Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7569,2,Mod(1,7569)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7569, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7569.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7569 = 3^{2} \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7569.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: | \(60.4387692899\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{9} - 4x^{8} - 6x^{7} + 33x^{6} + 6x^{5} - 90x^{4} + 21x^{3} + 84x^{2} - 36x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 87) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.14438\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7569.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.144378 | −0.102091 | −0.0510453 | − | 0.998696i | \(-0.516255\pi\) | ||||
−0.0510453 | + | 0.998696i | \(0.516255\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.97916 | −0.989578 | ||||||||
\(5\) | −1.55424 | −0.695076 | −0.347538 | − | 0.937666i | \(-0.612982\pi\) | ||||
−0.347538 | + | 0.937666i | \(0.612982\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.52752 | −0.577349 | −0.288674 | − | 0.957427i | \(-0.593214\pi\) | ||||
−0.288674 | + | 0.957427i | \(0.593214\pi\) | |||||||
\(8\) | 0.574502 | 0.203117 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.224397 | 0.0709607 | ||||||||
\(11\) | −0.767834 | −0.231511 | −0.115755 | − | 0.993278i | \(-0.536929\pi\) | ||||
−0.115755 | + | 0.993278i | \(0.536929\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.61812 | −0.726137 | −0.363068 | − | 0.931763i | \(-0.618271\pi\) | ||||
−0.363068 | + | 0.931763i | \(0.618271\pi\) | |||||||
\(14\) | 0.220540 | 0.0589419 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.87536 | 0.968841 | ||||||||
\(17\) | −3.51434 | −0.852353 | −0.426176 | − | 0.904640i | \(-0.640140\pi\) | ||||
−0.426176 | + | 0.904640i | \(0.640140\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.24800 | −1.20397 | −0.601987 | − | 0.798506i | \(-0.705624\pi\) | ||||
−0.601987 | + | 0.798506i | \(0.705624\pi\) | |||||||
\(20\) | 3.07607 | 0.687831 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.110858 | 0.0236351 | ||||||||
\(23\) | −8.49729 | −1.77181 | −0.885904 | − | 0.463869i | \(-0.846461\pi\) | ||||
−0.885904 | + | 0.463869i | \(0.846461\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.58435 | −0.516870 | ||||||||
\(26\) | 0.377999 | 0.0741317 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.02320 | 0.571331 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.41562 | 0.254254 | 0.127127 | − | 0.991886i | \(-0.459424\pi\) | ||||
0.127127 | + | 0.991886i | \(0.459424\pi\) | |||||||
\(32\) | −1.70852 | −0.302027 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.507393 | 0.0870172 | ||||||||
\(35\) | 2.37413 | 0.401301 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00581 | 0.494152 | 0.247076 | − | 0.968996i | \(-0.420530\pi\) | ||||
0.247076 | + | 0.968996i | \(0.420530\pi\) | |||||||
\(38\) | 0.757696 | 0.122915 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.892912 | −0.141182 | ||||||||
\(41\) | 5.79055 | 0.904332 | 0.452166 | − | 0.891934i | \(-0.350651\pi\) | ||||
0.452166 | + | 0.891934i | \(0.350651\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.29616 | −0.655159 | −0.327579 | − | 0.944824i | \(-0.606233\pi\) | ||||
−0.327579 | + | 0.944824i | \(0.606233\pi\) | |||||||
\(44\) | 1.51966 | 0.229098 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.22682 | 0.180885 | ||||||||
\(47\) | 1.77439 | 0.258821 | 0.129411 | − | 0.991591i | \(-0.458691\pi\) | ||||
0.129411 | + | 0.991591i | \(0.458691\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.66668 | −0.666669 | ||||||||
\(50\) | 0.373123 | 0.0527676 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.18167 | 0.718568 | ||||||||
\(53\) | −6.77178 | −0.930175 | −0.465087 | − | 0.885265i | \(-0.653977\pi\) | ||||
−0.465087 | + | 0.885265i | \(0.653977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.19340 | 0.160917 | ||||||||
\(56\) | −0.877564 | −0.117269 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.9605 | −1.94769 | −0.973845 | − | 0.227213i | \(-0.927039\pi\) | ||||
−0.973845 | + | 0.227213i | \(0.927039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.7169 | −1.75627 | −0.878133 | − | 0.478416i | \(-0.841211\pi\) | ||||
−0.878133 | + | 0.478416i | \(0.841211\pi\) | |||||||
\(62\) | −0.204385 | −0.0259569 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.50406 | −0.938007 | ||||||||
\(65\) | 4.06918 | 0.504720 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.29495 | −0.891220 | −0.445610 | − | 0.895227i | \(-0.647013\pi\) | ||||
−0.445610 | + | 0.895227i | \(0.647013\pi\) | |||||||
\(68\) | 6.95542 | 0.843469 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.342772 | −0.0409690 | ||||||||
\(71\) | 4.81074 | 0.570930 | 0.285465 | − | 0.958389i | \(-0.407852\pi\) | ||||
0.285465 | + | 0.958389i | \(0.407852\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.19937 | −1.07670 | −0.538352 | − | 0.842720i | \(-0.680953\pi\) | ||||
−0.538352 | + | 0.842720i | \(0.680953\pi\) | |||||||
\(74\) | −0.433973 | −0.0504483 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.3866 | 1.19143 | ||||||||
\(77\) | 1.17288 | 0.133662 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.545882 | −0.0614165 | −0.0307083 | − | 0.999528i | \(-0.509776\pi\) | ||||
−0.0307083 | + | 0.999528i | \(0.509776\pi\) | |||||||
\(80\) | −6.02323 | −0.673418 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.836028 | −0.0923238 | ||||||||
\(83\) | −11.6477 | −1.27851 | −0.639253 | − | 0.768997i | \(-0.720756\pi\) | ||||
−0.639253 | + | 0.768997i | \(0.720756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.46211 | 0.592449 | ||||||||
\(86\) | 0.620271 | 0.0668856 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.441122 | −0.0470238 | ||||||||
\(89\) | 13.7779 | 1.46046 | 0.730228 | − | 0.683203i | \(-0.239414\pi\) | ||||
0.730228 | + | 0.683203i | \(0.239414\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.99924 | 0.419234 | ||||||||
\(92\) | 16.8175 | 1.75334 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.256183 | −0.0264232 | ||||||||
\(95\) | 8.15664 | 0.836853 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.77624 | 0.180350 | 0.0901751 | − | 0.995926i | \(-0.471257\pi\) | ||||
0.0901751 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(98\) | 0.673766 | 0.0680606 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.11483 | 0.511483 | ||||||||
\(101\) | −4.46601 | −0.444384 | −0.222192 | − | 0.975003i | \(-0.571321\pi\) | ||||
−0.222192 | + | 0.975003i | \(0.571321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3199 | 1.01685 | 0.508424 | − | 0.861107i | \(-0.330228\pi\) | ||||
