Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{36})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 6x^{4} + 9x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.28558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.87939 | −1.08506 | −0.542532 | − | 0.840035i | \(-0.682534\pi\) | ||||
−0.542532 | + | 0.840035i | \(0.682534\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.26414 | 1.90698 | 0.953491 | − | 0.301423i | \(-0.0974615\pi\) | ||||
0.953491 | + | 0.301423i | \(0.0974615\pi\) | |||||||
\(6\) | 1.87939 | 0.767256 | ||||||||
\(7\) | 3.61144 | 1.36499 | 0.682497 | − | 0.730888i | \(-0.260894\pi\) | ||||
0.682497 | + | 0.730888i | \(0.260894\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.532089 | 0.177363 | ||||||||
\(10\) | −4.26414 | −1.34844 | ||||||||
\(11\) | 2.11681 | 0.638241 | 0.319120 | − | 0.947714i | \(-0.396613\pi\) | ||||
0.319120 | + | 0.947714i | \(0.396613\pi\) | |||||||
\(12\) | −1.87939 | −0.542532 | ||||||||
\(13\) | 2.88400 | 0.799878 | 0.399939 | − | 0.916542i | \(-0.369031\pi\) | ||||
0.399939 | + | 0.916542i | \(0.369031\pi\) | |||||||
\(14\) | −3.61144 | −0.965197 | ||||||||
\(15\) | −8.01396 | −2.06920 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.0267197 | −0.00648047 | −0.00324024 | − | 0.999995i | \(-0.501031\pi\) | ||||
−0.00324024 | + | 0.999995i | \(0.501031\pi\) | |||||||
\(18\) | −0.532089 | −0.125415 | ||||||||
\(19\) | 3.22847 | 0.740662 | 0.370331 | − | 0.928900i | \(-0.379244\pi\) | ||||
0.370331 | + | 0.928900i | \(0.379244\pi\) | |||||||
\(20\) | 4.26414 | 0.953491 | ||||||||
\(21\) | −6.78728 | −1.48111 | ||||||||
\(22\) | −2.11681 | −0.451304 | ||||||||
\(23\) | −2.97244 | −0.619797 | −0.309899 | − | 0.950770i | \(-0.600295\pi\) | ||||
−0.309899 | + | 0.950770i | \(0.600295\pi\) | |||||||
\(24\) | 1.87939 | 0.383628 | ||||||||
\(25\) | 13.1829 | 2.63658 | ||||||||
\(26\) | −2.88400 | −0.565599 | ||||||||
\(27\) | 4.63816 | 0.892613 | ||||||||
\(28\) | 3.61144 | 0.682497 | ||||||||
\(29\) | −5.73300 | −1.06459 | −0.532296 | − | 0.846558i | \(-0.678671\pi\) | ||||
−0.532296 | + | 0.846558i | \(0.678671\pi\) | |||||||
\(30\) | 8.01396 | 1.46314 | ||||||||
\(31\) | 6.76932 | 1.21581 | 0.607903 | − | 0.794011i | \(-0.292011\pi\) | ||||
0.607903 | + | 0.794011i | \(0.292011\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.97829 | −0.692532 | ||||||||
\(34\) | 0.0267197 | 0.00458239 | ||||||||
\(35\) | 15.3997 | 2.60302 | ||||||||
\(36\) | 0.532089 | 0.0886815 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −3.22847 | −0.523727 | ||||||||
\(39\) | −5.42015 | −0.867919 | ||||||||
\(40\) | −4.26414 | −0.674220 | ||||||||
\(41\) | −1.49152 | −0.232937 | −0.116468 | − | 0.993194i | \(-0.537157\pi\) | ||||
−0.116468 | + | 0.993194i | \(0.537157\pi\) | |||||||
\(42\) | 6.78728 | 1.04730 | ||||||||
\(43\) | 5.53737 | 0.844441 | 0.422221 | − | 0.906493i | \(-0.361251\pi\) | ||||
0.422221 | + | 0.906493i | \(0.361251\pi\) | |||||||
\(44\) | 2.11681 | 0.319120 | ||||||||
\(45\) | 2.26890 | 0.338228 | ||||||||
\(46\) | 2.97244 | 0.438263 | ||||||||
\(47\) | 2.61309 | 0.381158 | 0.190579 | − | 0.981672i | \(-0.438964\pi\) | ||||
0.190579 | + | 0.981672i | \(0.438964\pi\) | |||||||
\(48\) | −1.87939 | −0.271266 | ||||||||
\(49\) | 6.04247 | 0.863210 | ||||||||
\(50\) | −13.1829 | −1.86434 | ||||||||
\(51\) | 0.0502166 | 0.00703173 | ||||||||
\(52\) | 2.88400 | 0.399939 | ||||||||
\(53\) | 1.90902 | 0.262224 | 0.131112 | − | 0.991368i | \(-0.458145\pi\) | ||||
0.131112 | + | 0.991368i | \(0.458145\pi\) | |||||||
\(54\) | −4.63816 | −0.631173 | ||||||||
\(55\) | 9.02635 | 1.21711 | ||||||||
\(56\) | −3.61144 | −0.482598 | ||||||||
\(57\) | −6.06754 | −0.803665 | ||||||||
\(58\) | 5.73300 | 0.752780 | ||||||||
\(59\) | 5.62482 | 0.732289 | 0.366144 | − | 0.930558i | \(-0.380678\pi\) | ||||
0.366144 | + | 0.930558i | \(0.380678\pi\) | |||||||
\(60\) | −8.01396 | −1.03460 | ||||||||
\(61\) | 5.74087 | 0.735043 | 0.367522 | − | 0.930015i | \(-0.380206\pi\) | ||||
0.367522 | + | 0.930015i | \(0.380206\pi\) | |||||||
\(62\) | −6.76932 | −0.859705 | ||||||||
\(63\) | 1.92160 | 0.242099 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.2978 | 1.52535 | ||||||||
\(66\) | 3.97829 | 0.489694 | ||||||||
\(67\) | −6.92148 | −0.845593 | −0.422796 | − | 0.906225i | \(-0.638951\pi\) | ||||
−0.422796 | + | 0.906225i | \(0.638951\pi\) | |||||||
\(68\) | −0.0267197 | −0.00324024 | ||||||||
\(69\) | 5.58637 | 0.672519 | ||||||||
\(70\) | −15.3997 | −1.84061 | ||||||||
\(71\) | −9.27923 | −1.10124 | −0.550621 | − | 0.834755i | \(-0.685609\pi\) | ||||
−0.550621 | + | 0.834755i | \(0.685609\pi\) | |||||||
\(72\) | −0.532089 | −0.0627073 | ||||||||
\(73\) | −16.2707 | −1.90434 | −0.952169 | − | 0.305571i | \(-0.901153\pi\) | ||||
−0.952169 | + | 0.305571i | \(0.901153\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −24.7757 | −2.86085 | ||||||||
\(76\) | 3.22847 | 0.370331 | ||||||||
\(77\) | 7.64471 | 0.871195 | ||||||||
\(78\) | 5.42015 | 0.613711 | ||||||||
\(79\) | 1.41514 | 0.159216 | 0.0796078 | − | 0.996826i | \(-0.474633\pi\) | ||||
0.0796078 | + | 0.996826i | \(0.474633\pi\) | |||||||
\(80\) | 4.26414 | 0.476745 | ||||||||
\(81\) | −10.3131 | −1.14591 | ||||||||
\(82\) | 1.49152 | 0.164711 | ||||||||
\(83\) | −1.69642 | −0.186206 | −0.0931030 | − | 0.995656i | \(-0.529679\pi\) | ||||
−0.0931030 | + | 0.995656i | \(0.529679\pi\) | |||||||
\(84\) | −6.78728 | −0.740553 | ||||||||
\(85\) | −0.113936 | −0.0123581 | ||||||||
\(86\) | −5.53737 | −0.597110 | ||||||||
\(87\) | 10.7745 | 1.15515 | ||||||||
\(88\) | −2.11681 | −0.225652 | ||||||||
\(89\) | −8.27093 | −0.876717 | −0.438358 | − | 0.898800i | \(-0.644440\pi\) | ||||
−0.438358 | + | 0.898800i | \(0.644440\pi\) | |||||||
\(90\) | −2.26890 | −0.239163 | ||||||||
\(91\) | 10.4154 | 1.09183 | ||||||||
\(92\) | −2.97244 | −0.309899 | ||||||||
\(93\) | −12.7222 | −1.31923 | ||||||||
\(94\) | −2.61309 | −0.269519 | ||||||||
\(95\) | 13.7667 | 1.41243 | ||||||||
\(96\) | 1.87939 | 0.191814 | ||||||||
\(97\) | −6.52527 | −0.662541 | −0.331270 | − | 0.943536i | \(-0.607477\pi\) | ||||
−0.331270 | + | 0.943536i | \(0.607477\pi\) | |||||||
\(98\) | −6.04247 | −0.610382 | ||||||||
\(99\) | 1.12633 | 0.113200 | ||||||||
\(100\) | 13.1829 | 1.31829 | ||||||||
\(101\) | −16.5995 | −1.65171 | −0.825855 | − | 0.563882i | \(-0.809307\pi\) | ||||
−0.825855 | + | 0.563882i | \(0.809307\pi\) | |||||||
\(102\) | −0.0502166 | −0.00497218 | ||||||||
\(103\) | −1.89481 | −0.186701 | −0.0933504 | − | 0.995633i | \(-0.529758\pi\) | ||||
−0.0933504 | + | 0.995633i | \(0.529758\pi\) | |||||||
\(104\) | −2.88400 | −0.282800 | ||||||||
\(105\) | −28.9419 | −2.82444 | ||||||||
\(106\) | −1.90902 | −0.185421 | ||||||||
\(107\) | 0.382256 | 0.0369541 | 0.0184771 | − | 0.999829i | \(-0.494118\pi\) | ||||
0.0184771 | + | 0.999829i | \(0.494118\pi\) | |||||||
\(108\) | 4.63816 | 0.446307 | ||||||||
\(109\) | −0.965584 | −0.0924862 | −0.0462431 | − | 0.998930i | \(-0.514725\pi\) | ||||
−0.0462431 | + | 0.998930i | \(0.514725\pi\) | |||||||
\(110\) | −9.02635 | −0.860629 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.61144 | 0.341249 | ||||||||
