Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2523,2,Mod(1,2523)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2523, 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("2523.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2523 = 3 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2523.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: | \(20.1462564300\) |
Analytic rank: | \(1\) |
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 | 1.6 | ||
Root | \(1.14438\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2523.1 |
$q$-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 | \(-0.483745\pi\) | ||||
0.0510453 | + | 0.998696i | \(0.483745\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.97916 | −0.989578 | ||||||||
\(5\) | 1.55424 | 0.695076 | 0.347538 | − | 0.937666i | \(-0.387018\pi\) | ||||
0.347538 | + | 0.937666i | \(0.387018\pi\) | |||||||
\(6\) | −0.144378 | −0.0589420 | ||||||||
\(7\) | −1.52752 | −0.577349 | −0.288674 | − | 0.957427i | \(-0.593214\pi\) | ||||
−0.288674 | + | 0.957427i | \(0.593214\pi\) | |||||||
\(8\) | −0.574502 | −0.203117 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.224397 | 0.0709607 | ||||||||
\(11\) | 0.767834 | 0.231511 | 0.115755 | − | 0.993278i | \(-0.463071\pi\) | ||||
0.115755 | + | 0.993278i | \(0.463071\pi\) | |||||||
\(12\) | 1.97916 | 0.571333 | ||||||||
\(13\) | −2.61812 | −0.726137 | −0.363068 | − | 0.931763i | \(-0.618271\pi\) | ||||
−0.363068 | + | 0.931763i | \(0.618271\pi\) | |||||||
\(14\) | −0.220540 | −0.0589419 | ||||||||
\(15\) | −1.55424 | −0.401302 | ||||||||
\(16\) | 3.87536 | 0.968841 | ||||||||
\(17\) | 3.51434 | 0.852353 | 0.426176 | − | 0.904640i | \(-0.359860\pi\) | ||||
0.426176 | + | 0.904640i | \(0.359860\pi\) | |||||||
\(18\) | 0.144378 | 0.0340302 | ||||||||
\(19\) | −5.24800 | −1.20397 | −0.601987 | − | 0.798506i | \(-0.705624\pi\) | ||||
−0.601987 | + | 0.798506i | \(0.705624\pi\) | |||||||
\(20\) | −3.07607 | −0.687831 | ||||||||
\(21\) | 1.52752 | 0.333332 | ||||||||
\(22\) | 0.110858 | 0.0236351 | ||||||||
\(23\) | 8.49729 | 1.77181 | 0.885904 | − | 0.463869i | \(-0.153539\pi\) | ||||
0.885904 | + | 0.463869i | \(0.153539\pi\) | |||||||
\(24\) | 0.574502 | 0.117270 | ||||||||
\(25\) | −2.58435 | −0.516870 | ||||||||
\(26\) | −0.377999 | −0.0741317 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.02320 | 0.571331 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | −0.224397 | −0.0409692 | ||||||||
\(31\) | 1.41562 | 0.254254 | 0.127127 | − | 0.991886i | \(-0.459424\pi\) | ||||
0.127127 | + | 0.991886i | \(0.459424\pi\) | |||||||
\(32\) | 1.70852 | 0.302027 | ||||||||
\(33\) | −0.767834 | −0.133663 | ||||||||
\(34\) | 0.507393 | 0.0870172 | ||||||||
\(35\) | −2.37413 | −0.401301 | ||||||||
\(36\) | −1.97916 | −0.329859 | ||||||||
\(37\) | 3.00581 | 0.494152 | 0.247076 | − | 0.968996i | \(-0.420530\pi\) | ||||
0.247076 | + | 0.968996i | \(0.420530\pi\) | |||||||
\(38\) | −0.757696 | −0.122915 | ||||||||
\(39\) | 2.61812 | 0.419235 | ||||||||
\(40\) | −0.892912 | −0.141182 | ||||||||
\(41\) | −5.79055 | −0.904332 | −0.452166 | − | 0.891934i | \(-0.649349\pi\) | ||||
−0.452166 | + | 0.891934i | \(0.649349\pi\) | |||||||
\(42\) | 0.220540 | 0.0340301 | ||||||||
\(43\) | −4.29616 | −0.655159 | −0.327579 | − | 0.944824i | \(-0.606233\pi\) | ||||
−0.327579 | + | 0.944824i | \(0.606233\pi\) | |||||||
\(44\) | −1.51966 | −0.229098 | ||||||||
\(45\) | 1.55424 | 0.231692 | ||||||||
\(46\) | 1.22682 | 0.180885 | ||||||||
\(47\) | −1.77439 | −0.258821 | −0.129411 | − | 0.991591i | \(-0.541309\pi\) | ||||
−0.129411 | + | 0.991591i | \(0.541309\pi\) | |||||||
\(48\) | −3.87536 | −0.559361 | ||||||||
\(49\) | −4.66668 | −0.666669 | ||||||||
\(50\) | −0.373123 | −0.0527676 | ||||||||
\(51\) | −3.51434 | −0.492106 | ||||||||
\(52\) | 5.18167 | 0.718568 | ||||||||
\(53\) | 6.77178 | 0.930175 | 0.465087 | − | 0.885265i | \(-0.346023\pi\) | ||||
0.465087 | + | 0.885265i | \(0.346023\pi\) | |||||||
\(54\) | −0.144378 | −0.0196473 | ||||||||
\(55\) | 1.19340 | 0.160917 | ||||||||
\(56\) | 0.877564 | 0.117269 | ||||||||
\(57\) | 5.24800 | 0.695115 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.9605 | 1.94769 | 0.973845 | − | 0.227213i | \(-0.0729614\pi\) | ||||
0.973845 | + | 0.227213i | \(0.0729614\pi\) | |||||||
\(60\) | 3.07607 | 0.397119 | ||||||||
\(61\) | −13.7169 | −1.75627 | −0.878133 | − | 0.478416i | \(-0.841211\pi\) | ||||
−0.878133 | + | 0.478416i | \(0.841211\pi\) | |||||||
\(62\) | 0.204385 | 0.0259569 | ||||||||
\(63\) | −1.52752 | −0.192450 | ||||||||
\(64\) | −7.50406 | −0.938007 | ||||||||
\(65\) | −4.06918 | −0.504720 | ||||||||
\(66\) | −0.110858 | −0.0136457 | ||||||||
\(67\) | −7.29495 | −0.891220 | −0.445610 | − | 0.895227i | \(-0.647013\pi\) | ||||
−0.445610 | + | 0.895227i | \(0.647013\pi\) | |||||||
\(68\) | −6.95542 | −0.843469 | ||||||||
\(69\) | −8.49729 | −1.02295 | ||||||||
\(70\) | −0.342772 | −0.0409690 | ||||||||
\(71\) | −4.81074 | −0.570930 | −0.285465 | − | 0.958389i | \(-0.592148\pi\) | ||||
−0.285465 | + | 0.958389i | \(0.592148\pi\) | |||||||
\(72\) | −0.574502 | −0.0677057 | ||||||||
\(73\) | −9.19937 | −1.07670 | −0.538352 | − | 0.842720i | \(-0.680953\pi\) | ||||
−0.538352 | + | 0.842720i | \(0.680953\pi\) | |||||||
\(74\) | 0.433973 | 0.0504483 | ||||||||
\(75\) | 2.58435 | 0.298415 | ||||||||
\(76\) | 10.3866 | 1.19143 | ||||||||
\(77\) | −1.17288 | −0.133662 | ||||||||
\(78\) | 0.377999 | 0.0428000 | ||||||||
\(79\) | −0.545882 | −0.0614165 | −0.0307083 | − | 0.999528i | \(-0.509776\pi\) | ||||
−0.0307083 | + | 0.999528i | \(0.509776\pi\) | |||||||
\(80\) | 6.02323 | 0.673418 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.836028 | −0.0923238 | ||||||||
\(83\) | 11.6477 | 1.27851 | 0.639253 | − | 0.768997i | \(-0.279244\pi\) | ||||
0.639253 | + | 0.768997i | \(0.279244\pi\) | |||||||
\(84\) | −3.02320 | −0.329858 | ||||||||
\(85\) | 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 | \(-0.760586\pi\) | ||||
−0.730228 | + | 0.683203i | \(0.760586\pi\) | |||||||
\(90\) | 0.224397 | 0.0236536 | ||||||||
\(91\) | 3.99924 | 0.419234 | ||||||||
\(92\) | −16.8175 | −1.75334 | ||||||||
\(93\) | −1.41562 | −0.146793 | ||||||||
\(94\) | −0.256183 | −0.0264232 | ||||||||
\(95\) | −8.15664 | −0.836853 | ||||||||
\(96\) | −1.70852 | −0.174375 | ||||||||
\(97\) | 1.77624 | 0.180350 | 0.0901751 | − | 0.995926i | \(-0.471257\pi\) | ||||
0.0901751 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(98\) | −0.673766 | −0.0680606 | ||||||||
\(99\) | 0.767834 | 0.0771702 | ||||||||
\(100\) | 5.11483 | 0.511483 | ||||||||
\(101\) | 4.46601 | 0.444384 | 0.222192 | − | 0.975003i | \(-0.428679\pi\) | ||||
0.222192 | + | 0.975003i | \(0.428679\pi\) | |||||||
\(102\) | −0.507393 | −0.0502394 | ||||||||
\(103\) | 10.3199 | 1.01685 | 0.508424 | − | 0.861107i | \(-0.330228\pi\) | ||||
0.508424 | + | 0.861107i | \(0.330228\pi\) | |||||||
\(104\) | 1.50412 | 0.147491 | ||||||||
\(105\) | 2.37413 | 0.231691 | ||||||||
\(106\) | 0.977695 | 0.0949621 | ||||||||
\(107\) | −15.6906 | −1.51687 | −0.758435 | − | 0.651749i | \(-0.774036\pi\) | ||||