0.508424 | + | 0.861107i | \(0.330228\pi\) | |||||||
\(104\) | −1.50412 | −0.147491 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.977695 | 0.0949621 | ||||||||
\(107\) | 15.6906 | 1.51687 | 0.758435 | − | 0.651749i | \(-0.225964\pi\) | ||||
0.758435 | + | 0.651749i | \(0.225964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.83683 | −0.942197 | −0.471099 | − | 0.882081i | \(-0.656142\pi\) | ||||
−0.471099 | + | 0.882081i | \(0.656142\pi\) | |||||||
\(110\) | −0.172300 | −0.0164282 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.91970 | −0.559359 | ||||||||
\(113\) | −12.6581 | −1.19078 | −0.595389 | − | 0.803437i | \(-0.703002\pi\) | ||||
−0.595389 | + | 0.803437i | \(0.703002\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.2068 | 1.23154 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.15996 | 0.198841 | ||||||||
\(119\) | 5.36823 | 0.492105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4104 | −0.946403 | ||||||||
\(122\) | 1.98041 | 0.179298 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.80174 | −0.251604 | ||||||||
\(125\) | 11.7879 | 1.05434 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.3386 | −1.71602 | −0.858012 | − | 0.513630i | \(-0.828300\pi\) | ||||
−0.858012 | + | 0.513630i | \(0.828300\pi\) | |||||||
\(128\) | 4.50046 | 0.397788 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.587500 | −0.0515271 | ||||||||
\(131\) | 16.8082 | 1.46854 | 0.734271 | − | 0.678857i | \(-0.237524\pi\) | ||||
0.734271 | + | 0.678857i | \(0.237524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.01644 | 0.695113 | ||||||||
\(134\) | 1.05323 | 0.0909852 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.01900 | −0.173127 | ||||||||
\(137\) | 18.2512 | 1.55930 | 0.779652 | − | 0.626213i | \(-0.215396\pi\) | ||||
0.779652 | + | 0.626213i | \(0.215396\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.86591 | −0.582359 | −0.291180 | − | 0.956668i | \(-0.594048\pi\) | ||||
−0.291180 | + | 0.956668i | \(0.594048\pi\) | |||||||
\(140\) | −4.69877 | −0.397118 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.694565 | −0.0582866 | ||||||||
\(143\) | 2.01028 | 0.168108 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.32819 | 0.109921 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.94897 | −0.489002 | ||||||||
\(149\) | 1.82628 | 0.149615 | 0.0748074 | − | 0.997198i | \(-0.476166\pi\) | ||||
0.0748074 | + | 0.997198i | \(0.476166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.56174 | 0.533987 | 0.266993 | − | 0.963698i | \(-0.413970\pi\) | ||||
0.266993 | + | 0.963698i | \(0.413970\pi\) | |||||||
\(152\) | −3.01499 | −0.244548 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.169338 | −0.0136457 | ||||||||
\(155\) | −2.20021 | −0.176725 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.8825 | −1.66661 | −0.833304 | − | 0.552815i | \(-0.813553\pi\) | ||||
−0.833304 | + | 0.552815i | \(0.813553\pi\) | |||||||
\(158\) | 0.0788133 | 0.00627005 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.65545 | 0.209931 | ||||||||
\(161\) | 12.9798 | 1.02295 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.249811 | 0.0195667 | 0.00978335 | − | 0.999952i | \(-0.496886\pi\) | ||||
0.00978335 | + | 0.999952i | \(0.496886\pi\) | |||||||
\(164\) | −11.4604 | −0.894907 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.68168 | 0.130523 | ||||||||
\(167\) | −13.4150 | −1.03808 | −0.519042 | − | 0.854749i | \(-0.673711\pi\) | ||||
−0.519042 | + | 0.854749i | \(0.673711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.14543 | −0.472726 | ||||||||
\(170\) | −0.788609 | −0.0604835 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.50277 | 0.648330 | ||||||||
\(173\) | 3.51856 | 0.267511 | 0.133755 | − | 0.991014i | \(-0.457296\pi\) | ||||
0.133755 | + | 0.991014i | \(0.457296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.94765 | 0.298414 | ||||||||
\(176\) | −2.97564 | −0.224297 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.98923 | −0.149099 | ||||||||
\(179\) | 2.44064 | 0.182422 | 0.0912109 | − | 0.995832i | \(-0.470926\pi\) | ||||
0.0912109 | + | 0.995832i | \(0.470926\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.647356 | −0.0481176 | −0.0240588 | − | 0.999711i | \(-0.507659\pi\) | ||||
−0.0240588 | + | 0.999711i | \(0.507659\pi\) | |||||||
\(182\) | −0.577401 | −0.0427998 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.88171 | −0.359885 | ||||||||
\(185\) | −4.67174 | −0.343473 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.69843 | 0.197329 | ||||||||
\(188\) | −3.51179 | −0.256124 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.17764 | −0.0854349 | ||||||||
\(191\) | −20.7888 | −1.50422 | −0.752112 | − | 0.659035i | \(-0.770965\pi\) | ||||
−0.752112 | + | 0.659035i | \(0.770965\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.2432 | −1.45714 | −0.728569 | − | 0.684973i | \(-0.759814\pi\) | ||||
−0.728569 | + | 0.684973i | \(0.759814\pi\) | |||||||
\(194\) | −0.256450 | −0.0184121 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.23609 | 0.659720 | ||||||||
\(197\) | −3.44438 | −0.245402 | −0.122701 | − | 0.992444i | \(-0.539156\pi\) | ||||
−0.122701 | + | 0.992444i | \(0.539156\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0270 | 0.852574 | 0.426287 | − | 0.904588i | \(-0.359821\pi\) | ||||
0.426287 | + | 0.904588i | \(0.359821\pi\) | |||||||
\(200\) | −1.48471 | −0.104985 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.644793 | 0.0453675 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.99988 | −0.628579 | ||||||||
\(206\) | −1.48996 | −0.103811 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.1462 | −0.703511 | ||||||||
\(209\) | 4.02960 | 0.278733 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.16064 | −0.286430 | −0.143215 | − | 0.989692i | \(-0.545744\pi\) | ||||
−0.143215 | + | 0.989692i | \(0.545744\pi\) | |||||||
\(212\) | 13.4024 | 0.920480 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.26538 | −0.154858 | ||||||||
\(215\) | 6.67725 | 0.455385 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.16240 | −0.146793 | ||||||||
\(218\) | 1.42022 | 0.0961895 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.36191 | −0.159240 | ||||||||
\(221\) | 9.20097 | 0.618924 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.70372 | −0.314984 | −0.157492 | − | 0.987520i | \(-0.550341\pi\) | ||||
−0.157492 | + | 0.987520i | \(0.550341\pi\) | |||||||
\(224\) | 2.60980 | 0.174375 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.82756 | 0.121567 | ||||||||
\(227\) | 13.6864 | 0.908400 | 0.454200 | − | 0.890900i | \(-0.349925\pi\) | ||||
