Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.361.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.22188\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22188 | −0.863997 | −0.431998 | − | 0.901874i | \(-0.642191\pi\) | ||||
−0.431998 | + | 0.901874i | \(0.642191\pi\) | |||||||
\(3\) | −2.28514 | −1.31933 | −0.659664 | − | 0.751561i | \(-0.729301\pi\) | ||||
−0.659664 | + | 0.751561i | \(0.729301\pi\) | |||||||
\(4\) | −0.507019 | −0.253509 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.79216 | 1.13990 | ||||||||
\(7\) | −1.28514 | −0.485738 | −0.242869 | − | 0.970059i | \(-0.578089\pi\) | ||||
−0.242869 | + | 0.970059i | \(0.578089\pi\) | |||||||
\(8\) | 3.06327 | 1.08303 | ||||||||
\(9\) | 2.22188 | 0.740625 | ||||||||
\(10\) | 1.22188 | 0.386391 | ||||||||
\(11\) | 0.285142 | 0.0859737 | 0.0429868 | − | 0.999076i | \(-0.486313\pi\) | ||||
0.0429868 | + | 0.999076i | \(0.486313\pi\) | |||||||
\(12\) | 1.15861 | 0.334462 | ||||||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 1.57028 | 0.419676 | ||||||||
\(15\) | 2.28514 | 0.590021 | ||||||||
\(16\) | −2.72889 | −0.682224 | ||||||||
\(17\) | −6.23591 | −1.51243 | −0.756216 | − | 0.654323i | \(-0.772954\pi\) | ||||
−0.756216 | + | 0.654323i | \(0.772954\pi\) | |||||||
\(18\) | −2.71486 | −0.639898 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0.507019 | 0.113373 | ||||||||
\(21\) | 2.93673 | 0.640848 | ||||||||
\(22\) | −0.348409 | −0.0742810 | ||||||||
\(23\) | −5.23591 | −1.09176 | −0.545882 | − | 0.837862i | \(-0.683805\pi\) | ||||
−0.545882 | + | 0.837862i | \(0.683805\pi\) | |||||||
\(24\) | −7.00000 | −1.42887 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.10938 | −1.19815 | ||||||||
\(27\) | 1.77812 | 0.342200 | ||||||||
\(28\) | 0.651591 | 0.123139 | ||||||||
\(29\) | −1.28514 | −0.238645 | −0.119322 | − | 0.992856i | \(-0.538072\pi\) | ||||
−0.119322 | + | 0.992856i | \(0.538072\pi\) | |||||||
\(30\) | −2.79216 | −0.509777 | ||||||||
\(31\) | 1.22188 | 0.219455 | 0.109728 | − | 0.993962i | \(-0.465002\pi\) | ||||
0.109728 | + | 0.993962i | \(0.465002\pi\) | |||||||
\(32\) | −2.79216 | −0.493589 | ||||||||
\(33\) | −0.651591 | −0.113427 | ||||||||
\(34\) | 7.61951 | 1.30674 | ||||||||
\(35\) | 1.28514 | 0.217229 | ||||||||
\(36\) | −1.12653 | −0.187755 | ||||||||
\(37\) | −10.8695 | −1.78693 | −0.893464 | − | 0.449134i | \(-0.851733\pi\) | ||||
−0.893464 | + | 0.449134i | \(0.851733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.4257 | −1.82958 | ||||||||
\(40\) | −3.06327 | −0.484345 | ||||||||
\(41\) | 0.841390 | 0.131403 | 0.0657015 | − | 0.997839i | \(-0.479071\pi\) | ||||
0.0657015 | + | 0.997839i | \(0.479071\pi\) | |||||||
\(42\) | −3.58832 | −0.553691 | ||||||||
\(43\) | −4.95077 | −0.754985 | −0.377493 | − | 0.926013i | \(-0.623214\pi\) | ||||
−0.377493 | + | 0.926013i | \(0.623214\pi\) | |||||||
\(44\) | −0.144573 | −0.0217951 | ||||||||
\(45\) | −2.22188 | −0.331218 | ||||||||
\(46\) | 6.39764 | 0.943280 | ||||||||
\(47\) | 5.72889 | 0.835645 | 0.417823 | − | 0.908529i | \(-0.362793\pi\) | ||||
0.417823 | + | 0.908529i | \(0.362793\pi\) | |||||||
\(48\) | 6.23591 | 0.900077 | ||||||||
\(49\) | −5.34841 | −0.764058 | ||||||||
\(50\) | −1.22188 | −0.172799 | ||||||||
\(51\) | 14.2500 | 1.99539 | ||||||||
\(52\) | −2.53509 | −0.351554 | ||||||||
\(53\) | −12.3624 | −1.69811 | −0.849056 | − | 0.528302i | \(-0.822829\pi\) | ||||
−0.849056 | + | 0.528302i | \(0.822829\pi\) | |||||||
\(54\) | −2.17265 | −0.295660 | ||||||||
\(55\) | −0.285142 | −0.0384486 | ||||||||
\(56\) | −3.93673 | −0.526068 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.57028 | 0.206189 | ||||||||
\(59\) | −5.72889 | −0.745839 | −0.372919 | − | 0.927864i | \(-0.621643\pi\) | ||||
−0.372919 | + | 0.927864i | \(0.621643\pi\) | |||||||
\(60\) | −1.15861 | −0.149576 | ||||||||
\(61\) | 4.45779 | 0.570761 | 0.285381 | − | 0.958414i | \(-0.407880\pi\) | ||||
0.285381 | + | 0.958414i | \(0.407880\pi\) | |||||||
\(62\) | −1.49298 | −0.189609 | ||||||||
\(63\) | −2.85543 | −0.359750 | ||||||||
\(64\) | 8.86946 | 1.10868 | ||||||||
\(65\) | −5.00000 | −0.620174 | ||||||||
\(66\) | 0.796164 | 0.0980010 | ||||||||
\(67\) | 0.985963 | 0.120455 | 0.0602273 | − | 0.998185i | \(-0.480817\pi\) | ||||
0.0602273 | + | 0.998185i | \(0.480817\pi\) | |||||||
\(68\) | 3.16172 | 0.383415 | ||||||||
\(69\) | 11.9648 | 1.44039 | ||||||||
\(70\) | −1.57028 | −0.187685 | ||||||||
\(71\) | 2.92270 | 0.346860 | 0.173430 | − | 0.984846i | \(-0.444515\pi\) | ||||
0.173430 | + | 0.984846i | \(0.444515\pi\) | |||||||
\(72\) | 6.80620 | 0.802118 | ||||||||
\(73\) | −0.764087 | −0.0894296 | −0.0447148 | − | 0.999000i | \(-0.514238\pi\) | ||||
−0.0447148 | + | 0.999000i | \(0.514238\pi\) | |||||||
\(74\) | 13.2811 | 1.54390 | ||||||||
\(75\) | −2.28514 | −0.263866 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.366449 | −0.0417607 | ||||||||
\(78\) | 13.9608 | 1.58075 | ||||||||
\(79\) | 15.4578 | 1.73914 | 0.869569 | − | 0.493812i | \(-0.164397\pi\) | ||||
0.869569 | + | 0.493812i | \(0.164397\pi\) | |||||||
\(80\) | 2.72889 | 0.305100 | ||||||||
\(81\) | −10.7289 | −1.19210 | ||||||||
\(82\) | −1.02807 | −0.113532 | ||||||||
\(83\) | 1.66563 | 0.182826 | 0.0914132 | − | 0.995813i | \(-0.470862\pi\) | ||||
0.0914132 | + | 0.995813i | \(0.470862\pi\) | |||||||
\(84\) | −1.48898 | −0.162461 | ||||||||
\(85\) | 6.23591 | 0.676380 | ||||||||
\(86\) | 6.04923 | 0.652305 | ||||||||
\(87\) | 2.93673 | 0.314851 | ||||||||
\(88\) | 0.873467 | 0.0931119 | ||||||||
\(89\) | 16.0281 | 1.69897 | 0.849486 | − | 0.527611i | \(-0.176912\pi\) | ||||
0.849486 | + | 0.527611i | \(0.176912\pi\) | |||||||
\(90\) | 2.71486 | 0.286171 | ||||||||
\(91\) | −6.42571 | −0.673598 | ||||||||
\(92\) | 2.65471 | 0.276772 | ||||||||
\(93\) | −2.79216 | −0.289534 | ||||||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.38049 | 0.651206 | ||||||||
\(97\) | −11.7429 | −1.19231 | −0.596157 | − | 0.802868i | \(-0.703306\pi\) | ||||
−0.596157 | + | 0.802868i | \(0.703306\pi\) | |||||||
\(98\) | 6.53509 | 0.660144 | ||||||||
\(99\) | 0.633551 | 0.0636743 | ||||||||
\(100\) | −0.507019 | −0.0507019 | ||||||||
\(101\) | −7.91869 | −0.787939 | −0.393970 | − | 0.919123i | \(-0.628899\pi\) | ||||
−0.393970 | + | 0.919123i | \(0.628899\pi\) | |||||||
\(102\) | −17.4117 | −1.72401 | ||||||||
\(103\) | 12.8202 | 1.26322 | 0.631608 | − | 0.775288i | \(-0.282395\pi\) | ||||
0.631608 | + | 0.775288i | \(0.282395\pi\) | |||||||
\(104\) | 15.3163 | 1.50189 | ||||||||
\(105\) | −2.93673 | −0.286596 | ||||||||
\(106\) | 15.1054 | 1.46716 | ||||||||
\(107\) | −13.8062 | −1.33470 | −0.667348 | − | 0.744746i | \(-0.732571\pi\) | ||||
−0.667348 | + | 0.744746i | \(0.732571\pi\) | |||||||
\(108\) | −0.901542 | −0.0867509 | ||||||||
\(109\) | 9.20384 | 0.881568 | 0.440784 | − | 0.897613i | \(-0.354701\pi\) | ||||
0.440784 | + | 0.897613i | \(0.354701\pi\) | |||||||
\(110\) | 0.348409 | 0.0332195 | ||||||||
\(111\) | 24.8383 | 2.35754 | ||||||||
\(112\) | 3.50702 | 0.331382 | ||||||||
\(113\) | 17.3273 | 1.63001 | 0.815005 | − | 0.579453i | \(-0.196734\pi\) | ||||
0.815005 | + | 0.579453i | \(0.196734\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.23591 | 0.488251 | ||||||||
