Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.bc (of order \(6\), degree \(2\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 751.1 | ||
Root | \(0.500000 + 1.72434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.751 |
Dual form | 1950.2.bc.h.901.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −3.10934 | − | 1.79518i | −1.17522 | − | 0.678514i | −0.220317 | − | 0.975428i | \(-0.570709\pi\) |
−0.954904 | + | 0.296914i | \(0.904043\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.72163 | + | 2.72603i | −1.42362 | + | 0.821930i | −0.996607 | − | 0.0823128i | \(-0.973769\pi\) |
−0.427018 | + | 0.904243i | \(0.640436\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.0664404 | − | 3.60494i | −0.0184272 | − | 0.999830i | ||||
\(14\) | 3.59036 | 0.959564 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.65519 | − | 6.33097i | 0.886514 | − | 1.53549i | 0.0425445 | − | 0.999095i | \(-0.486454\pi\) |
0.843969 | − | 0.536392i | \(-0.180213\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −3.34713 | − | 1.93247i | −0.767884 | − | 0.443338i | 0.0642352 | − | 0.997935i | \(-0.479539\pi\) |
−0.832119 | + | 0.554597i | \(0.812873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.59036i | 0.783481i | ||||||||
\(22\) | 2.72603 | − | 4.72163i | 0.581192 | − | 1.00665i | ||||
\(23\) | 0.929155 | + | 1.60934i | 0.193742 | + | 0.335571i | 0.946487 | − | 0.322741i | \(-0.104604\pi\) |
−0.752745 | + | 0.658312i | \(0.771271\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.86001 | + | 3.08875i | 0.364778 | + | 0.605753i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.10934 | + | 1.79518i | −0.587611 | + | 0.339257i | ||||
\(29\) | 2.67578 | + | 4.63459i | 0.496881 | + | 0.860622i | 0.999994 | − | 0.00359821i | \(-0.00114535\pi\) |
−0.503113 | + | 0.864221i | \(0.667812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.23338i | − | 0.401127i | −0.979681 | − | 0.200563i | \(-0.935723\pi\) | ||
0.979681 | − | 0.200563i | \(-0.0642773\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 4.72163 | + | 2.72603i | 0.821930 | + | 0.474542i | ||||
\(34\) | 7.31038i | 1.25372i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 1.84713 | − | 1.06644i | 0.303666 | − | 0.175322i | −0.340423 | − | 0.940273i | \(-0.610570\pi\) |
0.644089 | + | 0.764951i | \(0.277237\pi\) | |||||||
\(38\) | 3.86493 | 0.626975 | ||||||||
\(39\) | −3.08875 | + | 1.86001i | −0.494596 | + | 0.297840i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.33097 | + | 3.65519i | −0.988732 | + | 0.570845i | −0.904895 | − | 0.425635i | \(-0.860051\pi\) |
−0.0838369 | + | 0.996479i | \(0.526717\pi\) | |||||||
\(42\) | −1.79518 | − | 3.10934i | −0.277002 | − | 0.479782i | ||||
\(43\) | −4.10494 | + | 7.10996i | −0.625997 | + | 1.08426i | 0.362350 | + | 0.932042i | \(0.381975\pi\) |
−0.988347 | + | 0.152217i | \(0.951359\pi\) | |||||||
\(44\) | 5.45207i | 0.821930i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.60934 | − | 0.929155i | −0.237285 | − | 0.136996i | ||||
\(47\) | − | 5.07700i | − | 0.740556i | −0.928921 | − | 0.370278i | \(-0.879262\pi\) | ||
0.928921 | − | 0.370278i | \(-0.120738\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 2.94535 | + | 5.10149i | 0.420764 | + | 0.728784i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.31038 | −1.02366 | ||||||||
\(52\) | −3.15519 | − | 1.74493i | −0.437546 | − | 0.241978i | ||||
\(53\) | −2.23338 | −0.306778 | −0.153389 | − | 0.988166i | \(-0.549019\pi\) | ||||
−0.153389 | + | 0.988166i | \(0.549019\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.79518 | − | 3.10934i | 0.239891 | − | 0.415504i | ||||
\(57\) | 3.86493i | 0.511923i | ||||||||
\(58\) | −4.63459 | − | 2.67578i | −0.608552 | − | 0.351348i | ||||
\(59\) | −0.237785 | − | 0.137285i | −0.0309570 | − | 0.0178730i | 0.484442 | − | 0.874824i | \(-0.339023\pi\) |
−0.515399 | + | 0.856951i | \(0.672356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.06644 | − | 3.57918i | 0.264581 | − | 0.458267i | −0.702873 | − | 0.711315i | \(-0.748100\pi\) |
0.967454 | + | 0.253048i | \(0.0814332\pi\) | |||||||
\(62\) | 1.11669 | + | 1.93416i | 0.141820 | + | 0.245639i | ||||
\(63\) | 3.10934 | − | 1.79518i | 0.391740 | − | 0.226171i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.45207 | −0.671103 | ||||||||
\(67\) | −12.8146 | + | 7.39851i | −1.56555 | + | 0.903872i | −0.568874 | + | 0.822425i | \(0.692621\pi\) |
−0.996678 | + | 0.0814466i | \(0.974046\pi\) | |||||||
\(68\) | −3.65519 | − | 6.33097i | −0.443257 | − | 0.767743i | ||||
\(69\) | 0.929155 | − | 1.60934i | 0.111857 | − | 0.193742i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3804 | + | 7.14784i | 1.46929 | + | 0.848293i | 0.999407 | − | 0.0344378i | \(-0.0109641\pi\) |
0.469879 | + | 0.882731i | \(0.344297\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 14.8975i | 1.74362i | 0.489842 | + | 0.871811i | \(0.337054\pi\) | ||||
−0.489842 | + | 0.871811i | \(0.662946\pi\) | |||||||
\(74\) | −1.06644 | + | 1.84713i | −0.123971 | + | 0.214724i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.34713 | + | 1.93247i | −0.383942 | + | 0.221669i | ||||
\(77\) | 19.5749 | 2.23077 | ||||||||
\(78\) | 1.74493 | − | 3.15519i | 0.197574 | − | 0.357255i | ||||
\(79\) | 2.62105 | 0.294891 | 0.147446 | − | 0.989070i | \(-0.452895\pi\) | ||||
0.147446 | + | 0.989070i | \(0.452895\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.65519 | − | 6.33097i | 0.403648 | − | 0.699139i | ||||
\(83\) | 7.15988i | 0.785899i | 0.919560 | + | 0.392949i | \(0.128545\pi\) | ||||
−0.919560 | + | 0.392949i | \(0.871455\pi\) | |||||||
\(84\) | 3.10934 | + | 1.79518i | 0.339257 | + | 0.195870i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 8.20988i | − | 0.885294i | ||||||
\(87\) | 2.67578 | − | 4.63459i | 0.286874 | − | 0.496881i | ||||
\(88\) | −2.72603 | − | 4.72163i | −0.290596 | − | 0.503327i | ||||
\(89\) | 8.30844 | − | 4.79688i | 0.880693 | − | 0.508468i | 0.00980594 | − | 0.999952i | \(-0.496879\pi\) |
0.870887 | + | 0.491484i | \(0.163545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.26493 | + | 11.3283i | −0.656743 | + | 1.18753i | ||||
\(92\) | 1.85831 | 0.193742 | ||||||||
\(93\) | −1.93416 | + | 1.11669i | −0.200563 | + | 0.115795i | ||||
\(94\) | 2.53850 | + | 4.39681i | 0.261826 | + | 0.453496i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 1.65264 | + | 0.954155i | 0.167801 | + | 0.0968797i | 0.581548 | − | 0.813512i | \(-0.302447\pi\) |
−0.413748 | + | 0.910392i | \(0.635780\pi\) | |||||||
\(98\) | −5.10149 | − | 2.94535i | −0.515328 | − | 0.297525i | ||||
\(99\) | − | 5.45207i | − | 0.547953i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.12785 | + | 14.0779i | 0.808752 | + | 1.40080i | 0.913729 | + | 0.406324i | \(0.133190\pi\) |
−0.104978 | + | 0.994475i | \(0.533477\pi\) | |||||||
\(102\) | 6.33097 | − | 3.65519i | 0.626860 | − | 0.361918i | ||||
\(103\) | 12.9760 | 1.27857 | 0.639284 | − | 0.768971i | \(-0.279231\pi\) | ||||
0.639284 | + | 0.768971i | \(0.279231\pi\) | |||||||
\(104\) | 3.60494 | − | 0.0664404i | 0.353493 | − | 0.00651501i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.93416 | − | 1.11669i | 0.187863 | − | 0.108463i | ||||
\(107\) | −4.95837 | − | 8.58814i | −0.479343 | − | 0.830247i | 0.520376 | − | 0.853937i | \(-0.325792\pi\) |
−0.999719 | + | 0.0236901i | \(0.992459\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 7.41088i | 0.709833i | 0.934898 | + | 0.354917i | \(0.115491\pi\) | ||||
−0.934898 | + | 0.354917i | \(0.884509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.84713 | − | 1.06644i | −0.175322 | − | 0.101222i | ||||
\(112\) | 3.59036i | 0.339257i | ||||||||
\(113\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(114\) | −1.93247 | − | 3.34713i | −0.180992 | − | 0.313487i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.35157 | 0.496881 | ||||||||
\(117\) | 3.15519 | + | 1.74493i | 0.291697 | + | 0.161319i | ||||
\(118\) | 0.274571 | 0.0252763 | ||||||||
\(119\) | −22.7305 | + | 13.1234i | −2.08370 | + | 1.20302i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.36252 | − | 16.2164i | 0.851138 | − | 1.47421i | ||||
\(122\) | 4.13288i | 0.374173i | ||||||||
\(123\) | 6.33097 | + | 3.65519i | 0.570845 | + | 0.329577i | ||||
\(124\) | −1.93416 | − | 1.11669i | −0.173693 | − | 0.100282i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.79518 | + | 3.10934i | −0.159927 | + | 0.277002i | ||||
\(127\) | −8.99351 | − | 15.5772i | −0.798045 | − | 1.38225i | −0.920888 | − | 0.389828i | \(-0.872534\pi\) |