0.454200 | + | 0.890900i | \(0.349925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1944 | −1.33448 | −0.667241 | − | 0.744842i | \(-0.732525\pi\) | ||||
−0.667241 | + | 0.744842i | \(0.732525\pi\) | |||||||
\(230\) | −1.90677 | −0.125729 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.28500 | 0.477257 | 0.238628 | − | 0.971111i | \(-0.423302\pi\) | ||||
0.238628 | + | 0.971111i | \(0.423302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.75782 | −0.179900 | ||||||||
\(236\) | 29.6091 | 1.92739 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.775053 | −0.0502393 | ||||||||
\(239\) | 23.3694 | 1.51164 | 0.755822 | − | 0.654777i | \(-0.227238\pi\) | ||||
0.755822 | + | 0.654777i | \(0.227238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.4593 | 1.63998 | 0.819989 | − | 0.572379i | \(-0.193980\pi\) | ||||
0.819989 | + | 0.572379i | \(0.193980\pi\) | |||||||
\(242\) | 1.50304 | 0.0966188 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 27.1478 | 1.73796 | ||||||||
\(245\) | 7.25312 | 0.463385 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.7399 | 0.874250 | ||||||||
\(248\) | 0.813279 | 0.0516433 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.70191 | −0.107638 | ||||||||
\(251\) | −13.0548 | −0.824009 | −0.412004 | − | 0.911182i | \(-0.635171\pi\) | ||||
−0.412004 | + | 0.911182i | \(0.635171\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.52451 | 0.410192 | ||||||||
\(254\) | 2.79207 | 0.175190 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.3583 | 0.897397 | ||||||||
\(257\) | −1.37201 | −0.0855836 | −0.0427918 | − | 0.999084i | \(-0.513625\pi\) | ||||
−0.0427918 | + | 0.999084i | \(0.513625\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.59144 | −0.285298 | ||||||||
\(260\) | −8.05354 | −0.499459 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.42674 | −0.149924 | ||||||||
\(263\) | 20.7538 | 1.27973 | 0.639866 | − | 0.768487i | \(-0.278990\pi\) | ||||
0.639866 | + | 0.768487i | \(0.278990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5249 | 0.646542 | ||||||||
\(266\) | −1.15740 | −0.0709645 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.4378 | 0.881931 | ||||||||
\(269\) | 0.958446 | 0.0584375 | 0.0292187 | − | 0.999573i | \(-0.490698\pi\) | ||||
0.0292187 | + | 0.999573i | \(0.490698\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1163 | 1.28272 | 0.641361 | − | 0.767240i | \(-0.278370\pi\) | ||||
0.641361 | + | 0.767240i | \(0.278370\pi\) | |||||||
\(272\) | −13.6193 | −0.825794 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.63507 | −0.159190 | ||||||||
\(275\) | 1.98435 | 0.119661 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4181 | 0.625963 | 0.312982 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312982 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(278\) | 0.991286 | 0.0594534 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.36394 | 0.0815111 | ||||||||
\(281\) | −3.34474 | −0.199530 | −0.0997651 | − | 0.995011i | \(-0.531809\pi\) | ||||
−0.0997651 | + | 0.995011i | \(0.531809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.7748 | −0.937713 | −0.468856 | − | 0.883274i | \(-0.655334\pi\) | ||||
−0.468856 | + | 0.883274i | \(0.655334\pi\) | |||||||
\(284\) | −9.52120 | −0.564979 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.290240 | −0.0171623 | ||||||||
\(287\) | −8.84518 | −0.522115 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.64941 | −0.273495 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18.2070 | 1.06548 | ||||||||
\(293\) | −15.8084 | −0.923538 | −0.461769 | − | 0.887000i | \(-0.652785\pi\) | ||||
−0.461769 | + | 0.887000i | \(0.652785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.2521 | 1.35379 | ||||||||
\(296\) | 1.72685 | 0.100371 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.263675 | −0.0152743 | ||||||||
\(299\) | 22.2470 | 1.28657 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.56248 | 0.378255 | ||||||||
\(302\) | −0.947370 | −0.0545150 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.3379 | −1.16646 | ||||||||
\(305\) | 21.3193 | 1.22074 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.83474 | −0.504225 | −0.252113 | − | 0.967698i | \(-0.581125\pi\) | ||||
−0.252113 | + | 0.967698i | \(0.581125\pi\) | |||||||
\(308\) | −2.32132 | −0.132269 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.317662 | 0.0180420 | ||||||||
\(311\) | −12.9878 | −0.736469 | −0.368235 | − | 0.929733i | \(-0.620038\pi\) | ||||
−0.368235 | + | 0.929733i | \(0.620038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1428 | 1.08201 | 0.541007 | − | 0.841018i | \(-0.318043\pi\) | ||||
0.541007 | + | 0.841018i | \(0.318043\pi\) | |||||||
\(314\) | 3.01498 | 0.170145 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.08039 | 0.0607764 | ||||||||
\(317\) | 26.6435 | 1.49645 | 0.748225 | − | 0.663445i | \(-0.230906\pi\) | ||||
0.748225 | + | 0.663445i | \(0.230906\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 11.6631 | 0.651986 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.87400 | −0.104434 | ||||||||
\(323\) | 18.4433 | 1.02621 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.76615 | 0.375318 | ||||||||
\(326\) | −0.0360672 | −0.00199758 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.32668 | 0.183685 | ||||||||
\(329\) | −2.71042 | −0.149430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.21519 | 0.121758 | 0.0608789 | − | 0.998145i | \(-0.480610\pi\) | ||||
0.0608789 | + | 0.998145i | \(0.480610\pi\) | |||||||
\(332\) | 23.0527 | 1.26518 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.93683 | 0.105979 | ||||||||
\(335\) | 11.3381 | 0.619465 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.01703 | −0.436715 | −0.218358 | − | 0.975869i | \(-0.570070\pi\) | ||||
−0.218358 | + | 0.975869i | \(0.570070\pi\) | |||||||
\(338\) | 0.887265 | 0.0482609 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.8104 | −0.586275 | ||||||||
\(341\) | −1.08696 | −0.0588624 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8211 | 0.962249 | ||||||||
\(344\) | −2.46815 | −0.133074 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.508002 | −0.0273104 | ||||||||
\(347\) | 26.2715 | 1.41033 | 0.705165 | − | 0.709044i | \(-0.250873\pi\) | ||||
0.705165 | + | 0.709044i | \(0.250873\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.86308 | −0.206786 | −0.103393 | − | 0.994641i | \(-0.532970\pi\) | ||||
−0.103393 | + | 0.994641i | \(0.532970\pi\) | |||||||
\(350\) | −0.569953 | −0.0304653 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.31186 | 0.0699224 | ||||||||
\(353\) | −20.0667 | −1.06804 | −0.534021 | − | 0.845471i | \(-0.679320\pi\) | ||||
