Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 24x^{4} + x^{3} - 35x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.98707\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | 2.98707 | 1.72458 | 0.862292 | − | 0.506411i | \(-0.169028\pi\) | ||||
0.862292 | + | 0.506411i | \(0.169028\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.980560 | −0.370617 | −0.185308 | − | 0.982680i | \(-0.559328\pi\) | ||||
−0.185308 | + | 0.982680i | \(0.559328\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.92257 | 1.97419 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.14721 | 1.85345 | 0.926727 | − | 0.375734i | \(-0.122609\pi\) | ||||
0.926727 | + | 0.375734i | \(0.122609\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.37400 | 1.76783 | 0.883914 | − | 0.467649i | \(-0.154899\pi\) | ||||
0.883914 | + | 0.467649i | \(0.154899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.36098 | −0.815157 | −0.407579 | − | 0.913170i | \(-0.633627\pi\) | ||||
−0.407579 | + | 0.913170i | \(0.633627\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.08276 | −0.248403 | −0.124202 | − | 0.992257i | \(-0.539637\pi\) | ||||
−0.124202 | + | 0.992257i | \(0.539637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.92900 | −0.639160 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.72993 | 1.68008 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.271042 | −0.0503313 | −0.0251657 | − | 0.999683i | \(-0.508011\pi\) | ||||
−0.0251657 | + | 0.999683i | \(0.508011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.77792 | 1.57656 | 0.788280 | − | 0.615316i | \(-0.210972\pi\) | ||||
0.788280 | + | 0.615316i | \(0.210972\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.3621 | 3.19644 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.84665 | 1.45438 | 0.727190 | − | 0.686436i | \(-0.240826\pi\) | ||||
0.727190 | + | 0.686436i | \(0.240826\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.0396 | 3.04877 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.85308 | −0.757923 | −0.378962 | − | 0.925412i | \(-0.623719\pi\) | ||||
−0.378962 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.87756 | 0.286326 | 0.143163 | − | 0.989699i | \(-0.454273\pi\) | ||||
0.143163 | + | 0.989699i | \(0.454273\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.196089 | 0.0286026 | 0.0143013 | − | 0.999898i | \(-0.495448\pi\) | ||||
0.0143013 | + | 0.999898i | \(0.495448\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.03850 | −0.862643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0395 | −1.40581 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.93157 | 0.265321 | 0.132661 | − | 0.991162i | \(-0.457648\pi\) | ||||
0.132661 | + | 0.991162i | \(0.457648\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.23429 | −0.428392 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.0036 | −1.69293 | −0.846465 | − | 0.532444i | \(-0.821274\pi\) | ||||
−0.846465 | + | 0.532444i | \(0.821274\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00189 | 0.768464 | 0.384232 | − | 0.923237i | \(-0.374466\pi\) | ||||
0.384232 | + | 0.923237i | \(0.374466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.80744 | −0.731668 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.26847 | 0.277138 | 0.138569 | − | 0.990353i | \(-0.455750\pi\) | ||||
0.138569 | + | 0.990353i | \(0.455750\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.98707 | −0.359601 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2677 | −1.21855 | −0.609277 | − | 0.792958i | \(-0.708540\pi\) | ||||
−0.609277 | + | 0.792958i | \(0.708540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.38188 | −0.161737 | −0.0808685 | − | 0.996725i | \(-0.525769\pi\) | ||||
−0.0808685 | + | 0.996725i | \(0.525769\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.02771 | −0.686921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.67459 | 0.525932 | 0.262966 | − | 0.964805i | \(-0.415299\pi\) | ||||
0.262966 | + | 0.964805i | \(0.415299\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.30917 | 0.923241 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7171 | −1.72517 | −0.862587 | − | 0.505909i | \(-0.831157\pi\) | ||||
−0.862587 | + | 0.505909i | \(0.831157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.809622 | −0.0868006 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.1548 | −1.18241 | −0.591206 | − | 0.806521i | \(-0.701348\pi\) | ||||
−0.591206 | + | 0.806521i | \(0.701348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.25008 | −0.655187 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.2202 | 2.71891 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2868 | 1.04447 | 0.522234 | − | 0.852802i | \(-0.325099\pi\) | ||||
0.522234 | + | 0.852802i | \(0.325099\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 36.4073 | 3.65908 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.2625 | −1.51868 | −0.759339 | − | 0.650695i | \(-0.774478\pi\) | ||||
−0.759339 | + | 0.650695i | \(0.774478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.60795 | −0.749634 | −0.374817 | − | 0.927099i | \(-0.622294\pi\) | ||||
−0.374817 | + | 0.927099i | \(0.622294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3081 | 1.09320 | 0.546599 | − | 0.837395i | \(-0.315922\pi\) | ||||
0.546599 | + | 0.837395i | \(0.315922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.45336 | 0.330772 | 0.165386 | − | 0.986229i | \(-0.447113\pi\) | ||||
