Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(364,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
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: | \( x^{12} + 21x^{10} + 164x^{8} + 589x^{6} + 965x^{4} + 576x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.4 | ||
Root | \(-1.53672i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.364 |
Dual form | 1815.2.c.i.364.9 |
$q$-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 \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).
\(n\) | \(727\) | \(1211\) | \(1696\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.53672i | − | 1.08663i | −0.839529 | − | 0.543314i | \(-0.817169\pi\) | ||
0.839529 | − | 0.543314i | \(-0.182831\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −0.361523 | −0.180762 | ||||||||
\(5\) | 1.20807 | + | 1.88164i | 0.540264 | + | 0.841495i | ||||
\(6\) | 1.53672 | 0.627365 | ||||||||
\(7\) | − | 2.86503i | − | 1.08288i | −0.840739 | − | 0.541440i | \(-0.817879\pi\) | ||
0.840739 | − | 0.541440i | \(-0.182121\pi\) | |||||||
\(8\) | − | 2.51789i | − | 0.890208i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.89156 | − | 1.85647i | 0.914393 | − | 0.587067i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 0.361523i | − | 0.104363i | ||||||
\(13\) | − | 2.43598i | − | 0.675620i | −0.941214 | − | 0.337810i | \(-0.890314\pi\) | ||
0.941214 | − | 0.337810i | \(-0.109686\pi\) | |||||||
\(14\) | −4.40277 | −1.17669 | ||||||||
\(15\) | −1.88164 | + | 1.20807i | −0.485838 | + | 0.311922i | ||||
\(16\) | −4.59235 | −1.14809 | ||||||||
\(17\) | − | 3.88488i | − | 0.942222i | −0.882074 | − | 0.471111i | \(-0.843853\pi\) | ||
0.882074 | − | 0.471111i | \(-0.156147\pi\) | |||||||
\(18\) | 1.53672i | 0.362210i | ||||||||
\(19\) | −5.93848 | −1.36238 | −0.681191 | − | 0.732106i | \(-0.738538\pi\) | ||||
−0.681191 | + | 0.732106i | \(0.738538\pi\) | |||||||
\(20\) | −0.436745 | − | 0.680257i | −0.0976591 | − | 0.152110i | ||||
\(21\) | 2.86503 | 0.625202 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.02732i | − | 1.25678i | −0.777897 | − | 0.628392i | \(-0.783714\pi\) | ||
0.777897 | − | 0.628392i | \(-0.216286\pi\) | |||||||
\(24\) | 2.51789 | 0.513962 | ||||||||
\(25\) | −2.08114 | + | 4.54630i | −0.416229 | + | 0.909260i | ||||
\(26\) | −3.74343 | −0.734148 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.03578i | 0.195743i | ||||||||
\(29\) | −4.03698 | −0.749648 | −0.374824 | − | 0.927096i | \(-0.622297\pi\) | ||||
−0.374824 | + | 0.927096i | \(0.622297\pi\) | |||||||
\(30\) | 1.85647 | + | 2.89156i | 0.338943 | + | 0.527925i | ||||
\(31\) | −0.783128 | −0.140654 | −0.0703270 | − | 0.997524i | \(-0.522404\pi\) | ||||
−0.0703270 | + | 0.997524i | \(0.522404\pi\) | |||||||
\(32\) | 2.02140i | 0.357336i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.96999 | −1.02385 | ||||||||
\(35\) | 5.39096 | − | 3.46116i | 0.911239 | − | 0.585042i | ||||
\(36\) | 0.361523 | 0.0602539 | ||||||||
\(37\) | − | 8.02406i | − | 1.31915i | −0.751640 | − | 0.659574i | \(-0.770737\pi\) | ||
0.751640 | − | 0.659574i | \(-0.229263\pi\) | |||||||
\(38\) | 9.12581i | 1.48040i | ||||||||
\(39\) | 2.43598 | 0.390069 | ||||||||
\(40\) | 4.73776 | − | 3.04178i | 0.749106 | − | 0.480948i | ||||
\(41\) | −7.54195 | −1.17785 | −0.588927 | − | 0.808186i | \(-0.700450\pi\) | ||||
−0.588927 | + | 0.808186i | \(0.700450\pi\) | |||||||
\(42\) | − | 4.40277i | − | 0.679362i | ||||||
\(43\) | 9.90572i | 1.51061i | 0.655374 | + | 0.755304i | \(0.272511\pi\) | ||||
−0.655374 | + | 0.755304i | \(0.727489\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.20807 | − | 1.88164i | −0.180088 | − | 0.280498i | ||||
\(46\) | −9.26233 | −1.36566 | ||||||||
\(47\) | − | 0.551103i | − | 0.0803866i | −0.999192 | − | 0.0401933i | \(-0.987203\pi\) | ||
0.999192 | − | 0.0401933i | \(-0.0127974\pi\) | |||||||
\(48\) | − | 4.59235i | − | 0.662848i | ||||||
\(49\) | −1.20842 | −0.172631 | ||||||||
\(50\) | 6.98641 | + | 3.19814i | 0.988028 | + | 0.452286i | ||||
\(51\) | 3.88488 | 0.543992 | ||||||||
\(52\) | 0.880664i | 0.122126i | ||||||||
\(53\) | 2.75907i | 0.378987i | 0.981882 | + | 0.189493i | \(0.0606846\pi\) | ||||
−0.981882 | + | 0.189493i | \(0.939315\pi\) | |||||||
\(54\) | −1.53672 | −0.209122 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.21383 | −0.963989 | ||||||||
\(57\) | − | 5.93848i | − | 0.786571i | ||||||
\(58\) | 6.20372i | 0.814589i | ||||||||
\(59\) | 14.5497 | 1.89421 | 0.947103 | − | 0.320931i | \(-0.103996\pi\) | ||||
0.947103 | + | 0.320931i | \(0.103996\pi\) | |||||||
\(60\) | 0.680257 | − | 0.436745i | 0.0878208 | − | 0.0563835i | ||||
\(61\) | 13.7901 | 1.76565 | 0.882824 | − | 0.469704i | \(-0.155639\pi\) | ||||
0.882824 | + | 0.469704i | \(0.155639\pi\) | |||||||
\(62\) | 1.20345i | 0.152839i | ||||||||
\(63\) | 2.86503i | 0.360960i | ||||||||
\(64\) | −6.07836 | −0.759795 | ||||||||
\(65\) | 4.58364 | − | 2.94283i | 0.568531 | − | 0.365013i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.96724i | − | 0.484675i | −0.970192 | − | 0.242338i | \(-0.922086\pi\) | ||
0.970192 | − | 0.242338i | \(-0.0779142\pi\) | |||||||
\(68\) | 1.40447i | 0.170318i | ||||||||
\(69\) | 6.02732 | 0.725604 | ||||||||
\(70\) | −5.31884 | − | 8.28443i | −0.635723 | − | 0.990178i | ||||
\(71\) | 9.27271 | 1.10047 | 0.550234 | − | 0.835010i | \(-0.314538\pi\) | ||||
0.550234 | + | 0.835010i | \(0.314538\pi\) | |||||||
\(72\) | 2.51789i | 0.296736i | ||||||||
\(73\) | 0.615424i | 0.0720300i | 0.999351 | + | 0.0360150i | \(0.0114664\pi\) | ||||
−0.999351 | + | 0.0360150i | \(0.988534\pi\) | |||||||
\(74\) | −12.3308 | −1.43342 | ||||||||
\(75\) | −4.54630 | − | 2.08114i | −0.524961 | − | 0.240310i | ||||
\(76\) | 2.14690 | 0.246266 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 3.74343i | − | 0.423861i | ||||||
\(79\) | −4.53993 | −0.510782 | −0.255391 | − | 0.966838i | \(-0.582204\pi\) | ||||
−0.255391 | + | 0.966838i | \(0.582204\pi\) | |||||||
\(80\) | −5.54787 | − | 8.64115i | −0.620270 | − | 0.966110i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.5899i | 1.27989i | ||||||||
\(83\) | − | 11.6797i | − | 1.28202i | −0.767534 | − | 0.641008i | \(-0.778517\pi\) | ||
0.767534 | − | 0.641008i | \(-0.221483\pi\) | |||||||
\(84\) | −1.03578 | −0.113012 | ||||||||
\(85\) | 7.30995 | − | 4.69320i | 0.792875 | − | 0.509049i | ||||
\(86\) | 15.2224 | 1.64147 | ||||||||
\(87\) | − | 4.03698i | − | 0.432809i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.9894 | −1.80087 | −0.900437 | − | 0.434986i | \(-0.856753\pi\) | ||||
−0.900437 | + | 0.434986i | \(0.856753\pi\) | |||||||
\(90\) | −2.89156 | + | 1.85647i | −0.304798 | + | 0.195689i | ||||
\(91\) | −6.97917 | −0.731616 | ||||||||
\(92\) | 2.17902i | 0.227178i | ||||||||
\(93\) | − | 0.783128i | − | 0.0812066i | ||||||
\(94\) | −0.846893 | −0.0873504 | ||||||||
\(95\) | −7.17409 | − | 11.1741i | −0.736046 | − | 1.14644i | ||||
\(96\) | −2.02140 | −0.206308 | ||||||||
\(97\) | − | 8.95511i | − | 0.909254i | −0.890682 | − | 0.454627i | \(-0.849773\pi\) | ||
0.890682 | − | 0.454627i | \(-0.150227\pi\) | |||||||
\(98\) | 1.85700i | 0.187586i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.752382 | − | 1.64359i | 0.0752382 | − | 0.164359i | ||||
\(101\) | −4.05035 | −0.403024 | −0.201512 | − | 0.979486i | \(-0.564586\pi\) | ||||
−0.201512 | + | 0.979486i | \(0.564586\pi\) | |||||||
\(102\) | − | 5.96999i | − | 0.591117i | ||||||
\(103\) | 3.09729i | 0.305185i | 0.988289 | + | 0.152593i | \(0.0487623\pi\) | ||||