−0.534021 | + | 0.845471i | \(0.679320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.47703 | −0.396839 | ||||||||
\(356\) | −27.2686 | −1.44524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.352374 | −0.0186236 | ||||||||
\(359\) | −21.2008 | −1.11894 | −0.559468 | − | 0.828852i | \(-0.688994\pi\) | ||||
−0.559468 | + | 0.828852i | \(0.688994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.54155 | 0.449555 | ||||||||
\(362\) | 0.0934640 | 0.00491236 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.91511 | −0.414864 | ||||||||
\(365\) | 14.2980 | 0.748391 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.5920 | 1.02269 | 0.511347 | − | 0.859374i | \(-0.329147\pi\) | ||||
0.511347 | + | 0.859374i | \(0.329147\pi\) | |||||||
\(368\) | −32.9301 | −1.71660 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.674496 | 0.0350654 | ||||||||
\(371\) | 10.3440 | 0.537035 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.197465 | 0.0102244 | 0.00511218 | − | 0.999987i | \(-0.498373\pi\) | ||||
0.00511218 | + | 0.999987i | \(0.498373\pi\) | |||||||
\(374\) | −0.389594 | −0.0201454 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.01939 | 0.0525711 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4911 | 1.15529 | 0.577645 | − | 0.816288i | \(-0.303972\pi\) | ||||
0.577645 | + | 0.816288i | \(0.303972\pi\) | |||||||
\(380\) | −16.1433 | −0.828131 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.00144 | 0.153567 | ||||||||
\(383\) | 0.603334 | 0.0308289 | 0.0154145 | − | 0.999881i | \(-0.495093\pi\) | ||||
0.0154145 | + | 0.999881i | \(0.495093\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.82294 | −0.0929054 | ||||||||
\(386\) | 2.92267 | 0.148760 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.51546 | −0.178471 | ||||||||
\(389\) | −21.8263 | −1.10664 | −0.553318 | − | 0.832970i | \(-0.686638\pi\) | ||||
−0.553318 | + | 0.832970i | \(0.686638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.8624 | 1.51021 | ||||||||
\(392\) | −2.68102 | −0.135412 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.497292 | 0.0250532 | ||||||||
\(395\) | 0.848430 | 0.0426891 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4481 | 0.725132 | 0.362566 | − | 0.931958i | \(-0.381901\pi\) | ||||
0.362566 | + | 0.931958i | \(0.381901\pi\) | |||||||
\(398\) | −1.73644 | −0.0870398 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.0153 | −0.500765 | ||||||||
\(401\) | 26.3790 | 1.31730 | 0.658652 | − | 0.752448i | \(-0.271127\pi\) | ||||
0.658652 | + | 0.752448i | \(0.271127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.70628 | −0.184623 | ||||||||
\(404\) | 8.83892 | 0.439753 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.30796 | −0.114402 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.0838 | 1.53700 | 0.768498 | − | 0.639852i | \(-0.221004\pi\) | ||||
0.768498 | + | 0.639852i | \(0.221004\pi\) | |||||||
\(410\) | 1.29938 | 0.0641720 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.4247 | −1.00625 | ||||||||
\(413\) | 22.8525 | 1.12450 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.1033 | 0.888658 | ||||||||
\(416\) | 4.47312 | 0.219313 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.581785 | −0.0284560 | ||||||||
\(419\) | −20.3478 | −0.994053 | −0.497026 | − | 0.867735i | \(-0.665575\pi\) | ||||
−0.497026 | + | 0.867735i | \(0.665575\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.52568 | 0.415516 | 0.207758 | − | 0.978180i | \(-0.433383\pi\) | ||||
0.207758 | + | 0.978180i | \(0.433383\pi\) | |||||||
\(422\) | 0.600705 | 0.0292419 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.89040 | −0.188934 | ||||||||
\(425\) | 9.08228 | 0.440556 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.9528 | 1.01398 | ||||||||
\(428\) | −31.0542 | −1.50106 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.964048 | −0.0464905 | ||||||||
\(431\) | 4.76237 | 0.229395 | 0.114698 | − | 0.993400i | \(-0.463410\pi\) | ||||
0.114698 | + | 0.993400i | \(0.463410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.22530 | −0.203055 | −0.101527 | − | 0.994833i | \(-0.532373\pi\) | ||||
−0.101527 | + | 0.994833i | \(0.532373\pi\) | |||||||
\(434\) | 0.312202 | 0.0149862 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.4686 | 0.932377 | ||||||||
\(437\) | 44.5938 | 2.13321 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.3895 | 1.30723 | 0.653615 | − | 0.756827i | \(-0.273252\pi\) | ||||
0.653615 | + | 0.756827i | \(0.273252\pi\) | |||||||
\(440\) | 0.685608 | 0.0326851 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.32842 | −0.0631864 | ||||||||
\(443\) | 0.777164 | 0.0369242 | 0.0184621 | − | 0.999830i | \(-0.494123\pi\) | ||||
0.0184621 | + | 0.999830i | \(0.494123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.4141 | −1.01513 | ||||||||
\(446\) | 0.679113 | 0.0321569 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.4626 | 0.541557 | ||||||||
\(449\) | −3.12702 | −0.147573 | −0.0737865 | − | 0.997274i | \(-0.523508\pi\) | ||||
−0.0737865 | + | 0.997274i | \(0.523508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.44618 | −0.209362 | ||||||||
\(452\) | 25.0524 | 1.17837 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.97602 | −0.0927391 | ||||||||
\(455\) | −6.21576 | −0.291399 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.6290 | −1.33921 | −0.669604 | − | 0.742718i | \(-0.733536\pi\) | ||||
−0.669604 | + | 0.742718i | \(0.733536\pi\) | |||||||
\(458\) | 2.91562 | 0.136238 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −26.1383 | −1.21870 | ||||||||
\(461\) | −27.8892 | −1.29893 | −0.649464 | − | 0.760392i | \(-0.725007\pi\) | ||||
−0.649464 | + | 0.760392i | \(0.725007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.3196 | −0.851382 | −0.425691 | − | 0.904869i | \(-0.639969\pi\) | ||||
−0.425691 | + | 0.904869i | \(0.639969\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.05179 | −0.0487234 | ||||||||
\(467\) | −21.8800 | −1.01249 | −0.506243 | − | 0.862391i | \(-0.668966\pi\) | ||||
−0.506243 | + | 0.862391i | \(0.668966\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.1432 | 0.514544 | ||||||||
\(470\) | 0.398168 | 0.0183661 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.59483 | −0.395609 | ||||||||
\(473\) | 3.29874 | 0.151676 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.5627 | 0.622298 | ||||||||
\(476\) | −10.6246 | −0.486976 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.37403 | −0.154325 | ||||||||
\(479\) | 23.4525 | 1.07157 | 0.535786 | − | 0.844354i | \(-0.320015\pi\) | ||||
0.535786 | + | 0.844354i | \(0.320015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.86958 | −0.358822 | ||||||||
\(482\) | −3.67576 | −0.167426 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.6039 | 0.936539 | ||||||||