\(116\) | 0.651591 | 0.0604987 | ||||||||
\(117\) | 11.1094 | 1.02706 | ||||||||
\(118\) | 7.00000 | 0.644402 | ||||||||
\(119\) | 8.01404 | 0.734646 | ||||||||
\(120\) | 7.00000 | 0.639010 | ||||||||
\(121\) | −10.9187 | −0.992609 | ||||||||
\(122\) | −5.44687 | −0.493136 | ||||||||
\(123\) | −1.92270 | −0.173364 | ||||||||
\(124\) | −0.619514 | −0.0556340 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.48898 | 0.310823 | ||||||||
\(127\) | −9.33126 | −0.828015 | −0.414008 | − | 0.910273i | \(-0.635871\pi\) | ||||
−0.414008 | + | 0.910273i | \(0.635871\pi\) | |||||||
\(128\) | −5.25307 | −0.464310 | ||||||||
\(129\) | 11.3132 | 0.996073 | ||||||||
\(130\) | 6.10938 | 0.535828 | ||||||||
\(131\) | 12.4257 | 1.08564 | 0.542820 | − | 0.839849i | \(-0.317357\pi\) | ||||
0.542820 | + | 0.839849i | \(0.317357\pi\) | |||||||
\(132\) | 0.330369 | 0.0287549 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.20472 | −0.104072 | ||||||||
\(135\) | −1.77812 | −0.153037 | ||||||||
\(136\) | −19.1023 | −1.63801 | ||||||||
\(137\) | −18.5351 | −1.58356 | −0.791780 | − | 0.610806i | \(-0.790845\pi\) | ||||
−0.791780 | + | 0.610806i | \(0.790845\pi\) | |||||||
\(138\) | −14.6195 | −1.24450 | ||||||||
\(139\) | −6.01404 | −0.510104 | −0.255052 | − | 0.966927i | \(-0.582093\pi\) | ||||
−0.255052 | + | 0.966927i | \(0.582093\pi\) | |||||||
\(140\) | −0.651591 | −0.0550695 | ||||||||
\(141\) | −13.0913 | −1.10249 | ||||||||
\(142\) | −3.57117 | −0.299686 | ||||||||
\(143\) | 1.42571 | 0.119224 | ||||||||
\(144\) | −6.06327 | −0.505272 | ||||||||
\(145\) | 1.28514 | 0.106725 | ||||||||
\(146\) | 0.933619 | 0.0772669 | ||||||||
\(147\) | 12.2219 | 1.00804 | ||||||||
\(148\) | 5.51102 | 0.453003 | ||||||||
\(149\) | −6.79216 | −0.556436 | −0.278218 | − | 0.960518i | \(-0.589744\pi\) | ||||
−0.278218 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(150\) | 2.79216 | 0.227979 | ||||||||
\(151\) | 15.8875 | 1.29291 | 0.646453 | − | 0.762953i | \(-0.276251\pi\) | ||||
0.646453 | + | 0.762953i | \(0.276251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.8554 | −1.12014 | ||||||||
\(154\) | 0.447755 | 0.0360811 | ||||||||
\(155\) | −1.22188 | −0.0981435 | ||||||||
\(156\) | 5.79305 | 0.463815 | ||||||||
\(157\) | 7.50702 | 0.599125 | 0.299563 | − | 0.954077i | \(-0.403159\pi\) | ||||
0.299563 | + | 0.954077i | \(0.403159\pi\) | |||||||
\(158\) | −18.8875 | −1.50261 | ||||||||
\(159\) | 28.2500 | 2.24037 | ||||||||
\(160\) | 2.79216 | 0.220740 | ||||||||
\(161\) | 6.72889 | 0.530311 | ||||||||
\(162\) | 13.1094 | 1.02997 | ||||||||
\(163\) | 21.8202 | 1.70909 | 0.854546 | − | 0.519375i | \(-0.173835\pi\) | ||||
0.854546 | + | 0.519375i | \(0.173835\pi\) | |||||||
\(164\) | −0.426600 | −0.0333119 | ||||||||
\(165\) | 0.651591 | 0.0507263 | ||||||||
\(166\) | −2.03519 | −0.157962 | ||||||||
\(167\) | −11.2851 | −0.873271 | −0.436635 | − | 0.899639i | \(-0.643830\pi\) | ||||
−0.436635 | + | 0.899639i | \(0.643830\pi\) | |||||||
\(168\) | 8.99600 | 0.694056 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | −7.61951 | −0.584390 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.51013 | 0.191396 | ||||||||
\(173\) | 5.85543 | 0.445180 | 0.222590 | − | 0.974912i | \(-0.428549\pi\) | ||||
0.222590 | + | 0.974912i | \(0.428549\pi\) | |||||||
\(174\) | −3.58832 | −0.272030 | ||||||||
\(175\) | −1.28514 | −0.0971476 | ||||||||
\(176\) | −0.778124 | −0.0586533 | ||||||||
\(177\) | 13.0913 | 0.984005 | ||||||||
\(178\) | −19.5843 | −1.46791 | ||||||||
\(179\) | 18.7922 | 1.40459 | 0.702296 | − | 0.711885i | \(-0.252158\pi\) | ||||
0.702296 | + | 0.711885i | \(0.252158\pi\) | |||||||
\(180\) | 1.12653 | 0.0839668 | ||||||||
\(181\) | −13.3453 | −0.991948 | −0.495974 | − | 0.868337i | \(-0.665189\pi\) | ||||
−0.495974 | + | 0.868337i | \(0.665189\pi\) | |||||||
\(182\) | 7.85142 | 0.581986 | ||||||||
\(183\) | −10.1867 | −0.753021 | ||||||||
\(184\) | −16.0390 | −1.18241 | ||||||||
\(185\) | 10.8695 | 0.799139 | ||||||||
\(186\) | 3.41168 | 0.250156 | ||||||||
\(187\) | −1.77812 | −0.130029 | ||||||||
\(188\) | −2.90466 | −0.211844 | ||||||||
\(189\) | −2.28514 | −0.166220 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.668743 | −0.0483885 | −0.0241943 | − | 0.999707i | \(-0.507702\pi\) | ||||
−0.0241943 | + | 0.999707i | \(0.507702\pi\) | |||||||
\(192\) | −20.2680 | −1.46272 | ||||||||
\(193\) | 3.76409 | 0.270945 | 0.135472 | − | 0.990781i | \(-0.456745\pi\) | ||||
0.135472 | + | 0.990781i | \(0.456745\pi\) | |||||||
\(194\) | 14.3484 | 1.03016 | ||||||||
\(195\) | 11.4257 | 0.818212 | ||||||||
\(196\) | 2.71174 | 0.193696 | ||||||||
\(197\) | 14.6164 | 1.04138 | 0.520688 | − | 0.853747i | \(-0.325676\pi\) | ||||
0.520688 | + | 0.853747i | \(0.325676\pi\) | |||||||
\(198\) | −0.774121 | −0.0550144 | ||||||||
\(199\) | 11.5211 | 0.816706 | 0.408353 | − | 0.912824i | \(-0.366103\pi\) | ||||
0.408353 | + | 0.912824i | \(0.366103\pi\) | |||||||
\(200\) | 3.06327 | 0.216606 | ||||||||
\(201\) | −2.25307 | −0.158919 | ||||||||
\(202\) | 9.67566 | 0.680777 | ||||||||
\(203\) | 1.65159 | 0.115919 | ||||||||
\(204\) | −7.22499 | −0.505851 | ||||||||
\(205\) | −0.841390 | −0.0587652 | ||||||||
\(206\) | −15.6647 | −1.09141 | ||||||||
\(207\) | −11.6336 | −0.808588 | ||||||||
\(208\) | −13.6445 | −0.946074 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.58832 | 0.247618 | ||||||||
\(211\) | 17.1406 | 1.18001 | 0.590003 | − | 0.807401i | \(-0.299127\pi\) | ||||
0.590003 | + | 0.807401i | \(0.299127\pi\) | |||||||
\(212\) | 6.26799 | 0.430487 | ||||||||
\(213\) | −6.67878 | −0.457622 | ||||||||
\(214\) | 16.8695 | 1.15317 | ||||||||
\(215\) | 4.95077 | 0.337640 | ||||||||
\(216\) | 5.44687 | 0.370612 | ||||||||
\(217\) | −1.57028 | −0.106598 | ||||||||
\(218\) | −11.2459 | −0.761672 | ||||||||
\(219\) | 1.74605 | 0.117987 | ||||||||
\(220\) | 0.144573 | 0.00974708 | ||||||||
\(221\) | −31.1796 | −2.09736 | ||||||||
\(222\) | −30.3493 | −2.03691 | ||||||||
\(223\) | −1.52417 | −0.102066 | −0.0510330 | − | 0.998697i | \(-0.516251\pi\) | ||||
−0.0510330 | + | 0.998697i | \(0.516251\pi\) | |||||||
\(224\) | 3.58832 | 0.239755 | ||||||||
\(225\) | 2.22188 | 0.148125 | ||||||||
\(226\) | −21.1718 | −1.40832 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4397 | 1.21853 | 0.609266 | − | 0.792966i | \(-0.291464\pi\) | ||||
0.609266 | + | 0.792966i | \(0.291464\pi\) | |||||||
\(230\) | −6.39764 | −0.421848 | ||||||||
\(231\) | 0.837388 | 0.0550961 | ||||||||
\(232\) | −3.93673 | −0.258459 | ||||||||
\(233\) | 12.7117 | 0.832774 | 0.416387 | − | 0.909187i | \(-0.363296\pi\) | ||||
0.416387 | + | 0.909187i | \(0.363296\pi\) | |||||||
\(234\) | −13.5743 | −0.887379 | ||||||||
\(235\) | −5.72889 | −0.373712 | ||||||||
\(236\) | 2.90466 | 0.189077 | ||||||||
\(237\) | −35.3233 | −2.29449 | ||||||||
\(238\) | −9.79216 | −0.634732 | ||||||||
\(239\) | −10.8343 | −0.700811 | −0.350405 | − | 0.936598i | \(-0.613956\pi\) | ||||
−0.350405 | + | 0.936598i | \(0.613956\pi\) | |||||||
\(240\) | −6.23591 | −0.402526 | ||||||||
\(241\) | 9.87347 | 0.636006 | 0.318003 | − | 0.948090i | \(-0.396988\pi\) | ||||
0.318003 | + | 0.948090i | \(0.396988\pi\) | |||||||
