Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1305,2,Mod(784,1305)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1305, 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("1305.784");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1305 = 3^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1305.c (of order \(2\), degree \(1\), 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: | \(10.4204774638\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} + 20x^{10} + 148x^{8} + 502x^{6} + 792x^{4} + 496x^{2} + 45 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 784.4 | ||
Root | \(-1.35513i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1305.784 |
Dual form | 1305.2.c.l.784.9 |
$q$-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 \(\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times\).
\(n\) | \(146\) | \(262\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.35513i | − | 0.958222i | −0.877754 | − | 0.479111i | \(-0.840959\pi\) | ||
0.877754 | − | 0.479111i | \(-0.159041\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.163621 | 0.0818103 | ||||||||
\(5\) | 1.94590 | − | 1.10158i | 0.870233 | − | 0.492640i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.26969i | − | 0.479897i | −0.970786 | − | 0.239949i | \(-0.922869\pi\) | ||
0.970786 | − | 0.239949i | \(-0.0771306\pi\) | |||||||
\(8\) | − | 2.93199i | − | 1.03661i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.49278 | − | 2.63695i | −0.472059 | − | 0.833877i | ||||
\(11\) | −0.474782 | −0.143152 | −0.0715761 | − | 0.997435i | \(-0.522803\pi\) | ||||
−0.0715761 | + | 0.997435i | \(0.522803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.407685i | 0.113071i | 0.998401 | + | 0.0565357i | \(0.0180055\pi\) | ||||
−0.998401 | + | 0.0565357i | \(0.981995\pi\) | |||||||
\(14\) | −1.72060 | −0.459848 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.64599 | −0.911497 | ||||||||
\(17\) | − | 2.97132i | − | 0.720651i | −0.932827 | − | 0.360326i | \(-0.882666\pi\) | ||
0.932827 | − | 0.360326i | \(-0.117334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.80491 | −1.33174 | −0.665868 | − | 0.746069i | \(-0.731939\pi\) | ||||
−0.665868 | + | 0.746069i | \(0.731939\pi\) | |||||||
\(20\) | 0.318389 | − | 0.180241i | 0.0711940 | − | 0.0403030i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.643392i | 0.137172i | ||||||||
\(23\) | − | 3.06516i | − | 0.639130i | −0.947564 | − | 0.319565i | \(-0.896463\pi\) | ||
0.947564 | − | 0.319565i | \(-0.103537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.57305 | − | 4.28712i | 0.514611 | − | 0.857424i | ||||
\(26\) | 0.552466 | 0.108348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 0.207747i | − | 0.0392605i | ||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.49210 | −0.806805 | −0.403403 | − | 0.915023i | \(-0.632173\pi\) | ||||
−0.403403 | + | 0.915023i | \(0.632173\pi\) | |||||||
\(32\) | − | 0.923188i | − | 0.163198i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.02653 | −0.690544 | ||||||||
\(35\) | −1.39866 | − | 2.47069i | −0.236417 | − | 0.417623i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.20325i | 1.18421i | 0.805862 | + | 0.592103i | \(0.201702\pi\) | ||||
−0.805862 | + | 0.592103i | \(0.798298\pi\) | |||||||
\(38\) | 7.86641i | 1.27610i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.22981 | − | 5.70536i | −0.510678 | − | 0.902096i | ||||
\(41\) | 12.0668 | 1.88452 | 0.942259 | − | 0.334886i | \(-0.108698\pi\) | ||||
0.942259 | + | 0.334886i | \(0.108698\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.03847i | 0.158365i | 0.996860 | + | 0.0791827i | \(0.0252310\pi\) | ||||
−0.996860 | + | 0.0791827i | \(0.974769\pi\) | |||||||
\(44\) | −0.0776841 | −0.0117113 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.15369 | −0.612428 | ||||||||
\(47\) | − | 2.97132i | − | 0.433412i | −0.976237 | − | 0.216706i | \(-0.930469\pi\) | ||
0.976237 | − | 0.216706i | \(-0.0695313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.38789 | 0.769698 | ||||||||
\(50\) | −5.80961 | − | 3.48682i | −0.821603 | − | 0.493111i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0667056i | 0.00925040i | ||||||||
\(53\) | 7.87199i | 1.08130i | 0.841247 | + | 0.540651i | \(0.181822\pi\) | ||||
−0.841247 | + | 0.540651i | \(0.818178\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.923879 | + | 0.523010i | −0.124576 | + | 0.0705226i | ||||
\(56\) | −3.72271 | −0.497469 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1.35513i | − | 0.177937i | ||||||
\(59\) | 4.45891 | 0.580501 | 0.290250 | − | 0.956951i | \(-0.406261\pi\) | ||||
0.290250 | + | 0.956951i | \(0.406261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.71609 | −0.219722 | −0.109861 | − | 0.993947i | \(-0.535041\pi\) | ||||
−0.109861 | + | 0.993947i | \(0.535041\pi\) | |||||||
\(62\) | 6.08739i | 0.773099i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.54301 | −1.06788 | ||||||||
\(65\) | 0.449097 | + | 0.793314i | 0.0557036 | + | 0.0983985i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 15.7754i | − | 1.92727i | −0.267218 | − | 0.963636i | \(-0.586104\pi\) | ||
0.267218 | − | 0.963636i | \(-0.413896\pi\) | |||||||
\(68\) | − | 0.486169i | − | 0.0589567i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.34811 | + | 1.89537i | −0.400175 | + | 0.226540i | ||||
\(71\) | 9.00806 | 1.06906 | 0.534530 | − | 0.845149i | \(-0.320489\pi\) | ||||
0.534530 | + | 0.845149i | \(0.320489\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.677990i | 0.0793527i | 0.999213 | + | 0.0396763i | \(0.0126327\pi\) | ||||
−0.999213 | + | 0.0396763i | \(0.987367\pi\) | |||||||
\(74\) | 9.76134 | 1.13473 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.949802 | −0.108950 | ||||||||
\(77\) | 0.602826i | 0.0686984i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.63957 | −0.184466 | −0.0922329 | − | 0.995737i | \(-0.529400\pi\) | ||||
−0.0922329 | + | 0.995737i | \(0.529400\pi\) | |||||||
\(80\) | −7.09473 | + | 4.01634i | −0.793215 | + | 0.449040i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 16.3521i | − | 1.80579i | ||||||
\(83\) | − | 15.5423i | − | 1.70599i | −0.521919 | − | 0.852995i | \(-0.674784\pi\) | ||
0.521919 | − | 0.852995i | \(-0.325216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.27314 | − | 5.78189i | −0.355022 | − | 0.627135i | ||||
\(86\) | 1.40726 | 0.151749 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.39206i | 0.148394i | ||||||||
\(89\) | −13.4175 | −1.42225 | −0.711126 | − | 0.703065i | \(-0.751814\pi\) | ||||
−0.711126 | + | 0.703065i | \(0.751814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.517633 | 0.0542627 | ||||||||
\(92\) | − | 0.501523i | − | 0.0522874i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.02653 | −0.415305 | ||||||||
\(95\) | −11.2958 | + | 6.39456i | −1.15892 | + | 0.656068i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.10733i | 0.721640i | 0.932636 | + | 0.360820i | \(0.117503\pi\) | ||||
−0.932636 | + | 0.360820i | \(0.882497\pi\) | |||||||
\(98\) | − | 7.30129i | − | 0.737542i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.421004 | − | 0.701461i | 0.0421004 | − | 0.0701461i | ||||
\(101\) | 4.68433 | 0.466108 | 0.233054 | − | 0.972464i | \(-0.425128\pi\) | ||||
0.233054 | + | 0.972464i | \(0.425128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5180i | 1.52904i | 0.644601 | + | 0.764519i | \(0.277024\pi\) | ||||