\(485\) | −2.76070 | −0.125357 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.6248 | −1.61431 | −0.807157 | − | 0.590336i | \(-0.798995\pi\) | ||||
−0.807157 | + | 0.590336i | \(0.798995\pi\) | |||||||
\(488\) | −7.88038 | −0.356728 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.04719 | −0.0473073 | ||||||||
\(491\) | 2.80650 | 0.126656 | 0.0633278 | − | 0.997993i | \(-0.479829\pi\) | ||||
0.0633278 | + | 0.997993i | \(0.479829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.98374 | −0.0892527 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.48606 | 0.246331 | ||||||||
\(497\) | −7.34851 | −0.329626 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.6599 | 1.82019 | 0.910094 | − | 0.414401i | \(-0.136009\pi\) | ||||
0.910094 | + | 0.414401i | \(0.136009\pi\) | |||||||
\(500\) | −23.3300 | −1.04335 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.88482 | 0.0841236 | ||||||||
\(503\) | −18.5373 | −0.826538 | −0.413269 | − | 0.910609i | \(-0.635613\pi\) | ||||
−0.413269 | + | 0.910609i | \(0.635613\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.94123 | 0.308881 | ||||||||
\(506\) | −0.941995 | −0.0418768 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 38.2741 | 1.69814 | ||||||||
\(509\) | 42.5525 | 1.88611 | 0.943054 | − | 0.332640i | \(-0.107939\pi\) | ||||
0.943054 | + | 0.332640i | \(0.107939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0522 | 0.621634 | ||||||||
\(512\) | −11.0740 | −0.489404 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.198088 | 0.00873728 | ||||||||
\(515\) | −16.0395 | −0.706786 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.36244 | −0.0599199 | ||||||||
\(518\) | 0.662902 | 0.0291263 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.33775 | 0.102517 | ||||||||
\(521\) | 27.6372 | 1.21081 | 0.605404 | − | 0.795919i | \(-0.293012\pi\) | ||||
0.605404 | + | 0.795919i | \(0.293012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.3122 | −0.931919 | −0.465959 | − | 0.884806i | \(-0.654291\pi\) | ||||
−0.465959 | + | 0.884806i | \(0.654291\pi\) | |||||||
\(524\) | −33.2661 | −1.45324 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.99638 | −0.130649 | ||||||||
\(527\) | −4.97499 | −0.216714 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.2040 | 2.13930 | ||||||||
\(530\) | −1.51957 | −0.0660058 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.8658 | −0.687868 | ||||||||
\(533\) | −15.1604 | −0.656668 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.3869 | −1.05434 | ||||||||
\(536\) | −4.19096 | −0.181022 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.138378 | −0.00596592 | ||||||||
\(539\) | 3.58324 | 0.154341 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.1075 | −0.950477 | −0.475239 | − | 0.879857i | \(-0.657638\pi\) | ||||
−0.475239 | + | 0.879857i | \(0.657638\pi\) | |||||||
\(542\) | −3.04872 | −0.130954 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.00433 | 0.257433 | ||||||||
\(545\) | 15.2888 | 0.654898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.5033 | 0.705630 | 0.352815 | − | 0.935693i | \(-0.385224\pi\) | ||||
0.352815 | + | 0.935693i | \(0.385224\pi\) | |||||||
\(548\) | −36.1219 | −1.54305 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.286497 | −0.0122163 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.833846 | 0.0354587 | ||||||||
\(554\) | −1.50414 | −0.0639050 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.5887 | 0.576290 | ||||||||
\(557\) | −5.47950 | −0.232174 | −0.116087 | − | 0.993239i | \(-0.537035\pi\) | ||||
−0.116087 | + | 0.993239i | \(0.537035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.2479 | 0.475735 | ||||||||
\(560\) | 9.20061 | 0.388797 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.482906 | 0.0203702 | ||||||||
\(563\) | 13.7797 | 0.580744 | 0.290372 | − | 0.956914i | \(-0.406221\pi\) | ||||
0.290372 | + | 0.956914i | \(0.406221\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.6738 | 0.827681 | ||||||||
\(566\) | 2.27753 | 0.0957317 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.76378 | 0.115966 | ||||||||
\(569\) | 35.9279 | 1.50618 | 0.753088 | − | 0.657920i | \(-0.228564\pi\) | ||||
0.753088 | + | 0.657920i | \(0.228564\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.56420 | −0.274703 | −0.137352 | − | 0.990522i | \(-0.543859\pi\) | ||||
−0.137352 | + | 0.990522i | \(0.543859\pi\) | |||||||
\(572\) | −3.97866 | −0.166356 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.27705 | 0.0533030 | ||||||||
\(575\) | 21.9600 | 0.915794 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.06782 | 0.335868 | 0.167934 | − | 0.985798i | \(-0.446290\pi\) | ||||
0.167934 | + | 0.985798i | \(0.446290\pi\) | |||||||
\(578\) | 0.671273 | 0.0279213 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.7922 | 0.738143 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.19960 | 0.215345 | ||||||||
\(584\) | −5.28506 | −0.218697 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.28239 | 0.0942845 | ||||||||
\(587\) | 8.05202 | 0.332343 | 0.166171 | − | 0.986097i | \(-0.446860\pi\) | ||||
0.166171 | + | 0.986097i | \(0.446860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.42920 | −0.306115 | ||||||||
\(590\) | −3.35710 | −0.138209 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.6486 | 0.478755 | ||||||||
\(593\) | −34.4563 | −1.41495 | −0.707474 | − | 0.706739i | \(-0.750165\pi\) | ||||
−0.707474 | + | 0.706739i | \(0.750165\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.34349 | −0.342050 | ||||||||
\(596\) | −3.61449 | −0.148055 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.21197 | −0.131347 | ||||||||
\(599\) | −31.6740 | −1.29416 | −0.647082 | − | 0.762421i | \(-0.724011\pi\) | ||||
−0.647082 | + | 0.762421i | \(0.724011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.86546 | −0.157675 | −0.0788376 | − | 0.996887i | \(-0.525121\pi\) | ||||
−0.0788376 | + | 0.996887i | \(0.525121\pi\) | |||||||
\(602\) | −0.947477 | −0.0386163 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.9867 | −0.528421 | ||||||||
\(605\) | 16.1803 | 0.657821 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.32954 | −0.0539645 | −0.0269823 | − | 0.999636i | \(-0.508590\pi\) | ||||
−0.0269823 | + | 0.999636i | \(0.508590\pi\) | |||||||
\(608\) | 8.96633 | 0.363633 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.07803 | −0.124626 | ||||||||
\(611\) | −4.64557 | −0.187940 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.02255 | 0.122080 | 0.0610399 | − | 0.998135i | \(-0.480558\pi\) | ||||
0.0610399 | + | 0.998135i | \(0.480558\pi\) | |||||||
\(614\) | 1.27554 | 0.0514767 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.673823 | 0.0271491 | ||||||||