\(113\) | −1.89075 | −0.177866 | −0.0889332 | − | 0.996038i | \(-0.528346\pi\) | ||||
−0.0889332 | + | 0.996038i | \(0.528346\pi\) | |||||||
\(114\) | 6.06754 | 0.568277 | ||||||||
\(115\) | −12.6749 | −1.18194 | ||||||||
\(116\) | −5.73300 | −0.532296 | ||||||||
\(117\) | 1.53455 | 0.141869 | ||||||||
\(118\) | −5.62482 | −0.517806 | ||||||||
\(119\) | −0.0964964 | −0.00884581 | ||||||||
\(120\) | 8.01396 | 0.731571 | ||||||||
\(121\) | −6.51914 | −0.592649 | ||||||||
\(122\) | −5.74087 | −0.519754 | ||||||||
\(123\) | 2.80315 | 0.252751 | ||||||||
\(124\) | 6.76932 | 0.607903 | ||||||||
\(125\) | 34.8930 | 3.12092 | ||||||||
\(126\) | −1.92160 | −0.171190 | ||||||||
\(127\) | −16.1144 | −1.42992 | −0.714961 | − | 0.699165i | \(-0.753555\pi\) | ||||
−0.714961 | + | 0.699165i | \(0.753555\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.4069 | −0.916273 | ||||||||
\(130\) | −12.2978 | −1.07859 | ||||||||
\(131\) | −0.822948 | −0.0719013 | −0.0359507 | − | 0.999354i | \(-0.511446\pi\) | ||||
−0.0359507 | + | 0.999354i | \(0.511446\pi\) | |||||||
\(132\) | −3.97829 | −0.346266 | ||||||||
\(133\) | 11.6594 | 1.01100 | ||||||||
\(134\) | 6.92148 | 0.597924 | ||||||||
\(135\) | 19.7777 | 1.70220 | ||||||||
\(136\) | 0.0267197 | 0.00229119 | ||||||||
\(137\) | 17.3569 | 1.48290 | 0.741452 | − | 0.671006i | \(-0.234138\pi\) | ||||
0.741452 | + | 0.671006i | \(0.234138\pi\) | |||||||
\(138\) | −5.58637 | −0.475543 | ||||||||
\(139\) | −9.22544 | −0.782491 | −0.391246 | − | 0.920286i | \(-0.627956\pi\) | ||||
−0.391246 | + | 0.920286i | \(0.627956\pi\) | |||||||
\(140\) | 15.3997 | 1.30151 | ||||||||
\(141\) | −4.91099 | −0.413580 | ||||||||
\(142\) | 9.27923 | 0.778696 | ||||||||
\(143\) | 6.10487 | 0.510515 | ||||||||
\(144\) | 0.532089 | 0.0443407 | ||||||||
\(145\) | −24.4463 | −2.03016 | ||||||||
\(146\) | 16.2707 | 1.34657 | ||||||||
\(147\) | −11.3561 | −0.936638 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.73776 | −0.633902 | −0.316951 | − | 0.948442i | \(-0.602659\pi\) | ||||
−0.316951 | + | 0.948442i | \(0.602659\pi\) | |||||||
\(150\) | 24.7757 | 2.02293 | ||||||||
\(151\) | 12.6363 | 1.02833 | 0.514165 | − | 0.857691i | \(-0.328102\pi\) | ||||
0.514165 | + | 0.857691i | \(0.328102\pi\) | |||||||
\(152\) | −3.22847 | −0.261864 | ||||||||
\(153\) | −0.0142172 | −0.00114940 | ||||||||
\(154\) | −7.64471 | −0.616028 | ||||||||
\(155\) | 28.8653 | 2.31852 | ||||||||
\(156\) | −5.42015 | −0.433959 | ||||||||
\(157\) | 13.0467 | 1.04124 | 0.520621 | − | 0.853788i | \(-0.325700\pi\) | ||||
0.520621 | + | 0.853788i | \(0.325700\pi\) | |||||||
\(158\) | −1.41514 | −0.112582 | ||||||||
\(159\) | −3.58779 | −0.284530 | ||||||||
\(160\) | −4.26414 | −0.337110 | ||||||||
\(161\) | −10.7348 | −0.846020 | ||||||||
\(162\) | 10.3131 | 0.810277 | ||||||||
\(163\) | 25.2564 | 1.97823 | 0.989117 | − | 0.147133i | \(-0.0470046\pi\) | ||||
0.989117 | + | 0.147133i | \(0.0470046\pi\) | |||||||
\(164\) | −1.49152 | −0.116468 | ||||||||
\(165\) | −16.9640 | −1.32065 | ||||||||
\(166\) | 1.69642 | 0.131668 | ||||||||
\(167\) | 10.2810 | 0.795569 | 0.397785 | − | 0.917479i | \(-0.369779\pi\) | ||||
0.397785 | + | 0.917479i | \(0.369779\pi\) | |||||||
\(168\) | 6.78728 | 0.523650 | ||||||||
\(169\) | −4.68253 | −0.360195 | ||||||||
\(170\) | 0.113936 | 0.00873853 | ||||||||
\(171\) | 1.71783 | 0.131366 | ||||||||
\(172\) | 5.53737 | 0.422221 | ||||||||
\(173\) | −23.6569 | −1.79860 | −0.899300 | − | 0.437332i | \(-0.855923\pi\) | ||||
−0.899300 | + | 0.437332i | \(0.855923\pi\) | |||||||
\(174\) | −10.7745 | −0.816814 | ||||||||
\(175\) | 47.6092 | 3.59891 | ||||||||
\(176\) | 2.11681 | 0.159560 | ||||||||
\(177\) | −10.5712 | −0.794580 | ||||||||
\(178\) | 8.27093 | 0.619932 | ||||||||
\(179\) | 5.05746 | 0.378013 | 0.189006 | − | 0.981976i | \(-0.439473\pi\) | ||||
0.189006 | + | 0.981976i | \(0.439473\pi\) | |||||||
\(180\) | 2.26890 | 0.169114 | ||||||||
\(181\) | −1.04545 | −0.0777075 | −0.0388537 | − | 0.999245i | \(-0.512371\pi\) | ||||
−0.0388537 | + | 0.999245i | \(0.512371\pi\) | |||||||
\(182\) | −10.4154 | −0.772040 | ||||||||
\(183\) | −10.7893 | −0.797569 | ||||||||
\(184\) | 2.97244 | 0.219131 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.7222 | 0.932834 | ||||||||
\(187\) | −0.0565603 | −0.00413610 | ||||||||
\(188\) | 2.61309 | 0.190579 | ||||||||
\(189\) | 16.7504 | 1.21841 | ||||||||
\(190\) | −13.7667 | −0.998738 | ||||||||
\(191\) | 13.4633 | 0.974173 | 0.487087 | − | 0.873354i | \(-0.338060\pi\) | ||||
0.487087 | + | 0.873354i | \(0.338060\pi\) | |||||||
\(192\) | −1.87939 | −0.135633 | ||||||||
\(193\) | 4.52228 | 0.325521 | 0.162760 | − | 0.986666i | \(-0.447960\pi\) | ||||
0.162760 | + | 0.986666i | \(0.447960\pi\) | |||||||
\(194\) | 6.52527 | 0.468487 | ||||||||
\(195\) | −23.1123 | −1.65510 | ||||||||
\(196\) | 6.04247 | 0.431605 | ||||||||
\(197\) | −12.3720 | −0.881469 | −0.440735 | − | 0.897637i | \(-0.645282\pi\) | ||||
−0.440735 | + | 0.897637i | \(0.645282\pi\) | |||||||
\(198\) | −1.12633 | −0.0800447 | ||||||||
\(199\) | −4.50965 | −0.319681 | −0.159840 | − | 0.987143i | \(-0.551098\pi\) | ||||
−0.159840 | + | 0.987143i | \(0.551098\pi\) | |||||||
\(200\) | −13.1829 | −0.932171 | ||||||||
\(201\) | 13.0081 | 0.917522 | ||||||||
\(202\) | 16.5995 | 1.16794 | ||||||||
\(203\) | −20.7044 | −1.45316 | ||||||||
\(204\) | 0.0502166 | 0.00351586 | ||||||||
\(205\) | −6.36006 | −0.444206 | ||||||||
\(206\) | 1.89481 | 0.132017 | ||||||||
\(207\) | −1.58160 | −0.109929 | ||||||||
\(208\) | 2.88400 | 0.199970 | ||||||||
\(209\) | 6.83404 | 0.472721 | ||||||||
\(210\) | 28.9419 | 1.99718 | ||||||||
\(211\) | −16.2460 | −1.11842 | −0.559209 | − | 0.829026i | \(-0.688895\pi\) | ||||
−0.559209 | + | 0.829026i | \(0.688895\pi\) | |||||||
\(212\) | 1.90902 | 0.131112 | ||||||||
\(213\) | 17.4392 | 1.19492 | ||||||||
\(214\) | −0.382256 | −0.0261305 | ||||||||
\(215\) | 23.6121 | 1.61033 | ||||||||
\(216\) | −4.63816 | −0.315587 | ||||||||
\(217\) | 24.4470 | 1.65957 | ||||||||
\(218\) | 0.965584 | 0.0653976 | ||||||||
\(219\) | 30.5789 | 2.06633 | ||||||||
\(220\) | 9.02635 | 0.608557 | ||||||||
\(221\) | −0.0770596 | −0.00518359 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.847777 | −0.0567713 | −0.0283857 | − | 0.999597i | \(-0.509037\pi\) | ||||
−0.0283857 | + | 0.999597i | \(0.509037\pi\) | |||||||
\(224\) | −3.61144 | −0.241299 | ||||||||
\(225\) | 7.01447 | 0.467631 | ||||||||
\(226\) | 1.89075 | 0.125770 | ||||||||
\(227\) | 12.1287 | 0.805013 | 0.402506 | − | 0.915417i | \(-0.368139\pi\) | ||||
0.402506 | + | 0.915417i | \(0.368139\pi\) | |||||||
\(228\) | −6.06754 | −0.401833 | ||||||||
\(229\) | 13.2675 | 0.876741 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(230\) | 12.6749 | 0.835759 | ||||||||
\(231\) | −14.3673 | −0.945302 | ||||||||
\(232\) | 5.73300 | 0.376390 | ||||||||
\(233\) | −4.30657 | −0.282133 | −0.141066 | − | 0.990000i | \(-0.545053\pi\) | ||||
−0.141066 | + | 0.990000i | \(0.545053\pi\) | |||||||
\(234\) | −1.53455 | −0.100316 | ||||||||
\(235\) | 11.1426 | 0.726860 | ||||||||
\(236\) | 5.62482 | 0.366144 | ||||||||
\(237\) | −2.65959 | −0.172759 | ||||||||
\(238\) | 0.0964964 | 0.00625493 | ||||||||
