Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2900,2,Mod(349,2900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2900.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2900.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(23.1566165862\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5089536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 580) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.4 | ||
Root | \(0.675970 - 0.675970i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2900.349 |
Dual form | 2900.2.c.f.349.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1277\) | \(1451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.35194i | 0.780542i | 0.920700 | + | 0.390271i | \(0.127619\pi\) | ||||
−0.920700 | + | 0.390271i | \(0.872381\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.648061i | 0.244944i | 0.992472 | + | 0.122472i | \(0.0390822\pi\) | ||||
−0.992472 | + | 0.122472i | \(0.960918\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.17226 | 0.390753 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.35194 | 1.01065 | 0.505324 | − | 0.862930i | \(-0.331373\pi\) | ||||
0.505324 | + | 0.862930i | \(0.331373\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.17226i | 1.15718i | 0.815620 | + | 0.578588i | \(0.196396\pi\) | ||||
−0.815620 | + | 0.578588i | \(0.803604\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.82032i | − 1.16910i | −0.811358 | − | 0.584550i | \(-0.801271\pi\) | ||||
0.811358 | − | 0.584550i | \(-0.198729\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.82032 | −1.56469 | −0.782344 | − | 0.622846i | \(-0.785976\pi\) | ||||
−0.782344 | + | 0.622846i | \(0.785976\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.876139 | −0.191189 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.52420i | 1.15188i | 0.817494 | + | 0.575938i | \(0.195363\pi\) | ||||
−0.817494 | + | 0.575938i | \(0.804637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64064i | 1.08554i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82032 | −0.506545 | −0.253272 | − | 0.967395i | \(-0.581507\pi\) | ||||
−0.253272 | + | 0.967395i | \(0.581507\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.53162i | 0.788853i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2281i | 1.68149i | 0.541435 | + | 0.840743i | \(0.317881\pi\) | ||||
−0.541435 | + | 0.840743i | \(0.682119\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.64064 | −0.903226 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.17226 | 1.27629 | 0.638146 | − | 0.769915i | \(-0.279701\pi\) | ||||
0.638146 | + | 0.769915i | \(0.279701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.69646i | − 0.868702i | −0.900744 | − | 0.434351i | \(-0.856978\pi\) | ||||
0.900744 | − | 0.434351i | \(-0.143022\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.64806i | 0.386259i | 0.981173 | + | 0.193130i | \(0.0618638\pi\) | ||||
−0.981173 | + | 0.193130i | \(0.938136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.58002 | 0.940002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.51678 | 0.912532 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.87614i | − 0.395068i | −0.980296 | − | 0.197534i | \(-0.936707\pi\) | ||||
0.980296 | − | 0.197534i | \(-0.0632933\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 9.22066i | − 1.22131i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.2207 | 1.72118 | 0.860592 | − | 0.509296i | \(-0.170094\pi\) | ||||
0.860592 | + | 0.509296i | \(0.170094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.12386 | −0.143896 | −0.0719478 | − | 0.997408i | \(-0.522922\pi\) | ||||
−0.0719478 | + | 0.997408i | \(0.522922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.759696i | 0.0957127i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.52420i | − 0.186211i | −0.995656 | − | 0.0931053i | \(-0.970321\pi\) | ||||
0.995656 | − | 0.0931053i | \(-0.0296793\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.46838 | −0.899088 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.87614 | −1.05340 | −0.526702 | − | 0.850050i | \(-0.676572\pi\) | ||||
−0.526702 | + | 0.850050i | \(0.676572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.69646i | 1.13488i | 0.823413 | + | 0.567442i | \(0.192067\pi\) | ||||
−0.823413 | + | 0.567442i | \(0.807933\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.17226i | 0.247552i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.99258 | −1.01174 | −0.505872 | − | 0.862608i | \(-0.668829\pi\) | ||||
−0.505872 | + | 0.862608i | \(0.668829\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.10902 | −0.456558 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.94418i | 0.213402i | 0.994291 | + | 0.106701i | \(0.0340287\pi\) | ||||
−0.994291 | + | 0.106701i | \(0.965971\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.35194i | 0.144943i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.0484 | −1.80713 | −0.903563 | − | 0.428455i | \(-0.859058\pi\) | ||||
−0.903563 | + | 0.428455i | \(0.859058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70388 | −0.283443 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3.81290i | − 0.395380i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3519i | 1.35568i | 0.735208 | + | 0.677842i | \(0.237085\pi\) | ||||
−0.735208 | + | 0.677842i | \(0.762915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.92935 | 0.394914 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.4562 | 1.83646 | 0.918228 | − | 0.396052i | \(-0.129620\pi\) | ||||
0.918228 | + | 0.396052i | \(0.129620\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 14.8203i | − 1.46029i | −0.683292 | − | 0.730145i | \(-0.739453\pi\) | ||||