\(242\) | 13.3413 | 0.857611 | ||||||||
\(243\) | 19.1827 | 1.23057 | ||||||||
\(244\) | −2.26018 | −0.144693 | ||||||||
\(245\) | 5.34841 | 0.341697 | ||||||||
\(246\) | 2.34930 | 0.149786 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.74293 | 0.237676 | ||||||||
\(249\) | −3.80620 | −0.241208 | ||||||||
\(250\) | 1.22188 | 0.0772782 | ||||||||
\(251\) | 17.7710 | 1.12170 | 0.560848 | − | 0.827919i | \(-0.310475\pi\) | ||||
0.560848 | + | 0.827919i | \(0.310475\pi\) | |||||||
\(252\) | 1.44775 | 0.0912000 | ||||||||
\(253\) | −1.49298 | −0.0938629 | ||||||||
\(254\) | 11.4016 | 0.715403 | ||||||||
\(255\) | −14.2500 | −0.892367 | ||||||||
\(256\) | −11.3203 | −0.707521 | ||||||||
\(257\) | −8.15861 | −0.508920 | −0.254460 | − | 0.967083i | \(-0.581898\pi\) | ||||
−0.254460 | + | 0.967083i | \(0.581898\pi\) | |||||||
\(258\) | −13.8234 | −0.860604 | ||||||||
\(259\) | 13.9688 | 0.867980 | ||||||||
\(260\) | 2.53509 | 0.157220 | ||||||||
\(261\) | −2.85543 | −0.176747 | ||||||||
\(262\) | −15.1827 | −0.937989 | ||||||||
\(263\) | 6.31722 | 0.389536 | 0.194768 | − | 0.980849i | \(-0.437605\pi\) | ||||
0.194768 | + | 0.980849i | \(0.437605\pi\) | |||||||
\(264\) | −1.99600 | −0.122845 | ||||||||
\(265\) | 12.3624 | 0.759419 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.6264 | −2.24150 | ||||||||
\(268\) | −0.499901 | −0.0305363 | ||||||||
\(269\) | −8.23903 | −0.502342 | −0.251171 | − | 0.967943i | \(-0.580816\pi\) | ||||
−0.251171 | + | 0.967943i | \(0.580816\pi\) | |||||||
\(270\) | 2.17265 | 0.132223 | ||||||||
\(271\) | −4.22188 | −0.256461 | −0.128230 | − | 0.991744i | \(-0.540930\pi\) | ||||
−0.128230 | + | 0.991744i | \(0.540930\pi\) | |||||||
\(272\) | 17.0172 | 1.03182 | ||||||||
\(273\) | 14.6837 | 0.888696 | ||||||||
\(274\) | 22.6476 | 1.36819 | ||||||||
\(275\) | 0.285142 | 0.0171947 | ||||||||
\(276\) | −6.06638 | −0.365153 | ||||||||
\(277\) | −9.83739 | −0.591071 | −0.295536 | − | 0.955332i | \(-0.595498\pi\) | ||||
−0.295536 | + | 0.955332i | \(0.595498\pi\) | |||||||
\(278\) | 7.34841 | 0.440728 | ||||||||
\(279\) | 2.71486 | 0.162534 | ||||||||
\(280\) | 3.93673 | 0.235265 | ||||||||
\(281\) | −5.38049 | −0.320973 | −0.160486 | − | 0.987038i | \(-0.551306\pi\) | ||||
−0.160486 | + | 0.987038i | \(0.551306\pi\) | |||||||
\(282\) | 15.9960 | 0.952548 | ||||||||
\(283\) | −4.96481 | −0.295127 | −0.147564 | − | 0.989053i | \(-0.547143\pi\) | ||||
−0.147564 | + | 0.989053i | \(0.547143\pi\) | |||||||
\(284\) | −1.48186 | −0.0879323 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.74204 | −0.103009 | ||||||||
\(287\) | −1.08131 | −0.0638275 | ||||||||
\(288\) | −6.20384 | −0.365565 | ||||||||
\(289\) | 21.8866 | 1.28745 | ||||||||
\(290\) | −1.57028 | −0.0922103 | ||||||||
\(291\) | 26.8343 | 1.57305 | ||||||||
\(292\) | 0.387406 | 0.0226712 | ||||||||
\(293\) | 3.80620 | 0.222360 | 0.111180 | − | 0.993800i | \(-0.464537\pi\) | ||||
0.111180 | + | 0.993800i | \(0.464537\pi\) | |||||||
\(294\) | −14.9336 | −0.870946 | ||||||||
\(295\) | 5.72889 | 0.333549 | ||||||||
\(296\) | −33.2961 | −1.93529 | ||||||||
\(297\) | 0.507019 | 0.0294202 | ||||||||
\(298\) | 8.29918 | 0.480759 | ||||||||
\(299\) | −26.1796 | −1.51400 | ||||||||
\(300\) | 1.15861 | 0.0668924 | ||||||||
\(301\) | 6.36245 | 0.366725 | ||||||||
\(302\) | −19.4126 | −1.11707 | ||||||||
\(303\) | 18.0953 | 1.03955 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.45779 | −0.255252 | ||||||||
\(306\) | 16.9296 | 0.967802 | ||||||||
\(307\) | −0.574288 | −0.0327763 | −0.0163882 | − | 0.999866i | \(-0.505217\pi\) | ||||
−0.0163882 | + | 0.999866i | \(0.505217\pi\) | |||||||
\(308\) | 0.185796 | 0.0105867 | ||||||||
\(309\) | −29.2961 | −1.66659 | ||||||||
\(310\) | 1.49298 | 0.0847956 | ||||||||
\(311\) | −8.61640 | −0.488591 | −0.244296 | − | 0.969701i | \(-0.578557\pi\) | ||||
−0.244296 | + | 0.969701i | \(0.578557\pi\) | |||||||
\(312\) | −35.0000 | −1.98148 | ||||||||
\(313\) | −34.1234 | −1.92877 | −0.964385 | − | 0.264503i | \(-0.914792\pi\) | ||||
−0.964385 | + | 0.264503i | \(0.914792\pi\) | |||||||
\(314\) | −9.17265 | −0.517642 | ||||||||
\(315\) | 2.85543 | 0.160885 | ||||||||
\(316\) | −7.83739 | −0.440887 | ||||||||
\(317\) | 11.0773 | 0.622163 | 0.311082 | − | 0.950383i | \(-0.399309\pi\) | ||||
0.311082 | + | 0.950383i | \(0.399309\pi\) | |||||||
\(318\) | −34.5179 | −1.93567 | ||||||||
\(319\) | −0.366449 | −0.0205172 | ||||||||
\(320\) | −8.86946 | −0.495818 | ||||||||
\(321\) | 31.5491 | 1.76090 | ||||||||
\(322\) | −8.22188 | −0.458187 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.43975 | 0.302208 | ||||||||
\(325\) | 5.00000 | 0.277350 | ||||||||
\(326\) | −26.6616 | −1.47665 | ||||||||
\(327\) | −21.0321 | −1.16308 | ||||||||
\(328\) | 2.57740 | 0.142313 | ||||||||
\(329\) | −7.36245 | −0.405905 | ||||||||
\(330\) | −0.796164 | −0.0438274 | ||||||||
\(331\) | −6.41168 | −0.352418 | −0.176209 | − | 0.984353i | \(-0.556383\pi\) | ||||
−0.176209 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(332\) | −0.844505 | −0.0463482 | ||||||||
\(333\) | −24.1506 | −1.32344 | ||||||||
\(334\) | 13.7890 | 0.754503 | ||||||||
\(335\) | −0.985963 | −0.0538689 | ||||||||
\(336\) | −8.01404 | −0.437202 | ||||||||
\(337\) | 25.2671 | 1.37639 | 0.688193 | − | 0.725527i | \(-0.258404\pi\) | ||||
0.688193 | + | 0.725527i | \(0.258404\pi\) | |||||||
\(338\) | −14.6625 | −0.797536 | ||||||||
\(339\) | −39.5952 | −2.15052 | ||||||||
\(340\) | −3.16172 | −0.171469 | ||||||||
\(341\) | 0.348409 | 0.0188674 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.8695 | 0.856871 | ||||||||
\(344\) | −15.1655 | −0.817671 | ||||||||
\(345\) | −11.9648 | −0.644164 | ||||||||
\(346\) | −7.15461 | −0.384634 | ||||||||
\(347\) | 12.4086 | 0.666126 | 0.333063 | − | 0.942904i | \(-0.391918\pi\) | ||||
0.333063 | + | 0.942904i | \(0.391918\pi\) | |||||||
\(348\) | −1.48898 | −0.0798176 | ||||||||
\(349\) | 6.20384 | 0.332084 | 0.166042 | − | 0.986119i | \(-0.446901\pi\) | ||||
0.166042 | + | 0.986119i | \(0.446901\pi\) | |||||||
\(350\) | 1.57028 | 0.0839353 | ||||||||
\(351\) | 8.89062 | 0.474546 | ||||||||
\(352\) | −0.796164 | −0.0424357 | ||||||||
\(353\) | −23.3484 | −1.24271 | −0.621355 | − | 0.783529i | \(-0.713418\pi\) | ||||
−0.621355 | + | 0.783529i | \(0.713418\pi\) | |||||||
\(354\) | −15.9960 | −0.850178 | ||||||||
\(355\) | −2.92270 | −0.155121 | ||||||||
\(356\) | −8.12653 | −0.430705 | ||||||||
\(357\) | −18.3132 | −0.969238 | ||||||||
\(358\) | −22.9617 | −1.21356 | ||||||||
\(359\) | −37.7218 | −1.99088 | −0.995440 | − | 0.0953935i | \(-0.969589\pi\) | ||||
−0.995440 | + | 0.0953935i | \(0.969589\pi\) | |||||||
\(360\) | −6.80620 | −0.358718 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 16.3063 | 0.857040 | ||||||||
\(363\) | 24.9508 | 1.30958 | ||||||||
\(364\) | 3.25796 | 0.170763 | ||||||||
\(365\) | 0.764087 | 0.0399941 | ||||||||
\(366\) | 12.4469 | 0.650608 | ||||||||
\(367\) | 29.4077 | 1.53507 | 0.767534 | − | 0.641008i | \(-0.221484\pi\) | ||||
0.767534 | + | 0.641008i | \(0.221484\pi\) | |||||||
\(368\) | 14.2883 | 0.744827 | ||||||||
\(369\) | 1.86946 | 0.0973204 | ||||||||
\(370\) | −13.2811 | −0.690454 | ||||||||
\(371\) | 15.8875 | 0.824838 | ||||||||