−0.758435 | + | 0.651749i | \(0.774036\pi\) | |||||||
\(108\) | 1.97916 | 0.190444 | ||||||||
\(109\) | −9.83683 | −0.942197 | −0.471099 | − | 0.882081i | \(-0.656142\pi\) | ||||
−0.471099 | + | 0.882081i | \(0.656142\pi\) | |||||||
\(110\) | 0.172300 | 0.0164282 | ||||||||
\(111\) | −3.00581 | −0.285299 | ||||||||
\(112\) | −5.91970 | −0.559359 | ||||||||
\(113\) | 12.6581 | 1.19078 | 0.595389 | − | 0.803437i | \(-0.296998\pi\) | ||||
0.595389 | + | 0.803437i | \(0.296998\pi\) | |||||||
\(114\) | 0.757696 | 0.0709647 | ||||||||
\(115\) | 13.2068 | 1.23154 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.61812 | −0.242046 | ||||||||
\(118\) | 2.15996 | 0.198841 | ||||||||
\(119\) | −5.36823 | −0.492105 | ||||||||
\(120\) | 0.892912 | 0.0815113 | ||||||||
\(121\) | −10.4104 | −0.946403 | ||||||||
\(122\) | −1.98041 | −0.179298 | ||||||||
\(123\) | 5.79055 | 0.522116 | ||||||||
\(124\) | −2.80174 | −0.251604 | ||||||||
\(125\) | −11.7879 | −1.05434 | ||||||||
\(126\) | −0.220540 | −0.0196473 | ||||||||
\(127\) | −19.3386 | −1.71602 | −0.858012 | − | 0.513630i | \(-0.828300\pi\) | ||||
−0.858012 | + | 0.513630i | \(0.828300\pi\) | |||||||
\(128\) | −4.50046 | −0.397788 | ||||||||
\(129\) | 4.29616 | 0.378256 | ||||||||
\(130\) | −0.587500 | −0.0515271 | ||||||||
\(131\) | −16.8082 | −1.46854 | −0.734271 | − | 0.678857i | \(-0.762476\pi\) | ||||
−0.734271 | + | 0.678857i | \(0.762476\pi\) | |||||||
\(132\) | 1.51966 | 0.132270 | ||||||||
\(133\) | 8.01644 | 0.695113 | ||||||||
\(134\) | −1.05323 | −0.0909852 | ||||||||
\(135\) | −1.55424 | −0.133767 | ||||||||
\(136\) | −2.01900 | −0.173127 | ||||||||
\(137\) | −18.2512 | −1.55930 | −0.779652 | − | 0.626213i | \(-0.784604\pi\) | ||||
−0.779652 | + | 0.626213i | \(0.784604\pi\) | |||||||
\(138\) | −1.22682 | −0.104434 | ||||||||
\(139\) | −6.86591 | −0.582359 | −0.291180 | − | 0.956668i | \(-0.594048\pi\) | ||||
−0.291180 | + | 0.956668i | \(0.594048\pi\) | |||||||
\(140\) | 4.69877 | 0.397118 | ||||||||
\(141\) | 1.77439 | 0.149431 | ||||||||
\(142\) | −0.694565 | −0.0582866 | ||||||||
\(143\) | −2.01028 | −0.168108 | ||||||||
\(144\) | 3.87536 | 0.322947 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.32819 | −0.109921 | ||||||||
\(147\) | 4.66668 | 0.384901 | ||||||||
\(148\) | −5.94897 | −0.489002 | ||||||||
\(149\) | −1.82628 | −0.149615 | −0.0748074 | − | 0.997198i | \(-0.523834\pi\) | ||||
−0.0748074 | + | 0.997198i | \(0.523834\pi\) | |||||||
\(150\) | 0.373123 | 0.0304654 | ||||||||
\(151\) | 6.56174 | 0.533987 | 0.266993 | − | 0.963698i | \(-0.413970\pi\) | ||||
0.266993 | + | 0.963698i | \(0.413970\pi\) | |||||||
\(152\) | 3.01499 | 0.244548 | ||||||||
\(153\) | 3.51434 | 0.284118 | ||||||||
\(154\) | −0.169338 | −0.0136457 | ||||||||
\(155\) | 2.20021 | 0.176725 | ||||||||
\(156\) | −5.18167 | −0.414866 | ||||||||
\(157\) | −20.8825 | −1.66661 | −0.833304 | − | 0.552815i | \(-0.813553\pi\) | ||||
−0.833304 | + | 0.552815i | \(0.813553\pi\) | |||||||
\(158\) | −0.0788133 | −0.00627005 | ||||||||
\(159\) | −6.77178 | −0.537037 | ||||||||
\(160\) | 2.65545 | 0.209931 | ||||||||
\(161\) | −12.9798 | −1.02295 | ||||||||
\(162\) | 0.144378 | 0.0113434 | ||||||||
\(163\) | 0.249811 | 0.0195667 | 0.00978335 | − | 0.999952i | \(-0.496886\pi\) | ||||
0.00978335 | + | 0.999952i | \(0.496886\pi\) | |||||||
\(164\) | 11.4604 | 0.894907 | ||||||||
\(165\) | −1.19340 | −0.0929057 | ||||||||
\(166\) | 1.68168 | 0.130523 | ||||||||
\(167\) | 13.4150 | 1.03808 | 0.519042 | − | 0.854749i | \(-0.326289\pi\) | ||||
0.519042 | + | 0.854749i | \(0.326289\pi\) | |||||||
\(168\) | −0.877564 | −0.0677055 | ||||||||
\(169\) | −6.14543 | −0.472726 | ||||||||
\(170\) | 0.788609 | 0.0604835 | ||||||||
\(171\) | −5.24800 | −0.401325 | ||||||||
\(172\) | 8.50277 | 0.648330 | ||||||||
\(173\) | −3.51856 | −0.267511 | −0.133755 | − | 0.991014i | \(-0.542704\pi\) | ||||
−0.133755 | + | 0.991014i | \(0.542704\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.94765 | 0.298414 | ||||||||
\(176\) | 2.97564 | 0.224297 | ||||||||
\(177\) | −14.9605 | −1.12450 | ||||||||
\(178\) | −1.98923 | −0.149099 | ||||||||
\(179\) | −2.44064 | −0.182422 | −0.0912109 | − | 0.995832i | \(-0.529074\pi\) | ||||
−0.0912109 | + | 0.995832i | \(0.529074\pi\) | |||||||
\(180\) | −3.07607 | −0.229277 | ||||||||
\(181\) | −0.647356 | −0.0481176 | −0.0240588 | − | 0.999711i | \(-0.507659\pi\) | ||||
−0.0240588 | + | 0.999711i | \(0.507659\pi\) | |||||||
\(182\) | 0.577401 | 0.0427998 | ||||||||
\(183\) | 13.7169 | 1.01398 | ||||||||
\(184\) | −4.88171 | −0.359885 | ||||||||
\(185\) | 4.67174 | 0.343473 | ||||||||
\(186\) | −0.204385 | −0.0149862 | ||||||||
\(187\) | 2.69843 | 0.197329 | ||||||||
\(188\) | 3.51179 | 0.256124 | ||||||||
\(189\) | 1.52752 | 0.111111 | ||||||||
\(190\) | −1.17764 | −0.0854349 | ||||||||
\(191\) | 20.7888 | 1.50422 | 0.752112 | − | 0.659035i | \(-0.229035\pi\) | ||||
0.752112 | + | 0.659035i | \(0.229035\pi\) | |||||||
\(192\) | 7.50406 | 0.541559 | ||||||||
\(193\) | −20.2432 | −1.45714 | −0.728569 | − | 0.684973i | \(-0.759814\pi\) | ||||
−0.728569 | + | 0.684973i | \(0.759814\pi\) | |||||||
\(194\) | 0.256450 | 0.0184121 | ||||||||
\(195\) | 4.06918 | 0.291400 | ||||||||
\(196\) | 9.23609 | 0.659720 | ||||||||
\(197\) | 3.44438 | 0.245402 | 0.122701 | − | 0.992444i | \(-0.460844\pi\) | ||||
0.122701 | + | 0.992444i | \(0.460844\pi\) | |||||||
\(198\) | 0.110858 | 0.00787835 | ||||||||
\(199\) | 12.0270 | 0.852574 | 0.426287 | − | 0.904588i | \(-0.359821\pi\) | ||||
0.426287 | + | 0.904588i | \(0.359821\pi\) | |||||||
\(200\) | 1.48471 | 0.104985 | ||||||||
\(201\) | 7.29495 | 0.514546 | ||||||||
\(202\) | 0.644793 | 0.0453675 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.95542 | 0.486977 | ||||||||
\(205\) | −8.99988 | −0.628579 | ||||||||
\(206\) | 1.48996 | 0.103811 | ||||||||
\(207\) | 8.49729 | 0.590603 | ||||||||
\(208\) | −10.1462 | −0.703511 | ||||||||
\(209\) | −4.02960 | −0.278733 | ||||||||
\(210\) | 0.342772 | 0.0236535 | ||||||||
\(211\) | −4.16064 | −0.286430 | −0.143215 | − | 0.989692i | \(-0.545744\pi\) | ||||
−0.143215 | + | 0.989692i | \(0.545744\pi\) | |||||||
\(212\) | −13.4024 | −0.920480 | ||||||||
\(213\) | 4.81074 | 0.329627 | ||||||||
\(214\) | −2.26538 | −0.154858 | ||||||||
\(215\) | −6.67725 | −0.455385 | ||||||||
\(216\) | 0.574502 | 0.0390899 | ||||||||
\(217\) | −2.16240 | −0.146793 | ||||||||
\(218\) | −1.42022 | −0.0961895 | ||||||||
\(219\) | 9.19937 | 0.621636 | ||||||||
\(220\) | −2.36191 | −0.159240 | ||||||||
\(221\) | −9.20097 | −0.618924 | ||||||||
\(222\) | −0.433973 | −0.0291263 | ||||||||
\(223\) | −4.70372 | −0.314984 | −0.157492 | − | 0.987520i | \(-0.550341\pi\) | ||||
−0.157492 | + | 0.987520i | \(0.550341\pi\) | |||||||
\(224\) | −2.60980 | −0.174375 | ||||||||
\(225\) | −2.58435 | −0.172290 | ||||||||
\(226\) | 1.82756 | 0.121567 | ||||||||
\(227\) | −13.6864 | −0.908400 | −0.454200 | − | 0.890900i | \(-0.650075\pi\) | ||||
−0.454200 | + | 0.890900i | \(0.650075\pi\) | |||||||
\(228\) | −10.3866 | −0.687870 | ||||||||
\(229\) | −20.1944 | −1.33448 | −0.667241 | − | 0.744842i | \(-0.732525\pi\) | ||||