0.122843 | − | 0.992426i | \(-0.460799\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 8.20988 | 0.722839 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.3462 | 1.77765 | 0.888827 | − | 0.458242i | \(-0.151521\pi\) | ||||
0.888827 | + | 0.458242i | \(0.151521\pi\) | |||||||
\(132\) | 4.72163 | − | 2.72603i | 0.410965 | − | 0.237271i | ||||
\(133\) | 6.93825 | + | 12.0174i | 0.601623 | + | 1.04204i | ||||
\(134\) | 7.39851 | − | 12.8146i | 0.639134 | − | 1.10701i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.33097 | + | 3.65519i | 0.542876 | + | 0.313430i | ||||
\(137\) | −9.56156 | − | 5.52037i | −0.816899 | − | 0.471637i | 0.0324469 | − | 0.999473i | \(-0.489670\pi\) |
−0.849346 | + | 0.527837i | \(0.823003\pi\) | |||||||
\(138\) | 1.85831i | 0.158190i | ||||||||
\(139\) | −4.85096 | + | 8.40212i | −0.411453 | + | 0.712658i | −0.995049 | − | 0.0993864i | \(-0.968312\pi\) |
0.583596 | + | 0.812044i | \(0.301645\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.39681 | + | 2.53850i | −0.370278 | + | 0.213780i | ||||
\(142\) | −14.2957 | −1.19967 | ||||||||
\(143\) | 10.1409 | + | 16.8401i | 0.848024 | + | 1.40824i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.44876 | − | 12.9016i | −0.616464 | − | 1.06775i | ||||
\(147\) | 2.94535 | − | 5.10149i | 0.242928 | − | 0.420764i | ||||
\(148\) | − | 2.13288i | − | 0.175322i | ||||||
\(149\) | −4.70959 | − | 2.71908i | −0.385825 | − | 0.222756i | 0.294525 | − | 0.955644i | \(-0.404839\pi\) |
−0.680350 | + | 0.732888i | \(0.738172\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8010i | 1.44862i | 0.689472 | + | 0.724312i | \(0.257843\pi\) | ||||
−0.689472 | + | 0.724312i | \(0.742157\pi\) | |||||||
\(152\) | 1.93247 | − | 3.34713i | 0.156744 | − | 0.271488i | ||||
\(153\) | 3.65519 | + | 6.33097i | 0.295505 | + | 0.511829i | ||||
\(154\) | −16.9524 | + | 9.78745i | −1.36606 | + | 0.788695i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0664404 | + | 3.60494i | 0.00531949 | + | 0.288626i | ||||
\(157\) | −5.93652 | −0.473786 | −0.236893 | − | 0.971536i | \(-0.576129\pi\) | ||||
−0.236893 | + | 0.971536i | \(0.576129\pi\) | |||||||
\(158\) | −2.26990 | + | 1.31052i | −0.180583 | + | 0.104260i | ||||
\(159\) | 1.11669 | + | 1.93416i | 0.0885593 | + | 0.153389i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.67200i | − | 0.525828i | ||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | −13.5046 | − | 7.79688i | −1.05776 | − | 0.610699i | −0.132949 | − | 0.991123i | \(-0.542445\pi\) |
−0.924812 | + | 0.380424i | \(0.875778\pi\) | |||||||
\(164\) | 7.31038i | 0.570845i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.57994 | − | 6.20064i | −0.277857 | − | 0.481263i | ||||
\(167\) | 1.60934 | − | 0.929155i | 0.124535 | − | 0.0719002i | −0.436439 | − | 0.899734i | \(-0.643760\pi\) |
0.560973 | + | 0.827834i | \(0.310427\pi\) | |||||||
\(168\) | −3.59036 | −0.277002 | ||||||||
\(169\) | −12.9912 | + | 0.479027i | −0.999321 | + | 0.0368482i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.34713 | − | 1.93247i | 0.255961 | − | 0.147779i | ||||
\(172\) | 4.10494 | + | 7.10996i | 0.312999 | + | 0.542130i | ||||
\(173\) | −12.1687 | + | 21.0768i | −0.925168 | + | 1.60244i | −0.133878 | + | 0.990998i | \(0.542743\pi\) |
−0.791290 | + | 0.611441i | \(0.790590\pi\) | |||||||
\(174\) | 5.35157i | 0.405701i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.72163 | + | 2.72603i | 0.355906 | + | 0.205483i | ||||
\(177\) | 0.274571i | 0.0206380i | ||||||||
\(178\) | −4.79688 | + | 8.30844i | −0.359541 | + | 0.622744i | ||||
\(179\) | 1.53429 | + | 2.65746i | 0.114678 | + | 0.198628i | 0.917651 | − | 0.397387i | \(-0.130083\pi\) |
−0.802973 | + | 0.596015i | \(0.796750\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.59376 | −0.341451 | −0.170726 | − | 0.985319i | \(-0.554611\pi\) | ||||
−0.170726 | + | 0.985319i | \(0.554611\pi\) | |||||||
\(182\) | −0.238545 | − | 12.9430i | −0.0176821 | − | 0.959401i | ||||
\(183\) | −4.13288 | −0.305511 | ||||||||
\(184\) | −1.60934 | + | 0.929155i | −0.118642 | + | 0.0684982i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.11669 | − | 1.93416i | 0.0818797 | − | 0.141820i | ||||
\(187\) | 39.8567i | 2.91461i | ||||||||
\(188\) | −4.39681 | − | 2.53850i | −0.320670 | − | 0.185139i | ||||
\(189\) | −3.10934 | − | 1.79518i | −0.226171 | − | 0.130580i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.03007 | + | 12.1764i | −0.508678 | + | 0.881056i | 0.491272 | + | 0.871006i | \(0.336532\pi\) |
−0.999950 | + | 0.0100494i | \(0.996801\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 21.7276 | − | 12.5444i | 1.56398 | − | 0.902966i | 0.567136 | − | 0.823624i | \(-0.308051\pi\) |
0.996847 | − | 0.0793424i | \(-0.0252820\pi\) | |||||||
\(194\) | −1.90831 | −0.137009 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.89069 | 0.420764 | ||||||||
\(197\) | 7.96287 | − | 4.59737i | 0.567331 | − | 0.327549i | −0.188752 | − | 0.982025i | \(-0.560444\pi\) |
0.756083 | + | 0.654476i | \(0.227111\pi\) | |||||||
\(198\) | 2.72603 | + | 4.72163i | 0.193731 | + | 0.335552i | ||||
\(199\) | −11.8396 | + | 20.5068i | −0.839286 | + | 1.45369i | 0.0512060 | + | 0.998688i | \(0.483694\pi\) |
−0.890492 | + | 0.454998i | \(0.849640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.8146 | + | 7.39851i | 0.903872 | + | 0.521850i | ||||
\(202\) | −14.0779 | − | 8.12785i | −0.990514 | − | 0.571874i | ||||
\(203\) | − | 19.2141i | − | 1.34856i | ||||||
\(204\) | −3.65519 | + | 6.33097i | −0.255914 | + | 0.443257i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.2376 | + | 6.48802i | −0.782960 | + | 0.452042i | ||||
\(207\) | −1.85831 | −0.129161 | ||||||||
\(208\) | −3.08875 | + | 1.86001i | −0.214166 | + | 0.128968i | ||||
\(209\) | 21.0719 | 1.45757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.99303 | + | 8.64818i | 0.343734 | + | 0.595366i | 0.985123 | − | 0.171851i | \(-0.0549747\pi\) |
−0.641389 | + | 0.767216i | \(0.721641\pi\) | |||||||
\(212\) | −1.11669 | + | 1.93416i | −0.0766946 | + | 0.132839i | ||||
\(213\) | − | 14.2957i | − | 0.979524i | ||||||
\(214\) | 8.58814 | + | 4.95837i | 0.587073 | + | 0.338947i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −4.00932 | + | 6.94435i | −0.272170 | + | 0.471413i | ||||
\(218\) | −3.70544 | − | 6.41801i | −0.250964 | − | 0.434682i | ||||
\(219\) | 12.9016 | − | 7.44876i | 0.871811 | − | 0.503340i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.0656 | − | 12.7561i | −1.55156 | − | 0.858068i | ||||
\(222\) | 2.13288 | 0.143150 | ||||||||
\(223\) | −19.3833 | + | 11.1910i | −1.29801 | + | 0.749404i | −0.980059 | − | 0.198705i | \(-0.936326\pi\) |
−0.317946 | + | 0.948109i | \(0.602993\pi\) | |||||||
\(224\) | −1.79518 | − | 3.10934i | −0.119946 | − | 0.207752i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.2456 | + | 6.49265i | 0.746397 | + | 0.430933i | 0.824391 | − | 0.566021i | \(-0.191518\pi\) |
−0.0779935 | + | 0.996954i | \(0.524851\pi\) | |||||||
\(228\) | 3.34713 | + | 1.93247i | 0.221669 | + | 0.127981i | ||||
\(229\) | − | 14.4455i | − | 0.954587i | −0.878744 | − | 0.477293i | \(-0.841618\pi\) | ||
0.878744 | − | 0.477293i | \(-0.158382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.78745 | − | 16.9524i | −0.643967 | − | 1.11538i | ||||
\(232\) | −4.63459 | + | 2.67578i | −0.304276 | + | 0.175674i | ||||
\(233\) | 12.4374 | 0.814800 | 0.407400 | − | 0.913250i | \(-0.366436\pi\) | ||||
0.407400 | + | 0.913250i | \(0.366436\pi\) | |||||||
\(234\) | −3.60494 | + | 0.0664404i | −0.235662 | + | 0.00434334i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.237785 | + | 0.137285i | −0.0154785 | + | 0.00893652i | ||||
\(237\) | −1.31052 | − | 2.26990i | −0.0851277 | − | 0.147446i | ||||
\(238\) | 13.1234 | − | 22.7305i | 0.850667 | − | 1.47340i | ||||
\(239\) | − | 4.16983i | − | 0.269724i | −0.990864 | − | 0.134862i | \(-0.956941\pi\) | ||
0.990864 | − | 0.134862i | \(-0.0430591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.63165 | + | 0.942035i | 0.105104 | + | 0.0606818i | 0.551631 | − | 0.834089i | \(-0.314006\pi\) |
−0.446527 | + | 0.894770i | \(0.647339\pi\) | |||||||
\(242\) | 18.7250i | 1.20369i | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −2.06644 | − | 3.57918i | −0.132290 | − | 0.229134i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.31038 | −0.466093 | ||||||||
\(247\) | −6.74404 | + | 12.1946i | −0.429113 | + | 0.775923i | ||||
\(248\) | 2.23338 | 0.141820 | ||||||||
\(249\) | 6.20064 | − | 3.57994i | 0.392949 | − | 0.226869i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.57502 | − | 6.19212i | 0.225653 | − | 0.390843i | −0.730862 | − | 0.682525i | \(-0.760882\pi\) |
0.956515 | + | 0.291682i | \(0.0942150\pi\) | |||||||