0.165386 | + | 0.986229i | \(0.447113\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.4256 | 2.50820 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.6889 | −1.38181 | −0.690907 | − | 0.722944i | \(-0.742788\pi\) | ||||
−0.690907 | + | 0.722944i | \(0.742788\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 37.7505 | 3.49003 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.29564 | 0.302111 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.7882 | 2.43530 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.4965 | −1.30710 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.19312 | −0.105873 | −0.0529363 | − | 0.998598i | \(-0.516858\pi\) | ||||
−0.0529363 | + | 0.998598i | \(0.516858\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.60841 | 0.493793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7326 | 1.02509 | 0.512543 | − | 0.858662i | \(-0.328704\pi\) | ||||
0.512543 | + | 0.858662i | \(0.328704\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.06171 | 0.0920623 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4665 | 0.894210 | 0.447105 | − | 0.894481i | \(-0.352455\pi\) | ||||
0.447105 | + | 0.894481i | \(0.352455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.11349 | −0.348902 | −0.174451 | − | 0.984666i | \(-0.555815\pi\) | ||||
−0.174451 | + | 0.984666i | \(0.555815\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.585732 | 0.0493275 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 39.1823 | 3.27659 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.0374 | −1.48770 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.37793 | 0.112885 | 0.0564424 | − | 0.998406i | \(-0.482024\pi\) | ||||
0.0564424 | + | 0.998406i | \(0.482024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.49384 | 0.284325 | 0.142162 | − | 0.989843i | \(-0.454594\pi\) | ||||
0.142162 | + | 0.989843i | \(0.454594\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.9057 | −1.60928 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.32373 | 0.265262 | 0.132631 | − | 0.991165i | \(-0.457657\pi\) | ||||
0.132631 | + | 0.991165i | \(0.457657\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.76973 | 0.457569 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.980560 | 0.0772789 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.52075 | −0.667397 | −0.333698 | − | 0.942680i | \(-0.608297\pi\) | ||||
−0.333698 | + | 0.942680i | \(0.608297\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.6190 | 1.20864 | 0.604319 | − | 0.796742i | \(-0.293445\pi\) | ||||
0.604319 | + | 0.796742i | \(0.293445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.6278 | 2.12522 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.41275 | −0.490395 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.42727 | 0.640713 | 0.320357 | − | 0.947297i | \(-0.396197\pi\) | ||||
0.320357 | + | 0.947297i | \(0.396197\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −38.8428 | −2.91960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8047 | −0.807580 | −0.403790 | − | 0.914852i | \(-0.632307\pi\) | ||||
−0.403790 | + | 0.914852i | \(0.632307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4282 | −1.14677 | −0.573385 | − | 0.819286i | \(-0.694370\pi\) | ||||
−0.573385 | + | 0.819286i | \(0.694370\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.9281 | 1.32528 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.6607 | −1.51086 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.56022 | −0.622664 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2634 | 1.61092 | 0.805462 | − | 0.592648i | \(-0.201917\pi\) | ||||
0.805462 | + | 0.592648i | \(0.201917\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.1399 | −1.16178 | −0.580889 | − | 0.813983i | \(-0.697295\pi\) | ||||
−0.580889 | + | 0.813983i | \(0.697295\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.9936 | −0.997004 | −0.498502 | − | 0.866889i | \(-0.666116\pi\) | ||||
−0.498502 | + | 0.866889i | \(0.666116\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.91926 | 0.490493 | 0.245246 | − | 0.969461i | \(-0.421131\pi\) | ||||
0.245246 | + | 0.969461i | \(0.421131\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.77608 | 0.477948 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.265773 | 0.0186536 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.92257 | −0.411647 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.65598 | −0.460404 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.9170 | −0.889246 | −0.444623 | − | 0.895718i | \(-0.646662\pi\) | ||||
−0.444623 | + | 0.895718i | \(0.646662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −30.6704 | −2.10150 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.60728 | −0.584300 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.12777 | −0.278929 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.4229 | −1.44106 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.6579 | 1.78514 | 0.892572 | − | 0.450905i | \(-0.148899\pi\) | ||||
0.892572 | + | 0.450905i | \(0.148899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.44407 | −0.626825 | −0.313412 | − | 0.949617i | \(-0.601472\pi\) | ||||
−0.313412 | + | 0.949617i | \(0.601472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.1994 | 0.938322 | 0.469161 | − | 0.883113i | \(-0.344556\pi\) | ||||
0.469161 | + | 0.883113i | \(0.344556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.0052 | −1.18465 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.41134 | 0.616557 | 0.308279 | − | 0.951296i | \(-0.400247\pi\) | ||||