−0.988289 | + | 0.152593i | \(0.951238\pi\) | |||||||
\(104\) | −6.13353 | −0.601442 | ||||||||
\(105\) | 3.46116 | + | 5.39096i | 0.337774 | + | 0.526104i | ||||
\(106\) | 4.23992 | 0.411818 | ||||||||
\(107\) | − | 5.42307i | − | 0.524268i | −0.965032 | − | 0.262134i | \(-0.915574\pi\) | ||
0.965032 | − | 0.262134i | \(-0.0844262\pi\) | |||||||
\(108\) | 0.361523i | 0.0347876i | ||||||||
\(109\) | 2.29776 | 0.220085 | 0.110043 | − | 0.993927i | \(-0.464901\pi\) | ||||
0.110043 | + | 0.993927i | \(0.464901\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.02406 | 0.761610 | ||||||||
\(112\) | 13.1572i | 1.24324i | ||||||||
\(113\) | − | 9.61495i | − | 0.904498i | −0.891892 | − | 0.452249i | \(-0.850622\pi\) | ||
0.891892 | − | 0.452249i | \(-0.149378\pi\) | |||||||
\(114\) | −9.12581 | −0.854711 | ||||||||
\(115\) | 11.3413 | − | 7.28141i | 1.05758 | − | 0.678995i | ||||
\(116\) | 1.45946 | 0.135508 | ||||||||
\(117\) | 2.43598i | 0.225207i | ||||||||
\(118\) | − | 22.3588i | − | 2.05830i | ||||||
\(119\) | −11.1303 | −1.02031 | ||||||||
\(120\) | 3.04178 | + | 4.73776i | 0.277675 | + | 0.432496i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 21.1917i | − | 1.91860i | ||||||
\(123\) | − | 7.54195i | − | 0.680035i | ||||||
\(124\) | 0.283119 | 0.0254248 | ||||||||
\(125\) | −11.0687 | + | 1.57628i | −0.990012 | + | 0.140986i | ||||
\(126\) | 4.40277 | 0.392230 | ||||||||
\(127\) | 19.6140i | 1.74046i | 0.492648 | + | 0.870229i | \(0.336029\pi\) | ||||
−0.492648 | + | 0.870229i | \(0.663971\pi\) | |||||||
\(128\) | 13.3836i | 1.18295i | ||||||||
\(129\) | −9.90572 | −0.872150 | ||||||||
\(130\) | −4.52232 | − | 7.04380i | −0.396634 | − | 0.617782i | ||||
\(131\) | 4.00843 | 0.350218 | 0.175109 | − | 0.984549i | \(-0.443972\pi\) | ||||
0.175109 | + | 0.984549i | \(0.443972\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.0140i | 1.47530i | ||||||||
\(134\) | −6.09655 | −0.526662 | ||||||||
\(135\) | 1.88164 | − | 1.20807i | 0.161946 | − | 0.103974i | ||||
\(136\) | −9.78169 | −0.838773 | ||||||||
\(137\) | − | 23.1747i | − | 1.97995i | −0.141242 | − | 0.989975i | \(-0.545109\pi\) | ||
0.141242 | − | 0.989975i | \(-0.454891\pi\) | |||||||
\(138\) | − | 9.26233i | − | 0.788462i | ||||||
\(139\) | 13.8238 | 1.17252 | 0.586260 | − | 0.810123i | \(-0.300600\pi\) | ||||
0.586260 | + | 0.810123i | \(0.300600\pi\) | |||||||
\(140\) | −1.94896 | + | 1.25129i | −0.164717 | + | 0.105753i | ||||
\(141\) | 0.551103 | 0.0464112 | ||||||||
\(142\) | − | 14.2496i | − | 1.19580i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.59235 | 0.382696 | ||||||||
\(145\) | −4.87694 | − | 7.59614i | −0.405008 | − | 0.630825i | ||||
\(146\) | 0.945738 | 0.0782698 | ||||||||
\(147\) | − | 1.20842i | − | 0.0996685i | ||||||
\(148\) | 2.90088i | 0.238451i | ||||||||
\(149\) | −13.5293 | −1.10836 | −0.554181 | − | 0.832396i | \(-0.686968\pi\) | ||||
−0.554181 | + | 0.832396i | \(0.686968\pi\) | |||||||
\(150\) | −3.19814 | + | 6.98641i | −0.261127 | + | 0.570438i | ||||
\(151\) | 21.7316 | 1.76849 | 0.884245 | − | 0.467024i | \(-0.154674\pi\) | ||||
0.884245 | + | 0.467024i | \(0.154674\pi\) | |||||||
\(152\) | 14.9524i | 1.21280i | ||||||||
\(153\) | 3.88488i | 0.314074i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.946072 | − | 1.47357i | −0.0759903 | − | 0.118360i | ||||
\(156\) | −0.880664 | −0.0705096 | ||||||||
\(157\) | 10.0477i | 0.801894i | 0.916101 | + | 0.400947i | \(0.131319\pi\) | ||||
−0.916101 | + | 0.400947i | \(0.868681\pi\) | |||||||
\(158\) | 6.97662i | 0.555030i | ||||||||
\(159\) | −2.75907 | −0.218808 | ||||||||
\(160\) | −3.80355 | + | 2.44199i | −0.300697 | + | 0.193056i | ||||
\(161\) | −17.2685 | −1.36095 | ||||||||
\(162\) | − | 1.53672i | − | 0.120737i | ||||||
\(163\) | 17.0119i | 1.33248i | 0.745739 | + | 0.666239i | \(0.232097\pi\) | ||||
−0.745739 | + | 0.666239i | \(0.767903\pi\) | |||||||
\(164\) | 2.72659 | 0.212911 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.9485 | −1.39308 | ||||||||
\(167\) | − | 8.17422i | − | 0.632540i | −0.948669 | − | 0.316270i | \(-0.897569\pi\) | ||
0.948669 | − | 0.316270i | \(-0.102431\pi\) | |||||||
\(168\) | − | 7.21383i | − | 0.556559i | ||||||
\(169\) | 7.06599 | 0.543538 | ||||||||
\(170\) | −7.21216 | − | 11.2334i | −0.553147 | − | 0.861561i | ||||
\(171\) | 5.93848 | 0.454127 | ||||||||
\(172\) | − | 3.58115i | − | 0.273060i | ||||||
\(173\) | − | 0.0419137i | − | 0.00318664i | −0.999999 | − | 0.00159332i | \(-0.999493\pi\) | ||
0.999999 | − | 0.00159332i | \(-0.000507170\pi\) | |||||||
\(174\) | −6.20372 | −0.470303 | ||||||||
\(175\) | 13.0253 | + | 5.96255i | 0.984620 | + | 0.450726i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.5497i | 1.09362i | ||||||||
\(178\) | 26.1081i | 1.95688i | ||||||||
\(179\) | 21.5288 | 1.60914 | 0.804570 | − | 0.593857i | \(-0.202396\pi\) | ||||
0.804570 | + | 0.593857i | \(0.202396\pi\) | |||||||
\(180\) | 0.436745 | + | 0.680257i | 0.0325530 | + | 0.0507033i | ||||
\(181\) | 10.9246 | 0.812020 | 0.406010 | − | 0.913869i | \(-0.366920\pi\) | ||||
0.406010 | + | 0.913869i | \(0.366920\pi\) | |||||||
\(182\) | 10.7251i | 0.794995i | ||||||||
\(183\) | 13.7901i | 1.01940i | ||||||||
\(184\) | −15.1761 | −1.11880 | ||||||||
\(185\) | 15.0984 | − | 9.69361i | 1.11006 | − | 0.712689i | ||||
\(186\) | −1.20345 | −0.0882414 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.199236i | 0.0145308i | ||||||||
\(189\) | −2.86503 | −0.208401 | ||||||||
\(190\) | −17.1715 | + | 11.0246i | −1.24575 | + | 0.799809i | ||||
\(191\) | −0.485281 | −0.0351137 | −0.0175569 | − | 0.999846i | \(-0.505589\pi\) | ||||
−0.0175569 | + | 0.999846i | \(0.505589\pi\) | |||||||
\(192\) | − | 6.07836i | − | 0.438668i | ||||||
\(193\) | 12.5864i | 0.905989i | 0.891513 | + | 0.452994i | \(0.149644\pi\) | ||||
−0.891513 | + | 0.452994i | \(0.850356\pi\) | |||||||
\(194\) | −13.7615 | −0.988021 | ||||||||
\(195\) | 2.94283 | + | 4.58364i | 0.210741 | + | 0.328242i | ||||
\(196\) | 0.436870 | 0.0312050 | ||||||||
\(197\) | 15.8941i | 1.13241i | 0.824265 | + | 0.566204i | \(0.191588\pi\) | ||||
−0.824265 | + | 0.566204i | \(0.808412\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.02089 | 0.355922 | 0.177961 | − | 0.984038i | \(-0.443050\pi\) | ||||
0.177961 | + | 0.984038i | \(0.443050\pi\) | |||||||
\(200\) | 11.4471 | + | 5.24009i | 0.809430 | + | 0.370530i | ||||
\(201\) | 3.96724 | 0.279827 | ||||||||
\(202\) | 6.22427i | 0.437938i | ||||||||
\(203\) | 11.5661i | 0.811779i | ||||||||
\(204\) | −1.40447 | −0.0983329 | ||||||||
\(205\) | −9.11119 | − | 14.1912i | −0.636353 | − | 0.991159i | ||||
\(206\) | 4.75969 | 0.331623 | ||||||||
\(207\) | 6.02732i | 0.418928i | ||||||||
\(208\) | 11.1869i | 0.775670i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 8.28443 | − | 5.31884i | 0.571680 | − | 0.367035i | ||||
\(211\) | 0.800040 | 0.0550770 | 0.0275385 | − | 0.999621i | \(-0.491233\pi\) | ||||
0.0275385 | + | 0.999621i | \(0.491233\pi\) | |||||||
\(212\) | − | 0.997466i | − | 0.0685063i | ||||||
\(213\) | 9.27271i | 0.635356i | ||||||||
\(214\) | −8.33376 | −0.569684 | ||||||||
\(215\) | −18.6390 | + | 11.9668i | −1.27117 | + | 0.816128i | ||||
\(216\) | −2.51789 | −0.171321 | ||||||||
\(217\) | 2.24369i | 0.152311i | ||||||||
\(218\) | − | 3.53102i | − | 0.239151i | ||||||
\(219\) | −0.615424 | −0.0415865 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.46350 | −0.636584 | ||||||||