−0.667241 | + | 0.744842i | \(0.732525\pi\) | |||||||
\(230\) | 1.90677 | 0.125729 | ||||||||
\(231\) | 1.17288 | 0.0771700 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.28500 | −0.477257 | −0.238628 | − | 0.971111i | \(-0.576698\pi\) | ||||
−0.238628 | + | 0.971111i | \(0.576698\pi\) | |||||||
\(234\) | −0.377999 | −0.0247106 | ||||||||
\(235\) | −2.75782 | −0.179900 | ||||||||
\(236\) | −29.6091 | −1.92739 | ||||||||
\(237\) | 0.545882 | 0.0354589 | ||||||||
\(238\) | −0.775053 | −0.0502393 | ||||||||
\(239\) | −23.3694 | −1.51164 | −0.755822 | − | 0.654777i | \(-0.772762\pi\) | ||||
−0.755822 | + | 0.654777i | \(0.772762\pi\) | |||||||
\(240\) | −6.02323 | −0.388798 | ||||||||
\(241\) | 25.4593 | 1.63998 | 0.819989 | − | 0.572379i | \(-0.193980\pi\) | ||||
0.819989 | + | 0.572379i | \(0.193980\pi\) | |||||||
\(242\) | −1.50304 | −0.0966188 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 27.1478 | 1.73796 | ||||||||
\(245\) | −7.25312 | −0.463385 | ||||||||
\(246\) | 0.836028 | 0.0533032 | ||||||||
\(247\) | 13.7399 | 0.874250 | ||||||||
\(248\) | −0.813279 | −0.0516433 | ||||||||
\(249\) | −11.6477 | −0.738145 | ||||||||
\(250\) | −1.70191 | −0.107638 | ||||||||
\(251\) | 13.0548 | 0.824009 | 0.412004 | − | 0.911182i | \(-0.364829\pi\) | ||||
0.412004 | + | 0.911182i | \(0.364829\pi\) | |||||||
\(252\) | 3.02320 | 0.190444 | ||||||||
\(253\) | 6.52451 | 0.410192 | ||||||||
\(254\) | −2.79207 | −0.175190 | ||||||||
\(255\) | −5.46211 | −0.342051 | ||||||||
\(256\) | 14.3583 | 0.897397 | ||||||||
\(257\) | 1.37201 | 0.0855836 | 0.0427918 | − | 0.999084i | \(-0.486375\pi\) | ||||
0.0427918 | + | 0.999084i | \(0.486375\pi\) | |||||||
\(258\) | 0.620271 | 0.0386164 | ||||||||
\(259\) | −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 | \(-0.721010\pi\) | ||||
−0.639866 | + | 0.768487i | \(0.721010\pi\) | |||||||
\(264\) | 0.441122 | 0.0271492 | ||||||||
\(265\) | 10.5249 | 0.646542 | ||||||||
\(266\) | 1.15740 | 0.0709645 | ||||||||
\(267\) | 13.7779 | 0.843195 | ||||||||
\(268\) | 14.4378 | 0.881931 | ||||||||
\(269\) | −0.958446 | −0.0584375 | −0.0292187 | − | 0.999573i | \(-0.509302\pi\) | ||||
−0.0292187 | + | 0.999573i | \(0.509302\pi\) | |||||||
\(270\) | −0.224397 | −0.0136564 | ||||||||
\(271\) | 21.1163 | 1.28272 | 0.641361 | − | 0.767240i | \(-0.278370\pi\) | ||||
0.641361 | + | 0.767240i | \(0.278370\pi\) | |||||||
\(272\) | 13.6193 | 0.825794 | ||||||||
\(273\) | −3.99924 | −0.242045 | ||||||||
\(274\) | −2.63507 | −0.159190 | ||||||||
\(275\) | −1.98435 | −0.119661 | ||||||||
\(276\) | 16.8175 | 1.01229 | ||||||||
\(277\) | 10.4181 | 0.625963 | 0.312982 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312982 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(278\) | −0.991286 | −0.0594534 | ||||||||
\(279\) | 1.41562 | 0.0847512 | ||||||||
\(280\) | 1.36394 | 0.0815111 | ||||||||
\(281\) | 3.34474 | 0.199530 | 0.0997651 | − | 0.995011i | \(-0.468191\pi\) | ||||
0.0997651 | + | 0.995011i | \(0.468191\pi\) | |||||||
\(282\) | 0.256183 | 0.0152555 | ||||||||
\(283\) | −15.7748 | −0.937713 | −0.468856 | − | 0.883274i | \(-0.655334\pi\) | ||||
−0.468856 | + | 0.883274i | \(0.655334\pi\) | |||||||
\(284\) | 9.52120 | 0.564979 | ||||||||
\(285\) | 8.15664 | 0.483158 | ||||||||
\(286\) | −0.290240 | −0.0171623 | ||||||||
\(287\) | 8.84518 | 0.522115 | ||||||||
\(288\) | 1.70852 | 0.100676 | ||||||||
\(289\) | −4.64941 | −0.273495 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.77624 | −0.104125 | ||||||||
\(292\) | 18.2070 | 1.06548 | ||||||||
\(293\) | 15.8084 | 0.923538 | 0.461769 | − | 0.887000i | \(-0.347215\pi\) | ||||
0.461769 | + | 0.887000i | \(0.347215\pi\) | |||||||
\(294\) | 0.673766 | 0.0392948 | ||||||||
\(295\) | 23.2521 | 1.35379 | ||||||||
\(296\) | −1.72685 | −0.100371 | ||||||||
\(297\) | −0.767834 | −0.0445542 | ||||||||
\(298\) | −0.263675 | −0.0152743 | ||||||||
\(299\) | −22.2470 | −1.28657 | ||||||||
\(300\) | −5.11483 | −0.295305 | ||||||||
\(301\) | 6.56248 | 0.378255 | ||||||||
\(302\) | 0.947370 | 0.0545150 | ||||||||
\(303\) | −4.46601 | −0.256565 | ||||||||
\(304\) | −20.3379 | −1.16646 | ||||||||
\(305\) | −21.3193 | −1.22074 | ||||||||
\(306\) | 0.507393 | 0.0290057 | ||||||||
\(307\) | −8.83474 | −0.504225 | −0.252113 | − | 0.967698i | \(-0.581125\pi\) | ||||
−0.252113 | + | 0.967698i | \(0.581125\pi\) | |||||||
\(308\) | 2.32132 | 0.132269 | ||||||||
\(309\) | −10.3199 | −0.587078 | ||||||||
\(310\) | 0.317662 | 0.0180420 | ||||||||
\(311\) | 12.9878 | 0.736469 | 0.368235 | − | 0.929733i | \(-0.379962\pi\) | ||||
0.368235 | + | 0.929733i | \(0.379962\pi\) | |||||||
\(312\) | −1.50412 | −0.0851539 | ||||||||
\(313\) | 19.1428 | 1.08201 | 0.541007 | − | 0.841018i | \(-0.318043\pi\) | ||||
0.541007 | + | 0.841018i | \(0.318043\pi\) | |||||||
\(314\) | −3.01498 | −0.170145 | ||||||||
\(315\) | −2.37413 | −0.133767 | ||||||||
\(316\) | 1.08039 | 0.0607764 | ||||||||
\(317\) | −26.6435 | −1.49645 | −0.748225 | − | 0.663445i | \(-0.769094\pi\) | ||||
−0.748225 | + | 0.663445i | \(0.769094\pi\) | |||||||
\(318\) | −0.977695 | −0.0548264 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −11.6631 | −0.651986 | ||||||||
\(321\) | 15.6906 | 0.875765 | ||||||||
\(322\) | −1.87400 | −0.104434 | ||||||||
\(323\) | −18.4433 | −1.02621 | ||||||||
\(324\) | −1.97916 | −0.109953 | ||||||||
\(325\) | 6.76615 | 0.375318 | ||||||||
\(326\) | 0.0360672 | 0.00199758 | ||||||||
\(327\) | 9.83683 | 0.543978 | ||||||||
\(328\) | 3.32668 | 0.183685 | ||||||||
\(329\) | 2.71042 | 0.149430 | ||||||||
\(330\) | −0.172300 | −0.00948480 | ||||||||
\(331\) | 2.21519 | 0.121758 | 0.0608789 | − | 0.998145i | \(-0.480610\pi\) | ||||
0.0608789 | + | 0.998145i | \(0.480610\pi\) | |||||||
\(332\) | −23.0527 | −1.26518 | ||||||||
\(333\) | 3.00581 | 0.164717 | ||||||||
\(334\) | 1.93683 | 0.105979 | ||||||||
\(335\) | −11.3381 | −0.619465 | ||||||||
\(336\) | 5.91970 | 0.322946 | ||||||||
\(337\) | −8.01703 | −0.436715 | −0.218358 | − | 0.975869i | \(-0.570070\pi\) | ||||
−0.218358 | + | 0.975869i | \(0.570070\pi\) | |||||||
\(338\) | −0.887265 | −0.0482609 | ||||||||
\(339\) | −12.6581 | −0.687496 | ||||||||
\(340\) | −10.8104 | −0.586275 | ||||||||
\(341\) | 1.08696 | 0.0588624 | ||||||||
\(342\) | −0.757696 | −0.0409715 | ||||||||
\(343\) | 17.8211 | 0.962249 | ||||||||
\(344\) | 2.46815 | 0.133074 | ||||||||
\(345\) | −13.2068 | −0.711030 | ||||||||
\(346\) | −0.508002 | −0.0273104 | ||||||||
\(347\) | −26.2715 | −1.41033 | −0.705165 | − | 0.709044i | \(-0.749127\pi\) | ||||
−0.705165 | + | 0.709044i | \(0.749127\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 2.61812 | 0.139745 | ||||||||
\(352\) | 1.31186 | 0.0699224 | ||||||||
\(353\) | 20.0667 | 1.06804 | 0.534021 | − | 0.845471i | \(-0.320680\pi\) | ||||
0.534021 | + | 0.845471i | \(0.320680\pi\) | |||||||
\(354\) | −2.15996 | −0.114801 | ||||||||
\(355\) | −7.47703 | −0.396839 | ||||||||
\(356\) | 27.2686 | 1.44524 | ||||||||
\(357\) | 5.36823 | 0.284117 | ||||||||
\(358\) | −0.352374 | −0.0186236 | ||||||||
\(359\) | 21.2008 | 1.11894 | 0.559468 | − | 0.828852i | \(-0.311006\pi\) | ||||
0.559468 | + | 0.828852i | \(0.311006\pi\) | |||||||