−0.644601 | + | 0.764519i | \(0.722976\pi\) | |||||||
\(104\) | 1.19533 | 0.117212 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6676 | 1.03613 | ||||||||
\(107\) | − | 0.676108i | − | 0.0653618i | −0.999466 | − | 0.0326809i | \(-0.989595\pi\) | ||
0.999466 | − | 0.0326809i | \(-0.0104045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.44734 | 0.713326 | 0.356663 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356663 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(110\) | 0.708746 | + | 1.25198i | 0.0675763 | + | 0.119371i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.62927i | 0.437425i | ||||||||
\(113\) | 14.1017i | 1.32658i | 0.748363 | + | 0.663290i | \(0.230840\pi\) | ||||
−0.748363 | + | 0.663290i | \(0.769160\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.37651 | − | 5.96449i | −0.314861 | − | 0.556192i | ||||
\(116\) | 0.163621 | 0.0151918 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.04241i | − | 0.556249i | ||||||
\(119\) | −3.77265 | −0.345839 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7746 | −0.979507 | ||||||||
\(122\) | 2.32552i | 0.210543i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.735000 | −0.0660050 | ||||||||
\(125\) | 0.284311 | − | 11.1767i | 0.0254295 | − | 0.999677i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5508i | 1.02497i | 0.858696 | + | 0.512486i | \(0.171275\pi\) | ||||
−0.858696 | + | 0.512486i | \(0.828725\pi\) | |||||||
\(128\) | 9.73053i | 0.860065i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.07504 | − | 0.608585i | 0.0942876 | − | 0.0533764i | ||||
\(131\) | 10.2432 | 0.894954 | 0.447477 | − | 0.894296i | \(-0.352323\pi\) | ||||
0.447477 | + | 0.894296i | \(0.352323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.37043i | 0.639097i | ||||||||
\(134\) | −21.3777 | −1.84676 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.71188 | −0.747038 | ||||||||
\(137\) | − | 2.06577i | − | 0.176491i | −0.996099 | − | 0.0882455i | \(-0.971874\pi\) | ||
0.996099 | − | 0.0882455i | \(-0.0281260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.48237 | −0.295370 | −0.147685 | − | 0.989034i | \(-0.547182\pi\) | ||||
−0.147685 | + | 0.989034i | \(0.547182\pi\) | |||||||
\(140\) | −0.228850 | − | 0.404255i | −0.0193413 | − | 0.0341658i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 12.2071i | − | 1.02440i | ||||||
\(143\) | − | 0.193562i | − | 0.0161864i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.94590 | − | 1.10158i | 0.161598 | − | 0.0914810i | ||||
\(146\) | 0.918765 | 0.0760375 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.17860i | 0.0968802i | ||||||||
\(149\) | −10.8558 | −0.889343 | −0.444672 | − | 0.895694i | \(-0.646680\pi\) | ||||
−0.444672 | + | 0.895694i | \(0.646680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3555 | 0.924097 | 0.462048 | − | 0.886855i | \(-0.347115\pi\) | ||||
0.462048 | + | 0.886855i | \(0.347115\pi\) | |||||||
\(152\) | 17.0199i | 1.38050i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.816908 | 0.0658283 | ||||||||
\(155\) | −8.74118 | + | 4.94840i | −0.702109 | + | 0.397465i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.9813i | − | 1.35526i | −0.735405 | − | 0.677628i | \(-0.763008\pi\) | ||
0.735405 | − | 0.677628i | \(-0.236992\pi\) | |||||||
\(158\) | 2.22183i | 0.176759i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.01696 | − | 1.79643i | −0.0803980 | − | 0.142020i | ||||
\(161\) | −3.89180 | −0.306717 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.78532i | 0.609793i | 0.952385 | + | 0.304897i | \(0.0986219\pi\) | ||||
−0.952385 | + | 0.304897i | \(0.901378\pi\) | |||||||
\(164\) | 1.97438 | 0.154173 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.0619 | −1.63472 | ||||||||
\(167\) | 2.06389i | 0.159709i | 0.996807 | + | 0.0798544i | \(0.0254455\pi\) | ||||
−0.996807 | + | 0.0798544i | \(0.974554\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8338 | 0.987215 | ||||||||
\(170\) | −7.83522 | + | 4.43553i | −0.600934 | + | 0.340190i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.169915i | 0.0129559i | ||||||||
\(173\) | − | 0.522120i | − | 0.0396960i | −0.999803 | − | 0.0198480i | \(-0.993682\pi\) | ||
0.999803 | − | 0.0198480i | \(-0.00631823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.44331 | − | 3.26698i | −0.411476 | − | 0.246960i | ||||
\(176\) | 1.73105 | 0.130483 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.1825i | 1.36283i | ||||||||
\(179\) | −10.4805 | −0.783346 | −0.391673 | − | 0.920104i | \(-0.628104\pi\) | ||||
−0.391673 | + | 0.920104i | \(0.628104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2724 | 0.912197 | 0.456099 | − | 0.889929i | \(-0.349246\pi\) | ||||
0.456099 | + | 0.889929i | \(0.349246\pi\) | |||||||
\(182\) | − | 0.701461i | − | 0.0519957i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.98701 | −0.662531 | ||||||||
\(185\) | 7.93494 | + | 14.0168i | 0.583388 | + | 1.03054i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.41073i | 0.103163i | ||||||||
\(188\) | − | 0.486169i | − | 0.0354575i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.66546 | + | 15.3072i | 0.628658 | + | 1.11050i | ||||
\(191\) | 9.69478 | 0.701490 | 0.350745 | − | 0.936471i | \(-0.385928\pi\) | ||||
0.350745 | + | 0.936471i | \(0.385928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0857i | 0.797963i | 0.916959 | + | 0.398982i | \(0.130636\pi\) | ||||
−0.916959 | + | 0.398982i | \(0.869364\pi\) | |||||||
\(194\) | 9.63136 | 0.691491 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.881569 | 0.0629692 | ||||||||
\(197\) | 2.00431i | 0.142801i | 0.997448 | + | 0.0714007i | \(0.0227469\pi\) | ||||
−0.997448 | + | 0.0714007i | \(0.977253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1170 | 1.28428 | 0.642140 | − | 0.766588i | \(-0.278047\pi\) | ||||
0.642140 | + | 0.766588i | \(0.278047\pi\) | |||||||
\(200\) | −12.5698 | − | 7.54416i | −0.888818 | − | 0.533453i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 6.34788i | − | 0.446635i | ||||||
\(203\) | − | 1.26969i | − | 0.0891147i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.4808 | − | 13.2925i | 1.63997 | − | 0.928390i | ||||
\(206\) | 21.0290 | 1.46516 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1.48641i | − | 0.103064i | ||||||
\(209\) | 2.75607 | 0.190641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4829 | 1.27241 | 0.636206 | − | 0.771519i | \(-0.280503\pi\) | ||||
0.636206 | + | 0.771519i | \(0.280503\pi\) | |||||||
\(212\) | 1.28802i | 0.0884615i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.916215 | −0.0626312 | ||||||||
\(215\) | 1.14396 | + | 2.02076i | 0.0780172 | + | 0.137815i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.70357i | 0.387184i | ||||||||
\(218\) | − | 10.0921i | − | 0.683525i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.151166 | + | 0.0855751i | −0.0101916 | + | 0.00576947i | ||||
\(221\) | 1.21136 | 0.0814851 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.6226i | 1.44796i | 0.689823 | + | 0.723978i | \(0.257688\pi\) | ||||
−0.689823 | + | 0.723978i | \(0.742312\pi\) | |||||||
\(224\) | −1.17216 | −0.0783184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.1097 | 1.27116 | ||||||||
\(227\) | − | 19.5621i | − | 1.29838i | −0.760625 | − | 0.649191i | \(-0.775108\pi\) | ||
0.760625 | − | 0.649191i | \(-0.224892\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7779 | −0.712220 | −0.356110 | − | 0.934444i | \(-0.615897\pi\) | ||||