\(372\) | 1.41568 | 0.0733995 | ||||||||
\(373\) | 21.5491 | 1.11577 | 0.557886 | − | 0.829918i | \(-0.311613\pi\) | ||||
0.557886 | + | 0.829918i | \(0.311613\pi\) | |||||||
\(374\) | 2.17265 | 0.112345 | ||||||||
\(375\) | 2.28514 | 0.118004 | ||||||||
\(376\) | 17.5491 | 0.905027 | ||||||||
\(377\) | −6.42571 | −0.330941 | ||||||||
\(378\) | 2.79216 | 0.143613 | ||||||||
\(379\) | 19.3945 | 0.996230 | 0.498115 | − | 0.867111i | \(-0.334026\pi\) | ||||
0.498115 | + | 0.867111i | \(0.334026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.3233 | 1.09242 | ||||||||
\(382\) | 0.817121 | 0.0418076 | ||||||||
\(383\) | −18.8866 | −0.965061 | −0.482531 | − | 0.875879i | \(-0.660282\pi\) | ||||
−0.482531 | + | 0.875879i | \(0.660282\pi\) | |||||||
\(384\) | 12.0040 | 0.612577 | ||||||||
\(385\) | 0.366449 | 0.0186760 | ||||||||
\(386\) | −4.59925 | −0.234096 | ||||||||
\(387\) | −11.0000 | −0.559161 | ||||||||
\(388\) | 5.95389 | 0.302263 | ||||||||
\(389\) | −9.08042 | −0.460395 | −0.230198 | − | 0.973144i | \(-0.573937\pi\) | ||||
−0.230198 | + | 0.973144i | \(0.573937\pi\) | |||||||
\(390\) | −13.9608 | −0.706933 | ||||||||
\(391\) | 32.6507 | 1.65122 | ||||||||
\(392\) | −16.3836 | −0.827497 | ||||||||
\(393\) | −28.3945 | −1.43231 | ||||||||
\(394\) | −17.8594 | −0.899745 | ||||||||
\(395\) | −15.4578 | −0.777766 | ||||||||
\(396\) | −0.321222 | −0.0161420 | ||||||||
\(397\) | 16.9960 | 0.853005 | 0.426502 | − | 0.904486i | \(-0.359746\pi\) | ||||
0.426502 | + | 0.904486i | \(0.359746\pi\) | |||||||
\(398\) | −14.0773 | −0.705631 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.72889 | −0.136445 | ||||||||
\(401\) | −1.59144 | −0.0794727 | −0.0397363 | − | 0.999210i | \(-0.512652\pi\) | ||||
−0.0397363 | + | 0.999210i | \(0.512652\pi\) | |||||||
\(402\) | 2.75297 | 0.137306 | ||||||||
\(403\) | 6.10938 | 0.304330 | ||||||||
\(404\) | 4.01493 | 0.199750 | ||||||||
\(405\) | 10.7289 | 0.533123 | ||||||||
\(406\) | −2.01804 | −0.100154 | ||||||||
\(407\) | −3.09935 | −0.153629 | ||||||||
\(408\) | 43.6514 | 2.16107 | ||||||||
\(409\) | 1.99689 | 0.0987396 | 0.0493698 | − | 0.998781i | \(-0.484279\pi\) | ||||
0.0493698 | + | 0.998781i | \(0.484279\pi\) | |||||||
\(410\) | 1.02807 | 0.0507730 | ||||||||
\(411\) | 42.3553 | 2.08923 | ||||||||
\(412\) | −6.50010 | −0.320237 | ||||||||
\(413\) | 7.36245 | 0.362282 | ||||||||
\(414\) | 14.2148 | 0.698617 | ||||||||
\(415\) | −1.66563 | −0.0817625 | ||||||||
\(416\) | −13.9608 | −0.684485 | ||||||||
\(417\) | 13.7429 | 0.672994 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.7781 | −1.11278 | −0.556392 | − | 0.830920i | \(-0.687815\pi\) | ||||
−0.556392 | + | 0.830920i | \(0.687815\pi\) | |||||||
\(420\) | 1.48898 | 0.0726547 | ||||||||
\(421\) | 13.8414 | 0.674588 | 0.337294 | − | 0.941399i | \(-0.390488\pi\) | ||||
0.337294 | + | 0.941399i | \(0.390488\pi\) | |||||||
\(422\) | −20.9437 | −1.01952 | ||||||||
\(423\) | 12.7289 | 0.618900 | ||||||||
\(424\) | −37.8695 | −1.83910 | ||||||||
\(425\) | −6.23591 | −0.302486 | ||||||||
\(426\) | 8.16064 | 0.395384 | ||||||||
\(427\) | −5.72889 | −0.277241 | ||||||||
\(428\) | 7.00000 | 0.338358 | ||||||||
\(429\) | −3.25796 | −0.157296 | ||||||||
\(430\) | −6.04923 | −0.291720 | ||||||||
\(431\) | −3.43975 | −0.165687 | −0.0828435 | − | 0.996563i | \(-0.526400\pi\) | ||||
−0.0828435 | + | 0.996563i | \(0.526400\pi\) | |||||||
\(432\) | −4.85231 | −0.233457 | ||||||||
\(433\) | 9.20072 | 0.442158 | 0.221079 | − | 0.975256i | \(-0.429042\pi\) | ||||
0.221079 | + | 0.975256i | \(0.429042\pi\) | |||||||
\(434\) | 1.91869 | 0.0921002 | ||||||||
\(435\) | −2.93673 | −0.140806 | ||||||||
\(436\) | −4.66652 | −0.223486 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −2.13345 | −0.101940 | ||||||||
\(439\) | 37.5099 | 1.79025 | 0.895126 | − | 0.445814i | \(-0.147086\pi\) | ||||
0.895126 | + | 0.445814i | \(0.147086\pi\) | |||||||
\(440\) | −0.873467 | −0.0416409 | ||||||||
\(441\) | −11.8835 | −0.565881 | ||||||||
\(442\) | 38.0976 | 1.81212 | ||||||||
\(443\) | 14.6788 | 0.697410 | 0.348705 | − | 0.937233i | \(-0.386622\pi\) | ||||
0.348705 | + | 0.937233i | \(0.386622\pi\) | |||||||
\(444\) | −12.5935 | −0.597660 | ||||||||
\(445\) | −16.0281 | −0.759804 | ||||||||
\(446\) | 1.86235 | 0.0881847 | ||||||||
\(447\) | 15.5211 | 0.734121 | ||||||||
\(448\) | −11.3985 | −0.538530 | ||||||||
\(449\) | 7.39052 | 0.348780 | 0.174390 | − | 0.984677i | \(-0.444205\pi\) | ||||
0.174390 | + | 0.984677i | \(0.444205\pi\) | |||||||
\(450\) | −2.71486 | −0.127980 | ||||||||
\(451\) | 0.239916 | 0.0112972 | ||||||||
\(452\) | −8.78524 | −0.413223 | ||||||||
\(453\) | −36.3052 | −1.70577 | ||||||||
\(454\) | 4.88750 | 0.229382 | ||||||||
\(455\) | 6.42571 | 0.301242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.30007 | 0.107593 | 0.0537963 | − | 0.998552i | \(-0.482868\pi\) | ||||
0.0537963 | + | 0.998552i | \(0.482868\pi\) | |||||||
\(458\) | −22.5311 | −1.05281 | ||||||||
\(459\) | −11.0882 | −0.517554 | ||||||||
\(460\) | −2.65471 | −0.123776 | ||||||||
\(461\) | 19.7570 | 0.920174 | 0.460087 | − | 0.887874i | \(-0.347818\pi\) | ||||
0.460087 | + | 0.887874i | \(0.347818\pi\) | |||||||
\(462\) | −1.02318 | −0.0476028 | ||||||||
\(463\) | 28.9468 | 1.34527 | 0.672635 | − | 0.739974i | \(-0.265162\pi\) | ||||
0.672635 | + | 0.739974i | \(0.265162\pi\) | |||||||
\(464\) | 3.50702 | 0.162809 | ||||||||
\(465\) | 2.79216 | 0.129483 | ||||||||
\(466\) | −15.5322 | −0.719514 | ||||||||
\(467\) | −3.31722 | −0.153503 | −0.0767513 | − | 0.997050i | \(-0.524455\pi\) | ||||
−0.0767513 | + | 0.997050i | \(0.524455\pi\) | |||||||
\(468\) | −5.63266 | −0.260370 | ||||||||
\(469\) | −1.26710 | −0.0585094 | ||||||||
\(470\) | 7.00000 | 0.322886 | ||||||||
\(471\) | −17.1546 | −0.790443 | ||||||||
\(472\) | −17.5491 | −0.807764 | ||||||||
\(473\) | −1.41168 | −0.0649089 | ||||||||
\(474\) | 43.1606 | 1.98243 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.06327 | −0.186240 | ||||||||
\(477\) | −27.4678 | −1.25767 | ||||||||
\(478\) | 13.2381 | 0.605498 | ||||||||
\(479\) | −39.5070 | −1.80512 | −0.902561 | − | 0.430562i | \(-0.858315\pi\) | ||||
−0.902561 | + | 0.430562i | \(0.858315\pi\) | |||||||
\(480\) | −6.38049 | −0.291228 | ||||||||
\(481\) | −54.3473 | −2.47802 | ||||||||
\(482\) | −12.0642 | −0.549507 | ||||||||
\(483\) | −15.3765 | −0.699654 | ||||||||
\(484\) | 5.53598 | 0.251636 | ||||||||
\(485\) | 11.7429 | 0.533219 | ||||||||
\(486\) | −23.4389 | −1.06321 | ||||||||
\(487\) | 24.7781 | 1.12280 | 0.561402 | − | 0.827543i | \(-0.310262\pi\) | ||||
0.561402 | + | 0.827543i | \(0.310262\pi\) | |||||||
\(488\) | 13.6554 | 0.618151 | ||||||||
\(489\) | −49.8623 | −2.25485 | ||||||||
\(490\) | −6.53509 | −0.295225 | ||||||||
\(491\) | −13.6235 | −0.614821 | −0.307410 | − | 0.951577i | \(-0.599462\pi\) | ||||
−0.307410 | + | 0.951577i | \(0.599462\pi\) | |||||||
\(492\) | 0.974843 | 0.0439493 | ||||||||
\(493\) | 8.01404 | 0.360934 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.633551 | −0.0284760 | ||||||||
\(496\) | −3.33437 | −0.149718 | ||||||||
\(497\) | −3.75608 | −0.168483 | ||||||||
\(498\) | 4.65070 | 0.208403 | ||||||||
\(499\) | 8.18980 | 0.366626 | 0.183313 | − | 0.983055i | \(-0.441318\pi\) | ||||