0.308279 | + | 0.951296i | \(0.400247\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.9633 | 0.907014 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4781 | 1.00119 | 0.500597 | − | 0.865680i | \(-0.333114\pi\) | ||||
0.500597 | + | 0.865680i | \(0.333114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.51052 | −0.226133 | −0.113066 | − | 0.993587i | \(-0.536067\pi\) | ||||
−0.113066 | + | 0.993587i | \(0.536067\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.36974 | −0.0878689 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.90153 | −0.439134 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −46.9480 | −2.97521 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.6649 | 1.49372 | 0.746859 | − | 0.664982i | \(-0.231561\pi\) | ||||
0.746859 | + | 0.664982i | \(0.231561\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.14721 | −0.386472 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.8326 | −1.92328 | −0.961641 | − | 0.274311i | \(-0.911550\pi\) | ||||
−0.961641 | + | 0.274311i | \(0.911550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.67467 | −0.539018 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.60527 | −0.0993636 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5880 | 1.26951 | 0.634755 | − | 0.772714i | \(-0.281101\pi\) | ||||
0.634755 | + | 0.772714i | \(0.281101\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −33.3203 | −2.03917 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.0277 | −1.03820 | −0.519099 | − | 0.854714i | \(-0.673732\pi\) | ||||
−0.519099 | + | 0.854714i | \(0.673732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6709 | −0.830450 | −0.415225 | − | 0.909719i | \(-0.636297\pi\) | ||||
−0.415225 | + | 0.909719i | \(0.636297\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.6694 | −1.12993 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2380 | −0.975647 | −0.487824 | − | 0.872942i | \(-0.662209\pi\) | ||||
−0.487824 | + | 0.872942i | \(0.662209\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 51.9879 | 3.11243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.362407 | −0.0216194 | −0.0108097 | − | 0.999942i | \(-0.503441\pi\) | ||||
−0.0108097 | + | 0.999942i | \(0.503441\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.80039 | 0.404241 | 0.202120 | − | 0.979361i | \(-0.435217\pi\) | ||||
0.202120 | + | 0.979361i | \(0.435217\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.75873 | 0.280899 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.70382 | −0.335519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.7274 | 1.80127 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.2172 | 1.53162 | 0.765812 | − | 0.643065i | \(-0.222337\pi\) | ||||
0.765812 | + | 0.643065i | \(0.222337\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 53.6647 | 3.11394 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.37400 | −0.368618 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.84106 | −0.106117 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −45.5902 | −2.61909 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.7146 | 1.12517 | 0.562587 | − | 0.826738i | \(-0.309806\pi\) | ||||
0.562587 | + | 0.826738i | \(0.309806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.7255 | −1.29281 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1003 | −0.856258 | −0.428129 | − | 0.903718i | \(-0.640827\pi\) | ||||
−0.428129 | + | 0.903718i | \(0.640827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.9813 | −0.733747 | −0.366874 | − | 0.930271i | \(-0.619572\pi\) | ||||
−0.366874 | + | 0.930271i | \(0.619572\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3503 | −0.974489 | −0.487244 | − | 0.873266i | \(-0.661998\pi\) | ||||
−0.487244 | + | 0.873266i | \(0.661998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.66616 | −0.0932868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.7781 | 1.88531 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.63915 | 0.202488 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.3154 | 0.570444 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.192277 | −0.0106006 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.984756 | −0.0541271 | −0.0270635 | − | 0.999634i | \(-0.508616\pi\) | ||||
−0.0270635 | + | 0.999634i | \(0.508616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 52.3950 | 2.87123 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.5575 | −1.28326 | −0.641629 | − | 0.767015i | \(-0.721741\pi\) | ||||
−0.641629 | + | 0.767015i | \(0.721741\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −43.8767 | −2.38305 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 53.9598 | 2.92208 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.7850 | 0.690327 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.0916 | 1.40067 | 0.700337 | − | 0.713813i | \(-0.253033\pi\) | ||||
0.700337 | + | 0.713813i | \(0.253033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.8609 | −0.956070 | −0.478035 | − | 0.878341i | \(-0.658651\pi\) | ||||
−0.478035 | + | 0.878341i | \(0.658651\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 55.6445 | 2.97009 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.1080 | 0.697667 | 0.348833 | − | 0.937185i | \(-0.386578\pi\) | ||||
0.348833 | + | 0.937185i | \(0.386578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.84430 | 0.521016 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.1119 | −1.16702 | −0.583510 | − | 0.812106i | \(-0.698321\pi\) | ||||