\(360\) | −0.892912 | −0.0470606 | ||||||||
\(361\) | 8.54155 | 0.449555 | ||||||||
\(362\) | −0.0934640 | −0.00491236 | ||||||||
\(363\) | 10.4104 | 0.546406 | ||||||||
\(364\) | −7.91511 | −0.414864 | ||||||||
\(365\) | −14.2980 | −0.748391 | ||||||||
\(366\) | 1.98041 | 0.103518 | ||||||||
\(367\) | 19.5920 | 1.02269 | 0.511347 | − | 0.859374i | \(-0.329147\pi\) | ||||
0.511347 | + | 0.859374i | \(0.329147\pi\) | |||||||
\(368\) | 32.9301 | 1.71660 | ||||||||
\(369\) | −5.79055 | −0.301444 | ||||||||
\(370\) | 0.674496 | 0.0350654 | ||||||||
\(371\) | −10.3440 | −0.537035 | ||||||||
\(372\) | 2.80174 | 0.145263 | ||||||||
\(373\) | 0.197465 | 0.0102244 | 0.00511218 | − | 0.999987i | \(-0.498373\pi\) | ||||
0.00511218 | + | 0.999987i | \(0.498373\pi\) | |||||||
\(374\) | 0.389594 | 0.0201454 | ||||||||
\(375\) | 11.7879 | 0.608723 | ||||||||
\(376\) | 1.01939 | 0.0525711 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.220540 | 0.0113434 | ||||||||
\(379\) | 22.4911 | 1.15529 | 0.577645 | − | 0.816288i | \(-0.303972\pi\) | ||||
0.577645 | + | 0.816288i | \(0.303972\pi\) | |||||||
\(380\) | 16.1433 | 0.828131 | ||||||||
\(381\) | 19.3386 | 0.990747 | ||||||||
\(382\) | 3.00144 | 0.153567 | ||||||||
\(383\) | −0.603334 | −0.0308289 | −0.0154145 | − | 0.999881i | \(-0.504907\pi\) | ||||
−0.0154145 | + | 0.999881i | \(0.504907\pi\) | |||||||
\(384\) | 4.50046 | 0.229663 | ||||||||
\(385\) | −1.82294 | −0.0929054 | ||||||||
\(386\) | −2.92267 | −0.148760 | ||||||||
\(387\) | −4.29616 | −0.218386 | ||||||||
\(388\) | −3.51546 | −0.178471 | ||||||||
\(389\) | 21.8263 | 1.10664 | 0.553318 | − | 0.832970i | \(-0.313362\pi\) | ||||
0.553318 | + | 0.832970i | \(0.313362\pi\) | |||||||
\(390\) | 0.587500 | 0.0297492 | ||||||||
\(391\) | 29.8624 | 1.51021 | ||||||||
\(392\) | 2.68102 | 0.135412 | ||||||||
\(393\) | 16.8082 | 0.847863 | ||||||||
\(394\) | 0.497292 | 0.0250532 | ||||||||
\(395\) | −0.848430 | −0.0426891 | ||||||||
\(396\) | −1.51966 | −0.0763659 | ||||||||
\(397\) | 14.4481 | 0.725132 | 0.362566 | − | 0.931958i | \(-0.381901\pi\) | ||||
0.362566 | + | 0.931958i | \(0.381901\pi\) | |||||||
\(398\) | 1.73644 | 0.0870398 | ||||||||
\(399\) | −8.01644 | −0.401324 | ||||||||
\(400\) | −10.0153 | −0.500765 | ||||||||
\(401\) | −26.3790 | −1.31730 | −0.658652 | − | 0.752448i | \(-0.728873\pi\) | ||||
−0.658652 | + | 0.752448i | \(0.728873\pi\) | |||||||
\(402\) | 1.05323 | 0.0525303 | ||||||||
\(403\) | −3.70628 | −0.184623 | ||||||||
\(404\) | −8.83892 | −0.439753 | ||||||||
\(405\) | 1.55424 | 0.0772306 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.30796 | 0.114402 | ||||||||
\(408\) | 2.01900 | 0.0999552 | ||||||||
\(409\) | 31.0838 | 1.53700 | 0.768498 | − | 0.639852i | \(-0.221004\pi\) | ||||
0.768498 | + | 0.639852i | \(0.221004\pi\) | |||||||
\(410\) | −1.29938 | −0.0641720 | ||||||||
\(411\) | 18.2512 | 0.900264 | ||||||||
\(412\) | −20.4247 | −1.00625 | ||||||||
\(413\) | −22.8525 | −1.12450 | ||||||||
\(414\) | 1.22682 | 0.0602950 | ||||||||
\(415\) | 18.1033 | 0.888658 | ||||||||
\(416\) | −4.47312 | −0.219313 | ||||||||
\(417\) | 6.86591 | 0.336225 | ||||||||
\(418\) | −0.581785 | −0.0284560 | ||||||||
\(419\) | 20.3478 | 0.994053 | 0.497026 | − | 0.867735i | \(-0.334425\pi\) | ||||
0.497026 | + | 0.867735i | \(0.334425\pi\) | |||||||
\(420\) | −4.69877 | −0.229276 | ||||||||
\(421\) | 8.52568 | 0.415516 | 0.207758 | − | 0.978180i | \(-0.433383\pi\) | ||||
0.207758 | + | 0.978180i | \(0.433383\pi\) | |||||||
\(422\) | −0.600705 | −0.0292419 | ||||||||
\(423\) | −1.77439 | −0.0862738 | ||||||||
\(424\) | −3.89040 | −0.188934 | ||||||||
\(425\) | −9.08228 | −0.440556 | ||||||||
\(426\) | 0.694565 | 0.0336518 | ||||||||
\(427\) | 20.9528 | 1.01398 | ||||||||
\(428\) | 31.0542 | 1.50106 | ||||||||
\(429\) | 2.01028 | 0.0970574 | ||||||||
\(430\) | −0.964048 | −0.0464905 | ||||||||
\(431\) | −4.76237 | −0.229395 | −0.114698 | − | 0.993400i | \(-0.536590\pi\) | ||||
−0.114698 | + | 0.993400i | \(0.536590\pi\) | |||||||
\(432\) | −3.87536 | −0.186454 | ||||||||
\(433\) | −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 | ||||||||
\(438\) | 1.32819 | 0.0634632 | ||||||||
\(439\) | 27.3895 | 1.30723 | 0.653615 | − | 0.756827i | \(-0.273252\pi\) | ||||
0.653615 | + | 0.756827i | \(0.273252\pi\) | |||||||
\(440\) | −0.685608 | −0.0326851 | ||||||||
\(441\) | −4.66668 | −0.222223 | ||||||||
\(442\) | −1.32842 | −0.0631864 | ||||||||
\(443\) | −0.777164 | −0.0369242 | −0.0184621 | − | 0.999830i | \(-0.505877\pi\) | ||||
−0.0184621 | + | 0.999830i | \(0.505877\pi\) | |||||||
\(444\) | 5.94897 | 0.282325 | ||||||||
\(445\) | −21.4141 | −1.01513 | ||||||||
\(446\) | −0.679113 | −0.0321569 | ||||||||
\(447\) | 1.82628 | 0.0863801 | ||||||||
\(448\) | 11.4626 | 0.541557 | ||||||||
\(449\) | 3.12702 | 0.147573 | 0.0737865 | − | 0.997274i | \(-0.476492\pi\) | ||||
0.0737865 | + | 0.997274i | \(0.476492\pi\) | |||||||
\(450\) | −0.373123 | −0.0175892 | ||||||||
\(451\) | −4.44618 | −0.209362 | ||||||||
\(452\) | −25.0524 | −1.17837 | ||||||||
\(453\) | −6.56174 | −0.308297 | ||||||||
\(454\) | −1.97602 | −0.0927391 | ||||||||
\(455\) | 6.21576 | 0.291399 | ||||||||
\(456\) | −3.01499 | −0.141190 | ||||||||
\(457\) | −28.6290 | −1.33921 | −0.669604 | − | 0.742718i | \(-0.733536\pi\) | ||||
−0.669604 | + | 0.742718i | \(0.733536\pi\) | |||||||
\(458\) | −2.91562 | −0.136238 | ||||||||
\(459\) | −3.51434 | −0.164035 | ||||||||
\(460\) | −26.1383 | −1.21870 | ||||||||
\(461\) | 27.8892 | 1.29893 | 0.649464 | − | 0.760392i | \(-0.274993\pi\) | ||||
0.649464 | + | 0.760392i | \(0.274993\pi\) | |||||||
\(462\) | 0.169338 | 0.00787833 | ||||||||
\(463\) | −18.3196 | −0.851382 | −0.425691 | − | 0.904869i | \(-0.639969\pi\) | ||||
−0.425691 | + | 0.904869i | \(0.639969\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.20021 | −0.102032 | ||||||||
\(466\) | −1.05179 | −0.0487234 | ||||||||
\(467\) | 21.8800 | 1.01249 | 0.506243 | − | 0.862391i | \(-0.331034\pi\) | ||||
0.506243 | + | 0.862391i | \(0.331034\pi\) | |||||||
\(468\) | 5.18167 | 0.239523 | ||||||||
\(469\) | 11.1432 | 0.514544 | ||||||||
\(470\) | −0.398168 | −0.0183661 | ||||||||
\(471\) | 20.8825 | 0.962216 | ||||||||
\(472\) | −8.59483 | −0.395609 | ||||||||
\(473\) | −3.29874 | −0.151676 | ||||||||
\(474\) | 0.0788133 | 0.00362002 | ||||||||
\(475\) | 13.5627 | 0.622298 | ||||||||
\(476\) | 10.6246 | 0.486976 | ||||||||
\(477\) | 6.77178 | 0.310058 | ||||||||
\(478\) | −3.37403 | −0.154325 | ||||||||
\(479\) | −23.4525 | −1.07157 | −0.535786 | − | 0.844354i | \(-0.679985\pi\) | ||||
−0.535786 | + | 0.844354i | \(0.679985\pi\) | |||||||
\(480\) | −2.65545 | −0.121204 | ||||||||
\(481\) | −7.86958 | −0.358822 | ||||||||
\(482\) | 3.67576 | 0.167426 | ||||||||
\(483\) | 12.9798 | 0.590601 | ||||||||
\(484\) | 20.6039 | 0.936539 | ||||||||
\(485\) | 2.76070 | 0.125357 | ||||||||
\(486\) | −0.144378 | −0.00654912 | ||||||||
\(487\) | −35.6248 | −1.61431 | −0.807157 | − | 0.590336i | \(-0.798995\pi\) | ||||
−0.807157 | + | 0.590336i | \(0.798995\pi\) | |||||||
\(488\) | 7.88038 | 0.356728 | ||||||||
\(489\) | −0.249811 | −0.0112968 | ||||||||