\(617\) | 1.92609 | 0.0775415 | 0.0387708 | − | 0.999248i | \(-0.487656\pi\) | ||||
0.0387708 | + | 0.999248i | \(0.487656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.295624 | −0.0118821 | −0.00594107 | − | 0.999982i | \(-0.501891\pi\) | ||||
−0.00594107 | + | 0.999982i | \(0.501891\pi\) | |||||||
\(620\) | 4.35457 | 0.174884 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.87515 | 0.0751866 | ||||||||
\(623\) | −21.0461 | −0.843192 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.39938 | −0.215975 | ||||||||
\(626\) | −2.76380 | −0.110464 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.3298 | 1.64924 | ||||||||
\(629\) | −10.5634 | −0.421192 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0085 | 1.31405 | 0.657024 | − | 0.753869i | \(-0.271815\pi\) | ||||
0.657024 | + | 0.753869i | \(0.271815\pi\) | |||||||
\(632\) | −0.313610 | −0.0124748 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.84674 | −0.152774 | ||||||||
\(635\) | 30.0568 | 1.19277 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.2179 | 0.484093 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.99478 | −0.276493 | ||||||||
\(641\) | −21.5035 | −0.849336 | −0.424668 | − | 0.905349i | \(-0.639609\pi\) | ||||
−0.424668 | + | 0.905349i | \(0.639609\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.6571 | −0.656891 | −0.328445 | − | 0.944523i | \(-0.606525\pi\) | ||||
−0.328445 | + | 0.944523i | \(0.606525\pi\) | |||||||
\(644\) | −25.6890 | −1.01229 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.66280 | −0.104767 | ||||||||
\(647\) | 0.641821 | 0.0252326 | 0.0126163 | − | 0.999920i | \(-0.495984\pi\) | ||||
0.0126163 | + | 0.999920i | \(0.495984\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.4872 | 0.450911 | ||||||||
\(650\) | −0.976882 | −0.0383165 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.494414 | −0.0193628 | ||||||||
\(653\) | −41.8052 | −1.63596 | −0.817982 | − | 0.575244i | \(-0.804907\pi\) | ||||
−0.817982 | + | 0.575244i | \(0.804907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.1239 | −1.02075 | ||||||||
\(656\) | 22.4405 | 0.876154 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.391324 | 0.0152554 | ||||||||
\(659\) | −6.28494 | −0.244827 | −0.122413 | − | 0.992479i | \(-0.539063\pi\) | ||||
−0.122413 | + | 0.992479i | \(0.539063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.2713 | −0.788461 | −0.394231 | − | 0.919012i | \(-0.628989\pi\) | ||||
−0.394231 | + | 0.919012i | \(0.628989\pi\) | |||||||
\(662\) | −0.319824 | −0.0124303 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.69165 | −0.259686 | ||||||||
\(665\) | −12.4594 | −0.483156 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 26.5504 | 1.02726 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.63697 | −0.0632416 | ||||||||
\(671\) | 10.5323 | 0.406594 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.7317 | −0.837694 | −0.418847 | − | 0.908057i | \(-0.637566\pi\) | ||||
−0.418847 | + | 0.908057i | \(0.637566\pi\) | |||||||
\(674\) | 1.15748 | 0.0445845 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.1628 | 0.467799 | ||||||||
\(677\) | 15.7988 | 0.607197 | 0.303599 | − | 0.952800i | \(-0.401812\pi\) | ||||
0.303599 | + | 0.952800i | \(0.401812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.71325 | −0.104125 | ||||||||
\(680\) | 3.13800 | 0.120337 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.156934 | 0.00600930 | ||||||||
\(683\) | 34.1996 | 1.30861 | 0.654306 | − | 0.756230i | \(-0.272961\pi\) | ||||
0.654306 | + | 0.756230i | \(0.272961\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.3666 | −1.08383 | ||||||||
\(686\) | −2.57297 | −0.0982366 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.6492 | −0.634745 | ||||||||
\(689\) | 17.7293 | 0.675434 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.3566 | −1.30699 | −0.653494 | − | 0.756931i | \(-0.726698\pi\) | ||||
−0.653494 | + | 0.756931i | \(0.726698\pi\) | |||||||
\(692\) | −6.96377 | −0.264723 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.79303 | −0.143981 | ||||||||
\(695\) | 10.6713 | 0.404784 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.3500 | −0.770810 | ||||||||
\(698\) | 0.557743 | 0.0211109 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.81301 | −0.295304 | ||||||||
\(701\) | −1.71987 | −0.0649588 | −0.0324794 | − | 0.999472i | \(-0.510340\pi\) | ||||
−0.0324794 | + | 0.999472i | \(0.510340\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.7745 | −0.594947 | ||||||||
\(704\) | 5.76187 | 0.217159 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.89719 | 0.109037 | ||||||||
\(707\) | 6.82192 | 0.256565 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.0692 | 1.57994 | 0.789970 | − | 0.613145i | \(-0.210096\pi\) | ||||
0.789970 | + | 0.613145i | \(0.210096\pi\) | |||||||
\(710\) | 1.07952 | 0.0405136 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.91545 | 0.296644 | ||||||||
\(713\) | −12.0290 | −0.450489 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.12445 | −0.116848 | ||||||||
\(716\) | −4.83040 | −0.180521 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.06093 | 0.114233 | ||||||||
\(719\) | −2.01196 | −0.0750335 | −0.0375168 | − | 0.999296i | \(-0.511945\pi\) | ||||
−0.0375168 | + | 0.999296i | \(0.511945\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7638 | −0.587076 | ||||||||
\(722\) | −1.23321 | −0.0458954 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.28122 | 0.0476161 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.32560 | −0.271692 | −0.135846 | − | 0.990730i | \(-0.543375\pi\) | ||||
−0.135846 | + | 0.990730i | \(0.543375\pi\) | |||||||
\(728\) | 2.29757 | 0.0851536 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.06431 | −0.0764037 | ||||||||
\(731\) | 15.0982 | 0.558426 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.24481 | −0.193722 | −0.0968608 | − | 0.995298i | \(-0.530880\pi\) | ||||
−0.0968608 | + | 0.995298i | \(0.530880\pi\) | |||||||
\(734\) | −2.82865 | −0.104407 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.5178 | 0.535133 | ||||||||
\(737\) | 5.60131 | 0.206327 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.5744 | −0.867198 | −0.433599 | − | 0.901106i | \(-0.642757\pi\) | ||||
−0.433599 | + | 0.901106i | \(0.642757\pi\) | |||||||
\(740\) | 9.24610 | 0.339893 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.49345 | −0.0548262 | ||||||||
\(743\) | −19.5239 | −0.716263 | −0.358131 | − | 0.933671i | \(-0.616586\pi\) | ||||
−0.358131 | + | 0.933671i | \(0.616586\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.83847 | −0.103994 | ||||||||
