Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [285,2,Mod(1,285)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(285, 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("285.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.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: | \(2.27573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 285.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64575 | −1.87083 | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||||
−0.935414 | + | 0.353553i | \(0.884973\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.00000 | 2.50000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.64575 | 1.08012 | ||||||||
\(7\) | 1.64575 | 0.622036 | 0.311018 | − | 0.950404i | \(-0.399330\pi\) | ||||
0.311018 | + | 0.950404i | \(0.399330\pi\) | |||||||
\(8\) | −7.93725 | −2.80624 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.64575 | −0.836660 | ||||||||
\(11\) | 0.354249 | 0.106810 | 0.0534050 | − | 0.998573i | \(-0.482993\pi\) | ||||
0.0534050 | + | 0.998573i | \(0.482993\pi\) | |||||||
\(12\) | −5.00000 | −1.44338 | ||||||||
\(13\) | −0.354249 | −0.0982509 | −0.0491255 | − | 0.998793i | \(-0.515643\pi\) | ||||
−0.0491255 | + | 0.998793i | \(0.515643\pi\) | |||||||
\(14\) | −4.35425 | −1.16372 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 11.0000 | 2.75000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | −2.64575 | −0.623610 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 5.00000 | 1.11803 | ||||||||
\(21\) | −1.64575 | −0.359132 | ||||||||
\(22\) | −0.937254 | −0.199823 | ||||||||
\(23\) | 9.29150 | 1.93741 | 0.968706 | − | 0.248211i | \(-0.0798425\pi\) | ||||
0.968706 | + | 0.248211i | \(0.0798425\pi\) | |||||||
\(24\) | 7.93725 | 1.62019 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.937254 | 0.183811 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 8.22876 | 1.55509 | ||||||||
\(29\) | 8.93725 | 1.65961 | 0.829803 | − | 0.558056i | \(-0.188453\pi\) | ||||
0.829803 | + | 0.558056i | \(0.188453\pi\) | |||||||
\(30\) | 2.64575 | 0.483046 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −13.2288 | −2.33854 | ||||||||
\(33\) | −0.354249 | −0.0616668 | ||||||||
\(34\) | 10.5830 | 1.81497 | ||||||||
\(35\) | 1.64575 | 0.278183 | ||||||||
\(36\) | 5.00000 | 0.833333 | ||||||||
\(37\) | 3.64575 | 0.599358 | 0.299679 | − | 0.954040i | \(-0.403120\pi\) | ||||
0.299679 | + | 0.954040i | \(0.403120\pi\) | |||||||
\(38\) | 2.64575 | 0.429198 | ||||||||
\(39\) | 0.354249 | 0.0567252 | ||||||||
\(40\) | −7.93725 | −1.25499 | ||||||||
\(41\) | −9.64575 | −1.50641 | −0.753207 | − | 0.657784i | \(-0.771494\pi\) | ||||
−0.753207 | + | 0.657784i | \(0.771494\pi\) | |||||||
\(42\) | 4.35425 | 0.671875 | ||||||||
\(43\) | 5.64575 | 0.860969 | 0.430485 | − | 0.902598i | \(-0.358343\pi\) | ||||
0.430485 | + | 0.902598i | \(0.358343\pi\) | |||||||
\(44\) | 1.77124 | 0.267025 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −24.5830 | −3.62457 | ||||||||
\(47\) | −1.29150 | −0.188385 | −0.0941925 | − | 0.995554i | \(-0.530027\pi\) | ||||
−0.0941925 | + | 0.995554i | \(0.530027\pi\) | |||||||
\(48\) | −11.0000 | −1.58771 | ||||||||
\(49\) | −4.29150 | −0.613072 | ||||||||
\(50\) | −2.64575 | −0.374166 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | −1.77124 | −0.245627 | ||||||||
\(53\) | 11.2915 | 1.55101 | 0.775504 | − | 0.631343i | \(-0.217496\pi\) | ||||
0.775504 | + | 0.631343i | \(0.217496\pi\) | |||||||
\(54\) | 2.64575 | 0.360041 | ||||||||
\(55\) | 0.354249 | 0.0477669 | ||||||||
\(56\) | −13.0627 | −1.74558 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −23.6458 | −3.10484 | ||||||||
\(59\) | 11.2915 | 1.47003 | 0.735014 | − | 0.678052i | \(-0.237175\pi\) | ||||
0.735014 | + | 0.678052i | \(0.237175\pi\) | |||||||
\(60\) | −5.00000 | −0.645497 | ||||||||
\(61\) | −11.2915 | −1.44573 | −0.722864 | − | 0.690990i | \(-0.757175\pi\) | ||||
−0.722864 | + | 0.690990i | \(0.757175\pi\) | |||||||
\(62\) | −15.8745 | −2.01606 | ||||||||
\(63\) | 1.64575 | 0.207345 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | −0.354249 | −0.0439391 | ||||||||
\(66\) | 0.937254 | 0.115368 | ||||||||
\(67\) | −6.58301 | −0.804242 | −0.402121 | − | 0.915587i | \(-0.631727\pi\) | ||||
−0.402121 | + | 0.915587i | \(0.631727\pi\) | |||||||
\(68\) | −20.0000 | −2.42536 | ||||||||
\(69\) | −9.29150 | −1.11857 | ||||||||
\(70\) | −4.35425 | −0.520432 | ||||||||
\(71\) | 7.29150 | 0.865342 | 0.432671 | − | 0.901552i | \(-0.357571\pi\) | ||||
0.432671 | + | 0.901552i | \(0.357571\pi\) | |||||||
\(72\) | −7.93725 | −0.935414 | ||||||||
\(73\) | 10.0000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | −9.64575 | −1.12130 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −5.00000 | −0.573539 | ||||||||
\(77\) | 0.583005 | 0.0664396 | ||||||||
\(78\) | −0.937254 | −0.106123 | ||||||||
\(79\) | 6.58301 | 0.740646 | 0.370323 | − | 0.928903i | \(-0.379247\pi\) | ||||
0.370323 | + | 0.928903i | \(0.379247\pi\) | |||||||
\(80\) | 11.0000 | 1.22984 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 25.5203 | 2.81824 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −8.22876 | −0.897831 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | −14.9373 | −1.61073 | ||||||||
\(87\) | −8.93725 | −0.958174 | ||||||||
\(88\) | −2.81176 | −0.299735 | ||||||||
\(89\) | −16.9373 | −1.79535 | −0.897673 | − | 0.440663i | \(-0.854743\pi\) | ||||
−0.897673 | + | 0.440663i | \(0.854743\pi\) | |||||||
\(90\) | −2.64575 | −0.278887 | ||||||||
\(91\) | −0.583005 | −0.0611156 | ||||||||
\(92\) | 46.4575 | 4.84353 | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 3.41699 | 0.352436 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 13.2288 | 1.35015 | ||||||||
\(97\) | −2.93725 | −0.298233 | −0.149116 | − | 0.988820i | \(-0.547643\pi\) | ||||
−0.149116 | + | 0.988820i | \(0.547643\pi\) | |||||||
\(98\) | 11.3542 | 1.14695 | ||||||||
\(99\) | 0.354249 | 0.0356033 | ||||||||
\(100\) | 5.00000 | 0.500000 | ||||||||
\(101\) | 9.29150 | 0.924539 | 0.462270 | − | 0.886739i | \(-0.347035\pi\) | ||||
0.462270 | + | 0.886739i | \(0.347035\pi\) | |||||||
\(102\) | −10.5830 | −1.04787 | ||||||||
\(103\) | −10.5830 | −1.04277 | −0.521387 | − | 0.853320i | \(-0.674585\pi\) | ||||
−0.521387 | + | 0.853320i | \(0.674585\pi\) | |||||||
\(104\) | 2.81176 | 0.275716 | ||||||||
\(105\) | −1.64575 | −0.160609 | ||||||||
\(106\) | −29.8745 | −2.90167 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −5.00000 | −0.481125 | ||||||||
\(109\) | 5.29150 | 0.506834 | 0.253417 | − | 0.967357i | \(-0.418446\pi\) | ||||
0.253417 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(110\) | −0.937254 | −0.0893637 | ||||||||
\(111\) | −3.64575 | −0.346039 | ||||||||
\(112\) | 18.1033 | 1.71060 | ||||||||
\(113\) | −4.00000 | −0.376288 | −0.188144 | − | 0.982141i | \(-0.560247\pi\) | ||||
−0.188144 | + | 0.982141i | \(0.560247\pi\) | |||||||
\(114\) | −2.64575 | −0.247797 | ||||||||
