Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.73145\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.66497 | 1.19181 | 0.595906 | − | 0.803054i | \(-0.296793\pi\) | ||||
0.595906 | + | 0.803054i | \(0.296793\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.36859 | 0.895243 | 0.447621 | − | 0.894223i | \(-0.352271\pi\) | ||||
0.447621 | + | 0.894223i | \(0.352271\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.66497 | −0.842738 | ||||||||
\(11\) | 2.99046 | 0.901657 | 0.450829 | − | 0.892611i | \(-0.351129\pi\) | ||||
0.450829 | + | 0.892611i | \(0.351129\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.36859 | −0.633032 | ||||||||
\(15\) | −2.66497 | −0.688093 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.10004 | −1.23694 | −0.618471 | − | 0.785808i | \(-0.712247\pi\) | ||||
−0.618471 | + | 0.785808i | \(0.712247\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.97673 | −1.14174 | −0.570871 | − | 0.821040i | \(-0.693394\pi\) | ||||
−0.570871 | + | 0.821040i | \(0.693394\pi\) | |||||||
\(20\) | 2.66497 | 0.595906 | ||||||||
\(21\) | −2.36859 | −0.516869 | ||||||||
\(22\) | −2.99046 | −0.637568 | ||||||||
\(23\) | 8.19215 | 1.70818 | 0.854091 | − | 0.520124i | \(-0.174114\pi\) | ||||
0.854091 | + | 0.520124i | \(0.174114\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 2.10207 | 0.420414 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.36859 | 0.447621 | ||||||||
\(29\) | −8.89325 | −1.65143 | −0.825717 | − | 0.564084i | \(-0.809229\pi\) | ||||
−0.825717 | + | 0.564084i | \(0.809229\pi\) | |||||||
\(30\) | 2.66497 | 0.486555 | ||||||||
\(31\) | 2.96518 | 0.532563 | 0.266281 | − | 0.963895i | \(-0.414205\pi\) | ||||
0.266281 | + | 0.963895i | \(0.414205\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.99046 | −0.520572 | ||||||||
\(34\) | 5.10004 | 0.874649 | ||||||||
\(35\) | 6.31222 | 1.06696 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.50176 | −1.23328 | −0.616641 | − | 0.787244i | \(-0.711507\pi\) | ||||
−0.616641 | + | 0.787244i | \(0.711507\pi\) | |||||||
\(38\) | 4.97673 | 0.807333 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.66497 | −0.421369 | ||||||||
\(41\) | −5.29737 | −0.827310 | −0.413655 | − | 0.910434i | \(-0.635748\pi\) | ||||
−0.413655 | + | 0.910434i | \(0.635748\pi\) | |||||||
\(42\) | 2.36859 | 0.365481 | ||||||||
\(43\) | 5.03485 | 0.767808 | 0.383904 | − | 0.923373i | \(-0.374579\pi\) | ||||
0.383904 | + | 0.923373i | \(0.374579\pi\) | |||||||
\(44\) | 2.99046 | 0.450829 | ||||||||
\(45\) | 2.66497 | 0.397270 | ||||||||
\(46\) | −8.19215 | −1.20787 | ||||||||
\(47\) | −6.68426 | −0.975000 | −0.487500 | − | 0.873123i | \(-0.662091\pi\) | ||||
−0.487500 | + | 0.873123i | \(0.662091\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.38978 | −0.198541 | ||||||||
\(50\) | −2.10207 | −0.297278 | ||||||||
\(51\) | 5.10004 | 0.714148 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −9.57222 | −1.31485 | −0.657423 | − | 0.753522i | \(-0.728353\pi\) | ||||
−0.657423 | + | 0.753522i | \(0.728353\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 7.96949 | 1.07461 | ||||||||
\(56\) | −2.36859 | −0.316516 | ||||||||
\(57\) | 4.97673 | 0.659185 | ||||||||
\(58\) | 8.89325 | 1.16774 | ||||||||
\(59\) | 4.13496 | 0.538326 | 0.269163 | − | 0.963095i | \(-0.413253\pi\) | ||||
0.269163 | + | 0.963095i | \(0.413253\pi\) | |||||||
\(60\) | −2.66497 | −0.344046 | ||||||||
\(61\) | −0.907884 | −0.116243 | −0.0581213 | − | 0.998310i | \(-0.518511\pi\) | ||||
−0.0581213 | + | 0.998310i | \(0.518511\pi\) | |||||||
\(62\) | −2.96518 | −0.376579 | ||||||||
\(63\) | 2.36859 | 0.298414 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.66497 | −0.330549 | ||||||||
\(66\) | 2.99046 | 0.368100 | ||||||||
\(67\) | −3.14935 | −0.384755 | −0.192377 | − | 0.981321i | \(-0.561620\pi\) | ||||
−0.192377 | + | 0.981321i | \(0.561620\pi\) | |||||||
\(68\) | −5.10004 | −0.618471 | ||||||||
\(69\) | −8.19215 | −0.986219 | ||||||||
\(70\) | −6.31222 | −0.754455 | ||||||||
\(71\) | −9.42543 | −1.11859 | −0.559296 | − | 0.828968i | \(-0.688929\pi\) | ||||
−0.559296 | + | 0.828968i | \(0.688929\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 1.53198 | 0.179305 | 0.0896526 | − | 0.995973i | \(-0.471424\pi\) | ||||
0.0896526 | + | 0.995973i | \(0.471424\pi\) | |||||||
\(74\) | 7.50176 | 0.872062 | ||||||||
\(75\) | −2.10207 | −0.242726 | ||||||||
\(76\) | −4.97673 | −0.570871 | ||||||||
\(77\) | 7.08317 | 0.807202 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −16.6133 | −1.86914 | −0.934571 | − | 0.355777i | \(-0.884216\pi\) | ||||
−0.934571 | + | 0.355777i | \(0.884216\pi\) | |||||||
\(80\) | 2.66497 | 0.297953 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.29737 | 0.584997 | ||||||||
\(83\) | −10.6717 | −1.17137 | −0.585687 | − | 0.810537i | \(-0.699175\pi\) | ||||
−0.585687 | + | 0.810537i | \(0.699175\pi\) | |||||||
\(84\) | −2.36859 | −0.258434 | ||||||||
\(85\) | −13.5915 | −1.47420 | ||||||||
\(86\) | −5.03485 | −0.542922 | ||||||||
\(87\) | 8.89325 | 0.953456 | ||||||||
\(88\) | −2.99046 | −0.318784 | ||||||||
\(89\) | 14.2388 | 1.50931 | 0.754654 | − | 0.656123i | \(-0.227805\pi\) | ||||
0.754654 | + | 0.656123i | \(0.227805\pi\) | |||||||
\(90\) | −2.66497 | −0.280913 | ||||||||
\(91\) | −2.36859 | −0.248296 | ||||||||
\(92\) | 8.19215 | 0.854091 | ||||||||
\(93\) | −2.96518 | −0.307475 | ||||||||
\(94\) | 6.68426 | 0.689429 | ||||||||
\(95\) | −13.2629 | −1.36074 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.63892 | −0.572546 | −0.286273 | − | 0.958148i | \(-0.592416\pi\) | ||||
−0.286273 | + | 0.958148i | \(0.592416\pi\) | |||||||
\(98\) | 1.38978 | 0.140389 | ||||||||
\(99\) | 2.99046 | 0.300552 | ||||||||
\(100\) | 2.10207 | 0.210207 | ||||||||
\(101\) | −8.11468 | −0.807440 | −0.403720 | − | 0.914882i | \(-0.632283\pi\) | ||||
−0.403720 | + | 0.914882i | \(0.632283\pi\) | |||||||
\(102\) | −5.10004 | −0.504979 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −6.31222 | −0.616010 | ||||||||
\(106\) | 9.57222 | 0.929736 | ||||||||
\(107\) | −8.82181 | −0.852837 | −0.426418 | − | 0.904526i | \(-0.640225\pi\) | ||||
−0.426418 | + | 0.904526i | \(0.640225\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −4.89164 | −0.468534 | −0.234267 | − | 0.972172i | \(-0.575269\pi\) | ||||
−0.234267 | + | 0.972172i | \(0.575269\pi\) | |||||||
\(110\) | −7.96949 | −0.759861 | ||||||||
\(111\) | 7.50176 | 0.712036 | ||||||||
\(112\) | 2.36859 | 0.223811 | ||||||||
\(113\) | 0.199059 | 0.0187259 | 0.00936296 | − | 0.999956i | \(-0.497020\pi\) | ||||
0.00936296 | + | 0.999956i | \(0.497020\pi\) | |||||||
\(114\) | −4.97673 | −0.466114 | ||||||||
\(115\) | 21.8318 | 2.03583 | ||||||||
\(116\) | −8.89325 | −0.825717 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −4.13496 | −0.380654 | ||||||||
\(119\) | −12.0799 | −1.10736 | ||||||||
\(120\) | 2.66497 | 0.243277 | ||||||||
\(121\) | −2.05715 | −0.187014 | ||||||||
\(122\) | 0.907884 | 0.0821959 | ||||||||
\(123\) | 5.29737 | 0.477648 | ||||||||