0.183313 | + | 0.983055i | \(0.441318\pi\) | |||||||
\(500\) | 0.507019 | 0.0226746 | ||||||||
\(501\) | 25.7882 | 1.15213 | ||||||||
\(502\) | −21.7140 | −0.969142 | ||||||||
\(503\) | 18.2851 | 0.815294 | 0.407647 | − | 0.913140i | \(-0.366349\pi\) | ||||
0.407647 | + | 0.913140i | \(0.366349\pi\) | |||||||
\(504\) | −8.74693 | −0.389619 | ||||||||
\(505\) | 7.91869 | 0.352377 | ||||||||
\(506\) | 1.82424 | 0.0810973 | ||||||||
\(507\) | −27.4217 | −1.21784 | ||||||||
\(508\) | 4.73112 | 0.209910 | ||||||||
\(509\) | −11.8844 | −0.526766 | −0.263383 | − | 0.964691i | \(-0.584838\pi\) | ||||
−0.263383 | + | 0.964691i | \(0.584838\pi\) | |||||||
\(510\) | 17.4117 | 0.771002 | ||||||||
\(511\) | 0.981960 | 0.0434394 | ||||||||
\(512\) | 24.3382 | 1.07561 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.96881 | 0.439705 | ||||||||
\(515\) | −12.8202 | −0.564927 | ||||||||
\(516\) | −5.73601 | −0.252514 | ||||||||
\(517\) | 1.63355 | 0.0718435 | ||||||||
\(518\) | −17.0682 | −0.749932 | ||||||||
\(519\) | −13.3805 | −0.587338 | ||||||||
\(520\) | −15.3163 | −0.671666 | ||||||||
\(521\) | −21.3725 | −0.936345 | −0.468173 | − | 0.883637i | \(-0.655087\pi\) | ||||
−0.468173 | + | 0.883637i | \(0.655087\pi\) | |||||||
\(522\) | 3.48898 | 0.152708 | ||||||||
\(523\) | 5.77724 | 0.252621 | 0.126310 | − | 0.991991i | \(-0.459686\pi\) | ||||
0.126310 | + | 0.991991i | \(0.459686\pi\) | |||||||
\(524\) | −6.30007 | −0.275220 | ||||||||
\(525\) | 2.93673 | 0.128170 | ||||||||
\(526\) | −7.71886 | −0.336558 | ||||||||
\(527\) | −7.61951 | −0.331911 | ||||||||
\(528\) | 1.77812 | 0.0773829 | ||||||||
\(529\) | 4.41479 | 0.191947 | ||||||||
\(530\) | −15.1054 | −0.656136 | ||||||||
\(531\) | −12.7289 | −0.552387 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.20695 | 0.182223 | ||||||||
\(534\) | 44.7530 | 1.93665 | ||||||||
\(535\) | 13.8062 | 0.596894 | ||||||||
\(536\) | 3.02027 | 0.130456 | ||||||||
\(537\) | −42.9428 | −1.85312 | ||||||||
\(538\) | 10.0671 | 0.434022 | ||||||||
\(539\) | −1.52506 | −0.0656889 | ||||||||
\(540\) | 0.901542 | 0.0387962 | ||||||||
\(541\) | 2.63355 | 0.113225 | 0.0566126 | − | 0.998396i | \(-0.481970\pi\) | ||||
0.0566126 | + | 0.998396i | \(0.481970\pi\) | |||||||
\(542\) | 5.15861 | 0.221581 | ||||||||
\(543\) | 30.4959 | 1.30870 | ||||||||
\(544\) | 17.4117 | 0.746519 | ||||||||
\(545\) | −9.20384 | −0.394249 | ||||||||
\(546\) | −17.9416 | −0.767831 | ||||||||
\(547\) | 36.3624 | 1.55475 | 0.777373 | − | 0.629040i | \(-0.216552\pi\) | ||||
0.777373 | + | 0.629040i | \(0.216552\pi\) | |||||||
\(548\) | 9.39764 | 0.401447 | ||||||||
\(549\) | 9.90466 | 0.422720 | ||||||||
\(550\) | −0.348409 | −0.0148562 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 36.6514 | 1.55999 | ||||||||
\(553\) | −19.8655 | −0.844765 | ||||||||
\(554\) | 12.0201 | 0.510684 | ||||||||
\(555\) | −24.8383 | −1.05433 | ||||||||
\(556\) | 3.04923 | 0.129316 | ||||||||
\(557\) | 23.9648 | 1.01542 | 0.507711 | − | 0.861528i | \(-0.330492\pi\) | ||||
0.507711 | + | 0.861528i | \(0.330492\pi\) | |||||||
\(558\) | −3.31722 | −0.140429 | ||||||||
\(559\) | −24.7539 | −1.04698 | ||||||||
\(560\) | −3.50702 | −0.148199 | ||||||||
\(561\) | 4.06327 | 0.171551 | ||||||||
\(562\) | 6.57429 | 0.277320 | ||||||||
\(563\) | 8.52017 | 0.359082 | 0.179541 | − | 0.983750i | \(-0.442539\pi\) | ||||
0.179541 | + | 0.983750i | \(0.442539\pi\) | |||||||
\(564\) | 6.63755 | 0.279491 | ||||||||
\(565\) | −17.3273 | −0.728963 | ||||||||
\(566\) | 6.06638 | 0.254989 | ||||||||
\(567\) | 13.7882 | 0.579048 | ||||||||
\(568\) | 8.95300 | 0.375659 | ||||||||
\(569\) | −16.3734 | −0.686407 | −0.343204 | − | 0.939261i | \(-0.611512\pi\) | ||||
−0.343204 | + | 0.939261i | \(0.611512\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.21876 | −0.218398 | −0.109199 | − | 0.994020i | \(-0.534829\pi\) | ||||
−0.109199 | + | 0.994020i | \(0.534829\pi\) | |||||||
\(572\) | −0.722863 | −0.0302244 | ||||||||
\(573\) | 1.52817 | 0.0638403 | ||||||||
\(574\) | 1.32122 | 0.0551468 | ||||||||
\(575\) | −5.23591 | −0.218353 | ||||||||
\(576\) | 19.7069 | 0.821119 | ||||||||
\(577\) | −32.0390 | −1.33380 | −0.666900 | − | 0.745147i | \(-0.732379\pi\) | ||||
−0.666900 | + | 0.745147i | \(0.732379\pi\) | |||||||
\(578\) | −26.7427 | −1.11235 | ||||||||
\(579\) | −8.60147 | −0.357465 | ||||||||
\(580\) | −0.651591 | −0.0270559 | ||||||||
\(581\) | −2.14057 | −0.0888058 | ||||||||
\(582\) | −32.7882 | −1.35911 | ||||||||
\(583\) | −3.52506 | −0.145993 | ||||||||
\(584\) | −2.34060 | −0.0968547 | ||||||||
\(585\) | −11.1094 | −0.459316 | ||||||||
\(586\) | −4.65070 | −0.192119 | ||||||||
\(587\) | −3.34441 | −0.138038 | −0.0690192 | − | 0.997615i | \(-0.521987\pi\) | ||||
−0.0690192 | + | 0.997615i | \(0.521987\pi\) | |||||||
\(588\) | −6.19672 | −0.255548 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −7.00000 | −0.288185 | ||||||||
\(591\) | −33.4006 | −1.37392 | ||||||||
\(592\) | 29.6616 | 1.21909 | ||||||||
\(593\) | 42.2108 | 1.73339 | 0.866694 | − | 0.498840i | \(-0.166241\pi\) | ||||
0.866694 | + | 0.498840i | \(0.166241\pi\) | |||||||
\(594\) | −0.619514 | −0.0254190 | ||||||||
\(595\) | −8.01404 | −0.328543 | ||||||||
\(596\) | 3.44375 | 0.141062 | ||||||||
\(597\) | −26.3273 | −1.07750 | ||||||||
\(598\) | 31.9882 | 1.30809 | ||||||||
\(599\) | 5.21876 | 0.213233 | 0.106616 | − | 0.994300i | \(-0.465998\pi\) | ||||
0.106616 | + | 0.994300i | \(0.465998\pi\) | |||||||
\(600\) | −7.00000 | −0.285774 | ||||||||
\(601\) | 10.1546 | 0.414215 | 0.207108 | − | 0.978318i | \(-0.433595\pi\) | ||||
0.207108 | + | 0.978318i | \(0.433595\pi\) | |||||||
\(602\) | −7.77412 | −0.316850 | ||||||||
\(603\) | 2.19069 | 0.0892117 | ||||||||
\(604\) | −8.05526 | −0.327764 | ||||||||
\(605\) | 10.9187 | 0.443908 | ||||||||
\(606\) | −22.1103 | −0.898168 | ||||||||
\(607\) | −42.8764 | −1.74030 | −0.870149 | − | 0.492788i | \(-0.835978\pi\) | ||||
−0.870149 | + | 0.492788i | \(0.835978\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.77412 | −0.152935 | ||||||||
\(610\) | 5.44687 | 0.220537 | ||||||||
\(611\) | 28.6445 | 1.15883 | ||||||||
\(612\) | 7.02496 | 0.283967 | ||||||||
\(613\) | 25.0733 | 1.01270 | 0.506351 | − | 0.862328i | \(-0.330994\pi\) | ||||
0.506351 | + | 0.862328i | \(0.330994\pi\) | |||||||
\(614\) | 0.701708 | 0.0283186 | ||||||||
\(615\) | 1.92270 | 0.0775306 | ||||||||
\(616\) | −1.12253 | −0.0452280 | ||||||||
\(617\) | −5.49698 | −0.221300 | −0.110650 | − | 0.993859i | \(-0.535293\pi\) | ||||
−0.110650 | + | 0.993859i | \(0.535293\pi\) | |||||||
\(618\) | 35.7962 | 1.43993 | ||||||||
\(619\) | 15.4899 | 0.622590 | 0.311295 | − | 0.950313i | \(-0.399237\pi\) | ||||
0.311295 | + | 0.950313i | \(0.399237\pi\) | |||||||
\(620\) | 0.619514 | 0.0248803 | ||||||||
\(621\) | −9.31010 | −0.373602 | ||||||||
\(622\) | 10.5282 | 0.422141 | ||||||||
\(623\) | −20.5984 | −0.825256 | ||||||||
\(624\) | 31.1796 | 1.24818 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 41.6946 | 1.66645 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.80620 | −0.151884 | ||||||||
\(629\) | 67.7810 | 2.70261 | ||||||||
\(630\) | −3.48898 | −0.139004 | ||||||||