\(239\) | 14.2423 | 0.921258 | 0.460629 | − | 0.887593i | \(-0.347624\pi\) | ||||
0.460629 | + | 0.887593i | \(0.347624\pi\) | |||||||
\(240\) | −8.01396 | −0.517299 | ||||||||
\(241\) | −14.2610 | −0.918633 | −0.459316 | − | 0.888273i | \(-0.651906\pi\) | ||||
−0.459316 | + | 0.888273i | \(0.651906\pi\) | |||||||
\(242\) | 6.51914 | 0.419066 | ||||||||
\(243\) | 5.46791 | 0.350767 | ||||||||
\(244\) | 5.74087 | 0.367522 | ||||||||
\(245\) | 25.7659 | 1.64613 | ||||||||
\(246\) | −2.80315 | −0.178722 | ||||||||
\(247\) | 9.31092 | 0.592440 | ||||||||
\(248\) | −6.76932 | −0.429852 | ||||||||
\(249\) | 3.18822 | 0.202045 | ||||||||
\(250\) | −34.8930 | −2.20683 | ||||||||
\(251\) | −24.7076 | −1.55953 | −0.779764 | − | 0.626074i | \(-0.784661\pi\) | ||||
−0.779764 | + | 0.626074i | \(0.784661\pi\) | |||||||
\(252\) | 1.92160 | 0.121050 | ||||||||
\(253\) | −6.29208 | −0.395580 | ||||||||
\(254\) | 16.1144 | 1.01111 | ||||||||
\(255\) | 0.214130 | 0.0134094 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.4123 | −1.02377 | −0.511886 | − | 0.859053i | \(-0.671053\pi\) | ||||
−0.511886 | + | 0.859053i | \(0.671053\pi\) | |||||||
\(258\) | 10.4069 | 0.647903 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.2978 | 0.762676 | ||||||||
\(261\) | −3.05047 | −0.188819 | ||||||||
\(262\) | 0.822948 | 0.0508419 | ||||||||
\(263\) | 28.1414 | 1.73527 | 0.867637 | − | 0.497198i | \(-0.165638\pi\) | ||||
0.867637 | + | 0.497198i | \(0.165638\pi\) | |||||||
\(264\) | 3.97829 | 0.244847 | ||||||||
\(265\) | 8.14034 | 0.500057 | ||||||||
\(266\) | −11.6594 | −0.714885 | ||||||||
\(267\) | 15.5443 | 0.951293 | ||||||||
\(268\) | −6.92148 | −0.422796 | ||||||||
\(269\) | 23.1703 | 1.41272 | 0.706359 | − | 0.707854i | \(-0.250336\pi\) | ||||
0.706359 | + | 0.707854i | \(0.250336\pi\) | |||||||
\(270\) | −19.7777 | −1.20364 | ||||||||
\(271\) | 10.6088 | 0.644437 | 0.322219 | − | 0.946665i | \(-0.395571\pi\) | ||||
0.322219 | + | 0.946665i | \(0.395571\pi\) | |||||||
\(272\) | −0.0267197 | −0.00162012 | ||||||||
\(273\) | −19.5745 | −1.18470 | ||||||||
\(274\) | −17.3569 | −1.04857 | ||||||||
\(275\) | 27.9056 | 1.68277 | ||||||||
\(276\) | 5.58637 | 0.336260 | ||||||||
\(277\) | 24.0416 | 1.44452 | 0.722261 | − | 0.691621i | \(-0.243103\pi\) | ||||
0.722261 | + | 0.691621i | \(0.243103\pi\) | |||||||
\(278\) | 9.22544 | 0.553305 | ||||||||
\(279\) | 3.60188 | 0.215639 | ||||||||
\(280\) | −15.3997 | −0.920306 | ||||||||
\(281\) | 12.7248 | 0.759101 | 0.379550 | − | 0.925171i | \(-0.376079\pi\) | ||||
0.379550 | + | 0.925171i | \(0.376079\pi\) | |||||||
\(282\) | 4.91099 | 0.292445 | ||||||||
\(283\) | 0.257708 | 0.0153192 | 0.00765959 | − | 0.999971i | \(-0.497562\pi\) | ||||
0.00765959 | + | 0.999971i | \(0.497562\pi\) | |||||||
\(284\) | −9.27923 | −0.550621 | ||||||||
\(285\) | −25.8728 | −1.53257 | ||||||||
\(286\) | −6.10487 | −0.360989 | ||||||||
\(287\) | −5.38654 | −0.317957 | ||||||||
\(288\) | −0.532089 | −0.0313536 | ||||||||
\(289\) | −16.9993 | −0.999958 | ||||||||
\(290\) | 24.4463 | 1.43554 | ||||||||
\(291\) | 12.2635 | 0.718899 | ||||||||
\(292\) | −16.2707 | −0.952169 | ||||||||
\(293\) | −8.98077 | −0.524662 | −0.262331 | − | 0.964978i | \(-0.584491\pi\) | ||||
−0.262331 | + | 0.964978i | \(0.584491\pi\) | |||||||
\(294\) | 11.3561 | 0.662303 | ||||||||
\(295\) | 23.9850 | 1.39646 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.81807 | 0.569702 | ||||||||
\(298\) | 7.73776 | 0.448236 | ||||||||
\(299\) | −8.57253 | −0.495762 | ||||||||
\(300\) | −24.7757 | −1.43043 | ||||||||
\(301\) | 19.9979 | 1.15266 | ||||||||
\(302\) | −12.6363 | −0.727140 | ||||||||
\(303\) | 31.1968 | 1.79221 | ||||||||
\(304\) | 3.22847 | 0.185166 | ||||||||
\(305\) | 24.4799 | 1.40171 | ||||||||
\(306\) | 0.0142172 | 0.000812746 0 | ||||||||
\(307\) | 14.7982 | 0.844580 | 0.422290 | − | 0.906461i | \(-0.361226\pi\) | ||||
0.422290 | + | 0.906461i | \(0.361226\pi\) | |||||||
\(308\) | 7.64471 | 0.435598 | ||||||||
\(309\) | 3.56107 | 0.202582 | ||||||||
\(310\) | −28.8653 | −1.63944 | ||||||||
\(311\) | −26.7159 | −1.51492 | −0.757460 | − | 0.652881i | \(-0.773560\pi\) | ||||
−0.757460 | + | 0.652881i | \(0.773560\pi\) | |||||||
\(312\) | 5.42015 | 0.306856 | ||||||||
\(313\) | −9.52374 | −0.538314 | −0.269157 | − | 0.963096i | \(-0.586745\pi\) | ||||
−0.269157 | + | 0.963096i | \(0.586745\pi\) | |||||||
\(314\) | −13.0467 | −0.736270 | ||||||||
\(315\) | 8.19399 | 0.461679 | ||||||||
\(316\) | 1.41514 | 0.0796078 | ||||||||
\(317\) | 15.1557 | 0.851226 | 0.425613 | − | 0.904905i | \(-0.360058\pi\) | ||||
0.425613 | + | 0.904905i | \(0.360058\pi\) | |||||||
\(318\) | 3.58779 | 0.201193 | ||||||||
\(319\) | −12.1357 | −0.679466 | ||||||||
\(320\) | 4.26414 | 0.238373 | ||||||||
\(321\) | −0.718407 | −0.0400976 | ||||||||
\(322\) | 10.7348 | 0.598226 | ||||||||
\(323\) | −0.0862637 | −0.00479984 | ||||||||
\(324\) | −10.3131 | −0.572953 | ||||||||
\(325\) | 38.0195 | 2.10894 | ||||||||
\(326\) | −25.2564 | −1.39882 | ||||||||
\(327\) | 1.81470 | 0.100353 | ||||||||
\(328\) | 1.49152 | 0.0823556 | ||||||||
\(329\) | 9.43699 | 0.520278 | ||||||||
\(330\) | 16.9640 | 0.933837 | ||||||||
\(331\) | 2.06618 | 0.113568 | 0.0567838 | − | 0.998386i | \(-0.481915\pi\) | ||||
0.0567838 | + | 0.998386i | \(0.481915\pi\) | |||||||
\(332\) | −1.69642 | −0.0931030 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.2810 | −0.562552 | ||||||||
\(335\) | −29.5141 | −1.61253 | ||||||||
\(336\) | −6.78728 | −0.370276 | ||||||||
\(337\) | 13.9267 | 0.758637 | 0.379319 | − | 0.925266i | \(-0.376158\pi\) | ||||
0.379319 | + | 0.925266i | \(0.376158\pi\) | |||||||
\(338\) | 4.68253 | 0.254696 | ||||||||
\(339\) | 3.55344 | 0.192996 | ||||||||
\(340\) | −0.113936 | −0.00617907 | ||||||||
\(341\) | 14.3293 | 0.775977 | ||||||||
\(342\) | −1.71783 | −0.0928898 | ||||||||
\(343\) | −3.45806 | −0.186718 | ||||||||
\(344\) | −5.53737 | −0.298555 | ||||||||
\(345\) | 23.8210 | 1.28248 | ||||||||
\(346\) | 23.6569 | 1.27180 | ||||||||
\(347\) | −20.2115 | −1.08501 | −0.542505 | − | 0.840052i | \(-0.682524\pi\) | ||||
−0.542505 | + | 0.840052i | \(0.682524\pi\) | |||||||
\(348\) | 10.7745 | 0.577575 | ||||||||
\(349\) | 10.9899 | 0.588277 | 0.294138 | − | 0.955763i | \(-0.404967\pi\) | ||||
0.294138 | + | 0.955763i | \(0.404967\pi\) | |||||||
\(350\) | −47.6092 | −2.54482 | ||||||||
\(351\) | 13.3765 | 0.713982 | ||||||||
\(352\) | −2.11681 | −0.112826 | ||||||||
\(353\) | −4.35642 | −0.231869 | −0.115934 | − | 0.993257i | \(-0.536986\pi\) | ||||
−0.115934 | + | 0.993257i | \(0.536986\pi\) | |||||||
\(354\) | 10.5712 | 0.561853 | ||||||||
\(355\) | −39.5679 | −2.10005 | ||||||||
\(356\) | −8.27093 | −0.438358 | ||||||||
\(357\) | 0.181354 | 0.00959827 | ||||||||
\(358\) | −5.05746 | −0.267295 | ||||||||
\(359\) | 7.68664 | 0.405686 | 0.202843 | − | 0.979211i | \(-0.434982\pi\) | ||||
0.202843 | + | 0.979211i | \(0.434982\pi\) | |||||||
\(360\) | −2.26890 | −0.119582 | ||||||||
\(361\) | −8.57697 | −0.451420 | ||||||||
\(362\) | 1.04545 | 0.0549475 | ||||||||
\(363\) | 12.2520 | 0.643061 | ||||||||
\(364\) | 10.4154 | 0.545915 | ||||||||
\(365\) | −69.3804 | −3.63154 | ||||||||