\(490\) | −1.04719 | −0.0473073 | ||||||||
\(491\) | −2.80650 | −0.126656 | −0.0633278 | − | 0.997993i | \(-0.520171\pi\) | ||||
−0.0633278 | + | 0.997993i | \(0.520171\pi\) | |||||||
\(492\) | −11.4604 | −0.516675 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.98374 | 0.0892527 | ||||||||
\(495\) | 1.19340 | 0.0536391 | ||||||||
\(496\) | 5.48606 | 0.246331 | ||||||||
\(497\) | 7.34851 | 0.329626 | ||||||||
\(498\) | −1.68168 | −0.0753577 | ||||||||
\(499\) | 40.6599 | 1.82019 | 0.910094 | − | 0.414401i | \(-0.136009\pi\) | ||||
0.910094 | + | 0.414401i | \(0.136009\pi\) | |||||||
\(500\) | 23.3300 | 1.04335 | ||||||||
\(501\) | −13.4150 | −0.599338 | ||||||||
\(502\) | 1.88482 | 0.0841236 | ||||||||
\(503\) | 18.5373 | 0.826538 | 0.413269 | − | 0.910609i | \(-0.364387\pi\) | ||||
0.413269 | + | 0.910609i | \(0.364387\pi\) | |||||||
\(504\) | 0.877564 | 0.0390898 | ||||||||
\(505\) | 6.94123 | 0.308881 | ||||||||
\(506\) | 0.941995 | 0.0418768 | ||||||||
\(507\) | 6.14543 | 0.272928 | ||||||||
\(508\) | 38.2741 | 1.69814 | ||||||||
\(509\) | −42.5525 | −1.88611 | −0.943054 | − | 0.332640i | \(-0.892061\pi\) | ||||
−0.943054 | + | 0.332640i | \(0.892061\pi\) | |||||||
\(510\) | −0.788609 | −0.0349202 | ||||||||
\(511\) | 14.0522 | 0.621634 | ||||||||
\(512\) | 11.0740 | 0.489404 | ||||||||
\(513\) | 5.24800 | 0.231705 | ||||||||
\(514\) | 0.198088 | 0.00873728 | ||||||||
\(515\) | 16.0395 | 0.706786 | ||||||||
\(516\) | −8.50277 | −0.374314 | ||||||||
\(517\) | −1.36244 | −0.0599199 | ||||||||
\(518\) | −0.662902 | −0.0291263 | ||||||||
\(519\) | 3.51856 | 0.154448 | ||||||||
\(520\) | 2.33775 | 0.102517 | ||||||||
\(521\) | −27.6372 | −1.21081 | −0.605404 | − | 0.795919i | \(-0.706988\pi\) | ||||
−0.605404 | + | 0.795919i | \(0.706988\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −3.94765 | −0.172289 | ||||||||
\(526\) | −2.99638 | −0.130649 | ||||||||
\(527\) | 4.97499 | 0.216714 | ||||||||
\(528\) | −2.97564 | −0.129498 | ||||||||
\(529\) | 49.2040 | 2.13930 | ||||||||
\(530\) | 1.51957 | 0.0660058 | ||||||||
\(531\) | 14.9605 | 0.649230 | ||||||||
\(532\) | −15.8658 | −0.687868 | ||||||||
\(533\) | 15.1604 | 0.656668 | ||||||||
\(534\) | 1.98923 | 0.0860823 | ||||||||
\(535\) | −24.3869 | −1.05434 | ||||||||
\(536\) | 4.19096 | 0.181022 | ||||||||
\(537\) | 2.44064 | 0.105321 | ||||||||
\(538\) | −0.138378 | −0.00596592 | ||||||||
\(539\) | −3.58324 | −0.154341 | ||||||||
\(540\) | 3.07607 | 0.132373 | ||||||||
\(541\) | −22.1075 | −0.950477 | −0.475239 | − | 0.879857i | \(-0.657638\pi\) | ||||
−0.475239 | + | 0.879857i | \(0.657638\pi\) | |||||||
\(542\) | 3.04872 | 0.130954 | ||||||||
\(543\) | 0.647356 | 0.0277807 | ||||||||
\(544\) | 6.00433 | 0.257433 | ||||||||
\(545\) | −15.2888 | −0.654898 | ||||||||
\(546\) | −0.577401 | −0.0247105 | ||||||||
\(547\) | 16.5033 | 0.705630 | 0.352815 | − | 0.935693i | \(-0.385224\pi\) | ||||
0.352815 | + | 0.935693i | \(0.385224\pi\) | |||||||
\(548\) | 36.1219 | 1.54305 | ||||||||
\(549\) | −13.7169 | −0.585422 | ||||||||
\(550\) | −0.286497 | −0.0122163 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 4.88171 | 0.207779 | ||||||||
\(553\) | 0.833846 | 0.0354587 | ||||||||
\(554\) | 1.50414 | 0.0639050 | ||||||||
\(555\) | −4.67174 | −0.198304 | ||||||||
\(556\) | 13.5887 | 0.576290 | ||||||||
\(557\) | 5.47950 | 0.232174 | 0.116087 | − | 0.993239i | \(-0.462965\pi\) | ||||
0.116087 | + | 0.993239i | \(0.462965\pi\) | |||||||
\(558\) | 0.204385 | 0.00865230 | ||||||||
\(559\) | 11.2479 | 0.475735 | ||||||||
\(560\) | −9.20061 | −0.388797 | ||||||||
\(561\) | −2.69843 | −0.113928 | ||||||||
\(562\) | 0.482906 | 0.0203702 | ||||||||
\(563\) | −13.7797 | −0.580744 | −0.290372 | − | 0.956914i | \(-0.593779\pi\) | ||||
−0.290372 | + | 0.956914i | \(0.593779\pi\) | |||||||
\(564\) | −3.51179 | −0.147873 | ||||||||
\(565\) | 19.6738 | 0.827681 | ||||||||
\(566\) | −2.27753 | −0.0957317 | ||||||||
\(567\) | −1.52752 | −0.0641498 | ||||||||
\(568\) | 2.76378 | 0.115966 | ||||||||
\(569\) | −35.9279 | −1.50618 | −0.753088 | − | 0.657920i | \(-0.771436\pi\) | ||||
−0.753088 | + | 0.657920i | \(0.771436\pi\) | |||||||
\(570\) | 1.17764 | 0.0493258 | ||||||||
\(571\) | −6.56420 | −0.274703 | −0.137352 | − | 0.990522i | \(-0.543859\pi\) | ||||
−0.137352 | + | 0.990522i | \(0.543859\pi\) | |||||||
\(572\) | 3.97866 | 0.166356 | ||||||||
\(573\) | −20.7888 | −0.868464 | ||||||||
\(574\) | 1.27705 | 0.0533030 | ||||||||
\(575\) | −21.9600 | −0.915794 | ||||||||
\(576\) | −7.50406 | −0.312669 | ||||||||
\(577\) | 8.06782 | 0.335868 | 0.167934 | − | 0.985798i | \(-0.446290\pi\) | ||||
0.167934 | + | 0.985798i | \(0.446290\pi\) | |||||||
\(578\) | −0.671273 | −0.0279213 | ||||||||
\(579\) | 20.2432 | 0.841278 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.7922 | −0.738143 | ||||||||
\(582\) | −0.256450 | −0.0106302 | ||||||||
\(583\) | 5.19960 | 0.215345 | ||||||||
\(584\) | 5.28506 | 0.218697 | ||||||||
\(585\) | −4.06918 | −0.168240 | ||||||||
\(586\) | 2.28239 | 0.0942845 | ||||||||
\(587\) | −8.05202 | −0.332343 | −0.166171 | − | 0.986097i | \(-0.553140\pi\) | ||||
−0.166171 | + | 0.986097i | \(0.553140\pi\) | |||||||
\(588\) | −9.23609 | −0.380890 | ||||||||
\(589\) | −7.42920 | −0.306115 | ||||||||
\(590\) | 3.35710 | 0.138209 | ||||||||
\(591\) | −3.44438 | −0.141683 | ||||||||
\(592\) | 11.6486 | 0.478755 | ||||||||
\(593\) | 34.4563 | 1.41495 | 0.707474 | − | 0.706739i | \(-0.249835\pi\) | ||||
0.707474 | + | 0.706739i | \(0.249835\pi\) | |||||||
\(594\) | −0.110858 | −0.00454857 | ||||||||
\(595\) | −8.34349 | −0.342050 | ||||||||
\(596\) | 3.61449 | 0.148055 | ||||||||
\(597\) | −12.0270 | −0.492234 | ||||||||
\(598\) | −3.21197 | −0.131347 | ||||||||
\(599\) | 31.6740 | 1.29416 | 0.647082 | − | 0.762421i | \(-0.275989\pi\) | ||||
0.647082 | + | 0.762421i | \(0.275989\pi\) | |||||||
\(600\) | −1.48471 | −0.0606132 | ||||||||
\(601\) | −3.86546 | −0.157675 | −0.0788376 | − | 0.996887i | \(-0.525121\pi\) | ||||
−0.0788376 | + | 0.996887i | \(0.525121\pi\) | |||||||
\(602\) | 0.947477 | 0.0386163 | ||||||||
\(603\) | −7.29495 | −0.297073 | ||||||||
\(604\) | −12.9867 | −0.528421 | ||||||||
\(605\) | −16.1803 | −0.657821 | ||||||||
\(606\) | −0.644793 | −0.0261929 | ||||||||
\(607\) | −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 | ||||||||
\(612\) | −6.95542 | −0.281156 | ||||||||
\(613\) | 3.02255 | 0.122080 | 0.0610399 | − | 0.998135i | \(-0.480558\pi\) | ||||
0.0610399 | + | 0.998135i | \(0.480558\pi\) | |||||||
\(614\) | −1.27554 | −0.0514767 | ||||||||
\(615\) | 8.99988 | 0.362910 | ||||||||
\(616\) | 0.673823 | 0.0271491 | ||||||||
\(617\) | −1.92609 | −0.0775415 | −0.0387708 | − | 0.999248i | \(-0.512344\pi\) | ||||
−0.0387708 | + | 0.999248i | \(0.512344\pi\) | |||||||
\(618\) | −1.48996 | −0.0599351 | ||||||||
\(619\) | −0.295624 | −0.0118821 | −0.00594107 | − | 0.999982i | \(-0.501891\pi\) | ||||
−0.00594107 | + | 0.999982i | \(0.501891\pi\) | |||||||
\(620\) | −4.35457 | −0.174884 | ||||||||
\(621\) | −8.49729 | −0.340985 | ||||||||
\(622\) | 1.87515 | 0.0751866 | ||||||||
\(623\) | 21.0461 | 0.843192 | ||||||||