−0.583510 | + | 0.812106i | \(0.698321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8276 | −0.938296 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 80.0183 | 4.19987 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.98495 | 0.416811 | 0.208406 | − | 0.978043i | \(-0.433173\pi\) | ||||
0.208406 | + | 0.978043i | \(0.433173\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.7427 | −1.49629 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.89402 | −0.0983326 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.8712 | −1.23600 | −0.618002 | − | 0.786177i | \(-0.712058\pi\) | ||||
−0.618002 | + | 0.786177i | \(0.712058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.72762 | −0.0889771 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.5647 | 1.77547 | 0.887735 | − | 0.460355i | \(-0.152278\pi\) | ||||
0.887735 | + | 0.460355i | \(0.152278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.56394 | −0.182586 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.3139 | 0.629211 | 0.314606 | − | 0.949223i | \(-0.398128\pi\) | ||||
0.314606 | + | 0.949223i | \(0.398128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.1200 | 0.565262 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.0447 | −1.37122 | −0.685611 | − | 0.727968i | \(-0.740465\pi\) | ||||
−0.685611 | + | 0.727968i | \(0.740465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.36098 | 0.169972 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.0462 | 1.76785 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.07631 | 0.455527 | 0.227763 | − | 0.973717i | \(-0.426859\pi\) | ||||
0.227763 | + | 0.973717i | \(0.426859\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.17141 | 0.158769 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.73762 | 0.336461 | 0.168230 | − | 0.985748i | \(-0.446195\pi\) | ||||
0.168230 | + | 0.985748i | \(0.446195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 55.9504 | 2.78709 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 54.3823 | 2.69563 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.7205 | 1.27180 | 0.635898 | − | 0.771773i | \(-0.280630\pi\) | ||||
0.635898 | + | 0.771773i | \(0.280630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.2640 | 1.54214 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.7509 | 0.627428 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.2873 | −0.601711 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.2666 | 0.794676 | 0.397338 | − | 0.917672i | \(-0.369934\pi\) | ||||
0.397338 | + | 0.917672i | \(0.369934\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9106 | −0.921645 | −0.460822 | − | 0.887492i | \(-0.652445\pi\) | ||||
−0.460822 | + | 0.887492i | \(0.652445\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.16135 | 0.0564669 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.88522 | −0.284806 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 117.040 | 5.65076 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4086 | 0.549535 | 0.274767 | − | 0.961511i | \(-0.411399\pi\) | ||||
0.274767 | + | 0.961511i | \(0.411399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.2756 | 1.11856 | 0.559278 | − | 0.828980i | \(-0.311078\pi\) | ||||
0.559278 | + | 0.828980i | \(0.311078\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.08276 | 0.0517956 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0581 | 0.623231 | 0.311615 | − | 0.950208i | \(-0.399130\pi\) | ||||
0.311615 | + | 0.950208i | \(0.399130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.7635 | −1.70302 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.113844 | −0.00540891 | −0.00270446 | − | 0.999996i | \(-0.500861\pi\) | ||||
−0.00270446 | + | 0.999996i | \(0.500861\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.11598 | 0.194679 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.0371 | −0.520874 | −0.260437 | − | 0.965491i | \(-0.583867\pi\) | ||||
−0.260437 | + | 0.965491i | \(0.583867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.8329 | −1.40478 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.4363 | 0.490342 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.1638 | 1.41100 | 0.705501 | − | 0.708709i | \(-0.250722\pi\) | ||||
0.705501 | + | 0.708709i | \(0.250722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.3411 | −1.36953 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.3908 | −1.74146 | −0.870732 | − | 0.491759i | \(-0.836354\pi\) | ||||
−0.870732 | + | 0.491759i | \(0.836354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.7365 | −0.777810 | −0.388905 | − | 0.921278i | \(-0.627147\pi\) | ||||
−0.388905 | + | 0.921278i | \(0.627147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.2260 | −0.843399 | −0.421699 | − | 0.906736i | \(-0.638566\pi\) | ||||
−0.421699 | + | 0.906736i | \(0.638566\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.22437 | −0.102712 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.92820 | 0.457467 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.5418 | 0.530692 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.4399 | 0.523795 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.31948 | −0.151671 | −0.0758355 | − | 0.997120i | \(-0.524162\pi\) | ||||
−0.0758355 | + | 0.997120i | \(0.524162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.3885 | 2.57110 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.92900 | 0.133274 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.7412 | −0.894558 | −0.447279 | − | 0.894395i | \(-0.647607\pi\) | ||||