\(366\) | 10.7893 | 0.563966 | ||||||||
\(367\) | 20.7176 | 1.08145 | 0.540726 | − | 0.841199i | \(-0.318150\pi\) | ||||
0.540726 | + | 0.841199i | \(0.318150\pi\) | |||||||
\(368\) | −2.97244 | −0.154949 | ||||||||
\(369\) | −0.793623 | −0.0413143 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.89431 | 0.357935 | ||||||||
\(372\) | −12.7222 | −0.659614 | ||||||||
\(373\) | −15.6066 | −0.808077 | −0.404038 | − | 0.914742i | \(-0.632394\pi\) | ||||
−0.404038 | + | 0.914742i | \(0.632394\pi\) | |||||||
\(374\) | 0.0565603 | 0.00292467 | ||||||||
\(375\) | −65.5773 | −3.38640 | ||||||||
\(376\) | −2.61309 | −0.134760 | ||||||||
\(377\) | −16.5340 | −0.851544 | ||||||||
\(378\) | −16.7504 | −0.861548 | ||||||||
\(379\) | −25.1769 | −1.29325 | −0.646626 | − | 0.762807i | \(-0.723820\pi\) | ||||
−0.646626 | + | 0.762807i | \(0.723820\pi\) | |||||||
\(380\) | 13.7667 | 0.706214 | ||||||||
\(381\) | 30.2852 | 1.55156 | ||||||||
\(382\) | −13.4633 | −0.688844 | ||||||||
\(383\) | −30.2135 | −1.54384 | −0.771919 | − | 0.635720i | \(-0.780703\pi\) | ||||
−0.771919 | + | 0.635720i | \(0.780703\pi\) | |||||||
\(384\) | 1.87939 | 0.0959070 | ||||||||
\(385\) | 32.5981 | 1.66135 | ||||||||
\(386\) | −4.52228 | −0.230178 | ||||||||
\(387\) | 2.94637 | 0.149773 | ||||||||
\(388\) | −6.52527 | −0.331270 | ||||||||
\(389\) | −25.0006 | −1.26758 | −0.633791 | − | 0.773505i | \(-0.718502\pi\) | ||||
−0.633791 | + | 0.773505i | \(0.718502\pi\) | |||||||
\(390\) | 23.1123 | 1.17034 | ||||||||
\(391\) | 0.0794227 | 0.00401658 | ||||||||
\(392\) | −6.04247 | −0.305191 | ||||||||
\(393\) | 1.54664 | 0.0780175 | ||||||||
\(394\) | 12.3720 | 0.623293 | ||||||||
\(395\) | 6.03435 | 0.303621 | ||||||||
\(396\) | 1.12633 | 0.0566001 | ||||||||
\(397\) | −13.6736 | −0.686260 | −0.343130 | − | 0.939288i | \(-0.611487\pi\) | ||||
−0.343130 | + | 0.939288i | \(0.611487\pi\) | |||||||
\(398\) | 4.50965 | 0.226048 | ||||||||
\(399\) | −21.9125 | −1.09700 | ||||||||
\(400\) | 13.1829 | 0.659144 | ||||||||
\(401\) | −1.62020 | −0.0809089 | −0.0404544 | − | 0.999181i | \(-0.512881\pi\) | ||||
−0.0404544 | + | 0.999181i | \(0.512881\pi\) | |||||||
\(402\) | −13.0081 | −0.648786 | ||||||||
\(403\) | 19.5227 | 0.972497 | ||||||||
\(404\) | −16.5995 | −0.825855 | ||||||||
\(405\) | −43.9767 | −2.18522 | ||||||||
\(406\) | 20.7044 | 1.02754 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.0502166 | −0.00248609 | ||||||||
\(409\) | 9.12867 | 0.451384 | 0.225692 | − | 0.974199i | \(-0.427536\pi\) | ||||
0.225692 | + | 0.974199i | \(0.427536\pi\) | |||||||
\(410\) | 6.36006 | 0.314101 | ||||||||
\(411\) | −32.6204 | −1.60904 | ||||||||
\(412\) | −1.89481 | −0.0933504 | ||||||||
\(413\) | 20.3137 | 0.999570 | ||||||||
\(414\) | 1.58160 | 0.0777316 | ||||||||
\(415\) | −7.23376 | −0.355091 | ||||||||
\(416\) | −2.88400 | −0.141400 | ||||||||
\(417\) | 17.3382 | 0.849053 | ||||||||
\(418\) | −6.83404 | −0.334264 | ||||||||
\(419\) | 14.2480 | 0.696060 | 0.348030 | − | 0.937483i | \(-0.386851\pi\) | ||||
0.348030 | + | 0.937483i | \(0.386851\pi\) | |||||||
\(420\) | −28.9419 | −1.41222 | ||||||||
\(421\) | 33.7943 | 1.64703 | 0.823516 | − | 0.567293i | \(-0.192009\pi\) | ||||
0.823516 | + | 0.567293i | \(0.192009\pi\) | |||||||
\(422\) | 16.2460 | 0.790842 | ||||||||
\(423\) | 1.39039 | 0.0676033 | ||||||||
\(424\) | −1.90902 | −0.0927103 | ||||||||
\(425\) | −0.352242 | −0.0170863 | ||||||||
\(426\) | −17.4392 | −0.844934 | ||||||||
\(427\) | 20.7328 | 1.00333 | ||||||||
\(428\) | 0.382256 | 0.0184771 | ||||||||
\(429\) | −11.4734 | −0.553941 | ||||||||
\(430\) | −23.6121 | −1.13868 | ||||||||
\(431\) | −38.8388 | −1.87080 | −0.935399 | − | 0.353594i | \(-0.884960\pi\) | ||||
−0.935399 | + | 0.353594i | \(0.884960\pi\) | |||||||
\(432\) | 4.63816 | 0.223153 | ||||||||
\(433\) | 18.1122 | 0.870417 | 0.435208 | − | 0.900330i | \(-0.356675\pi\) | ||||
0.435208 | + | 0.900330i | \(0.356675\pi\) | |||||||
\(434\) | −24.4470 | −1.17349 | ||||||||
\(435\) | 45.9441 | 2.20285 | ||||||||
\(436\) | −0.965584 | −0.0462431 | ||||||||
\(437\) | −9.59645 | −0.459060 | ||||||||
\(438\) | −30.5789 | −1.46111 | ||||||||
\(439\) | −14.3517 | −0.684967 | −0.342484 | − | 0.939524i | \(-0.611268\pi\) | ||||
−0.342484 | + | 0.939524i | \(0.611268\pi\) | |||||||
\(440\) | −9.02635 | −0.430315 | ||||||||
\(441\) | 3.21513 | 0.153101 | ||||||||
\(442\) | 0.0770596 | 0.00366535 | ||||||||
\(443\) | −5.43539 | −0.258243 | −0.129121 | − | 0.991629i | \(-0.541216\pi\) | ||||
−0.129121 | + | 0.991629i | \(0.541216\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.2684 | −1.67188 | ||||||||
\(446\) | 0.847777 | 0.0401434 | ||||||||
\(447\) | 14.5422 | 0.687824 | ||||||||
\(448\) | 3.61144 | 0.170624 | ||||||||
\(449\) | 0.130238 | 0.00614633 | 0.00307317 | − | 0.999995i | \(-0.499022\pi\) | ||||
0.00307317 | + | 0.999995i | \(0.499022\pi\) | |||||||
\(450\) | −7.01447 | −0.330665 | ||||||||
\(451\) | −3.15726 | −0.148670 | ||||||||
\(452\) | −1.89075 | −0.0889332 | ||||||||
\(453\) | −23.7485 | −1.11580 | ||||||||
\(454\) | −12.1287 | −0.569230 | ||||||||
\(455\) | 44.4127 | 2.08210 | ||||||||
\(456\) | 6.06754 | 0.284139 | ||||||||
\(457\) | 28.2675 | 1.32230 | 0.661150 | − | 0.750254i | \(-0.270069\pi\) | ||||
0.661150 | + | 0.750254i | \(0.270069\pi\) | |||||||
\(458\) | −13.2675 | −0.619950 | ||||||||
\(459\) | −0.123930 | −0.00578456 | ||||||||
\(460\) | −12.6749 | −0.590971 | ||||||||
\(461\) | 8.01301 | 0.373203 | 0.186601 | − | 0.982436i | \(-0.440253\pi\) | ||||
0.186601 | + | 0.982436i | \(0.440253\pi\) | |||||||
\(462\) | 14.3673 | 0.668430 | ||||||||
\(463\) | 34.2291 | 1.59076 | 0.795381 | − | 0.606110i | \(-0.207271\pi\) | ||||
0.795381 | + | 0.606110i | \(0.207271\pi\) | |||||||
\(464\) | −5.73300 | −0.266148 | ||||||||
\(465\) | −54.2491 | −2.51574 | ||||||||
\(466\) | 4.30657 | 0.199498 | ||||||||
\(467\) | 20.5376 | 0.950365 | 0.475182 | − | 0.879887i | \(-0.342382\pi\) | ||||
0.475182 | + | 0.879887i | \(0.342382\pi\) | |||||||
\(468\) | 1.53455 | 0.0709344 | ||||||||
\(469\) | −24.9965 | −1.15423 | ||||||||
\(470\) | −11.1426 | −0.513968 | ||||||||
\(471\) | −24.5198 | −1.12981 | ||||||||
\(472\) | −5.62482 | −0.258903 | ||||||||
\(473\) | 11.7215 | 0.538957 | ||||||||
\(474\) | 2.65959 | 0.122159 | ||||||||
\(475\) | 42.5606 | 1.95281 | ||||||||
\(476\) | −0.0964964 | −0.00442291 | ||||||||
\(477\) | 1.01577 | 0.0465089 | ||||||||
\(478\) | −14.2423 | −0.651428 | ||||||||
\(479\) | −6.29987 | −0.287848 | −0.143924 | − | 0.989589i | \(-0.545972\pi\) | ||||
−0.143924 | + | 0.989589i | \(0.545972\pi\) | |||||||
\(480\) | 8.01396 | 0.365786 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.2610 | 0.649572 | ||||||||
\(483\) | 20.1748 | 0.917985 | ||||||||
\(484\) | −6.51914 | −0.296324 | ||||||||
\(485\) | −27.8247 | −1.26345 | ||||||||
\(486\) | −5.46791 | −0.248029 | ||||||||
\(487\) | −27.5903 | −1.25024 | −0.625118 | − | 0.780530i | \(-0.714949\pi\) | ||||
−0.625118 | + | 0.780530i | \(0.714949\pi\) | |||||||
\(488\) | −5.74087 | −0.259877 | ||||||||
\(489\) | −47.4665 | −2.14651 | ||||||||
\(490\) | −25.7659 | −1.16399 | ||||||||
\(491\) | 33.0201 | 1.49018 | 0.745088 | − | 0.666967i | \(-0.232408\pi\) | ||||