\(631\) | 41.3233 | 1.64505 | 0.822526 | − | 0.568727i | \(-0.192564\pi\) | ||||
0.822526 | + | 0.568727i | \(0.192564\pi\) | |||||||
\(632\) | 47.3513 | 1.88353 | ||||||||
\(633\) | −39.1686 | −1.55681 | ||||||||
\(634\) | −13.5351 | −0.537547 | ||||||||
\(635\) | 9.33126 | 0.370300 | ||||||||
\(636\) | −14.3233 | −0.567954 | ||||||||
\(637\) | −26.7420 | −1.05956 | ||||||||
\(638\) | 0.447755 | 0.0177268 | ||||||||
\(639\) | 6.49387 | 0.256894 | ||||||||
\(640\) | 5.25307 | 0.207646 | ||||||||
\(641\) | 30.6717 | 1.21146 | 0.605729 | − | 0.795671i | \(-0.292882\pi\) | ||||
0.605729 | + | 0.795671i | \(0.292882\pi\) | |||||||
\(642\) | −38.5491 | −1.52141 | ||||||||
\(643\) | −8.01804 | −0.316201 | −0.158100 | − | 0.987423i | \(-0.550537\pi\) | ||||
−0.158100 | + | 0.987423i | \(0.550537\pi\) | |||||||
\(644\) | −3.41168 | −0.134439 | ||||||||
\(645\) | −11.3132 | −0.445457 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0272 | 0.394209 | 0.197105 | − | 0.980382i | \(-0.436846\pi\) | ||||
0.197105 | + | 0.980382i | \(0.436846\pi\) | |||||||
\(648\) | −32.8655 | −1.29108 | ||||||||
\(649\) | −1.63355 | −0.0641225 | ||||||||
\(650\) | −6.10938 | −0.239630 | ||||||||
\(651\) | 3.58832 | 0.140638 | ||||||||
\(652\) | −11.0633 | −0.433271 | ||||||||
\(653\) | 20.4117 | 0.798771 | 0.399385 | − | 0.916783i | \(-0.369224\pi\) | ||||
0.399385 | + | 0.916783i | \(0.369224\pi\) | |||||||
\(654\) | 25.6986 | 1.00489 | ||||||||
\(655\) | −12.4257 | −0.485513 | ||||||||
\(656\) | −2.29607 | −0.0896463 | ||||||||
\(657\) | −1.69771 | −0.0662338 | ||||||||
\(658\) | 8.99600 | 0.350700 | ||||||||
\(659\) | 36.9748 | 1.44034 | 0.720168 | − | 0.693800i | \(-0.244065\pi\) | ||||
0.720168 | + | 0.693800i | \(0.244065\pi\) | |||||||
\(660\) | −0.330369 | −0.0128596 | ||||||||
\(661\) | −3.19291 | −0.124190 | −0.0620950 | − | 0.998070i | \(-0.519778\pi\) | ||||
−0.0620950 | + | 0.998070i | \(0.519778\pi\) | |||||||
\(662\) | 7.83427 | 0.304488 | ||||||||
\(663\) | 71.2498 | 2.76711 | ||||||||
\(664\) | 5.10226 | 0.198006 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 29.5090 | 1.14345 | ||||||||
\(667\) | 6.72889 | 0.260544 | ||||||||
\(668\) | 5.72178 | 0.221382 | ||||||||
\(669\) | 3.48295 | 0.134658 | ||||||||
\(670\) | 1.20472 | 0.0465426 | ||||||||
\(671\) | 1.27111 | 0.0490705 | ||||||||
\(672\) | −8.19983 | −0.316315 | ||||||||
\(673\) | 15.0742 | 0.581067 | 0.290534 | − | 0.956865i | \(-0.406167\pi\) | ||||
0.290534 | + | 0.956865i | \(0.406167\pi\) | |||||||
\(674\) | −30.8733 | −1.18919 | ||||||||
\(675\) | 1.77812 | 0.0684400 | ||||||||
\(676\) | −6.08422 | −0.234009 | ||||||||
\(677\) | −17.9648 | −0.690444 | −0.345222 | − | 0.938521i | \(-0.612196\pi\) | ||||
−0.345222 | + | 0.938521i | \(0.612196\pi\) | |||||||
\(678\) | 48.3805 | 1.85804 | ||||||||
\(679\) | 15.0913 | 0.579153 | ||||||||
\(680\) | 19.1023 | 0.732538 | ||||||||
\(681\) | 9.14057 | 0.350267 | ||||||||
\(682\) | −0.425712 | −0.0163014 | ||||||||
\(683\) | 3.78524 | 0.144838 | 0.0724191 | − | 0.997374i | \(-0.476928\pi\) | ||||
0.0724191 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.5351 | 0.708190 | ||||||||
\(686\) | −19.3905 | −0.740334 | ||||||||
\(687\) | −42.1375 | −1.60764 | ||||||||
\(688\) | 13.5101 | 0.515069 | ||||||||
\(689\) | −61.8122 | −2.35486 | ||||||||
\(690\) | 14.6195 | 0.556555 | ||||||||
\(691\) | −10.3335 | −0.393104 | −0.196552 | − | 0.980493i | \(-0.562974\pi\) | ||||
−0.196552 | + | 0.980493i | \(0.562974\pi\) | |||||||
\(692\) | −2.96881 | −0.112857 | ||||||||
\(693\) | −0.814204 | −0.0309290 | ||||||||
\(694\) | −15.1617 | −0.575531 | ||||||||
\(695\) | 6.01404 | 0.228125 | ||||||||
\(696\) | 8.99600 | 0.340992 | ||||||||
\(697\) | −5.24684 | −0.198738 | ||||||||
\(698\) | −7.58032 | −0.286919 | ||||||||
\(699\) | −29.0481 | −1.09870 | ||||||||
\(700\) | 0.651591 | 0.0246278 | ||||||||
\(701\) | 35.9960 | 1.35955 | 0.679775 | − | 0.733421i | \(-0.262077\pi\) | ||||
0.679775 | + | 0.733421i | \(0.262077\pi\) | |||||||
\(702\) | −10.8632 | −0.410006 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.52906 | 0.0953176 | ||||||||
\(705\) | 13.0913 | 0.493048 | ||||||||
\(706\) | 28.5289 | 1.07370 | ||||||||
\(707\) | 10.1766 | 0.382732 | ||||||||
\(708\) | −6.63755 | −0.249455 | ||||||||
\(709\) | 8.80531 | 0.330690 | 0.165345 | − | 0.986236i | \(-0.447126\pi\) | ||||
0.165345 | + | 0.986236i | \(0.447126\pi\) | |||||||
\(710\) | 3.57117 | 0.134024 | ||||||||
\(711\) | 34.3453 | 1.28805 | ||||||||
\(712\) | 49.0983 | 1.84004 | ||||||||
\(713\) | −6.39764 | −0.239593 | ||||||||
\(714\) | 22.3765 | 0.837419 | ||||||||
\(715\) | −1.42571 | −0.0533186 | ||||||||
\(716\) | −9.52798 | −0.356077 | ||||||||
\(717\) | 24.7579 | 0.924599 | ||||||||
\(718\) | 46.0913 | 1.72011 | ||||||||
\(719\) | 18.9920 | 0.708282 | 0.354141 | − | 0.935192i | \(-0.384773\pi\) | ||||
0.354141 | + | 0.935192i | \(0.384773\pi\) | |||||||
\(720\) | 6.06327 | 0.225965 | ||||||||
\(721\) | −16.4758 | −0.613592 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.5623 | −0.839100 | ||||||||
\(724\) | 6.76631 | 0.251468 | ||||||||
\(725\) | −1.28514 | −0.0477290 | ||||||||
\(726\) | −30.4868 | −1.13147 | ||||||||
\(727\) | 4.09134 | 0.151739 | 0.0758697 | − | 0.997118i | \(-0.475827\pi\) | ||||
0.0758697 | + | 0.997118i | \(0.475827\pi\) | |||||||
\(728\) | −19.6837 | −0.729525 | ||||||||
\(729\) | −11.6485 | −0.431425 | ||||||||
\(730\) | −0.933619 | −0.0345548 | ||||||||
\(731\) | 30.8726 | 1.14186 | ||||||||
\(732\) | 5.16484 | 0.190898 | ||||||||
\(733\) | −50.4678 | −1.86407 | −0.932036 | − | 0.362366i | \(-0.881969\pi\) | ||||
−0.932036 | + | 0.362366i | \(0.881969\pi\) | |||||||
\(734\) | −35.9325 | −1.32629 | ||||||||
\(735\) | −12.2219 | −0.450811 | ||||||||
\(736\) | 14.6195 | 0.538882 | ||||||||
\(737\) | 0.281140 | 0.0103559 | ||||||||
\(738\) | −2.28425 | −0.0840846 | ||||||||
\(739\) | 34.2297 | 1.25916 | 0.629580 | − | 0.776936i | \(-0.283227\pi\) | ||||
0.629580 | + | 0.776936i | \(0.283227\pi\) | |||||||
\(740\) | −5.51102 | −0.202589 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.4126 | −0.712658 | ||||||||
\(743\) | −22.5992 | −0.829086 | −0.414543 | − | 0.910030i | \(-0.636059\pi\) | ||||
−0.414543 | + | 0.910030i | \(0.636059\pi\) | |||||||
\(744\) | −8.55313 | −0.313573 | ||||||||
\(745\) | 6.79216 | 0.248846 | ||||||||
\(746\) | −26.3304 | −0.964023 | ||||||||
\(747\) | 3.70082 | 0.135406 | ||||||||
\(748\) | 0.901542 | 0.0329636 | ||||||||
\(749\) | 17.7429 | 0.648313 | ||||||||
\(750\) | −2.79216 | −0.101955 | ||||||||
\(751\) | 25.4397 | 0.928310 | 0.464155 | − | 0.885754i | \(-0.346358\pi\) | ||||
0.464155 | + | 0.885754i | \(0.346358\pi\) | |||||||
\(752\) | −15.6336 | −0.570097 | ||||||||
\(753\) | −40.6093 | −1.47988 | ||||||||
\(754\) | 7.85142 | 0.285932 | ||||||||
\(755\) | −15.8875 | −0.578205 | ||||||||
\(756\) | 1.15861 | 0.0421382 | ||||||||
\(757\) | 42.8031 | 1.55570 | 0.777852 | − | 0.628447i | \(-0.216309\pi\) | ||||
0.777852 | + | 0.628447i | \(0.216309\pi\) | |||||||
\(758\) | −23.6977 | −0.860739 | ||||||||
\(759\) | 3.41168 | 0.123836 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8944 | −1.08367 | −0.541836 | − | 0.840484i | \(-0.682271\pi\) | ||||