−0.356110 | + | 0.934444i | \(0.615897\pi\) | |||||||
\(230\) | −8.08267 | + | 4.57561i | −0.532955 | + | 0.301707i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2.93199i | − | 0.192494i | ||||||
\(233\) | − | 4.25222i | − | 0.278572i | −0.990252 | − | 0.139286i | \(-0.955519\pi\) | ||
0.990252 | − | 0.139286i | \(-0.0444808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.27314 | − | 5.78189i | −0.213516 | − | 0.377169i | ||||
\(236\) | 0.729569 | 0.0474909 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.11244i | 0.331390i | ||||||||
\(239\) | −16.8385 | −1.08919 | −0.544596 | − | 0.838699i | \(-0.683317\pi\) | ||||
−0.544596 | + | 0.838699i | \(0.683317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.8396 | 1.40681 | 0.703405 | − | 0.710789i | \(-0.251662\pi\) | ||||
0.703405 | + | 0.710789i | \(0.251662\pi\) | |||||||
\(242\) | 14.6010i | 0.938586i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.280787 | −0.0179755 | ||||||||
\(245\) | 10.4843 | − | 5.93518i | 0.669817 | − | 0.379185i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.36657i | − | 0.150581i | ||||||
\(248\) | 13.1708i | 0.836346i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.1459 | − | 0.385278i | −0.957912 | − | 0.0243671i | ||||
\(251\) | 2.24264 | 0.141554 | 0.0707772 | − | 0.997492i | \(-0.477452\pi\) | ||||
0.0707772 | + | 0.997492i | \(0.477452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.45528i | 0.0914929i | ||||||||
\(254\) | 15.6529 | 0.982150 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.89989 | −0.243743 | ||||||||
\(257\) | − | 1.27685i | − | 0.0796479i | −0.999207 | − | 0.0398239i | \(-0.987320\pi\) | ||
0.999207 | − | 0.0398239i | \(-0.0126797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.14589 | 0.568298 | ||||||||
\(260\) | 0.0734814 | + | 0.129802i | 0.00455712 | + | 0.00805001i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 13.8809i | − | 0.857564i | ||||||
\(263\) | − | 19.6767i | − | 1.21332i | −0.794963 | − | 0.606658i | \(-0.792510\pi\) | ||
0.794963 | − | 0.606658i | \(-0.207490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.67161 | + | 15.3181i | 0.532693 | + | 0.940984i | ||||
\(266\) | 9.98789 | 0.612397 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2.58118i | − | 0.157671i | ||||||
\(269\) | 11.7353 | 0.715516 | 0.357758 | − | 0.933814i | \(-0.383541\pi\) | ||||
0.357758 | + | 0.933814i | \(0.383541\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.92348 | −0.602809 | −0.301404 | − | 0.953496i | \(-0.597455\pi\) | ||||
−0.301404 | + | 0.953496i | \(0.597455\pi\) | |||||||
\(272\) | 10.8334i | 0.656871i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.79940 | −0.169118 | ||||||||
\(275\) | −1.22164 | + | 2.03545i | −0.0736677 | + | 0.122742i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.50995i | 0.0907242i | 0.998971 | + | 0.0453621i | \(0.0144442\pi\) | ||||
−0.998971 | + | 0.0453621i | \(0.985556\pi\) | |||||||
\(278\) | 4.71906i | 0.283031i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.24403 | + | 4.10086i | −0.432914 | + | 0.245073i | ||||
\(281\) | 25.3285 | 1.51097 | 0.755487 | − | 0.655164i | \(-0.227400\pi\) | ||||
0.755487 | + | 0.655164i | \(0.227400\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.09287i | − | 0.124408i | −0.998063 | − | 0.0622041i | \(-0.980187\pi\) | ||
0.998063 | − | 0.0622041i | \(-0.0198130\pi\) | |||||||
\(284\) | 1.47390 | 0.0874601 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.262301 | −0.0155102 | ||||||||
\(287\) | − | 15.3211i | − | 0.904375i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17125 | 0.480662 | ||||||||
\(290\) | −1.49278 | − | 2.63695i | −0.0876592 | − | 0.154847i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.110933i | 0.00649186i | ||||||||
\(293\) | − | 10.8526i | − | 0.634013i | −0.948423 | − | 0.317007i | \(-0.897322\pi\) | ||
0.948423 | − | 0.317007i | \(-0.102678\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.67660 | − | 4.91184i | 0.505171 | − | 0.285978i | ||||
\(296\) | 21.1198 | 1.22757 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.7111i | 0.852189i | ||||||||
\(299\) | 1.24962 | 0.0722674 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.31854 | 0.0759991 | ||||||||
\(302\) | − | 15.3882i | − | 0.885490i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 21.1646 | 1.21387 | ||||||||
\(305\) | −3.33933 | + | 1.89040i | −0.191210 | + | 0.108244i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.8956i | 0.964281i | 0.876094 | + | 0.482141i | \(0.160141\pi\) | ||||
−0.876094 | + | 0.482141i | \(0.839859\pi\) | |||||||
\(308\) | 0.0986347i | 0.00562023i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.70573 | + | 11.8454i | 0.380860 | + | 0.672776i | ||||
\(311\) | −10.6643 | −0.604717 | −0.302359 | − | 0.953194i | \(-0.597774\pi\) | ||||
−0.302359 | + | 0.953194i | \(0.597774\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8702i | 0.783991i | 0.919967 | + | 0.391995i | \(0.128215\pi\) | ||||
−0.919967 | + | 0.391995i | \(0.871785\pi\) | |||||||
\(314\) | −23.0119 | −1.29864 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.268267 | −0.0150912 | ||||||||
\(317\) | 1.33953i | 0.0752355i | 0.999292 | + | 0.0376178i | \(0.0119769\pi\) | ||||
−0.999292 | + | 0.0376178i | \(0.988023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.474782 | −0.0265827 | ||||||||
\(320\) | −16.6239 | + | 9.41079i | −0.929302 | + | 0.526079i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.27390i | 0.293903i | ||||||||
\(323\) | 17.2482i | 0.959718i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.74779 | + | 1.04900i | 0.0969502 | + | 0.0581878i | ||||
\(326\) | 10.5501 | 0.584317 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 35.3797i | − | 1.95352i | ||||||
\(329\) | −3.77265 | −0.207993 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.00072 | −0.164934 | −0.0824672 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824672 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(332\) | − | 2.54304i | − | 0.139567i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.79685 | 0.153037 | ||||||||
\(335\) | −17.3778 | − | 30.6974i | −0.949452 | − | 1.67718i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.2763i | 1.32241i | 0.750203 | + | 0.661207i | \(0.229956\pi\) | ||||
−0.750203 | + | 0.661207i | \(0.770044\pi\) | |||||||
\(338\) | − | 17.3915i | − | 0.945971i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.535553 | − | 0.946037i | −0.0290444 | − | 0.0513060i | ||||
\(341\) | 2.13277 | 0.115496 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.7288i | − | 0.849274i | ||||||
\(344\) | 3.04479 | 0.164164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.707540 | −0.0380376 | ||||||||
\(347\) | 14.0792i | 0.755809i | 0.925845 | + | 0.377904i | \(0.123355\pi\) | ||||
−0.925845 | + | 0.377904i | \(0.876645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.9641 | 0.961597 | 0.480798 | − | 0.876831i | \(-0.340347\pi\) | ||||
0.480798 | + | 0.876831i | \(0.340347\pi\) | |||||||
\(350\) | −4.42718 | + | 7.37640i | −0.236643 | + | 0.394285i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.438313i | 0.0233622i | ||||||||
\(353\) | − | 9.49061i | − | 0.505134i | −0.967579 | − | 0.252567i | \(-0.918725\pi\) | ||
0.967579 | − | 0.252567i | \(-0.0812748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.5288 | − | 9.92308i | 0.930331 | − | 0.526662i | ||||