\(746\) | −0.0285096 | −0.00104381 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.34061 | −0.195272 | ||||||||
\(749\) | −23.9678 | −0.875763 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.41626 | −0.0516802 | −0.0258401 | − | 0.999666i | \(-0.508226\pi\) | ||||
−0.0258401 | + | 0.999666i | \(0.508226\pi\) | |||||||
\(752\) | 6.87641 | 0.250757 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.1985 | −0.371161 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.3206 | −1.57451 | −0.787257 | − | 0.616625i | \(-0.788500\pi\) | ||||
−0.787257 | + | 0.616625i | \(0.788500\pi\) | |||||||
\(758\) | −3.24722 | −0.117944 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.68601 | 0.169979 | ||||||||
\(761\) | −0.481297 | −0.0174470 | −0.00872351 | − | 0.999962i | \(-0.502777\pi\) | ||||
−0.00872351 | + | 0.999962i | \(0.502777\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.0260 | 0.543976 | ||||||||
\(764\) | 41.1443 | 1.48855 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.0871081 | −0.00314734 | ||||||||
\(767\) | 39.1684 | 1.41429 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.2798 | 0.587065 | 0.293532 | − | 0.955949i | \(-0.405169\pi\) | ||||
0.293532 | + | 0.955949i | \(0.405169\pi\) | |||||||
\(770\) | 0.263192 | 0.00948477 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 40.0644 | 1.44195 | ||||||||
\(773\) | 17.3203 | 0.622968 | 0.311484 | − | 0.950251i | \(-0.399174\pi\) | ||||
0.311484 | + | 0.950251i | \(0.399174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.65847 | −0.131416 | ||||||||
\(776\) | 1.02046 | 0.0366322 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.15123 | 0.112977 | ||||||||
\(779\) | −30.3888 | −1.08879 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.69385 | −0.132176 | ||||||||
\(782\) | −4.31147 | −0.154178 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.0851 | −0.645896 | ||||||||
\(785\) | 32.4564 | 1.15842 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.680377 | 0.0242528 | 0.0121264 | − | 0.999926i | \(-0.496140\pi\) | ||||
0.0121264 | + | 0.999926i | \(0.496140\pi\) | |||||||
\(788\) | 6.81695 | 0.242844 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.122495 | −0.00435816 | ||||||||
\(791\) | 19.3356 | 0.687494 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.9125 | 1.27529 | ||||||||
\(794\) | −2.08599 | −0.0740291 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.8034 | −0.843688 | ||||||||
\(797\) | 44.8530 | 1.58878 | 0.794388 | − | 0.607411i | \(-0.207792\pi\) | ||||
0.794388 | + | 0.607411i | \(0.207792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.23581 | −0.220607 | ||||||||
\(800\) | 4.41542 | 0.156109 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.80854 | −0.134484 | ||||||||
\(803\) | 7.06359 | 0.249269 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.1737 | −0.711028 | ||||||||
\(806\) | 0.535105 | 0.0188483 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.56573 | −0.0902621 | ||||||||
\(809\) | 29.4154 | 1.03419 | 0.517095 | − | 0.855928i | \(-0.327013\pi\) | ||||
0.517095 | + | 0.855928i | \(0.327013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6973 | −0.726781 | −0.363391 | − | 0.931637i | \(-0.618381\pi\) | ||||
−0.363391 | + | 0.931637i | \(0.618381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.333219 | 0.0116793 | ||||||||
\(815\) | −0.388265 | −0.0136003 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.5463 | 0.788795 | ||||||||
\(818\) | −4.48782 | −0.156913 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.8122 | 0.622028 | ||||||||
\(821\) | −27.5661 | −0.962063 | −0.481031 | − | 0.876703i | \(-0.659738\pi\) | ||||
−0.481031 | + | 0.876703i | \(0.659738\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0508 | −0.803499 | −0.401750 | − | 0.915750i | \(-0.631598\pi\) | ||||
−0.401750 | + | 0.915750i | \(0.631598\pi\) | |||||||
\(824\) | 5.92880 | 0.206539 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.29939 | −0.114800 | ||||||||
\(827\) | −44.5689 | −1.54981 | −0.774907 | − | 0.632076i | \(-0.782203\pi\) | ||||
−0.774907 | + | 0.632076i | \(0.782203\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.8796 | −1.55873 | −0.779367 | − | 0.626568i | \(-0.784459\pi\) | ||||
−0.779367 | + | 0.626568i | \(0.784459\pi\) | |||||||
\(830\) | −2.61372 | −0.0907236 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.6465 | 0.681121 | ||||||||
\(833\) | 16.4003 | 0.568237 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.8501 | 0.721546 | ||||||||
\(836\) | −7.97519 | −0.275828 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.93777 | 0.101483 | ||||||||
\(839\) | 13.0101 | 0.449157 | 0.224579 | − | 0.974456i | \(-0.427899\pi\) | ||||
0.224579 | + | 0.974456i | \(0.427899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −1.23092 | −0.0424203 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.23456 | 0.283445 | ||||||||
\(845\) | 9.55146 | 0.328580 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.9021 | 0.546404 | ||||||||
\(848\) | −26.2431 | −0.901192 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.31128 | −0.0449766 | ||||||||
\(851\) | −25.5413 | −0.875543 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.7373 | −0.949706 | −0.474853 | − | 0.880065i | \(-0.657499\pi\) | ||||
−0.474853 | + | 0.880065i | \(0.657499\pi\) | |||||||
\(854\) | −3.02512 | −0.103518 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.01430 | 0.308102 | ||||||||
\(857\) | −18.6936 | −0.638563 | −0.319281 | − | 0.947660i | \(-0.603442\pi\) | ||||
−0.319281 | + | 0.947660i | \(0.603442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.3360 | −0.796214 | −0.398107 | − | 0.917339i | \(-0.630333\pi\) | ||||
−0.398107 | + | 0.917339i | \(0.630333\pi\) | |||||||
\(860\) | −13.2153 | −0.450639 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.687581 | −0.0234191 | ||||||||
\(863\) | 10.7677 | 0.366538 | 0.183269 | − | 0.983063i | \(-0.441332\pi\) | ||||
0.183269 | + | 0.983063i | \(0.441332\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.46867 | −0.185940 | ||||||||
\(866\) | 0.610039 | 0.0207300 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.27972 | 0.145263 | ||||||||
\(869\) | 0.419147 | 0.0142186 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.0991 | 0.647147 | ||||||||
\(872\) | −5.65128 | −0.191376 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.43836 | −0.217781 | ||||||||
\(875\) | −18.0062 | −0.608721 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.6677 | −1.44079 | −0.720393 | − | 0.693567i | \(-0.756038\pi\) | ||||
−0.720393 | + | 0.693567i | \(0.756038\pi\) | |||||||
\(878\) | −3.95444 | −0.133456 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.62484 | 0.155903 | ||||||||