\(252\) | − | 3.59036i | − | 0.226171i | ||||||
\(253\) | −8.77425 | − | 5.06582i | −0.551632 | − | 0.318485i | ||||
\(254\) | 15.5772 | + | 8.99351i | 0.977401 | + | 0.564303i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.2489 | + | 17.7517i | 0.639312 | + | 1.10732i | 0.985584 | + | 0.169186i | \(0.0541140\pi\) |
−0.346272 | + | 0.938134i | \(0.612553\pi\) | |||||||
\(258\) | −7.10996 | + | 4.10494i | −0.442647 | + | 0.255562i | ||||
\(259\) | −7.65781 | −0.475833 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.35157 | −0.331254 | ||||||||
\(262\) | −17.6203 | + | 10.1731i | −1.08859 | + | 0.628496i | ||||
\(263\) | 8.85153 | + | 15.3313i | 0.545809 | + | 0.945369i | 0.998556 | + | 0.0537296i | \(0.0171109\pi\) |
−0.452747 | + | 0.891639i | \(0.649556\pi\) | |||||||
\(264\) | −2.72603 | + | 4.72163i | −0.167776 | + | 0.290596i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.0174 | − | 6.93825i | −0.736834 | − | 0.425411i | ||||
\(267\) | −8.30844 | − | 4.79688i | −0.508468 | − | 0.293564i | ||||
\(268\) | 14.7970i | 0.903872i | ||||||||
\(269\) | 9.09319 | − | 15.7499i | 0.554421 | − | 0.960286i | −0.443527 | − | 0.896261i | \(-0.646273\pi\) |
0.997948 | − | 0.0640250i | \(-0.0203937\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7188 | − | 11.3847i | 1.19783 | − | 0.691569i | 0.237762 | − | 0.971324i | \(-0.423586\pi\) |
0.960072 | + | 0.279754i | \(0.0902529\pi\) | |||||||
\(272\) | −7.31038 | −0.443257 | ||||||||
\(273\) | 12.9430 | − | 0.238545i | 0.783348 | − | 0.0144374i | ||||
\(274\) | 11.0407 | 0.666995 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.929155 | − | 1.60934i | −0.0559286 | − | 0.0968711i | ||||
\(277\) | −8.17814 | + | 14.1649i | −0.491377 | + | 0.851089i | −0.999951 | − | 0.00992898i | \(-0.996839\pi\) |
0.508574 | + | 0.861018i | \(0.330173\pi\) | |||||||
\(278\) | − | 9.70193i | − | 0.581883i | ||||||
\(279\) | 1.93416 | + | 1.11669i | 0.115795 | + | 0.0668545i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.82221i | − | 0.466634i | −0.972401 | − | 0.233317i | \(-0.925042\pi\) | ||
0.972401 | − | 0.233317i | \(-0.0749580\pi\) | |||||||
\(282\) | 2.53850 | − | 4.39681i | 0.151165 | − | 0.261826i | ||||
\(283\) | 3.47266 | + | 6.01483i | 0.206428 | + | 0.357544i | 0.950587 | − | 0.310459i | \(-0.100483\pi\) |
−0.744159 | + | 0.668003i | \(0.767149\pi\) | |||||||
\(284\) | 12.3804 | − | 7.14784i | 0.734643 | − | 0.424146i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.2023 | − | 9.51348i | −1.01719 | − | 0.562544i | ||||
\(287\) | 26.2469 | 1.54931 | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −18.2208 | − | 31.5594i | −1.07181 | − | 1.85643i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.90831i | − | 0.111867i | ||||||
\(292\) | 12.9016 | + | 7.44876i | 0.755011 | + | 0.435906i | ||||
\(293\) | −22.8841 | − | 13.2122i | −1.33691 | − | 0.771863i | −0.350558 | − | 0.936541i | \(-0.614008\pi\) |
−0.986347 | + | 0.164678i | \(0.947341\pi\) | |||||||
\(294\) | 5.89069i | 0.343552i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.06644 | + | 1.84713i | 0.0619856 | + | 0.107362i | ||||
\(297\) | −4.72163 | + | 2.72603i | −0.273977 | + | 0.158181i | ||||
\(298\) | 5.43817 | 0.315025 | ||||||||
\(299\) | 5.73985 | − | 3.45647i | 0.331944 | − | 0.199893i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.5273 | − | 14.7382i | 1.47137 | − | 0.849496i | ||||
\(302\) | −8.90050 | − | 15.4161i | −0.512166 | − | 0.887098i | ||||
\(303\) | 8.12785 | − | 14.0779i | 0.466933 | − | 0.808752i | ||||
\(304\) | 3.86493i | 0.221669i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.33097 | − | 3.65519i | −0.361918 | − | 0.208953i | ||||
\(307\) | 7.08581i | 0.404408i | 0.979343 | + | 0.202204i | \(0.0648105\pi\) | ||||
−0.979343 | + | 0.202204i | \(0.935190\pi\) | |||||||
\(308\) | 9.78745 | − | 16.9524i | 0.557691 | − | 0.965950i | ||||
\(309\) | −6.48802 | − | 11.2376i | −0.369091 | − | 0.639284i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.83017 | −0.103780 | −0.0518898 | − | 0.998653i | \(-0.516524\pi\) | ||||
−0.0518898 | + | 0.998653i | \(0.516524\pi\) | |||||||
\(312\) | −1.86001 | − | 3.08875i | −0.105302 | − | 0.174866i | ||||
\(313\) | −12.2499 | −0.692403 | −0.346201 | − | 0.938160i | \(-0.612529\pi\) | ||||
−0.346201 | + | 0.938160i | \(0.612529\pi\) | |||||||
\(314\) | 5.14117 | − | 2.96826i | 0.290133 | − | 0.167509i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.31052 | − | 2.26990i | 0.0737228 | − | 0.127692i | ||||
\(317\) | 6.25100i | 0.351091i | 0.984471 | + | 0.175546i | \(0.0561689\pi\) | ||||
−0.984471 | + | 0.175546i | \(0.943831\pi\) | |||||||
\(318\) | −1.93416 | − | 1.11669i | −0.108463 | − | 0.0626209i | ||||
\(319\) | −25.2681 | − | 14.5886i | −1.41474 | − | 0.816802i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.95837 | + | 8.58814i | −0.276749 | + | 0.479343i | ||||
\(322\) | 3.33600 | + | 5.77812i | 0.185908 | + | 0.322002i | ||||
\(323\) | −24.4688 | + | 14.1271i | −1.36148 | + | 0.786050i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.5938 | 0.863658 | ||||||||
\(327\) | 6.41801 | − | 3.70544i | 0.354917 | − | 0.204911i | ||||
\(328\) | −3.65519 | − | 6.33097i | −0.201824 | − | 0.349570i | ||||
\(329\) | −9.11413 | + | 15.7861i | −0.502478 | + | 0.870318i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6067 | − | 9.58790i | −0.912789 | − | 0.526999i | −0.0314613 | − | 0.999505i | \(-0.510016\pi\) |
−0.881327 | + | 0.472506i | \(0.843349\pi\) | |||||||
\(332\) | 6.20064 | + | 3.57994i | 0.340304 | + | 0.196475i | ||||
\(333\) | 2.13288i | 0.116881i | ||||||||
\(334\) | −0.929155 | + | 1.60934i | −0.0508411 | + | 0.0880594i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.10934 | − | 1.79518i | 0.169629 | − | 0.0979351i | ||||
\(337\) | −16.5450 | −0.901262 | −0.450631 | − | 0.892710i | \(-0.648801\pi\) | ||||
−0.450631 | + | 0.892710i | \(0.648801\pi\) | |||||||
\(338\) | 11.0112 | − | 6.91044i | 0.598929 | − | 0.375878i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.08827 | + | 10.5452i | 0.329698 | + | 0.571054i | ||||
\(342\) | −1.93247 | + | 3.34713i | −0.104496 | + | 0.180992i | ||||
\(343\) | 3.98282i | 0.215052i | ||||||||
\(344\) | −7.10996 | − | 4.10494i | −0.383344 | − | 0.221323i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 24.3374i | − | 1.30839i | ||||||
\(347\) | −2.98195 | + | 5.16489i | −0.160079 | + | 0.277266i | −0.934897 | − | 0.354919i | \(-0.884508\pi\) |
0.774818 | + | 0.632185i | \(0.217842\pi\) | |||||||
\(348\) | −2.67578 | − | 4.63459i | −0.143437 | − | 0.248440i | ||||
\(349\) | 2.76302 | − | 1.59523i | 0.147901 | − | 0.0853906i | −0.424223 | − | 0.905558i | \(-0.639453\pi\) |
0.572124 | + | 0.820167i | \(0.306120\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0664404 | − | 3.60494i | −0.00354632 | − | 0.192417i | ||||
\(352\) | −5.45207 | −0.290596 | ||||||||
\(353\) | 24.3395 | − | 14.0524i | 1.29546 | − | 0.747934i | 0.315844 | − | 0.948811i | \(-0.397712\pi\) |
0.979616 | + | 0.200877i | \(0.0643791\pi\) | |||||||
\(354\) | −0.137285 | − | 0.237785i | −0.00729663 | − | 0.0126381i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 9.59376i | − | 0.508468i | ||||||
\(357\) | 22.7305 | + | 13.1234i | 1.20302 | + | 0.694566i | ||||
\(358\) | −2.65746 | − | 1.53429i | −0.140451 | − | 0.0810895i | ||||
\(359\) | 22.7404i | 1.20019i | 0.799927 | + | 0.600097i | \(0.204872\pi\) | ||||
−0.799927 | + | 0.600097i | \(0.795128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03115 | − | 3.51806i | −0.106903 | − | 0.185161i | ||||
\(362\) | 3.97831 | − | 2.29688i | 0.209095 | − | 0.120721i | ||||
\(363\) | −18.7250 | −0.982810 | ||||||||
\(364\) | 6.67810 | + | 11.0897i | 0.350028 | + | 0.581259i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.57918 | − | 2.06644i | 0.187087 | − | 0.108015i | ||||
\(367\) | −15.1164 | − | 26.1824i | −0.789072 | − | 1.36671i | −0.926536 | − | 0.376206i | \(-0.877229\pi\) |
0.137464 | − | 0.990507i | \(-0.456105\pi\) | |||||||
\(368\) | 0.929155 | − | 1.60934i | 0.0484356 | − | 0.0838928i | ||||
\(369\) | − | 7.31038i | − | 0.380563i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.94435 | + | 4.00932i | 0.360533 | + | 0.208154i | ||||
\(372\) | 2.23338i | 0.115795i | ||||||||
\(373\) | −2.33807 | + | 4.04965i | −0.121061 | + | 0.209683i | −0.920186 | − | 0.391481i | \(-0.871963\pi\) |
0.799126 | + | 0.601164i | \(0.205296\pi\) | |||||||
\(374\) | −19.9283 | − | 34.5169i | −1.03047 | − | 1.78483i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.07700 | 0.261826 | ||||||||
\(377\) | 16.5296 | − | 9.95396i | 0.851320 | − | 0.512655i | ||||
\(378\) | 3.59036 | 0.184668 | ||||||||