\(356\) | −2.19538 | −0.116355 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.2024i | 0.750620i | ||||||||
\(359\) | 4.09130 | 0.215931 | 0.107965 | − | 0.994155i | \(-0.465566\pi\) | ||||
0.107965 | + | 0.994155i | \(0.465566\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6969 | 0.773523 | ||||||||
\(362\) | − | 16.6307i | − | 0.874088i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0846954 | 0.00443925 | ||||||||
\(365\) | 0.746858 | + | 1.31930i | 0.0390923 | + | 0.0690553i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.8383i | 0.983351i | 0.870778 | + | 0.491676i | \(0.163615\pi\) | ||||
−0.870778 | + | 0.491676i | \(0.836385\pi\) | |||||||
\(368\) | 11.1755i | 0.582565i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.9946 | − | 10.7529i | 0.987482 | − | 0.559015i | ||||
\(371\) | 9.99498 | 0.518914 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7.23999i | − | 0.374872i | −0.982277 | − | 0.187436i | \(-0.939982\pi\) | ||
0.982277 | − | 0.187436i | \(-0.0600178\pi\) | |||||||
\(374\) | 1.91172 | 0.0988529 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.71188 | −0.449281 | ||||||||
\(377\) | 0.407685i | 0.0209968i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.2420 | −1.03976 | −0.519881 | − | 0.854239i | \(-0.674024\pi\) | ||||
−0.519881 | + | 0.854239i | \(0.674024\pi\) | |||||||
\(380\) | −1.84822 | + | 1.04628i | −0.0948117 | + | 0.0536731i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 13.1377i | − | 0.672183i | ||||||
\(383\) | 4.34201i | 0.221866i | 0.993828 | + | 0.110933i | \(0.0353840\pi\) | ||||
−0.993828 | + | 0.110933i | \(0.964616\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.664060 | + | 1.17304i | 0.0338436 | + | 0.0597836i | ||||
\(386\) | 15.0225 | 0.764626 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.16290i | 0.0590375i | ||||||||
\(389\) | 0.508687 | 0.0257915 | 0.0128957 | − | 0.999917i | \(-0.495895\pi\) | ||||
0.0128957 | + | 0.999917i | \(0.495895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.10757 | −0.460590 | ||||||||
\(392\) | − | 15.7972i | − | 0.797881i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.71611 | 0.136835 | ||||||||
\(395\) | −3.19044 | + | 1.80611i | −0.160528 | + | 0.0908753i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.2135i | 1.56656i | 0.621669 | + | 0.783280i | \(0.286455\pi\) | ||||
−0.621669 | + | 0.783280i | \(0.713545\pi\) | |||||||
\(398\) | − | 24.5509i | − | 1.23063i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.38132 | + | 15.6308i | −0.469066 | + | 0.781539i | ||||
\(401\) | −5.60957 | −0.280129 | −0.140064 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140064 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.83136i | − | 0.0912267i | ||||||
\(404\) | 0.766452 | 0.0381324 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.72060 | −0.0853917 | ||||||||
\(407\) | − | 3.41997i | − | 0.169522i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.68080 | 0.478685 | 0.239342 | − | 0.970935i | \(-0.423068\pi\) | ||||
0.239342 | + | 0.970935i | \(0.423068\pi\) | |||||||
\(410\) | −18.0131 | − | 31.8195i | −0.889603 | − | 1.57145i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.53907i | 0.125091i | ||||||||
\(413\) | − | 5.66143i | − | 0.278581i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.1211 | − | 30.2438i | −0.840439 | − | 1.48461i | ||||
\(416\) | 0.376370 | 0.0184530 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 3.73483i | − | 0.182677i | ||||||
\(419\) | 18.2788 | 0.892979 | 0.446489 | − | 0.894789i | \(-0.352674\pi\) | ||||
0.446489 | + | 0.894789i | \(0.352674\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0517 | 1.26968 | 0.634842 | − | 0.772642i | \(-0.281065\pi\) | ||||
0.634842 | + | 0.772642i | \(0.281065\pi\) | |||||||
\(422\) | − | 25.0467i | − | 1.21925i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23.0806 | 1.12089 | ||||||||
\(425\) | −12.7384 | − | 7.64537i | −0.617904 | − | 0.370855i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.17890i | 0.105444i | ||||||||
\(428\) | − | 0.110625i | − | 0.00534727i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.73839 | − | 1.55021i | 0.132057 | − | 0.0747578i | ||||
\(431\) | 6.19278 | 0.298296 | 0.149148 | − | 0.988815i | \(-0.452347\pi\) | ||||
0.149148 | + | 0.988815i | \(0.452347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 35.1538i | − | 1.68938i | −0.535253 | − | 0.844692i | \(-0.679784\pi\) | ||
0.535253 | − | 0.844692i | \(-0.320216\pi\) | |||||||
\(434\) | 7.72909 | 0.371008 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.21854 | 0.0583574 | ||||||||
\(437\) | 17.7930i | 0.851153i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.1018 | 0.959408 | 0.479704 | − | 0.877430i | \(-0.340744\pi\) | ||||
0.479704 | + | 0.877430i | \(0.340744\pi\) | |||||||
\(440\) | 1.53346 | + | 2.70880i | 0.0731047 | + | 0.129137i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.64156i | − | 0.0780808i | ||||||
\(443\) | 20.8513i | 0.990676i | 0.868700 | + | 0.495338i | \(0.164956\pi\) | ||||
−0.868700 | + | 0.495338i | \(0.835044\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.1091 | + | 14.7804i | −1.23769 | + | 0.700659i | ||||
\(446\) | 29.3014 | 1.38746 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.8470i | 0.512471i | ||||||||
\(449\) | −39.5199 | −1.86506 | −0.932529 | − | 0.361094i | \(-0.882403\pi\) | ||||
−0.932529 | + | 0.361094i | \(0.882403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.72910 | −0.269773 | ||||||||
\(452\) | 2.30733i | 0.108528i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.5092 | −1.24414 | ||||||||
\(455\) | 1.00726 | − | 0.570213i | 0.0472212 | − | 0.0267320i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.6115i | 1.19806i | 0.800728 | + | 0.599028i | \(0.204446\pi\) | ||||
−0.800728 | + | 0.599028i | \(0.795554\pi\) | |||||||
\(458\) | 14.6054i | 0.682465i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.552466 | − | 0.975914i | −0.0257589 | − | 0.0455022i | ||||
\(461\) | −0.911675 | −0.0424609 | −0.0212305 | − | 0.999775i | \(-0.506758\pi\) | ||||
−0.0212305 | + | 0.999775i | \(0.506758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.9744i | − | 1.20713i | −0.797312 | − | 0.603567i | \(-0.793746\pi\) | ||
0.797312 | − | 0.603567i | \(-0.206254\pi\) | |||||||
\(464\) | −3.64599 | −0.169261 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.76231 | −0.266934 | ||||||||
\(467\) | 15.8506i | 0.733479i | 0.930324 | + | 0.366739i | \(0.119526\pi\) | ||||
−0.930324 | + | 0.366739i | \(0.880474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.0299 | −0.924893 | ||||||||
\(470\) | −7.83522 | + | 4.43553i | −0.361412 | + | 0.204596i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 13.0735i | − | 0.601756i | ||||||
\(473\) | − | 0.493048i | − | 0.0226704i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.9363 | + | 24.8863i | −0.685326 | + | 1.14186i | ||||
\(476\) | −0.617284 | −0.0282932 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.8184i | 1.04369i | ||||||||
\(479\) | −16.3087 | −0.745162 | −0.372581 | − | 0.928000i | \(-0.621527\pi\) | ||||
−0.372581 | + | 0.928000i | \(0.621527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.93666 | −0.133900 | ||||||||
\(482\) | − | 29.5955i | − | 1.34804i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.76294 | −0.0801338 | ||||||||