\(624\) | 10.1462 | 0.406172 | ||||||||
\(625\) | −5.39938 | −0.215975 | ||||||||
\(626\) | 2.76380 | 0.110464 | ||||||||
\(627\) | 4.02960 | 0.160927 | ||||||||
\(628\) | 41.3298 | 1.64924 | ||||||||
\(629\) | 10.5634 | 0.421192 | ||||||||
\(630\) | −0.342772 | −0.0136563 | ||||||||
\(631\) | 33.0085 | 1.31405 | 0.657024 | − | 0.753869i | \(-0.271815\pi\) | ||||
0.657024 | + | 0.753869i | \(0.271815\pi\) | |||||||
\(632\) | 0.313610 | 0.0124748 | ||||||||
\(633\) | 4.16064 | 0.165371 | ||||||||
\(634\) | −3.84674 | −0.152774 | ||||||||
\(635\) | −30.0568 | −1.19277 | ||||||||
\(636\) | 13.4024 | 0.531439 | ||||||||
\(637\) | 12.2179 | 0.484093 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.81074 | −0.190310 | ||||||||
\(640\) | −6.99478 | −0.276493 | ||||||||
\(641\) | 21.5035 | 0.849336 | 0.424668 | − | 0.905349i | \(-0.360391\pi\) | ||||
0.424668 | + | 0.905349i | \(0.360391\pi\) | |||||||
\(642\) | 2.26538 | 0.0894074 | ||||||||
\(643\) | −16.6571 | −0.656891 | −0.328445 | − | 0.944523i | \(-0.606525\pi\) | ||||
−0.328445 | + | 0.944523i | \(0.606525\pi\) | |||||||
\(644\) | 25.6890 | 1.01229 | ||||||||
\(645\) | 6.67725 | 0.262917 | ||||||||
\(646\) | −2.66280 | −0.104767 | ||||||||
\(647\) | −0.641821 | −0.0252326 | −0.0126163 | − | 0.999920i | \(-0.504016\pi\) | ||||
−0.0126163 | + | 0.999920i | \(0.504016\pi\) | |||||||
\(648\) | −0.574502 | −0.0225686 | ||||||||
\(649\) | 11.4872 | 0.450911 | ||||||||
\(650\) | 0.976882 | 0.0383165 | ||||||||
\(651\) | 2.16240 | 0.0847509 | ||||||||
\(652\) | −0.494414 | −0.0193628 | ||||||||
\(653\) | 41.8052 | 1.63596 | 0.817982 | − | 0.575244i | \(-0.195093\pi\) | ||||
0.817982 | + | 0.575244i | \(0.195093\pi\) | |||||||
\(654\) | 1.42022 | 0.0555350 | ||||||||
\(655\) | −26.1239 | −1.02075 | ||||||||
\(656\) | −22.4405 | −0.876154 | ||||||||
\(657\) | −9.19937 | −0.358902 | ||||||||
\(658\) | 0.391324 | 0.0152554 | ||||||||
\(659\) | 6.28494 | 0.244827 | 0.122413 | − | 0.992479i | \(-0.460937\pi\) | ||||
0.122413 | + | 0.992479i | \(0.460937\pi\) | |||||||
\(660\) | 2.36191 | 0.0919374 | ||||||||
\(661\) | −20.2713 | −0.788461 | −0.394231 | − | 0.919012i | \(-0.628989\pi\) | ||||
−0.394231 | + | 0.919012i | \(0.628989\pi\) | |||||||
\(662\) | 0.319824 | 0.0124303 | ||||||||
\(663\) | 9.20097 | 0.357336 | ||||||||
\(664\) | −6.69165 | −0.259686 | ||||||||
\(665\) | 12.4594 | 0.483156 | ||||||||
\(666\) | 0.433973 | 0.0168161 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −26.5504 | −1.02726 | ||||||||
\(669\) | 4.70372 | 0.181856 | ||||||||
\(670\) | −1.63697 | −0.0632416 | ||||||||
\(671\) | −10.5323 | −0.406594 | ||||||||
\(672\) | 2.60980 | 0.100675 | ||||||||
\(673\) | −21.7317 | −0.837694 | −0.418847 | − | 0.908057i | \(-0.637566\pi\) | ||||
−0.418847 | + | 0.908057i | \(0.637566\pi\) | |||||||
\(674\) | −1.15748 | −0.0445845 | ||||||||
\(675\) | 2.58435 | 0.0994717 | ||||||||
\(676\) | 12.1628 | 0.467799 | ||||||||
\(677\) | −15.7988 | −0.607197 | −0.303599 | − | 0.952800i | \(-0.598188\pi\) | ||||
−0.303599 | + | 0.952800i | \(0.598188\pi\) | |||||||
\(678\) | −1.82756 | −0.0701869 | ||||||||
\(679\) | −2.71325 | −0.104125 | ||||||||
\(680\) | −3.13800 | −0.120337 | ||||||||
\(681\) | 13.6864 | 0.524465 | ||||||||
\(682\) | 0.156934 | 0.00600930 | ||||||||
\(683\) | −34.1996 | −1.30861 | −0.654306 | − | 0.756230i | \(-0.727039\pi\) | ||||
−0.654306 | + | 0.756230i | \(0.727039\pi\) | |||||||
\(684\) | 10.3866 | 0.397142 | ||||||||
\(685\) | −28.3666 | −1.08383 | ||||||||
\(686\) | 2.57297 | 0.0982366 | ||||||||
\(687\) | 20.1944 | 0.770463 | ||||||||
\(688\) | −16.6492 | −0.634745 | ||||||||
\(689\) | −17.7293 | −0.675434 | ||||||||
\(690\) | −1.90677 | −0.0725895 | ||||||||
\(691\) | −34.3566 | −1.30699 | −0.653494 | − | 0.756931i | \(-0.726698\pi\) | ||||
−0.653494 | + | 0.756931i | \(0.726698\pi\) | |||||||
\(692\) | 6.96377 | 0.264723 | ||||||||
\(693\) | −1.17288 | −0.0445541 | ||||||||
\(694\) | −3.79303 | −0.143981 | ||||||||
\(695\) | −10.6713 | −0.404784 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.3500 | −0.770810 | ||||||||
\(698\) | −0.557743 | −0.0211109 | ||||||||
\(699\) | 7.28500 | 0.275544 | ||||||||
\(700\) | −7.81301 | −0.295304 | ||||||||
\(701\) | 1.71987 | 0.0649588 | 0.0324794 | − | 0.999472i | \(-0.489660\pi\) | ||||
0.0324794 | + | 0.999472i | \(0.489660\pi\) | |||||||
\(702\) | 0.377999 | 0.0142667 | ||||||||
\(703\) | −15.7745 | −0.594947 | ||||||||
\(704\) | −5.76187 | −0.217159 | ||||||||
\(705\) | 2.75782 | 0.103866 | ||||||||
\(706\) | 2.89719 | 0.109037 | ||||||||
\(707\) | −6.82192 | −0.256565 | ||||||||
\(708\) | 29.6091 | 1.11278 | ||||||||
\(709\) | 42.0692 | 1.57994 | 0.789970 | − | 0.613145i | \(-0.210096\pi\) | ||||
0.789970 | + | 0.613145i | \(0.210096\pi\) | |||||||
\(710\) | −1.07952 | −0.0405136 | ||||||||
\(711\) | −0.545882 | −0.0204722 | ||||||||
\(712\) | 7.91545 | 0.296644 | ||||||||
\(713\) | 12.0290 | 0.450489 | ||||||||
\(714\) | 0.775053 | 0.0290056 | ||||||||
\(715\) | −3.12445 | −0.116848 | ||||||||
\(716\) | 4.83040 | 0.180521 | ||||||||
\(717\) | 23.3694 | 0.872748 | ||||||||
\(718\) | 3.06093 | 0.114233 | ||||||||
\(719\) | 2.01196 | 0.0750335 | 0.0375168 | − | 0.999296i | \(-0.488055\pi\) | ||||
0.0375168 | + | 0.999296i | \(0.488055\pi\) | |||||||
\(720\) | 6.02323 | 0.224473 | ||||||||
\(721\) | −15.7638 | −0.587076 | ||||||||
\(722\) | 1.23321 | 0.0458954 | ||||||||
\(723\) | −25.4593 | −0.946842 | ||||||||
\(724\) | 1.28122 | 0.0476161 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.50304 | 0.0557829 | ||||||||
\(727\) | −7.32560 | −0.271692 | −0.135846 | − | 0.990730i | \(-0.543375\pi\) | ||||
−0.135846 | + | 0.990730i | \(0.543375\pi\) | |||||||
\(728\) | −2.29757 | −0.0851536 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.06431 | −0.0764037 | ||||||||
\(731\) | −15.0982 | −0.558426 | ||||||||
\(732\) | −27.1478 | −1.00341 | ||||||||
\(733\) | −5.24481 | −0.193722 | −0.0968608 | − | 0.995298i | \(-0.530880\pi\) | ||||
−0.0968608 | + | 0.995298i | \(0.530880\pi\) | |||||||
\(734\) | 2.82865 | 0.104407 | ||||||||
\(735\) | 7.25312 | 0.267536 | ||||||||
\(736\) | 14.5178 | 0.535133 | ||||||||
\(737\) | −5.60131 | −0.206327 | ||||||||
\(738\) | −0.836028 | −0.0307746 | ||||||||
\(739\) | −23.5744 | −0.867198 | −0.433599 | − | 0.901106i | \(-0.642757\pi\) | ||||
−0.433599 | + | 0.901106i | \(0.642757\pi\) | |||||||
\(740\) | −9.24610 | −0.339893 | ||||||||
\(741\) | −13.7399 | −0.504749 | ||||||||
\(742\) | −1.49345 | −0.0548262 | ||||||||
\(743\) | 19.5239 | 0.716263 | 0.358131 | − | 0.933671i | \(-0.383414\pi\) | ||||
0.358131 | + | 0.933671i | \(0.383414\pi\) | |||||||
\(744\) | 0.813279 | 0.0298163 | ||||||||
\(745\) | −2.83847 | −0.103994 | ||||||||
\(746\) | 0.0285096 | 0.00104381 | ||||||||
\(747\) | 11.6477 | 0.426169 | ||||||||
\(748\) | −5.34061 | −0.195272 | ||||||||
\(749\) | 23.9678 | 0.875763 | ||||||||
\(750\) | 1.70191 | 0.0621449 | ||||||||
\(751\) | −1.41626 | −0.0516802 | −0.0258401 | − | 0.999666i | \(-0.508226\pi\) | ||||
−0.0258401 | + | 0.999666i | \(0.508226\pi\) | |||||||
\(752\) | −6.87641 | −0.250757 | ||||||||