\(881\) | −23.9728 | −0.807664 | −0.403832 | − | 0.914833i | \(-0.632322\pi\) | ||||
−0.403832 | + | 0.914833i | \(0.632322\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.0935 | −1.04638 | −0.523191 | − | 0.852216i | \(-0.675258\pi\) | ||||
−0.523191 | + | 0.852216i | \(0.675258\pi\) | |||||||
\(884\) | −18.2102 | −0.612474 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.112205 | −0.00376961 | ||||||||
\(887\) | 10.1518 | 0.340864 | 0.170432 | − | 0.985369i | \(-0.445484\pi\) | ||||
0.170432 | + | 0.985369i | \(0.445484\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.5401 | 0.990744 | ||||||||
\(890\) | 3.09173 | 0.103635 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.30938 | 0.311701 | ||||||||
\(893\) | −9.31201 | −0.311614 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.79333 | −0.126797 | ||||||||
\(896\) | −6.87455 | −0.229663 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.451472 | 0.0150658 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.7983 | 0.792837 | ||||||||
\(902\) | 0.641930 | 0.0213739 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.27213 | −0.241868 | ||||||||
\(905\) | 1.00614 | 0.0334454 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.1396 | 1.59845 | 0.799225 | − | 0.601033i | \(-0.205244\pi\) | ||||
0.799225 | + | 0.601033i | \(0.205244\pi\) | |||||||
\(908\) | −27.0876 | −0.898932 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.897418 | 0.0297491 | ||||||||
\(911\) | −18.1251 | −0.600510 | −0.300255 | − | 0.953859i | \(-0.597072\pi\) | ||||
−0.300255 | + | 0.953859i | \(0.597072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.94353 | 0.295988 | ||||||||
\(914\) | 4.13340 | 0.136721 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 39.9678 | 1.32057 | ||||||||
\(917\) | −25.6749 | −0.847860 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.8715 | −1.21628 | −0.608139 | − | 0.793830i | \(-0.708084\pi\) | ||||
−0.608139 | + | 0.793830i | \(0.708084\pi\) | |||||||
\(920\) | 7.58733 | 0.250147 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.02658 | 0.132608 | ||||||||
\(923\) | −12.5951 | −0.414573 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.76807 | −0.255413 | ||||||||
\(926\) | 2.64494 | 0.0869181 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.3154 | −0.830571 | −0.415285 | − | 0.909691i | \(-0.636318\pi\) | ||||
−0.415285 | + | 0.909691i | \(0.636318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.4908 | 0.802652 | ||||||||
\(932\) | −14.4182 | −0.472282 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.15899 | 0.103365 | ||||||||
\(935\) | −4.19400 | −0.137158 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.7043 | −1.65644 | −0.828219 | − | 0.560404i | \(-0.810646\pi\) | ||||
−0.828219 | + | 0.560404i | \(0.810646\pi\) | |||||||
\(938\) | −1.60883 | −0.0525301 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.45816 | 0.178025 | ||||||||
\(941\) | −1.77666 | −0.0579175 | −0.0289587 | − | 0.999581i | \(-0.509219\pi\) | ||||
−0.0289587 | + | 0.999581i | \(0.509219\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.2040 | −1.60230 | ||||||||
\(944\) | −57.9774 | −1.88700 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.476265 | −0.0154847 | ||||||||
\(947\) | −13.6503 | −0.443575 | −0.221787 | − | 0.975095i | \(-0.571189\pi\) | ||||
−0.221787 | + | 0.975095i | \(0.571189\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0851 | 0.781835 | ||||||||
\(950\) | −1.95815 | −0.0635308 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.08406 | 0.0999549 | ||||||||
\(953\) | −28.3260 | −0.917571 | −0.458785 | − | 0.888547i | \(-0.651715\pi\) | ||||
−0.458785 | + | 0.888547i | \(0.651715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.3107 | 1.04555 | ||||||||
\(956\) | −46.2517 | −1.49589 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.38602 | −0.109397 | ||||||||
\(959\) | −27.8791 | −0.900262 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9960 | −0.935355 | ||||||||
\(962\) | 1.13619 | 0.0366324 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −50.3879 | −1.62289 | ||||||||
\(965\) | 31.4627 | 1.01282 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.7598 | −0.378169 | −0.189085 | − | 0.981961i | \(-0.560552\pi\) | ||||
−0.189085 | + | 0.981961i | \(0.560552\pi\) | |||||||
\(968\) | −5.98081 | −0.192231 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.398584 | 0.0127978 | ||||||||
\(971\) | −38.2018 | −1.22595 | −0.612976 | − | 0.790101i | \(-0.710028\pi\) | ||||
−0.612976 | + | 0.790101i | \(0.710028\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4878 | 0.336224 | ||||||||
\(974\) | 5.14344 | 0.164806 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −53.1579 | −1.70154 | ||||||||
\(977\) | 32.1135 | 1.02740 | 0.513701 | − | 0.857969i | \(-0.328274\pi\) | ||||
0.513701 | + | 0.857969i | \(0.328274\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5792 | −0.338111 | ||||||||
\(980\) | −14.3551 | −0.458555 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.405197 | −0.0129303 | ||||||||
\(983\) | 45.1079 | 1.43872 | 0.719359 | − | 0.694638i | \(-0.244436\pi\) | ||||
0.719359 | + | 0.694638i | \(0.244436\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.35337 | 0.170573 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.1934 | −0.865138 | ||||||||
\(989\) | 36.5058 | 1.16082 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.12567 | 0.194588 | 0.0972942 | − | 0.995256i | \(-0.468981\pi\) | ||||
0.0972942 | + | 0.995256i | \(0.468981\pi\) | |||||||
\(992\) | −2.41862 | −0.0767914 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.06096 | 0.0336517 | ||||||||
\(995\) | −18.6929 | −0.592603 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.2215 | 1.08381 | 0.541903 | − | 0.840441i | \(-0.317704\pi\) | ||||
0.541903 | + | 0.840441i | \(0.317704\pi\) | |||||||
\(998\) | −5.87040 | −0.185824 | ||||||||
\(999\) | 0 | 0 |
(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 | 7569.2.a.bm.1.4 | 9 | ||
3.2 | odd | 2 | 2523.2.a.o.1.6 | 9 | |||
29.5 | even | 14 | 261.2.k.c.199.2 | 18 | |||
29.6 | even | 14 | 261.2.k.c.181.2 | 18 | |||
29.28 | even | 2 | 7569.2.a.bj.1.6 | 9 | |||
87.5 | odd | 14 | 87.2.g.a.25.2 | yes | 18 | ||
87.35 | odd | 14 | 87.2.g.a.7.2 | ✓ | 18 | ||
87.86 | odd | 2 | 2523.2.a.r.1.4 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.g.a.7.2 | ✓ | 18 | 87.35 | odd | 14 | ||
87.2.g.a.25.2 | yes | 18 | 87.5 | odd | 14 | ||
261.2.k.c.181.2 | 18 | 29.6 | even | 14 | |||
261.2.k.c.199.2 | 18 | 29.5 | even | 14 | |||
2523.2.a.o.1.6 | 9 | 3.2 | odd | 2 | |||
2523.2.a.r.1.4 | 9 | 87.86 | odd | 2 | |||
7569.2.a.bj.1.6 | 9 | 29.28 | even | 2 | |||
7569.2.a.bm.1.4 | 9 | 1.1 | even | 1 | trivial |