\(115\) | 9.29150 | 0.866437 | ||||||||
\(116\) | 44.6863 | 4.14902 | ||||||||
\(117\) | −0.354249 | −0.0327503 | ||||||||
\(118\) | −29.8745 | −2.75017 | ||||||||
\(119\) | −6.58301 | −0.603463 | ||||||||
\(120\) | 7.93725 | 0.724569 | ||||||||
\(121\) | −10.8745 | −0.988592 | ||||||||
\(122\) | 29.8745 | 2.70471 | ||||||||
\(123\) | 9.64575 | 0.869728 | ||||||||
\(124\) | 30.0000 | 2.69408 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.35425 | −0.387907 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | −7.93725 | −0.701561 | ||||||||
\(129\) | −5.64575 | −0.497081 | ||||||||
\(130\) | 0.937254 | 0.0822026 | ||||||||
\(131\) | −14.2288 | −1.24317 | −0.621586 | − | 0.783346i | \(-0.713511\pi\) | ||||
−0.621586 | + | 0.783346i | \(0.713511\pi\) | |||||||
\(132\) | −1.77124 | −0.154167 | ||||||||
\(133\) | −1.64575 | −0.142705 | ||||||||
\(134\) | 17.4170 | 1.50460 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 31.7490 | 2.72246 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 24.5830 | 2.09264 | ||||||||
\(139\) | 17.8745 | 1.51610 | 0.758048 | − | 0.652199i | \(-0.226153\pi\) | ||||
0.758048 | + | 0.652199i | \(0.226153\pi\) | |||||||
\(140\) | 8.22876 | 0.695457 | ||||||||
\(141\) | 1.29150 | 0.108764 | ||||||||
\(142\) | −19.2915 | −1.61891 | ||||||||
\(143\) | −0.125492 | −0.0104942 | ||||||||
\(144\) | 11.0000 | 0.916667 | ||||||||
\(145\) | 8.93725 | 0.742199 | ||||||||
\(146\) | −26.4575 | −2.18964 | ||||||||
\(147\) | 4.29150 | 0.353957 | ||||||||
\(148\) | 18.2288 | 1.49839 | ||||||||
\(149\) | −20.5830 | −1.68623 | −0.843113 | − | 0.537737i | \(-0.819279\pi\) | ||||
−0.843113 | + | 0.537737i | \(0.819279\pi\) | |||||||
\(150\) | 2.64575 | 0.216025 | ||||||||
\(151\) | −8.58301 | −0.698475 | −0.349238 | − | 0.937034i | \(-0.613559\pi\) | ||||
−0.349238 | + | 0.937034i | \(0.613559\pi\) | |||||||
\(152\) | 7.93725 | 0.643796 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | −1.54249 | −0.124297 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 1.77124 | 0.141813 | ||||||||
\(157\) | −13.2915 | −1.06078 | −0.530389 | − | 0.847755i | \(-0.677954\pi\) | ||||
−0.530389 | + | 0.847755i | \(0.677954\pi\) | |||||||
\(158\) | −17.4170 | −1.38562 | ||||||||
\(159\) | −11.2915 | −0.895474 | ||||||||
\(160\) | −13.2288 | −1.04583 | ||||||||
\(161\) | 15.2915 | 1.20514 | ||||||||
\(162\) | −2.64575 | −0.207870 | ||||||||
\(163\) | −2.35425 | −0.184399 | −0.0921995 | − | 0.995741i | \(-0.529390\pi\) | ||||
−0.0921995 | + | 0.995741i | \(0.529390\pi\) | |||||||
\(164\) | −48.2288 | −3.76603 | ||||||||
\(165\) | −0.354249 | −0.0275782 | ||||||||
\(166\) | −15.8745 | −1.23210 | ||||||||
\(167\) | −21.2915 | −1.64759 | −0.823793 | − | 0.566891i | \(-0.808146\pi\) | ||||
−0.823793 | + | 0.566891i | \(0.808146\pi\) | |||||||
\(168\) | 13.0627 | 1.00781 | ||||||||
\(169\) | −12.8745 | −0.990347 | ||||||||
\(170\) | 10.5830 | 0.811679 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 28.2288 | 2.15242 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 23.6458 | 1.79258 | ||||||||
\(175\) | 1.64575 | 0.124407 | ||||||||
\(176\) | 3.89674 | 0.293727 | ||||||||
\(177\) | −11.2915 | −0.848721 | ||||||||
\(178\) | 44.8118 | 3.35878 | ||||||||
\(179\) | −7.29150 | −0.544992 | −0.272496 | − | 0.962157i | \(-0.587849\pi\) | ||||
−0.272496 | + | 0.962157i | \(0.587849\pi\) | |||||||
\(180\) | 5.00000 | 0.372678 | ||||||||
\(181\) | 17.2915 | 1.28527 | 0.642634 | − | 0.766174i | \(-0.277842\pi\) | ||||
0.642634 | + | 0.766174i | \(0.277842\pi\) | |||||||
\(182\) | 1.54249 | 0.114337 | ||||||||
\(183\) | 11.2915 | 0.834692 | ||||||||
\(184\) | −73.7490 | −5.43685 | ||||||||
\(185\) | 3.64575 | 0.268041 | ||||||||
\(186\) | 15.8745 | 1.16398 | ||||||||
\(187\) | −1.41699 | −0.103621 | ||||||||
\(188\) | −6.45751 | −0.470963 | ||||||||
\(189\) | −1.64575 | −0.119711 | ||||||||
\(190\) | 2.64575 | 0.191943 | ||||||||
\(191\) | 6.22876 | 0.450697 | 0.225349 | − | 0.974278i | \(-0.427648\pi\) | ||||
0.225349 | + | 0.974278i | \(0.427648\pi\) | |||||||
\(192\) | −13.0000 | −0.938194 | ||||||||
\(193\) | −11.6458 | −0.838280 | −0.419140 | − | 0.907922i | \(-0.637668\pi\) | ||||
−0.419140 | + | 0.907922i | \(0.637668\pi\) | |||||||
\(194\) | 7.77124 | 0.557943 | ||||||||
\(195\) | 0.354249 | 0.0253683 | ||||||||
\(196\) | −21.4575 | −1.53268 | ||||||||
\(197\) | −25.1660 | −1.79300 | −0.896502 | − | 0.443040i | \(-0.853900\pi\) | ||||
−0.896502 | + | 0.443040i | \(0.853900\pi\) | |||||||
\(198\) | −0.937254 | −0.0666077 | ||||||||
\(199\) | 7.29150 | 0.516881 | 0.258440 | − | 0.966027i | \(-0.416791\pi\) | ||||
0.258440 | + | 0.966027i | \(0.416791\pi\) | |||||||
\(200\) | −7.93725 | −0.561249 | ||||||||
\(201\) | 6.58301 | 0.464329 | ||||||||
\(202\) | −24.5830 | −1.72965 | ||||||||
\(203\) | 14.7085 | 1.03233 | ||||||||
\(204\) | 20.0000 | 1.40028 | ||||||||
\(205\) | −9.64575 | −0.673688 | ||||||||
\(206\) | 28.0000 | 1.95085 | ||||||||
\(207\) | 9.29150 | 0.645804 | ||||||||
\(208\) | −3.89674 | −0.270190 | ||||||||
\(209\) | −0.354249 | −0.0245039 | ||||||||
\(210\) | 4.35425 | 0.300472 | ||||||||
\(211\) | 2.58301 | 0.177821 | 0.0889107 | − | 0.996040i | \(-0.471661\pi\) | ||||
0.0889107 | + | 0.996040i | \(0.471661\pi\) | |||||||
\(212\) | 56.4575 | 3.87752 | ||||||||
\(213\) | −7.29150 | −0.499606 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.64575 | 0.385037 | ||||||||
\(216\) | 7.93725 | 0.540062 | ||||||||
\(217\) | 9.87451 | 0.670325 | ||||||||
\(218\) | −14.0000 | −0.948200 | ||||||||
\(219\) | −10.0000 | −0.675737 | ||||||||
\(220\) | 1.77124 | 0.119417 | ||||||||
\(221\) | 1.41699 | 0.0953174 | ||||||||
\(222\) | 9.64575 | 0.647380 | ||||||||
\(223\) | 2.58301 | 0.172971 | 0.0864854 | − | 0.996253i | \(-0.472436\pi\) | ||||
0.0864854 | + | 0.996253i | \(0.472436\pi\) | |||||||
\(224\) | −21.7712 | −1.45465 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 10.5830 | 0.703971 | ||||||||
\(227\) | −10.7085 | −0.710748 | −0.355374 | − | 0.934724i | \(-0.615646\pi\) | ||||
−0.355374 | + | 0.934724i | \(0.615646\pi\) | |||||||
\(228\) | 5.00000 | 0.331133 | ||||||||
\(229\) | 8.70850 | 0.575474 | 0.287737 | − | 0.957710i | \(-0.407097\pi\) | ||||
0.287737 | + | 0.957710i | \(0.407097\pi\) | |||||||
\(230\) | −24.5830 | −1.62096 | ||||||||
\(231\) | −0.583005 | −0.0383589 | ||||||||
\(232\) | −70.9373 | −4.65726 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0.937254 | 0.0612702 | ||||||||
\(235\) | −1.29150 | −0.0842483 | ||||||||
\(236\) | 56.4575 | 3.67507 | ||||||||
\(237\) | −6.58301 | −0.427612 | ||||||||
\(238\) | 17.4170 | 1.12898 | ||||||||
\(239\) | 15.6458 | 1.01204 | 0.506020 | − | 0.862522i | \(-0.331116\pi\) | ||||
0.506020 | + | 0.862522i | \(0.331116\pi\) | |||||||
\(240\) | −11.0000 | −0.710047 | ||||||||
\(241\) | 16.5830 | 1.06821 | 0.534103 | − | 0.845420i | \(-0.320650\pi\) | ||||
0.534103 | + | 0.845420i | \(0.320650\pi\) | |||||||
