | \(0.516385\pi\) | |||||||
\(798\) | 5.84035 | 0.206746 | ||||||||
\(799\) | 11.7184 | 0.414569 | ||||||||
\(800\) | 3.93662 | 0.139181 | ||||||||
\(801\) | 10.4285 | 0.368474 | ||||||||
\(802\) | 17.8910 | 0.631753 | ||||||||
\(803\) | 61.6917 | 2.17705 | ||||||||
\(804\) | 11.5926 | 0.408839 | ||||||||
\(805\) | 21.8382 | 0.769696 | ||||||||
\(806\) | −25.3152 | −0.891689 | ||||||||
\(807\) | 18.3949 | 0.647533 | ||||||||
\(808\) | 18.8205 | 0.662103 | ||||||||
\(809\) | 14.3462 | 0.504386 | 0.252193 | − | 0.967677i | \(-0.418848\pi\) | ||||
0.252193 | + | 0.967677i | \(0.418848\pi\) | |||||||
\(810\) | 1.03120 | 0.0362328 | ||||||||
\(811\) | 40.0121 | 1.40501 | 0.702507 | − | 0.711677i | \(-0.252064\pi\) | ||||
0.702507 | + | 0.711677i | \(0.252064\pi\) | |||||||
\(812\) | 27.7618 | 0.974247 | ||||||||
\(813\) | −16.0260 | −0.562055 | ||||||||
\(814\) | −19.8455 | −0.695584 | ||||||||
\(815\) | −21.5571 | −0.755111 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −1.84368 | −0.0645021 | ||||||||
\(818\) | 15.1451 | 0.529537 | ||||||||
\(819\) | −8.09755 | −0.282951 | ||||||||
\(820\) | 1.52594 | 0.0532882 | ||||||||
\(821\) | 2.35122 | 0.0820581 | 0.0410290 | − | 0.999158i | \(-0.486936\pi\) | ||||
0.0410290 | + | 0.999158i | \(0.486936\pi\) | |||||||
\(822\) | −21.2201 | −0.740137 | ||||||||
\(823\) | −8.96315 | −0.312436 | −0.156218 | − | 0.987723i | \(-0.549930\pi\) | ||||
−0.156218 | + | 0.987723i | \(0.549930\pi\) | |||||||
\(824\) | 4.20239 | 0.146397 | ||||||||
\(825\) | −16.3377 | −0.568807 | ||||||||
\(826\) | 2.85327 | 0.0992778 | ||||||||
\(827\) | −31.0802 | −1.08076 | −0.540381 | − | 0.841420i | \(-0.681720\pi\) | ||||
−0.540381 | + | 0.841420i | \(0.681720\pi\) | |||||||
\(828\) | 7.42217 | 0.257938 | ||||||||
\(829\) | −31.2205 | −1.08433 | −0.542167 | − | 0.840271i | \(-0.682396\pi\) | ||||
−0.542167 | + | 0.840271i | \(0.682396\pi\) | |||||||
\(830\) | −4.63581 | −0.160911 | ||||||||
\(831\) | 13.7057 | 0.475444 | ||||||||
\(832\) | 2.83799 | 0.0983897 | ||||||||
\(833\) | −1.14113 | −0.0395377 | ||||||||
\(834\) | 0.195248 | 0.00676090 | ||||||||
\(835\) | −12.3257 | −0.426548 | ||||||||
\(836\) | 8.49503 | 0.293807 | ||||||||
\(837\) | −8.92011 | −0.308324 | ||||||||
\(838\) | 9.60013 | 0.331631 | ||||||||
\(839\) | −52.3257 | −1.80648 | −0.903241 | − | 0.429134i | \(-0.858819\pi\) | ||||
−0.903241 | + | 0.429134i | \(0.858819\pi\) | |||||||
\(840\) | 2.94230 | 0.101519 | ||||||||
\(841\) | 65.6695 | 2.26447 | ||||||||
\(842\) | 19.7712 | 0.681360 | ||||||||
\(843\) | 7.42920 | 0.255875 | ||||||||
\(844\) | −14.2367 | −0.490049 | ||||||||
\(845\) | 5.10013 | 0.175450 | ||||||||
\(846\) | 11.7184 | 0.402888 | ||||||||
\(847\) | −17.7590 | −0.610208 | ||||||||
\(848\) | −0.396211 | −0.0136059 | ||||||||
\(849\) | 4.43689 | 0.152274 | ||||||||
\(850\) | −3.93662 | −0.135025 | ||||||||
\(851\) | −35.4915 | −1.21663 | ||||||||
\(852\) | 15.8105 | 0.541659 | ||||||||
\(853\) | −25.1915 | −0.862542 | −0.431271 | − | 0.902222i | \(-0.641935\pi\) | ||||
−0.431271 | + | 0.902222i | \(0.641935\pi\) | |||||||
\(854\) | 14.5936 | 0.499384 | ||||||||
\(855\) | 2.11077 | 0.0721868 | ||||||||
\(856\) | −5.99395 | −0.204869 | ||||||||
\(857\) | 20.1661 | 0.688862 | 0.344431 | − | 0.938812i | \(-0.388072\pi\) | ||||
0.344431 | + | 0.938812i | \(0.388072\pi\) | |||||||
\(858\) | −11.7782 | −0.402102 | ||||||||
\(859\) | −18.8529 | −0.643254 | −0.321627 | − | 0.946867i | \(-0.604230\pi\) | ||||
−0.321627 | + | 0.946867i | \(0.604230\pi\) | |||||||
\(860\) | −0.928822 | −0.0316726 | ||||||||
\(861\) | −4.22217 | −0.143891 | ||||||||
\(862\) | 1.01173 | 0.0344597 | ||||||||
\(863\) | 15.1503 | 0.515721 | 0.257860 | − | 0.966182i | \(-0.416983\pi\) | ||||
0.257860 | + | 0.966182i | \(0.416983\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −13.7368 | −0.467064 | ||||||||
\(866\) | −6.61470 | −0.224777 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −25.4514 | −0.863878 | ||||||||
\(869\) | −40.9781 | −1.39009 | ||||||||
\(870\) | 10.0334 | 0.340165 | ||||||||
\(871\) | −32.8996 | −1.11476 | ||||||||
\(872\) | 10.3925 | 0.351933 | ||||||||
\(873\) | 9.26422 | 0.313546 | ||||||||
\(874\) | 15.1924 | 0.513892 | ||||||||
\(875\) | −26.2942 | −0.888906 | ||||||||
\(876\) | 14.8648 | 0.502235 | ||||||||
\(877\) | 46.1047 | 1.55684 | 0.778422 | − | 0.627742i | \(-0.216021\pi\) | ||||
0.778422 | + | 0.627742i | \(0.216021\pi\) | |||||||
\(878\) | −2.17249 | −0.0733180 | ||||||||
\(879\) | −27.1947 | −0.917254 | ||||||||
\(880\) | 4.27969 | 0.144268 | ||||||||
\(881\) | −8.00830 | −0.269806 | −0.134903 | − | 0.990859i | \(-0.543072\pi\) | ||||
−0.134903 | + | 0.990859i | \(0.543072\pi\) | |||||||
\(882\) | −1.14113 | −0.0384238 | ||||||||
\(883\) | 46.4484 | 1.56311 | 0.781557 | − | 0.623834i | \(-0.214426\pi\) | ||||
0.781557 | + | 0.623834i | \(0.214426\pi\) | |||||||
\(884\) | −2.83799 | −0.0954520 | ||||||||
\(885\) | 1.03120 | 0.0346635 | ||||||||
\(886\) | 16.4903 | 0.554003 | ||||||||
\(887\) | 11.6316 | 0.390552 | 0.195276 | − | 0.980748i | \(-0.437440\pi\) | ||||
0.195276 | + | 0.980748i | \(0.437440\pi\) | |||||||
\(888\) | −4.78182 | −0.160467 | ||||||||
\(889\) | 29.7918 | 0.999184 | ||||||||
\(890\) | 10.7539 | 0.360472 | ||||||||
\(891\) | −4.15019 | −0.139037 | ||||||||
\(892\) | 13.2331 | 0.443075 | ||||||||
\(893\) | 23.9865 | 0.802677 | ||||||||
\(894\) | −14.4831 | −0.484388 | ||||||||
\(895\) | −2.02497 | −0.0676874 | ||||||||
\(896\) | 2.85327 | 0.0953209 | ||||||||
\(897\) | −21.0640 | −0.703308 | ||||||||
\(898\) | −33.2089 | −1.10820 | ||||||||
\(899\) | −86.7911 | −2.89464 | ||||||||