\(753\) | −13.0548 | −0.475742 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.1985 | 0.371161 | ||||||||
\(756\) | −3.02320 | −0.109953 | ||||||||
\(757\) | −43.3206 | −1.57451 | −0.787257 | − | 0.616625i | \(-0.788500\pi\) | ||||
−0.787257 | + | 0.616625i | \(0.788500\pi\) | |||||||
\(758\) | 3.24722 | 0.117944 | ||||||||
\(759\) | −6.52451 | −0.236825 | ||||||||
\(760\) | 4.68601 | 0.169979 | ||||||||
\(761\) | 0.481297 | 0.0174470 | 0.00872351 | − | 0.999962i | \(-0.497223\pi\) | ||||
0.00872351 | + | 0.999962i | \(0.497223\pi\) | |||||||
\(762\) | 2.79207 | 0.101146 | ||||||||
\(763\) | 15.0260 | 0.543976 | ||||||||
\(764\) | −41.1443 | −1.48855 | ||||||||
\(765\) | 5.46211 | 0.197483 | ||||||||
\(766\) | −0.0871081 | −0.00314734 | ||||||||
\(767\) | −39.1684 | −1.41429 | ||||||||
\(768\) | −14.3583 | −0.518112 | ||||||||
\(769\) | 16.2798 | 0.587065 | 0.293532 | − | 0.955949i | \(-0.405169\pi\) | ||||
0.293532 | + | 0.955949i | \(0.405169\pi\) | |||||||
\(770\) | −0.263192 | −0.00948477 | ||||||||
\(771\) | −1.37201 | −0.0494117 | ||||||||
\(772\) | 40.0644 | 1.44195 | ||||||||
\(773\) | −17.3203 | −0.622968 | −0.311484 | − | 0.950251i | \(-0.600826\pi\) | ||||
−0.311484 | + | 0.950251i | \(0.600826\pi\) | |||||||
\(774\) | −0.620271 | −0.0222952 | ||||||||
\(775\) | −3.65847 | −0.131416 | ||||||||
\(776\) | −1.02046 | −0.0366322 | ||||||||
\(777\) | 4.59144 | 0.164717 | ||||||||
\(778\) | 3.15123 | 0.112977 | ||||||||
\(779\) | 30.3888 | 1.08879 | ||||||||
\(780\) | −8.05354 | −0.288363 | ||||||||
\(781\) | −3.69385 | −0.132176 | ||||||||
\(782\) | 4.31147 | 0.154178 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.0851 | −0.645896 | ||||||||
\(785\) | −32.4564 | −1.15842 | ||||||||
\(786\) | 2.42674 | 0.0865588 | ||||||||
\(787\) | 0.680377 | 0.0242528 | 0.0121264 | − | 0.999926i | \(-0.496140\pi\) | ||||
0.0121264 | + | 0.999926i | \(0.496140\pi\) | |||||||
\(788\) | −6.81695 | −0.242844 | ||||||||
\(789\) | 20.7538 | 0.738853 | ||||||||
\(790\) | −0.122495 | −0.00435816 | ||||||||
\(791\) | −19.3356 | −0.687494 | ||||||||
\(792\) | −0.441122 | −0.0156746 | ||||||||
\(793\) | 35.9125 | 1.27529 | ||||||||
\(794\) | 2.08599 | 0.0740291 | ||||||||
\(795\) | −10.5249 | −0.373281 | ||||||||
\(796\) | −23.8034 | −0.843688 | ||||||||
\(797\) | −44.8530 | −1.58878 | −0.794388 | − | 0.607411i | \(-0.792208\pi\) | ||||
−0.794388 | + | 0.607411i | \(0.792208\pi\) | |||||||
\(798\) | −1.15740 | −0.0409714 | ||||||||
\(799\) | −6.23581 | −0.220607 | ||||||||
\(800\) | −4.41542 | −0.156109 | ||||||||
\(801\) | −13.7779 | −0.486819 | ||||||||
\(802\) | −3.80854 | −0.134484 | ||||||||
\(803\) | −7.06359 | −0.249269 | ||||||||
\(804\) | −14.4378 | −0.509183 | ||||||||
\(805\) | −20.1737 | −0.711028 | ||||||||
\(806\) | −0.535105 | −0.0188483 | ||||||||
\(807\) | 0.958446 | 0.0337389 | ||||||||
\(808\) | −2.56573 | −0.0902621 | ||||||||
\(809\) | −29.4154 | −1.03419 | −0.517095 | − | 0.855928i | \(-0.672987\pi\) | ||||
−0.517095 | + | 0.855928i | \(0.672987\pi\) | |||||||
\(810\) | 0.224397 | 0.00788452 | ||||||||
\(811\) | −20.6973 | −0.726781 | −0.363391 | − | 0.931637i | \(-0.618381\pi\) | ||||
−0.363391 | + | 0.931637i | \(0.618381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.1163 | −0.740580 | ||||||||
\(814\) | 0.333219 | 0.0116793 | ||||||||
\(815\) | 0.388265 | 0.0136003 | ||||||||
\(816\) | −13.6193 | −0.476773 | ||||||||
\(817\) | 22.5463 | 0.788795 | ||||||||
\(818\) | 4.48782 | 0.156913 | ||||||||
\(819\) | 3.99924 | 0.139745 | ||||||||
\(820\) | 17.8122 | 0.622028 | ||||||||
\(821\) | 27.5661 | 0.962063 | 0.481031 | − | 0.876703i | \(-0.340262\pi\) | ||||
0.481031 | + | 0.876703i | \(0.340262\pi\) | |||||||
\(822\) | 2.63507 | 0.0919085 | ||||||||
\(823\) | −23.0508 | −0.803499 | −0.401750 | − | 0.915750i | \(-0.631598\pi\) | ||||
−0.401750 | + | 0.915750i | \(0.631598\pi\) | |||||||
\(824\) | −5.92880 | −0.206539 | ||||||||
\(825\) | 1.98435 | 0.0690862 | ||||||||
\(826\) | −3.29939 | −0.114800 | ||||||||
\(827\) | 44.5689 | 1.54981 | 0.774907 | − | 0.632076i | \(-0.217797\pi\) | ||||
0.774907 | + | 0.632076i | \(0.217797\pi\) | |||||||
\(828\) | −16.8175 | −0.584447 | ||||||||
\(829\) | −44.8796 | −1.55873 | −0.779367 | − | 0.626568i | \(-0.784459\pi\) | ||||
−0.779367 | + | 0.626568i | \(0.784459\pi\) | |||||||
\(830\) | 2.61372 | 0.0907236 | ||||||||
\(831\) | −10.4181 | −0.361400 | ||||||||
\(832\) | 19.6465 | 0.681121 | ||||||||
\(833\) | −16.4003 | −0.568237 | ||||||||
\(834\) | 0.991286 | 0.0343254 | ||||||||
\(835\) | 20.8501 | 0.721546 | ||||||||
\(836\) | 7.97519 | 0.275828 | ||||||||
\(837\) | −1.41562 | −0.0489311 | ||||||||
\(838\) | 2.93777 | 0.101483 | ||||||||
\(839\) | −13.0101 | −0.449157 | −0.224579 | − | 0.974456i | \(-0.572101\pi\) | ||||
−0.224579 | + | 0.974456i | \(0.572101\pi\) | |||||||
\(840\) | −1.36394 | −0.0470604 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 1.23092 | 0.0424203 | ||||||||
\(843\) | −3.34474 | −0.115199 | ||||||||
\(844\) | 8.23456 | 0.283445 | ||||||||
\(845\) | −9.55146 | −0.328580 | ||||||||
\(846\) | −0.256183 | −0.00880774 | ||||||||
\(847\) | 15.9021 | 0.546404 | ||||||||
\(848\) | 26.2431 | 0.901192 | ||||||||
\(849\) | 15.7748 | 0.541389 | ||||||||
\(850\) | −1.31128 | −0.0449766 | ||||||||
\(851\) | 25.5413 | 0.875543 | ||||||||
\(852\) | −9.52120 | −0.326191 | ||||||||
\(853\) | −27.7373 | −0.949706 | −0.474853 | − | 0.880065i | \(-0.657499\pi\) | ||||
−0.474853 | + | 0.880065i | \(0.657499\pi\) | |||||||
\(854\) | 3.02512 | 0.103518 | ||||||||
\(855\) | −8.15664 | −0.278951 | ||||||||
\(856\) | 9.01430 | 0.308102 | ||||||||
\(857\) | 18.6936 | 0.638563 | 0.319281 | − | 0.947660i | \(-0.396558\pi\) | ||||
0.319281 | + | 0.947660i | \(0.396558\pi\) | |||||||
\(858\) | 0.290240 | 0.00990865 | ||||||||
\(859\) | −23.3360 | −0.796214 | −0.398107 | − | 0.917339i | \(-0.630333\pi\) | ||||
−0.398107 | + | 0.917339i | \(0.630333\pi\) | |||||||
\(860\) | 13.2153 | 0.450639 | ||||||||
\(861\) | −8.84518 | −0.301443 | ||||||||
\(862\) | −0.687581 | −0.0234191 | ||||||||
\(863\) | −10.7677 | −0.366538 | −0.183269 | − | 0.983063i | \(-0.558668\pi\) | ||||
−0.183269 | + | 0.983063i | \(0.558668\pi\) | |||||||
\(864\) | −1.70852 | −0.0581251 | ||||||||
\(865\) | −5.46867 | −0.185940 | ||||||||
\(866\) | −0.610039 | −0.0207300 | ||||||||
\(867\) | 4.64941 | 0.157902 | ||||||||
\(868\) | 4.27972 | 0.145263 | ||||||||
\(869\) | −0.419147 | −0.0142186 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.0991 | 0.647147 | ||||||||
\(872\) | 5.65128 | 0.191376 | ||||||||
\(873\) | 1.77624 | 0.0601167 | ||||||||
\(874\) | −6.43836 | −0.217781 | ||||||||
\(875\) | 18.0062 | 0.608721 | ||||||||
\(876\) | −18.2070 | −0.615157 | ||||||||
\(877\) | −42.6677 | −1.44079 | −0.720393 | − | 0.693567i | \(-0.756038\pi\) | ||||
−0.720393 | + | 0.693567i | \(0.756038\pi\) | |||||||
\(878\) | 3.95444 | 0.133456 | ||||||||
\(879\) | −15.8084 | −0.533205 | ||||||||
\(880\) | 4.62484 | 0.155903 | ||||||||
\(881\) | 23.9728 | 0.807664 | 0.403832 | − | 0.914833i | \(-0.367678\pi\) | ||||
0.403832 | + | 0.914833i | \(0.367678\pi\) | |||||||