0.745088 | + | 0.666967i | \(0.232408\pi\) | |||||||
\(492\) | 2.80315 | 0.126376 | ||||||||
\(493\) | 0.153184 | 0.00689906 | ||||||||
\(494\) | −9.31092 | −0.418918 | ||||||||
\(495\) | 4.80282 | 0.215871 | ||||||||
\(496\) | 6.76932 | 0.303952 | ||||||||
\(497\) | −33.5113 | −1.50319 | ||||||||
\(498\) | −3.18822 | −0.142868 | ||||||||
\(499\) | 21.0861 | 0.943944 | 0.471972 | − | 0.881613i | \(-0.343542\pi\) | ||||
0.471972 | + | 0.881613i | \(0.343542\pi\) | |||||||
\(500\) | 34.8930 | 1.56046 | ||||||||
\(501\) | −19.3220 | −0.863243 | ||||||||
\(502\) | 24.7076 | 1.10275 | ||||||||
\(503\) | 17.6544 | 0.787172 | 0.393586 | − | 0.919288i | \(-0.371234\pi\) | ||||
0.393586 | + | 0.919288i | \(0.371234\pi\) | |||||||
\(504\) | −1.92160 | −0.0855951 | ||||||||
\(505\) | −70.7825 | −3.14978 | ||||||||
\(506\) | 6.29208 | 0.279717 | ||||||||
\(507\) | 8.80028 | 0.390834 | ||||||||
\(508\) | −16.1144 | −0.714961 | ||||||||
\(509\) | −41.8141 | −1.85338 | −0.926688 | − | 0.375831i | \(-0.877357\pi\) | ||||
−0.926688 | + | 0.375831i | \(0.877357\pi\) | |||||||
\(510\) | −0.214130 | −0.00948186 | ||||||||
\(511\) | −58.7605 | −2.59941 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 14.9742 | 0.661125 | ||||||||
\(514\) | 16.4123 | 0.723916 | ||||||||
\(515\) | −8.07971 | −0.356035 | ||||||||
\(516\) | −10.4069 | −0.458136 | ||||||||
\(517\) | 5.53139 | 0.243270 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 44.4604 | 1.95160 | ||||||||
\(520\) | −12.2978 | −0.539294 | ||||||||
\(521\) | −35.9808 | −1.57635 | −0.788173 | − | 0.615453i | \(-0.788973\pi\) | ||||
−0.788173 | + | 0.615453i | \(0.788973\pi\) | |||||||
\(522\) | 3.05047 | 0.133515 | ||||||||
\(523\) | 32.8099 | 1.43468 | 0.717338 | − | 0.696725i | \(-0.245360\pi\) | ||||
0.717338 | + | 0.696725i | \(0.245360\pi\) | |||||||
\(524\) | −0.822948 | −0.0359507 | ||||||||
\(525\) | −89.4759 | −3.90505 | ||||||||
\(526\) | −28.1414 | −1.22702 | ||||||||
\(527\) | −0.180874 | −0.00787900 | ||||||||
\(528\) | −3.97829 | −0.173133 | ||||||||
\(529\) | −14.1646 | −0.615851 | ||||||||
\(530\) | −8.14034 | −0.353594 | ||||||||
\(531\) | 2.99290 | 0.129881 | ||||||||
\(532\) | 11.6594 | 0.505500 | ||||||||
\(533\) | −4.30156 | −0.186321 | ||||||||
\(534\) | −15.5443 | −0.672666 | ||||||||
\(535\) | 1.63000 | 0.0704708 | ||||||||
\(536\) | 6.92148 | 0.298962 | ||||||||
\(537\) | −9.50492 | −0.410168 | ||||||||
\(538\) | −23.1703 | −0.998943 | ||||||||
\(539\) | 12.7907 | 0.550936 | ||||||||
\(540\) | 19.7777 | 0.851099 | ||||||||
\(541\) | −37.5209 | −1.61315 | −0.806576 | − | 0.591131i | \(-0.798682\pi\) | ||||
−0.806576 | + | 0.591131i | \(0.798682\pi\) | |||||||
\(542\) | −10.6088 | −0.455686 | ||||||||
\(543\) | 1.96480 | 0.0843175 | ||||||||
\(544\) | 0.0267197 | 0.00114560 | ||||||||
\(545\) | −4.11739 | −0.176369 | ||||||||
\(546\) | 19.5745 | 0.837713 | ||||||||
\(547\) | 26.0779 | 1.11501 | 0.557505 | − | 0.830174i | \(-0.311759\pi\) | ||||
0.557505 | + | 0.830174i | \(0.311759\pi\) | |||||||
\(548\) | 17.3569 | 0.741452 | ||||||||
\(549\) | 3.05465 | 0.130369 | ||||||||
\(550\) | −27.9056 | −1.18990 | ||||||||
\(551\) | −18.5088 | −0.788503 | ||||||||
\(552\) | −5.58637 | −0.237772 | ||||||||
\(553\) | 5.11068 | 0.217328 | ||||||||
\(554\) | −24.0416 | −1.02143 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.22544 | −0.391246 | ||||||||
\(557\) | 6.50687 | 0.275705 | 0.137852 | − | 0.990453i | \(-0.455980\pi\) | ||||
0.137852 | + | 0.990453i | \(0.455980\pi\) | |||||||
\(558\) | −3.60188 | −0.152480 | ||||||||
\(559\) | 15.9698 | 0.675450 | ||||||||
\(560\) | 15.3997 | 0.650755 | ||||||||
\(561\) | 0.106299 | 0.00448793 | ||||||||
\(562\) | −12.7248 | −0.536765 | ||||||||
\(563\) | −38.7491 | −1.63308 | −0.816540 | − | 0.577289i | \(-0.804111\pi\) | ||||
−0.816540 | + | 0.577289i | \(0.804111\pi\) | |||||||
\(564\) | −4.91099 | −0.206790 | ||||||||
\(565\) | −8.06240 | −0.339188 | ||||||||
\(566\) | −0.257708 | −0.0108323 | ||||||||
\(567\) | −37.2453 | −1.56415 | ||||||||
\(568\) | 9.27923 | 0.389348 | ||||||||
\(569\) | 12.9149 | 0.541420 | 0.270710 | − | 0.962661i | \(-0.412742\pi\) | ||||
0.270710 | + | 0.962661i | \(0.412742\pi\) | |||||||
\(570\) | 25.8728 | 1.08369 | ||||||||
\(571\) | 2.99965 | 0.125531 | 0.0627657 | − | 0.998028i | \(-0.480008\pi\) | ||||
0.0627657 | + | 0.998028i | \(0.480008\pi\) | |||||||
\(572\) | 6.10487 | 0.255257 | ||||||||
\(573\) | −25.3028 | −1.05704 | ||||||||
\(574\) | 5.38654 | 0.224830 | ||||||||
\(575\) | −39.1854 | −1.63414 | ||||||||
\(576\) | 0.532089 | 0.0221704 | ||||||||
\(577\) | 28.8518 | 1.20112 | 0.600559 | − | 0.799581i | \(-0.294945\pi\) | ||||
0.600559 | + | 0.799581i | \(0.294945\pi\) | |||||||
\(578\) | 16.9993 | 0.707077 | ||||||||
\(579\) | −8.49911 | −0.353211 | ||||||||
\(580\) | −24.4463 | −1.01508 | ||||||||
\(581\) | −6.12650 | −0.254170 | ||||||||
\(582\) | −12.2635 | −0.508338 | ||||||||
\(583\) | 4.04103 | 0.167362 | ||||||||
\(584\) | 16.2707 | 0.673285 | ||||||||
\(585\) | 6.54352 | 0.270541 | ||||||||
\(586\) | 8.98077 | 0.370992 | ||||||||
\(587\) | 24.2762 | 1.00199 | 0.500993 | − | 0.865451i | \(-0.332968\pi\) | ||||
0.500993 | + | 0.865451i | \(0.332968\pi\) | |||||||
\(588\) | −11.3561 | −0.468319 | ||||||||
\(589\) | 21.8546 | 0.900502 | ||||||||
\(590\) | −23.9850 | −0.987447 | ||||||||
\(591\) | 23.2518 | 0.956450 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.0052 | 0.492995 | 0.246497 | − | 0.969143i | \(-0.420720\pi\) | ||||
0.246497 | + | 0.969143i | \(0.420720\pi\) | |||||||
\(594\) | −9.81807 | −0.402840 | ||||||||
\(595\) | −0.411474 | −0.0168688 | ||||||||
\(596\) | −7.73776 | −0.316951 | ||||||||
\(597\) | 8.47538 | 0.346874 | ||||||||
\(598\) | 8.57253 | 0.350557 | ||||||||
\(599\) | −19.0516 | −0.778426 | −0.389213 | − | 0.921148i | \(-0.627253\pi\) | ||||
−0.389213 | + | 0.921148i | \(0.627253\pi\) | |||||||
\(600\) | 24.7757 | 1.01146 | ||||||||
\(601\) | −22.7644 | −0.928579 | −0.464290 | − | 0.885683i | \(-0.653690\pi\) | ||||
−0.464290 | + | 0.885683i | \(0.653690\pi\) | |||||||
\(602\) | −19.9979 | −0.815052 | ||||||||
\(603\) | −3.68284 | −0.149977 | ||||||||
\(604\) | 12.6363 | 0.514165 | ||||||||
\(605\) | −27.7985 | −1.13017 | ||||||||
\(606\) | −31.1968 | −1.26728 | ||||||||
\(607\) | 19.6049 | 0.795739 | 0.397869 | − | 0.917442i | \(-0.369750\pi\) | ||||
0.397869 | + | 0.917442i | \(0.369750\pi\) | |||||||
\(608\) | −3.22847 | −0.130932 | ||||||||
\(609\) | 38.9115 | 1.57677 | ||||||||
\(610\) | −24.4799 | −0.991161 | ||||||||
\(611\) | 7.53614 | 0.304880 | ||||||||
\(612\) | −0.0142172 | −0.000574698 0 | ||||||||
\(613\) | 2.53879 | 0.102541 | 0.0512704 | − | 0.998685i | \(-0.483673\pi\) | ||||
0.0512704 | + | 0.998685i | \(0.483673\pi\) | |||||||
\(614\) | −14.7982 | −0.597208 | ||||||||
\(615\) | 11.9530 | 0.481992 | ||||||||
\(616\) | −7.64471 | −0.308014 | ||||||||
\(617\) | 18.9730 | 0.763825 | 0.381912 | − | 0.924199i | \(-0.375266\pi\) | ||||
0.381912 | + | 0.924199i | \(0.375266\pi\) | |||||||
\(618\) | −3.56107 | −0.143247 | ||||||||
\(619\) | −2.51358 | −0.101029 | −0.0505147 | − | 0.998723i | \(-0.516086\pi\) | ||||
−0.0505147 | + | 0.998723i | \(0.516086\pi\) | |||||||