\(379\) | 18.5598 | − | 10.7155i | 0.953353 | − | 0.550419i | 0.0592321 | − | 0.998244i | \(-0.481135\pi\) |
0.894121 | + | 0.447826i | \(0.147801\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.99351 | + | 15.5772i | −0.460751 | + | 0.798045i | ||||
\(382\) | − | 14.0601i | − | 0.719379i | ||||||
\(383\) | 0.0443481 | + | 0.0256044i | 0.00226608 | + | 0.00130832i | 0.501133 | − | 0.865371i | \(-0.332917\pi\) |
−0.498867 | + | 0.866679i | \(0.666250\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.5444 | + | 21.7276i | −0.638494 | + | 1.10590i | ||||
\(387\) | −4.10494 | − | 7.10996i | −0.208666 | − | 0.361420i | ||||
\(388\) | 1.65264 | − | 0.954155i | 0.0839003 | − | 0.0484399i | ||||
\(389\) | −5.35157 | −0.271335 | −0.135668 | − | 0.990754i | \(-0.543318\pi\) | ||||
−0.135668 | + | 0.990754i | \(0.543318\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5849 | 0.687020 | ||||||||
\(392\) | −5.10149 | + | 2.94535i | −0.257664 | + | 0.148762i | ||||
\(393\) | −10.1731 | − | 17.6203i | −0.513165 | − | 0.888827i | ||||
\(394\) | −4.59737 | + | 7.96287i | −0.231612 | + | 0.401164i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.72163 | − | 2.72603i | −0.237271 | − | 0.136988i | ||||
\(397\) | 7.36744 | + | 4.25359i | 0.369761 | + | 0.213482i | 0.673354 | − | 0.739320i | \(-0.264853\pi\) |
−0.303593 | + | 0.952802i | \(0.598186\pi\) | |||||||
\(398\) | − | 23.6792i | − | 1.18693i | ||||||
\(399\) | 6.93825 | − | 12.0174i | 0.347347 | − | 0.601623i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2467 | + | 11.6894i | −1.01107 | + | 0.583741i | −0.911505 | − | 0.411290i | \(-0.865078\pi\) |
−0.0995649 | + | 0.995031i | \(0.531745\pi\) | |||||||
\(402\) | −14.7970 | −0.738008 | ||||||||
\(403\) | −8.05120 | + | 0.148387i | −0.401059 | + | 0.00739166i | ||||
\(404\) | 16.2557 | 0.808752 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.60703 | + | 16.6399i | 0.476789 | + | 0.825823i | ||||
\(407\) | −5.81431 | + | 10.0707i | −0.288204 | + | 0.499185i | ||||
\(408\) | − | 7.31038i | − | 0.361918i | ||||||
\(409\) | −4.51511 | − | 2.60680i | −0.223258 | − | 0.128898i | 0.384200 | − | 0.923250i | \(-0.374477\pi\) |
−0.607458 | + | 0.794352i | \(0.707811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0407i | 0.544599i | ||||||||
\(412\) | 6.48802 | − | 11.2376i | 0.319642 | − | 0.553636i | ||||
\(413\) | 0.492904 | + | 0.853735i | 0.0242542 | + | 0.0420095i | ||||
\(414\) | 1.60934 | − | 0.929155i | 0.0790949 | − | 0.0456655i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.74493 | − | 3.15519i | 0.0855523 | − | 0.154696i | ||||
\(417\) | 9.70193 | 0.475105 | ||||||||
\(418\) | −18.2488 | + | 10.5359i | −0.892577 | + | 0.515329i | ||||
\(419\) | −9.10066 | − | 15.7628i | −0.444596 | − | 0.770064i | 0.553428 | − | 0.832897i | \(-0.313320\pi\) |
−0.998024 | + | 0.0628337i | \(0.979986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.6463i | 1.24992i | 0.780656 | + | 0.624961i | \(0.214885\pi\) | ||||
−0.780656 | + | 0.624961i | \(0.785115\pi\) | |||||||
\(422\) | −8.64818 | − | 4.99303i | −0.420987 | − | 0.243057i | ||||
\(423\) | 4.39681 | + | 2.53850i | 0.213780 | + | 0.123426i | ||||
\(424\) | − | 2.23338i | − | 0.108463i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.14784 | + | 12.3804i | 0.346314 | + | 0.599834i | ||||
\(427\) | −12.8505 | + | 7.41927i | −0.621882 | + | 0.359043i | ||||
\(428\) | −9.91673 | −0.479343 | ||||||||
\(429\) | 9.51348 | − | 17.2023i | 0.459315 | − | 0.830535i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.79193 | + | 1.03457i | −0.0863142 | + | 0.0498335i | −0.542536 | − | 0.840033i | \(-0.682536\pi\) |
0.456222 | + | 0.889866i | \(0.349202\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −0.470915 | + | 0.815649i | −0.0226307 | + | 0.0391976i | −0.877119 | − | 0.480273i | \(-0.840538\pi\) |
0.854488 | + | 0.519471i | \(0.173871\pi\) | |||||||
\(434\) | − | 8.01864i | − | 0.384907i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.41801 | + | 3.70544i | 0.307367 | + | 0.177458i | ||||
\(437\) | − | 7.18224i | − | 0.343573i | ||||||
\(438\) | −7.44876 | + | 12.9016i | −0.355915 | + | 0.616464i | ||||
\(439\) | −1.80132 | − | 3.11997i | −0.0859722 | − | 0.148908i | 0.819833 | − | 0.572603i | \(-0.194066\pi\) |
−0.905805 | + | 0.423695i | \(0.860733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.89069 | −0.280509 | ||||||||
\(442\) | 26.3535 | − | 0.485704i | 1.25351 | − | 0.0231026i | ||||
\(443\) | −5.05095 | −0.239978 | −0.119989 | − | 0.992775i | \(-0.538286\pi\) | ||||
−0.119989 | + | 0.992775i | \(0.538286\pi\) | |||||||
\(444\) | −1.84713 | + | 1.06644i | −0.0876609 | + | 0.0506110i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.1910 | − | 19.3833i | 0.529908 | − | 0.917828i | ||||
\(447\) | 5.43817i | 0.257217i | ||||||||
\(448\) | 3.10934 | + | 1.79518i | 0.146903 | + | 0.0848143i | ||||
\(449\) | −4.70017 | − | 2.71364i | −0.221815 | − | 0.128065i | 0.384976 | − | 0.922927i | \(-0.374210\pi\) |
−0.606790 | + | 0.794862i | \(0.707543\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.9283 | − | 34.5169i | 0.938389 | − | 1.62534i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.4161 | − | 8.90050i | 0.724312 | − | 0.418182i | ||||
\(454\) | −12.9853 | −0.609431 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.86493 | −0.180992 | ||||||||
\(457\) | 18.7782 | − | 10.8416i | 0.878405 | − | 0.507147i | 0.00827291 | − | 0.999966i | \(-0.497367\pi\) |
0.870132 | + | 0.492818i | \(0.164033\pi\) | |||||||
\(458\) | 7.22276 | + | 12.5102i | 0.337497 | + | 0.584562i | ||||
\(459\) | 3.65519 | − | 6.33097i | 0.170610 | − | 0.295505i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.6364 | − | 14.8012i | −1.19401 | − | 0.689359i | −0.234793 | − | 0.972045i | \(-0.575441\pi\) |
−0.959212 | + | 0.282686i | \(0.908775\pi\) | |||||||
\(462\) | 16.9524 | + | 9.78745i | 0.788695 | + | 0.455353i | ||||
\(463\) | − | 28.2075i | − | 1.31091i | −0.755232 | − | 0.655457i | \(-0.772476\pi\) | ||
0.755232 | − | 0.655457i | \(-0.227524\pi\) | |||||||
\(464\) | 2.67578 | − | 4.63459i | 0.124220 | − | 0.215156i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.7711 | + | 6.21869i | −0.498961 | + | 0.288075i | ||||
\(467\) | −8.17371 | −0.378234 | −0.189117 | − | 0.981955i | \(-0.560563\pi\) | ||||
−0.189117 | + | 0.981955i | \(0.560563\pi\) | |||||||
\(468\) | 3.08875 | − | 1.86001i | 0.142777 | − | 0.0859789i | ||||
\(469\) | 53.1266 | 2.45316 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.96826 | + | 5.14117i | 0.136770 | + | 0.236893i | ||||
\(472\) | 0.137285 | − | 0.237785i | 0.00631907 | − | 0.0109450i | ||||
\(473\) | − | 44.7608i | − | 2.05810i | ||||||
\(474\) | 2.26990 | + | 1.31052i | 0.104260 | + | 0.0601944i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 26.2469i | 1.20302i | ||||||||
\(477\) | 1.11669 | − | 1.93416i | 0.0511297 | − | 0.0885593i | ||||
\(478\) | 2.08491 | + | 3.61118i | 0.0953618 | + | 0.165171i | ||||
\(479\) | 10.1231 | − | 5.84458i | 0.462537 | − | 0.267046i | −0.250573 | − | 0.968098i | \(-0.580619\pi\) |
0.713110 | + | 0.701052i | \(0.247286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.96718 | − | 6.58793i | −0.180888 | − | 0.300384i | ||||
\(482\) | −1.88407 | −0.0858170 | ||||||||
\(483\) | −5.77812 | + | 3.33600i | −0.262914 | + | 0.151793i | ||||
\(484\) | −9.36252 | − | 16.2164i | −0.425569 | − | 0.737107i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −27.6154 | − | 15.9438i | −1.25137 | − | 0.722481i | −0.279991 | − | 0.960003i | \(-0.590332\pi\) |
−0.971382 | + | 0.237522i | \(0.923665\pi\) | |||||||
\(488\) | 3.57918 | + | 2.06644i | 0.162022 | + | 0.0935434i | ||||
\(489\) | 15.5938i | 0.705174i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.77506 | + | 16.9309i | 0.441142 | + | 0.764080i | 0.997775 | − | 0.0666784i | \(-0.0212402\pi\) |
−0.556632 | + | 0.830759i | \(0.687907\pi\) | |||||||
\(492\) | 6.33097 | − | 3.65519i | 0.285422 | − | 0.164789i | ||||
\(493\) | 39.1220 | 1.76197 | ||||||||
\(494\) | −0.256787 | − | 13.9328i | −0.0115534 | − | 0.626868i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.93416 | + | 1.11669i | −0.0868465 | + | 0.0501409i | ||||
\(497\) | −25.6633 | − | 44.4502i | −1.15116 | − | 1.99386i | ||||
\(498\) | −3.57994 | + | 6.20064i | −0.160421 | + | 0.277857i | ||||
\(499\) | − | 39.3428i | − | 1.76123i | −0.473836 | − | 0.880613i | \(-0.657131\pi\) | ||
0.473836 | − | 0.880613i | \(-0.342869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.60934 | − | 0.929155i | −0.0719002 | − | 0.0415116i | ||||
\(502\) | 7.15005i | 0.319122i | ||||||||