\(242\) | 28.7712 | 1.84949 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −56.4575 | −3.61432 | ||||||||
\(245\) | −4.29150 | −0.274174 | ||||||||
\(246\) | −25.5203 | −1.62711 | ||||||||
\(247\) | 0.354249 | 0.0225403 | ||||||||
\(248\) | −47.6235 | −3.02410 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | −2.64575 | −0.167332 | ||||||||
\(251\) | −16.3542 | −1.03227 | −0.516136 | − | 0.856507i | \(-0.672630\pi\) | ||||
−0.516136 | + | 0.856507i | \(0.672630\pi\) | |||||||
\(252\) | 8.22876 | 0.518363 | ||||||||
\(253\) | 3.29150 | 0.206935 | ||||||||
\(254\) | −10.5830 | −0.664037 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | −5.00000 | −0.312500 | ||||||||
\(257\) | −5.41699 | −0.337903 | −0.168951 | − | 0.985624i | \(-0.554038\pi\) | ||||
−0.168951 | + | 0.985624i | \(0.554038\pi\) | |||||||
\(258\) | 14.9373 | 0.929953 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | −1.77124 | −0.109848 | ||||||||
\(261\) | 8.93725 | 0.553202 | ||||||||
\(262\) | 37.6458 | 2.32576 | ||||||||
\(263\) | 4.58301 | 0.282600 | 0.141300 | − | 0.989967i | \(-0.454872\pi\) | ||||
0.141300 | + | 0.989967i | \(0.454872\pi\) | |||||||
\(264\) | 2.81176 | 0.173052 | ||||||||
\(265\) | 11.2915 | 0.693631 | ||||||||
\(266\) | 4.35425 | 0.266976 | ||||||||
\(267\) | 16.9373 | 1.03654 | ||||||||
\(268\) | −32.9150 | −2.01061 | ||||||||
\(269\) | 4.22876 | 0.257832 | 0.128916 | − | 0.991656i | \(-0.458850\pi\) | ||||
0.128916 | + | 0.991656i | \(0.458850\pi\) | |||||||
\(270\) | 2.64575 | 0.161015 | ||||||||
\(271\) | −4.70850 | −0.286021 | −0.143010 | − | 0.989721i | \(-0.545678\pi\) | ||||
−0.143010 | + | 0.989721i | \(0.545678\pi\) | |||||||
\(272\) | −44.0000 | −2.66789 | ||||||||
\(273\) | 0.583005 | 0.0352851 | ||||||||
\(274\) | −15.8745 | −0.959014 | ||||||||
\(275\) | 0.354249 | 0.0213620 | ||||||||
\(276\) | −46.4575 | −2.79641 | ||||||||
\(277\) | 0.583005 | 0.0350294 | 0.0175147 | − | 0.999847i | \(-0.494425\pi\) | ||||
0.0175147 | + | 0.999847i | \(0.494425\pi\) | |||||||
\(278\) | −47.2915 | −2.83636 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | −13.0627 | −0.780648 | ||||||||
\(281\) | −32.2288 | −1.92261 | −0.961303 | − | 0.275493i | \(-0.911159\pi\) | ||||
−0.961303 | + | 0.275493i | \(0.911159\pi\) | |||||||
\(282\) | −3.41699 | −0.203479 | ||||||||
\(283\) | −11.5203 | −0.684808 | −0.342404 | − | 0.939553i | \(-0.611241\pi\) | ||||
−0.342404 | + | 0.939553i | \(0.611241\pi\) | |||||||
\(284\) | 36.4575 | 2.16336 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0.332021 | 0.0196328 | ||||||||
\(287\) | −15.8745 | −0.937043 | ||||||||
\(288\) | −13.2288 | −0.779512 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −23.6458 | −1.38853 | ||||||||
\(291\) | 2.93725 | 0.172185 | ||||||||
\(292\) | 50.0000 | 2.92603 | ||||||||
\(293\) | 5.41699 | 0.316464 | 0.158232 | − | 0.987402i | \(-0.449421\pi\) | ||||
0.158232 | + | 0.987402i | \(0.449421\pi\) | |||||||
\(294\) | −11.3542 | −0.662193 | ||||||||
\(295\) | 11.2915 | 0.657417 | ||||||||
\(296\) | −28.9373 | −1.68194 | ||||||||
\(297\) | −0.354249 | −0.0205556 | ||||||||
\(298\) | 54.4575 | 3.15464 | ||||||||
\(299\) | −3.29150 | −0.190353 | ||||||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | 9.29150 | 0.535553 | ||||||||
\(302\) | 22.7085 | 1.30673 | ||||||||
\(303\) | −9.29150 | −0.533783 | ||||||||
\(304\) | −11.0000 | −0.630893 | ||||||||
\(305\) | −11.2915 | −0.646550 | ||||||||
\(306\) | 10.5830 | 0.604990 | ||||||||
\(307\) | −24.4575 | −1.39586 | −0.697932 | − | 0.716164i | \(-0.745896\pi\) | ||||
−0.697932 | + | 0.716164i | \(0.745896\pi\) | |||||||
\(308\) | 2.91503 | 0.166099 | ||||||||
\(309\) | 10.5830 | 0.602046 | ||||||||
\(310\) | −15.8745 | −0.901611 | ||||||||
\(311\) | 22.9373 | 1.30065 | 0.650326 | − | 0.759655i | \(-0.274632\pi\) | ||||
0.650326 | + | 0.759655i | \(0.274632\pi\) | |||||||
\(312\) | −2.81176 | −0.159185 | ||||||||
\(313\) | 17.2915 | 0.977374 | 0.488687 | − | 0.872459i | \(-0.337476\pi\) | ||||
0.488687 | + | 0.872459i | \(0.337476\pi\) | |||||||
\(314\) | 35.1660 | 1.98453 | ||||||||
\(315\) | 1.64575 | 0.0927276 | ||||||||
\(316\) | 32.9150 | 1.85161 | ||||||||
\(317\) | 20.4575 | 1.14901 | 0.574504 | − | 0.818502i | \(-0.305195\pi\) | ||||
0.574504 | + | 0.818502i | \(0.305195\pi\) | |||||||
\(318\) | 29.8745 | 1.67528 | ||||||||
\(319\) | 3.16601 | 0.177263 | ||||||||
\(320\) | 13.0000 | 0.726722 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −40.4575 | −2.25461 | ||||||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | 5.00000 | 0.277778 | ||||||||
\(325\) | −0.354249 | −0.0196502 | ||||||||
\(326\) | 6.22876 | 0.344979 | ||||||||
\(327\) | −5.29150 | −0.292621 | ||||||||
\(328\) | 76.5608 | 4.22736 | ||||||||
\(329\) | −2.12549 | −0.117182 | ||||||||
\(330\) | 0.937254 | 0.0515941 | ||||||||
\(331\) | 11.4170 | 0.627535 | 0.313767 | − | 0.949500i | \(-0.398409\pi\) | ||||
0.313767 | + | 0.949500i | \(0.398409\pi\) | |||||||
\(332\) | 30.0000 | 1.64646 | ||||||||
\(333\) | 3.64575 | 0.199786 | ||||||||
\(334\) | 56.3320 | 3.08235 | ||||||||
\(335\) | −6.58301 | −0.359668 | ||||||||
\(336\) | −18.1033 | −0.987614 | ||||||||
\(337\) | 14.9373 | 0.813684 | 0.406842 | − | 0.913499i | \(-0.366630\pi\) | ||||
0.406842 | + | 0.913499i | \(0.366630\pi\) | |||||||
\(338\) | 34.0627 | 1.85277 | ||||||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | −20.0000 | −1.08465 | ||||||||
\(341\) | 2.12549 | 0.115102 | ||||||||
\(342\) | 2.64575 | 0.143066 | ||||||||
\(343\) | −18.5830 | −1.00339 | ||||||||
\(344\) | −44.8118 | −2.41609 | ||||||||
\(345\) | −9.29150 | −0.500238 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.0000 | 1.39575 | 0.697877 | − | 0.716218i | \(-0.254128\pi\) | ||||
0.697877 | + | 0.716218i | \(0.254128\pi\) | |||||||
\(348\) | −44.6863 | −2.39544 | ||||||||
\(349\) | 23.1660 | 1.24005 | 0.620024 | − | 0.784583i | \(-0.287123\pi\) | ||||
0.620024 | + | 0.784583i | \(0.287123\pi\) | |||||||
\(350\) | −4.35425 | −0.232744 | ||||||||
\(351\) | 0.354249 | 0.0189084 | ||||||||
\(352\) | −4.68627 | −0.249779 | ||||||||
\(353\) | 0.583005 | 0.0310302 | 0.0155151 | − | 0.999880i | \(-0.495061\pi\) | ||||
0.0155151 | + | 0.999880i | \(0.495061\pi\) | |||||||
\(354\) | 29.8745 | 1.58781 | ||||||||
\(355\) | 7.29150 | 0.386993 | ||||||||
\(356\) | −84.6863 | −4.48836 | ||||||||
\(357\) | 6.58301 | 0.348410 | ||||||||
\(358\) | 19.2915 | 1.01959 | ||||||||
\(359\) | −36.1033 | −1.90546 | −0.952729 | − | 0.303822i | \(-0.901737\pi\) | ||||
−0.952729 | + | 0.303822i | \(0.901737\pi\) | |||||||
\(360\) | −7.93725 | −0.418330 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −45.7490 | −2.40451 | ||||||||
\(363\) | 10.8745 | 0.570764 | ||||||||
\(364\) | −2.91503 | −0.152789 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | −29.8745 | −1.56157 | ||||||||
\(367\) | 1.64575 | 0.0859075 | 0.0429538 | − | 0.999077i | \(-0.486323\pi\) | ||||
0.0429538 | + | 0.999077i | \(0.486323\pi\) | |||||||
\(368\) | 102.207 | 5.32788 | ||||||||
\(369\) | −9.64575 | −0.502138 | ||||||||
\(370\) | −9.64575 | −0.501459 | ||||||||
\(371\) | 18.5830 | 0.964782 | ||||||||
\(372\) | −30.0000 | −1.55543 | ||||||||
\(373\) | 5.06275 | 0.262139 | 0.131070 | − | 0.991373i | \(-0.458159\pi\) | ||||
0.131070 | + | 0.991373i | \(0.458159\pi\) | |||||||
\(374\) | 3.74902 | 0.193857 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 10.2510 | 0.528654 | ||||||||
\(377\) | −3.16601 | −0.163058 | ||||||||
\(378\) | 4.35425 | 0.223958 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | −5.00000 | −0.256495 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | −16.4797 | −0.843177 | ||||||||
\(383\) | −18.5830 | −0.949547 | −0.474774 | − | 0.880108i | \(-0.657470\pi\) | ||||
−0.474774 | + | 0.880108i | \(0.657470\pi\) | |||||||
\(384\) | 7.93725 | 0.405046 | ||||||||
\(385\) | 0.583005 | 0.0297127 | ||||||||
\(386\) | 30.8118 | 1.56828 | ||||||||
\(387\) | 5.64575 | 0.286990 | ||||||||
\(388\) | −14.6863 | −0.745582 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | −0.937254 | −0.0474597 | ||||||||
\(391\) | −37.1660 | −1.87957 | ||||||||
\(392\) | 34.0627 | 1.72043 | ||||||||
\(393\) | 14.2288 | 0.717746 | ||||||||
\(394\) | 66.5830 | 3.35440 | ||||||||
\(395\) | 6.58301 | 0.331227 | ||||||||
\(396\) | 1.77124 | 0.0890083 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | −19.2915 | −0.966996 | ||||||||
\(399\) | 1.64575 | 0.0823906 | ||||||||
\(400\) | 11.0000 | 0.550000 | ||||||||
\(401\) | −4.93725 | −0.246555 | −0.123277 | − | 0.992372i | \(-0.539340\pi\) | ||||
−0.123277 | + | 0.992372i | \(0.539340\pi\) | |||||||
\(402\) | −17.4170 | −0.868681 | ||||||||
\(403\) | −2.12549 | −0.105878 | ||||||||
\(404\) | 46.4575 | 2.31135 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −38.9150 | −1.93132 | ||||||||
\(407\) | 1.29150 | 0.0640174 | ||||||||
\(408\) | −31.7490 | −1.57181 | ||||||||
\(409\) | −6.70850 | −0.331714 | −0.165857 | − | 0.986150i | \(-0.553039\pi\) | ||||
−0.165857 | + | 0.986150i | \(0.553039\pi\) | |||||||
\(410\) | 25.5203 | 1.26036 | ||||||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | −52.9150 | −2.60694 | ||||||||
\(413\) | 18.5830 | 0.914410 | ||||||||
\(414\) | −24.5830 | −1.20819 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 4.68627 | 0.229763 | ||||||||
\(417\) | −17.8745 | −0.875318 | ||||||||
\(418\) | 0.937254 | 0.0458426 | ||||||||
\(419\) | 38.9373 | 1.90221 | 0.951105 | − | 0.308869i | \(-0.0999504\pi\) | ||||
0.951105 | + | 0.308869i | \(0.0999504\pi\) | |||||||
\(420\) | −8.22876 | −0.401522 | ||||||||
\(421\) | 28.5830 | 1.39305 | 0.696525 | − | 0.717532i | \(-0.254728\pi\) | ||||
0.696525 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(422\) | −6.83399 | −0.332673 | ||||||||
\(423\) | −1.29150 | −0.0627950 | ||||||||
\(424\) | −89.6235 | −4.35250 | ||||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | 19.2915 | 0.934676 | ||||||||
\(427\) | −18.5830 | −0.899295 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.125492 | 0.00605882 | ||||||||
\(430\) | −14.9373 | −0.720338 | ||||||||
\(431\) | 3.29150 | 0.158546 | 0.0792731 | − | 0.996853i | \(-0.474740\pi\) | ||||
0.0792731 | + | 0.996853i | \(0.474740\pi\) | |||||||
\(432\) | −11.0000 | −0.529238 | ||||||||
\(433\) | −27.6458 | −1.32857 | −0.664285 | − | 0.747479i | \(-0.731264\pi\) | ||||
−0.664285 | + | 0.747479i | \(0.731264\pi\) | |||||||
\(434\) | −26.1255 | −1.25406 | ||||||||
\(435\) | −8.93725 | −0.428509 | ||||||||
\(436\) | 26.4575 | 1.26709 | ||||||||
\(437\) | −9.29150 | −0.444473 | ||||||||
\(438\) | 26.4575 | 1.26419 | ||||||||
\(439\) | −1.41699 | −0.0676295 | −0.0338147 | − | 0.999428i | \(-0.510766\pi\) | ||||
−0.0338147 | + | 0.999428i | \(0.510766\pi\) | |||||||
\(440\) | −2.81176 | −0.134045 | ||||||||
\(441\) | −4.29150 | −0.204357 | ||||||||
\(442\) | −3.74902 | −0.178322 | ||||||||
\(443\) | 26.7085 | 1.26896 | 0.634480 | − | 0.772940i | \(-0.281214\pi\) | ||||
0.634480 | + | 0.772940i | \(0.281214\pi\) | |||||||
\(444\) | −18.2288 | −0.865099 | ||||||||
\(445\) | −16.9373 | −0.802903 | ||||||||
\(446\) | −6.83399 | −0.323599 | ||||||||
\(447\) | 20.5830 | 0.973543 | ||||||||
\(448\) | 21.3948 | 1.01081 | ||||||||
\(449\) | −36.2288 | −1.70974 | −0.854870 | − | 0.518842i | \(-0.826363\pi\) | ||||
−0.854870 | + | 0.518842i | \(0.826363\pi\) | |||||||
\(450\) | −2.64575 | −0.124722 | ||||||||
\(451\) | −3.41699 | −0.160900 | ||||||||
\(452\) | −20.0000 | −0.940721 | ||||||||
\(453\) | 8.58301 | 0.403265 | ||||||||
\(454\) | 28.3320 | 1.32969 | ||||||||
\(455\) | −0.583005 | −0.0273317 | ||||||||
\(456\) | −7.93725 | −0.371696 | ||||||||
\(457\) | 0.125492 | 0.00587027 | 0.00293514 | − | 0.999996i | \(-0.499066\pi\) | ||||
0.00293514 | + | 0.999996i | \(0.499066\pi\) | |||||||
\(458\) | −23.0405 | −1.07661 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | 46.4575 | 2.16609 | ||||||||
\(461\) | −37.7490 | −1.75815 | −0.879073 | − | 0.476686i | \(-0.841838\pi\) | ||||
−0.879073 | + | 0.476686i | \(0.841838\pi\) | |||||||
\(462\) | 1.54249 | 0.0717630 | ||||||||
\(463\) | −35.5203 | −1.65077 | −0.825383 | − | 0.564573i | \(-0.809041\pi\) | ||||
−0.825383 | + | 0.564573i | \(0.809041\pi\) | |||||||
\(464\) | 98.3098 | 4.56392 | ||||||||
\(465\) | −6.00000 | −0.278243 | ||||||||
\(466\) | 47.6235 | 2.20612 | ||||||||
\(467\) | 19.8745 | 0.919683 | 0.459841 | − | 0.888001i | \(-0.347906\pi\) | ||||
0.459841 | + | 0.888001i | \(0.347906\pi\) | |||||||
\(468\) | −1.77124 | −0.0818758 | ||||||||
\(469\) | −10.8340 | −0.500267 | ||||||||
\(470\) | 3.41699 | 0.157614 | ||||||||
\(471\) | 13.2915 | 0.612440 | ||||||||
\(472\) | −89.6235 | −4.12526 | ||||||||
\(473\) | 2.00000 | 0.0919601 | ||||||||
\(474\) | 17.4170 | 0.799989 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −32.9150 | −1.50866 | ||||||||
\(477\) | 11.2915 | 0.517002 | ||||||||
\(478\) | −41.3948 | −1.89335 | ||||||||
\(479\) | 4.35425 | 0.198951 | 0.0994754 | − | 0.995040i | \(-0.468284\pi\) | ||||
0.0994754 | + | 0.995040i | \(0.468284\pi\) | |||||||
\(480\) | 13.2288 | 0.603807 | ||||||||
\(481\) | −1.29150 | −0.0588875 | ||||||||
\(482\) | −43.8745 | −1.99843 | ||||||||
\(483\) | −15.2915 | −0.695787 | ||||||||
\(484\) | −54.3725 | −2.47148 | ||||||||
\(485\) | −2.93725 | −0.133374 | ||||||||
\(486\) | 2.64575 | 0.120014 | ||||||||
\(487\) | 17.8745 | 0.809971 | 0.404986 | − | 0.914323i | \(-0.367277\pi\) | ||||
0.404986 | + | 0.914323i | \(0.367277\pi\) | |||||||
\(488\) | 89.6235 | 4.05707 | ||||||||
\(489\) | 2.35425 | 0.106463 | ||||||||
\(490\) | 11.3542 | 0.512933 | ||||||||
\(491\) | −5.77124 | −0.260453 | −0.130226 | − | 0.991484i | \(-0.541570\pi\) | ||||
−0.130226 | + | 0.991484i | \(0.541570\pi\) | |||||||
\(492\) | 48.2288 | 2.17432 | ||||||||
\(493\) | −35.7490 | −1.61005 | ||||||||
\(494\) | −0.937254 | −0.0421690 | ||||||||
\(495\) | 0.354249 | 0.0159223 | ||||||||
\(496\) | 66.0000 | 2.96349 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 15.8745 | 0.711354 | ||||||||
\(499\) | −31.0405 | −1.38956 | −0.694782 | − | 0.719220i | \(-0.744499\pi\) | ||||
−0.694782 | + | 0.719220i | \(0.744499\pi\) | |||||||
\(500\) | 5.00000 | 0.223607 | ||||||||
\(501\) | 21.2915 | 0.951234 | ||||||||
\(502\) | 43.2693 | 1.93120 | ||||||||
\(503\) | −2.00000 | −0.0891756 | −0.0445878 | − | 0.999005i | \(-0.514197\pi\) | ||||
−0.0445878 | + | 0.999005i | \(0.514197\pi\) | |||||||
\(504\) | −13.0627 | −0.581861 | ||||||||
\(505\) | 9.29150 | 0.413466 | ||||||||
\(506\) | −8.70850 | −0.387140 | ||||||||
\(507\) | 12.8745 | 0.571777 | ||||||||
\(508\) | 20.0000 | 0.887357 | ||||||||
\(509\) | −34.1033 | −1.51160 | −0.755800 | − | 0.654802i | \(-0.772752\pi\) | ||||
−0.755800 | + | 0.654802i | \(0.772752\pi\) | |||||||
\(510\) | −10.5830 | −0.468623 | ||||||||
\(511\) | 16.4575 | 0.728038 | ||||||||
\(512\) | 29.1033 | 1.28619 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 14.3320 | 0.632158 | ||||||||
\(515\) | −10.5830 | −0.466343 | ||||||||
\(516\) | −28.2288 | −1.24270 | ||||||||
\(517\) | −0.457513 | −0.0201214 | ||||||||
\(518\) | −15.8745 | −0.697486 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.81176 | 0.123304 | ||||||||
\(521\) | 22.1033 | 0.968362 | 0.484181 | − | 0.874968i | \(-0.339118\pi\) | ||||
0.484181 | + | 0.874968i | \(0.339118\pi\) | |||||||
\(522\) | −23.6458 | −1.03495 | ||||||||
\(523\) | −23.2915 | −1.01847 | −0.509233 | − | 0.860629i | \(-0.670071\pi\) | ||||
−0.509233 | + | 0.860629i | \(0.670071\pi\) | |||||||
\(524\) | −71.1438 | −3.10793 | ||||||||
\(525\) | −1.64575 | −0.0718265 | ||||||||
\(526\) | −12.1255 | −0.528697 | ||||||||
\(527\) | −24.0000 | −1.04546 | ||||||||
\(528\) | −3.89674 | −0.169584 | ||||||||
\(529\) | 63.3320 | 2.75357 | ||||||||
\(530\) | −29.8745 | −1.29767 | ||||||||
\(531\) | 11.2915 | 0.490009 | ||||||||
\(532\) | −8.22876 | −0.356762 | ||||||||
\(533\) | 3.41699 | 0.148006 | ||||||||
\(534\) | −44.8118 | −1.93919 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 52.2510 | 2.25690 | ||||||||
\(537\) | 7.29150 | 0.314652 | ||||||||
\(538\) | −11.1882 | −0.482359 | ||||||||
\(539\) | −1.52026 | −0.0654822 | ||||||||
\(540\) | −5.00000 | −0.215166 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 12.4575 | 0.535096 | ||||||||
\(543\) | −17.2915 | −0.742049 | ||||||||
\(544\) | 52.9150 | 2.26871 | ||||||||
\(545\) | 5.29150 | 0.226663 | ||||||||
\(546\) | −1.54249 | −0.0660123 | ||||||||
\(547\) | 1.87451 | 0.0801482 | 0.0400741 | − | 0.999197i | \(-0.487241\pi\) | ||||
0.0400741 | + | 0.999197i | \(0.487241\pi\) | |||||||
\(548\) | 30.0000 | 1.28154 | ||||||||
\(549\) | −11.2915 | −0.481910 | ||||||||
\(550\) | −0.937254 | −0.0399646 | ||||||||
\(551\) | −8.93725 | −0.380740 | ||||||||
\(552\) | 73.7490 | 3.13897 | ||||||||
\(553\) | 10.8340 | 0.460708 | ||||||||
\(554\) | −1.54249 | −0.0655340 | ||||||||
\(555\) | −3.64575 | −0.154754 | ||||||||
\(556\) | 89.3725 | 3.79024 | ||||||||
\(557\) | −11.4170 | −0.483754 | −0.241877 | − | 0.970307i | \(-0.577763\pi\) | ||||
−0.241877 | + | 0.970307i | \(0.577763\pi\) | |||||||
\(558\) | −15.8745 | −0.672022 | ||||||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | 18.1033 | 0.765003 | ||||||||
\(561\) | 1.41699 | 0.0598256 | ||||||||
\(562\) | 85.2693 | 3.59687 | ||||||||
\(563\) | 8.12549 | 0.342449 | 0.171224 | − | 0.985232i | \(-0.445228\pi\) | ||||
0.171224 | + | 0.985232i | \(0.445228\pi\) | |||||||
\(564\) | 6.45751 | 0.271910 | ||||||||
\(565\) | −4.00000 | −0.168281 | ||||||||
\(566\) | 30.4797 | 1.28116 | ||||||||
\(567\) | 1.64575 | 0.0691151 | ||||||||
\(568\) | −57.8745 | −2.42836 | ||||||||
\(569\) | −7.06275 | −0.296086 | −0.148043 | − | 0.988981i | \(-0.547297\pi\) | ||||
−0.148043 | + | 0.988981i | \(0.547297\pi\) | |||||||
\(570\) | −2.64575 | −0.110818 | ||||||||
\(571\) | 16.7085 | 0.699229 | 0.349614 | − | 0.936894i | \(-0.386313\pi\) | ||||
0.349614 | + | 0.936894i | \(0.386313\pi\) | |||||||
\(572\) | −0.627461 | −0.0262354 | ||||||||
\(573\) | −6.22876 | −0.260210 | ||||||||
\(574\) | 42.0000 | 1.75305 | ||||||||
\(575\) | 9.29150 | 0.387482 | ||||||||
\(576\) | 13.0000 | 0.541667 | ||||||||
\(577\) | −13.2915 | −0.553332 | −0.276666 | − | 0.960966i | \(-0.589230\pi\) | ||||
−0.276666 | + | 0.960966i | \(0.589230\pi\) | |||||||
\(578\) | 2.64575 | 0.110049 | ||||||||
\(579\) | 11.6458 | 0.483981 | ||||||||
\(580\) | 44.6863 | 1.85550 | ||||||||
\(581\) | 9.87451 | 0.409664 | ||||||||
\(582\) | −7.77124 | −0.322128 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | −79.3725 | −3.28446 | ||||||||
\(585\) | −0.354249 | −0.0146464 | ||||||||
\(586\) | −14.3320 | −0.592050 | ||||||||
\(587\) | −33.2915 | −1.37409 | −0.687044 | − | 0.726616i | \(-0.741092\pi\) | ||||
−0.687044 | + | 0.726616i | \(0.741092\pi\) | |||||||
\(588\) | 21.4575 | 0.884893 | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | −29.8745 | −1.22991 | ||||||||
\(591\) | 25.1660 | 1.03519 | ||||||||
\(592\) | 40.1033 | 1.64823 | ||||||||
\(593\) | 3.41699 | 0.140319 | 0.0701596 | − | 0.997536i | \(-0.477649\pi\) | ||||
0.0701596 | + | 0.997536i | \(0.477649\pi\) | |||||||
\(594\) | 0.937254 | 0.0384560 | ||||||||
\(595\) | −6.58301 | −0.269877 | ||||||||
\(596\) | −102.915 | −4.21556 | ||||||||
\(597\) | −7.29150 | −0.298421 | ||||||||
\(598\) | 8.70850 | 0.356117 | ||||||||
\(599\) | 9.41699 | 0.384768 | 0.192384 | − | 0.981320i | \(-0.438378\pi\) | ||||
0.192384 | + | 0.981320i | \(0.438378\pi\) | |||||||
\(600\) | 7.93725 | 0.324037 | ||||||||
\(601\) | 22.7085 | 0.926299 | 0.463149 | − | 0.886280i | \(-0.346719\pi\) | ||||
0.463149 | + | 0.886280i | \(0.346719\pi\) | |||||||
\(602\) | −24.5830 | −1.00193 | ||||||||
\(603\) | −6.58301 | −0.268081 | ||||||||
\(604\) | −42.9150 | −1.74619 | ||||||||
\(605\) | −10.8745 | −0.442112 | ||||||||
\(606\) | 24.5830 | 0.998616 | ||||||||
\(607\) | −43.0405 | −1.74696 | −0.873480 | − | 0.486859i | \(-0.838142\pi\) | ||||
−0.873480 | + | 0.486859i | \(0.838142\pi\) | |||||||
\(608\) | 13.2288 | 0.536497 | ||||||||
\(609\) | −14.7085 | −0.596018 | ||||||||
\(610\) | 29.8745 | 1.20958 | ||||||||
\(611\) | 0.457513 | 0.0185090 | ||||||||
\(612\) | −20.0000 | −0.808452 | ||||||||
\(613\) | −30.4575 | −1.23017 | −0.615084 | − | 0.788462i | \(-0.710878\pi\) | ||||
−0.615084 | + | 0.788462i | \(0.710878\pi\) | |||||||
\(614\) | 64.7085 | 2.61142 | ||||||||
\(615\) | 9.64575 | 0.388954 | ||||||||
\(616\) | −4.62746 | −0.186446 | ||||||||
\(617\) | 12.0000 | 0.483102 | 0.241551 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241551 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(618\) | −28.0000 | −1.12633 | ||||||||
\(619\) | 23.2915 | 0.936165 | 0.468082 | − | 0.883685i | \(-0.344945\pi\) | ||||
0.468082 | + | 0.883685i | \(0.344945\pi\) | |||||||
\(620\) | 30.0000 | 1.20483 | ||||||||
\(621\) | −9.29150 | −0.372855 | ||||||||
\(622\) | −60.6863 | −2.43330 | ||||||||
\(623\) | −27.8745 | −1.11677 | ||||||||
\(624\) | 3.89674 | 0.155994 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −45.7490 | −1.82850 | ||||||||
\(627\) | 0.354249 | 0.0141473 | ||||||||
\(628\) | −66.4575 | −2.65194 | ||||||||
\(629\) | −14.5830 | −0.581462 | ||||||||
\(630\) | −4.35425 | −0.173477 | ||||||||
\(631\) | −14.5830 | −0.580540 | −0.290270 | − | 0.956945i | \(-0.593745\pi\) | ||||
−0.290270 | + | 0.956945i | \(0.593745\pi\) | |||||||
\(632\) | −52.2510 | −2.07843 | ||||||||
\(633\) | −2.58301 | −0.102665 | ||||||||
\(634\) | −54.1255 | −2.14960 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | −56.4575 | −2.23869 | ||||||||
\(637\) | 1.52026 | 0.0602349 | ||||||||
\(638\) | −8.37648 | −0.331628 | ||||||||
\(639\) | 7.29150 | 0.288447 | ||||||||
\(640\) | −7.93725 | −0.313748 | ||||||||
\(641\) | −16.9373 | −0.668981 | −0.334491 | − | 0.942399i | \(-0.608564\pi\) | ||||
−0.334491 | + | 0.942399i | \(0.608564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.6458 | −0.538136 | −0.269068 | − | 0.963121i | \(-0.586716\pi\) | ||||
−0.269068 | + | 0.963121i | \(0.586716\pi\) | |||||||
\(644\) | 76.4575 | 3.01285 | ||||||||
\(645\) | −5.64575 | −0.222301 | ||||||||
\(646\) | −10.5830 | −0.416383 | ||||||||
\(647\) | −3.41699 | −0.134336 | −0.0671680 | − | 0.997742i | \(-0.521396\pi\) | ||||
−0.0671680 | + | 0.997742i | \(0.521396\pi\) | |||||||
\(648\) | −7.93725 | −0.311805 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0.937254 | 0.0367621 | ||||||||
\(651\) | −9.87451 | −0.387012 | ||||||||
\(652\) | −11.7712 | −0.460997 | ||||||||
\(653\) | 9.41699 | 0.368515 | 0.184258 | − | 0.982878i | \(-0.441012\pi\) | ||||
0.184258 | + | 0.982878i | \(0.441012\pi\) | |||||||
\(654\) | 14.0000 | 0.547443 | ||||||||
\(655\) | −14.2288 | −0.555964 | ||||||||
\(656\) | −106.103 | −4.14264 | ||||||||
\(657\) | 10.0000 | 0.390137 | ||||||||
\(658\) | 5.62352 | 0.219228 | ||||||||
\(659\) | 25.4170 | 0.990106 | 0.495053 | − | 0.868863i | \(-0.335149\pi\) | ||||
0.495053 | + | 0.868863i | \(0.335149\pi\) | |||||||
\(660\) | −1.77124 | −0.0689456 | ||||||||
\(661\) | 1.29150 | 0.0502336 | 0.0251168 | − | 0.999685i | \(-0.492004\pi\) | ||||
0.0251168 | + | 0.999685i | \(0.492004\pi\) | |||||||
\(662\) | −30.2065 | −1.17401 | ||||||||
\(663\) | −1.41699 | −0.0550315 | ||||||||
\(664\) | −47.6235 | −1.84815 | ||||||||
\(665\) | −1.64575 | −0.0638195 | ||||||||
\(666\) | −9.64575 | −0.373765 | ||||||||
\(667\) | 83.0405 | 3.21534 | ||||||||
\(668\) | −106.458 | −4.11896 | ||||||||
\(669\) | −2.58301 | −0.0998648 | ||||||||
\(670\) | 17.4170 | 0.672877 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 21.7712 | 0.839844 | ||||||||
\(673\) | −13.0627 | −0.503532 | −0.251766 | − | 0.967788i | \(-0.581011\pi\) | ||||
−0.251766 | + | 0.967788i | \(0.581011\pi\) | |||||||
\(674\) | −39.5203 | −1.52226 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −64.3725 | −2.47587 | ||||||||
\(677\) | 40.4575 | 1.55491 | 0.777454 | − | 0.628939i | \(-0.216511\pi\) | ||||
0.777454 | + | 0.628939i | \(0.216511\pi\) | |||||||
\(678\) | −10.5830 | −0.406438 | ||||||||
\(679\) | −4.83399 | −0.185511 | ||||||||
\(680\) | 31.7490 | 1.21752 | ||||||||
\(681\) | 10.7085 | 0.410351 | ||||||||
\(682\) | −5.62352 | −0.215336 | ||||||||
\(683\) | 19.7490 | 0.755675 | 0.377838 | − | 0.925872i | \(-0.376668\pi\) | ||||
0.377838 | + | 0.925872i | \(0.376668\pi\) | |||||||
\(684\) | −5.00000 | −0.191180 | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 49.1660 | 1.87717 | ||||||||
\(687\) | −8.70850 | −0.332250 | ||||||||
\(688\) | 62.1033 | 2.36766 | ||||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 24.5830 | 0.935859 | ||||||||
\(691\) | −43.0405 | −1.63734 | −0.818669 | − | 0.574265i | \(-0.805288\pi\) | ||||
−0.818669 | + | 0.574265i | \(0.805288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.583005 | 0.0221465 | ||||||||
\(694\) | −68.7895 | −2.61122 | ||||||||
\(695\) | 17.8745 | 0.678019 | ||||||||
\(696\) | 70.9373 | 2.68887 | ||||||||
\(697\) | 38.5830 | 1.46144 | ||||||||
\(698\) | −61.2915 | −2.31992 | ||||||||
\(699\) | 18.0000 | 0.680823 | ||||||||
\(700\) | 8.22876 | 0.311018 | ||||||||
\(701\) | 16.5830 | 0.626331 | 0.313166 | − | 0.949698i | \(-0.398610\pi\) | ||||
0.313166 | + | 0.949698i | \(0.398610\pi\) | |||||||
\(702\) | −0.937254 | −0.0353744 | ||||||||
\(703\) | −3.64575 | −0.137502 | ||||||||
\(704\) | 4.60523 | 0.173566 | ||||||||
\(705\) | 1.29150 | 0.0486408 | ||||||||
\(706\) | −1.54249 | −0.0580523 | ||||||||
\(707\) | 15.2915 | 0.575096 | ||||||||
\(708\) | −56.4575 | −2.12180 | ||||||||
\(709\) | −4.70850 | −0.176831 | −0.0884157 | − | 0.996084i | \(-0.528180\pi\) | ||||
−0.0884157 | + | 0.996084i | \(0.528180\pi\) | |||||||
\(710\) | −19.2915 | −0.723997 | ||||||||
\(711\) | 6.58301 | 0.246882 | ||||||||
\(712\) | 134.435 | 5.03818 | ||||||||
\(713\) | 55.7490 | 2.08782 | ||||||||
\(714\) | −17.4170 | −0.651815 | ||||||||
\(715\) | −0.125492 | −0.00469314 | ||||||||
\(716\) | −36.4575 | −1.36248 | ||||||||
\(717\) | −15.6458 | −0.584301 | ||||||||
\(718\) | 95.5203 | 3.56478 | ||||||||
\(719\) | 32.8118 | 1.22367 | 0.611836 | − | 0.790985i | \(-0.290431\pi\) | ||||
0.611836 | + | 0.790985i | \(0.290431\pi\) | |||||||
\(720\) | 11.0000 | 0.409946 | ||||||||
\(721\) | −17.4170 | −0.648643 | ||||||||
\(722\) | −2.64575 | −0.0984647 | ||||||||
\(723\) | −16.5830 | −0.616729 | ||||||||
\(724\) | 86.4575 | 3.21317 | ||||||||
\(725\) | 8.93725 | 0.331921 | ||||||||
\(726\) | −28.7712 | −1.06780 | ||||||||
\(727\) | 14.1033 | 0.523061 | 0.261531 | − | 0.965195i | \(-0.415773\pi\) | ||||
0.261531 | + | 0.965195i | \(0.415773\pi\) | |||||||
\(728\) | 4.62746 | 0.171505 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −26.4575 | −0.979236 | ||||||||
\(731\) | −22.5830 | −0.835263 | ||||||||
\(732\) | 56.4575 | 2.08673 | ||||||||
\(733\) | 7.41699 | 0.273953 | 0.136976 | − | 0.990574i | \(-0.456262\pi\) | ||||
0.136976 | + | 0.990574i | \(0.456262\pi\) | |||||||
\(734\) | −4.35425 | −0.160718 | ||||||||
\(735\) | 4.29150 | 0.158294 | ||||||||
\(736\) | −122.915 | −4.53071 | ||||||||
\(737\) | −2.33202 | −0.0859011 | ||||||||
\(738\) | 25.5203 | 0.939414 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 18.2288 | 0.670102 | ||||||||
\(741\) | −0.354249 | −0.0130137 | ||||||||
\(742\) | −49.1660 | −1.80494 | ||||||||
\(743\) | −10.5830 | −0.388253 | −0.194126 | − | 0.980977i | \(-0.562187\pi\) | ||||
−0.194126 | + | 0.980977i | \(0.562187\pi\) | |||||||
\(744\) | 47.6235 | 1.74596 | ||||||||
\(745\) | −20.5830 | −0.754103 | ||||||||
\(746\) | −13.3948 | −0.490417 | ||||||||
\(747\) | 6.00000 | 0.219529 | ||||||||
\(748\) | −7.08497 | −0.259052 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.64575 | 0.0966092 | ||||||||
\(751\) | −44.5830 | −1.62686 | −0.813428 | − | 0.581665i | \(-0.802401\pi\) | ||||
−0.813428 | + | 0.581665i | \(0.802401\pi\) | |||||||
\(752\) | −14.2065 | −0.518059 | ||||||||
\(753\) | 16.3542 | 0.595982 | ||||||||
\(754\) | 8.37648 | 0.305053 | ||||||||
\(755\) | −8.58301 | −0.312368 | ||||||||
\(756\) | −8.22876 | −0.299277 | ||||||||
\(757\) | −23.8745 | −0.867734 | −0.433867 | − | 0.900977i | \(-0.642851\pi\) | ||||
−0.433867 | + | 0.900977i | \(0.642851\pi\) | |||||||
\(758\) | −26.4575 | −0.960980 | ||||||||
\(759\) | −3.29150 | −0.119474 | ||||||||
\(760\) | 7.93725 | 0.287914 | ||||||||
\(761\) | 25.7490 | 0.933401 | 0.466701 | − | 0.884415i | \(-0.345443\pi\) | ||||
0.466701 | + | 0.884415i | \(0.345443\pi\) | |||||||
\(762\) | 10.5830 | 0.383382 | ||||||||
\(763\) | 8.70850 | 0.315269 | ||||||||
\(764\) | 31.1438 | 1.12674 | ||||||||
\(765\) | −4.00000 | −0.144620 | ||||||||
\(766\) | 49.1660 | 1.77644 | ||||||||
\(767\) | −4.00000 | −0.144432 | ||||||||
\(768\) | 5.00000 | 0.180422 | ||||||||
\(769\) | −17.7490 | −0.640046 | −0.320023 | − | 0.947410i | \(-0.603691\pi\) | ||||
−0.320023 | + | 0.947410i | \(0.603691\pi\) | |||||||
\(770\) | −1.54249 | −0.0555874 | ||||||||
\(771\) | 5.41699 | 0.195088 | ||||||||
\(772\) | −58.2288 | −2.09570 | ||||||||
\(773\) | −8.70850 | −0.313223 | −0.156611 | − | 0.987660i | \(-0.550057\pi\) | ||||
−0.156611 | + | 0.987660i | \(0.550057\pi\) | |||||||
\(774\) | −14.9373 | −0.536909 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 23.3137 | 0.836914 | ||||||||
\(777\) | −6.00000 | −0.215249 | ||||||||
\(778\) | 15.8745 | 0.569129 | ||||||||
\(779\) | 9.64575 | 0.345595 | ||||||||
\(780\) | 1.77124 | 0.0634207 | ||||||||
\(781\) | 2.58301 | 0.0924272 | ||||||||
\(782\) | 98.3320 | 3.51635 | ||||||||
\(783\) | −8.93725 | −0.319391 | ||||||||
\(784\) | −47.2065 | −1.68595 | ||||||||
\(785\) | −13.2915 | −0.474394 | ||||||||
\(786\) | −37.6458 | −1.34278 | ||||||||
\(787\) | 37.8745 | 1.35008 | 0.675040 | − | 0.737781i | \(-0.264126\pi\) | ||||
0.675040 | + | 0.737781i | \(0.264126\pi\) | |||||||
\(788\) | −125.830 | −4.48251 | ||||||||
\(789\) | −4.58301 | −0.163159 | ||||||||
\(790\) | −17.4170 | −0.619669 | ||||||||
\(791\) | −6.58301 | −0.234065 | ||||||||
\(792\) | −2.81176 | −0.0999116 | ||||||||
\(793\) | 4.00000 | 0.142044 | ||||||||
\(794\) | 5.29150 | 0.187788 | ||||||||
\(795\) | −11.2915 | −0.400468 | ||||||||
\(796\) | 36.4575 | 1.29220 | ||||||||
\(797\) | 40.0000 | 1.41687 | 0.708436 | − | 0.705775i | \(-0.249401\pi\) | ||||
0.708436 | + | 0.705775i | \(0.249401\pi\) | |||||||
\(798\) | −4.35425 | −0.154139 | ||||||||
\(799\) | 5.16601 | 0.182760 | ||||||||
\(800\) | −13.2288 | −0.467707 | ||||||||
\(801\) | −16.9373 | −0.598448 | ||||||||
\(802\) | 13.0627 | 0.461262 | ||||||||
\(803\) | 3.54249 | 0.125012 | ||||||||
\(804\) | 32.9150 | 1.16082 | ||||||||
\(805\) | 15.2915 | 0.538955 | ||||||||
\(806\) | 5.62352 | 0.198080 | ||||||||
\(807\) | −4.22876 | −0.148859 | ||||||||
\(808\) | −73.7490 | −2.59448 | ||||||||
\(809\) | −19.4170 | −0.682665 | −0.341333 | − | 0.939943i | \(-0.610878\pi\) | ||||
−0.341333 | + | 0.939943i | \(0.610878\pi\) | |||||||
\(810\) | −2.64575 | −0.0929622 | ||||||||
\(811\) | 38.3320 | 1.34602 | 0.673010 | − | 0.739634i | \(-0.265001\pi\) | ||||
0.673010 | + | 0.739634i | \(0.265001\pi\) | |||||||
\(812\) | 73.5425 | 2.58084 | ||||||||
\(813\) | 4.70850 | 0.165134 | ||||||||
\(814\) | −3.41699 | −0.119766 | ||||||||
\(815\) | −2.35425 | −0.0824657 | ||||||||
\(816\) | 44.0000 | 1.54031 | ||||||||
\(817\) | −5.64575 | −0.197520 | ||||||||
\(818\) | 17.7490 | 0.620580 | ||||||||
\(819\) | −0.583005 | −0.0203719 | ||||||||
\(820\) | −48.2288 | −1.68422 | ||||||||
\(821\) | 47.6235 | 1.66207 | 0.831036 | − | 0.556218i | \(-0.187748\pi\) | ||||
0.831036 | + | 0.556218i | \(0.187748\pi\) | |||||||
\(822\) | 15.8745 | 0.553687 | ||||||||
\(823\) | 4.22876 | 0.147405 | 0.0737026 | − | 0.997280i | \(-0.476518\pi\) | ||||
0.0737026 | + | 0.997280i | \(0.476518\pi\) | |||||||
\(824\) | 84.0000 | 2.92628 | ||||||||
\(825\) | −0.354249 | −0.0123334 | ||||||||
\(826\) | −49.1660 | −1.71070 | ||||||||
\(827\) | 30.4575 | 1.05911 | 0.529556 | − | 0.848275i | \(-0.322359\pi\) | ||||
0.529556 | + | 0.848275i | \(0.322359\pi\) | |||||||
\(828\) | 46.4575 | 1.61451 | ||||||||
\(829\) | 2.70850 | 0.0940700 | 0.0470350 | − | 0.998893i | \(-0.485023\pi\) | ||||
0.0470350 | + | 0.998893i | \(0.485023\pi\) | |||||||
\(830\) | −15.8745 | −0.551012 | ||||||||
\(831\) | −0.583005 | −0.0202242 | ||||||||
\(832\) | −4.60523 | −0.159658 | ||||||||
\(833\) | 17.1660 | 0.594767 | ||||||||
\(834\) | 47.2915 | 1.63757 | ||||||||
\(835\) | −21.2915 | −0.736823 | ||||||||
\(836\) | −1.77124 | −0.0612597 | ||||||||
\(837\) | −6.00000 | −0.207390 | ||||||||
\(838\) | −103.018 | −3.55871 | ||||||||
\(839\) | −12.4575 | −0.430081 | −0.215041 | − | 0.976605i | \(-0.568988\pi\) | ||||
−0.215041 | + | 0.976605i | \(0.568988\pi\) | |||||||
\(840\) | 13.0627 | 0.450708 | ||||||||
\(841\) | 50.8745 | 1.75429 | ||||||||
\(842\) | −75.6235 | −2.60616 | ||||||||
\(843\) | 32.2288 | 1.11002 | ||||||||
\(844\) | 12.9150 | 0.444554 | ||||||||
\(845\) | −12.8745 | −0.442897 | ||||||||
\(846\) | 3.41699 | 0.117479 | ||||||||
\(847\) | −17.8967 | −0.614939 | ||||||||
\(848\) | 124.207 | 4.26527 | ||||||||
\(849\) | 11.5203 | 0.395374 | ||||||||
\(850\) | 10.5830 | 0.362994 | ||||||||
\(851\) | 33.8745 | 1.16120 | ||||||||
\(852\) | −36.4575 | −1.24901 | ||||||||
\(853\) | 14.7085 | 0.503609 | 0.251805 | − | 0.967778i | \(-0.418976\pi\) | ||||
0.251805 | + | 0.967778i | \(0.418976\pi\) | |||||||
\(854\) | 49.1660 | 1.68243 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.0405 | 1.06032 | 0.530162 | − | 0.847896i | \(-0.322131\pi\) | ||||
0.530162 | + | 0.847896i | \(0.322131\pi\) | |||||||
\(858\) | −0.332021 | −0.0113350 | ||||||||
\(859\) | −34.3320 | −1.17139 | −0.585697 | − | 0.810530i | \(-0.699179\pi\) | ||||
−0.585697 | + | 0.810530i | \(0.699179\pi\) | |||||||
\(860\) | 28.2288 | 0.962593 | ||||||||
\(861\) | 15.8745 | 0.541002 | ||||||||
\(862\) | −8.70850 | −0.296613 | ||||||||
\(863\) | −20.0000 | −0.680808 | −0.340404 | − | 0.940279i | \(-0.610564\pi\) | ||||
−0.340404 | + | 0.940279i | \(0.610564\pi\) | |||||||
\(864\) | 13.2288 | 0.450051 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 73.1438 | 2.48553 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 49.3725 | 1.67581 | ||||||||
\(869\) | 2.33202 | 0.0791084 | ||||||||
\(870\) | 23.6458 | 0.801666 | ||||||||
\(871\) | 2.33202 | 0.0790175 | ||||||||
\(872\) | −42.0000 | −1.42230 | ||||||||
\(873\) | −2.93725 | −0.0994110 | ||||||||
\(874\) | 24.5830 | 0.831533 | ||||||||
\(875\) | 1.64575 | 0.0556365 | ||||||||
\(876\) | −50.0000 | −1.68934 | ||||||||
\(877\) | −25.0627 | −0.846309 | −0.423154 | − | 0.906058i | \(-0.639077\pi\) | ||||
−0.423154 | + | 0.906058i | \(0.639077\pi\) | |||||||
\(878\) | 3.74902 | 0.126523 | ||||||||
\(879\) | −5.41699 | −0.182711 | ||||||||
\(880\) | 3.89674 | 0.131359 | ||||||||
\(881\) | −0.125492 | −0.00422794 | −0.00211397 | − | 0.999998i | \(-0.500673\pi\) | ||||
−0.00211397 | + | 0.999998i | \(0.500673\pi\) | |||||||
\(882\) | 11.3542 | 0.382317 | ||||||||
\(883\) | 10.8118 | 0.363845 | 0.181922 | − | 0.983313i | \(-0.441768\pi\) | ||||
0.181922 | + | 0.983313i | \(0.441768\pi\) | |||||||
\(884\) | 7.08497 | 0.238293 | ||||||||
\(885\) | −11.2915 | −0.379560 | ||||||||
\(886\) | −70.6640 | −2.37400 | ||||||||
\(887\) | −24.0000 | −0.805841 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(888\) | 28.9373 | 0.971071 | ||||||||
\(889\) | 6.58301 | 0.220787 | ||||||||
\(890\) | 44.8118 | 1.50209 | ||||||||
\(891\) | 0.354249 | 0.0118678 | ||||||||
\(892\) | 12.9150 | 0.432427 | ||||||||
\(893\) | 1.29150 | 0.0432185 | ||||||||
\(894\) | −54.4575 | −1.82133 | ||||||||
\(895\) | −7.29150 | −0.243728 | ||||||||
\(896\) | −13.0627 | −0.436396 | ||||||||
\(897\) | 3.29150 | 0.109900 | ||||||||
\(898\) | 95.8523 | 3.19863 | ||||||||
\(899\) | 53.6235 | 1.78844 | ||||||||
\(900\) | 5.00000 | 0.166667 | ||||||||
\(901\) | −45.1660 | −1.50470 | ||||||||
\(902\) | 9.04052 | 0.301016 | ||||||||
\(903\) | −9.29150 | −0.309202 | ||||||||
\(904\) | 31.7490 | 1.05596 | ||||||||
\(905\) | 17.2915 | 0.574789 | ||||||||
\(906\) | −22.7085 | −0.754439 | ||||||||
\(907\) | −47.0405 | −1.56195 | −0.780977 | − | 0.624559i | \(-0.785279\pi\) | ||||
−0.780977 | + | 0.624559i | \(0.785279\pi\) | |||||||
\(908\) | −53.5425 | −1.77687 | ||||||||
\(909\) | 9.29150 | 0.308180 | ||||||||
\(910\) | 1.54249 | 0.0511329 | ||||||||
\(911\) | 26.5830 | 0.880734 | 0.440367 | − | 0.897818i | \(-0.354848\pi\) | ||||
0.440367 | + | 0.897818i | \(0.354848\pi\) | |||||||
\(912\) | 11.0000 | 0.364246 | ||||||||
\(913\) | 2.12549 | 0.0703435 | ||||||||
\(914\) | −0.332021 | −0.0109823 | ||||||||
\(915\) | 11.2915 | 0.373286 | ||||||||
\(916\) | 43.5425 | 1.43868 | ||||||||
\(917\) | −23.4170 | −0.773297 | ||||||||
\(918\) | −10.5830 | −0.349291 | ||||||||
\(919\) | 14.8340 | 0.489328 | 0.244664 | − | 0.969608i | \(-0.421322\pi\) | ||||
0.244664 | + | 0.969608i | \(0.421322\pi\) | |||||||
\(920\) | −73.7490 | −2.43143 | ||||||||
\(921\) | 24.4575 | 0.805902 | ||||||||
\(922\) | 99.8745 | 3.28919 | ||||||||
\(923\) | −2.58301 | −0.0850207 | ||||||||
\(924\) | −2.91503 | −0.0958973 | ||||||||
\(925\) | 3.64575 | 0.119872 | ||||||||
\(926\) | 93.9778 | 3.08830 | ||||||||
\(927\) | −10.5830 | −0.347591 | ||||||||
\(928\) | −118.229 | −3.88105 | ||||||||
\(929\) | −11.8745 | −0.389590 | −0.194795 | − | 0.980844i | \(-0.562404\pi\) | ||||
−0.194795 | + | 0.980844i | \(0.562404\pi\) | |||||||
\(930\) | 15.8745 | 0.520546 | ||||||||
\(931\) | 4.29150 | 0.140648 | ||||||||
\(932\) | −90.0000 | −2.94805 | ||||||||
\(933\) | −22.9373 | −0.750932 | ||||||||
\(934\) | −52.5830 | −1.72057 | ||||||||
\(935\) | −1.41699 | −0.0463407 | ||||||||
\(936\) | 2.81176 | 0.0919053 | ||||||||
\(937\) | 20.1255 | 0.657471 | 0.328736 | − | 0.944422i | \(-0.393378\pi\) | ||||
0.328736 | + | 0.944422i | \(0.393378\pi\) | |||||||
\(938\) | 28.6640 | 0.935914 | ||||||||
\(939\) | −17.2915 | −0.564287 | ||||||||
\(940\) | −6.45751 | −0.210621 | ||||||||
\(941\) | −11.7712 | −0.383732 | −0.191866 | − | 0.981421i | \(-0.561454\pi\) | ||||
−0.191866 | + | 0.981421i | \(0.561454\pi\) | |||||||
\(942\) | −35.1660 | −1.14577 | ||||||||
\(943\) | −89.6235 | −2.91854 | ||||||||
\(944\) | 124.207 | 4.04258 | ||||||||
\(945\) | −1.64575 | −0.0535363 | ||||||||
\(946\) | −5.29150 | −0.172042 | ||||||||
\(947\) | 11.4170 | 0.371002 | 0.185501 | − | 0.982644i | \(-0.440609\pi\) | ||||
0.185501 | + | 0.982644i | \(0.440609\pi\) | |||||||
\(948\) | −32.9150 | −1.06903 | ||||||||
\(949\) | −3.54249 | −0.114994 | ||||||||
\(950\) | 2.64575 | 0.0858395 | ||||||||
\(951\) | −20.4575 | −0.663380 | ||||||||
\(952\) | 52.2510 | 1.69346 | ||||||||
\(953\) | −10.5830 | −0.342817 | −0.171409 | − | 0.985200i | \(-0.554832\pi\) | ||||
−0.171409 | + | 0.985200i | \(0.554832\pi\) | |||||||
\(954\) | −29.8745 | −0.967223 | ||||||||
\(955\) | 6.22876 | 0.201558 | ||||||||
\(956\) | 78.2288 | 2.53010 | ||||||||
\(957\) | −3.16601 | −0.102343 | ||||||||
\(958\) | −11.5203 | −0.372203 | ||||||||
\(959\) | 9.87451 | 0.318864 | ||||||||
\(960\) | −13.0000 | −0.419573 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 3.41699 | 0.110168 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 82.9150 | 2.67051 | ||||||||
\(965\) | −11.6458 | −0.374890 | ||||||||
\(966\) | 40.4575 | 1.30170 | ||||||||
\(967\) | −41.6458 | −1.33924 | −0.669619 | − | 0.742705i | \(-0.733542\pi\) | ||||
−0.669619 | + | 0.742705i | \(0.733542\pi\) | |||||||
\(968\) | 86.3137 | 2.77423 | ||||||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | 7.77124 | 0.249520 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −5.00000 | −0.160375 | ||||||||
\(973\) | 29.4170 | 0.943066 | ||||||||
\(974\) | −47.2915 | −1.51532 | ||||||||
\(975\) | 0.354249 | 0.0113450 | ||||||||
\(976\) | −124.207 | −3.97575 | ||||||||
\(977\) | −51.0405 | −1.63293 | −0.816465 | − | 0.577394i | \(-0.804070\pi\) | ||||
−0.816465 | + | 0.577394i | \(0.804070\pi\) | |||||||
\(978\) | −6.22876 | −0.199174 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | −21.4575 | −0.685435 | ||||||||
\(981\) | 5.29150 | 0.168945 | ||||||||
\(982\) | 15.2693 | 0.487262 | ||||||||
\(983\) | 34.4575 | 1.09902 | 0.549512 | − | 0.835486i | \(-0.314814\pi\) | ||||
0.549512 | + | 0.835486i | \(0.314814\pi\) | |||||||
\(984\) | −76.5608 | −2.44067 | ||||||||
\(985\) | −25.1660 | −0.801856 | ||||||||
\(986\) | 94.5830 | 3.01214 | ||||||||
\(987\) | 2.12549 | 0.0676552 | ||||||||
\(988\) | 1.77124 | 0.0563508 | ||||||||
\(989\) | 52.4575 | 1.66805 | ||||||||
\(990\) | −0.937254 | −0.0297879 | ||||||||
\(991\) | −35.7490 | −1.13560 | −0.567802 | − | 0.823165i | \(-0.692206\pi\) | ||||
−0.567802 | + | 0.823165i | \(0.692206\pi\) | |||||||
\(992\) | −79.3725 | −2.52008 | ||||||||
\(993\) | −11.4170 | −0.362307 | ||||||||
\(994\) | −31.7490 | −1.00702 | ||||||||
\(995\) | 7.29150 | 0.231156 | ||||||||
\(996\) | −30.0000 | −0.950586 | ||||||||
\(997\) | 26.7085 | 0.845867 | 0.422933 | − | 0.906161i | \(-0.361000\pi\) | ||||
0.422933 | + | 0.906161i | \(0.361000\pi\) | |||||||
\(998\) | 82.1255 | 2.59964 | ||||||||
\(999\) | −3.64575 | −0.115346 |
(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 | 285.2.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 855.2.a.g.1.2 | 2 | |||
4.3 | odd | 2 | 4560.2.a.bo.1.1 | 2 | |||
5.2 | odd | 4 | 1425.2.c.i.799.2 | 4 | |||
5.3 | odd | 4 | 1425.2.c.i.799.3 | 4 | |||
5.4 | even | 2 | 1425.2.a.p.1.2 | 2 | |||
15.14 | odd | 2 | 4275.2.a.u.1.1 | 2 | |||
19.18 | odd | 2 | 5415.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
855.2.a.g.1.2 | 2 | 3.2 | odd | 2 | |||
1425.2.a.p.1.2 | 2 | 5.4 | even | 2 | |||
1425.2.c.i.799.2 | 4 | 5.2 | odd | 4 | |||
1425.2.c.i.799.3 | 4 | 5.3 | odd | 4 | |||
4275.2.a.u.1.1 | 2 | 15.14 | odd | 2 | |||
4560.2.a.bo.1.1 | 2 | 4.3 | odd | 2 | |||
5415.2.a.s.1.2 | 2 | 19.18 | odd | 2 |