0.683292 | − | 0.730145i | \(-0.260547\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.35194i | 0.324044i | 0.986787 | + | 0.162022i | \(0.0518016\pi\) | ||||
−0.986787 | + | 0.162022i | \(0.948198\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.76450 | −0.264791 | −0.132396 | − | 0.991197i | \(-0.542267\pi\) | ||||
−0.132396 | + | 0.991197i | \(0.542267\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.8277 | −1.31247 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.94418i | 0.747326i | 0.927565 | + | 0.373663i | \(0.121898\pi\) | ||||
−0.927565 | + | 0.373663i | \(0.878102\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.89098i | 0.452171i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.12386 | 0.286364 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.235496 | 0.0214088 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.0484i | 0.996201i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6965i | 1.57031i | 0.619301 | + | 0.785153i | \(0.287416\pi\) | ||||
−0.619301 | + | 0.785153i | \(0.712584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.70127 | 0.678059 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.52420 | 0.482652 | 0.241326 | − | 0.970444i | \(-0.422418\pi\) | ||||
0.241326 | + | 0.970444i | \(0.422418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.41998i | − 0.383261i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.86872i | 0.330527i | 0.986249 | + | 0.165264i | \(0.0528475\pi\) | ||||
−0.986249 | + | 0.165264i | \(0.947153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.64064 | −0.478433 | −0.239217 | − | 0.970966i | \(-0.576891\pi\) | ||||
−0.239217 | + | 0.970966i | \(0.576891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.58002 | −0.301492 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.9852i | 1.16950i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.89578i | 0.733712i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2207 | −1.40140 | −0.700699 | − | 0.713457i | \(-0.747128\pi\) | ||||
−0.700699 | + | 0.713457i | \(0.747128\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 5.65067i | − 0.456830i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.69646i | 0.454627i | 0.973822 | + | 0.227314i | \(0.0729942\pi\) | ||||
−0.973822 | + | 0.227314i | \(0.927006\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.88836 | 0.308367 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.58002 | −0.282145 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4003i | 1.28457i | 0.766464 | + | 0.642287i | \(0.222014\pi\) | ||||
−0.766464 | + | 0.642287i | \(0.777986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.2765i | 1.80119i | 0.434661 | + | 0.900594i | \(0.356868\pi\) | ||||
−0.434661 | + | 0.900594i | \(0.643132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.40776 | −0.339058 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.99519 | −0.611408 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 13.9245i | − 1.05866i | −0.848415 | − | 0.529332i | \(-0.822443\pi\) | ||||
0.848415 | − | 0.529332i | \(-0.177557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.8735i | 1.34346i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.34452 | 0.324725 | 0.162362 | − | 0.986731i | \(-0.448089\pi\) | ||||
0.162362 | + | 0.986731i | \(0.448089\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.5168 | 1.52500 | 0.762500 | − | 0.646988i | \(-0.223972\pi\) | ||||
0.762500 | + | 0.646988i | \(0.223972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 1.51939i | − 0.112317i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 16.1574i | − 1.18155i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.65548 | −0.265897 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.10422 | −0.658758 | −0.329379 | − | 0.944198i | \(-0.606839\pi\) | ||||
−0.329379 | + | 0.944198i | \(0.606839\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 25.1648i | − 1.81140i | −0.423914 | − | 0.905702i | \(-0.639344\pi\) | ||||
0.423914 | − | 0.905702i | \(-0.360656\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.703878i | 0.0501493i | 0.999686 | + | 0.0250746i | \(0.00798234\pi\) | ||||
−0.999686 | + | 0.0250746i | \(0.992018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.22066 | 0.370083 | 0.185041 | − | 0.982731i | \(-0.440758\pi\) | ||||
0.185041 | + | 0.982731i | \(0.440758\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.06063 | 0.145345 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.648061i | 0.0454850i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.47580i | 0.450099i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.8613 | −1.58135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1042 | −0.902131 | −0.451066 | − | 0.892491i | \(-0.648956\pi\) | ||||
−0.451066 | + | 0.892491i | \(0.648956\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 12.0000i | − 0.822226i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.82774i | − 0.124075i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.1090 | −0.885826 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.1116 | 1.35285 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20.5726i | − 1.37764i | −0.724931 | − | 0.688822i | \(-0.758128\pi\) | ||||
0.724931 | − | 0.688822i | \(-0.241872\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.41256i | 0.624734i | 0.949962 | + | 0.312367i | \(0.101122\pi\) | ||||
−0.949962 | + | 0.312367i | \(0.898878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.93676 | −0.193225 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.3445i | 0.677692i | 0.940842 | + | 0.338846i | \(0.110037\pi\) | ||||