−0.541836 | + | 0.840484i | \(0.682271\pi\) | |||||||
\(762\) | −26.0544 | −0.943850 | ||||||||
\(763\) | −11.8282 | −0.428211 | ||||||||
\(764\) | 0.339065 | 0.0122669 | ||||||||
\(765\) | 13.8554 | 0.500944 | ||||||||
\(766\) | 23.0771 | 0.833810 | ||||||||
\(767\) | −28.6445 | −1.03429 | ||||||||
\(768\) | 25.8686 | 0.933452 | ||||||||
\(769\) | −16.6436 | −0.600183 | −0.300092 | − | 0.953910i | \(-0.597017\pi\) | ||||
−0.300092 | + | 0.953910i | \(0.597017\pi\) | |||||||
\(770\) | −0.447755 | −0.0161360 | ||||||||
\(771\) | 18.6436 | 0.671432 | ||||||||
\(772\) | −1.90846 | −0.0686871 | ||||||||
\(773\) | −6.11338 | −0.219883 | −0.109942 | − | 0.993938i | \(-0.535066\pi\) | ||||
−0.109942 | + | 0.993938i | \(0.535066\pi\) | |||||||
\(774\) | 13.4406 | 0.483114 | ||||||||
\(775\) | 1.22188 | 0.0438911 | ||||||||
\(776\) | −35.9717 | −1.29131 | ||||||||
\(777\) | −31.9207 | −1.14515 | ||||||||
\(778\) | 11.0951 | 0.397780 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −5.79305 | −0.207424 | ||||||||
\(781\) | 0.833385 | 0.0298209 | ||||||||
\(782\) | −39.8951 | −1.42665 | ||||||||
\(783\) | −2.28514 | −0.0816643 | ||||||||
\(784\) | 14.5952 | 0.521259 | ||||||||
\(785\) | −7.50702 | −0.267937 | ||||||||
\(786\) | 34.6946 | 1.23752 | ||||||||
\(787\) | 18.7781 | 0.669368 | 0.334684 | − | 0.942330i | \(-0.391370\pi\) | ||||
0.334684 | + | 0.942330i | \(0.391370\pi\) | |||||||
\(788\) | −7.41079 | −0.263998 | ||||||||
\(789\) | −14.4357 | −0.513926 | ||||||||
\(790\) | 18.8875 | 0.671987 | ||||||||
\(791\) | −22.2680 | −0.791759 | ||||||||
\(792\) | 1.94074 | 0.0689611 | ||||||||
\(793\) | 22.2889 | 0.791504 | ||||||||
\(794\) | −20.7670 | −0.736993 | ||||||||
\(795\) | −28.2500 | −1.00192 | ||||||||
\(796\) | −5.84139 | −0.207043 | ||||||||
\(797\) | −30.2851 | −1.07275 | −0.536377 | − | 0.843978i | \(-0.680208\pi\) | ||||
−0.536377 | + | 0.843978i | \(0.680208\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.7249 | −1.26386 | ||||||||
\(800\) | −2.79216 | −0.0987178 | ||||||||
\(801\) | 35.6124 | 1.25830 | ||||||||
\(802\) | 1.94454 | 0.0686642 | ||||||||
\(803\) | −0.217874 | −0.00768859 | ||||||||
\(804\) | 1.14235 | 0.0402874 | ||||||||
\(805\) | −6.72889 | −0.237162 | ||||||||
\(806\) | −7.46491 | −0.262940 | ||||||||
\(807\) | 18.8274 | 0.662754 | ||||||||
\(808\) | −24.2571 | −0.853361 | ||||||||
\(809\) | 13.6015 | 0.478202 | 0.239101 | − | 0.970995i | \(-0.423147\pi\) | ||||
0.239101 | + | 0.970995i | \(0.423147\pi\) | |||||||
\(810\) | −13.1094 | −0.460617 | ||||||||
\(811\) | −1.59836 | −0.0561260 | −0.0280630 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280630 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(812\) | −0.837388 | −0.0293865 | ||||||||
\(813\) | 9.64759 | 0.338356 | ||||||||
\(814\) | 3.78702 | 0.132735 | ||||||||
\(815\) | −21.8202 | −0.764330 | ||||||||
\(816\) | −38.8866 | −1.36130 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.43995 | −0.0853107 | ||||||||
\(819\) | −14.2771 | −0.498884 | ||||||||
\(820\) | 0.426600 | 0.0148975 | ||||||||
\(821\) | −18.8022 | −0.656201 | −0.328101 | − | 0.944643i | \(-0.606408\pi\) | ||||
−0.328101 | + | 0.944643i | \(0.606408\pi\) | |||||||
\(822\) | −51.7530 | −1.80509 | ||||||||
\(823\) | 53.1967 | 1.85432 | 0.927161 | − | 0.374664i | \(-0.122242\pi\) | ||||
0.927161 | + | 0.374664i | \(0.122242\pi\) | |||||||
\(824\) | 39.2718 | 1.36810 | ||||||||
\(825\) | −0.651591 | −0.0226855 | ||||||||
\(826\) | −8.99600 | −0.313011 | ||||||||
\(827\) | 25.0742 | 0.871915 | 0.435957 | − | 0.899967i | \(-0.356410\pi\) | ||||
0.435957 | + | 0.899967i | \(0.356410\pi\) | |||||||
\(828\) | 5.89843 | 0.204985 | ||||||||
\(829\) | 28.2740 | 0.981997 | 0.490999 | − | 0.871160i | \(-0.336632\pi\) | ||||
0.490999 | + | 0.871160i | \(0.336632\pi\) | |||||||
\(830\) | 2.03519 | 0.0706425 | ||||||||
\(831\) | 22.4798 | 0.779817 | ||||||||
\(832\) | 44.3473 | 1.53747 | ||||||||
\(833\) | 33.3522 | 1.15559 | ||||||||
\(834\) | −16.7922 | −0.581465 | ||||||||
\(835\) | 11.2851 | 0.390538 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.17265 | 0.0750977 | ||||||||
\(838\) | 27.8320 | 0.961442 | ||||||||
\(839\) | −14.6797 | −0.506798 | −0.253399 | − | 0.967362i | \(-0.581549\pi\) | ||||
−0.253399 | + | 0.967362i | \(0.581549\pi\) | |||||||
\(840\) | −8.99600 | −0.310391 | ||||||||
\(841\) | −27.3484 | −0.943049 | ||||||||
\(842\) | −16.9125 | −0.582842 | ||||||||
\(843\) | 12.2952 | 0.423468 | ||||||||
\(844\) | −8.69059 | −0.299142 | ||||||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | −15.5531 | −0.534728 | ||||||||
\(847\) | 14.0321 | 0.482148 | ||||||||
\(848\) | 33.7358 | 1.15849 | ||||||||
\(849\) | 11.3453 | 0.389369 | ||||||||
\(850\) | 7.61951 | 0.261347 | ||||||||
\(851\) | 56.9116 | 1.95090 | ||||||||
\(852\) | 3.38626 | 0.116012 | ||||||||
\(853\) | −25.9047 | −0.886959 | −0.443479 | − | 0.896285i | \(-0.646256\pi\) | ||||
−0.443479 | + | 0.896285i | \(0.646256\pi\) | |||||||
\(854\) | 7.00000 | 0.239535 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −42.2921 | −1.44551 | ||||||||
\(857\) | 12.9055 | 0.440845 | 0.220423 | − | 0.975404i | \(-0.429256\pi\) | ||||
0.220423 | + | 0.975404i | \(0.429256\pi\) | |||||||
\(858\) | 3.98082 | 0.135903 | ||||||||
\(859\) | −28.7178 | −0.979838 | −0.489919 | − | 0.871768i | \(-0.662974\pi\) | ||||
−0.489919 | + | 0.871768i | \(0.662974\pi\) | |||||||
\(860\) | −2.51013 | −0.0855948 | ||||||||
\(861\) | 2.47094 | 0.0842094 | ||||||||
\(862\) | 4.20295 | 0.143153 | ||||||||
\(863\) | 3.04300 | 0.103585 | 0.0517925 | − | 0.998658i | \(-0.483507\pi\) | ||||
0.0517925 | + | 0.998658i | \(0.483507\pi\) | |||||||
\(864\) | −4.96481 | −0.168906 | ||||||||
\(865\) | −5.85543 | −0.199091 | ||||||||
\(866\) | −11.2421 | −0.382024 | ||||||||
\(867\) | −50.0140 | −1.69857 | ||||||||
\(868\) | 0.796164 | 0.0270236 | ||||||||
\(869\) | 4.40767 | 0.149520 | ||||||||
\(870\) | 3.58832 | 0.121656 | ||||||||
\(871\) | 4.92981 | 0.167040 | ||||||||
\(872\) | 28.1938 | 0.954763 | ||||||||
\(873\) | −26.0913 | −0.883058 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.28514 | 0.0434457 | ||||||||
\(876\) | −0.885278 | −0.0299108 | ||||||||
\(877\) | −11.3694 | −0.383916 | −0.191958 | − | 0.981403i | \(-0.561484\pi\) | ||||
−0.191958 | + | 0.981403i | \(0.561484\pi\) | |||||||
\(878\) | −45.8325 | −1.54677 | ||||||||
\(879\) | −8.69771 | −0.293366 | ||||||||
\(880\) | 0.778124 | 0.0262305 | ||||||||
\(881\) | 36.4014 | 1.22640 | 0.613198 | − | 0.789929i | \(-0.289883\pi\) | ||||
0.613198 | + | 0.789929i | \(0.289883\pi\) | |||||||
\(882\) | 14.5202 | 0.488919 | ||||||||
\(883\) | −49.7679 | −1.67482 | −0.837411 | − | 0.546573i | \(-0.815932\pi\) | ||||
−0.837411 | + | 0.546573i | \(0.815932\pi\) | |||||||
\(884\) | 15.8086 | 0.531701 | ||||||||
\(885\) | −13.0913 | −0.440061 | ||||||||
\(886\) | −17.9356 | −0.602560 | ||||||||
\(887\) | 15.6977 | 0.527077 | 0.263539 | − | 0.964649i | \(-0.415110\pi\) | ||||
0.263539 | + | 0.964649i | \(0.415110\pi\) | |||||||
\(888\) | 76.0863 | 2.55329 | ||||||||
\(889\) | 11.9920 | 0.402199 | ||||||||
\(890\) | 19.5843 | 0.656468 | ||||||||
\(891\) | −3.05926 | −0.102489 | ||||||||