\(620\) | 28.8653 | 1.15926 | ||||||||
\(621\) | −13.7867 | −0.553239 | ||||||||
\(622\) | 26.7159 | 1.07121 | ||||||||
\(623\) | −29.8699 | −1.19671 | ||||||||
\(624\) | −5.42015 | −0.216980 | ||||||||
\(625\) | 82.8741 | 3.31496 | ||||||||
\(626\) | 9.52374 | 0.380645 | ||||||||
\(627\) | −12.8438 | −0.512932 | ||||||||
\(628\) | 13.0467 | 0.520621 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −8.19399 | −0.326456 | ||||||||
\(631\) | 6.64305 | 0.264456 | 0.132228 | − | 0.991219i | \(-0.457787\pi\) | ||||
0.132228 | + | 0.991219i | \(0.457787\pi\) | |||||||
\(632\) | −1.41514 | −0.0562912 | ||||||||
\(633\) | 30.5324 | 1.21356 | ||||||||
\(634\) | −15.1557 | −0.601908 | ||||||||
\(635\) | −68.7140 | −2.72683 | ||||||||
\(636\) | −3.58779 | −0.142265 | ||||||||
\(637\) | 17.4265 | 0.690463 | ||||||||
\(638\) | 12.1357 | 0.480455 | ||||||||
\(639\) | −4.93737 | −0.195320 | ||||||||
\(640\) | −4.26414 | −0.168555 | ||||||||
\(641\) | 8.23442 | 0.325240 | 0.162620 | − | 0.986689i | \(-0.448006\pi\) | ||||
0.162620 | + | 0.986689i | \(0.448006\pi\) | |||||||
\(642\) | 0.718407 | 0.0283533 | ||||||||
\(643\) | −14.2192 | −0.560750 | −0.280375 | − | 0.959891i | \(-0.590459\pi\) | ||||
−0.280375 | + | 0.959891i | \(0.590459\pi\) | |||||||
\(644\) | −10.7348 | −0.423010 | ||||||||
\(645\) | −44.3763 | −1.74731 | ||||||||
\(646\) | 0.0862637 | 0.00339400 | ||||||||
\(647\) | 39.8752 | 1.56766 | 0.783828 | − | 0.620977i | \(-0.213264\pi\) | ||||
0.783828 | + | 0.620977i | \(0.213264\pi\) | |||||||
\(648\) | 10.3131 | 0.405139 | ||||||||
\(649\) | 11.9066 | 0.467377 | ||||||||
\(650\) | −38.0195 | −1.49125 | ||||||||
\(651\) | −45.9453 | −1.80074 | ||||||||
\(652\) | 25.2564 | 0.989117 | ||||||||
\(653\) | −8.11503 | −0.317566 | −0.158783 | − | 0.987314i | \(-0.550757\pi\) | ||||
−0.158783 | + | 0.987314i | \(0.550757\pi\) | |||||||
\(654\) | −1.81470 | −0.0709606 | ||||||||
\(655\) | −3.50917 | −0.137114 | ||||||||
\(656\) | −1.49152 | −0.0582342 | ||||||||
\(657\) | −8.65745 | −0.337759 | ||||||||
\(658\) | −9.43699 | −0.367892 | ||||||||
\(659\) | 28.0448 | 1.09247 | 0.546235 | − | 0.837632i | \(-0.316061\pi\) | ||||
0.546235 | + | 0.837632i | \(0.316061\pi\) | |||||||
\(660\) | −16.9640 | −0.660323 | ||||||||
\(661\) | −4.52498 | −0.176001 | −0.0880007 | − | 0.996120i | \(-0.528048\pi\) | ||||
−0.0880007 | + | 0.996120i | \(0.528048\pi\) | |||||||
\(662\) | −2.06618 | −0.0803044 | ||||||||
\(663\) | 0.144825 | 0.00562452 | ||||||||
\(664\) | 1.69642 | 0.0658338 | ||||||||
\(665\) | 49.7174 | 1.92796 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.0410 | 0.659831 | ||||||||
\(668\) | 10.2810 | 0.397785 | ||||||||
\(669\) | 1.59330 | 0.0616005 | ||||||||
\(670\) | 29.5141 | 1.14023 | ||||||||
\(671\) | 12.1523 | 0.469135 | ||||||||
\(672\) | 6.78728 | 0.261825 | ||||||||
\(673\) | 10.4858 | 0.404199 | 0.202100 | − | 0.979365i | \(-0.435224\pi\) | ||||
0.202100 | + | 0.979365i | \(0.435224\pi\) | |||||||
\(674\) | −13.9267 | −0.536438 | ||||||||
\(675\) | 61.1443 | 2.35344 | ||||||||
\(676\) | −4.68253 | −0.180097 | ||||||||
\(677\) | −26.8553 | −1.03213 | −0.516067 | − | 0.856549i | \(-0.672604\pi\) | ||||
−0.516067 | + | 0.856549i | \(0.672604\pi\) | |||||||
\(678\) | −3.55344 | −0.136469 | ||||||||
\(679\) | −23.5656 | −0.904365 | ||||||||
\(680\) | 0.113936 | 0.00436926 | ||||||||
\(681\) | −22.7946 | −0.873490 | ||||||||
\(682\) | −14.3293 | −0.548699 | ||||||||
\(683\) | −17.8721 | −0.683858 | −0.341929 | − | 0.939726i | \(-0.611080\pi\) | ||||
−0.341929 | + | 0.939726i | \(0.611080\pi\) | |||||||
\(684\) | 1.71783 | 0.0656830 | ||||||||
\(685\) | 74.0124 | 2.82787 | ||||||||
\(686\) | 3.45806 | 0.132029 | ||||||||
\(687\) | −24.9347 | −0.951320 | ||||||||
\(688\) | 5.53737 | 0.211110 | ||||||||
\(689\) | 5.50563 | 0.209748 | ||||||||
\(690\) | −23.8210 | −0.906852 | ||||||||
\(691\) | −21.1083 | −0.802999 | −0.401499 | − | 0.915859i | \(-0.631511\pi\) | ||||
−0.401499 | + | 0.915859i | \(0.631511\pi\) | |||||||
\(692\) | −23.6569 | −0.899300 | ||||||||
\(693\) | 4.06766 | 0.154518 | ||||||||
\(694\) | 20.2115 | 0.767218 | ||||||||
\(695\) | −39.3386 | −1.49220 | ||||||||
\(696\) | −10.7745 | −0.408407 | ||||||||
\(697\) | 0.0398530 | 0.00150954 | ||||||||
\(698\) | −10.9899 | −0.415974 | ||||||||
\(699\) | 8.09370 | 0.306132 | ||||||||
\(700\) | 47.6092 | 1.79946 | ||||||||
\(701\) | 4.57469 | 0.172784 | 0.0863919 | − | 0.996261i | \(-0.472466\pi\) | ||||
0.0863919 | + | 0.996261i | \(0.472466\pi\) | |||||||
\(702\) | −13.3765 | −0.504862 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.11681 | 0.0797801 | ||||||||
\(705\) | −20.9412 | −0.788690 | ||||||||
\(706\) | 4.35642 | 0.163956 | ||||||||
\(707\) | −59.9480 | −2.25458 | ||||||||
\(708\) | −10.5712 | −0.397290 | ||||||||
\(709\) | −4.67695 | −0.175647 | −0.0878233 | − | 0.996136i | \(-0.527991\pi\) | ||||
−0.0878233 | + | 0.996136i | \(0.527991\pi\) | |||||||
\(710\) | 39.5679 | 1.48496 | ||||||||
\(711\) | 0.752980 | 0.0282389 | ||||||||
\(712\) | 8.27093 | 0.309966 | ||||||||
\(713\) | −20.1214 | −0.753553 | ||||||||
\(714\) | −0.181354 | −0.00678700 | ||||||||
\(715\) | 26.0320 | 0.973542 | ||||||||
\(716\) | 5.05746 | 0.189006 | ||||||||
\(717\) | −26.7668 | −0.999624 | ||||||||
\(718\) | −7.68664 | −0.286863 | ||||||||
\(719\) | 46.0624 | 1.71784 | 0.858919 | − | 0.512112i | \(-0.171137\pi\) | ||||
0.858919 | + | 0.512112i | \(0.171137\pi\) | |||||||
\(720\) | 2.26890 | 0.0845570 | ||||||||
\(721\) | −6.84297 | −0.254845 | ||||||||
\(722\) | 8.57697 | 0.319202 | ||||||||
\(723\) | 26.8019 | 0.996775 | ||||||||
\(724\) | −1.04545 | −0.0388537 | ||||||||
\(725\) | −75.5775 | −2.80688 | ||||||||
\(726\) | −12.2520 | −0.454713 | ||||||||
\(727\) | 43.5632 | 1.61567 | 0.807835 | − | 0.589408i | \(-0.200639\pi\) | ||||
0.807835 | + | 0.589408i | \(0.200639\pi\) | |||||||
\(728\) | −10.4154 | −0.386020 | ||||||||
\(729\) | 20.6631 | 0.765301 | ||||||||
\(730\) | 69.3804 | 2.56789 | ||||||||
\(731\) | −0.147957 | −0.00547238 | ||||||||
\(732\) | −10.7893 | −0.398784 | ||||||||
\(733\) | 27.8003 | 1.02683 | 0.513414 | − | 0.858141i | \(-0.328380\pi\) | ||||
0.513414 | + | 0.858141i | \(0.328380\pi\) | |||||||
\(734\) | −20.7176 | −0.764702 | ||||||||
\(735\) | −48.4241 | −1.78615 | ||||||||
\(736\) | 2.97244 | 0.109566 | ||||||||
\(737\) | −14.6514 | −0.539692 | ||||||||
\(738\) | 0.793623 | 0.0292137 | ||||||||
\(739\) | −26.4463 | −0.972843 | −0.486421 | − | 0.873724i | \(-0.661698\pi\) | ||||
−0.486421 | + | 0.873724i | \(0.661698\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.4988 | −0.642835 | ||||||||
\(742\) | −6.89431 | −0.253098 | ||||||||
\(743\) | −40.5404 | −1.48728 | −0.743641 | − | 0.668579i | \(-0.766903\pi\) | ||||
−0.743641 | + | 0.668579i | \(0.766903\pi\) | |||||||
\(744\) | 12.7222 | 0.466417 | ||||||||
\(745\) | −32.9949 | −1.20884 | ||||||||
\(746\) | 15.6066 | 0.571397 | ||||||||
\(747\) | −0.902645 | −0.0330261 | ||||||||
\(748\) | −0.0565603 | −0.00206805 | ||||||||
\(749\) | 1.38049 | 0.0504422 | ||||||||
\(750\) | 65.5773 | 2.39455 | ||||||||
\(751\) | −10.2833 | −0.375242 | −0.187621 | − | 0.982241i | \(-0.560078\pi\) | ||||