−0.940842 | + | 0.338846i | \(0.889963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 12.1574i | − 0.789710i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.8761 | −1.35037 | −0.675183 | − | 0.737651i | \(-0.735935\pi\) | ||||
−0.675183 | + | 0.737651i | \(0.735935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.1600 | 1.36304 | 0.681519 | − | 0.731801i | \(-0.261320\pi\) | ||||
0.681519 | + | 0.731801i | \(0.261320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3668i | 0.729179i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 28.4562i | − 1.81062i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.62842 | −0.166569 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.64806 | −0.545861 | −0.272930 | − | 0.962034i | \(-0.587993\pi\) | ||||
−0.272930 | + | 0.962034i | \(0.587993\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.5168i | 1.16414i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 27.4535i | − 1.71251i | −0.516557 | − | 0.856253i | \(-0.672787\pi\) | ||||
0.516557 | − | 0.856253i | \(-0.327213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.62842 | −0.411870 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.17226 | 0.0725611 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 11.3371i | − 0.699076i | −0.936922 | − | 0.349538i | \(-0.886339\pi\) | ||||
0.936922 | − | 0.349538i | \(-0.113661\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 23.0484i | − 1.41054i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.1723 | 1.22992 | 0.614962 | − | 0.788557i | \(-0.289171\pi\) | ||||
0.614962 | + | 0.788557i | \(0.289171\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7449 | −0.652704 | −0.326352 | − | 0.945248i | \(-0.605819\pi\) | ||||
−0.326352 | + | 0.945248i | \(0.605819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 3.65548i | − 0.221240i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6284i | 0.758768i | 0.925239 | + | 0.379384i | \(0.123864\pi\) | ||||
−0.925239 | + | 0.379384i | \(0.876136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.30615 | −0.197934 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.76450 | 0.403536 | 0.201768 | − | 0.979433i | \(-0.435331\pi\) | ||||
0.201768 | + | 0.979433i | \(0.435331\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.06804i | 0.0634886i | 0.999496 | + | 0.0317443i | \(0.0101062\pi\) | ||||
−0.999496 | + | 0.0317443i | \(0.989894\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.29612i | 0.312620i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.23550 | −0.366794 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.0510 | −1.05817 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.46357i | 0.319185i | 0.987183 | + | 0.159593i | \(0.0510181\pi\) | ||||
−0.987183 | + | 0.159593i | \(0.948982\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.9071i | 1.09710i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.0484 | −1.33292 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.69165 | 0.212783 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.9516i | 1.43343i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.30354i | − 0.359762i | −0.983688 | − | 0.179881i | \(-0.942429\pi\) | ||||
0.983688 | − | 0.179881i | \(-0.0575713\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.0362 | 1.13982 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.6842 | 1.39971 | 0.699857 | − | 0.714283i | \(-0.253247\pi\) | ||||
0.699857 | + | 0.714283i | \(0.253247\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 24.1723i | − 1.36630i | −0.730280 | − | 0.683148i | \(-0.760610\pi\) | ||||
0.730280 | − | 0.683148i | \(-0.239390\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.42740i | − 0.0801708i | −0.999196 | − | 0.0400854i | \(-0.987237\pi\) | ||||
0.999196 | − | 0.0400854i | \(-0.0127630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.35194 | 0.187673 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.53162 | −0.252930 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.8761i | 1.82928i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 3.73744i | − 0.206681i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.71610 | −0.0946119 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.2132 | 1.88053 | 0.940265 | − | 0.340444i | \(-0.110577\pi\) | ||||
0.940265 | + | 0.340444i | \(0.110577\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.9900i | 0.657046i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 4.40034i | − 0.239702i | −0.992792 | − | 0.119851i | \(-0.961758\pi\) | ||||
0.992792 | − | 0.119851i | \(-0.0382416\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.7401 | −0.583320 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.45355 | −0.511938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.80068i | 0.475192i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 12.9926i | − 0.697478i | −0.937220 | − | 0.348739i | \(-0.886610\pi\) | ||||
0.937220 | − | 0.348739i | \(-0.113390\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0968 | 1.07576 | 0.537878 | − | 0.843022i | \(-0.319226\pi\) | ||||
0.537878 | + | 0.843022i | \(0.319226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.5342 | −1.25616 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 17.8129i | − 0.948085i | −0.880502 | − | 0.474043i | \(-0.842794\pi\) | ||||
0.880502 | − | 0.474043i | \(-0.157206\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.22327i | 0.223519i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.52420 | −0.291556 | −0.145778 | − | 0.989317i | \(-0.546569\pi\) | ||||