\(222\) | − | 12.3308i | − | 0.827587i | ||||||
\(223\) | − | 8.10773i | − | 0.542933i | −0.962448 | − | 0.271467i | \(-0.912491\pi\) | ||
0.962448 | − | 0.271467i | \(-0.0875087\pi\) | |||||||
\(224\) | 5.79137 | 0.386952 | ||||||||
\(225\) | 2.08114 | − | 4.54630i | 0.138743 | − | 0.303087i | ||||
\(226\) | −14.7755 | −0.982853 | ||||||||
\(227\) | − | 8.70426i | − | 0.577722i | −0.957371 | − | 0.288861i | \(-0.906723\pi\) | ||
0.957371 | − | 0.288861i | \(-0.0932766\pi\) | |||||||
\(228\) | 2.14690i | 0.142182i | ||||||||
\(229\) | −29.6210 | −1.95741 | −0.978705 | − | 0.205272i | \(-0.934192\pi\) | ||||
−0.978705 | + | 0.205272i | \(0.934192\pi\) | |||||||
\(230\) | −11.1895 | − | 17.4284i | −0.737816 | − | 1.14919i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.1647i | 0.667342i | ||||||||
\(233\) | − | 6.71715i | − | 0.440055i | −0.975494 | − | 0.220028i | \(-0.929385\pi\) | ||
0.975494 | − | 0.220028i | \(-0.0706148\pi\) | |||||||
\(234\) | 3.74343 | 0.244716 | ||||||||
\(235\) | 1.03698 | − | 0.665769i | 0.0676449 | − | 0.0434300i | ||||
\(236\) | −5.26004 | −0.342400 | ||||||||
\(237\) | − | 4.53993i | − | 0.294900i | ||||||
\(238\) | 17.1042i | 1.10870i | ||||||||
\(239\) | −2.23252 | −0.144409 | −0.0722047 | − | 0.997390i | \(-0.523003\pi\) | ||||
−0.0722047 | + | 0.997390i | \(0.523003\pi\) | |||||||
\(240\) | 8.64115 | − | 5.54787i | 0.557784 | − | 0.358113i | ||||
\(241\) | −8.20298 | −0.528400 | −0.264200 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264200 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −4.98546 | −0.319161 | ||||||||
\(245\) | −1.45985 | − | 2.27381i | −0.0932663 | − | 0.145268i | ||||
\(246\) | −11.5899 | −0.738945 | ||||||||
\(247\) | 14.4660i | 0.920452i | ||||||||
\(248\) | 1.97183i | 0.125211i | ||||||||
\(249\) | 11.6797 | 0.740172 | ||||||||
\(250\) | 2.42230 | + | 17.0095i | 0.153200 | + | 1.07577i | ||||
\(251\) | −0.900721 | −0.0568530 | −0.0284265 | − | 0.999596i | \(-0.509050\pi\) | ||||
−0.0284265 | + | 0.999596i | \(0.509050\pi\) | |||||||
\(252\) | − | 1.03578i | − | 0.0652478i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 30.1413 | 1.89123 | ||||||||
\(255\) | 4.69320 | + | 7.30995i | 0.293900 | + | 0.457767i | ||||
\(256\) | 8.41013 | 0.525633 | ||||||||
\(257\) | − | 4.27720i | − | 0.266804i | −0.991062 | − | 0.133402i | \(-0.957410\pi\) | ||
0.991062 | − | 0.133402i | \(-0.0425902\pi\) | |||||||
\(258\) | 15.2224i | 0.947703i | ||||||||
\(259\) | −22.9892 | −1.42848 | ||||||||
\(260\) | −1.65709 | + | 1.06390i | −0.102769 | + | 0.0659804i | ||||
\(261\) | 4.03698 | 0.249883 | ||||||||
\(262\) | − | 6.15986i | − | 0.380557i | ||||||
\(263\) | − | 3.64614i | − | 0.224831i | −0.993661 | − | 0.112415i | \(-0.964141\pi\) | ||
0.993661 | − | 0.112415i | \(-0.0358587\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.19157 | + | 3.33314i | −0.318916 | + | 0.204753i | ||||
\(266\) | 26.1458 | 1.60310 | ||||||||
\(267\) | − | 16.9894i | − | 1.03974i | ||||||
\(268\) | 1.43425i | 0.0876107i | ||||||||
\(269\) | 11.2872 | 0.688192 | 0.344096 | − | 0.938934i | \(-0.388185\pi\) | ||||
0.344096 | + | 0.938934i | \(0.388185\pi\) | |||||||
\(270\) | −1.85647 | − | 2.89156i | −0.112981 | − | 0.175975i | ||||
\(271\) | 9.58466 | 0.582227 | 0.291113 | − | 0.956689i | \(-0.405974\pi\) | ||||
0.291113 | + | 0.956689i | \(0.405974\pi\) | |||||||
\(272\) | 17.8407i | 1.08175i | ||||||||
\(273\) | − | 6.97917i | − | 0.422399i | ||||||
\(274\) | −35.6132 | −2.15147 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.17902 | −0.131161 | ||||||||
\(277\) | 26.9810i | 1.62113i | 0.585648 | + | 0.810565i | \(0.300840\pi\) | ||||
−0.585648 | + | 0.810565i | \(0.699160\pi\) | |||||||
\(278\) | − | 21.2434i | − | 1.27409i | ||||||
\(279\) | 0.783128 | 0.0468846 | ||||||||
\(280\) | −8.71480 | − | 13.5738i | −0.520809 | − | 0.811192i | ||||
\(281\) | 18.9918 | 1.13296 | 0.566479 | − | 0.824076i | \(-0.308305\pi\) | ||||
0.566479 | + | 0.824076i | \(0.308305\pi\) | |||||||
\(282\) | − | 0.846893i | − | 0.0504317i | ||||||
\(283\) | − | 27.0944i | − | 1.61060i | −0.592870 | − | 0.805298i | \(-0.702005\pi\) | ||
0.592870 | − | 0.805298i | \(-0.297995\pi\) | |||||||
\(284\) | −3.35230 | −0.198922 | ||||||||
\(285\) | 11.1741 | − | 7.17409i | 0.661896 | − | 0.424956i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.6079i | 1.27548i | ||||||||
\(288\) | − | 2.02140i | − | 0.119112i | ||||||
\(289\) | 1.90771 | 0.112218 | ||||||||
\(290\) | −11.6732 | + | 7.49452i | −0.685473 | + | 0.440093i | ||||
\(291\) | 8.95511 | 0.524958 | ||||||||
\(292\) | − | 0.222490i | − | 0.0130202i | ||||||
\(293\) | − | 9.07599i | − | 0.530225i | −0.964218 | − | 0.265112i | \(-0.914591\pi\) | ||
0.964218 | − | 0.265112i | \(-0.0854091\pi\) | |||||||
\(294\) | −1.85700 | −0.108303 | ||||||||
\(295\) | 17.5770 | + | 27.3772i | 1.02337 | + | 1.59396i | ||||
\(296\) | −20.2037 | −1.17432 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.7908i | 1.20438i | ||||||||
\(299\) | −14.6824 | −0.849108 | ||||||||
\(300\) | 1.64359 | + | 0.752382i | 0.0948929 | + | 0.0434388i | ||||
\(301\) | 28.3802 | 1.63581 | ||||||||
\(302\) | − | 33.3954i | − | 1.92169i | ||||||
\(303\) | − | 4.05035i | − | 0.232686i | ||||||
\(304\) | 27.2716 | 1.56413 | ||||||||
\(305\) | 16.6594 | + | 25.9481i | 0.953917 | + | 1.48578i | ||||
\(306\) | 5.96999 | 0.341282 | ||||||||
\(307\) | 6.10964i | 0.348696i | 0.984684 | + | 0.174348i | \(0.0557817\pi\) | ||||
−0.984684 | + | 0.174348i | \(0.944218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.09729 | −0.176199 | ||||||||
\(310\) | −2.26446 | + | 1.45385i | −0.128613 | + | 0.0825732i | ||||
\(311\) | −14.8604 | −0.842655 | −0.421327 | − | 0.906909i | \(-0.638436\pi\) | ||||
−0.421327 | + | 0.906909i | \(0.638436\pi\) | |||||||
\(312\) | − | 6.13353i | − | 0.347243i | ||||||
\(313\) | 27.4142i | 1.54954i | 0.632240 | + | 0.774772i | \(0.282136\pi\) | ||||
−0.632240 | + | 0.774772i | \(0.717864\pi\) | |||||||
\(314\) | 15.4406 | 0.871361 | ||||||||
\(315\) | −5.39096 | + | 3.46116i | −0.303746 | + | 0.195014i | ||||
\(316\) | 1.64129 | 0.0923298 | ||||||||
\(317\) | − | 13.9328i | − | 0.782543i | −0.920275 | − | 0.391272i | \(-0.872035\pi\) | ||
0.920275 | − | 0.391272i | \(-0.127965\pi\) | |||||||
\(318\) | 4.23992i | 0.237763i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −7.34307 | − | 11.4373i | −0.410490 | − | 0.639364i | ||||
\(321\) | 5.42307 | 0.302686 | ||||||||
\(322\) | 26.5369i | 1.47884i | ||||||||
\(323\) | 23.0703i | 1.28367i | ||||||||
\(324\) | −0.361523 | −0.0200846 | ||||||||
\(325\) | 11.0747 | + | 5.06963i | 0.614314 | + | 0.281212i | ||||
\(326\) | 26.1427 | 1.44791 | ||||||||
\(327\) | 2.29776i | 0.127066i | ||||||||
\(328\) | 18.9898i | 1.04854i | ||||||||
\(329\) | −1.57893 | −0.0870491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9385 | 1.37074 | 0.685371 | − | 0.728194i | \(-0.259640\pi\) | ||||
0.685371 | + | 0.728194i | \(0.259640\pi\) | |||||||
\(332\) | 4.22249i | 0.231739i | ||||||||
\(333\) | 8.02406i | 0.439716i | ||||||||
\(334\) | −12.5615 | −0.687336 | ||||||||
\(335\) | 7.46492 | − | 4.79269i | 0.407852 | − | 0.261853i | ||||
\(336\) | −13.1572 | −0.717786 | ||||||||
\(337\) | − | 16.2380i | − | 0.884541i | −0.896882 | − | 0.442271i | \(-0.854173\pi\) | ||
0.896882 | − | 0.442271i | \(-0.145827\pi\) | |||||||
\(338\) | − | 10.8585i | − | 0.590623i | ||||||
\(339\) | 9.61495 | 0.522212 | ||||||||