−0.187621 | + | 0.982241i | \(0.560078\pi\) | |||||||
\(752\) | 2.61309 | 0.0952894 | ||||||||
\(753\) | 46.4350 | 1.69219 | ||||||||
\(754\) | 16.5340 | 0.602133 | ||||||||
\(755\) | 53.8831 | 1.96101 | ||||||||
\(756\) | 16.7504 | 0.609206 | ||||||||
\(757\) | 35.4525 | 1.28854 | 0.644271 | − | 0.764797i | \(-0.277161\pi\) | ||||
0.644271 | + | 0.764797i | \(0.277161\pi\) | |||||||
\(758\) | 25.1769 | 0.914467 | ||||||||
\(759\) | 11.8252 | 0.429229 | ||||||||
\(760\) | −13.7667 | −0.499369 | ||||||||
\(761\) | −4.99043 | −0.180903 | −0.0904515 | − | 0.995901i | \(-0.528831\pi\) | ||||
−0.0904515 | + | 0.995901i | \(0.528831\pi\) | |||||||
\(762\) | −30.2852 | −1.09712 | ||||||||
\(763\) | −3.48715 | −0.126243 | ||||||||
\(764\) | 13.4633 | 0.487087 | ||||||||
\(765\) | −0.0606243 | −0.00219188 | ||||||||
\(766\) | 30.2135 | 1.09166 | ||||||||
\(767\) | 16.2220 | 0.585742 | ||||||||
\(768\) | −1.87939 | −0.0678165 | ||||||||
\(769\) | 35.2184 | 1.27001 | 0.635004 | − | 0.772509i | \(-0.280999\pi\) | ||||
0.635004 | + | 0.772509i | \(0.280999\pi\) | |||||||
\(770\) | −32.5981 | −1.17475 | ||||||||
\(771\) | 30.8451 | 1.11086 | ||||||||
\(772\) | 4.52228 | 0.162760 | ||||||||
\(773\) | −10.7155 | −0.385409 | −0.192704 | − | 0.981257i | \(-0.561726\pi\) | ||||
−0.192704 | + | 0.981257i | \(0.561726\pi\) | |||||||
\(774\) | −2.94637 | −0.105905 | ||||||||
\(775\) | 89.2392 | 3.20557 | ||||||||
\(776\) | 6.52527 | 0.234244 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.0006 | 0.896316 | ||||||||
\(779\) | −4.81534 | −0.172527 | ||||||||
\(780\) | −23.1123 | −0.827552 | ||||||||
\(781\) | −19.6423 | −0.702857 | ||||||||
\(782\) | −0.0794227 | −0.00284015 | ||||||||
\(783\) | −26.5906 | −0.950269 | ||||||||
\(784\) | 6.04247 | 0.215803 | ||||||||
\(785\) | 55.6331 | 1.98563 | ||||||||
\(786\) | −1.54664 | −0.0551667 | ||||||||
\(787\) | 27.2203 | 0.970297 | 0.485149 | − | 0.874432i | \(-0.338766\pi\) | ||||
0.485149 | + | 0.874432i | \(0.338766\pi\) | |||||||
\(788\) | −12.3720 | −0.440735 | ||||||||
\(789\) | −52.8886 | −1.88288 | ||||||||
\(790\) | −6.03435 | −0.214693 | ||||||||
\(791\) | −6.82831 | −0.242787 | ||||||||
\(792\) | −1.12633 | −0.0400223 | ||||||||
\(793\) | 16.5567 | 0.587945 | ||||||||
\(794\) | 13.6736 | 0.485259 | ||||||||
\(795\) | −15.2988 | −0.542594 | ||||||||
\(796\) | −4.50965 | −0.159840 | ||||||||
\(797\) | 3.10673 | 0.110046 | 0.0550231 | − | 0.998485i | \(-0.482477\pi\) | ||||
0.0550231 | + | 0.998485i | \(0.482477\pi\) | |||||||
\(798\) | 21.9125 | 0.775695 | ||||||||
\(799\) | −0.0698208 | −0.00247008 | ||||||||
\(800\) | −13.1829 | −0.466085 | ||||||||
\(801\) | −4.40087 | −0.155497 | ||||||||
\(802\) | 1.62020 | 0.0572112 | ||||||||
\(803\) | −34.4419 | −1.21543 | ||||||||
\(804\) | 13.0081 | 0.458761 | ||||||||
\(805\) | −45.7746 | −1.61334 | ||||||||
\(806\) | −19.5227 | −0.687659 | ||||||||
\(807\) | −43.5459 | −1.53289 | ||||||||
\(808\) | 16.5995 | 0.583968 | ||||||||
\(809\) | −5.19497 | −0.182645 | −0.0913227 | − | 0.995821i | \(-0.529109\pi\) | ||||
−0.0913227 | + | 0.995821i | \(0.529109\pi\) | |||||||
\(810\) | 43.9767 | 1.54518 | ||||||||
\(811\) | 31.9817 | 1.12303 | 0.561514 | − | 0.827467i | \(-0.310219\pi\) | ||||
0.561514 | + | 0.827467i | \(0.310219\pi\) | |||||||
\(812\) | −20.7044 | −0.726581 | ||||||||
\(813\) | −19.9380 | −0.699255 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 107.697 | 3.77245 | ||||||||
\(816\) | 0.0502166 | 0.00175793 | ||||||||
\(817\) | 17.8772 | 0.625446 | ||||||||
\(818\) | −9.12867 | −0.319176 | ||||||||
\(819\) | 5.54191 | 0.193650 | ||||||||
\(820\) | −6.36006 | −0.222103 | ||||||||
\(821\) | 7.49467 | 0.261566 | 0.130783 | − | 0.991411i | \(-0.458251\pi\) | ||||
0.130783 | + | 0.991411i | \(0.458251\pi\) | |||||||
\(822\) | 32.6204 | 1.13777 | ||||||||
\(823\) | −40.9456 | −1.42727 | −0.713637 | − | 0.700516i | \(-0.752953\pi\) | ||||
−0.713637 | + | 0.700516i | \(0.752953\pi\) | |||||||
\(824\) | 1.89481 | 0.0660087 | ||||||||
\(825\) | −52.4454 | −1.82591 | ||||||||
\(826\) | −20.3137 | −0.706803 | ||||||||
\(827\) | 43.8214 | 1.52382 | 0.761909 | − | 0.647684i | \(-0.224262\pi\) | ||||
0.761909 | + | 0.647684i | \(0.224262\pi\) | |||||||
\(828\) | −1.58160 | −0.0549645 | ||||||||
\(829\) | −36.3976 | −1.26414 | −0.632071 | − | 0.774911i | \(-0.717795\pi\) | ||||
−0.632071 | + | 0.774911i | \(0.717795\pi\) | |||||||
\(830\) | 7.23376 | 0.251088 | ||||||||
\(831\) | −45.1835 | −1.56740 | ||||||||
\(832\) | 2.88400 | 0.0999848 | ||||||||
\(833\) | −0.161453 | −0.00559401 | ||||||||
\(834\) | −17.3382 | −0.600371 | ||||||||
\(835\) | 43.8397 | 1.51714 | ||||||||
\(836\) | 6.83404 | 0.236360 | ||||||||
\(837\) | 31.3972 | 1.08525 | ||||||||
\(838\) | −14.2480 | −0.492189 | ||||||||
\(839\) | −22.1035 | −0.763099 | −0.381549 | − | 0.924348i | \(-0.624609\pi\) | ||||
−0.381549 | + | 0.924348i | \(0.624609\pi\) | |||||||
\(840\) | 28.9419 | 0.998591 | ||||||||
\(841\) | 3.86732 | 0.133356 | ||||||||
\(842\) | −33.7943 | −1.16463 | ||||||||
\(843\) | −23.9149 | −0.823673 | ||||||||
\(844\) | −16.2460 | −0.559209 | ||||||||
\(845\) | −19.9670 | −0.686885 | ||||||||
\(846\) | −1.39039 | −0.0478027 | ||||||||
\(847\) | −23.5434 | −0.808962 | ||||||||
\(848\) | 1.90902 | 0.0655561 | ||||||||
\(849\) | −0.484333 | −0.0166223 | ||||||||
\(850\) | 0.352242 | 0.0120818 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 17.4392 | 0.597459 | ||||||||
\(853\) | −41.7706 | −1.43020 | −0.715100 | − | 0.699023i | \(-0.753619\pi\) | ||||
−0.715100 | + | 0.699023i | \(0.753619\pi\) | |||||||
\(854\) | −20.7328 | −0.709462 | ||||||||
\(855\) | 7.32508 | 0.250513 | ||||||||
\(856\) | −0.382256 | −0.0130653 | ||||||||
\(857\) | 2.80039 | 0.0956595 | 0.0478297 | − | 0.998856i | \(-0.484770\pi\) | ||||
0.0478297 | + | 0.998856i | \(0.484770\pi\) | |||||||
\(858\) | 11.4734 | 0.391696 | ||||||||
\(859\) | −33.5977 | −1.14634 | −0.573169 | − | 0.819437i | \(-0.694286\pi\) | ||||
−0.573169 | + | 0.819437i | \(0.694286\pi\) | |||||||
\(860\) | 23.6121 | 0.805167 | ||||||||
\(861\) | 10.1234 | 0.345004 | ||||||||
\(862\) | 38.8388 | 1.32285 | ||||||||
\(863\) | −25.4084 | −0.864913 | −0.432456 | − | 0.901655i | \(-0.642353\pi\) | ||||
−0.432456 | + | 0.901655i | \(0.642353\pi\) | |||||||
\(864\) | −4.63816 | −0.157793 | ||||||||
\(865\) | −100.876 | −3.42990 | ||||||||
\(866\) | −18.1122 | −0.615478 | ||||||||
\(867\) | 31.9482 | 1.08502 | ||||||||
\(868\) | 24.4470 | 0.829784 | ||||||||
\(869\) | 2.99557 | 0.101618 | ||||||||
\(870\) | −45.9441 | −1.55765 | ||||||||
\(871\) | −19.9616 | −0.676371 | ||||||||
\(872\) | 0.965584 | 0.0326988 | ||||||||
\(873\) | −3.47202 | −0.117510 | ||||||||
\(874\) | 9.59645 | 0.324605 | ||||||||
\(875\) | 126.014 | 4.26004 | ||||||||
\(876\) | 30.5789 | 1.03316 | ||||||||
\(877\) | 21.1796 | 0.715183 | 0.357591 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357591 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(878\) | 14.3517 | 0.484345 | ||||||||
\(879\) | 16.8783 | 0.569292 | ||||||||
\(880\) | 9.02635 | 0.304278 | ||||||||
\(881\) | 14.5051 | 0.488690 | 0.244345 | − | 0.969688i | \(-0.421427\pi\) | ||||