−0.145778 | + | 0.989317i | \(0.546569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.5168 | 1.44825 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.318377i | 0.0167104i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0558i | 1.04691i | 0.852055 | + | 0.523453i | \(0.175356\pi\) | ||||
−0.852055 | + | 0.523453i | \(0.824644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.58002 | 0.498716 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.86391 | 0.0967695 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.88836i | − 0.0977758i | −0.998804 | − | 0.0488879i | \(-0.984432\pi\) | ||||
0.998804 | − | 0.0488879i | \(-0.0155677\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.17226i | 0.214882i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0894 | 0.775089 | 0.387545 | − | 0.921851i | \(-0.373323\pi\) | ||||
0.387545 | + | 0.921851i | \(0.373323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.9245 | −1.22569 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.3371i | 0.885885i | 0.896550 | + | 0.442942i | \(0.146065\pi\) | ||||
−0.896550 | + | 0.442942i | \(0.853935\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 6.67773i | − 0.339448i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.890976 | 0.0451743 | 0.0225871 | − | 0.999745i | \(-0.492810\pi\) | ||||
0.0225871 | + | 0.999745i | \(0.492810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.6284 | 1.34666 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.46838i | 0.376730i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.39292i | − 0.270663i | −0.990800 | − | 0.135331i | \(-0.956790\pi\) | ||||
0.990800 | − | 0.135331i | \(-0.0432099\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.97555 | 0.299152 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.23550 | 0.261448 | 0.130724 | − | 0.991419i | \(-0.458270\pi\) | ||||
0.130724 | + | 0.991419i | \(0.458270\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 11.7671i | − 0.586162i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.2839i | 1.69939i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0606 | 0.794147 | 0.397073 | − | 0.917787i | \(-0.370026\pi\) | ||||
0.397073 | + | 0.917787i | \(0.370026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.23027 | −0.257990 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.56779i | 0.421593i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 7.62581i | − 0.373437i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.9245 | 0.973377 | 0.486689 | − | 0.873575i | \(-0.338205\pi\) | ||||
0.486689 | + | 0.873575i | \(0.338205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5652 | −0.758600 | −0.379300 | − | 0.925274i | \(-0.623835\pi\) | ||||
−0.379300 | + | 0.925274i | \(0.623835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.10422i | 0.150932i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.728330i | − 0.0352464i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.9071 | −0.912843 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.4078 | −0.645829 | −0.322914 | − | 0.946428i | \(-0.604663\pi\) | ||||
−0.322914 | + | 0.946428i | \(0.604663\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 34.6842i | − 1.66682i | −0.552657 | − | 0.833409i | \(-0.686386\pi\) | ||||
0.552657 | − | 0.833409i | \(-0.313614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 37.6768i | − 1.80233i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.2355 | 0.727151 | 0.363575 | − | 0.931565i | \(-0.381556\pi\) | ||||
0.363575 | + | 0.931565i | \(0.381556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.71349 | 0.367309 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.00742i | 0.237910i | 0.992900 | + | 0.118955i | \(0.0379544\pi\) | ||||
−0.992900 | + | 0.118955i | \(0.962046\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 24.3349i | − 1.15100i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.8129 | 0.840643 | 0.420321 | − | 0.907375i | \(-0.361917\pi\) | ||||
0.420321 | + | 0.907375i | \(0.361917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.3929 | 1.28988 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 23.2813i | − 1.09385i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 24.4051i | − 1.14162i | −0.821081 | − | 0.570812i | \(-0.806628\pi\) | ||||
0.821081 | − | 0.570812i | \(-0.193372\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 27.1897 | 1.26911 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.98516 | −0.371906 | −0.185953 | − | 0.982559i | \(-0.559537\pi\) | ||||
−0.185953 | + | 0.982559i | \(0.559537\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.6210i | 0.540074i | 0.962850 | + | 0.270037i | \(0.0870359\pi\) | ||||
−0.962850 | + | 0.270037i | \(0.912964\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.24030i | − 0.0573944i | −0.999588 | − | 0.0286972i | \(-0.990864\pi\) | ||||
0.999588 | − | 0.0286972i | \(-0.00913586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.987774 | 0.0456112 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.70127 | −0.354856 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 19.0942i | − 0.877952i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.37158i | − 0.154374i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.6965 | −0.899954 | −0.449977 | − | 0.893040i | \(-0.648568\pi\) | ||||
−0.449977 | + | 0.893040i | \(0.648568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.6742 | −1.94578 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.83997i | − 0.220226i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0894i | 0.683765i | 0.939743 | + | 0.341883i | \(0.111064\pi\) | ||||