\(503\) | 7.16650 | − | 12.4127i | 0.319538 | − | 0.553457i | −0.660853 | − | 0.750515i | \(-0.729806\pi\) |
0.980392 | + | 0.197058i | \(0.0631388\pi\) | |||||||
\(504\) | 1.79518 | + | 3.10934i | 0.0799637 | + | 0.138501i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.1316 | 0.450406 | ||||||||
\(507\) | 6.91044 | + | 11.0112i | 0.306903 | + | 0.489023i | ||||
\(508\) | −17.9870 | −0.798045 | ||||||||
\(509\) | −3.23839 | + | 1.86968i | −0.143539 | + | 0.0828723i | −0.570050 | − | 0.821610i | \(-0.693076\pi\) |
0.426511 | + | 0.904483i | \(0.359743\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.7437 | − | 46.3215i | 1.18307 | − | 2.04914i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.34713 | − | 1.93247i | −0.147779 | − | 0.0853204i | ||||
\(514\) | −17.7517 | − | 10.2489i | −0.782994 | − | 0.452062i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.10494 | − | 7.10996i | 0.180710 | − | 0.312999i | ||||
\(517\) | 13.8401 | + | 23.9717i | 0.608685 | + | 1.05427i | ||||
\(518\) | 6.63186 | − | 3.82891i | 0.291387 | − | 0.168232i | ||||
\(519\) | 24.3374 | 1.06829 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.2722 | −1.76436 | −0.882178 | − | 0.470915i | \(-0.843924\pi\) | ||||
−0.882178 | + | 0.470915i | \(0.843924\pi\) | |||||||
\(522\) | 4.63459 | − | 2.67578i | 0.202851 | − | 0.117116i | ||||
\(523\) | −11.4230 | − | 19.7853i | −0.499495 | − | 0.865150i | 0.500505 | − | 0.865734i | \(-0.333148\pi\) |
−1.00000 | 0.000583330i | \(0.999814\pi\) | ||||||||
\(524\) | 10.1731 | − | 17.6203i | 0.444414 | − | 0.769747i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.3313 | − | 8.85153i | −0.668477 | − | 0.385945i | ||||
\(527\) | −14.1395 | − | 8.16343i | −0.615925 | − | 0.355605i | ||||
\(528\) | − | 5.45207i | − | 0.237271i | ||||||
\(529\) | 9.77334 | − | 16.9279i | 0.424928 | − | 0.735997i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.237785 | − | 0.137285i | 0.0103190 | − | 0.00595768i | ||||
\(532\) | 13.8765 | 0.601623 | ||||||||
\(533\) | 13.5974 | + | 22.5799i | 0.588967 | + | 0.978045i | ||||
\(534\) | 9.59376 | 0.415163 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.39851 | − | 12.8146i | −0.319567 | − | 0.553506i | ||||
\(537\) | 1.53429 | − | 2.65746i | 0.0662093 | − | 0.114678i | ||||
\(538\) | 18.1864i | 0.784070i | ||||||||
\(539\) | −27.8137 | − | 16.0582i | −1.19802 | − | 0.691677i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.9610i | 0.815196i | 0.913162 | + | 0.407598i | \(0.133633\pi\) | ||||
−0.913162 | + | 0.407598i | \(0.866367\pi\) | |||||||
\(542\) | −11.3847 | + | 19.7188i | −0.489013 | + | 0.846996i | ||||
\(543\) | 2.29688 | + | 3.97831i | 0.0985685 | + | 0.170726i | ||||
\(544\) | 6.33097 | − | 3.65519i | 0.271438 | − | 0.156715i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.0897 | + | 6.67810i | −0.474596 | + | 0.285796i | ||||
\(547\) | 26.7863 | 1.14530 | 0.572649 | − | 0.819801i | \(-0.305916\pi\) | ||||
0.572649 | + | 0.819801i | \(0.305916\pi\) | |||||||
\(548\) | −9.56156 | + | 5.52037i | −0.408450 | + | 0.235818i | ||||
\(549\) | 2.06644 | + | 3.57918i | 0.0881935 | + | 0.152756i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 20.6834i | − | 0.881144i | ||||||
\(552\) | 1.60934 | + | 0.929155i | 0.0684982 | + | 0.0395475i | ||||
\(553\) | −8.14974 | − | 4.70526i | −0.346562 | − | 0.200088i | ||||
\(554\) | − | 16.3563i | − | 0.694911i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.85096 | + | 8.40212i | 0.205727 | + | 0.356329i | ||||
\(557\) | −22.7227 | + | 13.1189i | −0.962791 | + | 0.555867i | −0.897031 | − | 0.441968i | \(-0.854280\pi\) |
−0.0657599 | + | 0.997835i | \(0.520947\pi\) | |||||||
\(558\) | −2.23338 | −0.0945465 | ||||||||
\(559\) | 25.9037 | + | 14.3257i | 1.09561 | + | 0.605911i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.5169 | − | 19.9283i | 1.45730 | − | 0.841375i | ||||
\(562\) | 3.91110 | + | 6.77423i | 0.164980 | + | 0.285754i | ||||
\(563\) | 8.10900 | − | 14.0452i | 0.341754 | − | 0.591935i | −0.643005 | − | 0.765862i | \(-0.722312\pi\) |
0.984758 | + | 0.173927i | \(0.0556458\pi\) | |||||||
\(564\) | 5.07700i | 0.213780i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.01483 | − | 3.47266i | −0.252822 | − | 0.145967i | ||||
\(567\) | 3.59036i | 0.150781i | ||||||||
\(568\) | −7.14784 | + | 12.3804i | −0.299917 | + | 0.519471i | ||||
\(569\) | 17.1092 | + | 29.6340i | 0.717255 | + | 1.24232i | 0.962083 | + | 0.272755i | \(0.0879350\pi\) |
−0.244829 | + | 0.969566i | \(0.578732\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.151070 | 0.00632206 | 0.00316103 | − | 0.999995i | \(-0.498994\pi\) | ||||
0.00316103 | + | 0.999995i | \(0.498994\pi\) | |||||||
\(572\) | 19.6544 | − | 0.362237i | 0.821791 | − | 0.0151459i | ||||
\(573\) | 14.0601 | 0.587371 | ||||||||
\(574\) | −22.7305 | + | 13.1234i | −0.948752 | + | 0.547762i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 33.7742i | 1.40604i | 0.711171 | + | 0.703019i | \(0.248165\pi\) | ||||
−0.711171 | + | 0.703019i | \(0.751835\pi\) | |||||||
\(578\) | 31.5594 | + | 18.2208i | 1.31270 | + | 0.757886i | ||||
\(579\) | −21.7276 | − | 12.5444i | −0.902966 | − | 0.521328i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8533 | − | 22.2625i | 0.533244 | − | 0.923605i | ||||
\(582\) | 0.954155 | + | 1.65264i | 0.0395510 | + | 0.0685043i | ||||
\(583\) | 10.5452 | − | 6.08827i | 0.436737 | − | 0.252150i | ||||
\(584\) | −14.8975 | −0.616464 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.4243 | 1.09158 | ||||||||
\(587\) | −29.1037 | + | 16.8030i | −1.20124 | + | 0.693535i | −0.960831 | − | 0.277137i | \(-0.910615\pi\) |
−0.240408 | + | 0.970672i | \(0.577281\pi\) | |||||||
\(588\) | −2.94535 | − | 5.10149i | −0.121464 | − | 0.210382i | ||||
\(589\) | −4.31593 | + | 7.47541i | −0.177835 | + | 0.308019i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.96287 | − | 4.59737i | −0.327549 | − | 0.189110i | ||||
\(592\) | −1.84713 | − | 1.06644i | −0.0759165 | − | 0.0438304i | ||||
\(593\) | 36.7529i | 1.50926i | 0.656150 | + | 0.754630i | \(0.272184\pi\) | ||||
−0.656150 | + | 0.754630i | \(0.727816\pi\) | |||||||
\(594\) | 2.72603 | − | 4.72163i | 0.111851 | − | 0.193731i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.70959 | + | 2.71908i | −0.192912 | + | 0.111378i | ||||
\(597\) | 23.6792 | 0.969124 | ||||||||
\(598\) | −3.24262 | + | 5.86332i | −0.132601 | + | 0.239769i | ||||
\(599\) | −24.5241 | −1.00203 | −0.501015 | − | 0.865439i | \(-0.667040\pi\) | ||||
−0.501015 | + | 0.865439i | \(0.667040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7548 | + | 32.4843i | 0.765025 | + | 1.32506i | 0.940233 | + | 0.340531i | \(0.110607\pi\) |
−0.175208 | + | 0.984531i | \(0.556060\pi\) | |||||||
\(602\) | −14.7382 | + | 25.5273i | −0.600685 | + | 1.04042i | ||||
\(603\) | − | 14.7970i | − | 0.602581i | ||||||
\(604\) | 15.4161 | + | 8.90050i | 0.627273 | + | 0.362156i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.2557i | 0.660343i | ||||||||
\(607\) | 23.2554 | − | 40.2796i | 0.943909 | − | 1.63490i | 0.185988 | − | 0.982552i | \(-0.440452\pi\) |
0.757921 | − | 0.652346i | \(-0.226215\pi\) | |||||||
\(608\) | −1.93247 | − | 3.34713i | −0.0783718 | − | 0.135744i | ||||
\(609\) | −16.6399 | + | 9.60703i | −0.674281 | + | 0.389297i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.3023 | + | 0.337318i | −0.740430 | + | 0.0136464i | ||||
\(612\) | 7.31038 | 0.295505 | ||||||||
\(613\) | 8.91634 | − | 5.14785i | 0.360128 | − | 0.207920i | −0.309009 | − | 0.951059i | \(-0.599997\pi\) |
0.669137 | + | 0.743139i | \(0.266664\pi\) | |||||||
\(614\) | −3.54290 | − | 6.13649i | −0.142980 | − | 0.247649i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.5749i | 0.788695i | ||||||||
\(617\) | 30.9005 | + | 17.8404i | 1.24401 | + | 0.718228i | 0.969908 | − | 0.243473i | \(-0.0782869\pi\) |
0.274100 | + | 0.961701i | \(0.411620\pi\) | |||||||
\(618\) | 11.2376 | + | 6.48802i | 0.452042 | + | 0.260987i | ||||
\(619\) | 12.9815i | 0.521772i | 0.965370 | + | 0.260886i | \(0.0840146\pi\) | ||||
−0.965370 | + | 0.260886i | \(0.915985\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.929155 | + | 1.60934i | 0.0372857 | + | 0.0645807i | ||||
\(622\) | 1.58498 | − | 0.915086i | 0.0635517 | − | 0.0366916i | ||||
\(623\) | −34.4451 | −1.38001 | ||||||||
\(624\) | 3.15519 | + | 1.74493i | 0.126309 | + | 0.0698531i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.6087 | − | 6.12493i | 0.424008 | − | 0.244801i | ||||
\(627\) | −10.5359 | − | 18.2488i | −0.420765 | − | 0.728786i | ||||
\(628\) | −2.96826 | + | 5.14117i | −0.118446 | + | 0.205155i | ||||