−0.447279 | + | 0.894395i | \(0.647607\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.4521 | −1.15098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1353 | −0.818432 | −0.409216 | − | 0.912437i | \(-0.634198\pi\) | ||||
−0.409216 | + | 0.912437i | \(0.634198\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.910968 | 0.0410279 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.0681 | 0.451616 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9797 | −0.670582 | −0.335291 | − | 0.942115i | \(-0.608835\pi\) | ||||
−0.335291 | + | 0.942115i | \(0.608835\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.6552 | 2.08440 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.90238 | 0.352350 | 0.176175 | − | 0.984359i | \(-0.443628\pi\) | ||||
0.176175 | + | 0.984359i | \(0.443628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 82.5262 | 3.66512 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.1882 | −0.939152 | −0.469576 | − | 0.882892i | \(-0.655593\pi\) | ||||
−0.469576 | + | 0.882892i | \(0.655593\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35502 | 0.0599425 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.45245 | −0.417336 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.20540 | 0.0530136 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.1728 | 1.10496 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.1210 | −0.487219 | −0.243610 | − | 0.969873i | \(-0.578332\pi\) | ||||
−0.243610 | + | 0.969873i | \(0.578332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.2670 | 0.711304 | 0.355652 | − | 0.934618i | \(-0.384259\pi\) | ||||
0.355652 | + | 0.934618i | \(0.384259\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.5024 | −1.28515 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −77.0151 | −3.34217 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.9335 | −1.33988 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −32.2743 | −1.39274 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.1200 | −1.59887 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.8797 | −0.596733 | −0.298367 | − | 0.954451i | \(-0.596442\pi\) | ||||
−0.298367 | + | 0.954451i | \(0.596442\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −46.0851 | −1.97770 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.91647 | 0.252970 | 0.126485 | − | 0.991969i | \(-0.459630\pi\) | ||||
0.126485 | + | 0.991969i | \(0.459630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.5467 | 1.51709 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.293475 | 0.0125025 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.58371 | −0.194919 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.2857 | 1.19850 | 0.599252 | − | 0.800560i | \(-0.295465\pi\) | ||||
0.599252 | + | 0.800560i | \(0.295465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.9676 | 0.506175 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −61.7148 | −2.60560 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.7025 | −1.33610 | −0.668050 | − | 0.744117i | \(-0.732871\pi\) | ||||
−0.668050 | + | 0.744117i | \(0.732871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.14763 | −0.342169 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.0702 | −1.00907 | −0.504537 | − | 0.863390i | \(-0.668337\pi\) | ||||
−0.504537 | + | 0.863390i | \(0.668337\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.3935 | −0.602349 | −0.301175 | − | 0.953569i | \(-0.597379\pi\) | ||||
−0.301175 | + | 0.953569i | \(0.597379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 66.5023 | 2.77817 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.77998 | 0.240624 | 0.120312 | − | 0.992736i | \(-0.461611\pi\) | ||||
0.120312 | + | 0.992736i | \(0.461611\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −48.2111 | −2.00358 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.4115 | 0.639378 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.8738 | 0.491761 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.7897 | 1.14700 | 0.573502 | − | 0.819204i | \(-0.305584\pi\) | ||||
0.573502 | + | 0.819204i | \(0.305584\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.50441 | −0.391623 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.7999 | −1.71942 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.1872 | 0.911118 | 0.455559 | − | 0.890205i | \(-0.349439\pi\) | ||||
0.455559 | + | 0.890205i | \(0.349439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.6683 | 0.845897 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.1380 | −0.618521 | −0.309260 | − | 0.950977i | \(-0.600081\pi\) | ||||
−0.309260 | + | 0.950977i | \(0.600081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5353 | 0.837652 | 0.418826 | − | 0.908067i | \(-0.362442\pi\) | ||||
0.418826 | + | 0.908067i | \(0.362442\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.4352 | 0.547123 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.9906 | 1.17669 | 0.588345 | − | 0.808610i | \(-0.299780\pi\) | ||||
0.588345 | + | 0.808610i | \(0.299780\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.793883 | 0.0321698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.24987 | 0.0505644 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.03621 | 0.364969 | 0.182485 | − | 0.983209i | \(-0.441586\pi\) | ||||
0.182485 | + | 0.983209i | \(0.441586\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.42741 | 0.178241 | 0.0891203 | − | 0.996021i | \(-0.471594\pi\) | ||||
0.0891203 | + | 0.996021i | \(0.471594\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.8403 | −0.596483 | −0.298241 | − | 0.954490i | \(-0.596400\pi\) | ||||