−0.939743 | + | 0.341883i | \(0.888936\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.1723 | −1.00266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.2281 | −0.551845 | −0.275923 | − | 0.961180i | \(-0.588983\pi\) | ||||
−0.275923 | + | 0.961180i | \(0.588983\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.82032i | − 0.217096i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 5.75228i | − 0.258025i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.52901 | 0.247512 | 0.123756 | − | 0.992313i | \(-0.460506\pi\) | ||||
0.123756 | + | 0.992313i | \(0.460506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.4684 | −1.40590 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.2887i | 1.08298i | 0.840707 | + | 0.541490i | \(0.182140\pi\) | ||||
−0.840707 | + | 0.541490i | \(0.817860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 5.95902i | − 0.264649i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.58002 | 0.424627 | 0.212313 | − | 0.977202i | \(-0.431900\pi\) | ||||
0.212313 | + | 0.977202i | \(0.431900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.28390 | −0.277983 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 38.4710i | − 1.69854i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.87614i | 0.390372i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.8251 | 0.826331 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.5800 | −0.945438 | −0.472719 | − | 0.881213i | \(-0.656727\pi\) | ||||
−0.472719 | + | 0.881213i | \(0.656727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 42.2132i | − 1.84586i | −0.384972 | − | 0.922928i | \(-0.625789\pi\) | ||||
0.384972 | − | 0.922928i | \(-0.374211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.5949i | 0.592201i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.51678 | −0.326817 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.4981 | 0.672558 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.0968i | 1.47690i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.87353i | 0.253461i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.0558 | 0.950011 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.5530 | 1.57153 | 0.785767 | − | 0.618522i | \(-0.212268\pi\) | ||||
0.785767 | + | 0.618522i | \(0.212268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.7374i | 1.19033i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 26.6236i | − 1.13834i | −0.822219 | − | 0.569172i | \(-0.807264\pi\) | ||||
0.822219 | − | 0.569172i | \(-0.192736\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.31746 | −0.0562277 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.82032 | −0.290555 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 5.82774i | − 0.247821i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 22.2233i | − 0.941630i | −0.882232 | − | 0.470815i | \(-0.843960\pi\) | ||||
0.882232 | − | 0.470815i | \(-0.156040\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.7671 | 1.00524 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.8439 | 0.922248 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.11905i | 0.0471625i | 0.999722 | + | 0.0235812i | \(0.00750684\pi\) | ||||
−0.999722 | + | 0.0235812i | \(0.992493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 2.66290i | − 0.111831i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.5316 | 0.441508 | 0.220754 | − | 0.975329i | \(-0.429148\pi\) | ||||
0.220754 | + | 0.975329i | \(0.429148\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.18449 | −0.0495692 | −0.0247846 | − | 0.999693i | \(-0.507890\pi\) | ||||
−0.0247846 | + | 0.999693i | \(0.507890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 12.3083i | − 0.514189i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 11.8687i | − 0.494101i | −0.969003 | − | 0.247051i | \(-0.920539\pi\) | ||||
0.969003 | − | 0.247051i | \(-0.0794614\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.0213 | 1.41388 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.25995 | −0.0522715 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9.64064i | − 0.399275i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 32.4610i | − 1.33981i | −0.742448 | − | 0.669904i | \(-0.766335\pi\) | ||||
0.742448 | − | 0.669904i | \(-0.233665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.2355 | 0.792585 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.951601 | −0.0391436 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.12386i | 0.374672i | 0.982296 | + | 0.187336i | \(0.0599853\pi\) | ||||
−0.982296 | + | 0.187336i | \(0.940015\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.05801i | 0.288865i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.2887 | 1.23756 | 0.618781 | − | 0.785563i | \(-0.287627\pi\) | ||||
0.618781 | + | 0.785563i | \(0.287627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5168 | 0.836897 | 0.418448 | − | 0.908241i | \(-0.362574\pi\) | ||||
0.418448 | + | 0.908241i | \(0.362574\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.78676i | − 0.0727624i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.9293i | 0.565375i | 0.959212 | + | 0.282687i | \(0.0912259\pi\) | ||||
−0.959212 | + | 0.282687i | \(0.908774\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.876139 | −0.0355029 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0484 | −0.446970 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.7523i | 0.797787i | 0.916997 | + | 0.398893i | \(0.130606\pi\) | ||||
−0.916997 | + | 0.398893i | \(0.869394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.2010i | 1.49766i | 0.662764 | + | 0.748828i | \(0.269383\pi\) | ||||