0.244345 | + | 0.969688i | \(0.421427\pi\) | |||||||
\(882\) | −3.21513 | −0.108259 | ||||||||
\(883\) | 37.1477 | 1.25012 | 0.625060 | − | 0.780577i | \(-0.285075\pi\) | ||||
0.625060 | + | 0.780577i | \(0.285075\pi\) | |||||||
\(884\) | −0.0770596 | −0.00259179 | ||||||||
\(885\) | −45.0771 | −1.51525 | ||||||||
\(886\) | 5.43539 | 0.182605 | ||||||||
\(887\) | −2.08616 | −0.0700464 | −0.0350232 | − | 0.999386i | \(-0.511151\pi\) | ||||
−0.0350232 | + | 0.999386i | \(0.511151\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −58.1961 | −1.95183 | ||||||||
\(890\) | 35.2684 | 1.18220 | ||||||||
\(891\) | −21.8309 | −0.731364 | ||||||||
\(892\) | −0.847777 | −0.0283857 | ||||||||
\(893\) | 8.43627 | 0.282309 | ||||||||
\(894\) | −14.5422 | −0.486365 | ||||||||
\(895\) | 21.5657 | 0.720863 | ||||||||
\(896\) | −3.61144 | −0.120650 | ||||||||
\(897\) | 16.1111 | 0.537934 | ||||||||
\(898\) | −0.130238 | −0.00434611 | ||||||||
\(899\) | −38.8085 | −1.29434 | ||||||||
\(900\) | 7.01447 | 0.233816 | ||||||||
\(901\) | −0.0510085 | −0.00169934 | ||||||||
\(902\) | 3.15726 | 0.105125 | ||||||||
\(903\) | −37.5837 | −1.25071 | ||||||||
\(904\) | 1.89075 | 0.0628852 | ||||||||
\(905\) | −4.45793 | −0.148187 | ||||||||
\(906\) | 23.7485 | 0.788993 | ||||||||
\(907\) | −10.3856 | −0.344849 | −0.172425 | − | 0.985023i | \(-0.555160\pi\) | ||||
−0.172425 | + | 0.985023i | \(0.555160\pi\) | |||||||
\(908\) | 12.1287 | 0.402506 | ||||||||
\(909\) | −8.83240 | −0.292952 | ||||||||
\(910\) | −44.4127 | −1.47227 | ||||||||
\(911\) | 6.68612 | 0.221521 | 0.110761 | − | 0.993847i | \(-0.464671\pi\) | ||||
0.110761 | + | 0.993847i | \(0.464671\pi\) | |||||||
\(912\) | −6.06754 | −0.200916 | ||||||||
\(913\) | −3.59099 | −0.118844 | ||||||||
\(914\) | −28.2675 | −0.935007 | ||||||||
\(915\) | −46.0071 | −1.52095 | ||||||||
\(916\) | 13.2675 | 0.438371 | ||||||||
\(917\) | −2.97202 | −0.0981449 | ||||||||
\(918\) | 0.123930 | 0.00409030 | ||||||||
\(919\) | −48.7881 | −1.60937 | −0.804685 | − | 0.593702i | \(-0.797666\pi\) | ||||
−0.804685 | + | 0.593702i | \(0.797666\pi\) | |||||||
\(920\) | 12.6749 | 0.417879 | ||||||||
\(921\) | −27.8116 | −0.916423 | ||||||||
\(922\) | −8.01301 | −0.263894 | ||||||||
\(923\) | −26.7613 | −0.880859 | ||||||||
\(924\) | −14.3673 | −0.472651 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34.2291 | −1.12484 | ||||||||
\(927\) | −1.00820 | −0.0331138 | ||||||||
\(928\) | 5.73300 | 0.188195 | ||||||||
\(929\) | 24.1954 | 0.793825 | 0.396913 | − | 0.917856i | \(-0.370082\pi\) | ||||
0.396913 | + | 0.917856i | \(0.370082\pi\) | |||||||
\(930\) | 54.2491 | 1.77890 | ||||||||
\(931\) | 19.5079 | 0.639347 | ||||||||
\(932\) | −4.30657 | −0.141066 | ||||||||
\(933\) | 50.2095 | 1.64378 | ||||||||
\(934\) | −20.5376 | −0.672009 | ||||||||
\(935\) | −0.241181 | −0.00788747 | ||||||||
\(936\) | −1.53455 | −0.0501582 | ||||||||
\(937\) | −58.5924 | −1.91413 | −0.957065 | − | 0.289873i | \(-0.906387\pi\) | ||||
−0.957065 | + | 0.289873i | \(0.906387\pi\) | |||||||
\(938\) | 24.9965 | 0.816164 | ||||||||
\(939\) | 17.8988 | 0.584105 | ||||||||
\(940\) | 11.1426 | 0.363430 | ||||||||
\(941\) | −47.0814 | −1.53481 | −0.767405 | − | 0.641163i | \(-0.778452\pi\) | ||||
−0.767405 | + | 0.641163i | \(0.778452\pi\) | |||||||
\(942\) | 24.5198 | 0.798900 | ||||||||
\(943\) | 4.43347 | 0.144374 | ||||||||
\(944\) | 5.62482 | 0.183072 | ||||||||
\(945\) | 71.4261 | 2.32349 | ||||||||
\(946\) | −11.7215 | −0.381100 | ||||||||
\(947\) | 19.1273 | 0.621553 | 0.310776 | − | 0.950483i | \(-0.399411\pi\) | ||||
0.310776 | + | 0.950483i | \(0.399411\pi\) | |||||||
\(948\) | −2.65959 | −0.0863795 | ||||||||
\(949\) | −46.9247 | −1.52324 | ||||||||
\(950\) | −42.5606 | −1.38085 | ||||||||
\(951\) | −28.4833 | −0.923635 | ||||||||
\(952\) | 0.0964964 | 0.00312747 | ||||||||
\(953\) | −0.858570 | −0.0278118 | −0.0139059 | − | 0.999903i | \(-0.504427\pi\) | ||||
−0.0139059 | + | 0.999903i | \(0.504427\pi\) | |||||||
\(954\) | −1.01577 | −0.0328868 | ||||||||
\(955\) | 57.4096 | 1.85773 | ||||||||
\(956\) | 14.2423 | 0.460629 | ||||||||
\(957\) | 22.8076 | 0.737264 | ||||||||
\(958\) | 6.29987 | 0.203540 | ||||||||
\(959\) | 62.6835 | 2.02416 | ||||||||
\(960\) | −8.01396 | −0.258649 | ||||||||
\(961\) | 14.8237 | 0.478185 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.203394 | 0.00655429 | ||||||||
\(964\) | −14.2610 | −0.459316 | ||||||||
\(965\) | 19.2836 | 0.620762 | ||||||||
\(966\) | −20.1748 | −0.649114 | ||||||||
\(967\) | −60.3645 | −1.94119 | −0.970596 | − | 0.240714i | \(-0.922618\pi\) | ||||
−0.970596 | + | 0.240714i | \(0.922618\pi\) | |||||||
\(968\) | 6.51914 | 0.209533 | ||||||||
\(969\) | 0.162123 | 0.00520813 | ||||||||
\(970\) | 27.8247 | 0.893396 | ||||||||
\(971\) | −35.3779 | −1.13533 | −0.567665 | − | 0.823260i | \(-0.692153\pi\) | ||||
−0.567665 | + | 0.823260i | \(0.692153\pi\) | |||||||
\(972\) | 5.46791 | 0.175383 | ||||||||
\(973\) | −33.3171 | −1.06810 | ||||||||
\(974\) | 27.5903 | 0.884050 | ||||||||
\(975\) | −71.4532 | −2.28834 | ||||||||
\(976\) | 5.74087 | 0.183761 | ||||||||
\(977\) | 34.2781 | 1.09665 | 0.548327 | − | 0.836264i | \(-0.315265\pi\) | ||||
0.548327 | + | 0.836264i | \(0.315265\pi\) | |||||||
\(978\) | 47.4665 | 1.51781 | ||||||||
\(979\) | −17.5079 | −0.559556 | ||||||||
\(980\) | 25.7659 | 0.823063 | ||||||||
\(981\) | −0.513777 | −0.0164036 | ||||||||
\(982\) | −33.0201 | −1.05371 | ||||||||
\(983\) | −16.2324 | −0.517734 | −0.258867 | − | 0.965913i | \(-0.583349\pi\) | ||||
−0.258867 | + | 0.965913i | \(0.583349\pi\) | |||||||
\(984\) | −2.80315 | −0.0893610 | ||||||||
\(985\) | −52.7560 | −1.68095 | ||||||||
\(986\) | −0.153184 | −0.00487837 | ||||||||
\(987\) | −17.7357 | −0.564535 | ||||||||
\(988\) | 9.31092 | 0.296220 | ||||||||
\(989\) | −16.4595 | −0.523382 | ||||||||
\(990\) | −4.80282 | −0.152644 | ||||||||
\(991\) | 3.38215 | 0.107437 | 0.0537187 | − | 0.998556i | \(-0.482893\pi\) | ||||
0.0537187 | + | 0.998556i | \(0.482893\pi\) | |||||||
\(992\) | −6.76932 | −0.214926 | ||||||||
\(993\) | −3.88315 | −0.123228 | ||||||||
\(994\) | 33.5113 | 1.06292 | ||||||||
\(995\) | −19.2298 | −0.609625 | ||||||||
\(996\) | 3.18822 | 0.101023 | ||||||||
\(997\) | −40.0933 | −1.26977 | −0.634883 | − | 0.772608i | \(-0.718952\pi\) | ||||
−0.634883 | + | 0.772608i | \(0.718952\pi\) | |||||||
\(998\) | −21.0861 | −0.667469 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2738.2.a.r.1.2 | 6 | ||
37.5 | odd | 36 | 74.2.h.a.25.2 | yes | 12 | ||
37.15 | odd | 36 | 74.2.h.a.3.2 | ✓ | 12 | ||
37.36 | even | 2 | 2738.2.a.s.1.1 | 6 | |||
111.5 | even | 36 | 666.2.bj.c.469.1 | 12 | |||
111.89 | even | 36 | 666.2.bj.c.595.1 | 12 | |||
148.15 | even | 36 | 592.2.bq.b.225.1 | 12 | |||
148.79 | even | 36 | 592.2.bq.b.321.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.h.a.3.2 | ✓ | 12 | 37.15 | odd | 36 | ||
74.2.h.a.25.2 | yes | 12 | 37.5 | odd | 36 | ||
592.2.bq.b.225.1 | 12 | 148.15 | even | 36 | |||
592.2.bq.b.321.1 | 12 | 148.79 | even | 36 | |||
666.2.bj.c.469.1 | 12 | 111.5 | even | 36 | |||
666.2.bj.c.595.1 | 12 | 111.89 | even | 36 | |||
2738.2.a.r.1.2 | 6 | 1.1 | even | 1 | trivial | ||
2738.2.a.s.1.1 | 6 | 37.36 | even | 2 |