−0.298241 | + | 0.954490i | \(0.596400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.72993 | −0.350320 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.9380 | 0.438222 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.8819 | −0.794005 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.7334 | −1.18555 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.8369 | −1.66550 | −0.832751 | − | 0.553648i | \(-0.813235\pi\) | ||||
−0.832751 | + | 0.553648i | \(0.813235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.5841 | −1.53358 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.4894 | −1.52501 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −60.8113 | −2.40566 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.86478 | 0.231645 | 0.115822 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115822 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.460745 | −0.0181700 | −0.00908500 | − | 0.999959i | \(-0.502892\pi\) | ||||
−0.00908500 | + | 0.999959i | \(0.502892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.5690 | 0.612079 | 0.306040 | − | 0.952019i | \(-0.400996\pi\) | ||||
0.306040 | + | 0.952019i | \(0.400996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −79.9362 | −3.13777 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.7105 | −1.00767 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.4538 | −1.15262 | −0.576308 | − | 0.817233i | \(-0.695507\pi\) | ||||
−0.576308 | + | 0.817233i | \(0.695507\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.18430 | −0.319300 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.5604 | −0.878829 | −0.439415 | − | 0.898284i | \(-0.644814\pi\) | ||||
−0.439415 | + | 0.898284i | \(0.644814\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.7530 | −1.54621 | −0.773106 | − | 0.634277i | \(-0.781298\pi\) | ||||
−0.773106 | + | 0.634277i | \(0.781298\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −63.9916 | −2.48523 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.271042 | 0.0104948 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 79.6289 | 3.07863 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.8949 | 1.42431 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.5047 | 0.443475 | 0.221737 | − | 0.975106i | \(-0.428827\pi\) | ||||
0.221737 | + | 0.975106i | \(0.428827\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.7703 | 1.22103 | 0.610515 | − | 0.792005i | \(-0.290962\pi\) | ||||
0.610515 | + | 0.792005i | \(0.290962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0868 | −0.387098 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.2101 | −1.08101 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.22683 | −0.276527 | −0.138264 | − | 0.990395i | \(-0.544152\pi\) | ||||
−0.138264 | + | 0.990395i | \(0.544152\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.4145 | 1.61822 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.3118 | 0.469043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.29788 | −0.125457 | −0.0627286 | − | 0.998031i | \(-0.519980\pi\) | ||||
−0.0627286 | + | 0.998031i | \(0.519980\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −35.6996 | −1.35611 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.3111 | 0.617827 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.1123 | 1.06331 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.7936 | 0.709824 | 0.354912 | − | 0.934900i | \(-0.384511\pi\) | ||||
0.354912 | + | 0.934900i | \(0.384511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.57884 | −0.361273 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.9658 | 0.562848 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.1039 | 0.529685 | 0.264842 | − | 0.964292i | \(-0.414680\pi\) | ||||
0.264842 | + | 0.964292i | \(0.414680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.6856 | 1.03829 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.77792 | −0.328736 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 46.2341 | 1.72664 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.5631 | 0.878754 | 0.439377 | − | 0.898303i | \(-0.355199\pi\) | ||||
0.439377 | + | 0.898303i | \(0.355199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.46005 | 0.277827 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.4862 | −0.389985 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.57021 | 0.132412 | 0.0662059 | − | 0.997806i | \(-0.478911\pi\) | ||||
0.0662059 | + | 0.997806i | \(0.478911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0190 | −1.07478 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.31045 | −0.233401 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.3158 | 0.381022 | 0.190511 | − | 0.981685i | \(-0.438985\pi\) | ||||
0.190511 | + | 0.981685i | \(0.438985\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.9448 | 0.513663 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.2056 | 1.33185 | 0.665923 | − | 0.746021i | \(-0.268038\pi\) | ||||
0.665923 | + | 0.746021i | \(0.268038\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.6153 | −0.757324 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.24466 | −0.119035 | −0.0595174 | − | 0.998227i | \(-0.518956\pi\) | ||||
−0.0595174 | + | 0.998227i | \(0.518956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −93.0856 | −3.40582 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0883 | −0.405157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.9796 | −0.984499 | −0.492250 | − | 0.870454i | \(-0.663825\pi\) | ||||