−0.662764 | + | 0.748828i | \(0.730617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.46357 | −0.299986 | −0.149993 | − | 0.988687i | \(-0.547925\pi\) | ||||
−0.149993 | + | 0.988687i | \(0.547925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.1600 | −1.25041 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 11.0484i | − 0.442645i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 30.9071i | − 1.23431i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 49.3026 | 1.96582 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.4562 | 1.76977 | 0.884886 | − | 0.465808i | \(-0.154236\pi\) | ||||
0.884886 | + | 0.465808i | \(0.154236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 17.7161i | − 0.704152i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.4535i | 1.08775i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.4051 | −0.411621 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.7401 | −1.60914 | −0.804568 | − | 0.593861i | \(-0.797603\pi\) | ||||
−0.804568 | + | 0.593861i | \(0.797603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3493i | 0.802499i | 0.915969 | + | 0.401250i | \(0.131424\pi\) | ||||
−0.915969 | + | 0.401250i | \(0.868576\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 41.7933i | − 1.64306i | −0.570163 | − | 0.821531i | \(-0.693120\pi\) | ||||
0.570163 | − | 0.821531i | \(-0.306880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.3148 | 1.73951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.47099 | 0.0968458 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7933i | 0.931102i | 0.885021 | + | 0.465551i | \(0.154144\pi\) | ||||
−0.885021 | + | 0.465551i | \(0.845856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.3668i | 0.443460i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.50936 | −0.292523 | −0.146262 | − | 0.989246i | \(-0.546724\pi\) | ||||
−0.146262 | + | 0.989246i | \(0.546724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.9245 | 1.78626 | 0.893129 | − | 0.449801i | \(-0.148505\pi\) | ||||
0.893129 | + | 0.449801i | \(0.148505\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.1897i | 1.05596i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.52420i | 0.213898i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.8129 | 1.07531 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.76711 | −0.145428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.29612i | 0.281245i | 0.990063 | + | 0.140622i | \(0.0449104\pi\) | ||||
−0.990063 | + | 0.140622i | \(0.955090\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 36.2494i | − 1.39318i | −0.717470 | − | 0.696589i | \(-0.754700\pi\) | ||||
0.717470 | − | 0.696589i | \(-0.245300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.65287 | −0.332067 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.7252 | −0.487631 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.40295i | − 0.206738i | −0.994643 | − | 0.103369i | \(-0.967038\pi\) | ||||
0.994643 | − | 0.103369i | \(-0.0329623\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 2.70388i | − 0.103159i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0458 | −1.37125 | −0.685623 | − | 0.727957i | \(-0.740470\pi\) | ||||
−0.685623 | + | 0.727957i | \(0.740470\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.54645i | 0.0967318i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 39.3929i | − 1.49211i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.9852 | −0.528967 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.33229 | 0.125859 | 0.0629295 | − | 0.998018i | \(-0.479956\pi\) | ||||
0.0629295 | + | 0.998018i | \(0.479956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 69.7588i | − 2.63100i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.9607i | 0.449829i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.48322 | −0.281038 | −0.140519 | − | 0.990078i | \(-0.544877\pi\) | ||||
−0.140519 | + | 0.990078i | \(0.544877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.5416 | −0.395343 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 15.5800i | − 0.583476i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 28.2233i | − 1.05402i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.6620 | 1.47914 | 0.739571 | − | 0.673078i | \(-0.235028\pi\) | ||||
0.739571 | + | 0.673078i | \(0.235028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.60447 | 0.357689 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.6071i | 1.06391i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.05582i | 0.298774i | 0.988779 | + | 0.149387i | \(0.0477300\pi\) | ||||
−0.988779 | + | 0.149387i | \(0.952270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.6943 | −1.02571 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.4588 | −1.01560 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 28.9320i | − 1.06863i | −0.845287 | − | 0.534313i | \(-0.820570\pi\) | ||||
0.845287 | − | 0.534313i | \(-0.179430\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 5.10902i | − 0.188193i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.0772 | −1.32712 | −0.663560 | − | 0.748123i | \(-0.730955\pi\) | ||||
−0.663560 | + | 0.748123i | \(0.730955\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.4710 | 1.41327 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 40.9681i | − 1.50297i | −0.659747 | − | 0.751487i | \(-0.729337\pi\) | ||||
0.659747 | − | 0.751487i | \(-0.270663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.27909i | 0.0833875i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.17226 | −0.0793727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.2861 | 0.849722 | 0.424861 | − | 0.905259i | \(-0.360323\pi\) | ||||
0.424861 | + | 0.905259i | \(0.360323\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 11.6917i | − 0.426067i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 27.3275i | − 0.993234i | −0.867970 | − | 0.496617i | \(-0.834575\pi\) | ||||
0.867970 | − | 0.496617i | \(-0.165425\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.0336 | −0.908661 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.5626 | 1.61539 | 0.807696 | − | 0.589599i | \(-0.200714\pi\) | ||||
0.807696 | + | 0.589599i | \(0.200714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.79157i | − 0.0648591i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 55.1600i | 1.99171i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.6110 | −1.86114 | −0.930570 | − | 0.366115i | \(-0.880688\pi\) | ||||
−0.930570 | + | 0.366115i | \(0.880688\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.1155 | 1.33668 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 19.6358i | − 0.706252i | −0.935576 | − | 0.353126i | \(-0.885119\pi\) | ||||
0.935576 | − | 0.353126i | \(-0.114881\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 8.96122i | − 0.321482i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −55.7374 | −1.99700 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.7523 | −1.06462 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.64064i | 0.201580i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 37.3371i | − 1.33092i | −0.746432 | − | 0.665462i | \(-0.768235\pi\) | ||||
0.746432 | − | 0.665462i | \(-0.231765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.3271 | 0.545658 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.14831 | −0.183053 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 4.68904i | − 0.166513i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2159i | 0.397286i | 0.980072 | + | 0.198643i | \(0.0636534\pi\) | ||||
−0.980072 | + | 0.198643i | \(0.936347\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.7645 | 0.451576 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.9852 | −0.706141 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.5019i | 1.14697i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.2717i | 0.960008i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.1749 | −0.392888 | −0.196444 | − | 0.980515i | \(-0.562939\pi\) | ||||
−0.196444 | + | 0.980515i | \(0.562939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6406 | 0.619447 | 0.309723 | − | 0.950827i | \(-0.399764\pi\) | ||||
0.309723 | + | 0.950827i | \(0.399764\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 14.5264i | − 0.509463i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.8517i | 1.35925i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.16965 | −0.110757 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.2477 | 0.846251 | 0.423126 | − | 0.906071i | \(-0.360933\pi\) | ||||
0.423126 | + | 0.906071i | \(0.360933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.9777i | 0.591807i | 0.955218 | + | 0.295903i | \(0.0956207\pi\) | ||||
−0.955218 | + | 0.295903i | \(0.904379\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.58482i | 0.194203i | 0.995274 | + | 0.0971017i | \(0.0309572\pi\) | ||||
−0.995274 | + | 0.0971017i | \(0.969043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.6136 | −0.646476 | −0.323238 | − | 0.946318i | \(-0.604771\pi\) | ||||
−0.323238 | + | 0.946318i | \(0.604771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.0729 | −0.592251 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 31.7178i | − 1.09896i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 15.9084i | − 0.549876i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.9293 | 0.549942 | 0.274971 | − | 0.961453i | \(-0.411332\pi\) | ||||
0.274971 | + | 0.961453i | \(0.411332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.14520i | 0.314977i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.152616i | 0.00524395i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.44393 | −0.0495555 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −56.5019 | −1.93686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 27.0288i | − 0.925447i | −0.886503 | − | 0.462723i | \(-0.846872\pi\) | ||||
0.886503 | − | 0.462723i | \(-0.153128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 30.2691i | − 1.03397i | −0.855994 | − | 0.516986i | \(-0.827054\pi\) | ||||
0.855994 | − | 0.516986i | \(-0.172946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.4487 | 1.41421 | 0.707106 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707106 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.16003 | −0.244013 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.2494i | 1.43819i | 0.694913 | + | 0.719093i | \(0.255443\pi\) | ||||
−0.694913 | + | 0.719093i | \(0.744557\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 8.43001i | − 0.286298i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.1426 | −1.02252 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.35936 | 0.215479 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.6519i | 0.529738i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 37.8129i | − 1.27685i | −0.769684 | − | 0.638426i | \(-0.779586\pi\) | ||||
0.769684 | − | 0.638426i | \(-0.220414\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.38642 | −0.249138 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.35675 | −0.180473 | −0.0902367 | − | 0.995920i | \(-0.528762\pi\) | ||||
−0.0902367 | + | 0.995920i | \(0.528762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.53643i | 0.287274i | 0.989630 | + | 0.143637i | \(0.0458797\pi\) | ||||