\(629\) | − | 15.5922i | − | 0.621700i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4953 | − | 10.6783i | −0.736287 | − | 0.425096i | 0.0844307 | − | 0.996429i | \(-0.473093\pi\) |
−0.820718 | + | 0.571334i | \(0.806426\pi\) | |||||||
\(632\) | 2.62105i | 0.104260i | ||||||||
\(633\) | 4.99303 | − | 8.64818i | 0.198455 | − | 0.343734i | ||||
\(634\) | −3.12550 | − | 5.41352i | −0.124129 | − | 0.214999i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.23338 | 0.0885593 | ||||||||
\(637\) | 18.1949 | − | 10.9567i | 0.720907 | − | 0.434122i | ||||
\(638\) | 29.1771 | 1.15513 | ||||||||
\(639\) | −12.3804 | + | 7.14784i | −0.489762 | + | 0.282764i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.49169 | + | 11.2439i | −0.256407 | + | 0.444109i | −0.965277 | − | 0.261230i | \(-0.915872\pi\) |
0.708870 | + | 0.705339i | \(0.249205\pi\) | |||||||
\(642\) | − | 9.91673i | − | 0.391382i | ||||||
\(643\) | 13.6888 | + | 7.90323i | 0.539834 | + | 0.311673i | 0.745012 | − | 0.667052i | \(-0.232444\pi\) |
−0.205178 | + | 0.978725i | \(0.565777\pi\) | |||||||
\(644\) | −5.77812 | − | 3.33600i | −0.227690 | − | 0.131457i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.1271 | − | 24.4688i | 0.555822 | − | 0.962711i | ||||
\(647\) | 11.4442 | + | 19.8219i | 0.449916 | + | 0.779277i | 0.998380 | − | 0.0568967i | \(-0.0181206\pi\) |
−0.548464 | + | 0.836174i | \(0.684787\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 1.49698 | 0.0587615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.01864 | 0.314275 | ||||||||
\(652\) | −13.5046 | + | 7.79688i | −0.528881 | + | 0.305349i | ||||
\(653\) | 1.08070 | + | 1.87183i | 0.0422911 | + | 0.0732504i | 0.886396 | − | 0.462927i | \(-0.153201\pi\) |
−0.844105 | + | 0.536178i | \(0.819868\pi\) | |||||||
\(654\) | −3.70544 | + | 6.41801i | −0.144894 | + | 0.250964i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.33097 | + | 3.65519i | 0.247183 | + | 0.142711i | ||||
\(657\) | −12.9016 | − | 7.44876i | −0.503340 | − | 0.290604i | ||||
\(658\) | − | 18.2283i | − | 0.710611i | ||||||
\(659\) | −9.79863 | + | 16.9717i | −0.381700 | + | 0.661124i | −0.991305 | − | 0.131581i | \(-0.957995\pi\) |
0.609605 | + | 0.792705i | \(0.291328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.8286 | + | 14.3348i | −0.965719 | + | 0.557558i | −0.897929 | − | 0.440141i | \(-0.854928\pi\) |
−0.0677909 | + | 0.997700i | \(0.521595\pi\) | |||||||
\(662\) | 19.1758 | 0.745289 | ||||||||
\(663\) | 0.485704 | + | 26.3535i | 0.0188632 | + | 1.02348i | ||||
\(664\) | −7.15988 | −0.277857 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.06644 | − | 1.84713i | −0.0413237 | − | 0.0715748i | ||||
\(667\) | −4.97244 | + | 8.61251i | −0.192534 | + | 0.333478i | ||||
\(668\) | − | 1.85831i | − | 0.0719002i | ||||||
\(669\) | 19.3833 | + | 11.1910i | 0.749404 | + | 0.432668i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.5327i | 0.869867i | ||||||||
\(672\) | −1.79518 | + | 3.10934i | −0.0692506 | + | 0.119946i | ||||
\(673\) | −25.4130 | − | 44.0166i | −0.979599 | − | 1.69672i | −0.663837 | − | 0.747878i | \(-0.731073\pi\) |
−0.315763 | − | 0.948838i | \(-0.602260\pi\) | |||||||
\(674\) | 14.3284 | − | 8.27248i | 0.551908 | − | 0.318644i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.08074 | + | 11.4902i | −0.233874 | + | 0.441931i | ||||
\(677\) | 15.4058 | 0.592093 | 0.296046 | − | 0.955174i | \(-0.404332\pi\) | ||||
0.296046 | + | 0.955174i | \(0.404332\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.42576 | − | 5.93359i | −0.131469 | − | 0.227710i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 12.9853i | − | 0.497598i | ||||||
\(682\) | −10.5452 | − | 6.08827i | −0.403796 | − | 0.233132i | ||||
\(683\) | 19.2650 | + | 11.1227i | 0.737155 | + | 0.425597i | 0.821034 | − | 0.570879i | \(-0.193398\pi\) |
−0.0838788 | + | 0.996476i | \(0.526731\pi\) | |||||||
\(684\) | − | 3.86493i | − | 0.147779i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.99141 | − | 3.44922i | −0.0760324 | − | 0.131692i | ||||
\(687\) | −12.5102 | + | 7.22276i | −0.477293 | + | 0.275565i | ||||
\(688\) | 8.20988 | 0.312999 | ||||||||
\(689\) | 0.148387 | + | 8.05120i | 0.00565308 | + | 0.306726i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.31663 | − | 3.06956i | 0.202254 | − | 0.116771i | −0.395452 | − | 0.918486i | \(-0.629412\pi\) |
0.597706 | + | 0.801715i | \(0.296079\pi\) | |||||||
\(692\) | 12.1687 | + | 21.0768i | 0.462584 | + | 0.801219i | ||||
\(693\) | −9.78745 | + | 16.9524i | −0.371794 | + | 0.643967i | ||||
\(694\) | − | 5.96390i | − | 0.226387i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.63459 | + | 2.67578i | 0.175674 | + | 0.101425i | ||||
\(697\) | 53.4416i | 2.02425i | ||||||||
\(698\) | −1.59523 | + | 2.76302i | −0.0603803 | + | 0.104582i | ||||
\(699\) | −6.21869 | − | 10.7711i | −0.235212 | − | 0.407400i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.7793 | −0.935902 | −0.467951 | − | 0.883754i | \(-0.655008\pi\) | ||||
−0.467951 | + | 0.883754i | \(0.655008\pi\) | |||||||
\(702\) | 1.86001 | + | 3.08875i | 0.0702015 | + | 0.116577i | ||||
\(703\) | −8.24344 | −0.310907 | ||||||||
\(704\) | 4.72163 | − | 2.72603i | 0.177953 | − | 0.102741i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.0524 | + | 24.3395i | −0.528869 | + | 0.916029i | ||||
\(707\) | − | 58.3638i | − | 2.19500i | ||||||
\(708\) | 0.237785 | + | 0.137285i | 0.00893652 | + | 0.00515950i | ||||
\(709\) | 22.3507 | + | 12.9042i | 0.839398 | + | 0.484627i | 0.857060 | − | 0.515217i | \(-0.172289\pi\) |
−0.0176613 | + | 0.999844i | \(0.505622\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.31052 | + | 2.26990i | −0.0491485 | + | 0.0851277i | ||||
\(712\) | 4.79688 | + | 8.30844i | 0.179771 | + | 0.311372i | ||||
\(713\) | 3.59428 | − | 2.07516i | 0.134607 | − | 0.0777152i | ||||
\(714\) | −26.2469 | −0.982265 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.06857 | 0.114678 | ||||||||
\(717\) | −3.61118 | + | 2.08491i | −0.134862 | + | 0.0778625i | ||||
\(718\) | −11.3702 | − | 19.6938i | −0.424333 | − | 0.734966i | ||||
\(719\) | −11.7949 | + | 20.4293i | −0.439874 | + | 0.761884i | −0.997679 | − | 0.0680879i | \(-0.978310\pi\) |
0.557806 | + | 0.829972i | \(0.311643\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.3470 | − | 23.2943i | −1.50260 | − | 0.867527i | ||||
\(722\) | 3.51806 | + | 2.03115i | 0.130929 | + | 0.0755917i | ||||
\(723\) | − | 1.88407i | − | 0.0700693i | ||||||
\(724\) | −2.29688 | + | 3.97831i | −0.0853628 | + | 0.147853i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.2164 | − | 9.36252i | 0.601846 | − | 0.347476i | ||||
\(727\) | −31.4651 | −1.16698 | −0.583489 | − | 0.812121i | \(-0.698313\pi\) | ||||
−0.583489 | + | 0.812121i | \(0.698313\pi\) | |||||||
\(728\) | −11.3283 | − | 6.26493i | −0.419854 | − | 0.232194i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.0087 | + | 51.9765i | 1.10991 | + | 1.92242i | ||||
\(732\) | −2.06644 | + | 3.57918i | −0.0763778 | + | 0.132290i | ||||
\(733\) | 32.2822i | 1.19237i | 0.802847 | + | 0.596186i | \(0.203318\pi\) | ||||
−0.802847 | + | 0.596186i | \(0.796682\pi\) | |||||||
\(734\) | 26.1824 | + | 15.1164i | 0.966412 | + | 0.557958i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.85831i | 0.0684982i | ||||||||
\(737\) | 40.3372 | − | 69.8660i | 1.48584 | − | 2.57355i | ||||
\(738\) | 3.65519 | + | 6.33097i | 0.134549 | + | 0.233046i | ||||
\(739\) | −13.2643 | + | 7.65817i | −0.487936 | + | 0.281710i | −0.723718 | − | 0.690096i | \(-0.757568\pi\) |
0.235782 | + | 0.971806i | \(0.424235\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.9328 | − | 0.256787i | 0.511836 | − | 0.00943332i | ||||
\(742\) | −8.01864 | −0.294374 | ||||||||
\(743\) | −21.8518 | + | 12.6161i | −0.801663 | + | 0.462841i | −0.844052 | − | 0.536261i | \(-0.819836\pi\) |
0.0423891 | + | 0.999101i | \(0.486503\pi\) | |||||||
\(744\) | −1.11669 | − | 1.93416i | −0.0409399 | − | 0.0709099i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 4.67614i | − | 0.171206i | ||||||
\(747\) | −6.20064 | − | 3.57994i | −0.226869 | − | 0.130983i | ||||
\(748\) | 34.5169 | + | 19.9283i | 1.26206 | + | 0.728652i | ||||
\(749\) | 35.6047i | 1.30097i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.69444 | + | 13.3272i | 0.280774 | + | 0.486315i | 0.971576 | − | 0.236729i | \(-0.0760755\pi\) |
−0.690802 | + | 0.723044i | \(0.742742\pi\) | |||||||
\(752\) | −4.39681 | + | 2.53850i | −0.160335 | + | 0.0925695i | ||||
\(753\) | −7.15005 | −0.260562 | ||||||||
\(754\) | −9.33811 | + | 16.8852i | −0.340074 | + | 0.614923i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.10934 | + | 1.79518i | −0.113086 | + | 0.0652901i | ||||
\(757\) | −18.1796 | − | 31.4879i | −0.660747 | − | 1.14445i | −0.980420 | − | 0.196920i | \(-0.936906\pi\) |
0.319673 | − | 0.947528i | \(-0.396427\pi\) | |||||||
\(758\) | −10.7155 | + | 18.5598i | −0.389205 | + | 0.674122i | ||||
\(759\) | 10.1316i | 0.367755i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.4056 | − | 15.8226i | −0.993453 | − | 0.573570i | −0.0871481 | − | 0.996195i | \(-0.527775\pi\) |
−0.906305 | + | 0.422625i | \(0.861109\pi\) | |||||||
\(762\) | − | 17.9870i | − | 0.651601i | ||||||
\(763\) | 13.3039 | − | 23.0430i | 0.481632 | − | 0.834211i | ||||
\(764\) | 7.03007 | + | 12.1764i | 0.254339 | + | 0.440528i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.0512087 | −0.00185025 | ||||||||
\(767\) | −0.479107 | + | 0.866322i | −0.0172995 | + | 0.0312811i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −10.0722 | + | 5.81521i | −0.363214 | + | 0.209702i | −0.670490 | − | 0.741919i | \(-0.733916\pi\) |
0.307276 | + | 0.951621i | \(0.400583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.2489 | − | 17.7517i | 0.369107 | − | 0.639312i | ||||
\(772\) | − | 25.0888i | − | 0.902966i | ||||||
\(773\) | 25.2573 | + | 14.5823i | 0.908443 | + | 0.524490i | 0.879930 | − | 0.475104i | \(-0.157590\pi\) |
0.0285128 | + | 0.999593i | \(0.490923\pi\) | |||||||
\(774\) | 7.10996 | + | 4.10494i | 0.255562 | + | 0.147549i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.954155 | + | 1.65264i | −0.0342522 | + | 0.0593265i | ||||
\(777\) | 3.82891 | + | 6.63186i | 0.137361 | + | 0.237917i | ||||
\(778\) | 4.63459 | − | 2.67578i | 0.166158 | − | 0.0959315i | ||||
\(779\) | 28.2541 | 1.01231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −77.9410 | −2.78895 | ||||||||
\(782\) | −11.7649 | + | 6.79247i | −0.420712 | + | 0.242898i | ||||
\(783\) | 2.67578 | + | 4.63459i | 0.0956247 | + | 0.165627i | ||||
\(784\) | 2.94535 | − | 5.10149i | 0.105191 | − | 0.182196i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.6203 | + | 10.1731i | 0.628496 | + | 0.362862i | ||||
\(787\) | −13.9155 | − | 8.03414i | −0.496035 | − | 0.286386i | 0.231039 | − | 0.972944i | \(-0.425787\pi\) |
−0.727075 | + | 0.686558i | \(0.759121\pi\) | |||||||
\(788\) | − | 9.19473i | − | 0.327549i | ||||||
\(789\) | 8.85153 | − | 15.3313i | 0.315123 | − | 0.545809i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.45207 | 0.193731 | ||||||||
\(793\) | −13.0400 | − | 7.21159i | −0.463065 | − | 0.256091i | ||||
\(794\) | −8.50719 | −0.301909 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.8396 | + | 20.5068i | 0.419643 | + | 0.726843i | ||||
\(797\) | −19.5288 | + | 33.8249i | −0.691745 | + | 1.19814i | 0.279520 | + | 0.960140i | \(0.409825\pi\) |
−0.971266 | + | 0.237998i | \(0.923509\pi\) | |||||||
\(798\) | 13.8765i | 0.491223i | ||||||||
\(799\) | −32.1423 | − | 18.5574i | −1.13711 | − | 0.656513i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.59376i | 0.338979i | ||||||||
\(802\) | 11.6894 | − | 20.2467i | 0.412767 | − | 0.714934i | ||||
\(803\) | −40.6111 | − | 70.3405i | −1.43314 | − | 2.48226i | ||||
\(804\) | 12.8146 | − | 7.39851i | 0.451936 | − | 0.260925i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.89835 | − | 4.15411i | 0.242984 | − | 0.146322i | ||||
\(807\) | −18.1864 | −0.640191 | ||||||||
\(808\) | −14.0779 | + | 8.12785i | −0.495257 | + | 0.285937i | ||||
\(809\) | −7.04891 | − | 12.2091i | −0.247827 | − | 0.429248i | 0.715096 | − | 0.699026i | \(-0.246383\pi\) |
−0.962923 | + | 0.269778i | \(0.913050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.3869i | − | 0.399846i | −0.979812 | − | 0.199923i | \(-0.935931\pi\) | ||
0.979812 | − | 0.199923i | \(-0.0640693\pi\) | |||||||
\(812\) | −16.6399 | − | 9.60703i | −0.583945 | − | 0.337141i | ||||
\(813\) | −19.7188 | − | 11.3847i | −0.691569 | − | 0.399278i | ||||
\(814\) | − | 11.6286i | − | 0.407583i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.65519 | + | 6.33097i | 0.127957 | + | 0.221628i | ||||
\(817\) | 27.4795 | − | 15.8653i | 0.961387 | − | 0.555057i | ||||
\(818\) | 5.21360 | 0.182289 | ||||||||
\(819\) | −6.67810 | − | 11.0897i | −0.233352 | − | 0.387506i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2924 | − | 14.6026i | 0.882710 | − | 0.509633i | 0.0111593 | − | 0.999938i | \(-0.496448\pi\) |
0.871551 | + | 0.490305i | \(0.163114\pi\) | |||||||
\(822\) | −5.52037 | − | 9.56156i | −0.192545 | − | 0.333498i | ||||
\(823\) | −14.1230 | + | 24.4617i | −0.492296 | + | 0.852681i | −0.999961 | − | 0.00887332i | \(-0.997175\pi\) |
0.507665 | + | 0.861555i | \(0.330509\pi\) | |||||||
\(824\) | 12.9760i | 0.452042i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.853735 | − | 0.492904i | −0.0297052 | − | 0.0171503i | ||||
\(827\) | 37.3963i | 1.30040i | 0.759765 | + | 0.650198i | \(0.225314\pi\) | ||||
−0.759765 | + | 0.650198i | \(0.774686\pi\) | |||||||
\(828\) | −0.929155 | + | 1.60934i | −0.0322904 | + | 0.0559286i | ||||
\(829\) | −0.925320 | − | 1.60270i | −0.0321377 | − | 0.0556641i | 0.849509 | − | 0.527574i | \(-0.176898\pi\) |
−0.881647 | + | 0.471910i | \(0.843565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.3563 | 0.567393 | ||||||||
\(832\) | 0.0664404 | + | 3.60494i | 0.00230341 | + | 0.124979i | ||||
\(833\) | 43.0632 | 1.49205 | ||||||||
\(834\) | −8.40212 | + | 4.85096i | −0.290941 | + | 0.167975i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.5359 | − | 18.2488i | 0.364393 | − | 0.631147i | ||||
\(837\) | − | 2.23338i | − | 0.0771969i | ||||||
\(838\) | 15.7628 | + | 9.10066i | 0.544517 | + | 0.314377i | ||||
\(839\) | −38.8940 | − | 22.4555i | −1.34277 | − | 0.775249i | −0.355557 | − | 0.934655i | \(-0.615709\pi\) |
−0.987213 | + | 0.159406i | \(0.949042\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.180359 | − | 0.312392i | 0.00621929 | − | 0.0107721i | ||||
\(842\) | −12.8231 | − | 22.2103i | −0.441914 | − | 0.765418i | ||||
\(843\) | −6.77423 | + | 3.91110i | −0.233317 | + | 0.134706i | ||||
\(844\) | 9.98606 | 0.343734 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.07700 | −0.174551 | ||||||||
\(847\) | −58.2226 | + | 33.6148i | −2.00055 | + | 1.15502i | ||||
\(848\) | 1.11669 | + | 1.93416i | 0.0383473 | + | 0.0664195i | ||||
\(849\) | 3.47266 | − | 6.01483i | 0.119181 | − | 0.206428i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.43254 | + | 1.98178i | 0.117666 | + | 0.0679344i | ||||
\(852\) | −12.3804 | − | 7.14784i | −0.424146 | − | 0.244881i | ||||
\(853\) | 6.75772i | 0.231380i | 0.993285 | + | 0.115690i | \(0.0369079\pi\) | ||||
−0.993285 | + | 0.115690i | \(0.963092\pi\) | |||||||
\(854\) | 7.41927 | − | 12.8505i | 0.253882 | − | 0.439737i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.58814 | − | 4.95837i | 0.293537 | − | 0.169474i | ||||
\(857\) | 9.16177 | 0.312960 | 0.156480 | − | 0.987681i | \(-0.449985\pi\) | ||||
0.156480 | + | 0.987681i | \(0.449985\pi\) | |||||||
\(858\) | 0.362237 | + | 19.6544i | 0.0123666 | + | 0.670989i | ||||
\(859\) | 11.9538 | 0.407857 | 0.203928 | − | 0.978986i | \(-0.434629\pi\) | ||||
0.203928 | + | 0.978986i | \(0.434629\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.1234 | − | 22.7305i | −0.447246 | − | 0.774653i | ||||
\(862\) | 1.03457 | − | 1.79193i | 0.0352376 | − | 0.0610334i | ||||
\(863\) | 31.6465i | 1.07726i | 0.842542 | + | 0.538630i | \(0.181058\pi\) | ||||
−0.842542 | + | 0.538630i | \(0.818942\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 0.941830i | − | 0.0320047i | ||||||
\(867\) | −18.2208 | + | 31.5594i | −0.618811 | + | 1.07181i | ||||
\(868\) | 4.00932 | + | 6.94435i | 0.136085 | + | 0.235707i | ||||
\(869\) | −12.3756 | + | 7.14507i | −0.419814 | + | 0.242380i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5226 | + | 45.7043i | 0.932567 | + | 1.54863i | ||||
\(872\) | −7.41088 | −0.250964 | ||||||||
\(873\) | −1.65264 | + | 0.954155i | −0.0559335 | + | 0.0322932i | ||||
\(874\) | 3.59112 | + | 6.22000i | 0.121471 | + | 0.210395i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 14.8975i | − | 0.503340i | ||||||
\(877\) | 12.2372 | + | 7.06515i | 0.413221 | + | 0.238573i | 0.692173 | − | 0.721732i | \(-0.256654\pi\) |
−0.278952 | + | 0.960305i | \(0.589987\pi\) | |||||||
\(878\) | 3.11997 | + | 1.80132i | 0.105294 | + | 0.0607915i | ||||
\(879\) | 26.4243i | 0.891270i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.56417 | − | 16.5656i | −0.322225 | − | 0.558110i | 0.658722 | − | 0.752387i | \(-0.271097\pi\) |
−0.980947 | + | 0.194276i | \(0.937764\pi\) | |||||||
\(882\) | 5.10149 | − | 2.94535i | 0.171776 | − | 0.0991749i | ||||
\(883\) | −7.19528 | −0.242140 | −0.121070 | − | 0.992644i | \(-0.538633\pi\) | ||||
−0.121070 | + | 0.992644i | \(0.538633\pi\) | |||||||
\(884\) | −22.5799 | + | 13.5974i | −0.759445 | + | 0.457329i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.37425 | − | 2.52548i | 0.146956 | − | 0.0848451i | ||||
\(887\) | −14.4022 | − | 24.9453i | −0.483577 | − | 0.837580i | 0.516245 | − | 0.856441i | \(-0.327329\pi\) |
−0.999822 | + | 0.0188611i | \(0.993996\pi\) | |||||||
\(888\) | 1.06644 | − | 1.84713i | 0.0357874 | − | 0.0619856i | ||||
\(889\) | 64.5799i | 2.16594i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.72163 | + | 2.72603i | 0.158181 | + | 0.0913256i | ||||
\(892\) | 22.3820i | 0.749404i | ||||||||
\(893\) | −9.81112 | + | 16.9934i | −0.328317 | + | 0.568661i | ||||
\(894\) | −2.71908 | − | 4.70959i | −0.0909398 | − | 0.157512i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.59036 | −0.119946 | ||||||||
\(897\) | −5.86332 | − | 3.24262i | −0.195771 | − | 0.108268i | ||||
\(898\) | 5.42729 | 0.181111 | ||||||||
\(899\) | 10.3508 | − | 5.97604i | 0.345219 | − | 0.199312i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.16343 | + | 14.1395i | −0.271963 | + | 0.471054i | ||||
\(902\) | 39.8567i | 1.32708i | ||||||||
\(903\) | −25.5273 | − | 14.7382i | −0.849496 | − | 0.490457i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.90050 | + | 15.4161i | −0.295699 | + | 0.512166i | ||||
\(907\) | −19.5856 | − | 33.9233i | −0.650331 | − | 1.12641i | −0.983043 | − | 0.183377i | \(-0.941297\pi\) |
0.332712 | − | 0.943029i | \(-0.392036\pi\) | |||||||
\(908\) | 11.2456 | − | 6.49265i | 0.373199 | − | 0.215466i | ||||
\(909\) | −16.2557 | −0.539168 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3352 | 0.872526 | 0.436263 | − | 0.899819i | \(-0.356302\pi\) | ||||
0.436263 | + | 0.899819i | \(0.356302\pi\) | |||||||
\(912\) | 3.34713 | − | 1.93247i | 0.110835 | − | 0.0639903i | ||||
\(913\) | −19.5181 | − | 33.8063i | −0.645954 | − | 1.11883i | ||||
\(914\) | −10.8416 | + | 18.7782i | −0.358607 | + | 0.621126i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.5102 | − | 7.22276i | −0.413348 | − | 0.238647i | ||||
\(917\) | −63.2633 | − | 36.5251i | −2.08914 | − | 1.20616i | ||||
\(918\) | 7.31038i | 0.241278i | ||||||||
\(919\) | −4.85456 | + | 8.40834i | −0.160137 | + | 0.277365i | −0.934918 | − | 0.354865i | \(-0.884527\pi\) |
0.774781 | + | 0.632230i | \(0.217860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.13649 | − | 3.54290i | 0.202204 | − | 0.116743i | ||||
\(922\) | 29.6023 | 0.974901 | ||||||||
\(923\) | 24.9450 | − | 45.1056i | 0.821074 | − | 1.48467i | ||||
\(924\) | −19.5749 | −0.643967 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.1038 | + | 24.4284i | 0.463478 | + | 0.802768i | ||||
\(927\) | −6.48802 | + | 11.2376i | −0.213095 | + | 0.369091i | ||||
\(928\) | 5.35157i | 0.175674i | ||||||||
\(929\) | 2.68782 | + | 1.55181i | 0.0881844 | + | 0.0509133i | 0.543444 | − | 0.839446i | \(-0.317120\pi\) |
−0.455259 | + | 0.890359i | \(0.650453\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 22.7671i | − | 0.746162i | ||||||
\(932\) | 6.21869 | − | 10.7711i | 0.203700 | − | 0.352819i | ||||
\(933\) | 0.915086 | + | 1.58498i | 0.0299586 | + | 0.0518898i | ||||
\(934\) | 7.07864 | − | 4.08685i | 0.231620 | − | 0.133726i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.74493 | + | 3.15519i | −0.0570348 | + | 0.103131i | ||||
\(937\) | 53.5929 | 1.75080 | 0.875402 | − | 0.483396i | \(-0.160597\pi\) | ||||
0.875402 | + | 0.483396i | \(0.160597\pi\) | |||||||
\(938\) | −46.0090 | + | 26.5633i | −1.50225 | + | 0.867323i | ||||
\(939\) | 6.12493 | + | 10.6087i | 0.199880 | + | 0.346201i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.9758i | − | 1.40097i | −0.713667 | − | 0.700485i | \(-0.752967\pi\) | ||
0.713667 | − | 0.700485i | \(-0.247033\pi\) | |||||||
\(942\) | −5.14117 | − | 2.96826i | −0.167509 | − | 0.0967111i | ||||
\(943\) | −11.7649 | − | 6.79247i | −0.383118 | − | 0.221193i | ||||
\(944\) | 0.274571i | 0.00893652i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.3804 | + | 38.7640i | 0.727650 | + | 1.26033i | ||||
\(947\) | 9.60349 | − | 5.54457i | 0.312071 | − | 0.180174i | −0.335782 | − | 0.941940i | \(-0.609000\pi\) |
0.647853 | + | 0.761765i | \(0.275667\pi\) | |||||||
\(948\) | −2.62105 | −0.0851277 | ||||||||
\(949\) | 53.7046 | − | 0.989796i | 1.74333 | − | 0.0321301i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.41352 | − | 3.12550i | 0.175546 | − | 0.101351i | ||||
\(952\) | −13.1234 | − | 22.7305i | −0.425333 | − | 0.736699i | ||||
\(953\) | −28.8278 | + | 49.9313i | −0.933825 | + | 1.61743i | −0.157110 | + | 0.987581i | \(0.550218\pi\) |
−0.776715 | + | 0.629852i | \(0.783116\pi\) | |||||||
\(954\) | 2.23338i | 0.0723084i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.61118 | − | 2.08491i | −0.116794 | − | 0.0674309i | ||||
\(957\) | 29.1771i | 0.943162i | ||||||||
\(958\) | −5.84458 | + | 10.1231i | −0.188830 | + | 0.327063i | ||||
\(959\) | 19.8201 | + | 34.3294i | 0.640025 | + | 1.10856i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.0120 | 0.839097 | ||||||||
\(962\) | 6.72964 | + | 3.72173i | 0.216972 | + | 0.119993i | ||||
\(963\) | 9.91673 | 0.319562 | ||||||||
\(964\) | 1.63165 | − | 0.942035i | 0.0525520 | − | 0.0303409i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.33600 | − | 5.77812i | 0.107334 | − | 0.185908i | ||||
\(967\) | 30.5218i | 0.981516i | 0.871296 | + | 0.490758i | \(0.163280\pi\) | ||||
−0.871296 | + | 0.490758i | \(0.836720\pi\) | |||||||
\(968\) | 16.2164 | + | 9.36252i | 0.521214 | + | 0.300923i | ||||
\(969\) | 24.4688 | + | 14.1271i | 0.786050 | + | 0.453826i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.9787 | + | 24.2119i | −0.448599 | + | 0.776996i | −0.998295 | − | 0.0583686i | \(-0.981410\pi\) |
0.549696 | + | 0.835365i | \(0.314743\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 30.1666 | − | 17.4167i | 0.967098 | − | 0.558354i | ||||
\(974\) | 31.8875 | 1.02174 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.13288 | −0.132290 | ||||||||
\(977\) | 1.70870 | − | 0.986516i | 0.0546660 | − | 0.0315614i | −0.472418 | − | 0.881375i | \(-0.656619\pi\) |
0.527084 | + | 0.849813i | \(0.323285\pi\) | |||||||
\(978\) | −7.79688 | − | 13.5046i | −0.249317 | − | 0.431829i | ||||
\(979\) | −26.1529 | + | 45.2982i | −0.835851 | + | 1.44774i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.41801 | − | 3.70544i | −0.204911 | − | 0.118306i | ||||
\(982\) | −16.9309 | − | 9.77506i | −0.540286 | − | 0.311935i | ||||
\(983\) | − | 8.00792i | − | 0.255413i | −0.991812 | − | 0.127707i | \(-0.959238\pi\) | ||
0.991812 | − | 0.127707i | \(-0.0407616\pi\) | |||||||
\(984\) | −3.65519 | + | 6.33097i | −0.116523 | + | 0.201824i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −33.8806 | + | 19.5610i | −1.07898 | + | 0.622949i | ||||
\(987\) | 18.2283 | 0.580212 | ||||||||
\(988\) | 7.18881 | + | 11.9378i | 0.228706 | + | 0.379792i | ||||
\(989\) | −15.2565 | −0.485128 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0138 | − | 31.2007i | −0.572226 | − | 0.991124i | −0.996337 | − | 0.0855139i | \(-0.972747\pi\) |
0.424111 | − | 0.905610i | \(-0.360587\pi\) | |||||||
\(992\) | 1.11669 | − | 1.93416i | 0.0354550 | − | 0.0614098i | ||||
\(993\) | 19.1758i | 0.608526i | ||||||||
\(994\) | 44.4502 | + | 25.6633i | 1.40987 | + | 0.813992i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 7.15988i | − | 0.226869i | ||||||
\(997\) | 25.5906 | − | 44.3242i | 0.810463 | − | 1.40376i | −0.102078 | − | 0.994776i | \(-0.532549\pi\) |
0.912541 | − | 0.408986i | \(-0.134117\pi\) | |||||||
\(998\) | 19.6714 | + | 34.0719i | 0.622688 | + | 1.07853i | ||||
\(999\) | 1.84713 | − | 1.06644i | 0.0584406 | − | 0.0337407i |
(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 | 1950.2.bc.h.751.1 | ✓ | 12 | |
5.2 | odd | 4 | 1950.2.y.m.49.3 | 12 | |||
5.3 | odd | 4 | 1950.2.y.n.49.4 | 12 | |||
5.4 | even | 2 | 1950.2.bc.k.751.6 | yes | 12 | ||
13.4 | even | 6 | inner | 1950.2.bc.h.901.1 | yes | 12 | |
65.4 | even | 6 | 1950.2.bc.k.901.6 | yes | 12 | ||
65.17 | odd | 12 | 1950.2.y.n.199.4 | 12 | |||
65.43 | odd | 12 | 1950.2.y.m.199.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.m.49.3 | 12 | 5.2 | odd | 4 | |||
1950.2.y.m.199.3 | 12 | 65.43 | odd | 12 | |||
1950.2.y.n.49.4 | 12 | 5.3 | odd | 4 | |||
1950.2.y.n.199.4 | 12 | 65.17 | odd | 12 | |||
1950.2.bc.h.751.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1950.2.bc.h.901.1 | yes | 12 | 13.4 | even | 6 | inner | |
1950.2.bc.k.751.6 | yes | 12 | 5.4 | even | 2 | ||
1950.2.bc.k.901.6 | yes | 12 | 65.4 | even | 6 |