−0.492250 | + | 0.870454i | \(0.663825\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 70.6888 | 2.57604 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.7249 | −0.426148 | −0.213074 | − | 0.977036i | \(-0.568348\pi\) | ||||
−0.213074 | + | 0.977036i | \(0.568348\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.3621 | −0.666504 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4303 | −0.885599 | −0.442800 | − | 0.896621i | \(-0.646015\pi\) | ||||
−0.442800 | + | 0.896621i | \(0.646015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.38623 | −0.122590 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −82.8852 | −2.99281 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.804588 | 0.0290142 | 0.0145071 | − | 0.999895i | \(-0.495382\pi\) | ||||
0.0145071 | + | 0.999895i | \(0.495382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −92.0989 | −3.31686 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.02477 | 0.216696 | 0.108348 | − | 0.994113i | \(-0.465444\pi\) | ||||
0.108348 | + | 0.994113i | \(0.465444\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.9118 | −0.929582 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.25474 | 0.188270 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −63.1179 | −2.25853 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.36618 | −0.0845604 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9326 | 0.460996 | 0.230498 | − | 0.973073i | \(-0.425964\pi\) | ||||
0.230498 | + | 0.973073i | \(0.425964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 61.4977 | 2.18938 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.4033 | 0.512123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.2561 | 1.35851 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.3660 | 1.28815 | 0.644075 | − | 0.764962i | \(-0.277242\pi\) | ||||
0.644075 | + | 0.764962i | \(0.277242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.659052 | −0.0233156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −66.0654 | −2.33431 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.49472 | −0.299772 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −50.8629 | −1.79046 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.5840 | 0.934642 | 0.467321 | − | 0.884088i | \(-0.345219\pi\) | ||||
0.467321 | + | 0.884088i | \(0.345219\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.7712 | 1.57213 | 0.786064 | − | 0.618145i | \(-0.212116\pi\) | ||||
0.786064 | + | 0.618145i | \(0.212116\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.8360 | −1.43218 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.03296 | −0.0711242 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −37.0166 | −1.29346 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3949 | 0.781587 | 0.390794 | − | 0.920478i | \(-0.372201\pi\) | ||||
0.390794 | + | 0.920478i | \(0.372201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.18913 | −0.0763081 | −0.0381541 | − | 0.999272i | \(-0.512148\pi\) | ||||
−0.0381541 | + | 0.999272i | \(0.512148\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.4367 | −1.37135 | −0.685674 | − | 0.727909i | \(-0.740492\pi\) | ||||
−0.685674 | + | 0.727909i | \(0.740492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0629 | −0.384229 | −0.192115 | − | 0.981373i | \(-0.561535\pi\) | ||||
−0.192115 | + | 0.981373i | \(0.561535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.5040 | −1.68259 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.2953 | 0.703190 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 76.6306 | 2.64874 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.8510 | 1.30676 | 0.653381 | − | 0.757030i | \(-0.273350\pi\) | ||||
0.653381 | + | 0.757030i | \(0.273350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9265 | −0.997467 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.08254 | −0.0372845 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.2675 | −0.902561 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.3132 | 0.697148 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.84665 | −0.303259 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9770 | 0.992155 | 0.496078 | − | 0.868278i | \(-0.334773\pi\) | ||||
0.496078 | + | 0.868278i | \(0.334773\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.0462 | −1.91450 | −0.957250 | − | 0.289261i | \(-0.906590\pi\) | ||||
−0.957250 | + | 0.289261i | \(0.906590\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.8866 | −1.49739 | −0.748695 | − | 0.662914i | \(-0.769319\pi\) | ||||
−0.748695 | + | 0.662914i | \(0.769319\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.2147 | 0.484434 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.1955 | −0.755542 | −0.377771 | − | 0.925899i | \(-0.623309\pi\) | ||||
−0.377771 | + | 0.925899i | \(0.623309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0377 | −0.578630 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.7357 | 0.974791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.4592 | 0.489932 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 60.9245 | 2.06198 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.44979 | −0.184026 | −0.0920131 | − | 0.995758i | \(-0.529330\pi\) | ||||
−0.0920131 | + | 0.995758i | \(0.529330\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 78.3125 | 2.64141 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.7854 | −0.397060 | −0.198530 | − | 0.980095i | \(-0.563617\pi\) | ||||
−0.198530 | + | 0.980095i | \(0.563617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.7945 | −0.800748 | −0.400374 | − | 0.916352i | \(-0.631120\pi\) | ||||