\(900\) | −3.93662 | −0.131221 | ||||||||
\(901\) | 0.396211 | 0.0131997 | ||||||||
\(902\) | −6.14133 | −0.204484 | ||||||||
\(903\) | 2.56999 | 0.0855238 | ||||||||
\(904\) | −15.8258 | −0.526359 | ||||||||
\(905\) | −5.41403 | −0.179968 | ||||||||
\(906\) | 23.7118 | 0.787773 | ||||||||
\(907\) | 26.1930 | 0.869723 | 0.434862 | − | 0.900497i | \(-0.356797\pi\) | ||||
0.434862 | + | 0.900497i | \(0.356797\pi\) | |||||||
\(908\) | 6.46192 | 0.214446 | ||||||||
\(909\) | −18.8205 | −0.624237 | ||||||||
\(910\) | −8.35021 | −0.276807 | ||||||||
\(911\) | 3.08448 | 0.102194 | 0.0510968 | − | 0.998694i | \(-0.483728\pi\) | ||||
0.0510968 | + | 0.998694i | \(0.483728\pi\) | |||||||
\(912\) | 2.04690 | 0.0677796 | ||||||||
\(913\) | 18.6573 | 0.617468 | ||||||||
\(914\) | 4.22666 | 0.139805 | ||||||||
\(915\) | 5.27431 | 0.174363 | ||||||||
\(916\) | 3.06685 | 0.101332 | ||||||||
\(917\) | −39.8589 | −1.31626 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −54.6821 | −1.80380 | −0.901899 | − | 0.431948i | \(-0.857826\pi\) | ||||
−0.901899 | + | 0.431948i | \(0.857826\pi\) | |||||||
\(920\) | 7.65376 | 0.252337 | ||||||||
\(921\) | −8.18518 | −0.269711 | ||||||||
\(922\) | −30.0219 | −0.988719 | ||||||||
\(923\) | −44.8701 | −1.47692 | ||||||||
\(924\) | −11.8416 | −0.389560 | ||||||||
\(925\) | 18.8242 | 0.618936 | ||||||||
\(926\) | −11.2614 | −0.370073 | ||||||||
\(927\) | −4.20239 | −0.138025 | ||||||||
\(928\) | 9.72983 | 0.319397 | ||||||||
\(929\) | −0.283339 | −0.00929607 | −0.00464803 | − | 0.999989i | \(-0.501480\pi\) | ||||
−0.00464803 | + | 0.999989i | \(0.501480\pi\) | |||||||
\(930\) | −9.19844 | −0.301629 | ||||||||
\(931\) | −2.33577 | −0.0765519 | ||||||||
\(932\) | 8.04281 | 0.263451 | ||||||||
\(933\) | −18.1124 | −0.592973 | ||||||||
\(934\) | −21.2014 | −0.693732 | ||||||||
\(935\) | −4.27969 | −0.139961 | ||||||||
\(936\) | −2.83799 | −0.0927627 | ||||||||
\(937\) | 19.3764 | 0.632998 | 0.316499 | − | 0.948593i | \(-0.397493\pi\) | ||||
0.316499 | + | 0.948593i | \(0.397493\pi\) | |||||||
\(938\) | −33.0767 | −1.07999 | ||||||||
\(939\) | 22.5547 | 0.736046 | ||||||||
\(940\) | 12.0841 | 0.394140 | ||||||||
\(941\) | −32.1218 | −1.04714 | −0.523571 | − | 0.851982i | \(-0.675400\pi\) | ||||
−0.523571 | + | 0.851982i | \(0.675400\pi\) | |||||||
\(942\) | 2.87240 | 0.0935878 | ||||||||
\(943\) | −10.9831 | −0.357659 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | −2.94230 | −0.0957129 | ||||||||
\(946\) | 3.73815 | 0.121538 | ||||||||
\(947\) | −51.6508 | −1.67843 | −0.839213 | − | 0.543803i | \(-0.816984\pi\) | ||||
−0.839213 | + | 0.543803i | \(0.816984\pi\) | |||||||
\(948\) | −9.87378 | −0.320686 | ||||||||
\(949\) | −42.1861 | −1.36942 | ||||||||
\(950\) | −8.05787 | −0.261432 | ||||||||
\(951\) | 13.9298 | 0.451705 | ||||||||