\(485\) | 7.82927 | + | 13.8301i | 0.355509 | + | 0.627995i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.93950i | 0.450402i | 0.974312 | + | 0.225201i | \(0.0723039\pi\) | ||||
−0.974312 | + | 0.225201i | \(0.927696\pi\) | |||||||
\(488\) | 5.03155i | 0.227767i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.04294 | − | 14.2076i | −0.363343 | − | 0.641833i | ||||
\(491\) | 38.0638 | 1.71779 | 0.858897 | − | 0.512149i | \(-0.171150\pi\) | ||||
0.858897 | + | 0.512149i | \(0.171150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.97132i | − | 0.133822i | ||||||
\(494\) | −3.20702 | −0.144290 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.3781 | 0.735401 | ||||||||
\(497\) | − | 11.4374i | − | 0.513039i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −44.3795 | −1.98670 | −0.993349 | − | 0.115143i | \(-0.963267\pi\) | ||||
−0.993349 | + | 0.115143i | \(0.963267\pi\) | |||||||
\(500\) | 0.0465190 | − | 1.82874i | 0.00208039 | − | 0.0817838i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 3.03908i | − | 0.135641i | ||||||
\(503\) | − | 3.18073i | − | 0.141822i | −0.997483 | − | 0.0709108i | \(-0.977409\pi\) | ||
0.997483 | − | 0.0709108i | \(-0.0225906\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.11524 | − | 5.16015i | 0.405623 | − | 0.229624i | ||||
\(506\) | 1.97210 | 0.0876705 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.88995i | 0.0838532i | ||||||||
\(509\) | −30.5882 | −1.35580 | −0.677899 | − | 0.735155i | \(-0.737109\pi\) | ||||
−0.677899 | + | 0.735155i | \(0.737109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.860836 | 0.0380811 | ||||||||
\(512\) | 24.7459i | 1.09363i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.73030 | −0.0763203 | ||||||||
\(515\) | 17.0943 | + | 30.1966i | 0.753266 | + | 1.33062i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.41073i | 0.0620439i | ||||||||
\(518\) | − | 12.3939i | − | 0.544555i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.32599 | − | 1.31675i | 0.102001 | − | 0.0577431i | ||||
\(521\) | 28.7858 | 1.26113 | 0.630564 | − | 0.776138i | \(-0.282824\pi\) | ||||
0.630564 | + | 0.776138i | \(0.282824\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 27.2018i | − | 1.18945i | −0.803928 | − | 0.594726i | \(-0.797261\pi\) | ||
0.803928 | − | 0.594726i | \(-0.202739\pi\) | |||||||
\(524\) | 1.67600 | 0.0732164 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.6645 | −1.16263 | ||||||||
\(527\) | 13.3475i | 0.581425i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.6048 | 0.591513 | ||||||||
\(530\) | 20.7580 | − | 11.7512i | 0.901672 | − | 0.510438i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.20595i | 0.0522847i | ||||||||
\(533\) | 4.91945i | 0.213085i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.744785 | − | 1.31564i | −0.0321999 | − | 0.0568800i | ||||
\(536\) | −46.2533 | −1.99784 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 15.9029i | − | 0.685623i | ||||||
\(539\) | −2.55807 | −0.110184 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.84584 | 0.251332 | 0.125666 | − | 0.992073i | \(-0.459893\pi\) | ||||
0.125666 | + | 0.992073i | \(0.459893\pi\) | |||||||
\(542\) | 13.4476i | 0.577625i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.74309 | −0.117609 | ||||||||
\(545\) | 14.4918 | − | 8.20382i | 0.620760 | − | 0.351413i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.9324i | − | 0.809489i | −0.914430 | − | 0.404745i | \(-0.867360\pi\) | ||
0.914430 | − | 0.404745i | \(-0.132640\pi\) | |||||||
\(548\) | − | 0.338003i | − | 0.0144388i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.75830 | + | 1.65548i | 0.117614 | + | 0.0705900i | ||||
\(551\) | −5.80491 | −0.247297 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.08174i | 0.0885247i | ||||||||
\(554\) | 2.04618 | 0.0869340 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.569787 | −0.0241643 | ||||||||
\(557\) | 29.6529i | 1.25643i | 0.778038 | + | 0.628217i | \(0.216215\pi\) | ||||
−0.778038 | + | 0.628217i | \(0.783785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.423369 | −0.0179066 | ||||||||
\(560\) | 5.09950 | + | 9.00810i | 0.215493 | + | 0.380662i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 34.3235i | − | 1.44785i | ||||||
\(563\) | 19.3966i | 0.817471i | 0.912653 | + | 0.408736i | \(0.134030\pi\) | ||||
−0.912653 | + | 0.408736i | \(0.865970\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.5342 | + | 27.4406i | 0.653527 | + | 1.15443i | ||||
\(566\) | −2.83611 | −0.119211 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 26.4115i | − | 1.10820i | ||||||
\(569\) | 6.00700 | 0.251826 | 0.125913 | − | 0.992041i | \(-0.459814\pi\) | ||||
0.125913 | + | 0.992041i | \(0.459814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.1469 | −1.17791 | −0.588957 | − | 0.808165i | \(-0.700461\pi\) | ||||
−0.588957 | + | 0.808165i | \(0.700461\pi\) | |||||||
\(572\) | − | 0.0316706i | − | 0.00132422i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20.7621 | −0.866592 | ||||||||
\(575\) | −13.1407 | − | 7.88682i | −0.548005 | − | 0.328903i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.9966i | 1.37367i | 0.726815 | + | 0.686834i | \(0.241000\pi\) | ||||
−0.726815 | + | 0.686834i | \(0.759000\pi\) | |||||||
\(578\) | − | 11.0731i | − | 0.460581i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.318389 | − | 0.180241i | 0.0132204 | − | 0.00748409i | ||||
\(581\) | −19.7339 | −0.818700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.73748i | − | 0.154791i | ||||||
\(584\) | 1.98786 | 0.0822581 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.7066 | −0.607526 | ||||||||
\(587\) | 7.81241i | 0.322453i | 0.986917 | + | 0.161226i | \(0.0515449\pi\) | ||||
−0.986917 | + | 0.161226i | \(0.948455\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.0762 | 1.07445 | ||||||||
\(590\) | −6.65618 | − | 11.7579i | −0.274031 | − | 0.484066i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 26.2629i | − | 1.07940i | ||||||
\(593\) | 33.5131i | 1.37622i | 0.725608 | + | 0.688108i | \(0.241559\pi\) | ||||
−0.725608 | + | 0.688108i | \(0.758441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.34121 | + | 4.15587i | −0.300960 | + | 0.170374i | ||||
\(596\) | −1.77623 | −0.0727574 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 1.69340i | − | 0.0692482i | ||||||
\(599\) | −27.1213 | −1.10815 | −0.554074 | − | 0.832468i | \(-0.686927\pi\) | ||||
−0.554074 | + | 0.832468i | \(0.686927\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.4641 | −0.712376 | −0.356188 | − | 0.934414i | \(-0.615924\pi\) | ||||
−0.356188 | + | 0.934414i | \(0.615924\pi\) | |||||||
\(602\) | − | 1.78679i | − | 0.0728240i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.85799 | 0.0756006 | ||||||||
\(605\) | −20.9663 | + | 11.8690i | −0.852400 | + | 0.482545i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 32.9273i | − | 1.33648i | −0.743947 | − | 0.668239i | \(-0.767049\pi\) | ||
0.743947 | − | 0.668239i | \(-0.232951\pi\) | |||||||
\(608\) | 5.35902i | 0.217337i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.56174 | + | 4.52523i | 0.103722 | + | 0.183221i | ||||
\(611\) | 1.21136 | 0.0490065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.97228i | 0.120049i | 0.998197 | + | 0.0600245i | \(0.0191179\pi\) | ||||
−0.998197 | + | 0.0600245i | \(0.980882\pi\) | |||||||
\(614\) | 22.8957 | 0.923996 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.76748 | 0.0712138 | ||||||||
\(617\) | − | 0.0642578i | − | 0.00258692i | −0.999999 | − | 0.00129346i | \(-0.999588\pi\) | ||
0.999999 | − | 0.00129346i | \(-0.000411722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.45588 | −0.299677 | −0.149839 | − | 0.988710i | \(-0.547875\pi\) | ||||
−0.149839 | + | 0.988710i | \(0.547875\pi\) | |||||||
\(620\) | −1.43024 | + | 0.809660i | −0.0574397 | + | 0.0325167i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.4515i | 0.579454i | ||||||||
\(623\) | 17.0360i | 0.682535i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.7588 | − | 22.0620i | −0.470352 | − | 0.882479i | ||||
\(626\) | 18.7960 | 0.751237 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 2.77849i | − | 0.110874i | ||||||
\(629\) | 21.4032 | 0.853400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.0735 | −1.51568 | −0.757841 | − | 0.652439i | \(-0.773746\pi\) | ||||
−0.757841 | + | 0.652439i | \(0.773746\pi\) | |||||||
\(632\) | 4.80720i | 0.191220i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.81524 | 0.0720924 | ||||||||
\(635\) | 12.7241 | + | 22.4768i | 0.504942 | + | 0.891964i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.19656i | 0.0870309i | ||||||||
\(638\) | 0.643392i | 0.0254721i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.7189 | + | 18.9346i | 0.423703 | + | 0.748457i | ||||
\(641\) | −4.49665 | −0.177607 | −0.0888035 | − | 0.996049i | \(-0.528304\pi\) | ||||
−0.0888035 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 20.9607i | − | 0.826610i | −0.910593 | − | 0.413305i | \(-0.864374\pi\) | ||
0.910593 | − | 0.413305i | \(-0.135626\pi\) | |||||||
\(644\) | −0.636778 | −0.0250926 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.3736 | 0.919623 | ||||||||
\(647\) | 37.8398i | 1.48764i | 0.668381 | + | 0.743819i | \(0.266987\pi\) | ||||
−0.668381 | + | 0.743819i | \(0.733013\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.11701 | −0.0831000 | ||||||||
\(650\) | 1.42153 | − | 2.36849i | 0.0557568 | − | 0.0928998i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.27384i | 0.0498873i | ||||||||
\(653\) | 48.0703i | 1.88114i | 0.339606 | + | 0.940568i | \(0.389706\pi\) | ||||
−0.339606 | + | 0.940568i | \(0.610294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.9323 | − | 11.2837i | 0.778818 | − | 0.440890i | ||||
\(656\) | −43.9954 | −1.71773 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.11244i | 0.199304i | ||||||||
\(659\) | −26.0861 | −1.01617 | −0.508084 | − | 0.861307i | \(-0.669646\pi\) | ||||
−0.508084 | + | 0.861307i | \(0.669646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00120 | 0.194524 | 0.0972620 | − | 0.995259i | \(-0.468992\pi\) | ||||
0.0972620 | + | 0.995259i | \(0.468992\pi\) | |||||||
\(662\) | 4.06636i | 0.158044i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −45.5699 | −1.76845 | ||||||||
\(665\) | 8.11910 | + | 14.3421i | 0.314845 | + | 0.556163i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.06516i | − | 0.118683i | ||||||
\(668\) | 0.337695i | 0.0130658i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −41.5989 | + | 23.5492i | −1.60711 | + | 0.909786i | ||||
\(671\) | 0.814768 | 0.0314538 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.1113i | 1.00652i | 0.864136 | + | 0.503258i | \(0.167866\pi\) | ||||
−0.864136 | + | 0.503258i | \(0.832134\pi\) | |||||||
\(674\) | 32.8976 | 1.26717 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.09987 | 0.0807643 | ||||||||
\(677\) | − | 32.0992i | − | 1.23367i | −0.787092 | − | 0.616836i | \(-0.788414\pi\) | ||
0.787092 | − | 0.616836i | \(-0.211586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.02410 | 0.346313 | ||||||||
\(680\) | −16.9524 | + | 9.59681i | −0.650097 | + | 0.368021i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 2.89018i | − | 0.110671i | ||||||
\(683\) | − | 4.70468i | − | 0.180020i | −0.995941 | − | 0.0900098i | \(-0.971310\pi\) | ||
0.995941 | − | 0.0900098i | \(-0.0286898\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.27561 | − | 4.01979i | −0.0869466 | − | 0.153588i | ||||
\(686\) | −21.3145 | −0.813793 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 3.78625i | − | 0.144349i | ||||||
\(689\) | −3.20929 | −0.122264 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.881335 | 0.0335276 | 0.0167638 | − | 0.999859i | \(-0.494664\pi\) | ||||
0.0167638 | + | 0.999859i | \(0.494664\pi\) | |||||||
\(692\) | − | 0.0854295i | − | 0.00324754i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.0791 | 0.724233 | ||||||||
\(695\) | −6.77634 | + | 3.83610i | −0.257041 | + | 0.145511i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 35.8543i | − | 1.35808i | ||||||
\(698\) | − | 24.3437i | − | 0.921423i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.890637 | − | 0.534545i | −0.0336629 | − | 0.0202039i | ||||
\(701\) | −45.1606 | −1.70569 | −0.852847 | − | 0.522161i | \(-0.825126\pi\) | ||||
−0.852847 | + | 0.522161i | \(0.825126\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 41.8142i | − | 1.57705i | ||||||
\(704\) | 4.05607 | 0.152869 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.8610 | −0.484031 | ||||||||
\(707\) | − | 5.94764i | − | 0.223684i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.8061 | −0.706277 | −0.353139 | − | 0.935571i | \(-0.614886\pi\) | ||||
−0.353139 | + | 0.935571i | \(0.614886\pi\) | |||||||
\(710\) | −13.4471 | − | 23.7538i | −0.504660 | − | 0.891464i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 39.3399i | 1.47433i | ||||||||
\(713\) | 13.7690i | 0.515653i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.213223 | − | 0.376652i | −0.00797409 | − | 0.0140860i | ||||
\(716\) | −1.71482 | −0.0640857 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 5.54425i | − | 0.206910i | ||||||
\(719\) | 18.7384 | 0.698824 | 0.349412 | − | 0.936969i | \(-0.386381\pi\) | ||||
0.349412 | + | 0.936969i | \(0.386381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.7031 | 0.733782 | ||||||||
\(722\) | − | 19.9163i | − | 0.741207i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.00801 | 0.0746271 | ||||||||
\(725\) | 2.57305 | − | 4.28712i | 0.0955608 | − | 0.159220i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 20.2155i | − | 0.749752i | −0.927075 | − | 0.374876i | \(-0.877685\pi\) | ||
0.927075 | − | 0.374876i | \(-0.122315\pi\) | |||||||
\(728\) | − | 1.51769i | − | 0.0562495i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.78782 | − | 1.01209i | 0.0661703 | − | 0.0374591i | ||||
\(731\) | 3.08563 | 0.114126 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 45.1963i | − | 1.66936i | −0.550732 | − | 0.834682i | \(-0.685651\pi\) | ||
0.550732 | − | 0.834682i | \(-0.314349\pi\) | |||||||
\(734\) | 25.5284 | 0.942269 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.82972 | −0.104305 | ||||||||
\(737\) | 7.48988i | 0.275893i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.2473 | −1.55409 | −0.777046 | − | 0.629443i | \(-0.783283\pi\) | ||||
−0.777046 | + | 0.629443i | \(0.783283\pi\) | |||||||
\(740\) | 1.29832 | + | 2.29344i | 0.0477271 | + | 0.0843084i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 13.5445i | − | 0.497235i | ||||||
\(743\) | − | 38.5919i | − | 1.41580i | −0.706313 | − | 0.707900i | \(-0.749643\pi\) | ||
0.706313 | − | 0.707900i | \(-0.250357\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.1243 | + | 11.9585i | −0.773936 | + | 0.438127i | ||||
\(746\) | −9.81113 | −0.359211 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.230825i | 0.00843978i | ||||||||
\(749\) | −0.858447 | −0.0313670 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.50634 | −0.0549670 | −0.0274835 | − | 0.999622i | \(-0.508749\pi\) | ||||
−0.0274835 | + | 0.999622i | \(0.508749\pi\) | |||||||
\(752\) | 10.8334i | 0.395053i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.552466 | 0.0201196 | ||||||||
\(755\) | 22.0966 | − | 12.5090i | 0.804179 | − | 0.455247i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.3890i | 0.632016i | 0.948757 | + | 0.316008i | \(0.102343\pi\) | ||||
−0.948757 | + | 0.316008i | \(0.897657\pi\) | |||||||
\(758\) | 27.4306i | 0.996324i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.7488 | + | 33.1191i | 0.680089 | + | 1.20135i | ||||
\(761\) | 9.21457 | 0.334028 | 0.167014 | − | 0.985955i | \(-0.446587\pi\) | ||||
0.167014 | + | 0.985955i | \(0.446587\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 9.45581i | − | 0.342323i | ||||||
\(764\) | 1.58626 | 0.0573890 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.88399 | 0.212597 | ||||||||
\(767\) | 1.81783i | 0.0656381i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.6939 | −0.926547 | −0.463273 | − | 0.886215i | \(-0.653325\pi\) | ||||
−0.463273 | + | 0.886215i | \(0.653325\pi\) | |||||||
\(770\) | 1.58962 | − | 0.899888i | 0.0572860 | − | 0.0324297i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.81384i | 0.0652816i | ||||||||
\(773\) | − | 42.9070i | − | 1.54326i | −0.636074 | − | 0.771628i | \(-0.719443\pi\) | ||
0.636074 | − | 0.771628i | \(-0.280557\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.5584 | + | 19.2582i | −0.415191 | + | 0.691774i | ||||
\(776\) | 20.8386 | 0.748062 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 0.689338i | − | 0.0247140i | ||||||
\(779\) | −70.0466 | −2.50968 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.27687 | −0.153038 | ||||||||
\(782\) | 12.3420i | 0.441347i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.6442 | −0.701578 | ||||||||
\(785\) | −18.7062 | − | 33.0439i | −0.667653 | − | 1.17939i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.2120i | 0.791772i | 0.918300 | + | 0.395886i | \(0.129562\pi\) | ||||
−0.918300 | + | 0.395886i | \(0.870438\pi\) | |||||||
\(788\) | 0.327947i | 0.0116826i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.44752 | + | 4.32346i | 0.0870788 | + | 0.153822i | ||||
\(791\) | 17.9048 | 0.636622 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.699623i | − | 0.0248443i | ||||||
\(794\) | 42.2984 | 1.50111 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.96431 | 0.105067 | ||||||||
\(797\) | − | 46.2386i | − | 1.63785i | −0.573897 | − | 0.818927i | \(-0.694569\pi\) | ||
0.573897 | − | 0.818927i | \(-0.305431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.82875 | −0.312339 | ||||||||
\(800\) | −3.95782 | − | 2.37541i | −0.139930 | − | 0.0839835i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.60171i | 0.268426i | ||||||||
\(803\) | − | 0.321897i | − | 0.0113595i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.57305 | + | 4.28712i | −0.266915 | + | 0.151101i | ||||
\(806\) | −2.48174 | −0.0874154 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 13.7344i | − | 0.483175i | ||||||
\(809\) | −23.9257 | −0.841184 | −0.420592 | − | 0.907250i | \(-0.638178\pi\) | ||||
−0.420592 | + | 0.907250i | \(0.638178\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.0210 | −1.82670 | −0.913352 | − | 0.407170i | \(-0.866516\pi\) | ||||
−0.913352 | + | 0.407170i | \(0.866516\pi\) | |||||||
\(812\) | − | 0.207747i | − | 0.00729050i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.63451 | −0.162440 | ||||||||
\(815\) | 8.57613 | + | 15.1494i | 0.300409 | + | 0.530662i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.02823i | − | 0.210901i | ||||||
\(818\) | − | 13.1188i | − | 0.458686i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.84194 | − | 2.17493i | 0.134166 | − | 0.0759518i | ||||
\(821\) | 15.0444 | 0.525052 | 0.262526 | − | 0.964925i | \(-0.415444\pi\) | ||||
0.262526 | + | 0.964925i | \(0.415444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.8652i | 1.56390i | 0.623339 | + | 0.781952i | \(0.285776\pi\) | ||||
−0.623339 | + | 0.781952i | \(0.714224\pi\) | |||||||
\(824\) | 45.4987 | 1.58502 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.67198 | −0.266942 | ||||||||
\(827\) | − | 41.5569i | − | 1.44508i | −0.691331 | − | 0.722538i | \(-0.742975\pi\) | ||
0.691331 | − | 0.722538i | \(-0.257025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.3645 | 0.880946 | 0.440473 | − | 0.897766i | \(-0.354811\pi\) | ||||
0.440473 | + | 0.897766i | \(0.354811\pi\) | |||||||
\(830\) | −40.9843 | + | 23.2013i | −1.42258 | + | 0.805328i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 3.48286i | − | 0.120746i | ||||||
\(833\) | − | 16.0092i | − | 0.554684i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.27354 | + | 4.01613i | 0.0786790 | + | 0.138984i | ||||
\(836\) | 0.450949 | 0.0155964 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 24.7702i | − | 0.855672i | ||||||
\(839\) | 3.34480 | 0.115475 | 0.0577376 | − | 0.998332i | \(-0.481611\pi\) | ||||
0.0577376 | + | 0.998332i | \(0.481611\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | − | 35.3035i | − | 1.21664i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.02417 | 0.104096 | ||||||||
\(845\) | 24.9733 | − | 14.1374i | 0.859107 | − | 0.486342i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.6804i | 0.470063i | ||||||||
\(848\) | − | 28.7012i | − | 0.985603i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.3605 | + | 17.2622i | −0.355361 | + | 0.592089i | ||||
\(851\) | 22.0791 | 0.756862 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 45.8873i | − | 1.57115i | −0.618766 | − | 0.785575i | \(-0.712367\pi\) | ||
0.618766 | − | 0.785575i | \(-0.287633\pi\) | |||||||
\(854\) | 2.95269 | 0.101039 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.98234 | −0.0677550 | ||||||||
\(857\) | 51.8755i | 1.77203i | 0.463652 | + | 0.886017i | \(0.346539\pi\) | ||||
−0.463652 | + | 0.886017i | \(0.653461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.7698 | −1.08397 | −0.541987 | − | 0.840387i | \(-0.682328\pi\) | ||||
−0.541987 | + | 0.840387i | \(0.682328\pi\) | |||||||
\(860\) | 0.187175 | + | 0.330638i | 0.00638260 | + | 0.0112747i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 8.39203i | − | 0.285834i | ||||||
\(863\) | − | 39.9472i | − | 1.35982i | −0.733296 | − | 0.679909i | \(-0.762019\pi\) | ||
0.733296 | − | 0.679909i | \(-0.237981\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.575155 | − | 1.01599i | −0.0195559 | − | 0.0345448i | ||||
\(866\) | −47.6380 | −1.61880 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.933222i | 0.0316756i | ||||||||
\(869\) | 0.778438 | 0.0264067 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.43139 | 0.217920 | ||||||||
\(872\) | − | 21.8355i | − | 0.739444i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.1118 | 0.815594 | ||||||||
\(875\) | −14.1910 | − | 0.360986i | −0.479742 | − | 0.0122036i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 44.8875i | − | 1.51574i | −0.652403 | − | 0.757872i | \(-0.726239\pi\) | ||
0.652403 | − | 0.757872i | \(-0.273761\pi\) | |||||||
\(878\) | − | 27.2406i | − | 0.919326i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.36845 | − | 1.90689i | 0.113550 | − | 0.0642811i | ||||