−0.400374 | + | 0.916352i | \(0.631120\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.4300 | 1.49181 | 0.745907 | − | 0.666050i | \(-0.232016\pi\) | ||||
0.745907 | + | 0.666050i | \(0.232016\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.16993 | 0.0392381 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.0782 | 1.71119 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.212318 | −0.00710496 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.0396 | −0.635712 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.37919 | −0.0793504 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.49196 | −0.216279 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.49938 | −0.183008 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.7542 | 1.35322 | 0.676611 | − | 0.736341i | \(-0.263448\pi\) | ||||
0.676611 | + | 0.736341i | \(0.263448\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −90.3934 | −2.99816 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.71520 | 0.0899587 | 0.0449794 | − | 0.998988i | \(-0.485678\pi\) | ||||
0.0449794 | + | 0.998988i | \(0.485678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −96.6163 | −3.19753 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.5046 | −0.379914 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.7227 | −0.353708 | −0.176854 | − | 0.984237i | \(-0.556592\pi\) | ||||
−0.176854 | + | 0.984237i | \(0.556592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 58.8890 | 1.94046 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −65.4464 | −2.15419 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.0587 | −1.47992 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.8670 | 1.27518 | 0.637592 | − | 0.770374i | \(-0.279930\pi\) | ||||
0.637592 | + | 0.770374i | \(0.279930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.53827 | 0.214283 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −45.1055 | −1.47669 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.6117 | −1.26139 | −0.630694 | − | 0.776032i | \(-0.717230\pi\) | ||||
−0.630694 | + | 0.776032i | \(0.717230\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.7761 | −1.26541 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.3928 | 0.860381 | 0.430191 | − | 0.902738i | \(-0.358446\pi\) | ||||
0.430191 | + | 0.902738i | \(0.358446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.85308 | 0.158038 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.3777 | −0.727179 | −0.363589 | − | 0.931559i | \(-0.618449\pi\) | ||||
−0.363589 | + | 0.931559i | \(0.618449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.80811 | −0.285923 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51.8265 | −1.68059 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.4362 | 0.564815 | 0.282407 | − | 0.959295i | \(-0.408867\pi\) | ||||
0.282407 | + | 0.959295i | \(0.408867\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.97692 | −0.160881 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.2630 | −0.331409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.0519 | 1.48554 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 66.9732 | 2.15818 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.1587 | −1.45221 | −0.726103 | − | 0.687586i | \(-0.758670\pi\) | ||||
−0.726103 | + | 0.687586i | \(0.758670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.8704 | 0.349207 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.3123 | 1.10113 | 0.550567 | − | 0.834791i | \(-0.314412\pi\) | ||||
0.550567 | + | 0.834791i | \(0.314412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.03353 | 0.129309 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.51320 | 0.0484115 | 0.0242058 | − | 0.999707i | \(-0.492294\pi\) | ||||
0.0242058 | + | 0.999707i | \(0.492294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −68.5713 | −2.19155 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.4528 | 0.653007 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.1715 | −0.483895 | −0.241947 | − | 0.970289i | \(-0.577786\pi\) | ||||
−0.241947 | + | 0.970289i | \(0.577786\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.574345 | −0.0182816 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.87756 | −0.0597031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.4470 | 1.25307 | 0.626537 | − | 0.779392i | \(-0.284472\pi\) | ||||
0.626537 | + | 0.779392i | \(0.284472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.94153 | −0.0933467 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.33319 | −0.0738928 | −0.0369464 | − | 0.999317i | \(-0.511763\pi\) | ||||
−0.0369464 | + | 0.999317i | \(0.511763\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 77.2307 | 2.44347 |
(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 | 9200.2.a.dc.1.7 | 7 | ||
4.3 | odd | 2 | 4600.2.a.bh.1.1 | 7 | |||
5.2 | odd | 4 | 1840.2.e.g.369.1 | 14 | |||
5.3 | odd | 4 | 1840.2.e.g.369.14 | 14 | |||
5.4 | even | 2 | 9200.2.a.cz.1.1 | 7 | |||
20.3 | even | 4 | 920.2.e.b.369.1 | ✓ | 14 | ||
20.7 | even | 4 | 920.2.e.b.369.14 | yes | 14 | ||
20.19 | odd | 2 | 4600.2.a.bi.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.1 | ✓ | 14 | 20.3 | even | 4 | ||
920.2.e.b.369.14 | yes | 14 | 20.7 | even | 4 | ||
1840.2.e.g.369.1 | 14 | 5.2 | odd | 4 | |||
1840.2.e.g.369.14 | 14 | 5.3 | odd | 4 | |||
4600.2.a.bh.1.1 | 7 | 4.3 | odd | 2 | |||
4600.2.a.bi.1.7 | 7 | 20.19 | odd | 2 | |||
9200.2.a.cz.1.1 | 7 | 5.4 | even | 2 | |||
9200.2.a.dc.1.7 | 7 | 1.1 | even | 1 | trivial |