\(882\) | −0.673766 | −0.0226869 | ||||||||
\(883\) | −31.0935 | −1.04638 | −0.523191 | − | 0.852216i | \(-0.675258\pi\) | ||||
−0.523191 | + | 0.852216i | \(0.675258\pi\) | |||||||
\(884\) | 18.2102 | 0.612474 | ||||||||
\(885\) | −23.2521 | −0.781612 | ||||||||
\(886\) | −0.112205 | −0.00376961 | ||||||||
\(887\) | −10.1518 | −0.340864 | −0.170432 | − | 0.985369i | \(-0.554516\pi\) | ||||
−0.170432 | + | 0.985369i | \(0.554516\pi\) | |||||||
\(888\) | 1.72685 | 0.0579491 | ||||||||
\(889\) | 29.5401 | 0.990744 | ||||||||
\(890\) | −3.09173 | −0.103635 | ||||||||
\(891\) | 0.767834 | 0.0257234 | ||||||||
\(892\) | 9.30938 | 0.311701 | ||||||||
\(893\) | 9.31201 | 0.311614 | ||||||||
\(894\) | 0.263675 | 0.00881860 | ||||||||
\(895\) | −3.79333 | −0.126797 | ||||||||
\(896\) | 6.87455 | 0.229663 | ||||||||
\(897\) | 22.2470 | 0.742804 | ||||||||
\(898\) | 0.451472 | 0.0150658 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.11483 | 0.170494 | ||||||||
\(901\) | 23.7983 | 0.792837 | ||||||||
\(902\) | −0.641930 | −0.0213739 | ||||||||
\(903\) | −6.56248 | −0.218386 | ||||||||
\(904\) | −7.27213 | −0.241868 | ||||||||
\(905\) | −1.00614 | −0.0334454 | ||||||||
\(906\) | −0.947370 | −0.0314743 | ||||||||
\(907\) | 48.1396 | 1.59845 | 0.799225 | − | 0.601033i | \(-0.205244\pi\) | ||||
0.799225 | + | 0.601033i | \(0.205244\pi\) | |||||||
\(908\) | 27.0876 | 0.898932 | ||||||||
\(909\) | 4.46601 | 0.148128 | ||||||||
\(910\) | 0.897418 | 0.0297491 | ||||||||
\(911\) | 18.1251 | 0.600510 | 0.300255 | − | 0.953859i | \(-0.402928\pi\) | ||||
0.300255 | + | 0.953859i | \(0.402928\pi\) | |||||||
\(912\) | 20.3379 | 0.673456 | ||||||||
\(913\) | 8.94353 | 0.295988 | ||||||||
\(914\) | −4.13340 | −0.136721 | ||||||||
\(915\) | 21.3193 | 0.704793 | ||||||||
\(916\) | 39.9678 | 1.32057 | ||||||||
\(917\) | 25.6749 | 0.847860 | ||||||||
\(918\) | −0.507393 | −0.0167465 | ||||||||
\(919\) | −36.8715 | −1.21628 | −0.608139 | − | 0.793830i | \(-0.708084\pi\) | ||||
−0.608139 | + | 0.793830i | \(0.708084\pi\) | |||||||
\(920\) | −7.58733 | −0.250147 | ||||||||
\(921\) | 8.83474 | 0.291115 | ||||||||
\(922\) | 4.02658 | 0.132608 | ||||||||
\(923\) | 12.5951 | 0.414573 | ||||||||
\(924\) | −2.32132 | −0.0763657 | ||||||||
\(925\) | −7.76807 | −0.255413 | ||||||||
\(926\) | −2.64494 | −0.0869181 | ||||||||
\(927\) | 10.3199 | 0.338949 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.3154 | 0.830571 | 0.415285 | − | 0.909691i | \(-0.363682\pi\) | ||||
0.415285 | + | 0.909691i | \(0.363682\pi\) | |||||||
\(930\) | −0.317662 | −0.0104166 | ||||||||
\(931\) | 24.4908 | 0.802652 | ||||||||
\(932\) | 14.4182 | 0.472282 | ||||||||
\(933\) | −12.9878 | −0.425201 | ||||||||
\(934\) | 3.15899 | 0.103365 | ||||||||
\(935\) | 4.19400 | 0.137158 | ||||||||
\(936\) | 1.50412 | 0.0491636 | ||||||||
\(937\) | −50.7043 | −1.65644 | −0.828219 | − | 0.560404i | \(-0.810646\pi\) | ||||
−0.828219 | + | 0.560404i | \(0.810646\pi\) | |||||||
\(938\) | 1.60883 | 0.0525301 | ||||||||
\(939\) | −19.1428 | −0.624701 | ||||||||
\(940\) | 5.45816 | 0.178025 | ||||||||
\(941\) | 1.77666 | 0.0579175 | 0.0289587 | − | 0.999581i | \(-0.490781\pi\) | ||||
0.0289587 | + | 0.999581i | \(0.490781\pi\) | |||||||
\(942\) | 3.01498 | 0.0982332 | ||||||||
\(943\) | −49.2040 | −1.60230 | ||||||||
\(944\) | 57.9774 | 1.88700 | ||||||||
\(945\) | 2.37413 | 0.0772304 | ||||||||
\(946\) | −0.476265 | −0.0154847 | ||||||||
\(947\) | 13.6503 | 0.443575 | 0.221787 | − | 0.975095i | \(-0.428811\pi\) | ||||
0.221787 | + | 0.975095i | \(0.428811\pi\) | |||||||
\(948\) | −1.08039 | −0.0350893 | ||||||||
\(949\) | 24.0851 | 0.781835 | ||||||||
\(950\) | 1.95815 | 0.0635308 | ||||||||
\(951\) | 26.6435 | 0.863976 | ||||||||
\(952\) | 3.08406 | 0.0999549 | ||||||||
\(953\) | 28.3260 | 0.917571 | 0.458785 | − | 0.888547i | \(-0.348285\pi\) | ||||
0.458785 | + | 0.888547i | \(0.348285\pi\) | |||||||
\(954\) | 0.977695 | 0.0316540 | ||||||||
\(955\) | 32.3107 | 1.04555 | ||||||||
\(956\) | 46.2517 | 1.49589 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.38602 | −0.109397 | ||||||||
\(959\) | 27.8791 | 0.900262 | ||||||||
\(960\) | 11.6631 | 0.376424 | ||||||||
\(961\) | −28.9960 | −0.935355 | ||||||||
\(962\) | −1.13619 | −0.0366324 | ||||||||
\(963\) | −15.6906 | −0.505623 | ||||||||
\(964\) | −50.3879 | −1.62289 | ||||||||
\(965\) | −31.4627 | −1.01282 | ||||||||
\(966\) | 1.87400 | 0.0602948 | ||||||||
\(967\) | −11.7598 | −0.378169 | −0.189085 | − | 0.981961i | \(-0.560552\pi\) | ||||
−0.189085 | + | 0.981961i | \(0.560552\pi\) | |||||||
\(968\) | 5.98081 | 0.192231 | ||||||||
\(969\) | 18.4433 | 0.592483 | ||||||||
\(970\) | 0.398584 | 0.0127978 | ||||||||
\(971\) | 38.2018 | 1.22595 | 0.612976 | − | 0.790101i | \(-0.289972\pi\) | ||||
0.612976 | + | 0.790101i | \(0.289972\pi\) | |||||||
\(972\) | 1.97916 | 0.0634814 | ||||||||
\(973\) | 10.4878 | 0.336224 | ||||||||
\(974\) | −5.14344 | −0.164806 | ||||||||
\(975\) | −6.76615 | −0.216690 | ||||||||
\(976\) | −53.1579 | −1.70154 | ||||||||
\(977\) | −32.1135 | −1.02740 | −0.513701 | − | 0.857969i | \(-0.671726\pi\) | ||||
−0.513701 | + | 0.857969i | \(0.671726\pi\) | |||||||
\(978\) | −0.0360672 | −0.00115330 | ||||||||
\(979\) | −10.5792 | −0.338111 | ||||||||
\(980\) | 14.3551 | 0.458555 | ||||||||
\(981\) | −9.83683 | −0.314066 | ||||||||
\(982\) | −0.405197 | −0.0129303 | ||||||||
\(983\) | −45.1079 | −1.43872 | −0.719359 | − | 0.694638i | \(-0.755564\pi\) | ||||
−0.719359 | + | 0.694638i | \(0.755564\pi\) | |||||||
\(984\) | −3.32668 | −0.106051 | ||||||||
\(985\) | 5.35337 | 0.170573 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.71042 | −0.0862735 | ||||||||
\(988\) | −27.1934 | −0.865138 | ||||||||
\(989\) | −36.5058 | −1.16082 | ||||||||
\(990\) | 0.172300 | 0.00547605 | ||||||||
\(991\) | 6.12567 | 0.194588 | 0.0972942 | − | 0.995256i | \(-0.468981\pi\) | ||||
0.0972942 | + | 0.995256i | \(0.468981\pi\) | |||||||
\(992\) | 2.41862 | 0.0767914 | ||||||||
\(993\) | −2.21519 | −0.0702968 | ||||||||
\(994\) | 1.06096 | 0.0336517 | ||||||||
\(995\) | 18.6929 | 0.592603 | ||||||||
\(996\) | 23.0527 | 0.730452 | ||||||||
\(997\) | 34.2215 | 1.08381 | 0.541903 | − | 0.840441i | \(-0.317704\pi\) | ||||
0.541903 | + | 0.840441i | \(0.317704\pi\) | |||||||
\(998\) | 5.87040 | 0.185824 | ||||||||
\(999\) | −3.00581 | −0.0950997 |
(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 | 2523.2.a.o.1.6 | 9 | ||
3.2 | odd | 2 | 7569.2.a.bm.1.4 | 9 | |||
29.5 | even | 14 | 87.2.g.a.25.2 | yes | 18 | ||
29.6 | even | 14 | 87.2.g.a.7.2 | ✓ | 18 | ||
29.28 | even | 2 | 2523.2.a.r.1.4 | 9 | |||
87.5 | odd | 14 | 261.2.k.c.199.2 | 18 | |||
87.35 | odd | 14 | 261.2.k.c.181.2 | 18 | |||
87.86 | odd | 2 | 7569.2.a.bj.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.g.a.7.2 | ✓ | 18 | 29.6 | even | 14 | ||
87.2.g.a.25.2 | yes | 18 | 29.5 | even | 14 | ||
261.2.k.c.181.2 | 18 | 87.35 | odd | 14 | |||
261.2.k.c.199.2 | 18 | 87.5 | odd | 14 | |||
2523.2.a.o.1.6 | 9 | 1.1 | even | 1 | trivial | ||
2523.2.a.r.1.4 | 9 | 29.28 | even | 2 | |||
7569.2.a.bj.1.6 | 9 | 87.86 | odd | 2 | |||
7569.2.a.bm.1.4 | 9 | 3.2 | odd | 2 |