\(124\) | 2.96518 | 0.266281 | ||||||||
\(125\) | −7.72290 | −0.690757 | ||||||||
\(126\) | −2.36859 | −0.211011 | ||||||||
\(127\) | −14.4539 | −1.28258 | −0.641290 | − | 0.767299i | \(-0.721600\pi\) | ||||
−0.641290 | + | 0.767299i | \(0.721600\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.03485 | −0.443294 | ||||||||
\(130\) | 2.66497 | 0.233733 | ||||||||
\(131\) | 11.1968 | 0.978269 | 0.489134 | − | 0.872208i | \(-0.337313\pi\) | ||||
0.489134 | + | 0.872208i | \(0.337313\pi\) | |||||||
\(132\) | −2.99046 | −0.260286 | ||||||||
\(133\) | −11.7878 | −1.02214 | ||||||||
\(134\) | 3.14935 | 0.272063 | ||||||||
\(135\) | −2.66497 | −0.229364 | ||||||||
\(136\) | 5.10004 | 0.437325 | ||||||||
\(137\) | −1.38948 | −0.118711 | −0.0593555 | − | 0.998237i | \(-0.518905\pi\) | ||||
−0.0593555 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(138\) | 8.19215 | 0.697362 | ||||||||
\(139\) | −14.7431 | −1.25049 | −0.625245 | − | 0.780428i | \(-0.715001\pi\) | ||||
−0.625245 | + | 0.780428i | \(0.715001\pi\) | |||||||
\(140\) | 6.31222 | 0.533480 | ||||||||
\(141\) | 6.68426 | 0.562917 | ||||||||
\(142\) | 9.42543 | 0.790964 | ||||||||
\(143\) | −2.99046 | −0.250075 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −23.7002 | −1.96820 | ||||||||
\(146\) | −1.53198 | −0.126788 | ||||||||
\(147\) | 1.38978 | 0.114627 | ||||||||
\(148\) | −7.50176 | −0.616641 | ||||||||
\(149\) | −9.30260 | −0.762099 | −0.381049 | − | 0.924555i | \(-0.624437\pi\) | ||||
−0.381049 | + | 0.924555i | \(0.624437\pi\) | |||||||
\(150\) | 2.10207 | 0.171633 | ||||||||
\(151\) | −19.5117 | −1.58784 | −0.793919 | − | 0.608024i | \(-0.791963\pi\) | ||||
−0.793919 | + | 0.608024i | \(0.791963\pi\) | |||||||
\(152\) | 4.97673 | 0.403666 | ||||||||
\(153\) | −5.10004 | −0.412314 | ||||||||
\(154\) | −7.08317 | −0.570778 | ||||||||
\(155\) | 7.90213 | 0.634714 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 12.7383 | 1.01663 | 0.508314 | − | 0.861172i | \(-0.330269\pi\) | ||||
0.508314 | + | 0.861172i | \(0.330269\pi\) | |||||||
\(158\) | 16.6133 | 1.32168 | ||||||||
\(159\) | 9.57222 | 0.759126 | ||||||||
\(160\) | −2.66497 | −0.210684 | ||||||||
\(161\) | 19.4038 | 1.52924 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 20.0360 | 1.56934 | 0.784671 | − | 0.619912i | \(-0.212832\pi\) | ||||
0.784671 | + | 0.619912i | \(0.212832\pi\) | |||||||
\(164\) | −5.29737 | −0.413655 | ||||||||
\(165\) | −7.96949 | −0.620424 | ||||||||
\(166\) | 10.6717 | 0.828287 | ||||||||
\(167\) | −12.2588 | −0.948611 | −0.474305 | − | 0.880360i | \(-0.657301\pi\) | ||||
−0.474305 | + | 0.880360i | \(0.657301\pi\) | |||||||
\(168\) | 2.36859 | 0.182741 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 13.5915 | 1.04242 | ||||||||
\(171\) | −4.97673 | −0.380580 | ||||||||
\(172\) | 5.03485 | 0.383904 | ||||||||
\(173\) | −10.4013 | −0.790795 | −0.395398 | − | 0.918510i | \(-0.629393\pi\) | ||||
−0.395398 | + | 0.918510i | \(0.629393\pi\) | |||||||
\(174\) | −8.89325 | −0.674195 | ||||||||
\(175\) | 4.97894 | 0.376373 | ||||||||
\(176\) | 2.99046 | 0.225414 | ||||||||
\(177\) | −4.13496 | −0.310803 | ||||||||
\(178\) | −14.2388 | −1.06724 | ||||||||
\(179\) | 25.8043 | 1.92870 | 0.964352 | − | 0.264622i | \(-0.0852471\pi\) | ||||
0.964352 | + | 0.264622i | \(0.0852471\pi\) | |||||||
\(180\) | 2.66497 | 0.198635 | ||||||||
\(181\) | −1.38863 | −0.103216 | −0.0516082 | − | 0.998667i | \(-0.516435\pi\) | ||||
−0.0516082 | + | 0.998667i | \(0.516435\pi\) | |||||||
\(182\) | 2.36859 | 0.175572 | ||||||||
\(183\) | 0.907884 | 0.0671127 | ||||||||
\(184\) | −8.19215 | −0.603933 | ||||||||
\(185\) | −19.9920 | −1.46984 | ||||||||
\(186\) | 2.96518 | 0.217418 | ||||||||
\(187\) | −15.2515 | −1.11530 | ||||||||
\(188\) | −6.68426 | −0.487500 | ||||||||
\(189\) | −2.36859 | −0.172290 | ||||||||
\(190\) | 13.2629 | 0.962189 | ||||||||
\(191\) | 20.9559 | 1.51632 | 0.758159 | − | 0.652070i | \(-0.226099\pi\) | ||||
0.758159 | + | 0.652070i | \(0.226099\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 14.1557 | 1.01895 | 0.509474 | − | 0.860486i | \(-0.329840\pi\) | ||||
0.509474 | + | 0.860486i | \(0.329840\pi\) | |||||||
\(194\) | 5.63892 | 0.404851 | ||||||||
\(195\) | 2.66497 | 0.190843 | ||||||||
\(196\) | −1.38978 | −0.0992703 | ||||||||
\(197\) | 3.89385 | 0.277426 | 0.138713 | − | 0.990333i | \(-0.455704\pi\) | ||||
0.138713 | + | 0.990333i | \(0.455704\pi\) | |||||||
\(198\) | −2.99046 | −0.212523 | ||||||||
\(199\) | −0.00132986 | −9.42710e−5 0 | −4.71355e−5 | − | 1.00000i | \(-0.500015\pi\) | ||||
−4.71355e−5 | 1.00000i | \(0.500015\pi\) | ||||||||
\(200\) | −2.10207 | −0.148639 | ||||||||
\(201\) | 3.14935 | 0.222138 | ||||||||
\(202\) | 8.11468 | 0.570947 | ||||||||
\(203\) | −21.0644 | −1.47843 | ||||||||
\(204\) | 5.10004 | 0.357074 | ||||||||
\(205\) | −14.1173 | −0.985998 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 8.19215 | 0.569394 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −14.8827 | −1.02946 | ||||||||
\(210\) | 6.31222 | 0.435585 | ||||||||
\(211\) | −3.76040 | −0.258877 | −0.129438 | − | 0.991587i | \(-0.541317\pi\) | ||||
−0.129438 | + | 0.991587i | \(0.541317\pi\) | |||||||
\(212\) | −9.57222 | −0.657423 | ||||||||
\(213\) | 9.42543 | 0.645820 | ||||||||
\(214\) | 8.82181 | 0.603047 | ||||||||
\(215\) | 13.4177 | 0.915082 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 7.02330 | 0.476773 | ||||||||
\(218\) | 4.89164 | 0.331304 | ||||||||
\(219\) | −1.53198 | −0.103522 | ||||||||
\(220\) | 7.96949 | 0.537303 | ||||||||
\(221\) | 5.10004 | 0.343066 | ||||||||
\(222\) | −7.50176 | −0.503485 | ||||||||
\(223\) | −20.0488 | −1.34257 | −0.671285 | − | 0.741200i | \(-0.734257\pi\) | ||||
−0.671285 | + | 0.741200i | \(0.734257\pi\) | |||||||
\(224\) | −2.36859 | −0.158258 | ||||||||
\(225\) | 2.10207 | 0.140138 | ||||||||
\(226\) | −0.199059 | −0.0132412 | ||||||||
\(227\) | 15.7644 | 1.04632 | 0.523159 | − | 0.852235i | \(-0.324753\pi\) | ||||
0.523159 | + | 0.852235i | \(0.324753\pi\) | |||||||
\(228\) | 4.97673 | 0.329592 | ||||||||
\(229\) | 23.7161 | 1.56720 | 0.783602 | − | 0.621263i | \(-0.213380\pi\) | ||||
0.783602 | + | 0.621263i | \(0.213380\pi\) | |||||||
\(230\) | −21.8318 | −1.43955 | ||||||||
\(231\) | −7.08317 | −0.466038 | ||||||||
\(232\) | 8.89325 | 0.583870 | ||||||||
\(233\) | 23.6830 | 1.55153 | 0.775763 | − | 0.631024i | \(-0.217365\pi\) | ||||
0.775763 | + | 0.631024i | \(0.217365\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −17.8134 | −1.16202 | ||||||||
\(236\) | 4.13496 | 0.269163 | ||||||||
\(237\) | 16.6133 | 1.07915 | ||||||||
\(238\) | 12.0799 | 0.783024 | ||||||||
\(239\) | −12.8452 | −0.830884 | −0.415442 | − | 0.909620i | \(-0.636373\pi\) | ||||
−0.415442 | + | 0.909620i | \(0.636373\pi\) | |||||||
\(240\) | −2.66497 | −0.172023 | ||||||||
\(241\) | −16.9050 | −1.08895 | −0.544473 | − | 0.838778i | \(-0.683270\pi\) | ||||
−0.544473 | + | 0.838778i | \(0.683270\pi\) | |||||||