\(340\) | −2.64272 | + | 1.69670i | −0.143321 | + | 0.0920165i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 9.12581i | − | 0.493468i | ||||||
\(343\) | − | 16.5931i | − | 0.895942i | ||||||
\(344\) | 24.9415 | 1.34476 | ||||||||
\(345\) | 7.28141 | + | 11.3413i | 0.392018 | + | 0.610592i | ||||
\(346\) | −0.0644098 | −0.00346269 | ||||||||
\(347\) | − | 27.4616i | − | 1.47422i | −0.675774 | − | 0.737109i | \(-0.736191\pi\) | ||
0.675774 | − | 0.737109i | \(-0.263809\pi\) | |||||||
\(348\) | 1.45946i | 0.0782353i | ||||||||
\(349\) | 25.1370 | 1.34555 | 0.672777 | − | 0.739845i | \(-0.265101\pi\) | ||||
0.672777 | + | 0.739845i | \(0.265101\pi\) | |||||||
\(350\) | 9.16279 | − | 20.0163i | 0.489772 | − | 1.06992i | ||||
\(351\) | −2.43598 | −0.130023 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.2362i | 0.651267i | 0.945496 | + | 0.325633i | \(0.105577\pi\) | ||||
−0.945496 | + | 0.325633i | \(0.894423\pi\) | |||||||
\(354\) | 22.3588 | 1.18836 | ||||||||
\(355\) | 11.2021 | + | 17.4479i | 0.594544 | + | 0.926039i | ||||
\(356\) | 6.14207 | 0.325529 | ||||||||
\(357\) | − | 11.1303i | − | 0.589079i | ||||||
\(358\) | − | 33.0839i | − | 1.74854i | ||||||
\(359\) | −3.88413 | −0.204997 | −0.102498 | − | 0.994733i | \(-0.532684\pi\) | ||||
−0.102498 | + | 0.994733i | \(0.532684\pi\) | |||||||
\(360\) | −4.73776 | + | 3.04178i | −0.249702 | + | 0.160316i | ||||
\(361\) | 16.2656 | 0.856083 | ||||||||
\(362\) | − | 16.7881i | − | 0.882364i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.52313 | 0.132248 | ||||||||
\(365\) | −1.15801 | + | 0.743474i | −0.0606129 | + | 0.0389152i | ||||
\(366\) | 21.1917 | 1.10771 | ||||||||
\(367\) | 19.5703i | 1.02156i | 0.859712 | + | 0.510780i | \(0.170643\pi\) | ||||
−0.859712 | + | 0.510780i | \(0.829357\pi\) | |||||||
\(368\) | 27.6795i | 1.44290i | ||||||||
\(369\) | 7.54195 | 0.392618 | ||||||||
\(370\) | −14.8964 | − | 23.2021i | −0.774428 | − | 1.20622i | ||||
\(371\) | 7.90482 | 0.410398 | ||||||||
\(372\) | 0.283119i | 0.0146790i | ||||||||
\(373\) | − | 0.729978i | − | 0.0377968i | −0.999821 | − | 0.0188984i | \(-0.993984\pi\) | ||
0.999821 | − | 0.0188984i | \(-0.00601591\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.57628 | − | 11.0687i | −0.0813985 | − | 0.571583i | ||||
\(376\) | −1.38761 | −0.0715608 | ||||||||
\(377\) | 9.83401i | 0.506477i | ||||||||
\(378\) | 4.40277i | 0.226454i | ||||||||
\(379\) | −36.0155 | −1.84999 | −0.924997 | − | 0.379975i | \(-0.875933\pi\) | ||||
−0.924997 | + | 0.379975i | \(0.875933\pi\) | |||||||
\(380\) | 2.59360 | + | 4.03969i | 0.133049 | + | 0.207232i | ||||
\(381\) | −19.6140 | −1.00485 | ||||||||
\(382\) | 0.745744i | 0.0381556i | ||||||||
\(383\) | 12.4551i | 0.636428i | 0.948019 | + | 0.318214i | \(0.103083\pi\) | ||||
−0.948019 | + | 0.318214i | \(0.896917\pi\) | |||||||
\(384\) | −13.3836 | −0.682977 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.3418 | 0.984473 | ||||||||
\(387\) | − | 9.90572i | − | 0.503536i | ||||||
\(388\) | 3.23748i | 0.164358i | ||||||||
\(389\) | 20.4612 | 1.03742 | 0.518711 | − | 0.854950i | \(-0.326412\pi\) | ||||
0.518711 | + | 0.854950i | \(0.326412\pi\) | |||||||
\(390\) | 7.04380 | − | 4.52232i | 0.356677 | − | 0.228997i | ||||
\(391\) | −23.4154 | −1.18417 | ||||||||
\(392\) | 3.04266i | 0.153677i | ||||||||
\(393\) | 4.00843i | 0.202199i | ||||||||
\(394\) | 24.4249 | 1.23051 | ||||||||
\(395\) | −5.48455 | − | 8.54252i | −0.275957 | − | 0.429821i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 23.9046i | − | 1.19974i | −0.800098 | − | 0.599869i | \(-0.795219\pi\) | ||
0.800098 | − | 0.599869i | \(-0.204781\pi\) | |||||||
\(398\) | − | 7.71573i | − | 0.386755i | ||||||
\(399\) | −17.0140 | −0.851763 | ||||||||
\(400\) | 9.55733 | − | 20.8782i | 0.477867 | − | 1.04391i | ||||
\(401\) | −9.45101 | −0.471961 | −0.235980 | − | 0.971758i | \(-0.575830\pi\) | ||||
−0.235980 | + | 0.971758i | \(0.575830\pi\) | |||||||
\(402\) | − | 6.09655i | − | 0.304068i | ||||||
\(403\) | 1.90769i | 0.0950286i | ||||||||
\(404\) | 1.46429 | 0.0728513 | ||||||||
\(405\) | 1.20807 | + | 1.88164i | 0.0600294 | + | 0.0934995i | ||||
\(406\) | 17.7739 | 0.882103 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 9.78169i | − | 0.484266i | ||||||
\(409\) | −7.69520 | −0.380503 | −0.190252 | − | 0.981735i | \(-0.560930\pi\) | ||||
−0.190252 | + | 0.981735i | \(0.560930\pi\) | |||||||
\(410\) | −21.8080 | + | 14.0014i | −1.07702 | + | 0.691479i | ||||
\(411\) | 23.1747 | 1.14312 | ||||||||
\(412\) | − | 1.11974i | − | 0.0551658i | ||||||
\(413\) | − | 41.6853i | − | 2.05120i | ||||||
\(414\) | 9.26233 | 0.455219 | ||||||||
\(415\) | 21.9770 | − | 14.1099i | 1.07881 | − | 0.692628i | ||||
\(416\) | 4.92409 | 0.241423 | ||||||||
\(417\) | 13.8238i | 0.676955i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0599 | 1.46852 | 0.734262 | − | 0.678866i | \(-0.237528\pi\) | ||||
0.734262 | + | 0.678866i | \(0.237528\pi\) | |||||||
\(420\) | −1.25129 | − | 1.94896i | −0.0610566 | − | 0.0950994i | ||||
\(421\) | −23.8194 | −1.16088 | −0.580442 | − | 0.814301i | \(-0.697120\pi\) | ||||
−0.580442 | + | 0.814301i | \(0.697120\pi\) | |||||||
\(422\) | − | 1.22944i | − | 0.0598482i | ||||||
\(423\) | 0.551103i | 0.0267955i | ||||||||
\(424\) | 6.94702 | 0.337377 | ||||||||
\(425\) | 17.6618 | + | 8.08499i | 0.856725 | + | 0.392180i | ||||
\(426\) | 14.2496 | 0.690396 | ||||||||
\(427\) | − | 39.5092i | − | 1.91199i | ||||||
\(428\) | 1.96056i | 0.0947675i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.3897 | + | 28.6430i | 0.886828 | + | 1.38129i | ||||
\(431\) | 0.608493 | 0.0293101 | 0.0146550 | − | 0.999893i | \(-0.495335\pi\) | ||||
0.0146550 | + | 0.999893i | \(0.495335\pi\) | |||||||
\(432\) | 4.59235i | 0.220949i | ||||||||
\(433\) | − | 17.1030i | − | 0.821919i | −0.911654 | − | 0.410959i | \(-0.865194\pi\) | ||
0.911654 | − | 0.410959i | \(-0.134806\pi\) | |||||||
\(434\) | 3.44793 | 0.165506 | ||||||||
\(435\) | 7.59614 | − | 4.87694i | 0.364207 | − | 0.233832i | ||||
\(436\) | −0.830693 | −0.0397830 | ||||||||
\(437\) | 35.7931i | 1.71222i | ||||||||
\(438\) | 0.945738i | 0.0451891i | ||||||||
\(439\) | 11.5579 | 0.551628 | 0.275814 | − | 0.961211i | \(-0.411053\pi\) | ||||
0.275814 | + | 0.961211i | \(0.411053\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.20842 | 0.0575436 | ||||||||
\(442\) | 14.5428i | 0.691730i | ||||||||
\(443\) | 17.7741i | 0.844471i | 0.906486 | + | 0.422235i | \(0.138754\pi\) | ||||
−0.906486 | + | 0.422235i | \(0.861246\pi\) | |||||||
\(444\) | −2.90088 | −0.137670 | ||||||||
\(445\) | −20.5244 | − | 31.9680i | −0.972948 | − | 1.51543i | ||||
\(446\) | −12.4593 | −0.589967 | ||||||||
\(447\) | − | 13.5293i | − | 0.639913i | ||||||
\(448\) | 17.4147i | 0.822768i | ||||||||
\(449\) | −21.7125 | −1.02467 | −0.512337 | − | 0.858784i | \(-0.671220\pi\) | ||||
−0.512337 | + | 0.858784i | \(0.671220\pi\) | |||||||
\(450\) | −6.98641 | − | 3.19814i | −0.329343 | − | 0.150762i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.47603i | 0.163499i | ||||||||
\(453\) | 21.7316i | 1.02104i | ||||||||
\(454\) | −13.3761 | −0.627769 | ||||||||
\(455\) | −8.43131 | − | 13.1323i | −0.395266 | − | 0.615651i | ||||
\(456\) | −14.9524 | −0.700212 | ||||||||
\(457\) | − | 0.874148i | − | 0.0408909i | −0.999791 | − | 0.0204455i | \(-0.993492\pi\) | ||
0.999791 | − | 0.0204455i | \(-0.00650845\pi\) | |||||||
\(458\) | 45.5193i | 2.12698i | ||||||||
\(459\) | −3.88488 | −0.181331 | ||||||||
\(460\) | −4.10013 | + | 2.63240i | −0.191169 | + | 0.122736i | ||||
\(461\) | −6.51959 | −0.303648 | −0.151824 | − | 0.988408i | \(-0.548515\pi\) | ||||
−0.151824 | + | 0.988408i | \(0.548515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5689i | 0.584124i | 0.956399 | + | 0.292062i | \(0.0943414\pi\) | ||||
−0.956399 | + | 0.292062i | \(0.905659\pi\) | |||||||
\(464\) | 18.5392 | 0.860661 | ||||||||
\(465\) | 1.47357 | − | 0.946072i | 0.0683350 | − | 0.0438730i | ||||
\(466\) | −10.3224 | −0.478177 | ||||||||
\(467\) | 26.3110i | 1.21753i | 0.793352 | + | 0.608764i | \(0.208334\pi\) | ||||
−0.793352 | + | 0.608764i | \(0.791666\pi\) | |||||||
\(468\) | − | 0.880664i | − | 0.0407087i | ||||||
\(469\) | −11.3663 | −0.524846 | ||||||||
\(470\) | −1.02310 | − | 1.59355i | −0.0471923 | − | 0.0735049i | ||||
\(471\) | −10.0477 | −0.462974 | ||||||||
\(472\) | − | 36.6344i | − | 1.68624i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.97662 | −0.320447 | ||||||||
\(475\) | 12.3588 | − | 26.9981i | 0.567062 | − | 1.23876i | ||||
\(476\) | 4.02387 | 0.184434 | ||||||||
\(477\) | − | 2.75907i | − | 0.126329i | ||||||
\(478\) | 3.43076i | 0.156919i | ||||||||
\(479\) | −6.99425 | −0.319575 | −0.159788 | − | 0.987151i | \(-0.551081\pi\) | ||||
−0.159788 | + | 0.987151i | \(0.551081\pi\) | |||||||
\(480\) | −2.44199 | − | 3.80355i | −0.111461 | − | 0.173607i | ||||
\(481\) | −19.5465 | −0.891243 | ||||||||
\(482\) | 12.6057i | 0.574175i | ||||||||
\(483\) | − | 17.2685i | − | 0.785743i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.8503 | − | 10.8184i | 0.765133 | − | 0.491237i | ||||
\(486\) | 1.53672 | 0.0697073 | ||||||||
\(487\) | 6.08580i | 0.275774i | 0.990448 | + | 0.137887i | \(0.0440311\pi\) | ||||
−0.990448 | + | 0.137887i | \(0.955969\pi\) | |||||||
\(488\) | − | 34.7220i | − | 1.57179i | ||||||
\(489\) | −17.0119 | −0.769306 | ||||||||
\(490\) | −3.49421 | + | 2.24339i | −0.157852 | + | 0.101346i | ||||
\(491\) | −4.58064 | −0.206722 | −0.103361 | − | 0.994644i | \(-0.532960\pi\) | ||||
−0.103361 | + | 0.994644i | \(0.532960\pi\) | |||||||
\(492\) | 2.72659i | 0.122924i | ||||||||
\(493\) | 15.6832i | 0.706335i | ||||||||
\(494\) | 22.2303 | 1.00019 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.59640 | 0.161483 | ||||||||
\(497\) | − | 26.5666i | − | 1.19168i | ||||||
\(498\) | − | 17.9485i | − | 0.804292i | ||||||
\(499\) | 21.2025 | 0.949152 | 0.474576 | − | 0.880214i | \(-0.342601\pi\) | ||||
0.474576 | + | 0.880214i | \(0.342601\pi\) | |||||||
\(500\) | 4.00158 | − | 0.569860i | 0.178956 | − | 0.0254849i | ||||
\(501\) | 8.17422 | 0.365197 | ||||||||
\(502\) | 1.38416i | 0.0617781i | ||||||||
\(503\) | − | 14.8190i | − | 0.660746i | −0.943850 | − | 0.330373i | \(-0.892825\pi\) | ||
0.943850 | − | 0.330373i | \(-0.107175\pi\) | |||||||
\(504\) | 7.21383 | 0.321330 | ||||||||
\(505\) | −4.89309 | − | 7.62129i | −0.217740 | − | 0.339143i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.06599i | 0.313812i | ||||||||
\(508\) | − | 7.09090i | − | 0.314608i | ||||||
\(509\) | 23.6991 | 1.05044 | 0.525222 | − | 0.850965i | \(-0.323982\pi\) | ||||
0.525222 | + | 0.850965i | \(0.323982\pi\) | |||||||
\(510\) | 11.2334 | − | 7.21216i | 0.497422 | − | 0.319360i | ||||
\(511\) | 1.76321 | 0.0779999 | ||||||||
\(512\) | 13.8431i | 0.611783i | ||||||||
\(513\) | 5.93848i | 0.262190i | ||||||||
\(514\) | −6.57287 | −0.289917 | ||||||||
\(515\) | −5.82799 | + | 3.74174i | −0.256812 | + | 0.164881i | ||||
\(516\) | 3.58115 | 0.157651 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 35.3281i | 1.55223i | ||||||||
\(519\) | 0.0419137 | 0.00183981 | ||||||||
\(520\) | −7.40972 | − | 11.5411i | −0.324938 | − | 0.506111i | ||||
\(521\) | −34.8182 | −1.52541 | −0.762707 | − | 0.646745i | \(-0.776130\pi\) | ||||
−0.762707 | + | 0.646745i | \(0.776130\pi\) | |||||||
\(522\) | − | 6.20372i | − | 0.271530i | ||||||
\(523\) | − | 16.6591i | − | 0.728453i | −0.931310 | − | 0.364226i | \(-0.881333\pi\) | ||
0.931310 | − | 0.364226i | \(-0.118667\pi\) | |||||||
\(524\) | −1.44914 | −0.0633060 | ||||||||
\(525\) | −5.96255 | + | 13.0253i | −0.260227 | + | 0.568471i | ||||
\(526\) | −5.60312 | −0.244307 | ||||||||
\(527\) | 3.04236i | 0.132527i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.3286 | −0.579504 | ||||||||
\(530\) | 5.12212 | + | 7.97801i | 0.222491 | + | 0.346543i | ||||
\(531\) | −14.5497 | −0.631402 | ||||||||
\(532\) | − | 6.15094i | − | 0.266677i | ||||||
\(533\) | 18.3721i | 0.795782i | ||||||||
\(534\) | −26.1081 | −1.12981 | ||||||||
\(535\) | 10.2043 | − | 6.55143i | 0.441169 | − | 0.283243i | ||||
\(536\) | −9.98906 | −0.431462 | ||||||||
\(537\) | 21.5288i | 0.929038i | ||||||||
\(538\) | − | 17.3453i | − | 0.747810i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.680257 | + | 0.436745i | −0.0292736 | + | 0.0187945i | ||||
\(541\) | −4.99608 | −0.214798 | −0.107399 | − | 0.994216i | \(-0.534252\pi\) | ||||
−0.107399 | + | 0.994216i | \(0.534252\pi\) | |||||||
\(542\) | − | 14.7290i | − | 0.632664i | ||||||
\(543\) | 10.9246i | 0.468820i | ||||||||
\(544\) | 7.85289 | 0.336690 | ||||||||
\(545\) | 2.77585 | + | 4.32356i | 0.118904 | + | 0.185201i | ||||
\(546\) | −10.7251 | −0.458990 | ||||||||
\(547\) | 27.0209i | 1.15533i | 0.816274 | + | 0.577665i | \(0.196036\pi\) | ||||
−0.816274 | + | 0.577665i | \(0.803964\pi\) | |||||||
\(548\) | 8.37820i | 0.357899i | ||||||||
\(549\) | −13.7901 | −0.588549 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.9735 | 1.02131 | ||||||||
\(552\) | − | 15.1761i | − | 0.645938i | ||||||
\(553\) | 13.0071i | 0.553116i | ||||||||
\(554\) | 41.4624 | 1.76157 | ||||||||
\(555\) | 9.69361 | + | 15.0984i | 0.411471 | + | 0.640891i | ||||
\(556\) | −4.99763 | −0.211947 | ||||||||
\(557\) | 8.26537i | 0.350215i | 0.984549 | + | 0.175107i | \(0.0560273\pi\) | ||||
−0.984549 | + | 0.175107i | \(0.943973\pi\) | |||||||
\(558\) | − | 1.20345i | − | 0.0509462i | ||||||
\(559\) | 24.1302 | 1.02060 | ||||||||
\(560\) | −24.7572 | + | 15.8948i | −1.04618 | + | 0.671679i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 29.1852i | − | 1.23110i | ||||||
\(563\) | 18.9867i | 0.800194i | 0.916473 | + | 0.400097i | \(0.131024\pi\) | ||||
−0.916473 | + | 0.400097i | \(0.868976\pi\) | |||||||
\(564\) | −0.199236 | −0.00838936 | ||||||||
\(565\) | 18.0919 | − | 11.6155i | 0.761131 | − | 0.488668i | ||||
\(566\) | −41.6367 | −1.75012 | ||||||||
\(567\) | − | 2.86503i | − | 0.120320i | ||||||
\(568\) | − | 23.3477i | − | 0.979646i | ||||||
\(569\) | 43.0309 | 1.80395 | 0.901974 | − | 0.431790i | \(-0.142118\pi\) | ||||
0.901974 | + | 0.431790i | \(0.142118\pi\) | |||||||
\(570\) | −11.0246 | − | 17.1715i | −0.461770 | − | 0.719235i | ||||
\(571\) | −8.68683 | −0.363533 | −0.181766 | − | 0.983342i | \(-0.558181\pi\) | ||||
−0.181766 | + | 0.983342i | \(0.558181\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.485281i | − | 0.0202729i | ||||||
\(574\) | 33.2055 | 1.38597 | ||||||||
\(575\) | 27.4020 | + | 12.5437i | 1.14274 | + | 0.523109i | ||||
\(576\) | 6.07836 | 0.253265 | ||||||||
\(577\) | 11.0409i | 0.459639i | 0.973233 | + | 0.229819i | \(0.0738136\pi\) | ||||
−0.973233 | + | 0.229819i | \(0.926186\pi\) | |||||||
\(578\) | − | 2.93162i | − | 0.121939i | ||||||
\(579\) | −12.5864 | −0.523073 | ||||||||
\(580\) | 1.76313 | + | 2.74618i | 0.0732099 | + | 0.114029i | ||||
\(581\) | −33.4628 | −1.38827 | ||||||||
\(582\) | − | 13.7615i | − | 0.570434i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.54957 | 0.0641216 | ||||||||
\(585\) | −4.58364 | + | 2.94283i | −0.189510 | + | 0.121671i | ||||
\(586\) | −13.9473 | −0.576157 | ||||||||
\(587\) | − | 26.1401i | − | 1.07892i | −0.842012 | − | 0.539459i | \(-0.818629\pi\) | ||
0.842012 | − | 0.539459i | \(-0.181371\pi\) | |||||||
\(588\) | 0.436870i | 0.0180162i | ||||||||
\(589\) | 4.65059 | 0.191624 | ||||||||
\(590\) | 42.0713 | − | 27.0110i | 1.73205 | − | 1.11202i | ||||
\(591\) | −15.8941 | −0.653796 | ||||||||
\(592\) | 36.8493i | 1.51450i | ||||||||
\(593\) | 12.0171i | 0.493484i | 0.969081 | + | 0.246742i | \(0.0793601\pi\) | ||||
−0.969081 | + | 0.246742i | \(0.920640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.4462 | − | 20.9432i | −0.551239 | − | 0.858589i | ||||
\(596\) | 4.89115 | 0.200349 | ||||||||
\(597\) | 5.02089i | 0.205491i | ||||||||
\(598\) | 22.5629i | 0.922665i | ||||||||
\(599\) | 41.8072 | 1.70820 | 0.854098 | − | 0.520112i | \(-0.174110\pi\) | ||||
0.854098 | + | 0.520112i | \(0.174110\pi\) | |||||||
\(600\) | −5.24009 | + | 11.4471i | −0.213926 | + | 0.467325i | ||||
\(601\) | −40.5539 | −1.65423 | −0.827115 | − | 0.562033i | \(-0.810019\pi\) | ||||
−0.827115 | + | 0.562033i | \(0.810019\pi\) | |||||||
\(602\) | − | 43.6126i | − | 1.77752i | ||||||
\(603\) | 3.96724i | 0.161558i | ||||||||
\(604\) | −7.85646 | −0.319675 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.22427 | −0.252844 | ||||||||
\(607\) | 29.2269i | 1.18628i | 0.805099 | + | 0.593141i | \(0.202112\pi\) | ||||
−0.805099 | + | 0.593141i | \(0.797888\pi\) | |||||||
\(608\) | − | 12.0040i | − | 0.486828i | ||||||
\(609\) | −11.5661 | −0.468681 | ||||||||
\(610\) | 39.8751 | − | 25.6010i | 1.61450 | − | 1.03655i | ||||
\(611\) | −1.34248 | −0.0543108 | ||||||||
\(612\) | − | 1.40447i | − | 0.0567725i | ||||||
\(613\) | − | 20.1259i | − | 0.812876i | −0.913678 | − | 0.406438i | \(-0.866771\pi\) | ||
0.913678 | − | 0.406438i | \(-0.133229\pi\) | |||||||
\(614\) | 9.38884 | 0.378903 | ||||||||
\(615\) | 14.1912 | − | 9.11119i | 0.572246 | − | 0.367399i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.98070i | 0.361550i | 0.983525 | + | 0.180775i | \(0.0578605\pi\) | ||||
−0.983525 | + | 0.180775i | \(0.942139\pi\) | |||||||
\(618\) | 4.75969i | 0.191463i | ||||||||
\(619\) | −24.0303 | −0.965860 | −0.482930 | − | 0.875659i | \(-0.660427\pi\) | ||||
−0.482930 | + | 0.875659i | \(0.660427\pi\) | |||||||
\(620\) | 0.342027 | + | 0.532728i | 0.0137361 | + | 0.0213949i | ||||
\(621\) | −6.02732 | −0.241868 | ||||||||
\(622\) | 22.8363i | 0.915653i | ||||||||
\(623\) | 48.6752i | 1.95013i | ||||||||
\(624\) | −11.1869 | −0.447834 | ||||||||
\(625\) | −16.3377 | − | 18.9230i | −0.653507 | − | 0.756920i | ||||
\(626\) | 42.1282 | 1.68378 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 3.63248i | − | 0.144952i | ||||||
\(629\) | −31.1725 | −1.24293 | ||||||||
\(630\) | 5.31884 | + | 8.28443i | 0.211908 | + | 0.330059i | ||||
\(631\) | 23.0323 | 0.916902 | 0.458451 | − | 0.888720i | \(-0.348404\pi\) | ||||
0.458451 | + | 0.888720i | \(0.348404\pi\) | |||||||
\(632\) | 11.4310i | 0.454702i | ||||||||
\(633\) | 0.800040i | 0.0317987i | ||||||||
\(634\) | −21.4109 | −0.850334 | ||||||||
\(635\) | −36.9064 | + | 23.6950i | −1.46459 | + | 0.940308i | ||||
\(636\) | 0.997466 | 0.0395521 | ||||||||
\(637\) | 2.94368i | 0.116633i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.27271 | −0.366823 | ||||||||
\(640\) | −25.1831 | + | 16.1683i | −0.995448 | + | 0.639107i | ||||
\(641\) | 17.8410 | 0.704677 | 0.352339 | − | 0.935873i | \(-0.385387\pi\) | ||||
0.352339 | + | 0.935873i | \(0.385387\pi\) | |||||||
\(642\) | − | 8.33376i | − | 0.328907i | ||||||
\(643\) | 21.4561i | 0.846147i | 0.906095 | + | 0.423074i | \(0.139049\pi\) | ||||
−0.906095 | + | 0.423074i | \(0.860951\pi\) | |||||||
\(644\) | 6.24295 | 0.246007 | ||||||||
\(645\) | −11.9668 | − | 18.6390i | −0.471192 | − | 0.733910i | ||||
\(646\) | 35.4527 | 1.39487 | ||||||||
\(647\) | − | 7.91168i | − | 0.311040i | −0.987833 | − | 0.155520i | \(-0.950295\pi\) | ||
0.987833 | − | 0.155520i | \(-0.0497054\pi\) | |||||||
\(648\) | − | 2.51789i | − | 0.0989120i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 7.79062 | − | 17.0188i | 0.305573 | − | 0.667531i | ||||
\(651\) | −2.24369 | −0.0879371 | ||||||||
\(652\) | − | 6.15021i | − | 0.240861i | ||||||
\(653\) | 20.7286i | 0.811171i | 0.914057 | + | 0.405585i | \(0.132932\pi\) | ||||
−0.914057 | + | 0.405585i | \(0.867068\pi\) | |||||||
\(654\) | 3.53102 | 0.138074 | ||||||||
\(655\) | 4.84246 | + | 7.54243i | 0.189210 | + | 0.294707i | ||||
\(656\) | 34.6353 | 1.35228 | ||||||||
\(657\) | − | 0.615424i | − | 0.0240100i | ||||||
\(658\) | 2.42638i | 0.0945900i | ||||||||
\(659\) | 44.9515 | 1.75106 | 0.875531 | − | 0.483162i | \(-0.160512\pi\) | ||||
0.875531 | + | 0.483162i | \(0.160512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.0760 | 1.24761 | 0.623806 | − | 0.781579i | \(-0.285585\pi\) | ||||
0.623806 | + | 0.781579i | \(0.285585\pi\) | |||||||
\(662\) | − | 38.3235i | − | 1.48949i | ||||||
\(663\) | − | 9.46350i | − | 0.367532i | ||||||
\(664\) | −29.4082 | −1.14126 | ||||||||
\(665\) | −32.0141 | + | 20.5540i | −1.24146 | + | 0.797050i | ||||
\(666\) | 12.3308 | 0.477808 | ||||||||
\(667\) | 24.3322i | 0.942145i | ||||||||
\(668\) | 2.95517i | 0.114339i | ||||||||
\(669\) | 8.10773 | 0.313463 | ||||||||
\(670\) | −7.36505 | − | 11.4715i | −0.284537 | − | 0.443184i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5.79137i | 0.223407i | ||||||||
\(673\) | 11.0442i | 0.425723i | 0.977082 | + | 0.212861i | \(0.0682783\pi\) | ||||
−0.977082 | + | 0.212861i | \(0.931722\pi\) | |||||||
\(674\) | −24.9534 | −0.961168 | ||||||||
\(675\) | 4.54630 | + | 2.08114i | 0.174987 | + | 0.0801032i | ||||
\(676\) | −2.55452 | −0.0982507 | ||||||||
\(677\) | 7.99883i | 0.307420i | 0.988116 | + | 0.153710i | \(0.0491221\pi\) | ||||
−0.988116 | + | 0.153710i | \(0.950878\pi\) | |||||||
\(678\) | − | 14.7755i | − | 0.567451i | ||||||
\(679\) | −25.6567 | −0.984613 | ||||||||
\(680\) | −11.8169 | − | 18.4056i | −0.453159 | − | 0.705824i | ||||
\(681\) | 8.70426 | 0.333548 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 16.6442i | − | 0.636873i | −0.947944 | − | 0.318436i | \(-0.896842\pi\) | ||
0.947944 | − | 0.318436i | \(-0.103158\pi\) | |||||||
\(684\) | −2.14690 | −0.0820887 | ||||||||
\(685\) | 43.6065 | − | 27.9966i | 1.66612 | − | 1.06970i | ||||
\(686\) | −25.4990 | −0.973556 | ||||||||
\(687\) | − | 29.6210i | − | 1.13011i | ||||||
\(688\) | − | 45.4905i | − | 1.73431i | ||||||
\(689\) | 6.72104 | 0.256051 | ||||||||
\(690\) | 17.4284 | − | 11.1895i | 0.663487 | − | 0.425978i | ||||
\(691\) | −12.4814 | −0.474815 | −0.237408 | − | 0.971410i | \(-0.576298\pi\) | ||||
−0.237408 | + | 0.971410i | \(0.576298\pi\) | |||||||
\(692\) | 0.0151528i | 0.000576022i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −42.2010 | −1.60193 | ||||||||
\(695\) | 16.7001 | + | 26.0115i | 0.633471 | + | 0.986671i | ||||
\(696\) | −10.1647 | −0.385290 | ||||||||
\(697\) | 29.2996i | 1.10980i | ||||||||
\(698\) | − | 38.6287i | − | 1.46212i | ||||||
\(699\) | 6.71715 | 0.254066 | ||||||||
\(700\) | −4.70895 | − | 2.15560i | −0.177982 | − | 0.0814740i | ||||
\(701\) | 3.13045 | 0.118235 | 0.0591177 | − | 0.998251i | \(-0.481171\pi\) | ||||
0.0591177 | + | 0.998251i | \(0.481171\pi\) | |||||||
\(702\) | 3.74343i | 0.141287i | ||||||||
\(703\) | 47.6508i | 1.79718i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.665769 | + | 1.03698i | 0.0250743 | + | 0.0390548i | ||||
\(706\) | 18.8037 | 0.707685 | ||||||||
\(707\) | 11.6044i | 0.436427i | ||||||||
\(708\) | − | 5.26004i | − | 0.197684i | ||||||
\(709\) | 8.71471 | 0.327288 | 0.163644 | − | 0.986519i | \(-0.447675\pi\) | ||||
0.163644 | + | 0.986519i | \(0.447675\pi\) | |||||||
\(710\) | 26.8126 | − | 17.2145i | 1.00626 | − | 0.646049i | ||||
\(711\) | 4.53993 | 0.170261 | ||||||||
\(712\) | 42.7774i | 1.60315i | ||||||||
\(713\) | 4.72016i | 0.176771i | ||||||||
\(714\) | −17.1042 | −0.640110 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.78317 | −0.290871 | ||||||||
\(717\) | − | 2.23252i | − | 0.0833748i | ||||||
\(718\) | 5.96884i | 0.222755i | ||||||||
\(719\) | −10.3566 | −0.386237 | −0.193118 | − | 0.981175i | \(-0.561860\pi\) | ||||
−0.193118 | + | 0.981175i | \(0.561860\pi\) | |||||||
\(720\) | 5.54787 | + | 8.64115i | 0.206757 | + | 0.322037i | ||||
\(721\) | 8.87385 | 0.330479 | ||||||||
\(722\) | − | 24.9957i | − | 0.930244i | ||||||
\(723\) | − | 8.20298i | − | 0.305072i | ||||||
\(724\) | −3.94950 | −0.146782 | ||||||||
\(725\) | 8.40153 | − | 18.3533i | 0.312025 | − | 0.681625i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 18.2456i | − | 0.676693i | −0.941022 | − | 0.338346i | \(-0.890132\pi\) | ||
0.941022 | − | 0.338346i | \(-0.109868\pi\) | |||||||
\(728\) | 17.5728i | 0.651290i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 1.14252 | + | 1.77954i | 0.0422864 | + | 0.0658637i | ||||
\(731\) | 38.4825 | 1.42333 | ||||||||
\(732\) | − | 4.98546i | − | 0.184268i | ||||||
\(733\) | 3.14121i | 0.116023i | 0.998316 | + | 0.0580116i | \(0.0184760\pi\) | ||||
−0.998316 | + | 0.0580116i | \(0.981524\pi\) | |||||||
\(734\) | 30.0741 | 1.11006 | ||||||||
\(735\) | 2.27381 | − | 1.45985i | 0.0838706 | − | 0.0538473i | ||||
\(736\) | 12.1836 | 0.449094 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 11.5899i | − | 0.426630i | ||||||
\(739\) | 33.9751 | 1.24980 | 0.624898 | − | 0.780706i | \(-0.285141\pi\) | ||||
0.624898 | + | 0.780706i | \(0.285141\pi\) | |||||||
\(740\) | −5.45842 | + | 3.50447i | −0.200656 | + | 0.128827i | ||||
\(741\) | −14.4660 | −0.531423 | ||||||||
\(742\) | − | 12.1475i | − | 0.445950i | ||||||
\(743\) | 40.2606i | 1.47702i | 0.674243 | + | 0.738510i | \(0.264470\pi\) | ||||
−0.674243 | + | 0.738510i | \(0.735530\pi\) | |||||||
\(744\) | −1.97183 | −0.0722907 | ||||||||
\(745\) | −16.3443 | − | 25.4572i | −0.598808 | − | 0.932681i | ||||
\(746\) | −1.12178 | −0.0410711 | ||||||||
\(747\) | 11.6797i | 0.427339i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.5373 | −0.567719 | ||||||||
\(750\) | −17.0095 | + | 2.42230i | −0.621099 | + | 0.0884499i | ||||
\(751\) | 39.7342 | 1.44992 | 0.724960 | − | 0.688791i | \(-0.241858\pi\) | ||||
0.724960 | + | 0.688791i | \(0.241858\pi\) | |||||||
\(752\) | 2.53085i | 0.0922908i | ||||||||
\(753\) | − | 0.900721i | − | 0.0328241i | ||||||
\(754\) | 15.1122 | 0.550352 | ||||||||
\(755\) | 26.2532 | + | 40.8910i | 0.955452 | + | 1.48818i | ||||
\(756\) | 1.03578 | 0.0376708 | ||||||||
\(757\) | − | 51.6449i | − | 1.87707i | −0.345188 | − | 0.938533i | \(-0.612185\pi\) | ||
0.345188 | − | 0.938533i | \(-0.387815\pi\) | |||||||
\(758\) | 55.3460i | 2.01026i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −28.1351 | + | 18.0636i | −1.02057 | + | 0.655234i | ||||
\(761\) | −39.8286 | −1.44379 | −0.721893 | − | 0.692004i | \(-0.756728\pi\) | ||||
−0.721893 | + | 0.692004i | \(0.756728\pi\) | |||||||
\(762\) | 30.1413i | 1.09190i | ||||||||
\(763\) | − | 6.58315i | − | 0.238326i | ||||||
\(764\) | 0.175440 | 0.00634721 | ||||||||
\(765\) | −7.30995 | + | 4.69320i | −0.264292 | + | 0.169683i | ||||
\(766\) | 19.1401 | 0.691560 | ||||||||
\(767\) | − | 35.4427i | − | 1.27976i | ||||||
\(768\) | 8.41013i | 0.303475i | ||||||||
\(769\) | −46.2949 | −1.66944 | −0.834719 | − | 0.550676i | \(-0.814370\pi\) | ||||
−0.834719 | + | 0.550676i | \(0.814370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.27720 | 0.154039 | ||||||||
\(772\) | − | 4.55028i | − | 0.163768i | ||||||
\(773\) | 7.01535i | 0.252325i | 0.992010 | + | 0.126162i | \(0.0402660\pi\) | ||||
−0.992010 | + | 0.126162i | \(0.959734\pi\) | |||||||
\(774\) | −15.2224 | −0.547157 | ||||||||
\(775\) | 1.62980 | − | 3.56033i | 0.0585442 | − | 0.127891i | ||||
\(776\) | −22.5480 | −0.809425 | ||||||||
\(777\) | − | 22.9892i | − | 0.824733i | ||||||
\(778\) | − | 31.4432i | − | 1.12729i | ||||||
\(779\) | 44.7877 | 1.60469 | ||||||||
\(780\) | −1.06390 | − | 1.65709i | −0.0380938 | − | 0.0593335i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 35.9830i | 1.28675i | ||||||||
\(783\) | 4.03698i | 0.144270i | ||||||||
\(784\) | 5.54947 | 0.198195 | ||||||||
\(785\) | −18.9062 | + | 12.1383i | −0.674790 | + | 0.433235i | ||||
\(786\) | 6.15986 | 0.219715 | ||||||||
\(787\) | 2.77476i | 0.0989095i | 0.998776 | + | 0.0494548i | \(0.0157484\pi\) | ||||
−0.998776 | + | 0.0494548i | \(0.984252\pi\) | |||||||
\(788\) | − | 5.74608i | − | 0.204696i | ||||||
\(789\) | 3.64614 | 0.129806 | ||||||||
\(790\) | −13.1275 | + | 8.42824i | −0.467056 | + | 0.299863i | ||||
\(791\) | −27.5471 | −0.979464 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 33.5926i | − | 1.19291i | ||||||
\(794\) | −36.7348 | −1.30367 | ||||||||
\(795\) | −3.33314 | − | 5.19157i | −0.118214 | − | 0.184126i | ||||
\(796\) | −1.81517 | −0.0643370 | ||||||||
\(797\) | − | 42.9669i | − | 1.52197i | −0.648772 | − | 0.760983i | \(-0.724717\pi\) | ||
0.648772 | − | 0.760983i | \(-0.275283\pi\) | |||||||
\(798\) | 26.1458i | 0.925550i | ||||||||
\(799\) | −2.14097 | −0.0757420 | ||||||||
\(800\) | −9.18988 | − | 4.20682i | −0.324911 | − | 0.148734i | ||||
\(801\) | 16.9894 | 0.600291 | ||||||||
\(802\) | 14.5236i | 0.512846i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.43425 | −0.0505821 | ||||||||
\(805\) | −20.8615 | − | 32.4931i | −0.735271 | − | 1.14523i | ||||
\(806\) | 2.93159 | 0.103261 | ||||||||
\(807\) | 11.2872i | 0.397328i | ||||||||
\(808\) | 10.1983i | 0.358775i | ||||||||
\(809\) | 33.2867 | 1.17030 | 0.585149 | − | 0.810926i | \(-0.301036\pi\) | ||||
0.585149 | + | 0.810926i | \(0.301036\pi\) | |||||||
\(810\) | 2.89156 | − | 1.85647i | 0.101599 | − | 0.0652296i | ||||
\(811\) | −37.8675 | −1.32971 | −0.664855 | − | 0.746973i | \(-0.731507\pi\) | ||||
−0.664855 | + | 0.746973i | \(0.731507\pi\) | |||||||
\(812\) | − | 4.18140i | − | 0.146739i | ||||||
\(813\) | 9.58466i | 0.336149i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.0103 | + | 20.5516i | −1.12127 | + | 0.719890i | ||||
\(816\) | −17.8407 | −0.624550 | ||||||||
\(817\) | − | 58.8250i | − | 2.05802i | ||||||
\(818\) | 11.8254i | 0.413465i | ||||||||
\(819\) | 6.97917 | 0.243872 | ||||||||
\(820\) | 3.29391 | + | 5.13046i | 0.115028 | + | 0.179164i | ||||
\(821\) | −15.5524 | −0.542782 | −0.271391 | − | 0.962469i | \(-0.587484\pi\) | ||||
−0.271391 | + | 0.962469i | \(0.587484\pi\) | |||||||
\(822\) | − | 35.6132i | − | 1.24215i | ||||||
\(823\) | − | 19.7207i | − | 0.687421i | −0.939076 | − | 0.343710i | \(-0.888316\pi\) | ||
0.939076 | − | 0.343710i | \(-0.111684\pi\) | |||||||
\(824\) | 7.79864 | 0.271678 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −64.0588 | −2.22889 | ||||||||
\(827\) | 5.77933i | 0.200967i | 0.994939 | + | 0.100483i | \(0.0320390\pi\) | ||||