\(952\) | −2.85327 | −0.0924749 | ||||||||
\(953\) | −36.1579 | −1.17127 | −0.585634 | − | 0.810576i | \(-0.699154\pi\) | ||||
−0.585634 | + | 0.810576i | \(0.699154\pi\) | |||||||
\(954\) | 0.396211 | 0.0128278 | ||||||||
\(955\) | 12.9622 | 0.419446 | ||||||||
\(956\) | −16.3115 | −0.527550 | ||||||||
\(957\) | −40.3807 | −1.30532 | ||||||||
\(958\) | 17.0838 | 0.551953 | ||||||||
\(959\) | 60.5467 | 1.95516 | ||||||||
\(960\) | 1.03120 | 0.0332819 | ||||||||
\(961\) | 48.5683 | 1.56672 | ||||||||
\(962\) | 13.5708 | 0.437539 | ||||||||
\(963\) | 5.99395 | 0.193152 | ||||||||
\(964\) | 17.8390 | 0.574556 | ||||||||
\(965\) | −25.3065 | −0.814647 | ||||||||
\(966\) | −21.1774 | −0.681372 | ||||||||
\(967\) | −22.6614 | −0.728742 | −0.364371 | − | 0.931254i | \(-0.618716\pi\) | ||||
−0.364371 | + | 0.931254i | \(0.618716\pi\) | |||||||
\(968\) | −6.22411 | −0.200051 | ||||||||
\(969\) | −2.04690 | −0.0657559 | ||||||||
\(970\) | 9.55329 | 0.306738 | ||||||||
\(971\) | 24.8841 | 0.798568 | 0.399284 | − | 0.916827i | \(-0.369259\pi\) | ||||
0.399284 | + | 0.916827i | \(0.369259\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −0.557095 | −0.0178597 | ||||||||
\(974\) | −22.8872 | −0.733353 | ||||||||
\(975\) | 11.1721 | 0.357793 | ||||||||
\(976\) | 5.11471 | 0.163718 | ||||||||
\(977\) | 7.67116 | 0.245422 | 0.122711 | − | 0.992442i | \(-0.460841\pi\) | ||||
0.122711 | + | 0.992442i | \(0.460841\pi\) | |||||||
\(978\) | 20.9048 | 0.668461 | ||||||||
\(979\) | −43.2804 | −1.38325 | ||||||||
\(980\) | −1.17673 | −0.0375894 | ||||||||
\(981\) | −10.3925 | −0.331806 | ||||||||
\(982\) | 13.2217 | 0.421920 | ||||||||
\(983\) | 36.1355 | 1.15254 | 0.576271 | − | 0.817259i | \(-0.304507\pi\) | ||||
0.576271 | + | 0.817259i | \(0.304507\pi\) | |||||||
\(984\) | −1.47977 | −0.0471733 | ||||||||
\(985\) | 22.2074 | 0.707587 | ||||||||
\(986\) | −9.72983 | −0.309861 | ||||||||
\(987\) | −33.4358 | −1.06427 | ||||||||
\(988\) | −5.80908 | −0.184812 | ||||||||
\(989\) | 6.68527 | 0.212579 | ||||||||
\(990\) | −4.27969 | −0.136018 | ||||||||
\(991\) | 34.1460 | 1.08468 | 0.542342 | − | 0.840158i | \(-0.317538\pi\) | ||||
0.542342 | + | 0.840158i | \(0.317538\pi\) | |||||||
\(992\) | −8.92011 | −0.283214 | ||||||||
\(993\) | −8.91532 | −0.282919 | ||||||||
\(994\) | −45.1116 | −1.43085 | ||||||||
\(995\) | −13.7770 | −0.436759 | ||||||||
\(996\) | 4.49553 | 0.142446 | ||||||||
\(997\) | 16.2682 | 0.515220 | 0.257610 | − | 0.966249i | \(-0.417065\pi\) | ||||
0.257610 | + | 0.966249i | \(0.417065\pi\) | |||||||
\(998\) | −17.8300 | −0.564399 | ||||||||
\(999\) | 4.78182 | 0.151290 |
(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 | 6018.2.a.s.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.s.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial |