Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, 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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.61803 | −1.51152 | −0.755761 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.23607 | −0.342824 | −0.171412 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171412 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.47214 | 2.44569 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.47214 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.763932 | 0.159291 | 0.0796454 | − | 0.996823i | \(-0.474621\pi\) | ||||
0.0796454 | + | 0.996823i | \(0.474621\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.09017 | 1.61803 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.23607 | 1.34370 | 0.671852 | − | 0.740685i | \(-0.265499\pi\) | ||||
0.671852 | + | 0.740685i | \(0.265499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5623 | 1.89705 | 0.948523 | − | 0.316708i | \(-0.102578\pi\) | ||||
0.948523 | + | 0.316708i | \(0.102578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.70820 | −1.59602 | −0.798009 | − | 0.602645i | \(-0.794114\pi\) | ||||
−0.798009 | + | 0.602645i | \(0.794114\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.23607 | 0.518186 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.85410 | 1.22660 | 0.613302 | − | 0.789848i | \(-0.289841\pi\) | ||||
0.613302 | + | 0.789848i | \(0.289841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.85410 | −0.282748 | −0.141374 | − | 0.989956i | \(-0.545152\pi\) | ||||
−0.141374 | + | 0.989956i | \(0.545152\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.9443 | −2.07869 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.94427 | 1.01293 | 0.506463 | − | 0.862262i | \(-0.330953\pi\) | ||||
0.506463 | + | 0.862262i | \(0.330953\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.61803 | 0.366598 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.32624 | −0.456894 | −0.228447 | − | 0.973556i | \(-0.573365\pi\) | ||||
−0.228447 | + | 0.973556i | \(0.573365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.9443 | 2.24432 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.763932 | −0.0994555 | −0.0497277 | − | 0.998763i | \(-0.515835\pi\) | ||||
−0.0497277 | + | 0.998763i | \(0.515835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.56231 | 0.968254 | 0.484127 | − | 0.874998i | \(-0.339137\pi\) | ||||
0.484127 | + | 0.874998i | \(0.339137\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47214 | 0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.09017 | 0.744033 | 0.372016 | − | 0.928226i | \(-0.378667\pi\) | ||||
0.372016 | + | 0.928226i | \(0.378667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.23607 | −1.09612 | −0.548060 | − | 0.836439i | \(-0.684633\pi\) | ||||
−0.548060 | + | 0.836439i | \(0.684633\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.85410 | −0.451089 | −0.225544 | − | 0.974233i | \(-0.572416\pi\) | ||||
−0.225544 | + | 0.974233i | \(0.572416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −21.1803 | −2.44569 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7082 | 1.31728 | 0.658638 | − | 0.752460i | \(-0.271133\pi\) | ||||
0.658638 | + | 0.752460i | \(0.271133\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.4721 | 1.14947 | 0.574733 | − | 0.818341i | \(-0.305106\pi\) | ||||
0.574733 | + | 0.818341i | \(0.305106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.61803 | 0.392431 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.9443 | −2.03104 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.76393 | −0.928975 | −0.464487 | − | 0.885580i | \(-0.653761\pi\) | ||||
−0.464487 | + | 0.885580i | \(0.653761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −27.6525 | −2.86743 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.4164 | 2.40247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.85410 | 0.289790 | 0.144895 | − | 0.989447i | \(-0.453716\pi\) | ||||
0.144895 | + | 0.989447i | \(0.453716\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.52786 | −0.749050 | −0.374525 | − | 0.927217i | \(-0.622194\pi\) | ||||
−0.374525 | + | 0.927217i | \(0.622194\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1803 | 1.16666 | 0.583332 | − | 0.812233i | \(-0.301748\pi\) | ||||
0.583332 | + | 0.812233i | \(0.301748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.4164 | 2.41242 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9443 | 1.21769 | 0.608847 | − | 0.793287i | \(-0.291632\pi\) | ||||
0.608847 | + | 0.793287i | \(0.291632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.76393 | −0.257738 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.76393 | −0.440426 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −20.5623 | −1.85404 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6180 | −1.38588 | −0.692938 | − | 0.720997i | \(-0.743684\pi\) | ||||
−0.692938 | + | 0.720997i | \(0.743684\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.85410 | 0.427380 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.47214 | −0.565473 | −0.282737 | − | 0.959198i | \(-0.591242\pi\) | ||||
−0.282737 | + | 0.959198i | \(0.591242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.09017 | 0.696291 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.0902 | 0.947497 | 0.473749 | − | 0.880660i | \(-0.342901\pi\) | ||||
0.473749 | + | 0.880660i | \(0.342901\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.6180 | 1.15507 | 0.577533 | − | 0.816367i | \(-0.304015\pi\) | ||||
0.577533 | + | 0.816367i | \(0.304015\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.1803 | −1.53106 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.1803 | −2.17416 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.38197 | −0.277061 | −0.138531 | − | 0.990358i | \(-0.544238\pi\) | ||||
−0.138531 | + | 0.990358i | \(0.544238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2705 | −1.73097 | −0.865485 | − | 0.500935i | \(-0.832989\pi\) | ||||
−0.865485 | + | 0.500935i | \(0.832989\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.85410 | −0.311586 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −38.2148 | −3.06949 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.7082 | −1.89212 | −0.946060 | − | 0.323991i | \(-0.894975\pi\) | ||||
−0.946060 | + | 0.323991i | \(0.894975\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.70820 | 0.690605 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00000 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.437694 | 0.0338698 | 0.0169349 | − | 0.999857i | \(-0.494609\pi\) | ||||
0.0169349 | + | 0.999857i | \(0.494609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.9443 | −1.90754 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.3262 | −1.69743 | −0.848716 | − | 0.528849i | \(-0.822624\pi\) | ||||
−0.848716 | + | 0.528849i | \(0.822624\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00000 | 0.150329 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.09017 | −0.230970 | −0.115485 | − | 0.993309i | \(-0.536842\pi\) | ||||
−0.115485 | + | 0.993309i | \(0.536842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.7984 | −1.46354 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 35.1246 | 2.58241 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.0902 | 1.59839 | 0.799194 | − | 0.601073i | \(-0.205260\pi\) | ||||
0.799194 | + | 0.601073i | \(0.205260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.52786 | −0.397904 | −0.198952 | − | 0.980009i | \(-0.563754\pi\) | ||||
−0.198952 | + | 0.980009i | \(0.563754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.7082 | −0.838442 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.7082 | −1.11916 | −0.559582 | − | 0.828775i | \(-0.689038\pi\) | ||||
−0.559582 | + | 0.828775i | \(0.689038\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1459 | −0.861000 | −0.430500 | − | 0.902591i | \(-0.641663\pi\) | ||||
−0.430500 | + | 0.902591i | \(0.641663\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.9443 | −1.12462 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.4164 | −1.98469 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.94427 | 0.204641 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5967 | 1.62447 | 0.812234 | − | 0.583332i | \(-0.198251\pi\) | ||||
0.812234 | + | 0.583332i | \(0.198251\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.1803 | 1.65681 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.70820 | 0.457496 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.0902 | 0.681830 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.23607 | 0.0831469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.8885 | −1.06398 | −0.531988 | − | 0.846752i | \(-0.678555\pi\) | ||||
−0.531988 | + | 0.846752i | \(0.678555\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 31.1803 | 2.07869 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.14590 | 0.474290 | 0.237145 | − | 0.971474i | \(-0.423788\pi\) | ||||
0.237145 | + | 0.971474i | \(0.423788\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4164 | 1.15091 | 0.575454 | − | 0.817834i | \(-0.304825\pi\) | ||||
0.575454 | + | 0.817834i | \(0.304825\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.18034 | −0.142839 | −0.0714194 | − | 0.997446i | \(-0.522753\pi\) | ||||
−0.0714194 | + | 0.997446i | \(0.522753\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.1246 | −1.63895 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.6525 | −1.99109 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3820 | −1.25372 | −0.626858 | − | 0.779134i | \(-0.715659\pi\) | ||||
−0.626858 | + | 0.779134i | \(0.715659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.61803 | −0.233058 | −0.116529 | − | 0.993187i | \(-0.537177\pi\) | ||||
−0.116529 | + | 0.993187i | \(0.537177\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.00000 | 0.509028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.4164 | −1.73744 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.1803 | 1.27377 | 0.636886 | − | 0.770958i | \(-0.280222\pi\) | ||||
0.636886 | + | 0.770958i | \(0.280222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.47214 | −0.593168 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.52786 | −0.0953055 | −0.0476528 | − | 0.998864i | \(-0.515174\pi\) | ||||
−0.0476528 | + | 0.998864i | \(0.515174\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.8885 | 1.72626 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.4164 | 1.19727 | 0.598633 | − | 0.801023i | \(-0.295711\pi\) | ||||
0.598633 | + | 0.801023i | \(0.295711\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0344 | 0.739270 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.9443 | 1.40417 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4164 | −0.818013 | −0.409006 | − | 0.912532i | \(-0.634125\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4721 | 1.24359 | 0.621797 | − | 0.783179i | \(-0.286403\pi\) | ||||
0.621797 | + | 0.783179i | \(0.286403\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.1246 | −1.87010 | −0.935048 | − | 0.354520i | \(-0.884644\pi\) | ||||
−0.935048 | + | 0.354520i | \(0.884644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 40.7082 | 2.43714 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.5066 | −1.40228 | −0.701142 | − | 0.713021i | \(-0.747326\pi\) | ||||
−0.701142 | + | 0.713021i | \(0.747326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.1459 | −1.13811 | −0.569053 | − | 0.822301i | \(-0.692690\pi\) | ||||
−0.569053 | + | 0.822301i | \(0.692690\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −61.3050 | −3.63139 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.47214 | −0.438024 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.5967 | 1.61222 | 0.806110 | − | 0.591766i | \(-0.201569\pi\) | ||||
0.806110 | + | 0.591766i | \(0.201569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.76393 | 0.160922 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.944272 | −0.0546087 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.7082 | 1.13221 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.3607 | −1.56667 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.41641 | 0.537423 | 0.268711 | − | 0.963221i | \(-0.413402\pi\) | ||||
0.268711 | + | 0.963221i | \(0.413402\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.7082 | 0.893609 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.7426 | 1.74326 | 0.871628 | − | 0.490168i | \(-0.163065\pi\) | ||||
0.871628 | + | 0.490168i | \(0.163065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.1459 | −0.969143 | −0.484572 | − | 0.874752i | \(-0.661025\pi\) | ||||
−0.484572 | + | 0.874752i | \(0.661025\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.8885 | 1.34171 | 0.670857 | − | 0.741587i | \(-0.265926\pi\) | ||||
0.670857 | + | 0.741587i | \(0.265926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.47214 | 0.360119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.0000 | −0.554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −31.8885 | −1.76344 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.3262 | 0.732476 | 0.366238 | − | 0.930521i | \(-0.380646\pi\) | ||||
0.366238 | + | 0.930521i | \(0.380646\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −37.4164 | −2.05041 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.0344 | −1.20387 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4164 | −0.730838 | −0.365419 | − | 0.930843i | \(-0.619074\pi\) | ||||
−0.365419 | + | 0.930843i | \(0.619074\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −33.8885 | −1.84057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.23607 | 0.389577 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.8885 | 1.38977 | 0.694885 | − | 0.719121i | \(-0.255455\pi\) | ||||
0.694885 | + | 0.719121i | \(0.255455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.47214 | −0.453503 | −0.226752 | − | 0.973953i | \(-0.572811\pi\) | ||||
−0.226752 | + | 0.973953i | \(0.572811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.76393 | 0.147528 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.0689 | −1.81330 | −0.906652 | − | 0.421880i | \(-0.861370\pi\) | ||||
−0.906652 | + | 0.421880i | \(0.861370\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.4164 | 1.77356 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.8541 | 0.572858 | 0.286429 | − | 0.958102i | \(-0.407532\pi\) | ||||
0.286429 | + | 0.958102i | \(0.407532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.7984 | 1.51152 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.9443 | 0.729877 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.3820 | 0.698533 | 0.349266 | − | 0.937023i | \(-0.386431\pi\) | ||||
0.349266 | + | 0.937023i | \(0.386431\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.2705 | 1.57582 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.5066 | −1.57957 | −0.789785 | − | 0.613383i | \(-0.789808\pi\) | ||||
−0.789785 | + | 0.613383i | \(0.789808\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.2705 | 1.51152 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.94427 | −0.460653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.12461 | −0.468700 | −0.234350 | − | 0.972152i | \(-0.575296\pi\) | ||||
−0.234350 | + | 0.972152i | \(0.575296\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 40.8885 | 2.09478 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.88854 | 0.505281 | 0.252640 | − | 0.967560i | \(-0.418701\pi\) | ||||
0.252640 | + | 0.967560i | \(0.418701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.14590 | −0.363246 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.5066 | 1.39464 | 0.697319 | − | 0.716761i | \(-0.254376\pi\) | ||||
0.697319 | + | 0.716761i | \(0.254376\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.763932 | −0.0386337 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.9443 | 0.854725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −42.3607 | −2.13140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.3262 | 0.869579 | 0.434789 | − | 0.900532i | \(-0.356823\pi\) | ||||
0.434789 | + | 0.900532i | \(0.356823\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.0557 | 0.552097 | 0.276048 | − | 0.961144i | \(-0.410975\pi\) | ||||
0.276048 | + | 0.961144i | \(0.410975\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0557 | −0.650352 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.6525 | 1.02623 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | −0.791149 | −0.395575 | − | 0.918434i | \(-0.629455\pi\) | ||||
−0.395575 | + | 0.918434i | \(0.629455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.0344 | −1.43216 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.8885 | −1.85988 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.6525 | −1.74591 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.5066 | −1.73461 | −0.867305 | − | 0.497777i | \(-0.834150\pi\) | ||||
−0.867305 | + | 0.497777i | \(0.834150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.1459 | −0.494481 | −0.247240 | − | 0.968954i | \(-0.579524\pi\) | ||||
−0.247240 | + | 0.968954i | \(0.579524\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.7639 | 1.30131 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.09017 | −0.392431 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.94427 | −0.141821 | −0.0709103 | − | 0.997483i | \(-0.522590\pi\) | ||||
−0.0709103 | + | 0.997483i | \(0.522590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 68.5410 | 3.28629 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.94427 | −0.236517 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.1459 | 0.770602 | 0.385301 | − | 0.922791i | \(-0.374098\pi\) | ||||
0.385301 | + | 0.922791i | \(0.374098\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.05573 | −0.335228 | −0.167614 | − | 0.985853i | \(-0.553606\pi\) | ||||
−0.167614 | + | 0.985853i | \(0.553606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.7082 | 1.50311 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.85410 | 0.418785 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.944272 | 0.0445629 | 0.0222815 | − | 0.999752i | \(-0.492907\pi\) | ||||
0.0222815 | + | 0.999752i | \(0.492907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 55.6869 | 2.61640 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2705 | 0.573990 | 0.286995 | − | 0.957932i | \(-0.407344\pi\) | ||||
0.286995 | + | 0.957932i | \(0.407344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.23607 | 0.104371 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.8328 | 1.24973 | 0.624864 | − | 0.780733i | \(-0.285154\pi\) | ||||
0.624864 | + | 0.780733i | \(0.285154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.79837 | −0.130051 | −0.0650257 | − | 0.997884i | \(-0.520713\pi\) | ||||
−0.0650257 | + | 0.997884i | \(0.520713\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 100.048 | 4.63960 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.7639 | 1.33104 | 0.665518 | − | 0.746382i | \(-0.268211\pi\) | ||||
0.665518 | + | 0.746382i | \(0.268211\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62.0689 | 2.85998 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −52.3607 | −2.40247 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.8197 | −0.586972 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.6180 | 0.485150 | 0.242575 | − | 0.970133i | \(-0.422008\pi\) | ||||
0.242575 | + | 0.970133i | \(0.422008\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | 0.547153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.3262 | −0.468890 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0557 | 0.863497 | 0.431749 | − | 0.901994i | \(-0.357897\pi\) | ||||
0.431749 | + | 0.901994i | \(0.357897\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.7082 | 0.710350 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.7984 | −1.79608 | −0.898038 | − | 0.439918i | \(-0.855007\pi\) | ||||
−0.898038 | + | 0.439918i | \(0.855007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.23607 | −0.325896 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.3050 | −1.58047 | −0.790233 | − | 0.612806i | \(-0.790041\pi\) | ||||
−0.790233 | + | 0.612806i | \(0.790041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.14590 | −0.0511949 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.2705 | −0.547115 | −0.273557 | − | 0.961856i | \(-0.588200\pi\) | ||||
−0.273557 | + | 0.961856i | \(0.588200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.2361 | 1.21199 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.0344 | 1.33388 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.2361 | 1.02992 | 0.514960 | − | 0.857214i | \(-0.327807\pi\) | ||||
0.514960 | + | 0.857214i | \(0.327807\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.4721 | 0.638960 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.7082 | 0.956578 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 58.4508 | 2.56571 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0902 | 0.573491 | 0.286745 | − | 0.958007i | \(-0.407427\pi\) | ||||
0.286745 | + | 0.958007i | \(0.407427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.34752 | 0.321285 | 0.160642 | − | 0.987013i | \(-0.448643\pi\) | ||||
0.160642 | + | 0.987013i | \(0.448643\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.5623 | −0.460101 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4164 | −0.974626 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.94427 | −0.127771 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.70820 | −0.420509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.09017 | 0.349117 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.6525 | 1.57291 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.0689 | −1.88770 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.1246 | −0.561168 | −0.280584 | − | 0.959829i | \(-0.590528\pi\) | ||||
−0.280584 | + | 0.959829i | \(0.590528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.1459 | 1.24392 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.8328 | −1.99515 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −91.9574 | −3.90338 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.4721 | 1.03692 | 0.518459 | − | 0.855103i | \(-0.326506\pi\) | ||||
0.518459 | + | 0.855103i | \(0.326506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.29180 | 0.0969326 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.1246 | 0.721716 | 0.360858 | − | 0.932621i | \(-0.382484\pi\) | ||||
0.360858 | + | 0.932621i | \(0.382484\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −46.8328 | −1.97027 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.09017 | 0.297235 | 0.148618 | − | 0.988895i | \(-0.452518\pi\) | ||||
0.148618 | + | 0.988895i | \(0.452518\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.6525 | 1.19907 | 0.599534 | − | 0.800349i | \(-0.295352\pi\) | ||||
0.599534 | + | 0.800349i | \(0.295352\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −57.8328 | −2.41600 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.18034 | 0.257738 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.4164 | −1.89071 | −0.945355 | − | 0.326043i | \(-0.894285\pi\) | ||||
−0.945355 | + | 0.326043i | \(0.894285\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.4721 | 0.601441 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.2361 | 0.712624 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.0000 | 1.23823 | 0.619116 | − | 0.785299i | \(-0.287491\pi\) | ||||
0.619116 | + | 0.785299i | \(0.287491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −68.3607 | −2.81675 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.1246 | 1.69164 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.5967 | −1.21539 | −0.607696 | − | 0.794169i | \(-0.707906\pi\) | ||||
−0.607696 | + | 0.794169i | \(0.707906\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.7984 | 1.30142 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0344 | −0.491714 | −0.245857 | − | 0.969306i | \(-0.579069\pi\) | ||||
−0.245857 | + | 0.969306i | \(0.579069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.5279 | −0.959722 | −0.479861 | − | 0.877345i | \(-0.659313\pi\) | ||||
−0.479861 | + | 0.877345i | \(0.659313\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.4721 | 0.955859 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 39.7984 | 1.61803 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.8541 | 1.00880 | 0.504398 | − | 0.863471i | \(-0.331714\pi\) | ||||
0.504398 | + | 0.863471i | \(0.331714\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.58359 | −0.347255 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.854102 | −0.0344969 | −0.0172484 | − | 0.999851i | \(-0.505491\pi\) | ||||
−0.0172484 | + | 0.999851i | \(0.505491\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 74.3951 | 2.99990 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.5967 | 1.83566 | 0.917828 | − | 0.396978i | \(-0.129941\pi\) | ||||
0.917828 | + | 0.396978i | \(0.129941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.8328 | −1.88237 | −0.941185 | − | 0.337892i | \(-0.890286\pi\) | ||||
−0.941185 | + | 0.337892i | \(0.890286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.70820 | −0.0685479 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.70820 | 0.387091 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9787 | 0.636103 | 0.318051 | − | 0.948074i | \(-0.396972\pi\) | ||||
0.318051 | + | 0.948074i | \(0.396972\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −61.7771 | −2.45542 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 56.5066 | 2.24240 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −35.5967 | −1.40819 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.7771 | 1.65010 | 0.825048 | − | 0.565063i | \(-0.191148\pi\) | ||||
0.825048 | + | 0.565063i | \(0.191148\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.3820 | −1.15871 | −0.579356 | − | 0.815075i | \(-0.696696\pi\) | ||||
−0.579356 | + | 0.815075i | \(0.696696\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.5623 | −0.691515 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.5967 | −1.08494 | −0.542470 | − | 0.840075i | \(-0.682511\pi\) | ||||
−0.542470 | + | 0.840075i | \(0.682511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.2361 | −0.987564 | −0.493782 | − | 0.869586i | \(-0.664386\pi\) | ||||
−0.493782 | + | 0.869586i | \(0.664386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.4164 | 0.914955 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.8541 | −0.579514 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.90983 | −0.386032 | −0.193016 | − | 0.981196i | \(-0.561827\pi\) | ||||
−0.193016 | + | 0.981196i | \(0.561827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.58359 | 0.178281 | 0.0891405 | − | 0.996019i | \(-0.471588\pi\) | ||||
0.0891405 | + | 0.996019i | \(0.471588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.23607 | −0.125678 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.52786 | 0.214040 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 41.5967 | 1.60822 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.944272 | 0.0363990 | 0.0181995 | − | 0.999834i | \(-0.494207\pi\) | ||||
0.0181995 | + | 0.999834i | \(0.494207\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.0902 | −0.696291 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.8328 | 0.800670 | 0.400335 | − | 0.916369i | \(-0.368894\pi\) | ||||
0.400335 | + | 0.916369i | \(0.368894\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.7082 | −0.716900 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.8885 | −1.75588 | −0.877938 | − | 0.478774i | \(-0.841081\pi\) | ||||
−0.877938 | + | 0.478774i | \(0.841081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.1246 | −1.53308 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −45.5967 | −1.73962 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.11146 | 0.156634 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.9787 | −0.417650 | −0.208825 | − | 0.977953i | \(-0.566964\pi\) | ||||
−0.208825 | + | 0.977953i | \(0.566964\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −49.2705 | −1.86894 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.85410 | −0.297495 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.70820 | 0.215904 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.3050 | −0.880216 | −0.440108 | − | 0.897945i | \(-0.645060\pi\) | ||||
−0.440108 | + | 0.897945i | \(0.645060\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 62.8328 | 2.36978 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 65.7771 | 2.47731 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.65248 | −0.0996158 | −0.0498079 | − | 0.998759i | \(-0.515861\pi\) | ||||
−0.0498079 | + | 0.998759i | \(0.515861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 45.1246 | 1.69231 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.06888 | 0.302182 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 50.7426 | 1.89502 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.9098 | 0.406868 | 0.203434 | − | 0.979089i | \(-0.434790\pi\) | ||||
0.203434 | + | 0.979089i | \(0.434790\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.47214 | 0.352273 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 58.5410 | 2.17416 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.7082 | 0.508409 | 0.254205 | − | 0.967150i | \(-0.418186\pi\) | ||||
0.254205 | + | 0.967150i | \(0.418186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.85410 | 0.0685764 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.2492 | −1.70825 | −0.854127 | − | 0.520064i | \(-0.825908\pi\) | ||||
−0.854127 | + | 0.520064i | \(0.825908\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.38197 | 0.271550 | 0.135775 | − | 0.990740i | \(-0.456648\pi\) | ||||
0.135775 | + | 0.990740i | \(0.456648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.9443 | −0.769407 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.111456 | 0.00408893 | 0.00204447 | − | 0.999998i | \(-0.499349\pi\) | ||||
0.00204447 | + | 0.999998i | \(0.499349\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2361 | 0.448295 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.3607 | 1.47672 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.8328 | 1.85492 | 0.927458 | − | 0.373928i | \(-0.121989\pi\) | ||||
0.927458 | + | 0.373928i | \(0.121989\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −52.8328 | −1.92533 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 76.9574 | 2.80077 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.56231 | −0.202165 | −0.101083 | − | 0.994878i | \(-0.532231\pi\) | ||||
−0.101083 | + | 0.994878i | \(0.532231\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.1115 | −0.656540 | −0.328270 | − | 0.944584i | \(-0.606466\pi\) | ||||
−0.328270 | + | 0.944584i | \(0.606466\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.9443 | 0.504156 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.944272 | 0.0340957 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.5967 | −1.28365 | −0.641826 | − | 0.766850i | \(-0.721823\pi\) | ||||
−0.641826 | + | 0.766850i | \(0.721823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.00000 | 0.144056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.5279 | 0.414628 | 0.207314 | − | 0.978274i | \(-0.433528\pi\) | ||||
0.207314 | + | 0.978274i | \(0.433528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 85.4508 | 3.06949 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −50.8328 | −1.82127 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.1803 | −0.578238 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 85.7771 | 3.06152 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.00000 | −0.285169 | −0.142585 | − | 0.989783i | \(-0.545541\pi\) | ||||
−0.142585 | + | 0.989783i | \(0.545541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −50.8328 | −1.80970 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.34752 | −0.331940 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −31.5066 | −1.11742 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.0000 | −0.425062 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.94427 | −0.245671 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.7771 | −1.19345 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.1246 | 1.23644 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.1246 | −1.44586 | −0.722932 | − | 0.690919i | \(-0.757206\pi\) | ||||
−0.722932 | + | 0.690919i | \(0.757206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.9787 | 0.525974 | 0.262987 | − | 0.964799i | \(-0.415292\pi\) | ||||
0.262987 | + | 0.964799i | \(0.415292\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −53.5967 | −1.87972 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.7082 | 0.760405 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | 0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.5279 | 1.30973 | 0.654866 | − | 0.755745i | \(-0.272725\pi\) | ||||
0.654866 | + | 0.755745i | \(0.272725\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.5410 | −1.48289 | −0.741443 | − | 0.671015i | \(-0.765858\pi\) | ||||
−0.741443 | + | 0.671015i | \(0.765858\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.7639 | −1.27841 | −0.639204 | − | 0.769038i | \(-0.720736\pi\) | ||||
−0.639204 | + | 0.769038i | \(0.720736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.5967 | 0.402772 | 0.201386 | − | 0.979512i | \(-0.435455\pi\) | ||||
0.201386 | + | 0.979512i | \(0.435455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 81.4853 | 2.82669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.58359 | −0.0548025 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.6180 | −0.816359 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.9443 | 1.13736 | 0.568681 | − | 0.822558i | \(-0.307454\pi\) | ||||
0.568681 | + | 0.822558i | \(0.307454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.3607 | 0.805541 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 61.5410 | 2.11959 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.5066 | 1.42787 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50.1246 | 1.72027 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.41641 | −0.254231 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.7771 | 0.882591 | 0.441295 | − | 0.897362i | \(-0.354519\pi\) | ||||
0.441295 | + | 0.897362i | \(0.354519\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 90.2492 | 3.08646 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.2016 | 0.690074 | 0.345037 | − | 0.938589i | \(-0.387866\pi\) | ||||
0.345037 | + | 0.938589i | \(0.387866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.8328 | −0.574328 | −0.287164 | − | 0.957881i | \(-0.592713\pi\) | ||||
−0.287164 | + | 0.957881i | \(0.592713\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.6738 | −0.363339 | −0.181670 | − | 0.983360i | \(-0.558150\pi\) | ||||
−0.181670 | + | 0.983360i | \(0.558150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 80.7771 | 2.74650 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.61803 | −0.0889131 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.52786 | −0.255072 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.0000 | 0.372294 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.3050 | 1.52984 | 0.764920 | − | 0.644126i | \(-0.222779\pi\) | ||||
0.764920 | + | 0.644126i | \(0.222779\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −72.2492 | −2.43691 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.1591 | −1.62252 | −0.811260 | − | 0.584686i | \(-0.801218\pi\) | ||||
−0.811260 | + | 0.584686i | \(0.801218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.6869 | 1.53749 | 0.768744 | − | 0.639557i | \(-0.220882\pi\) | ||||
0.768744 | + | 0.639557i | \(0.220882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.23607 | −0.243238 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.7426 | −1.03224 | −0.516119 | − | 0.856517i | \(-0.672624\pi\) | ||||
−0.516119 | + | 0.856517i | \(0.672624\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −44.9443 | −1.50400 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1803 | 0.373718 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.47214 | 0.0825422 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 76.4296 | 2.54907 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.32624 | 0.110813 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.6525 | 1.68375 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.8197 | −0.458874 | −0.229437 | − | 0.973323i | \(-0.573689\pi\) | ||||
−0.229437 | + | 0.973323i | \(0.573689\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −29.0132 | −0.962306 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.7214 | −1.28290 | −0.641448 | − | 0.767167i | \(-0.721666\pi\) | ||||
−0.641448 | + | 0.767167i | \(0.721666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 71.6312 | 2.36805 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.6869 | 1.21019 | 0.605095 | − | 0.796153i | \(-0.293135\pi\) | ||||
0.605095 | + | 0.796153i | \(0.293135\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.6525 | −0.812327 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.4164 | 0.375776 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −78.5410 | −2.58241 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.1246 | −0.759512 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.2016 | 0.662794 | 0.331397 | − | 0.943491i | \(-0.392480\pi\) | ||||
0.331397 | + | 0.943491i | \(0.392480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −80.4853 | −2.63497 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.58359 | −0.149739 | −0.0748697 | − | 0.997193i | \(-0.523854\pi\) | ||||
−0.0748697 | + | 0.997193i | \(0.523854\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.8885 | 1.46488 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.2016 | 0.625955 | 0.312978 | − | 0.949761i | \(-0.398674\pi\) | ||||
0.312978 | + | 0.949761i | \(0.398674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | 0.195387 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.1935 | −1.33861 | −0.669304 | − | 0.742988i | \(-0.733408\pi\) | ||||
−0.669304 | + | 0.742988i | \(0.733408\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.76393 | 0.154644 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −62.5410 | −2.02803 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.9098 | −0.644943 | −0.322471 | − | 0.946579i | \(-0.604514\pi\) | ||||
−0.322471 | + | 0.946579i | \(0.604514\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −79.9230 | −2.58625 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 80.5623 | 2.59878 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.0000 | 0.643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.9098 | −0.801046 | −0.400523 | − | 0.916287i | \(-0.631172\pi\) | ||||
−0.400523 | + | 0.916287i | \(0.631172\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.9443 | −0.544328 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.7639 | −0.730529 | −0.365265 | − | 0.930904i | \(-0.619022\pi\) | ||||
−0.365265 | + | 0.930904i | \(0.619022\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.1803 | 0.838442 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.4508 | −1.16617 | −0.583083 | − | 0.812413i | \(-0.698154\pi\) | ||||
−0.583083 | + | 0.812413i | \(0.698154\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.9443 | 1.49882 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.270510 | −0.00862792 | −0.00431396 | − | 0.999991i | \(-0.501373\pi\) | ||||
−0.00431396 | + | 0.999991i | \(0.501373\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 56.8328 | 1.81084 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.41641 | −0.0450391 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.54102 | 0.271314 | 0.135657 | − | 0.990756i | \(-0.456685\pi\) | ||||
0.135657 | + | 0.990756i | \(0.456685\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.8885 | −1.10715 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.9443 | 1.39313 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.7426 | −0.941959 | −0.470980 | − | 0.882144i | \(-0.656099\pi\) | ||||
−0.470980 | + | 0.882144i | \(0.656099\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.7082 | 0.686817 |
(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 | 3332.2.a.g.1.1 | ✓ | 2 | |
7.6 | odd | 2 | 3332.2.a.o.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3332.2.a.g.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3332.2.a.o.1.2 | yes | 2 | 7.6 | odd | 2 |