\(242\) | 2.05715 | 0.132239 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.907884 | −0.0581213 | ||||||||
\(245\) | −3.70373 | −0.236623 | ||||||||
\(246\) | −5.29737 | −0.337748 | ||||||||
\(247\) | 4.97673 | 0.316662 | ||||||||
\(248\) | −2.96518 | −0.188289 | ||||||||
\(249\) | 10.6717 | 0.676293 | ||||||||
\(250\) | 7.72290 | 0.488439 | ||||||||
\(251\) | 26.3714 | 1.66455 | 0.832274 | − | 0.554364i | \(-0.187039\pi\) | ||||
0.832274 | + | 0.554364i | \(0.187039\pi\) | |||||||
\(252\) | 2.36859 | 0.149207 | ||||||||
\(253\) | 24.4983 | 1.54019 | ||||||||
\(254\) | 14.4539 | 0.906921 | ||||||||
\(255\) | 13.5915 | 0.851130 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2911 | −0.766700 | −0.383350 | − | 0.923603i | \(-0.625230\pi\) | ||||
−0.383350 | + | 0.923603i | \(0.625230\pi\) | |||||||
\(258\) | 5.03485 | 0.313456 | ||||||||
\(259\) | −17.7686 | −1.10409 | ||||||||
\(260\) | −2.66497 | −0.165274 | ||||||||
\(261\) | −8.89325 | −0.550478 | ||||||||
\(262\) | −11.1968 | −0.691741 | ||||||||
\(263\) | −3.65412 | −0.225323 | −0.112661 | − | 0.993633i | \(-0.535938\pi\) | ||||
−0.112661 | + | 0.993633i | \(0.535938\pi\) | |||||||
\(264\) | 2.99046 | 0.184050 | ||||||||
\(265\) | −25.5097 | −1.56705 | ||||||||
\(266\) | 11.7878 | 0.722759 | ||||||||
\(267\) | −14.2388 | −0.871399 | ||||||||
\(268\) | −3.14935 | −0.192377 | ||||||||
\(269\) | 8.85845 | 0.540109 | 0.270055 | − | 0.962845i | \(-0.412958\pi\) | ||||
0.270055 | + | 0.962845i | \(0.412958\pi\) | |||||||
\(270\) | 2.66497 | 0.162185 | ||||||||
\(271\) | −17.8907 | −1.08679 | −0.543393 | − | 0.839479i | \(-0.682860\pi\) | ||||
−0.543393 | + | 0.839479i | \(0.682860\pi\) | |||||||
\(272\) | −5.10004 | −0.309235 | ||||||||
\(273\) | 2.36859 | 0.143354 | ||||||||
\(274\) | 1.38948 | 0.0839414 | ||||||||
\(275\) | 6.28616 | 0.379070 | ||||||||
\(276\) | −8.19215 | −0.493109 | ||||||||
\(277\) | −19.2663 | −1.15760 | −0.578799 | − | 0.815470i | \(-0.696478\pi\) | ||||
−0.578799 | + | 0.815470i | \(0.696478\pi\) | |||||||
\(278\) | 14.7431 | 0.884230 | ||||||||
\(279\) | 2.96518 | 0.177521 | ||||||||
\(280\) | −6.31222 | −0.377227 | ||||||||
\(281\) | 26.0446 | 1.55369 | 0.776846 | − | 0.629691i | \(-0.216819\pi\) | ||||
0.776846 | + | 0.629691i | \(0.216819\pi\) | |||||||
\(282\) | −6.68426 | −0.398042 | ||||||||
\(283\) | 14.4965 | 0.861729 | 0.430864 | − | 0.902417i | \(-0.358209\pi\) | ||||
0.430864 | + | 0.902417i | \(0.358209\pi\) | |||||||
\(284\) | −9.42543 | −0.559296 | ||||||||
\(285\) | 13.2629 | 0.785624 | ||||||||
\(286\) | 2.99046 | 0.176830 | ||||||||
\(287\) | −12.5473 | −0.740644 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 9.01040 | 0.530023 | ||||||||
\(290\) | 23.7002 | 1.39173 | ||||||||
\(291\) | 5.63892 | 0.330559 | ||||||||
\(292\) | 1.53198 | 0.0896526 | ||||||||
\(293\) | 29.9123 | 1.74750 | 0.873749 | − | 0.486377i | \(-0.161682\pi\) | ||||
0.873749 | + | 0.486377i | \(0.161682\pi\) | |||||||
\(294\) | −1.38978 | −0.0810539 | ||||||||
\(295\) | 11.0196 | 0.641583 | ||||||||
\(296\) | 7.50176 | 0.436031 | ||||||||
\(297\) | −2.99046 | −0.173524 | ||||||||
\(298\) | 9.30260 | 0.538885 | ||||||||
\(299\) | −8.19215 | −0.473764 | ||||||||
\(300\) | −2.10207 | −0.121363 | ||||||||
\(301\) | 11.9255 | 0.687375 | ||||||||
\(302\) | 19.5117 | 1.12277 | ||||||||
\(303\) | 8.11468 | 0.466176 | ||||||||
\(304\) | −4.97673 | −0.285435 | ||||||||
\(305\) | −2.41948 | −0.138539 | ||||||||
\(306\) | 5.10004 | 0.291550 | ||||||||
\(307\) | 31.7716 | 1.81330 | 0.906651 | − | 0.421881i | \(-0.138630\pi\) | ||||
0.906651 | + | 0.421881i | \(0.138630\pi\) | |||||||
\(308\) | 7.08317 | 0.403601 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −7.90213 | −0.448811 | ||||||||
\(311\) | 4.13303 | 0.234363 | 0.117181 | − | 0.993111i | \(-0.462614\pi\) | ||||
0.117181 | + | 0.993111i | \(0.462614\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 22.5791 | 1.27624 | 0.638122 | − | 0.769935i | \(-0.279711\pi\) | ||||
0.638122 | + | 0.769935i | \(0.279711\pi\) | |||||||
\(314\) | −12.7383 | −0.718864 | ||||||||
\(315\) | 6.31222 | 0.355653 | ||||||||
\(316\) | −16.6133 | −0.934571 | ||||||||
\(317\) | 25.2757 | 1.41962 | 0.709812 | − | 0.704391i | \(-0.248780\pi\) | ||||
0.709812 | + | 0.704391i | \(0.248780\pi\) | |||||||
\(318\) | −9.57222 | −0.536783 | ||||||||
\(319\) | −26.5949 | −1.48903 | ||||||||
\(320\) | 2.66497 | 0.148976 | ||||||||
\(321\) | 8.82181 | 0.492385 | ||||||||
\(322\) | −19.4038 | −1.08133 | ||||||||
\(323\) | 25.3815 | 1.41227 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.10207 | −0.116602 | ||||||||
\(326\) | −20.0360 | −1.10969 | ||||||||
\(327\) | 4.89164 | 0.270508 | ||||||||
\(328\) | 5.29737 | 0.292498 | ||||||||
\(329\) | −15.8323 | −0.872862 | ||||||||
\(330\) | 7.96949 | 0.438706 | ||||||||
\(331\) | 15.2198 | 0.836558 | 0.418279 | − | 0.908319i | \(-0.362633\pi\) | ||||
0.418279 | + | 0.908319i | \(0.362633\pi\) | |||||||
\(332\) | −10.6717 | −0.585687 | ||||||||
\(333\) | −7.50176 | −0.411094 | ||||||||
\(334\) | 12.2588 | 0.670769 | ||||||||
\(335\) | −8.39293 | −0.458555 | ||||||||
\(336\) | −2.36859 | −0.129217 | ||||||||
\(337\) | 10.7086 | 0.583336 | 0.291668 | − | 0.956520i | \(-0.405790\pi\) | ||||
0.291668 | + | 0.956520i | \(0.405790\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −0.199059 | −0.0108114 | ||||||||
\(340\) | −13.5915 | −0.737100 | ||||||||
\(341\) | 8.86726 | 0.480189 | ||||||||
\(342\) | 4.97673 | 0.269111 | ||||||||
\(343\) | −19.8720 | −1.07298 | ||||||||
\(344\) | −5.03485 | −0.271461 | ||||||||
\(345\) | −21.8318 | −1.17539 | ||||||||
\(346\) | 10.4013 | 0.559177 | ||||||||
\(347\) | −9.32187 | −0.500424 | −0.250212 | − | 0.968191i | \(-0.580500\pi\) | ||||
−0.250212 | + | 0.968191i | \(0.580500\pi\) | |||||||
\(348\) | 8.89325 | 0.476728 | ||||||||
\(349\) | −7.12865 | −0.381588 | −0.190794 | − | 0.981630i | \(-0.561106\pi\) | ||||
−0.190794 | + | 0.981630i | \(0.561106\pi\) | |||||||
\(350\) | −4.97894 | −0.266136 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −2.99046 | −0.159392 | ||||||||
\(353\) | −1.14759 | −0.0610801 | −0.0305401 | − | 0.999534i | \(-0.509723\pi\) | ||||
−0.0305401 | + | 0.999534i | \(0.509723\pi\) | |||||||
\(354\) | 4.13496 | 0.219771 | ||||||||
\(355\) | −25.1185 | −1.33315 | ||||||||
\(356\) | 14.2388 | 0.754654 | ||||||||
\(357\) | 12.0799 | 0.639336 | ||||||||
\(358\) | −25.8043 | −1.36380 | ||||||||
\(359\) | 36.2087 | 1.91102 | 0.955510 | − | 0.294959i | \(-0.0953060\pi\) | ||||
0.955510 | + | 0.294959i | \(0.0953060\pi\) | |||||||
\(360\) | −2.66497 | −0.140456 | ||||||||
\(361\) | 5.76789 | 0.303573 | ||||||||
\(362\) | 1.38863 | 0.0729850 | ||||||||
\(363\) | 2.05715 | 0.107973 | ||||||||
\(364\) | −2.36859 | −0.124148 | ||||||||
\(365\) | 4.08269 | 0.213698 | ||||||||
\(366\) | −0.907884 | −0.0474558 | ||||||||
\(367\) | −33.5446 | −1.75101 | −0.875507 | − | 0.483206i | \(-0.839472\pi\) | ||||
−0.875507 | + | 0.483206i | \(0.839472\pi\) | |||||||
\(368\) | 8.19215 | 0.427045 | ||||||||
\(369\) | −5.29737 | −0.275770 | ||||||||
\(370\) | 19.9920 | 1.03933 | ||||||||
\(371\) | −22.6727 | −1.17711 | ||||||||
\(372\) | −2.96518 | −0.153738 | ||||||||
\(373\) | −15.4244 | −0.798647 | −0.399323 | − | 0.916810i | \(-0.630755\pi\) | ||||
−0.399323 | + | 0.916810i | \(0.630755\pi\) | |||||||
\(374\) | 15.2515 | 0.788634 | ||||||||
\(375\) | 7.72290 | 0.398809 | ||||||||
\(376\) | 6.68426 | 0.344715 | ||||||||
\(377\) | 8.89325 | 0.458025 | ||||||||
\(378\) | 2.36859 | 0.121827 | ||||||||
\(379\) | −35.1670 | −1.80641 | −0.903204 | − | 0.429212i | \(-0.858791\pi\) | ||||
−0.903204 | + | 0.429212i | \(0.858791\pi\) | |||||||
\(380\) | −13.2629 | −0.680370 | ||||||||
\(381\) | 14.4539 | 0.740498 | ||||||||
\(382\) | −20.9559 | −1.07220 | ||||||||
\(383\) | 19.8437 | 1.01397 | 0.506983 | − | 0.861956i | \(-0.330761\pi\) | ||||
0.506983 | + | 0.861956i | \(0.330761\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 18.8764 | 0.962033 | ||||||||
\(386\) | −14.1557 | −0.720505 | ||||||||
\(387\) | 5.03485 | 0.255936 | ||||||||
\(388\) | −5.63892 | −0.286273 | ||||||||
\(389\) | −6.15603 | −0.312123 | −0.156062 | − | 0.987747i | \(-0.549880\pi\) | ||||
−0.156062 | + | 0.987747i | \(0.549880\pi\) | |||||||
\(390\) | −2.66497 | −0.134946 | ||||||||
\(391\) | −41.7803 | −2.11292 | ||||||||
\(392\) | 1.38978 | 0.0701947 | ||||||||
\(393\) | −11.1968 | −0.564804 | ||||||||
\(394\) | −3.89385 | −0.196170 | ||||||||
\(395\) | −44.2739 | −2.22766 | ||||||||
\(396\) | 2.99046 | 0.150276 | ||||||||
\(397\) | −10.2420 | −0.514030 | −0.257015 | − | 0.966407i | \(-0.582739\pi\) | ||||
−0.257015 | + | 0.966407i | \(0.582739\pi\) | |||||||
\(398\) | 0.00132986 | 6.66597e−5 0 | ||||||||
\(399\) | 11.7878 | 0.590130 | ||||||||
\(400\) | 2.10207 | 0.105104 | ||||||||
\(401\) | 2.63594 | 0.131633 | 0.0658163 | − | 0.997832i | \(-0.479035\pi\) | ||||
0.0658163 | + | 0.997832i | \(0.479035\pi\) | |||||||
\(402\) | −3.14935 | −0.157075 | ||||||||
\(403\) | −2.96518 | −0.147706 | ||||||||
\(404\) | −8.11468 | −0.403720 | ||||||||
\(405\) | 2.66497 | 0.132423 | ||||||||
\(406\) | 21.0644 | 1.04541 | ||||||||
\(407\) | −22.4337 | −1.11200 | ||||||||
\(408\) | −5.10004 | −0.252490 | ||||||||
\(409\) | 30.9063 | 1.52822 | 0.764110 | − | 0.645087i | \(-0.223179\pi\) | ||||
0.764110 | + | 0.645087i | \(0.223179\pi\) | |||||||
\(410\) | 14.1173 | 0.697206 | ||||||||
\(411\) | 1.38948 | 0.0685379 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 9.79403 | 0.481933 | ||||||||
\(414\) | −8.19215 | −0.402622 | ||||||||
\(415\) | −28.4398 | −1.39606 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 14.7431 | 0.721971 | ||||||||
\(418\) | 14.8827 | 0.727938 | ||||||||
\(419\) | −32.7095 | −1.59796 | −0.798981 | − | 0.601357i | \(-0.794627\pi\) | ||||
−0.798981 | + | 0.601357i | \(0.794627\pi\) | |||||||
\(420\) | −6.31222 | −0.308005 | ||||||||
\(421\) | 31.0744 | 1.51448 | 0.757238 | − | 0.653140i | \(-0.226548\pi\) | ||||
0.757238 | + | 0.653140i | \(0.226548\pi\) | |||||||
\(422\) | 3.76040 | 0.183053 | ||||||||
\(423\) | −6.68426 | −0.325000 | ||||||||
\(424\) | 9.57222 | 0.464868 | ||||||||
\(425\) | −10.7206 | −0.520028 | ||||||||
\(426\) | −9.42543 | −0.456663 | ||||||||
\(427\) | −2.15040 | −0.104065 | ||||||||
\(428\) | −8.82181 | −0.426418 | ||||||||
\(429\) | 2.99046 | 0.144381 | ||||||||
\(430\) | −13.4177 | −0.647061 | ||||||||
\(431\) | 33.4471 | 1.61109 | 0.805544 | − | 0.592536i | \(-0.201873\pi\) | ||||
0.805544 | + | 0.592536i | \(0.201873\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 19.6562 | 0.944619 | 0.472309 | − | 0.881433i | \(-0.343420\pi\) | ||||
0.472309 | + | 0.881433i | \(0.343420\pi\) | |||||||
\(434\) | −7.02330 | −0.337129 | ||||||||
\(435\) | 23.7002 | 1.13634 | ||||||||
\(436\) | −4.89164 | −0.234267 | ||||||||
\(437\) | −40.7701 | −1.95030 | ||||||||
\(438\) | 1.53198 | 0.0732010 | ||||||||
\(439\) | −17.4337 | −0.832064 | −0.416032 | − | 0.909350i | \(-0.636579\pi\) | ||||
−0.416032 | + | 0.909350i | \(0.636579\pi\) | |||||||
\(440\) | −7.96949 | −0.379930 | ||||||||
\(441\) | −1.38978 | −0.0661802 | ||||||||
\(442\) | −5.10004 | −0.242584 | ||||||||
\(443\) | −33.1504 | −1.57502 | −0.787511 | − | 0.616301i | \(-0.788631\pi\) | ||||
−0.787511 | + | 0.616301i | \(0.788631\pi\) | |||||||
\(444\) | 7.50176 | 0.356018 | ||||||||
\(445\) | 37.9459 | 1.79881 | ||||||||
\(446\) | 20.0488 | 0.949340 | ||||||||
\(447\) | 9.30260 | 0.439998 | ||||||||
\(448\) | 2.36859 | 0.111905 | ||||||||
\(449\) | −17.4809 | −0.824974 | −0.412487 | − | 0.910963i | \(-0.635340\pi\) | ||||
−0.412487 | + | 0.910963i | \(0.635340\pi\) | |||||||
\(450\) | −2.10207 | −0.0990926 | ||||||||
\(451\) | −15.8416 | −0.745951 | ||||||||
\(452\) | 0.199059 | 0.00936296 | ||||||||
\(453\) | 19.5117 | 0.916738 | ||||||||
\(454\) | −15.7644 | −0.739859 | ||||||||
\(455\) | −6.31222 | −0.295922 | ||||||||
\(456\) | −4.97673 | −0.233057 | ||||||||
\(457\) | 5.47979 | 0.256334 | 0.128167 | − | 0.991753i | \(-0.459091\pi\) | ||||
0.128167 | + | 0.991753i | \(0.459091\pi\) | |||||||
\(458\) | −23.7161 | −1.10818 | ||||||||
\(459\) | 5.10004 | 0.238049 | ||||||||
\(460\) | 21.8318 | 1.01791 | ||||||||
\(461\) | 14.4209 | 0.671650 | 0.335825 | − | 0.941924i | \(-0.390985\pi\) | ||||
0.335825 | + | 0.941924i | \(0.390985\pi\) | |||||||
\(462\) | 7.08317 | 0.329539 | ||||||||
\(463\) | −14.3003 | −0.664593 | −0.332296 | − | 0.943175i | \(-0.607823\pi\) | ||||
−0.332296 | + | 0.943175i | \(0.607823\pi\) | |||||||
\(464\) | −8.89325 | −0.412859 | ||||||||
\(465\) | −7.90213 | −0.366452 | ||||||||
\(466\) | −23.6830 | −1.09709 | ||||||||
\(467\) | −20.5623 | −0.951510 | −0.475755 | − | 0.879578i | \(-0.657825\pi\) | ||||
−0.475755 | + | 0.879578i | \(0.657825\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −7.45952 | −0.344449 | ||||||||
\(470\) | 17.8134 | 0.821669 | ||||||||
\(471\) | −12.7383 | −0.586950 | ||||||||
\(472\) | −4.13496 | −0.190327 | ||||||||
\(473\) | 15.0565 | 0.692300 | ||||||||
\(474\) | −16.6133 | −0.763074 | ||||||||
\(475\) | −10.4614 | −0.480004 | ||||||||
\(476\) | −12.0799 | −0.553681 | ||||||||
\(477\) | −9.57222 | −0.438282 | ||||||||
\(478\) | 12.8452 | 0.587524 | ||||||||
\(479\) | −38.1472 | −1.74299 | −0.871494 | − | 0.490406i | \(-0.836848\pi\) | ||||
−0.871494 | + | 0.490406i | \(0.836848\pi\) | |||||||
\(480\) | 2.66497 | 0.121639 | ||||||||
\(481\) | 7.50176 | 0.342051 | ||||||||
\(482\) | 16.9050 | 0.770001 | ||||||||
\(483\) | −19.4038 | −0.882905 | ||||||||
\(484\) | −2.05715 | −0.0935070 | ||||||||
\(485\) | −15.0276 | −0.682366 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 2.46128 | 0.111531 | 0.0557657 | − | 0.998444i | \(-0.482240\pi\) | ||||
0.0557657 | + | 0.998444i | \(0.482240\pi\) | |||||||
\(488\) | 0.907884 | 0.0410980 | ||||||||
\(489\) | −20.0360 | −0.906060 | ||||||||
\(490\) | 3.70373 | 0.167318 | ||||||||
\(491\) | 1.04891 | 0.0473368 | 0.0236684 | − | 0.999720i | \(-0.492465\pi\) | ||||
0.0236684 | + | 0.999720i | \(0.492465\pi\) | |||||||
\(492\) | 5.29737 | 0.238824 | ||||||||
\(493\) | 45.3559 | 2.04273 | ||||||||
\(494\) | −4.97673 | −0.223914 | ||||||||
\(495\) | 7.96949 | 0.358202 | ||||||||
\(496\) | 2.96518 | 0.133141 | ||||||||
\(497\) | −22.3250 | −1.00141 | ||||||||
\(498\) | −10.6717 | −0.478212 | ||||||||
\(499\) | −12.0797 | −0.540761 | −0.270380 | − | 0.962754i | \(-0.587149\pi\) | ||||
−0.270380 | + | 0.962754i | \(0.587149\pi\) | |||||||
\(500\) | −7.72290 | −0.345378 | ||||||||
\(501\) | 12.2588 | 0.547681 | ||||||||
\(502\) | −26.3714 | −1.17701 | ||||||||
\(503\) | 5.46186 | 0.243532 | 0.121766 | − | 0.992559i | \(-0.461144\pi\) | ||||
0.121766 | + | 0.992559i | \(0.461144\pi\) | |||||||
\(504\) | −2.36859 | −0.105505 | ||||||||
\(505\) | −21.6254 | −0.962317 | ||||||||
\(506\) | −24.4983 | −1.08908 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −14.4539 | −0.641290 | ||||||||
\(509\) | 19.5818 | 0.867948 | 0.433974 | − | 0.900925i | \(-0.357111\pi\) | ||||
0.433974 | + | 0.900925i | \(0.357111\pi\) | |||||||
\(510\) | −13.5915 | −0.601840 | ||||||||
\(511\) | 3.62864 | 0.160522 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.97673 | 0.219728 | ||||||||
\(514\) | 12.2911 | 0.542139 | ||||||||
\(515\) | −2.66497 | −0.117433 | ||||||||
\(516\) | −5.03485 | −0.221647 | ||||||||
\(517\) | −19.9890 | −0.879116 | ||||||||
\(518\) | 17.7686 | 0.780707 | ||||||||
\(519\) | 10.4013 | 0.456566 | ||||||||
\(520\) | 2.66497 | 0.116867 | ||||||||
\(521\) | −10.9348 | −0.479062 | −0.239531 | − | 0.970889i | \(-0.576994\pi\) | ||||
−0.239531 | + | 0.970889i | \(0.576994\pi\) | |||||||
\(522\) | 8.89325 | 0.389247 | ||||||||
\(523\) | −7.86901 | −0.344088 | −0.172044 | − | 0.985089i | \(-0.555037\pi\) | ||||
−0.172044 | + | 0.985089i | \(0.555037\pi\) | |||||||
\(524\) | 11.1968 | 0.489134 | ||||||||
\(525\) | −4.97894 | −0.217299 | ||||||||
\(526\) | 3.65412 | 0.159327 | ||||||||
\(527\) | −15.1226 | −0.658749 | ||||||||
\(528\) | −2.99046 | −0.130143 | ||||||||
\(529\) | 44.1113 | 1.91788 | ||||||||
\(530\) | 25.5097 | 1.10807 | ||||||||
\(531\) | 4.13496 | 0.179442 | ||||||||
\(532\) | −11.7878 | −0.511068 | ||||||||
\(533\) | 5.29737 | 0.229455 | ||||||||
\(534\) | 14.2388 | 0.616172 | ||||||||
\(535\) | −23.5099 | −1.01642 | ||||||||
\(536\) | 3.14935 | 0.136031 | ||||||||
\(537\) | −25.8043 | −1.11354 | ||||||||
\(538\) | −8.85845 | −0.381915 | ||||||||
\(539\) | −4.15609 | −0.179016 | ||||||||
\(540\) | −2.66497 | −0.114682 | ||||||||
\(541\) | −0.912894 | −0.0392484 | −0.0196242 | − | 0.999807i | \(-0.506247\pi\) | ||||
−0.0196242 | + | 0.999807i | \(0.506247\pi\) | |||||||
\(542\) | 17.8907 | 0.768473 | ||||||||
\(543\) | 1.38863 | 0.0595920 | ||||||||
\(544\) | 5.10004 | 0.218662 | ||||||||
\(545\) | −13.0361 | −0.558404 | ||||||||
\(546\) | −2.36859 | −0.101366 | ||||||||
\(547\) | 37.8306 | 1.61752 | 0.808759 | − | 0.588140i | \(-0.200139\pi\) | ||||
0.808759 | + | 0.588140i | \(0.200139\pi\) | |||||||
\(548\) | −1.38948 | −0.0593555 | ||||||||
\(549\) | −0.907884 | −0.0387475 | ||||||||
\(550\) | −6.28616 | −0.268043 | ||||||||
\(551\) | 44.2593 | 1.88551 | ||||||||
\(552\) | 8.19215 | 0.348681 | ||||||||
\(553\) | −39.3501 | −1.67334 | ||||||||
\(554\) | 19.2663 | 0.818545 | ||||||||
\(555\) | 19.9920 | 0.848612 | ||||||||
\(556\) | −14.7431 | −0.625245 | ||||||||
\(557\) | 38.7902 | 1.64359 | 0.821796 | − | 0.569781i | \(-0.192972\pi\) | ||||
0.821796 | + | 0.569781i | \(0.192972\pi\) | |||||||
\(558\) | −2.96518 | −0.125526 | ||||||||
\(559\) | −5.03485 | −0.212952 | ||||||||
\(560\) | 6.31222 | 0.266740 | ||||||||
\(561\) | 15.2515 | 0.643917 | ||||||||
\(562\) | −26.0446 | −1.09863 | ||||||||
\(563\) | 11.3724 | 0.479291 | 0.239646 | − | 0.970860i | \(-0.422969\pi\) | ||||
0.239646 | + | 0.970860i | \(0.422969\pi\) | |||||||
\(564\) | 6.68426 | 0.281458 | ||||||||
\(565\) | 0.530487 | 0.0223178 | ||||||||
\(566\) | −14.4965 | −0.609334 | ||||||||
\(567\) | 2.36859 | 0.0994714 | ||||||||
\(568\) | 9.42543 | 0.395482 | ||||||||
\(569\) | −22.9131 | −0.960567 | −0.480283 | − | 0.877113i | \(-0.659466\pi\) | ||||
−0.480283 | + | 0.877113i | \(0.659466\pi\) | |||||||
\(570\) | −13.2629 | −0.555520 | ||||||||
\(571\) | 5.11351 | 0.213994 | 0.106997 | − | 0.994259i | \(-0.465876\pi\) | ||||
0.106997 | + | 0.994259i | \(0.465876\pi\) | |||||||
\(572\) | −2.99046 | −0.125037 | ||||||||
\(573\) | −20.9559 | −0.875446 | ||||||||
\(574\) | 12.5473 | 0.523714 | ||||||||
\(575\) | 17.2205 | 0.718144 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 1.23404 | 0.0513737 | 0.0256869 | − | 0.999670i | \(-0.491823\pi\) | ||||
0.0256869 | + | 0.999670i | \(0.491823\pi\) | |||||||
\(578\) | −9.01040 | −0.374783 | ||||||||
\(579\) | −14.1557 | −0.588290 | ||||||||
\(580\) | −23.7002 | −0.984099 | ||||||||
\(581\) | −25.2769 | −1.04866 | ||||||||
\(582\) | −5.63892 | −0.233741 | ||||||||
\(583\) | −28.6253 | −1.18554 | ||||||||
\(584\) | −1.53198 | −0.0633940 | ||||||||
\(585\) | −2.66497 | −0.110183 | ||||||||
\(586\) | −29.9123 | −1.23567 | ||||||||
\(587\) | 43.7486 | 1.80570 | 0.902850 | − | 0.429956i | \(-0.141471\pi\) | ||||
0.902850 | + | 0.429956i | \(0.141471\pi\) | |||||||
\(588\) | 1.38978 | 0.0573137 | ||||||||
\(589\) | −14.7569 | −0.608049 | ||||||||
\(590\) | −11.0196 | −0.453668 | ||||||||
\(591\) | −3.89385 | −0.160172 | ||||||||
\(592\) | −7.50176 | −0.308321 | ||||||||
\(593\) | 42.4140 | 1.74173 | 0.870867 | − | 0.491519i | \(-0.163558\pi\) | ||||
0.870867 | + | 0.491519i | \(0.163558\pi\) | |||||||
\(594\) | 2.99046 | 0.122700 | ||||||||
\(595\) | −32.1926 | −1.31977 | ||||||||
\(596\) | −9.30260 | −0.381049 | ||||||||
\(597\) | 0.00132986 | 5.44274e−5 0 | ||||||||
\(598\) | 8.19215 | 0.335002 | ||||||||
\(599\) | −5.37854 | −0.219761 | −0.109881 | − | 0.993945i | \(-0.535047\pi\) | ||||
−0.109881 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(600\) | 2.10207 | 0.0858167 | ||||||||
\(601\) | −39.0827 | −1.59422 | −0.797108 | − | 0.603836i | \(-0.793638\pi\) | ||||
−0.797108 | + | 0.603836i | \(0.793638\pi\) | |||||||
\(602\) | −11.9255 | −0.486047 | ||||||||
\(603\) | −3.14935 | −0.128252 | ||||||||
\(604\) | −19.5117 | −0.793919 | ||||||||
\(605\) | −5.48226 | −0.222885 | ||||||||
\(606\) | −8.11468 | −0.329636 | ||||||||
\(607\) | −1.75743 | −0.0713319 | −0.0356660 | − | 0.999364i | \(-0.511355\pi\) | ||||
−0.0356660 | + | 0.999364i | \(0.511355\pi\) | |||||||
\(608\) | 4.97673 | 0.201833 | ||||||||
\(609\) | 21.0644 | 0.853574 | ||||||||
\(610\) | 2.41948 | 0.0979620 | ||||||||
\(611\) | 6.68426 | 0.270416 | ||||||||
\(612\) | −5.10004 | −0.206157 | ||||||||
\(613\) | 43.1060 | 1.74104 | 0.870518 | − | 0.492137i | \(-0.163784\pi\) | ||||
0.870518 | + | 0.492137i | \(0.163784\pi\) | |||||||
\(614\) | −31.7716 | −1.28220 | ||||||||
\(615\) | 14.1173 | 0.569266 | ||||||||
\(616\) | −7.08317 | −0.285389 | ||||||||
\(617\) | −8.90061 | −0.358325 | −0.179163 | − | 0.983819i | \(-0.557339\pi\) | ||||
−0.179163 | + | 0.983819i | \(0.557339\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −18.6732 | −0.750539 | −0.375269 | − | 0.926916i | \(-0.622450\pi\) | ||||
−0.375269 | + | 0.926916i | \(0.622450\pi\) | |||||||
\(620\) | 7.90213 | 0.317357 | ||||||||
\(621\) | −8.19215 | −0.328740 | ||||||||
\(622\) | −4.13303 | −0.165719 | ||||||||
\(623\) | 33.7258 | 1.35120 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −31.0917 | −1.24367 | ||||||||
\(626\) | −22.5791 | −0.902441 | ||||||||
\(627\) | 14.8827 | 0.594359 | ||||||||
\(628\) | 12.7383 | 0.508314 | ||||||||
\(629\) | 38.2593 | 1.52550 | ||||||||
\(630\) | −6.31222 | −0.251485 | ||||||||
\(631\) | −25.6853 | −1.02252 | −0.511258 | − | 0.859427i | \(-0.670820\pi\) | ||||
−0.511258 | + | 0.859427i | \(0.670820\pi\) | |||||||
\(632\) | 16.6133 | 0.660841 | ||||||||
\(633\) | 3.76040 | 0.149463 | ||||||||
\(634\) | −25.2757 | −1.00383 | ||||||||
\(635\) | −38.5193 | −1.52859 | ||||||||
\(636\) | 9.57222 | 0.379563 | ||||||||
\(637\) | 1.38978 | 0.0550652 | ||||||||
\(638\) | 26.5949 | 1.05290 | ||||||||
\(639\) | −9.42543 | −0.372864 | ||||||||
\(640\) | −2.66497 | −0.105342 | ||||||||
\(641\) | −38.5952 | −1.52442 | −0.762210 | − | 0.647330i | \(-0.775886\pi\) | ||||
−0.762210 | + | 0.647330i | \(0.775886\pi\) | |||||||
\(642\) | −8.82181 | −0.348169 | ||||||||
\(643\) | 9.19011 | 0.362422 | 0.181211 | − | 0.983444i | \(-0.441998\pi\) | ||||
0.181211 | + | 0.983444i | \(0.441998\pi\) | |||||||
\(644\) | 19.4038 | 0.764618 | ||||||||
\(645\) | −13.4177 | −0.528323 | ||||||||
\(646\) | −25.3815 | −0.998623 | ||||||||
\(647\) | 39.2802 | 1.54426 | 0.772131 | − | 0.635463i | \(-0.219191\pi\) | ||||
0.772131 | + | 0.635463i | \(0.219191\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 12.3654 | 0.485386 | ||||||||
\(650\) | 2.10207 | 0.0824500 | ||||||||
\(651\) | −7.02330 | −0.275265 | ||||||||
\(652\) | 20.0360 | 0.784671 | ||||||||
\(653\) | 15.5078 | 0.606868 | 0.303434 | − | 0.952853i | \(-0.401867\pi\) | ||||
0.303434 | + | 0.952853i | \(0.401867\pi\) | |||||||
\(654\) | −4.89164 | −0.191278 | ||||||||
\(655\) | 29.8391 | 1.16591 | ||||||||
\(656\) | −5.29737 | −0.206828 | ||||||||
\(657\) | 1.53198 | 0.0597684 | ||||||||
\(658\) | 15.8323 | 0.617206 | ||||||||
\(659\) | 0.674271 | 0.0262659 | 0.0131329 | − | 0.999914i | \(-0.495820\pi\) | ||||
0.0131329 | + | 0.999914i | \(0.495820\pi\) | |||||||
\(660\) | −7.96949 | −0.310212 | ||||||||
\(661\) | −11.5269 | −0.448346 | −0.224173 | − | 0.974549i | \(-0.571968\pi\) | ||||
−0.224173 | + | 0.974549i | \(0.571968\pi\) | |||||||
\(662\) | −15.2198 | −0.591536 | ||||||||
\(663\) | −5.10004 | −0.198069 | ||||||||
\(664\) | 10.6717 | 0.414143 | ||||||||
\(665\) | −31.4143 | −1.21819 | ||||||||
\(666\) | 7.50176 | 0.290687 | ||||||||
\(667\) | −72.8548 | −2.82095 | ||||||||
\(668\) | −12.2588 | −0.474305 | ||||||||
\(669\) | 20.0488 | 0.775133 | ||||||||
\(670\) | 8.39293 | 0.324247 | ||||||||
\(671\) | −2.71499 | −0.104811 | ||||||||
\(672\) | 2.36859 | 0.0913703 | ||||||||
\(673\) | −32.8853 | −1.26763 | −0.633817 | − | 0.773483i | \(-0.718513\pi\) | ||||
−0.633817 | + | 0.773483i | \(0.718513\pi\) | |||||||
\(674\) | −10.7086 | −0.412481 | ||||||||
\(675\) | −2.10207 | −0.0809088 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −35.9038 | −1.37989 | −0.689947 | − | 0.723860i | \(-0.742366\pi\) | ||||
−0.689947 | + | 0.723860i | \(0.742366\pi\) | |||||||
\(678\) | 0.199059 | 0.00764483 | ||||||||
\(679\) | −13.3563 | −0.512567 | ||||||||
\(680\) | 13.5915 | 0.521209 | ||||||||
\(681\) | −15.7644 | −0.604092 | ||||||||
\(682\) | −8.86726 | −0.339545 | ||||||||
\(683\) | 48.6651 | 1.86212 | 0.931058 | − | 0.364870i | \(-0.118887\pi\) | ||||
0.931058 | + | 0.364870i | \(0.118887\pi\) | |||||||
\(684\) | −4.97673 | −0.190290 | ||||||||
\(685\) | −3.70292 | −0.141481 | ||||||||
\(686\) | 19.8720 | 0.758715 | ||||||||
\(687\) | −23.7161 | −0.904825 | ||||||||
\(688\) | 5.03485 | 0.191952 | ||||||||
\(689\) | 9.57222 | 0.364672 | ||||||||
\(690\) | 21.8318 | 0.831124 | ||||||||
\(691\) | −47.6923 | −1.81430 | −0.907151 | − | 0.420805i | \(-0.861748\pi\) | ||||
−0.907151 | + | 0.420805i | \(0.861748\pi\) | |||||||
\(692\) | −10.4013 | −0.395398 | ||||||||
\(693\) | 7.08317 | 0.269067 | ||||||||
\(694\) | 9.32187 | 0.353853 | ||||||||
\(695\) | −39.2898 | −1.49035 | ||||||||
\(696\) | −8.89325 | −0.337098 | ||||||||
\(697\) | 27.0168 | 1.02333 | ||||||||
\(698\) | 7.12865 | 0.269823 | ||||||||
\(699\) | −23.6830 | −0.895774 | ||||||||
\(700\) | 4.97894 | 0.188186 | ||||||||
\(701\) | −25.7819 | −0.973770 | −0.486885 | − | 0.873466i | \(-0.661867\pi\) | ||||
−0.486885 | + | 0.873466i | \(0.661867\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 37.3343 | 1.40809 | ||||||||
\(704\) | 2.99046 | 0.112707 | ||||||||
\(705\) | 17.8134 | 0.670890 | ||||||||
\(706\) | 1.14759 | 0.0431902 | ||||||||
\(707\) | −19.2203 | −0.722855 | ||||||||
\(708\) | −4.13496 | −0.155401 | ||||||||
\(709\) | −18.4148 | −0.691582 | −0.345791 | − | 0.938311i | \(-0.612389\pi\) | ||||
−0.345791 | + | 0.938311i | \(0.612389\pi\) | |||||||
\(710\) | 25.1185 | 0.942680 | ||||||||
\(711\) | −16.6133 | −0.623047 | ||||||||
\(712\) | −14.2388 | −0.533621 | ||||||||
\(713\) | 24.2912 | 0.909714 | ||||||||
\(714\) | −12.0799 | −0.452079 | ||||||||
\(715\) | −7.96949 | −0.298042 | ||||||||
\(716\) | 25.8043 | 0.964352 | ||||||||
\(717\) | 12.8452 | 0.479711 | ||||||||
\(718\) | −36.2087 | −1.35130 | ||||||||
\(719\) | −12.1404 | −0.452761 | −0.226380 | − | 0.974039i | \(-0.572689\pi\) | ||||
−0.226380 | + | 0.974039i | \(0.572689\pi\) | |||||||
\(720\) | 2.66497 | 0.0993176 | ||||||||
\(721\) | −2.36859 | −0.0882109 | ||||||||
\(722\) | −5.76789 | −0.214659 | ||||||||
\(723\) | 16.9050 | 0.628704 | ||||||||
\(724\) | −1.38863 | −0.0516082 | ||||||||
\(725\) | −18.6942 | −0.694286 | ||||||||
\(726\) | −2.05715 | −0.0763482 | ||||||||
\(727\) | 12.6521 | 0.469241 | 0.234620 | − | 0.972087i | \(-0.424615\pi\) | ||||
0.234620 | + | 0.972087i | \(0.424615\pi\) | |||||||
\(728\) | 2.36859 | 0.0877858 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.08269 | −0.151107 | ||||||||
\(731\) | −25.6780 | −0.949733 | ||||||||
\(732\) | 0.907884 | 0.0335563 | ||||||||
\(733\) | 37.5181 | 1.38576 | 0.692882 | − | 0.721051i | \(-0.256341\pi\) | ||||
0.692882 | + | 0.721051i | \(0.256341\pi\) | |||||||
\(734\) | 33.5446 | 1.23815 | ||||||||
\(735\) | 3.70373 | 0.136614 | ||||||||
\(736\) | −8.19215 | −0.301967 | ||||||||
\(737\) | −9.41801 | −0.346917 | ||||||||
\(738\) | 5.29737 | 0.194999 | ||||||||
\(739\) | 11.4565 | 0.421434 | 0.210717 | − | 0.977547i | \(-0.432420\pi\) | ||||
0.210717 | + | 0.977547i | \(0.432420\pi\) | |||||||
\(740\) | −19.9920 | −0.734920 | ||||||||
\(741\) | −4.97673 | −0.182825 | ||||||||
\(742\) | 22.6727 | 0.832339 | ||||||||
\(743\) | −36.5129 | −1.33953 | −0.669765 | − | 0.742574i | \(-0.733605\pi\) | ||||
−0.669765 | + | 0.742574i | \(0.733605\pi\) | |||||||
\(744\) | 2.96518 | 0.108709 | ||||||||
\(745\) | −24.7912 | −0.908278 | ||||||||
\(746\) | 15.4244 | 0.564729 | ||||||||
\(747\) | −10.6717 | −0.390458 | ||||||||
\(748\) | −15.2515 | −0.557649 | ||||||||
\(749\) | −20.8952 | −0.763496 | ||||||||
\(750\) | −7.72290 | −0.282000 | ||||||||
\(751\) | 13.9344 | 0.508474 | 0.254237 | − | 0.967142i | \(-0.418176\pi\) | ||||
0.254237 | + | 0.967142i | \(0.418176\pi\) | |||||||
\(752\) | −6.68426 | −0.243750 | ||||||||
\(753\) | −26.3714 | −0.961027 | ||||||||
\(754\) | −8.89325 | −0.323873 | ||||||||
\(755\) | −51.9980 | −1.89240 | ||||||||
\(756\) | −2.36859 | −0.0861448 | ||||||||
\(757\) | −2.38247 | −0.0865923 | −0.0432961 | − | 0.999062i | \(-0.513786\pi\) | ||||
−0.0432961 | + | 0.999062i | \(0.513786\pi\) | |||||||
\(758\) | 35.1670 | 1.27732 | ||||||||
\(759\) | −24.4983 | −0.889231 | ||||||||
\(760\) | 13.2629 | 0.481094 | ||||||||
\(761\) | 34.7359 | 1.25918 | 0.629588 | − | 0.776929i | \(-0.283224\pi\) | ||||
0.629588 | + | 0.776929i | \(0.283224\pi\) | |||||||
\(762\) | −14.4539 | −0.523611 | ||||||||
\(763\) | −11.5863 | −0.419452 | ||||||||
\(764\) | 20.9559 | 0.758159 | ||||||||
\(765\) | −13.5915 | −0.491400 | ||||||||
\(766\) | −19.8437 | −0.716982 | ||||||||
\(767\) | −4.13496 | −0.149305 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −37.7064 | −1.35973 | −0.679863 | − | 0.733339i | \(-0.737961\pi\) | ||||
−0.679863 | + | 0.733339i | \(0.737961\pi\) | |||||||
\(770\) | −18.8764 | −0.680260 | ||||||||
\(771\) | 12.2911 | 0.442655 | ||||||||
\(772\) | 14.1557 | 0.509474 | ||||||||
\(773\) | 20.7852 | 0.747590 | 0.373795 | − | 0.927511i | \(-0.378056\pi\) | ||||
0.373795 | + | 0.927511i | \(0.378056\pi\) | |||||||
\(774\) | −5.03485 | −0.180974 | ||||||||
\(775\) | 6.23303 | 0.223897 | ||||||||
\(776\) | 5.63892 | 0.202425 | ||||||||
\(777\) | 17.7686 | 0.637445 | ||||||||
\(778\) | 6.15603 | 0.220704 | ||||||||
\(779\) | 26.3636 | 0.944574 | ||||||||
\(780\) | 2.66497 | 0.0954213 | ||||||||
\(781\) | −28.1864 | −1.00859 | ||||||||
\(782\) | 41.7803 | 1.49406 | ||||||||
\(783\) | 8.89325 | 0.317819 | ||||||||
\(784\) | −1.38978 | −0.0496351 | ||||||||
\(785\) | 33.9472 | 1.21163 | ||||||||
\(786\) | 11.1968 | 0.399377 | ||||||||
\(787\) | −11.9047 | −0.424356 | −0.212178 | − | 0.977231i | \(-0.568056\pi\) | ||||
−0.212178 | + | 0.977231i | \(0.568056\pi\) | |||||||
\(788\) | 3.89385 | 0.138713 | ||||||||
\(789\) | 3.65412 | 0.130090 | ||||||||
\(790\) | 44.2739 | 1.57520 | ||||||||
\(791\) | 0.471490 | 0.0167642 | ||||||||
\(792\) | −2.99046 | −0.106261 | ||||||||
\(793\) | 0.907884 | 0.0322399 | ||||||||
\(794\) | 10.2420 | 0.363474 | ||||||||
\(795\) | 25.5097 | 0.904735 | ||||||||
\(796\) | −0.00132986 | −4.71355e−5 0 | ||||||||
\(797\) | −13.5767 | −0.480913 | −0.240456 | − | 0.970660i | \(-0.577297\pi\) | ||||
−0.240456 | + | 0.970660i | \(0.577297\pi\) | |||||||
\(798\) | −11.7878 | −0.417285 | ||||||||
\(799\) | 34.0900 | 1.20602 | ||||||||
\(800\) | −2.10207 | −0.0743194 | ||||||||
\(801\) | 14.2388 | 0.503103 | ||||||||
\(802\) | −2.63594 | −0.0930784 | ||||||||
\(803\) | 4.58134 | 0.161672 | ||||||||
\(804\) | 3.14935 | 0.111069 | ||||||||
\(805\) | 51.7107 | 1.82256 | ||||||||
\(806\) | 2.96518 | 0.104444 | ||||||||
\(807\) | −8.85845 | −0.311832 | ||||||||
\(808\) | 8.11468 | 0.285473 | ||||||||
\(809\) | 25.5432 | 0.898052 | 0.449026 | − | 0.893519i | \(-0.351771\pi\) | ||||
0.449026 | + | 0.893519i | \(0.351771\pi\) | |||||||
\(810\) | −2.66497 | −0.0936375 | ||||||||
\(811\) | 7.57835 | 0.266112 | 0.133056 | − | 0.991109i | \(-0.457521\pi\) | ||||
0.133056 | + | 0.991109i | \(0.457521\pi\) | |||||||
\(812\) | −21.0644 | −0.739217 | ||||||||
\(813\) | 17.8907 | 0.627456 | ||||||||
\(814\) | 22.4337 | 0.786301 | ||||||||
\(815\) | 53.3954 | 1.87036 | ||||||||
\(816\) | 5.10004 | 0.178537 | ||||||||
\(817\) | −25.0571 | −0.876638 | ||||||||
\(818\) | −30.9063 | −1.08061 | ||||||||
\(819\) | −2.36859 | −0.0827652 | ||||||||
\(820\) | −14.1173 | −0.492999 | ||||||||
\(821\) | −52.6488 | −1.83745 | −0.918727 | − | 0.394893i | \(-0.870782\pi\) | ||||
−0.918727 | + | 0.394893i | \(0.870782\pi\) | |||||||
\(822\) | −1.38948 | −0.0484636 | ||||||||
\(823\) | 30.3736 | 1.05876 | 0.529378 | − | 0.848386i | \(-0.322425\pi\) | ||||
0.529378 | + | 0.848386i | \(0.322425\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −6.28616 | −0.218856 | ||||||||
\(826\) | −9.79403 | −0.340778 | ||||||||
\(827\) | 19.3903 | 0.674267 | 0.337134 | − | 0.941457i | \(-0.390543\pi\) | ||||
0.337134 | + | 0.941457i | \(0.390543\pi\) | |||||||
\(828\) | 8.19215 | 0.284697 | ||||||||
\(829\) | 16.0871 | 0.558729 | 0.279365 | − | 0.960185i | \(-0.409876\pi\) | ||||
0.279365 | + | 0.960185i | \(0.409876\pi\) | |||||||
\(830\) | 28.4398 | 0.987162 | ||||||||
\(831\) | 19.2663 | 0.668339 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 7.08795 | 0.245583 | ||||||||
\(834\) | −14.7431 | −0.510511 | ||||||||
\(835\) | −32.6692 | −1.13057 | ||||||||
\(836\) | −14.8827 | −0.514730 | ||||||||
\(837\) | −2.96518 | −0.102492 | ||||||||
\(838\) | 32.7095 | 1.12993 | ||||||||
\(839\) | 11.8089 | 0.407689 | 0.203845 | − | 0.979003i | \(-0.434656\pi\) | ||||
0.203845 | + | 0.979003i | \(0.434656\pi\) | |||||||
\(840\) | 6.31222 | 0.217792 | ||||||||
\(841\) | 50.0898 | 1.72723 | ||||||||
\(842\) | −31.0744 | −1.07090 | ||||||||
\(843\) | −26.0446 | −0.897024 | ||||||||
\(844\) | −3.76040 | −0.129438 | ||||||||
\(845\) | 2.66497 | 0.0916778 | ||||||||
\(846\) | 6.68426 | 0.229810 | ||||||||
\(847\) | −4.87255 | −0.167423 | ||||||||
\(848\) | −9.57222 | −0.328711 | ||||||||
\(849\) | −14.4965 | −0.497519 | ||||||||
\(850\) | 10.7206 | 0.367715 | ||||||||
\(851\) | −61.4556 | −2.10667 | ||||||||
\(852\) | 9.42543 | 0.322910 | ||||||||
\(853\) | −52.8427 | −1.80930 | −0.904649 | − | 0.426157i | \(-0.859867\pi\) | ||||
−0.904649 | + | 0.426157i | \(0.859867\pi\) | |||||||
\(854\) | 2.15040 | 0.0735853 | ||||||||
\(855\) | −13.2629 | −0.453580 | ||||||||
\(856\) | 8.82181 | 0.301523 | ||||||||
\(857\) | 3.42181 | 0.116887 | 0.0584435 | − | 0.998291i | \(-0.481386\pi\) | ||||
0.0584435 | + | 0.998291i | \(0.481386\pi\) | |||||||
\(858\) | −2.99046 | −0.102093 | ||||||||
\(859\) | 24.6277 | 0.840286 | 0.420143 | − | 0.907458i | \(-0.361980\pi\) | ||||
0.420143 | + | 0.907458i | \(0.361980\pi\) | |||||||
\(860\) | 13.4177 | 0.457541 | ||||||||
\(861\) | 12.5473 | 0.427611 | ||||||||
\(862\) | −33.4471 | −1.13921 | ||||||||
\(863\) | −29.4581 | −1.00277 | −0.501383 | − | 0.865225i | \(-0.667175\pi\) | ||||
−0.501383 | + | 0.865225i | \(0.667175\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −27.7191 | −0.942479 | ||||||||
\(866\) | −19.6562 | −0.667946 | ||||||||
\(867\) | −9.01040 | −0.306009 | ||||||||
\(868\) | 7.02330 | 0.238386 | ||||||||
\(869\) | −49.6814 | −1.68533 | ||||||||
\(870\) | −23.7002 | −0.803513 | ||||||||
\(871\) | 3.14935 | 0.106712 | ||||||||
\(872\) | 4.89164 | 0.165652 | ||||||||
\(873\) | −5.63892 | −0.190849 | ||||||||
\(874\) | 40.7701 | 1.37907 | ||||||||
\(875\) | −18.2924 | −0.618395 | ||||||||
\(876\) | −1.53198 | −0.0517609 | ||||||||
\(877\) | −28.3168 | −0.956191 | −0.478096 | − | 0.878308i | \(-0.658673\pi\) | ||||
−0.478096 | + | 0.878308i | \(0.658673\pi\) | |||||||
\(878\) | 17.4337 | 0.588358 | ||||||||
\(879\) | −29.9123 | −1.00892 | ||||||||
\(880\) | 7.96949 | 0.268651 | ||||||||
\(881\) | −31.1817 | −1.05054 | −0.525269 | − | 0.850936i | \(-0.676035\pi\) | ||||
−0.525269 | + | 0.850936i | \(0.676035\pi\) | |||||||
\(882\) | 1.38978 | 0.0467965 | ||||||||
\(883\) | 8.37798 | 0.281941 | 0.140971 | − | 0.990014i | \(-0.454978\pi\) | ||||
0.140971 | + | 0.990014i | \(0.454978\pi\) | |||||||
\(884\) | 5.10004 | 0.171533 | ||||||||
\(885\) | −11.0196 | −0.370418 | ||||||||
\(886\) | 33.1504 | 1.11371 | ||||||||
\(887\) | 15.5261 | 0.521315 | 0.260657 | − | 0.965431i | \(-0.416061\pi\) | ||||
0.260657 | + | 0.965431i | \(0.416061\pi\) | |||||||
\(888\) | −7.50176 | −0.251743 | ||||||||
\(889\) | −34.2355 | −1.14822 | ||||||||
\(890\) | −37.9459 | −1.27195 | ||||||||
\(891\) | 2.99046 | 0.100184 | ||||||||
\(892\) | −20.0488 | −0.671285 | ||||||||
\(893\) | 33.2658 | 1.11320 | ||||||||
\(894\) | −9.30260 | −0.311126 | ||||||||
\(895\) | 68.7677 | 2.29865 | ||||||||
\(896\) | −2.36859 | −0.0791290 | ||||||||
\(897\) | 8.19215 | 0.273528 | ||||||||
\(898\) | 17.4809 | 0.583345 | ||||||||
\(899\) | −26.3701 | −0.879492 | ||||||||
\(900\) | 2.10207 | 0.0700690 | ||||||||
\(901\) | 48.8187 | 1.62639 | ||||||||
\(902\) | 15.8416 | 0.527467 | ||||||||
\(903\) | −11.9255 | −0.396856 | ||||||||
\(904\) | −0.199059 | −0.00662062 | ||||||||
\(905\) | −3.70067 | −0.123014 | ||||||||
\(906\) | −19.5117 | −0.648232 | ||||||||
\(907\) | 16.8837 | 0.560614 | 0.280307 | − | 0.959910i | \(-0.409564\pi\) | ||||
0.280307 | + | 0.959910i | \(0.409564\pi\) | |||||||
\(908\) | 15.7644 | 0.523159 | ||||||||
\(909\) | −8.11468 | −0.269147 | ||||||||
\(910\) | 6.31222 | 0.209248 | ||||||||
\(911\) | −20.4608 | −0.677897 | −0.338948 | − | 0.940805i | \(-0.610071\pi\) | ||||
−0.338948 | + | 0.940805i | \(0.610071\pi\) | |||||||
\(912\) | 4.97673 | 0.164796 | ||||||||
\(913\) | −31.9134 | −1.05618 | ||||||||
\(914\) | −5.47979 | −0.181255 | ||||||||
\(915\) | 2.41948 | 0.0799857 | ||||||||
\(916\) | 23.7161 | 0.783602 | ||||||||
\(917\) | 26.5206 | 0.875788 | ||||||||
\(918\) | −5.10004 | −0.168326 | ||||||||
\(919\) | −37.9458 | −1.25172 | −0.625859 | − | 0.779936i | \(-0.715251\pi\) | ||||
−0.625859 | + | 0.779936i | \(0.715251\pi\) | |||||||
\(920\) | −21.8318 | −0.719774 | ||||||||
\(921\) | −31.7716 | −1.04691 | ||||||||
\(922\) | −14.4209 | −0.474928 | ||||||||
\(923\) | 9.42543 | 0.310242 | ||||||||
\(924\) | −7.08317 | −0.233019 | ||||||||
\(925\) | −15.7692 | −0.518489 | ||||||||
\(926\) | 14.3003 | 0.469938 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 8.89325 | 0.291935 | ||||||||
\(929\) | 35.4190 | 1.16206 | 0.581029 | − | 0.813883i | \(-0.302650\pi\) | ||||
0.581029 | + | 0.813883i | \(0.302650\pi\) | |||||||
\(930\) | 7.90213 | 0.259121 | ||||||||
\(931\) | 6.91659 | 0.226682 | ||||||||
\(932\) | 23.6830 | 0.775763 | ||||||||
\(933\) | −4.13303 | −0.135309 | ||||||||
\(934\) | 20.5623 | 0.672819 | ||||||||
\(935\) | −40.6447 | −1.32922 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 1.85281 | 0.0605286 | 0.0302643 | − | 0.999542i | \(-0.490365\pi\) | ||||
0.0302643 | + | 0.999542i | \(0.490365\pi\) | |||||||
\(938\) | 7.45952 | 0.243562 | ||||||||
\(939\) | −22.5791 | −0.736840 | ||||||||
\(940\) | −17.8134 | −0.581008 | ||||||||
\(941\) | −22.7289 | −0.740943 | −0.370471 | − | 0.928844i | \(-0.620804\pi\) | ||||
−0.370471 | + | 0.928844i | \(0.620804\pi\) | |||||||
\(942\) | 12.7383 | 0.415036 | ||||||||
\(943\) | −43.3969 | −1.41320 | ||||||||
\(944\) | 4.13496 | 0.134582 | ||||||||
\(945\) | −6.31222 | −0.205337 | ||||||||
\(946\) | −15.0565 | −0.489530 | ||||||||
\(947\) | −33.6662 | −1.09401 | −0.547003 | − | 0.837131i | \(-0.684231\pi\) | ||||
−0.547003 | + | 0.837131i | \(0.684231\pi\) | |||||||
\(948\) | 16.6133 | 0.539575 | ||||||||
\(949\) | −1.53198 | −0.0497303 | ||||||||
\(950\) | 10.4614 | 0.339414 | ||||||||
\(951\) | −25.2757 | −0.819621 | ||||||||
\(952\) | 12.0799 | 0.391512 | ||||||||
\(953\) | −8.12488 | −0.263191 | −0.131595 | − | 0.991304i | \(-0.542010\pi\) | ||||
−0.131595 | + | 0.991304i | \(0.542010\pi\) | |||||||
\(954\) | 9.57222 | 0.309912 | ||||||||
\(955\) | 55.8469 | 1.80716 | ||||||||
\(956\) | −12.8452 | −0.415442 | ||||||||
\(957\) | 26.5949 | 0.859691 | ||||||||
\(958\) | 38.1472 | 1.23248 | ||||||||
\(959\) | −3.29110 | −0.106275 | ||||||||
\(960\) | −2.66497 | −0.0860116 | ||||||||
\(961\) | −22.2077 | −0.716377 | ||||||||
\(962\) | −7.50176 | −0.241867 | ||||||||
\(963\) | −8.82181 | −0.284279 | ||||||||
\(964\) | −16.9050 | −0.544473 | ||||||||
\(965\) | 37.7245 | 1.21439 | ||||||||
\(966\) | 19.4038 | 0.624308 | ||||||||
\(967\) | −59.1015 | −1.90058 | −0.950288 | − | 0.311371i | \(-0.899212\pi\) | ||||
−0.950288 | + | 0.311371i | \(0.899212\pi\) | |||||||
\(968\) | 2.05715 | 0.0661195 | ||||||||
\(969\) | −25.3815 | −0.815373 | ||||||||
\(970\) | 15.0276 | 0.482506 | ||||||||
\(971\) | 49.7150 | 1.59543 | 0.797715 | − | 0.603034i | \(-0.206042\pi\) | ||||
0.797715 | + | 0.603034i | \(0.206042\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −34.9203 | −1.11949 | ||||||||
\(974\) | −2.46128 | −0.0788646 | ||||||||
\(975\) | 2.10207 | 0.0673202 | ||||||||
\(976\) | −0.907884 | −0.0290607 | ||||||||
\(977\) | −57.6564 | −1.84459 | −0.922296 | − | 0.386483i | \(-0.873690\pi\) | ||||
−0.922296 | + | 0.386483i | \(0.873690\pi\) | |||||||
\(978\) | 20.0360 | 0.640681 | ||||||||
\(979\) | 42.5805 | 1.36088 | ||||||||
\(980\) | −3.70373 | −0.118311 | ||||||||
\(981\) | −4.89164 | −0.156178 | ||||||||
\(982\) | −1.04891 | −0.0334721 | ||||||||
\(983\) | −21.3741 | −0.681728 | −0.340864 | − | 0.940113i | \(-0.610720\pi\) | ||||
−0.340864 | + | 0.940113i | \(0.610720\pi\) | |||||||
\(984\) | −5.29737 | −0.168874 | ||||||||
\(985\) | 10.3770 | 0.330639 | ||||||||
\(986\) | −45.3559 | −1.44443 | ||||||||
\(987\) | 15.8323 | 0.503947 | ||||||||
\(988\) | 4.97673 | 0.158331 | ||||||||
\(989\) | 41.2463 | 1.31156 | ||||||||
\(990\) | −7.96949 | −0.253287 | ||||||||
\(991\) | −47.2476 | −1.50087 | −0.750435 | − | 0.660945i | \(-0.770156\pi\) | ||||
−0.750435 | + | 0.660945i | \(0.770156\pi\) | |||||||
\(992\) | −2.96518 | −0.0941447 | ||||||||
\(993\) | −15.2198 | −0.482987 | ||||||||
\(994\) | 22.3250 | 0.708105 | ||||||||
\(995\) | −0.00354403 | −0.000112353 0 | ||||||||
\(996\) | 10.6717 | 0.338147 | ||||||||
\(997\) | 12.5339 | 0.396953 | 0.198477 | − | 0.980106i | \(-0.436401\pi\) | ||||
0.198477 | + | 0.980106i | \(0.436401\pi\) | |||||||
\(998\) | 12.0797 | 0.382376 | ||||||||
\(999\) | 7.50176 | 0.237345 |
(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 | 8034.2.a.s.1.8 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.s.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial |