Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5 x^{13} - 9 x^{12} + 76 x^{11} - 12 x^{10} - 414 x^{9} + 331 x^{8} + 959 x^{7} - 1067 x^{6} - 875 x^{5} + 1134 x^{4} + 301 x^{3} - 418 x^{2} - 42 x + 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.66571\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.66571 | 1.88494 | 0.942472 | − | 0.334286i | \(-0.108495\pi\) | ||||
0.942472 | + | 0.334286i | \(0.108495\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.10602 | 2.55301 | ||||||||
\(5\) | −0.697799 | −0.312065 | −0.156032 | − | 0.987752i | \(-0.549870\pi\) | ||||
−0.156032 | + | 0.987752i | \(0.549870\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 8.27977 | 2.92734 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.86013 | −0.588225 | ||||||||
\(11\) | 1.70540 | 0.514197 | 0.257099 | − | 0.966385i | \(-0.417233\pi\) | ||||
0.257099 | + | 0.966385i | \(0.417233\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0102354 | −0.00283879 | −0.00141940 | − | 0.999999i | \(-0.500452\pi\) | ||||
−0.00141940 | + | 0.999999i | \(0.500452\pi\) | |||||||
\(14\) | −2.66571 | −0.712442 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.8594 | 2.96486 | ||||||||
\(17\) | 3.99137 | 0.968049 | 0.484025 | − | 0.875054i | \(-0.339174\pi\) | ||||
0.484025 | + | 0.875054i | \(0.339174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.49924 | 0.802780 | 0.401390 | − | 0.915907i | \(-0.368527\pi\) | ||||
0.401390 | + | 0.915907i | \(0.368527\pi\) | |||||||
\(20\) | −3.56298 | −0.796706 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.54610 | 0.969233 | ||||||||
\(23\) | 0.546914 | 0.114040 | 0.0570198 | − | 0.998373i | \(-0.481840\pi\) | ||||
0.0570198 | + | 0.998373i | \(0.481840\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.51308 | −0.902615 | ||||||||
\(26\) | −0.0272847 | −0.00535096 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.10602 | −0.964948 | ||||||||
\(29\) | −9.46348 | −1.75732 | −0.878662 | − | 0.477444i | \(-0.841564\pi\) | ||||
−0.878662 | + | 0.477444i | \(0.841564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.67461 | 1.37840 | 0.689200 | − | 0.724571i | \(-0.257962\pi\) | ||||
0.689200 | + | 0.724571i | \(0.257962\pi\) | |||||||
\(32\) | 15.0543 | 2.66125 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.6398 | 1.82472 | ||||||||
\(35\) | 0.697799 | 0.117949 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.99554 | 1.31446 | 0.657229 | − | 0.753691i | \(-0.271728\pi\) | ||||
0.657229 | + | 0.753691i | \(0.271728\pi\) | |||||||
\(38\) | 9.32796 | 1.51319 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.77761 | −0.913520 | ||||||||
\(41\) | 11.1674 | 1.74406 | 0.872030 | − | 0.489453i | \(-0.162803\pi\) | ||||
0.872030 | + | 0.489453i | \(0.162803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.72337 | −1.48280 | −0.741400 | − | 0.671064i | \(-0.765838\pi\) | ||||
−0.741400 | + | 0.671064i | \(0.765838\pi\) | |||||||
\(44\) | 8.70781 | 1.31275 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.45792 | 0.214958 | ||||||||
\(47\) | −1.31107 | −0.191239 | −0.0956195 | − | 0.995418i | \(-0.530483\pi\) | ||||
−0.0956195 | + | 0.995418i | \(0.530483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −12.0306 | −1.70138 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0522622 | −0.00724747 | ||||||||
\(53\) | 11.1980 | 1.53816 | 0.769080 | − | 0.639152i | \(-0.220715\pi\) | ||||
0.769080 | + | 0.639152i | \(0.220715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.19002 | −0.160463 | ||||||||
\(56\) | −8.27977 | −1.10643 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −25.2269 | −3.31246 | ||||||||
\(59\) | −6.94604 | −0.904297 | −0.452149 | − | 0.891943i | \(-0.649342\pi\) | ||||
−0.452149 | + | 0.891943i | \(0.649342\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.17872 | −0.663067 | −0.331534 | − | 0.943443i | \(-0.607566\pi\) | ||||
−0.331534 | + | 0.943443i | \(0.607566\pi\) | |||||||
\(62\) | 20.4583 | 2.59821 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 16.4116 | 2.05145 | ||||||||
\(65\) | 0.00714225 | 0.000885887 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.8318 | 1.93416 | 0.967082 | − | 0.254464i | \(-0.0818989\pi\) | ||||
0.967082 | + | 0.254464i | \(0.0818989\pi\) | |||||||
\(68\) | 20.3800 | 2.47144 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.86013 | 0.222328 | ||||||||
\(71\) | 1.12772 | 0.133835 | 0.0669176 | − | 0.997759i | \(-0.478684\pi\) | ||||
0.0669176 | + | 0.997759i | \(0.478684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3097 | 1.32370 | 0.661852 | − | 0.749634i | \(-0.269771\pi\) | ||||
0.661852 | + | 0.749634i | \(0.269771\pi\) | |||||||
\(74\) | 21.3138 | 2.47768 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.8672 | 2.04951 | ||||||||
\(77\) | −1.70540 | −0.194348 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4520 | −1.28845 | −0.644225 | − | 0.764836i | \(-0.722820\pi\) | ||||
−0.644225 | + | 0.764836i | \(0.722820\pi\) | |||||||
\(80\) | −8.27549 | −0.925228 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 29.7692 | 3.28745 | ||||||||
\(83\) | 12.8969 | 1.41561 | 0.707807 | − | 0.706406i | \(-0.249685\pi\) | ||||
0.707807 | + | 0.706406i | \(0.249685\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.78517 | −0.302094 | ||||||||
\(86\) | −25.9197 | −2.79499 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.1203 | 1.50523 | ||||||||
\(89\) | 6.13283 | 0.650079 | 0.325039 | − | 0.945700i | \(-0.394622\pi\) | ||||
0.325039 | + | 0.945700i | \(0.394622\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0102354 | 0.00107296 | ||||||||
\(92\) | 2.79256 | 0.291144 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.49493 | −0.360475 | ||||||||
\(95\) | −2.44176 | −0.250519 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.18095 | −0.627581 | −0.313790 | − | 0.949492i | \(-0.601599\pi\) | ||||
−0.313790 | + | 0.949492i | \(0.601599\pi\) | |||||||
\(98\) | 2.66571 | 0.269278 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −23.0439 | −2.30439 | ||||||||
\(101\) | −7.01657 | −0.698175 | −0.349087 | − | 0.937090i | \(-0.613508\pi\) | ||||
−0.349087 | + | 0.937090i | \(0.613508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.28644 | −0.323822 | −0.161911 | − | 0.986805i | \(-0.551766\pi\) | ||||
−0.161911 | + | 0.986805i | \(0.551766\pi\) | |||||||
\(104\) | −0.0847468 | −0.00831011 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 29.8506 | 2.89935 | ||||||||
\(107\) | 11.2210 | 1.08478 | 0.542389 | − | 0.840127i | \(-0.317520\pi\) | ||||
0.542389 | + | 0.840127i | \(0.317520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.788467 | −0.0755215 | −0.0377607 | − | 0.999287i | \(-0.512022\pi\) | ||||
−0.0377607 | + | 0.999287i | \(0.512022\pi\) | |||||||
\(110\) | −3.17226 | −0.302464 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.8594 | −1.12061 | ||||||||
\(113\) | −16.5540 | −1.55727 | −0.778636 | − | 0.627476i | \(-0.784088\pi\) | ||||
−0.778636 | + | 0.627476i | \(0.784088\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.381636 | −0.0355877 | ||||||||
\(116\) | −48.3208 | −4.48647 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.5161 | −1.70455 | ||||||||
\(119\) | −3.99137 | −0.365888 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.09161 | −0.735601 | ||||||||
\(122\) | −13.8050 | −1.24984 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 39.1867 | 3.51907 | ||||||||
\(125\) | 6.63821 | 0.593740 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 13.6399 | 1.20561 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0190392 | 0.00166985 | ||||||||
\(131\) | −8.91085 | −0.778544 | −0.389272 | − | 0.921123i | \(-0.627273\pi\) | ||||
−0.389272 | + | 0.921123i | \(0.627273\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.49924 | −0.303422 | ||||||||
\(134\) | 42.2031 | 3.64579 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 33.0476 | 2.83381 | ||||||||
\(137\) | 6.18977 | 0.528827 | 0.264414 | − | 0.964409i | \(-0.414822\pi\) | ||||
0.264414 | + | 0.964409i | \(0.414822\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.96079 | 0.590407 | 0.295203 | − | 0.955434i | \(-0.404613\pi\) | ||||
0.295203 | + | 0.955434i | \(0.404613\pi\) | |||||||
\(140\) | 3.56298 | 0.301126 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00617 | 0.252272 | ||||||||
\(143\) | −0.0174555 | −0.00145970 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.60361 | 0.548400 | ||||||||
\(146\) | 30.1485 | 2.49511 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 40.8254 | 3.35583 | ||||||||
\(149\) | −5.97383 | −0.489395 | −0.244698 | − | 0.969599i | \(-0.578689\pi\) | ||||
−0.244698 | + | 0.969599i | \(0.578689\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.78433 | 0.714859 | 0.357429 | − | 0.933940i | \(-0.383653\pi\) | ||||
0.357429 | + | 0.933940i | \(0.383653\pi\) | |||||||
\(152\) | 28.9729 | 2.35001 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.54610 | −0.366335 | ||||||||
\(155\) | −5.35533 | −0.430150 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.8843 | 1.98598 | 0.992992 | − | 0.118184i | \(-0.0377073\pi\) | ||||
0.992992 | + | 0.118184i | \(0.0377073\pi\) | |||||||
\(158\) | −30.5277 | −2.42866 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.5049 | −0.830483 | ||||||||
\(161\) | −0.546914 | −0.0431029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.07138 | −0.318895 | −0.159448 | − | 0.987206i | \(-0.550971\pi\) | ||||
−0.159448 | + | 0.987206i | \(0.550971\pi\) | |||||||
\(164\) | 57.0212 | 4.45261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 34.3793 | 2.66835 | ||||||||
\(167\) | 7.18537 | 0.556021 | 0.278010 | − | 0.960578i | \(-0.410325\pi\) | ||||
0.278010 | + | 0.960578i | \(0.410325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9999 | −0.999992 | ||||||||
\(170\) | −7.42447 | −0.569431 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −49.6477 | −3.78561 | ||||||||
\(173\) | 0.291915 | 0.0221939 | 0.0110969 | − | 0.999938i | \(-0.496468\pi\) | ||||
0.0110969 | + | 0.999938i | \(0.496468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.51308 | 0.341157 | ||||||||
\(176\) | 20.2251 | 1.52452 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.3484 | 1.22536 | ||||||||
\(179\) | −18.3836 | −1.37405 | −0.687026 | − | 0.726633i | \(-0.741084\pi\) | ||||
−0.687026 | + | 0.726633i | \(0.741084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1403 | −1.05104 | −0.525520 | − | 0.850782i | \(-0.676129\pi\) | ||||
−0.525520 | + | 0.850782i | \(0.676129\pi\) | |||||||
\(182\) | 0.0272847 | 0.00202247 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.52832 | 0.333832 | ||||||||
\(185\) | −5.57928 | −0.410197 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.80688 | 0.497768 | ||||||||
\(188\) | −6.69435 | −0.488235 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.50904 | −0.472215 | ||||||||
\(191\) | −2.42758 | −0.175654 | −0.0878269 | − | 0.996136i | \(-0.527992\pi\) | ||||
−0.0878269 | + | 0.996136i | \(0.527992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.3314 | −1.39150 | −0.695752 | − | 0.718282i | \(-0.744929\pi\) | ||||
−0.695752 | + | 0.718282i | \(0.744929\pi\) | |||||||
\(194\) | −16.4766 | −1.18295 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.10602 | 0.364716 | ||||||||
\(197\) | 12.2529 | 0.872981 | 0.436491 | − | 0.899709i | \(-0.356221\pi\) | ||||
0.436491 | + | 0.899709i | \(0.356221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.9153 | 1.55353 | 0.776767 | − | 0.629788i | \(-0.216858\pi\) | ||||
0.776767 | + | 0.629788i | \(0.216858\pi\) | |||||||
\(200\) | −37.3672 | −2.64226 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.7042 | −1.31602 | ||||||||
\(203\) | 9.46348 | 0.664206 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.79262 | −0.544260 | ||||||||
\(206\) | −8.76070 | −0.610387 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.121386 | −0.00841661 | ||||||||
\(209\) | 5.96759 | 0.412787 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.68672 | −0.598019 | −0.299009 | − | 0.954250i | \(-0.596656\pi\) | ||||
−0.299009 | + | 0.954250i | \(0.596656\pi\) | |||||||
\(212\) | 57.1772 | 3.92694 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 29.9121 | 2.04475 | ||||||||
\(215\) | 6.78495 | 0.462730 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.67461 | −0.520986 | ||||||||
\(218\) | −2.10183 | −0.142354 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.07630 | −0.409664 | ||||||||
\(221\) | −0.0408533 | −0.00274809 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8361 | −0.792602 | −0.396301 | − | 0.918121i | \(-0.629706\pi\) | ||||
−0.396301 | + | 0.918121i | \(0.629706\pi\) | |||||||
\(224\) | −15.0543 | −1.00586 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −44.1283 | −2.93537 | ||||||||
\(227\) | −10.1957 | −0.676711 | −0.338356 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338356 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.2567 | −1.60293 | −0.801465 | − | 0.598042i | \(-0.795946\pi\) | ||||
−0.801465 | + | 0.598042i | \(0.795946\pi\) | |||||||
\(230\) | −1.01733 | −0.0670809 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −78.3554 | −5.14429 | ||||||||
\(233\) | 23.1487 | 1.51652 | 0.758260 | − | 0.651953i | \(-0.226050\pi\) | ||||
0.758260 | + | 0.651953i | \(0.226050\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.914861 | 0.0596790 | ||||||||
\(236\) | −35.4666 | −2.30868 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.6398 | −0.689679 | ||||||||
\(239\) | 13.0898 | 0.846711 | 0.423355 | − | 0.905964i | \(-0.360852\pi\) | ||||
0.423355 | + | 0.905964i | \(0.360852\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.2424 | −1.81925 | −0.909627 | − | 0.415427i | \(-0.863632\pi\) | ||||
−0.909627 | + | 0.415427i | \(0.863632\pi\) | |||||||
\(242\) | −21.5699 | −1.38657 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −26.4427 | −1.69282 | ||||||||
\(245\) | −0.697799 | −0.0445807 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0358161 | −0.00227892 | ||||||||
\(248\) | 63.5439 | 4.03504 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.6956 | 1.11917 | ||||||||
\(251\) | 19.8373 | 1.25212 | 0.626061 | − | 0.779774i | \(-0.284666\pi\) | ||||
0.626061 | + | 0.779774i | \(0.284666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.932707 | 0.0586388 | ||||||||
\(254\) | −2.66571 | −0.167262 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.53703 | 0.221064 | ||||||||
\(257\) | 28.3219 | 1.76667 | 0.883335 | − | 0.468743i | \(-0.155293\pi\) | ||||
0.883335 | + | 0.468743i | \(0.155293\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.99554 | −0.496819 | ||||||||
\(260\) | 0.0364685 | 0.00226168 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −23.7538 | −1.46751 | ||||||||
\(263\) | 6.43901 | 0.397046 | 0.198523 | − | 0.980096i | \(-0.436386\pi\) | ||||
0.198523 | + | 0.980096i | \(0.436386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.81393 | −0.480006 | ||||||||
\(266\) | −9.32796 | −0.571934 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 80.8377 | 4.93795 | ||||||||
\(269\) | 27.2248 | 1.65992 | 0.829962 | − | 0.557819i | \(-0.188362\pi\) | ||||
0.829962 | + | 0.557819i | \(0.188362\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.70599 | 0.346614 | 0.173307 | − | 0.984868i | \(-0.444555\pi\) | ||||
0.173307 | + | 0.984868i | \(0.444555\pi\) | |||||||
\(272\) | 47.3354 | 2.87013 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.5001 | 0.996810 | ||||||||
\(275\) | −7.69660 | −0.464122 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.494362 | 0.0297033 | 0.0148517 | − | 0.999890i | \(-0.495272\pi\) | ||||
0.0148517 | + | 0.999890i | \(0.495272\pi\) | |||||||
\(278\) | 18.5555 | 1.11288 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.77761 | 0.345278 | ||||||||
\(281\) | −13.8067 | −0.823637 | −0.411819 | − | 0.911266i | \(-0.635106\pi\) | ||||
−0.411819 | + | 0.911266i | \(0.635106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.1913 | −1.49746 | −0.748732 | − | 0.662873i | \(-0.769337\pi\) | ||||
−0.748732 | + | 0.662873i | \(0.769337\pi\) | |||||||
\(284\) | 5.75814 | 0.341683 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0465312 | −0.00275145 | ||||||||
\(287\) | −11.1674 | −0.659193 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06897 | −0.0628804 | ||||||||
\(290\) | 17.6033 | 1.03370 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 57.7478 | 3.37943 | ||||||||
\(293\) | −2.14027 | −0.125036 | −0.0625178 | − | 0.998044i | \(-0.519913\pi\) | ||||
−0.0625178 | + | 0.998044i | \(0.519913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.84693 | 0.282199 | ||||||||
\(296\) | 66.2012 | 3.84787 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.9245 | −0.922482 | ||||||||
\(299\) | −0.00559789 | −0.000323734 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.72337 | 0.560446 | ||||||||
\(302\) | 23.4165 | 1.34747 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 41.4990 | 2.38013 | ||||||||
\(305\) | 3.61370 | 0.206920 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.47832 | −0.312664 | −0.156332 | − | 0.987705i | \(-0.549967\pi\) | ||||
−0.156332 | + | 0.987705i | \(0.549967\pi\) | |||||||
\(308\) | −8.70781 | −0.496173 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.2758 | −0.810809 | ||||||||
\(311\) | −13.3059 | −0.754511 | −0.377256 | − | 0.926109i | \(-0.623132\pi\) | ||||
−0.377256 | + | 0.926109i | \(0.623132\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.71810 | −0.492776 | −0.246388 | − | 0.969171i | \(-0.579244\pi\) | ||||
−0.246388 | + | 0.969171i | \(0.579244\pi\) | |||||||
\(314\) | 66.3344 | 3.74347 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −58.4742 | −3.28943 | ||||||||
\(317\) | −14.1949 | −0.797264 | −0.398632 | − | 0.917111i | \(-0.630515\pi\) | ||||
−0.398632 | + | 0.917111i | \(0.630515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.1390 | −0.903611 | ||||||||
\(320\) | −11.4520 | −0.640185 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.45792 | −0.0812465 | ||||||||
\(323\) | 13.9667 | 0.777131 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0461932 | 0.00256234 | ||||||||
\(326\) | −10.8531 | −0.601099 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 92.4637 | 5.10546 | ||||||||
\(329\) | 1.31107 | 0.0722815 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.6752 | −1.68606 | −0.843032 | − | 0.537864i | \(-0.819231\pi\) | ||||
−0.843032 | + | 0.537864i | \(0.819231\pi\) | |||||||
\(332\) | 65.8516 | 3.61408 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.1541 | 1.04807 | ||||||||
\(335\) | −11.0474 | −0.603585 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.340026 | 0.0185224 | 0.00926119 | − | 0.999957i | \(-0.497052\pi\) | ||||
0.00926119 | + | 0.999957i | \(0.497052\pi\) | |||||||
\(338\) | −34.6540 | −1.88493 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.2212 | −0.771250 | ||||||||
\(341\) | 13.0883 | 0.708769 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −80.5072 | −4.34066 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.778161 | 0.0418342 | ||||||||
\(347\) | 13.9628 | 0.749563 | 0.374782 | − | 0.927113i | \(-0.377718\pi\) | ||||
0.374782 | + | 0.927113i | \(0.377718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5697 | 0.779898 | 0.389949 | − | 0.920836i | \(-0.372493\pi\) | ||||
0.389949 | + | 0.920836i | \(0.372493\pi\) | |||||||
\(350\) | 12.0306 | 0.643061 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25.6736 | 1.36841 | ||||||||
\(353\) | 9.29100 | 0.494510 | 0.247255 | − | 0.968950i | \(-0.420471\pi\) | ||||
0.247255 | + | 0.968950i | \(0.420471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.786918 | −0.0417653 | ||||||||
\(356\) | 31.3144 | 1.65966 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −49.0053 | −2.59001 | ||||||||
\(359\) | −27.8926 | −1.47211 | −0.736056 | − | 0.676920i | \(-0.763314\pi\) | ||||
−0.736056 | + | 0.676920i | \(0.763314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.75535 | −0.355544 | ||||||||
\(362\) | −37.6939 | −1.98115 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0522622 | 0.00273929 | ||||||||
\(365\) | −7.89192 | −0.413082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.8398 | 1.55763 | 0.778813 | − | 0.627256i | \(-0.215822\pi\) | ||||
0.778813 | + | 0.627256i | \(0.215822\pi\) | |||||||
\(368\) | 6.48609 | 0.338111 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.8727 | −0.773197 | ||||||||
\(371\) | −11.1980 | −0.581370 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.4048 | 1.93675 | 0.968375 | − | 0.249500i | \(-0.0802664\pi\) | ||||
0.968375 | + | 0.249500i | \(0.0802664\pi\) | |||||||
\(374\) | 18.1452 | 0.938265 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.8553 | −0.559821 | ||||||||
\(377\) | 0.0968626 | 0.00498868 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.0365 | −1.74834 | −0.874170 | − | 0.485620i | \(-0.838594\pi\) | ||||
−0.874170 | + | 0.485620i | \(0.838594\pi\) | |||||||
\(380\) | −12.4677 | −0.639579 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.47124 | −0.331098 | ||||||||
\(383\) | −1.54300 | −0.0788439 | −0.0394219 | − | 0.999223i | \(-0.512552\pi\) | ||||
−0.0394219 | + | 0.999223i | \(0.512552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.19002 | 0.0606493 | ||||||||
\(386\) | −51.5319 | −2.62291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −31.5601 | −1.60222 | ||||||||
\(389\) | 14.2392 | 0.721956 | 0.360978 | − | 0.932574i | \(-0.382443\pi\) | ||||
0.360978 | + | 0.932574i | \(0.382443\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.18294 | 0.110396 | ||||||||
\(392\) | 8.27977 | 0.418191 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 32.6626 | 1.64552 | ||||||||
\(395\) | 7.99119 | 0.402080 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.10450 | −0.205999 | −0.102999 | − | 0.994681i | \(-0.532844\pi\) | ||||
−0.102999 | + | 0.994681i | \(0.532844\pi\) | |||||||
\(398\) | 58.4199 | 2.92832 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −53.5225 | −2.67613 | ||||||||
\(401\) | 23.1443 | 1.15577 | 0.577885 | − | 0.816118i | \(-0.303878\pi\) | ||||
0.577885 | + | 0.816118i | \(0.303878\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0785527 | −0.00391299 | ||||||||
\(404\) | −35.8268 | −1.78245 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.2269 | 1.25199 | ||||||||
\(407\) | 13.6356 | 0.675891 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.7189 | −1.12338 | −0.561689 | − | 0.827348i | \(-0.689848\pi\) | ||||
−0.561689 | + | 0.827348i | \(0.689848\pi\) | |||||||
\(410\) | −20.7729 | −1.02590 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.7806 | −0.826723 | ||||||||
\(413\) | 6.94604 | 0.341792 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.99941 | −0.441763 | ||||||||
\(416\) | −0.154087 | −0.00755473 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.9079 | 0.778080 | ||||||||
\(419\) | −25.2172 | −1.23194 | −0.615972 | − | 0.787768i | \(-0.711236\pi\) | ||||
−0.615972 | + | 0.787768i | \(0.711236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.51746 | 0.122693 | 0.0613467 | − | 0.998117i | \(-0.480460\pi\) | ||||
0.0613467 | + | 0.998117i | \(0.480460\pi\) | |||||||
\(422\) | −23.1563 | −1.12723 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 92.7167 | 4.50272 | ||||||||
\(425\) | −18.0134 | −0.873776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.17872 | 0.250616 | ||||||||
\(428\) | 57.2949 | 2.76945 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.0867 | 0.872220 | ||||||||
\(431\) | 0.00500045 | 0.000240863 0 | 0.000120432 | − | 1.00000i | \(-0.499962\pi\) | ||||
0.000120432 | 1.00000i | \(0.499962\pi\) | ||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.6977 | −0.514098 | −0.257049 | − | 0.966398i | \(-0.582750\pi\) | ||||
−0.257049 | + | 0.966398i | \(0.582750\pi\) | |||||||
\(434\) | −20.4583 | −0.982029 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.02593 | −0.192807 | ||||||||
\(437\) | 1.91378 | 0.0915486 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.0780 | 0.910546 | 0.455273 | − | 0.890352i | \(-0.349542\pi\) | ||||
0.455273 | + | 0.890352i | \(0.349542\pi\) | |||||||
\(440\) | −9.85313 | −0.469729 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.108903 | −0.00517999 | ||||||||
\(443\) | −24.9616 | −1.18596 | −0.592980 | − | 0.805217i | \(-0.702049\pi\) | ||||
−0.592980 | + | 0.805217i | \(0.702049\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.27948 | −0.202867 | ||||||||
\(446\) | −31.5516 | −1.49401 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.4116 | −0.775374 | ||||||||
\(449\) | 22.7503 | 1.07365 | 0.536827 | − | 0.843692i | \(-0.319623\pi\) | ||||
0.536827 | + | 0.843692i | \(0.319623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.0449 | 0.896791 | ||||||||
\(452\) | −84.5253 | −3.97573 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −27.1788 | −1.27556 | ||||||||
\(455\) | −0.00714225 | −0.000334834 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.0127 | −1.26360 | −0.631801 | − | 0.775131i | \(-0.717684\pi\) | ||||
−0.631801 | + | 0.775131i | \(0.717684\pi\) | |||||||
\(458\) | −64.6615 | −3.02143 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.94864 | −0.0908559 | ||||||||
\(461\) | −25.5587 | −1.19039 | −0.595194 | − | 0.803582i | \(-0.702925\pi\) | ||||
−0.595194 | + | 0.803582i | \(0.702925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.3000 | −1.73348 | −0.866740 | − | 0.498761i | \(-0.833789\pi\) | ||||
−0.866740 | + | 0.498761i | \(0.833789\pi\) | |||||||
\(464\) | −112.232 | −5.21022 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 61.7077 | 2.85855 | ||||||||
\(467\) | −8.52627 | −0.394549 | −0.197274 | − | 0.980348i | \(-0.563209\pi\) | ||||
−0.197274 | + | 0.980348i | \(0.563209\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.8318 | −0.731046 | ||||||||
\(470\) | 2.43876 | 0.112492 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −57.5116 | −2.64718 | ||||||||
\(473\) | −16.5822 | −0.762451 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.7923 | −0.724602 | ||||||||
\(476\) | −20.3800 | −0.934117 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 34.8937 | 1.59600 | ||||||||
\(479\) | 23.6098 | 1.07876 | 0.539380 | − | 0.842062i | \(-0.318659\pi\) | ||||
0.539380 | + | 0.842062i | \(0.318659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0818376 | −0.00373147 | ||||||||
\(482\) | −75.2861 | −3.42919 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −41.3160 | −1.87800 | ||||||||
\(485\) | 4.31306 | 0.195846 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.23519 | −0.418487 | −0.209243 | − | 0.977864i | \(-0.567100\pi\) | ||||
−0.209243 | + | 0.977864i | \(0.567100\pi\) | |||||||
\(488\) | −42.8786 | −1.94102 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.86013 | −0.0840321 | ||||||||
\(491\) | −1.62814 | −0.0734769 | −0.0367385 | − | 0.999325i | \(-0.511697\pi\) | ||||
−0.0367385 | + | 0.999325i | \(0.511697\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.7723 | −1.70118 | ||||||||
\(494\) | −0.0954754 | −0.00429564 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 91.0164 | 4.08676 | ||||||||
\(497\) | −1.12772 | −0.0505850 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.9739 | −0.715090 | −0.357545 | − | 0.933896i | \(-0.616386\pi\) | ||||
−0.357545 | + | 0.933896i | \(0.616386\pi\) | |||||||
\(500\) | 33.8949 | 1.51582 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 52.8807 | 2.36018 | ||||||||
\(503\) | 0.578955 | 0.0258143 | 0.0129072 | − | 0.999917i | \(-0.495891\pi\) | ||||
0.0129072 | + | 0.999917i | \(0.495891\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.89615 | 0.217876 | ||||||||
\(506\) | 2.48633 | 0.110531 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.10602 | −0.226543 | ||||||||
\(509\) | 6.21944 | 0.275672 | 0.137836 | − | 0.990455i | \(-0.455985\pi\) | ||||
0.137836 | + | 0.990455i | \(0.455985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3097 | −0.500313 | ||||||||
\(512\) | −17.8512 | −0.788919 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 75.4980 | 3.33007 | ||||||||
\(515\) | 2.29327 | 0.101054 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.23589 | −0.0983345 | ||||||||
\(518\) | −21.3138 | −0.936475 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0591362 | 0.00259329 | ||||||||
\(521\) | −4.12288 | −0.180627 | −0.0903134 | − | 0.995913i | \(-0.528787\pi\) | ||||
−0.0903134 | + | 0.995913i | \(0.528787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.3058 | −0.800455 | −0.400228 | − | 0.916416i | \(-0.631069\pi\) | ||||
−0.400228 | + | 0.916416i | \(0.631069\pi\) | |||||||
\(524\) | −45.4990 | −1.98763 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.1645 | 0.748409 | ||||||||
\(527\) | 30.6322 | 1.33436 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7009 | −0.986995 | ||||||||
\(530\) | −20.8297 | −0.904784 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.8672 | −0.774641 | ||||||||
\(533\) | −0.114303 | −0.00495102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.83002 | −0.338521 | ||||||||
\(536\) | 131.084 | 5.66196 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 72.5735 | 3.12886 | ||||||||
\(539\) | 1.70540 | 0.0734567 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.80919 | −0.206763 | −0.103382 | − | 0.994642i | \(-0.532966\pi\) | ||||
−0.103382 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(542\) | 15.2105 | 0.653349 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 60.0873 | 2.57622 | ||||||||
\(545\) | 0.550191 | 0.0235676 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1167 | −1.03115 | −0.515577 | − | 0.856843i | \(-0.672422\pi\) | ||||
−0.515577 | + | 0.856843i | \(0.672422\pi\) | |||||||
\(548\) | 31.6051 | 1.35010 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.5169 | −0.874844 | ||||||||
\(551\) | −33.1150 | −1.41075 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.4520 | 0.486988 | ||||||||
\(554\) | 1.31783 | 0.0559891 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 35.5420 | 1.50732 | ||||||||
\(557\) | −0.973727 | −0.0412581 | −0.0206291 | − | 0.999787i | \(-0.506567\pi\) | ||||
−0.0206291 | + | 0.999787i | \(0.506567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0995226 | 0.00420936 | ||||||||
\(560\) | 8.27549 | 0.349703 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −36.8046 | −1.55251 | ||||||||
\(563\) | −36.6265 | −1.54362 | −0.771811 | − | 0.635853i | \(-0.780649\pi\) | ||||
−0.771811 | + | 0.635853i | \(0.780649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.5514 | 0.485970 | ||||||||
\(566\) | −67.1526 | −2.82264 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.33722 | 0.391781 | ||||||||
\(569\) | 31.6724 | 1.32777 | 0.663887 | − | 0.747833i | \(-0.268906\pi\) | ||||
0.663887 | + | 0.747833i | \(0.268906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.40096 | −0.393418 | −0.196709 | − | 0.980462i | \(-0.563025\pi\) | ||||
−0.196709 | + | 0.980462i | \(0.563025\pi\) | |||||||
\(572\) | −0.0891279 | −0.00372663 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −29.7692 | −1.24254 | ||||||||
\(575\) | −2.46827 | −0.102934 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.4828 | −1.51880 | −0.759399 | − | 0.650626i | \(-0.774507\pi\) | ||||
−0.759399 | + | 0.650626i | \(0.774507\pi\) | |||||||
\(578\) | −2.84956 | −0.118526 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 33.7182 | 1.40007 | ||||||||
\(581\) | −12.8969 | −0.535052 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.0970 | 0.790918 | ||||||||
\(584\) | 93.6420 | 3.87493 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.70533 | −0.235685 | ||||||||
\(587\) | −4.16140 | −0.171759 | −0.0858797 | − | 0.996306i | \(-0.527370\pi\) | ||||
−0.0858797 | + | 0.996306i | \(0.527370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.8553 | 1.10655 | ||||||||
\(590\) | 12.9205 | 0.531930 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 94.8226 | 3.89718 | ||||||||
\(593\) | −27.5376 | −1.13084 | −0.565418 | − | 0.824805i | \(-0.691285\pi\) | ||||
−0.565418 | + | 0.824805i | \(0.691285\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.78517 | 0.114181 | ||||||||
\(596\) | −30.5025 | −1.24943 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.0149224 | −0.000610221 0 | ||||||||
\(599\) | −12.0678 | −0.493077 | −0.246538 | − | 0.969133i | \(-0.579293\pi\) | ||||
−0.246538 | + | 0.969133i | \(0.579293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.7149 | −1.21209 | −0.606047 | − | 0.795429i | \(-0.707246\pi\) | ||||
−0.606047 | + | 0.795429i | \(0.707246\pi\) | |||||||
\(602\) | 25.9197 | 1.05641 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 44.8530 | 1.82504 | ||||||||
\(605\) | 5.64632 | 0.229555 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.3965 | 0.665514 | 0.332757 | − | 0.943013i | \(-0.392021\pi\) | ||||
0.332757 | + | 0.943013i | \(0.392021\pi\) | |||||||
\(608\) | 52.6786 | 2.13640 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.63309 | 0.390033 | ||||||||
\(611\) | 0.0134193 | 0.000542887 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.61788 | 0.348073 | 0.174036 | − | 0.984739i | \(-0.444319\pi\) | ||||
0.174036 | + | 0.984739i | \(0.444319\pi\) | |||||||
\(614\) | −14.6036 | −0.589355 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.1203 | −0.568923 | ||||||||
\(617\) | 12.6133 | 0.507794 | 0.253897 | − | 0.967231i | \(-0.418288\pi\) | ||||
0.253897 | + | 0.967231i | \(0.418288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.2706 | 1.77938 | 0.889692 | − | 0.456561i | \(-0.150919\pi\) | ||||
0.889692 | + | 0.456561i | \(0.150919\pi\) | |||||||
\(620\) | −27.3444 | −1.09818 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −35.4698 | −1.42221 | ||||||||
\(623\) | −6.13283 | −0.245707 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.9333 | 0.717330 | ||||||||
\(626\) | −23.2400 | −0.928855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 127.060 | 5.07024 | ||||||||
\(629\) | 31.9132 | 1.27246 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.6008 | 1.01915 | 0.509576 | − | 0.860425i | \(-0.329802\pi\) | ||||
0.509576 | + | 0.860425i | \(0.329802\pi\) | |||||||
\(632\) | −94.8198 | −3.77173 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −37.8395 | −1.50280 | ||||||||
\(635\) | 0.697799 | 0.0276913 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0102354 | −0.000405542 0 | ||||||||
\(638\) | −43.0220 | −1.70326 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.51794 | −0.376229 | ||||||||
\(641\) | −18.3429 | −0.724500 | −0.362250 | − | 0.932081i | \(-0.617991\pi\) | ||||
−0.362250 | + | 0.932081i | \(0.617991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.9655 | −0.432437 | −0.216219 | − | 0.976345i | \(-0.569372\pi\) | ||||
−0.216219 | + | 0.976345i | \(0.569372\pi\) | |||||||
\(644\) | −2.79256 | −0.110042 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 37.2313 | 1.46485 | ||||||||
\(647\) | −34.8051 | −1.36833 | −0.684164 | − | 0.729328i | \(-0.739833\pi\) | ||||
−0.684164 | + | 0.729328i | \(0.739833\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.8458 | −0.464987 | ||||||||
\(650\) | 0.123138 | 0.00482986 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.7886 | −0.814143 | ||||||||
\(653\) | −33.2092 | −1.29958 | −0.649789 | − | 0.760115i | \(-0.725143\pi\) | ||||
−0.649789 | + | 0.760115i | \(0.725143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.21797 | 0.242956 | ||||||||
\(656\) | 132.439 | 5.17089 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.49493 | 0.136247 | ||||||||
\(659\) | −5.32002 | −0.207239 | −0.103619 | − | 0.994617i | \(-0.533042\pi\) | ||||
−0.103619 | + | 0.994617i | \(0.533042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.8478 | −0.538616 | −0.269308 | − | 0.963054i | \(-0.586795\pi\) | ||||
−0.269308 | + | 0.963054i | \(0.586795\pi\) | |||||||
\(662\) | −81.7714 | −3.17813 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 106.783 | 4.14398 | ||||||||
\(665\) | 2.44176 | 0.0946875 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.17572 | −0.200405 | ||||||||
\(668\) | 36.6887 | 1.41953 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −29.4492 | −1.13772 | ||||||||
\(671\) | −8.83178 | −0.340947 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0513 | 0.387451 | 0.193725 | − | 0.981056i | \(-0.437943\pi\) | ||||
0.193725 | + | 0.981056i | \(0.437943\pi\) | |||||||
\(674\) | 0.906410 | 0.0349136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −66.3778 | −2.55299 | ||||||||
\(677\) | −23.6492 | −0.908912 | −0.454456 | − | 0.890769i | \(-0.650166\pi\) | ||||
−0.454456 | + | 0.890769i | \(0.650166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.18095 | 0.237203 | ||||||||
\(680\) | −23.0606 | −0.884333 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 34.8895 | 1.33599 | ||||||||
\(683\) | 37.4785 | 1.43407 | 0.717037 | − | 0.697035i | \(-0.245498\pi\) | ||||
0.717037 | + | 0.697035i | \(0.245498\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.31921 | −0.165029 | ||||||||
\(686\) | −2.66571 | −0.101777 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −115.314 | −4.39629 | ||||||||
\(689\) | −0.114616 | −0.00436652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0034 | 1.06530 | 0.532650 | − | 0.846336i | \(-0.321196\pi\) | ||||
0.532650 | + | 0.846336i | \(0.321196\pi\) | |||||||
\(692\) | 1.49052 | 0.0566612 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 37.2209 | 1.41288 | ||||||||
\(695\) | −4.85723 | −0.184245 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 44.5734 | 1.68834 | ||||||||
\(698\) | 38.8386 | 1.47006 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 23.0439 | 0.870977 | ||||||||
\(701\) | 23.3548 | 0.882099 | 0.441050 | − | 0.897483i | \(-0.354606\pi\) | ||||
0.441050 | + | 0.897483i | \(0.354606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.9783 | 1.05522 | ||||||||
\(704\) | 27.9883 | 1.05485 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.7671 | 0.932123 | ||||||||
\(707\) | 7.01657 | 0.263885 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.1473 | −1.50776 | −0.753881 | − | 0.657011i | \(-0.771821\pi\) | ||||
−0.753881 | + | 0.657011i | \(0.771821\pi\) | |||||||
\(710\) | −2.09770 | −0.0787252 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 50.7784 | 1.90300 | ||||||||
\(713\) | 4.19735 | 0.157192 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0121804 | 0.000455521 0 | ||||||||
\(716\) | −93.8669 | −3.50797 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −74.3535 | −2.77485 | ||||||||
\(719\) | −17.7423 | −0.661677 | −0.330839 | − | 0.943687i | \(-0.607332\pi\) | ||||
−0.330839 | + | 0.943687i | \(0.607332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.28644 | 0.122393 | ||||||||
\(722\) | −18.0078 | −0.670181 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −72.2006 | −2.68332 | ||||||||
\(725\) | 42.7094 | 1.58619 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.4263 | −0.757568 | −0.378784 | − | 0.925485i | \(-0.623658\pi\) | ||||
−0.378784 | + | 0.925485i | \(0.623658\pi\) | |||||||
\(728\) | 0.0847468 | 0.00314092 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.0376 | −0.778636 | ||||||||
\(731\) | −38.8096 | −1.43542 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.8007 | −1.13765 | −0.568825 | − | 0.822458i | \(-0.692602\pi\) | ||||
−0.568825 | + | 0.822458i | \(0.692602\pi\) | |||||||
\(734\) | 79.5444 | 2.93604 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.23341 | 0.303488 | ||||||||
\(737\) | 26.9996 | 0.994542 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.8782 | −1.65087 | −0.825435 | − | 0.564497i | \(-0.809070\pi\) | ||||
−0.825435 | + | 0.564497i | \(0.809070\pi\) | |||||||
\(740\) | −28.4879 | −1.04724 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −29.8506 | −1.09585 | ||||||||
\(743\) | 14.8611 | 0.545200 | 0.272600 | − | 0.962127i | \(-0.412116\pi\) | ||||
0.272600 | + | 0.962127i | \(0.412116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.16853 | 0.152723 | ||||||||
\(746\) | 99.7106 | 3.65066 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 34.7561 | 1.27081 | ||||||||
\(749\) | −11.2210 | −0.410008 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.90762 | −0.215572 | −0.107786 | − | 0.994174i | \(-0.534376\pi\) | ||||
−0.107786 | + | 0.994174i | \(0.534376\pi\) | |||||||
\(752\) | −15.5485 | −0.566996 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.258208 | 0.00940338 | ||||||||
\(755\) | −6.12969 | −0.223082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.5497 | −1.87360 | −0.936802 | − | 0.349860i | \(-0.886229\pi\) | ||||
−0.936802 | + | 0.349860i | \(0.886229\pi\) | |||||||
\(758\) | −90.7316 | −3.29552 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.2172 | −0.733356 | ||||||||
\(761\) | 8.05458 | 0.291978 | 0.145989 | − | 0.989286i | \(-0.453364\pi\) | ||||
0.145989 | + | 0.989286i | \(0.453364\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.788467 | 0.0285444 | ||||||||
\(764\) | −12.3953 | −0.448446 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.11321 | −0.148616 | ||||||||
\(767\) | 0.0710955 | 0.00256711 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.9759 | −0.395800 | −0.197900 | − | 0.980222i | \(-0.563412\pi\) | ||||
−0.197900 | + | 0.980222i | \(0.563412\pi\) | |||||||
\(770\) | 3.17226 | 0.114320 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −98.7065 | −3.55252 | ||||||||
\(773\) | 32.9115 | 1.18374 | 0.591871 | − | 0.806032i | \(-0.298389\pi\) | ||||
0.591871 | + | 0.806032i | \(0.298389\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.6361 | −1.24416 | ||||||||
\(776\) | −51.1769 | −1.83714 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.9576 | 1.36085 | ||||||||
\(779\) | 39.0775 | 1.40010 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.92321 | 0.0688177 | ||||||||
\(782\) | 5.81908 | 0.208090 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.8594 | 0.423551 | ||||||||
\(785\) | −17.3642 | −0.619756 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.9996 | −1.31889 | −0.659446 | − | 0.751752i | \(-0.729209\pi\) | ||||
−0.659446 | + | 0.751752i | \(0.729209\pi\) | |||||||
\(788\) | 62.5635 | 2.22873 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.3022 | 0.757898 | ||||||||
\(791\) | 16.5540 | 0.588593 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0530063 | 0.00188231 | ||||||||
\(794\) | −10.9414 | −0.388296 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 111.900 | 3.96619 | ||||||||
\(797\) | 0.129949 | 0.00460303 | 0.00230151 | − | 0.999997i | \(-0.499267\pi\) | ||||
0.00230151 | + | 0.999997i | \(0.499267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.23296 | −0.185129 | ||||||||
\(800\) | −67.9412 | −2.40208 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 61.6960 | 2.17856 | ||||||||
\(803\) | 19.2876 | 0.680645 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.381636 | 0.0134509 | ||||||||
\(806\) | −0.209399 | −0.00737576 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −58.0956 | −2.04379 | ||||||||
\(809\) | 29.4117 | 1.03406 | 0.517031 | − | 0.855967i | \(-0.327037\pi\) | ||||
0.517031 | + | 0.855967i | \(0.327037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.5962 | −0.793458 | −0.396729 | − | 0.917936i | \(-0.629855\pi\) | ||||
−0.396729 | + | 0.917936i | \(0.629855\pi\) | |||||||
\(812\) | 48.3208 | 1.69573 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 36.3486 | 1.27402 | ||||||||
\(815\) | 2.84100 | 0.0995160 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.0244 | −1.19036 | ||||||||
\(818\) | −60.5621 | −2.11751 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39.7893 | −1.38950 | ||||||||
\(821\) | 12.7636 | 0.445452 | 0.222726 | − | 0.974881i | \(-0.428504\pi\) | ||||
0.222726 | + | 0.974881i | \(0.428504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.8621 | 1.11064 | 0.555321 | − | 0.831636i | \(-0.312595\pi\) | ||||
0.555321 | + | 0.831636i | \(0.312595\pi\) | |||||||
\(824\) | −27.2109 | −0.947938 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.5161 | 0.644259 | ||||||||
\(827\) | 17.0949 | 0.594447 | 0.297223 | − | 0.954808i | \(-0.403939\pi\) | ||||
0.297223 | + | 0.954808i | \(0.403939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.7797 | 1.79838 | 0.899191 | − | 0.437556i | \(-0.144156\pi\) | ||||
0.899191 | + | 0.437556i | \(0.144156\pi\) | |||||||
\(830\) | −23.9898 | −0.832699 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.167979 | −0.00582363 | ||||||||
\(833\) | 3.99137 | 0.138293 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.01394 | −0.173515 | ||||||||
\(836\) | 30.4707 | 1.05385 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −67.2219 | −2.32214 | ||||||||
\(839\) | −7.47622 | −0.258108 | −0.129054 | − | 0.991638i | \(-0.541194\pi\) | ||||
−0.129054 | + | 0.991638i | \(0.541194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.5575 | 2.08819 | ||||||||
\(842\) | 6.71082 | 0.231270 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −44.3546 | −1.52675 | ||||||||
\(845\) | 9.07131 | 0.312062 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.09161 | 0.278031 | ||||||||
\(848\) | 132.802 | 4.56043 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −48.0184 | −1.64702 | ||||||||
\(851\) | 4.37288 | 0.149900 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.2445 | −1.13827 | −0.569134 | − | 0.822244i | \(-0.692722\pi\) | ||||
−0.569134 | + | 0.822244i | \(0.692722\pi\) | |||||||
\(854\) | 13.8050 | 0.472397 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 92.9076 | 3.17551 | ||||||||
\(857\) | −1.97724 | −0.0675412 | −0.0337706 | − | 0.999430i | \(-0.510752\pi\) | ||||
−0.0337706 | + | 0.999430i | \(0.510752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.6972 | 1.21797 | 0.608986 | − | 0.793181i | \(-0.291577\pi\) | ||||
0.608986 | + | 0.793181i | \(0.291577\pi\) | |||||||
\(860\) | 34.6441 | 1.18135 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.0133298 | 0.000454014 0 | ||||||||
\(863\) | −6.28198 | −0.213841 | −0.106920 | − | 0.994268i | \(-0.534099\pi\) | ||||
−0.106920 | + | 0.994268i | \(0.534099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.203698 | −0.00692593 | ||||||||
\(866\) | −28.5170 | −0.969046 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −39.1867 | −1.33008 | ||||||||
\(869\) | −19.5302 | −0.662517 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.162045 | −0.00549069 | ||||||||