\(881\) | −3.90189 | −0.131458 | −0.0657290 | − | 0.997838i | \(-0.520937\pi\) | ||||
−0.0657290 | + | 0.997838i | \(0.520937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 52.7256i | − | 1.77436i | −0.461427 | − | 0.887178i | \(-0.652662\pi\) | ||
0.461427 | − | 0.887178i | \(-0.347338\pi\) | |||||||
\(884\) | 0.198204 | 0.00666632 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.2563 | 0.949288 | ||||||||
\(887\) | 20.7833i | 0.697834i | 0.937154 | + | 0.348917i | \(0.113450\pi\) | ||||
−0.937154 | + | 0.348917i | \(0.886550\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.6660 | 0.491881 | ||||||||
\(890\) | 20.0294 | + | 35.3813i | 0.671387 | + | 1.18598i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.53790i | 0.118458i | ||||||||
\(893\) | 17.2482i | 0.577190i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.3939 | + | 11.5450i | −0.681694 | + | 0.385908i | ||||
\(896\) | 12.3547 | 0.412743 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 53.5546i | 1.78714i | ||||||||
\(899\) | −4.49210 | −0.149820 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.3902 | 0.779241 | ||||||||
\(902\) | 7.76368i | 0.258502i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.3461 | 1.37515 | ||||||||
\(905\) | 23.8808 | − | 13.5190i | 0.793824 | − | 0.449385i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 26.2116i | − | 0.870342i | −0.900348 | − | 0.435171i | \(-0.856688\pi\) | ||
0.900348 | − | 0.435171i | \(-0.143312\pi\) | |||||||
\(908\) | − | 3.20076i | − | 0.106221i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.772713 | − | 1.36497i | −0.0256152 | − | 0.0452484i | ||||
\(911\) | 31.4264 | 1.04120 | 0.520601 | − | 0.853800i | \(-0.325708\pi\) | ||||
0.520601 | + | 0.853800i | \(0.325708\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.37921i | 0.244216i | ||||||||
\(914\) | 34.7070 | 1.14800 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.76348 | −0.0582669 | ||||||||
\(917\) | − | 13.0057i | − | 0.429486i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.0083 | 0.693000 | 0.346500 | − | 0.938050i | \(-0.387370\pi\) | ||||
0.346500 | + | 0.938050i | \(0.387370\pi\) | |||||||
\(920\) | −17.4878 | + | 9.89989i | −0.576557 | + | 0.326390i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.23544i | 0.0406870i | ||||||||
\(923\) | 3.67245i | 0.120880i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.8812 | + | 18.5343i | 1.01537 | + | 0.609405i | ||||
\(926\) | −35.1988 | −1.15670 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 0.923188i | − | 0.0303051i | ||||||
\(929\) | −37.3920 | −1.22679 | −0.613395 | − | 0.789776i | \(-0.710197\pi\) | ||||
−0.613395 | + | 0.789776i | \(0.710197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.2762 | −1.02504 | ||||||||
\(932\) | − | 0.695750i | − | 0.0227901i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.4796 | 0.702836 | ||||||||
\(935\) | 1.55403 | + | 2.74514i | 0.0508222 | + | 0.0897757i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13.8377i | − | 0.452057i | −0.974121 | − | 0.226029i | \(-0.927426\pi\) | ||
0.974121 | − | 0.226029i | \(-0.0725743\pi\) | |||||||
\(938\) | 27.1431i | 0.886253i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.535553 | − | 0.946037i | −0.0174678 | − | 0.0308563i | ||||
\(941\) | 14.5708 | 0.474995 | 0.237497 | − | 0.971388i | \(-0.423673\pi\) | ||||
0.237497 | + | 0.971388i | \(0.423673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 36.9867i | − | 1.20445i | ||||||
\(944\) | −16.2571 | −0.529125 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.668144 | −0.0217232 | ||||||||
\(947\) | 43.4267i | 1.41118i | 0.708622 | + | 0.705589i | \(0.249317\pi\) | ||||
−0.708622 | + | 0.705589i | \(0.750683\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.276406 | −0.00897252 | ||||||||
\(950\) | 33.7242 | + | 20.2407i | 1.09416 | + | 0.656695i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.0614i | 0.358501i | ||||||||
\(953\) | − | 51.0500i | − | 1.65367i | −0.562442 | − | 0.826836i | \(-0.690138\pi\) | ||
0.562442 | − | 0.826836i | \(-0.309862\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.8651 | − | 10.6796i | 0.610459 | − | 0.345582i | ||||
\(956\) | −2.75512 | −0.0891071 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.1004i | 0.714030i | ||||||||
\(959\) | −2.62289 | −0.0846976 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8210 | −0.349065 | ||||||||
\(962\) | 3.97955i | 0.128306i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.57340 | 0.115091 | ||||||||
\(965\) | 12.2117 | + | 21.5716i | 0.393109 | + | 0.694414i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.0658i | 1.80295i | 0.432828 | + | 0.901477i | \(0.357516\pi\) | ||||
−0.432828 | + | 0.901477i | \(0.642484\pi\) | |||||||
\(968\) | 31.5910i | 1.01537i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.7417 | − | 10.6097i | 0.601758 | − | 0.340657i | ||||
\(971\) | −6.58898 | −0.211450 | −0.105725 | − | 0.994395i | \(-0.533716\pi\) | ||||
−0.105725 | + | 0.994395i | \(0.533716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.42152i | 0.141748i | ||||||||
\(974\) | 13.4693 | 0.431585 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.25683 | 0.200276 | ||||||||
\(977\) | 29.3327i | 0.938437i | 0.883082 | + | 0.469218i | \(0.155464\pi\) | ||||
−0.883082 | + | 0.469218i | \(0.844536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.37039 | 0.203599 | ||||||||
\(980\) | 1.71545 | − | 0.971117i | 0.0547979 | − | 0.0310212i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 51.5814i | − | 1.64603i | ||||||
\(983\) | − | 13.6719i | − | 0.436064i | −0.975942 | − | 0.218032i | \(-0.930036\pi\) | ||
0.975942 | − | 0.218032i | \(-0.0699638\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.20791 | + | 3.90019i | 0.0703497 | + | 0.124270i | ||||
\(986\) | −4.02653 | −0.128231 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 0.387220i | − | 0.0123191i | ||||||
\(989\) | 3.18308 | 0.101216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.7210 | 0.626459 | 0.313230 | − | 0.949677i | \(-0.398589\pi\) | ||||
0.313230 | + | 0.949677i | \(0.398589\pi\) | |||||||
\(992\) | 4.14705i | 0.131669i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.4992 | −0.491606 | ||||||||
\(995\) | 35.2539 | − | 19.9573i | 1.11762 | − | 0.632688i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.4618i | 1.69315i | 0.532268 | + | 0.846576i | \(0.321340\pi\) | ||||
−0.532268 | + | 0.846576i | \(0.678660\pi\) | |||||||
\(998\) | 60.1400i | 1.90370i | ||||||||
\(999\) | 0 | 0 |
(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 | 1305.2.c.l.784.4 | yes | 12 | |
3.2 | odd | 2 | 1305.2.c.k.784.9 | yes | 12 | ||
5.2 | odd | 4 | 6525.2.a.cf.1.9 | 12 | |||
5.3 | odd | 4 | 6525.2.a.cf.1.4 | 12 | |||
5.4 | even | 2 | inner | 1305.2.c.l.784.9 | yes | 12 | |
15.2 | even | 4 | 6525.2.a.ce.1.4 | 12 | |||
15.8 | even | 4 | 6525.2.a.ce.1.9 | 12 | |||
15.14 | odd | 2 | 1305.2.c.k.784.4 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1305.2.c.k.784.4 | ✓ | 12 | 15.14 | odd | 2 | ||
1305.2.c.k.784.9 | yes | 12 | 3.2 | odd | 2 | ||
1305.2.c.l.784.4 | yes | 12 | 1.1 | even | 1 | trivial | |
1305.2.c.l.784.9 | yes | 12 | 5.4 | even | 2 | inner | |
6525.2.a.ce.1.4 | 12 | 15.2 | even | 4 | |||
6525.2.a.ce.1.9 | 12 | 15.8 | even | 4 | |||
6525.2.a.cf.1.4 | 12 | 5.3 | odd | 4 | |||
6525.2.a.cf.1.9 | 12 | 5.2 | odd | 4 |