−0.989630 | + | 0.143637i | \(0.954120\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.7597i | 0.764196i | 0.924122 | + | 0.382098i | \(0.124798\pi\) | ||||
−0.924122 | + | 0.382098i | \(0.875202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.4684 | −0.384637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.7732 | −0.461420 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 18.0606i | − 0.604376i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 31.1600i | − 1.04040i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.82032 | −0.0940630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.8639 | −0.461874 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.99089i | 0.166086i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.94418i | − 0.130964i | −0.997854 | − | 0.0654822i | \(-0.979141\pi\) | ||||
0.997854 | − | 0.0654822i | \(-0.0208586\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.6354 | 0.717602 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.6546 | −1.34695 | −0.673473 | − | 0.739212i | \(-0.735198\pi\) | ||||
−0.673473 | + | 0.739212i | \(0.735198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.51678i | 0.215674i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.58002i | 0.118223i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.3471 | −0.902099 | −0.451049 | − | 0.892499i | \(-0.648950\pi\) | ||||
−0.451049 | + | 0.892499i | \(0.648950\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.52200 | 0.280810 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 37.0336i | − 1.21897i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 17.3733i | − 0.570613i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.9368 | −0.686913 | −0.343456 | − | 0.939169i | \(-0.611598\pi\) | ||||
−0.343456 | + | 0.939169i | \(0.611598\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.8778 | −1.47081 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.3716i | 1.09254i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 36.4051i | − 1.18930i | −0.803983 | − | 0.594652i | \(-0.797290\pi\) | ||||
0.803983 | − | 0.594652i | \(-0.202710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.6794 | 1.06645 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.0968 | 0.915929 | 0.457965 | − | 0.888970i | \(-0.348579\pi\) | ||||
0.457965 | + | 0.888970i | \(0.348579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.1452i | 1.47013i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.8809i | 0.353583i | 0.984248 | + | 0.176792i | \(0.0565719\pi\) | ||||
−0.984248 | + | 0.176792i | \(0.943428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.4562 | −1.31326 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.92976 | 0.0625767 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.8103i | 1.25719i | 0.777733 | + | 0.628594i | \(0.216369\pi\) | ||||
−0.777733 | + | 0.628594i | \(0.783631\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.53162i | 0.146486i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.50717 | −0.0809606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0458 | −0.743413 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.92935i | 0.126621i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 47.1862i | − 1.51741i | −0.651437 | − | 0.758703i | \(-0.725834\pi\) | ||||
0.651437 | − | 0.758703i | \(-0.274166\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44.4465 | −1.42783 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0772 | 1.28614 | 0.643069 | − | 0.765809i | \(-0.277661\pi\) | ||||
0.643069 | + | 0.765809i | \(0.277661\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3.65548i | − 0.117189i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 2.29873i | − 0.0735430i | −0.999324 | − | 0.0367715i | \(-0.988293\pi\) | ||||
0.999324 | − | 0.0367715i | \(-0.0117074\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57.1452 | −1.82637 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.24072 | −0.103468 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 8.89578i | − 0.283731i | −0.989886 | − | 0.141866i | \(-0.954690\pi\) | ||||
0.989886 | − | 0.141866i | \(-0.0453101\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.32007i | − 0.0738486i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.4684 | 1.00064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.5652 | 1.19330 | 0.596649 | − | 0.802503i | \(-0.296499\pi\) | ||||
0.596649 | + | 0.802503i | \(0.296499\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 46.2542i | 1.46783i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.8081i | 0.817351i | 0.912680 | + | 0.408675i | \(0.134009\pi\) | ||||
−0.912680 | + | 0.408675i | \(0.865991\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −57.6929 | −1.82532 |
(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 | 2900.2.c.f.349.4 | 6 | ||
5.2 | odd | 4 | 580.2.a.c.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 2900.2.a.g.1.2 | 3 | |||
5.4 | even | 2 | inner | 2900.2.c.f.349.3 | 6 | ||
15.2 | even | 4 | 5220.2.a.x.1.2 | 3 | |||
20.7 | even | 4 | 2320.2.a.m.1.2 | 3 | |||
40.27 | even | 4 | 9280.2.a.bw.1.2 | 3 | |||
40.37 | odd | 4 | 9280.2.a.bk.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
580.2.a.c.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
2320.2.a.m.1.2 | 3 | 20.7 | even | 4 | |||
2900.2.a.g.1.2 | 3 | 5.3 | odd | 4 | |||
2900.2.c.f.349.3 | 6 | 5.4 | even | 2 | inner | ||
2900.2.c.f.349.4 | 6 | 1.1 | even | 1 | trivial | ||
5220.2.a.x.1.2 | 3 | 15.2 | even | 4 | |||
9280.2.a.bk.1.2 | 3 | 40.37 | odd | 4 | |||
9280.2.a.bw.1.2 | 3 | 40.27 | even | 4 |