\(872\) | −6.52832 | −0.221077 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.10159 | 0.172564 | ||||||||
\(875\) | −6.63821 | −0.224412 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.5476 | −1.13282 | −0.566411 | − | 0.824123i | \(-0.691668\pi\) | ||||
−0.566411 | + | 0.824123i | \(0.691668\pi\) | |||||||
\(878\) | 50.8566 | 1.71633 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −14.1130 | −0.475750 | ||||||||
\(881\) | −18.4440 | −0.621393 | −0.310696 | − | 0.950509i | \(-0.600562\pi\) | ||||
−0.310696 | + | 0.950509i | \(0.600562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.3811 | −0.786836 | −0.393418 | − | 0.919360i | \(-0.628707\pi\) | ||||
−0.393418 | + | 0.919360i | \(0.628707\pi\) | |||||||
\(884\) | −0.208598 | −0.00701591 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −66.5403 | −2.23547 | ||||||||
\(887\) | 10.3669 | 0.348086 | 0.174043 | − | 0.984738i | \(-0.444317\pi\) | ||||
0.174043 | + | 0.984738i | \(0.444317\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −11.4079 | −0.382393 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −60.4353 | −2.02352 | ||||||||
\(893\) | −4.58774 | −0.153523 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.8280 | 0.428793 | ||||||||
\(896\) | −13.6399 | −0.455679 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 60.6458 | 2.02378 | ||||||||
\(899\) | −72.6285 | −2.42230 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.6953 | 1.48902 | ||||||||
\(902\) | 50.7683 | 1.69040 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −137.063 | −4.55866 | ||||||||
\(905\) | 9.86707 | 0.327992 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.7034 | 1.88281 | 0.941403 | − | 0.337285i | \(-0.109509\pi\) | ||||
0.941403 | + | 0.337285i | \(0.109509\pi\) | |||||||
\(908\) | −52.0594 | −1.72765 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.0190392 | −0.000631143 0 | ||||||||
\(911\) | 6.97305 | 0.231028 | 0.115514 | − | 0.993306i | \(-0.463149\pi\) | ||||
0.115514 | + | 0.993306i | \(0.463149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.9943 | 0.727904 | ||||||||
\(914\) | −72.0082 | −2.38182 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −123.855 | −4.09230 | ||||||||
\(917\) | 8.91085 | 0.294262 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.1712 | 1.45707 | 0.728537 | − | 0.685007i | \(-0.240201\pi\) | ||||
0.728537 | + | 0.685007i | \(0.240201\pi\) | |||||||
\(920\) | −3.15986 | −0.104177 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −68.1322 | −2.24382 | ||||||||
\(923\) | −0.0115426 | −0.000379930 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.0845 | −1.18645 | ||||||||
\(926\) | −99.4312 | −3.26751 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −142.466 | −4.67668 | ||||||||
\(929\) | 22.7442 | 0.746215 | 0.373107 | − | 0.927788i | \(-0.378292\pi\) | ||||
0.373107 | + | 0.927788i | \(0.378292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.49924 | 0.114683 | ||||||||
\(932\) | 118.198 | 3.87169 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.7286 | −0.743702 | ||||||||
\(935\) | −4.74983 | −0.155336 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.43632 | −0.144928 | −0.0724641 | − | 0.997371i | \(-0.523086\pi\) | ||||
−0.0724641 | + | 0.997371i | \(0.523086\pi\) | |||||||
\(938\) | −42.2031 | −1.37798 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.67130 | 0.152361 | ||||||||
\(941\) | 21.2474 | 0.692644 | 0.346322 | − | 0.938116i | \(-0.387430\pi\) | ||||
0.346322 | + | 0.938116i | \(0.387430\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.10763 | 0.198892 | ||||||||
\(944\) | −82.3761 | −2.68111 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.2034 | −1.43718 | ||||||||
\(947\) | 27.7982 | 0.903320 | 0.451660 | − | 0.892190i | \(-0.350832\pi\) | ||||
0.451660 | + | 0.892190i | \(0.350832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.115760 | −0.00375772 | ||||||||
\(950\) | −42.0978 | −1.36583 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −33.0476 | −1.07108 | ||||||||
\(953\) | −8.88868 | −0.287933 | −0.143966 | − | 0.989583i | \(-0.545986\pi\) | ||||
−0.143966 | + | 0.989583i | \(0.545986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.69396 | 0.0548154 | ||||||||
\(956\) | 66.8370 | 2.16166 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 62.9370 | 2.03340 | ||||||||
\(959\) | −6.18977 | −0.199878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.8996 | 0.899986 | ||||||||
\(962\) | −0.218156 | −0.00703362 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −144.206 | −4.64457 | ||||||||
\(965\) | 13.4894 | 0.434240 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.7376 | 0.473930 | 0.236965 | − | 0.971518i | \(-0.423847\pi\) | ||||
0.236965 | + | 0.971518i | \(0.423847\pi\) | |||||||
\(968\) | −66.9967 | −2.15335 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.4974 | 0.369159 | ||||||||
\(971\) | −16.9135 | −0.542780 | −0.271390 | − | 0.962469i | \(-0.587483\pi\) | ||||
−0.271390 | + | 0.962469i | \(0.587483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.96079 | −0.223153 | ||||||||
\(974\) | −24.6184 | −0.788824 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.4167 | −1.96590 | ||||||||
\(977\) | −7.07125 | −0.226229 | −0.113115 | − | 0.993582i | \(-0.536083\pi\) | ||||
−0.113115 | + | 0.993582i | \(0.536083\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.4589 | 0.334269 | ||||||||
\(980\) | −3.56298 | −0.113815 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.34015 | −0.138500 | ||||||||
\(983\) | 0.986817 | 0.0314746 | 0.0157373 | − | 0.999876i | \(-0.494990\pi\) | ||||
0.0157373 | + | 0.999876i | \(0.494990\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.55004 | −0.272427 | ||||||||
\(986\) | −100.690 | −3.20662 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.182878 | −0.00581812 | ||||||||
\(989\) | −5.31785 | −0.169098 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.6954 | −0.593877 | −0.296939 | − | 0.954897i | \(-0.595966\pi\) | ||||
−0.296939 | + | 0.954897i | \(0.595966\pi\) | |||||||
\(992\) | 115.536 | 3.66827 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.00617 | −0.0953498 | ||||||||
\(995\) | −15.2925 | −0.484804 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.3561 | 1.91150 | 0.955748 | − | 0.294185i | \(-0.0950483\pi\) | ||||
0.955748 | + | 0.294185i | \(0.0950483\pi\) | |||||||
\(998\) | −42.5818 | −1.34790 | ||||||||
\(999\) | 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 | 8001.2.a.p.1.13 | 14 | ||
3.2 | odd | 2 | 2667.2.a.m.1.2 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.m.1.2 | ✓ | 14 | 3.2 | odd | 2 | ||
8001.2.a.p.1.13 | 14 | 1.1 | even | 1 | trivial |