\(892\) | 0.772783 | 0.0258747 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −18.9648 | −0.634278 | ||||||||
\(895\) | −18.7922 | −0.628153 | ||||||||
\(896\) | 6.75094 | 0.225533 | ||||||||
\(897\) | 59.8240 | 1.99747 | ||||||||
\(898\) | −9.03030 | −0.301345 | ||||||||
\(899\) | −1.57028 | −0.0523719 | ||||||||
\(900\) | −1.12653 | −0.0375511 | ||||||||
\(901\) | 77.0911 | 2.56828 | ||||||||
\(902\) | −0.293148 | −0.00976075 | ||||||||
\(903\) | −14.5391 | −0.483831 | ||||||||
\(904\) | 53.0780 | 1.76535 | ||||||||
\(905\) | 13.3453 | 0.443613 | ||||||||
\(906\) | 44.3605 | 1.47378 | ||||||||
\(907\) | 32.9156 | 1.09294 | 0.546472 | − | 0.837477i | \(-0.315971\pi\) | ||||
0.546472 | + | 0.837477i | \(0.315971\pi\) | |||||||
\(908\) | 2.02807 | 0.0673040 | ||||||||
\(909\) | −17.5944 | −0.583568 | ||||||||
\(910\) | −7.85142 | −0.260272 | ||||||||
\(911\) | 18.7109 | 0.619918 | 0.309959 | − | 0.950750i | \(-0.399685\pi\) | ||||
0.309959 | + | 0.950750i | \(0.399685\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.474941 | 0.0157183 | ||||||||
\(914\) | −2.81040 | −0.0929597 | ||||||||
\(915\) | 10.1867 | 0.336761 | ||||||||
\(916\) | −9.34930 | −0.308909 | ||||||||
\(917\) | −15.9688 | −0.527337 | ||||||||
\(918\) | 13.5484 | 0.447165 | ||||||||
\(919\) | −50.9506 | −1.68070 | −0.840352 | − | 0.542041i | \(-0.817652\pi\) | ||||
−0.840352 | + | 0.542041i | \(0.817652\pi\) | |||||||
\(920\) | 16.0390 | 0.528790 | ||||||||
\(921\) | 1.31233 | 0.0432427 | ||||||||
\(922\) | −24.1406 | −0.795027 | ||||||||
\(923\) | 14.6135 | 0.481009 | ||||||||
\(924\) | −0.424571 | −0.0139674 | ||||||||
\(925\) | −10.8695 | −0.357386 | ||||||||
\(926\) | −35.3694 | −1.16231 | ||||||||
\(927\) | 28.4850 | 0.935569 | ||||||||
\(928\) | 3.58832 | 0.117793 | ||||||||
\(929\) | 11.4850 | 0.376810 | 0.188405 | − | 0.982091i | \(-0.439668\pi\) | ||||
0.188405 | + | 0.982091i | \(0.439668\pi\) | |||||||
\(930\) | −3.41168 | −0.111873 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.44509 | −0.211116 | ||||||||
\(933\) | 19.6897 | 0.644612 | ||||||||
\(934\) | 4.05323 | 0.132626 | ||||||||
\(935\) | 1.77812 | 0.0581509 | ||||||||
\(936\) | 34.0310 | 1.11234 | ||||||||
\(937\) | 16.1695 | 0.528236 | 0.264118 | − | 0.964490i | \(-0.414919\pi\) | ||||
0.264118 | + | 0.964490i | \(0.414919\pi\) | |||||||
\(938\) | 1.54824 | 0.0505519 | ||||||||
\(939\) | 77.9769 | 2.54468 | ||||||||
\(940\) | 2.90466 | 0.0947394 | ||||||||
\(941\) | 25.3874 | 0.827606 | 0.413803 | − | 0.910367i | \(-0.364200\pi\) | ||||
0.413803 | + | 0.910367i | \(0.364200\pi\) | |||||||
\(942\) | 20.9608 | 0.682940 | ||||||||
\(943\) | −4.40545 | −0.143461 | ||||||||
\(944\) | 15.6336 | 0.508829 | ||||||||
\(945\) | 2.28514 | 0.0743357 | ||||||||
\(946\) | 1.72489 | 0.0560811 | ||||||||
\(947\) | 23.3805 | 0.759764 | 0.379882 | − | 0.925035i | \(-0.375965\pi\) | ||||
0.379882 | + | 0.925035i | \(0.375965\pi\) | |||||||
\(948\) | 17.9095 | 0.581675 | ||||||||
\(949\) | −3.82043 | −0.124016 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.3132 | −0.820837 | ||||||||
\(952\) | 24.5491 | 0.795642 | ||||||||
\(953\) | 22.1787 | 0.718438 | 0.359219 | − | 0.933253i | \(-0.383043\pi\) | ||||
0.359219 | + | 0.933253i | \(0.383043\pi\) | |||||||
\(954\) | 33.5623 | 1.08662 | ||||||||
\(955\) | 0.668743 | 0.0216400 | ||||||||
\(956\) | 5.49318 | 0.177662 | ||||||||
\(957\) | 0.837388 | 0.0270689 | ||||||||
\(958\) | 48.2727 | 1.55962 | ||||||||
\(959\) | 23.8202 | 0.769196 | ||||||||
\(960\) | 20.2680 | 0.654147 | ||||||||
\(961\) | −29.5070 | −0.951839 | ||||||||
\(962\) | 66.4057 | 2.14101 | ||||||||
\(963\) | −30.6757 | −0.988509 | ||||||||
\(964\) | −5.00603 | −0.161233 | ||||||||
\(965\) | −3.76409 | −0.121170 | ||||||||
\(966\) | 18.7882 | 0.604499 | ||||||||
\(967\) | −40.8594 | −1.31395 | −0.656975 | − | 0.753912i | \(-0.728164\pi\) | ||||
−0.656975 | + | 0.753912i | \(0.728164\pi\) | |||||||
\(968\) | −33.4469 | −1.07502 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.3484 | −0.460700 | ||||||||
\(971\) | −24.6476 | −0.790979 | −0.395489 | − | 0.918471i | \(-0.629425\pi\) | ||||
−0.395489 | + | 0.918471i | \(0.629425\pi\) | |||||||
\(972\) | −9.72598 | −0.311961 | ||||||||
\(973\) | 7.72889 | 0.247777 | ||||||||
\(974\) | −30.2758 | −0.970099 | ||||||||
\(975\) | −11.4257 | −0.365916 | ||||||||
\(976\) | −12.1648 | −0.389387 | ||||||||
\(977\) | 13.7077 | 0.438549 | 0.219275 | − | 0.975663i | \(-0.429631\pi\) | ||||
0.219275 | + | 0.975663i | \(0.429631\pi\) | |||||||
\(978\) | 60.9256 | 1.94819 | ||||||||
\(979\) | 4.57028 | 0.146067 | ||||||||
\(980\) | −2.71174 | −0.0866235 | ||||||||
\(981\) | 20.4498 | 0.652911 | ||||||||
\(982\) | 16.6463 | 0.531203 | ||||||||
\(983\) | −0.282028 | −0.00899529 | −0.00449765 | − | 0.999990i | \(-0.501432\pi\) | ||||
−0.00449765 | + | 0.999990i | \(0.501432\pi\) | |||||||
\(984\) | −5.88973 | −0.187758 | ||||||||
\(985\) | −14.6164 | −0.465717 | ||||||||
\(986\) | −9.79216 | −0.311846 | ||||||||
\(987\) | 16.8242 | 0.535521 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.9218 | 0.824266 | ||||||||
\(990\) | 0.774121 | 0.0246032 | ||||||||
\(991\) | −24.5984 | −0.781393 | −0.390696 | − | 0.920520i | \(-0.627766\pi\) | ||||
−0.390696 | + | 0.920520i | \(0.627766\pi\) | |||||||
\(992\) | −3.41168 | −0.108321 | ||||||||
\(993\) | 14.6516 | 0.464954 | ||||||||
\(994\) | 4.58947 | 0.145569 | ||||||||
\(995\) | −11.5211 | −0.365242 | ||||||||
\(996\) | 1.92981 | 0.0611485 | ||||||||
\(997\) | −23.1827 | −0.734203 | −0.367101 | − | 0.930181i | \(-0.619650\pi\) | ||||
−0.367101 | + | 0.930181i | \(0.619650\pi\) | |||||||
\(998\) | −10.0069 | −0.316764 | ||||||||
\(999\) | −19.3273 | −0.611487 |
(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 | 1805.2.a.g.1.2 | 3 | ||
5.4 | even | 2 | 9025.2.a.ba.1.2 | 3 | |||
19.8 | odd | 6 | 95.2.e.b.26.2 | yes | 6 | ||
19.12 | odd | 6 | 95.2.e.b.11.2 | ✓ | 6 | ||
19.18 | odd | 2 | 1805.2.a.h.1.2 | 3 | |||
57.8 | even | 6 | 855.2.k.g.406.2 | 6 | |||
57.50 | even | 6 | 855.2.k.g.676.2 | 6 | |||
76.27 | even | 6 | 1520.2.q.j.881.3 | 6 | |||
76.31 | even | 6 | 1520.2.q.j.961.3 | 6 | |||
95.8 | even | 12 | 475.2.j.b.349.3 | 12 | |||
95.12 | even | 12 | 475.2.j.b.49.3 | 12 | |||
95.27 | even | 12 | 475.2.j.b.349.4 | 12 | |||
95.69 | odd | 6 | 475.2.e.d.201.2 | 6 | |||
95.84 | odd | 6 | 475.2.e.d.26.2 | 6 | |||
95.88 | even | 12 | 475.2.j.b.49.4 | 12 | |||
95.94 | odd | 2 | 9025.2.a.z.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.b.11.2 | ✓ | 6 | 19.12 | odd | 6 | ||
95.2.e.b.26.2 | yes | 6 | 19.8 | odd | 6 | ||
475.2.e.d.26.2 | 6 | 95.84 | odd | 6 | |||
475.2.e.d.201.2 | 6 | 95.69 | odd | 6 | |||
475.2.j.b.49.3 | 12 | 95.12 | even | 12 | |||
475.2.j.b.49.4 | 12 | 95.88 | even | 12 | |||
475.2.j.b.349.3 | 12 | 95.8 | even | 12 | |||
475.2.j.b.349.4 | 12 | 95.27 | even | 12 | |||
855.2.k.g.406.2 | 6 | 57.8 | even | 6 | |||
855.2.k.g.676.2 | 6 | 57.50 | even | 6 | |||
1520.2.q.j.881.3 | 6 | 76.27 | even | 6 | |||
1520.2.q.j.961.3 | 6 | 76.31 | even | 6 | |||
1805.2.a.g.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1805.2.a.h.1.2 | 3 | 19.18 | odd | 2 | |||
9025.2.a.z.1.2 | 3 | 95.94 | odd | 2 | |||
9025.2.a.ba.1.2 | 3 | 5.4 | even | 2 |