−0.994939 | + | 0.100483i | \(0.967961\pi\) | |||||||
\(828\) | − | 2.17902i | − | 0.0757260i | ||||||
\(829\) | −34.0085 | −1.18116 | −0.590581 | − | 0.806978i | \(-0.701102\pi\) | ||||
−0.590581 | + | 0.806978i | \(0.701102\pi\) | |||||||
\(830\) | −21.6830 | − | 33.7727i | −0.752629 | − | 1.17227i | ||||
\(831\) | −26.9810 | −0.935960 | ||||||||
\(832\) | 14.8068i | 0.513333i | ||||||||
\(833\) | 4.69455i | 0.162657i | ||||||||
\(834\) | 21.2434 | 0.735599 | ||||||||
\(835\) | 15.3809 | − | 9.87501i | 0.532280 | − | 0.341739i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.783128i | 0.0270689i | ||||||||
\(838\) | − | 46.1939i | − | 1.59574i | ||||||
\(839\) | −38.0383 | −1.31323 | −0.656614 | − | 0.754226i | \(-0.728012\pi\) | ||||
−0.656614 | + | 0.754226i | \(0.728012\pi\) | |||||||
\(840\) | 13.5738 | − | 8.71480i | 0.468342 | − | 0.300689i | ||||
\(841\) | −12.7028 | −0.438028 | ||||||||
\(842\) | 36.6038i | 1.26145i | ||||||||
\(843\) | 18.9918i | 0.654114i | ||||||||
\(844\) | −0.289233 | −0.00995580 | ||||||||
\(845\) | 8.53620 | + | 13.2957i | 0.293654 | + | 0.457384i | ||||
\(846\) | 0.846893 | 0.0291168 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 12.6706i | − | 0.435110i | ||||||
\(849\) | 27.0944 | 0.929878 | ||||||||
\(850\) | 12.4244 | − | 27.1414i | 0.426154 | − | 0.930941i | ||||
\(851\) | −48.3636 | −1.65788 | ||||||||
\(852\) | − | 3.35230i | − | 0.114848i | ||||||
\(853\) | 48.9458i | 1.67587i | 0.545769 | + | 0.837936i | \(0.316238\pi\) | ||||
−0.545769 | + | 0.837936i | \(0.683762\pi\) | |||||||
\(854\) | −60.7148 | −2.07762 | ||||||||
\(855\) | 7.17409 | + | 11.1741i | 0.245349 | + | 0.382146i | ||||
\(856\) | −13.6547 | −0.466707 | ||||||||
\(857\) | − | 27.4604i | − | 0.938030i | −0.883190 | − | 0.469015i | \(-0.844609\pi\) | ||
0.883190 | − | 0.469015i | \(-0.155391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.25914 | 0.0429613 | 0.0214806 | − | 0.999769i | \(-0.493162\pi\) | ||||
0.0214806 | + | 0.999769i | \(0.493162\pi\) | |||||||
\(860\) | 6.73843 | − | 4.32627i | 0.229779 | − | 0.147525i | ||||
\(861\) | −21.6079 | −0.736397 | ||||||||
\(862\) | − | 0.935086i | − | 0.0318491i | ||||||
\(863\) | 26.7154i | 0.909404i | 0.890644 | + | 0.454702i | \(0.150254\pi\) | ||||
−0.890644 | + | 0.454702i | \(0.849746\pi\) | |||||||
\(864\) | 2.02140 | 0.0687694 | ||||||||
\(865\) | 0.0788665 | − | 0.0506346i | 0.00268154 | − | 0.00172163i | ||||
\(866\) | −26.2826 | −0.893120 | ||||||||
\(867\) | 1.90771i | 0.0647892i | ||||||||
\(868\) | − | 0.811145i | − | 0.0275321i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −7.49452 | − | 11.6732i | −0.254088 | − | 0.395758i | ||||
\(871\) | −9.66412 | −0.327456 | ||||||||
\(872\) | − | 5.78550i | − | 0.195922i | ||||||
\(873\) | 8.95511i | 0.303085i | ||||||||
\(874\) | 55.0042 | 1.86054 | ||||||||
\(875\) | 4.51608 | + | 31.7121i | 0.152671 | + | 1.07206i | ||||
\(876\) | 0.222490 | 0.00751724 | ||||||||
\(877\) | − | 26.7109i | − | 0.901962i | −0.892533 | − | 0.450981i | \(-0.851074\pi\) | ||
0.892533 | − | 0.450981i | \(-0.148926\pi\) | |||||||
\(878\) | − | 17.7613i | − | 0.599415i | ||||||
\(879\) | 9.07599 | 0.306125 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.7144 | −1.06849 | −0.534243 | − | 0.845331i | \(-0.679403\pi\) | ||||
−0.534243 | + | 0.845331i | \(0.679403\pi\) | |||||||
\(882\) | − | 1.85700i | − | 0.0625286i | ||||||
\(883\) | − | 47.8895i | − | 1.61161i | −0.592182 | − | 0.805804i | \(-0.701733\pi\) | ||
0.592182 | − | 0.805804i | \(-0.298267\pi\) | |||||||
\(884\) | 3.42127 | 0.115070 | ||||||||
\(885\) | −27.3772 | + | 17.5770i | −0.920276 | + | 0.590844i | ||||
\(886\) | 27.3138 | 0.917626 | ||||||||
\(887\) | − | 34.0800i | − | 1.14429i | −0.820151 | − | 0.572147i | \(-0.806111\pi\) | ||
0.820151 | − | 0.572147i | \(-0.193889\pi\) | |||||||
\(888\) | − | 20.2037i | − | 0.677991i | ||||||
\(889\) | 56.1947 | 1.88471 | ||||||||
\(890\) | −49.1260 | + | 31.5403i | −1.64671 | + | 1.05723i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.93113i | 0.0981415i | ||||||||
\(893\) | 3.27271i | 0.109517i | ||||||||
\(894\) | −20.7908 | −0.695348 | ||||||||
\(895\) | 26.0083 | + | 40.5095i | 0.869362 | + | 1.35408i | ||||
\(896\) | 38.3444 | 1.28100 | ||||||||
\(897\) | − | 14.6824i | − | 0.490233i | ||||||
\(898\) | 33.3661i | 1.11344i | ||||||||
\(899\) | 3.16147 | 0.105441 | ||||||||
\(900\) | −0.752382 | + | 1.64359i | −0.0250794 | + | 0.0547864i | ||||
\(901\) | 10.7186 | 0.357090 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.3802i | 0.944435i | ||||||||
\(904\) | −24.2094 | −0.805191 | ||||||||
\(905\) | 13.1977 | + | 20.5562i | 0.438705 | + | 0.683311i | ||||
\(906\) | 33.3954 | 1.10949 | ||||||||
\(907\) | 22.5941i | 0.750226i | 0.926979 | + | 0.375113i | \(0.122396\pi\) | ||||
−0.926979 | + | 0.375113i | \(0.877604\pi\) | |||||||
\(908\) | 3.14679i | 0.104430i | ||||||||
\(909\) | 4.05035 | 0.134341 | ||||||||
\(910\) | −20.1807 | + | 12.9566i | −0.668984 | + | 0.429507i | ||||
\(911\) | −15.8393 | −0.524779 | −0.262390 | − | 0.964962i | \(-0.584511\pi\) | ||||
−0.262390 | + | 0.964962i | \(0.584511\pi\) | |||||||
\(912\) | 27.2716i | 0.903052i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.34333 | −0.0444333 | ||||||||
\(915\) | −25.9481 | + | 16.6594i | −0.857818 | + | 0.550744i | ||||
\(916\) | 10.7087 | 0.353825 | ||||||||
\(917\) | − | 11.4843i | − | 0.379245i | ||||||
\(918\) | 5.96999i | 0.197039i | ||||||||
\(919\) | 0.360925 | 0.0119058 | 0.00595291 | − | 0.999982i | \(-0.498105\pi\) | ||||
0.00595291 | + | 0.999982i | \(0.498105\pi\) | |||||||
\(920\) | −18.3338 | − | 28.5560i | −0.604447 | − | 0.941463i | ||||
\(921\) | −6.10964 | −0.201320 | ||||||||
\(922\) | 10.0188i | 0.329952i | ||||||||
\(923\) | − | 22.5882i | − | 0.743499i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.4798 | + | 16.6992i | 1.19945 | + | 0.549067i | ||||
\(926\) | 19.3149 | 0.634726 | ||||||||
\(927\) | − | 3.09729i | − | 0.101728i | ||||||
\(928\) | − | 8.16034i | − | 0.267876i | ||||||
\(929\) | −0.480345 | −0.0157596 | −0.00787980 | − | 0.999969i | \(-0.502508\pi\) | ||||
−0.00787980 | + | 0.999969i | \(0.502508\pi\) | |||||||
\(930\) | −1.45385 | − | 2.26446i | −0.0476737 | − | 0.0742547i | ||||
\(931\) | 7.17616 | 0.235189 | ||||||||
\(932\) | 2.42841i | 0.0795451i | ||||||||
\(933\) | − | 14.8604i | − | 0.486507i | ||||||
\(934\) | 40.4328 | 1.32300 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.13353 | 0.200481 | ||||||||
\(937\) | 52.1442i | 1.70348i | 0.523967 | + | 0.851739i | \(0.324452\pi\) | ||||
−0.523967 | + | 0.851739i | \(0.675548\pi\) | |||||||
\(938\) | 17.4668i | 0.570312i | ||||||||
\(939\) | −27.4142 | −0.894630 | ||||||||
\(940\) | −0.374891 | + | 0.240691i | −0.0122276 | + | 0.00785048i | ||||
\(941\) | −14.9475 | −0.487275 | −0.243637 | − | 0.969866i | \(-0.578341\pi\) | ||||
−0.243637 | + | 0.969866i | \(0.578341\pi\) | |||||||
\(942\) | 15.4406i | 0.503081i | ||||||||
\(943\) | 45.4577i | 1.48031i | ||||||||
\(944\) | −66.8171 | −2.17471 | ||||||||
\(945\) | −3.46116 | − | 5.39096i | −0.112591 | − | 0.175368i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.2440i | 0.885311i | 0.896692 | + | 0.442656i | \(0.145964\pi\) | ||||
−0.896692 | + | 0.442656i | \(0.854036\pi\) | |||||||
\(948\) | 1.64129i | 0.0533066i | ||||||||
\(949\) | 1.49916 | 0.0486649 | ||||||||
\(950\) | −41.4887 | − | 18.9921i | −1.34607 | − | 0.616186i | ||||
\(951\) | 13.9328 | 0.451802 | ||||||||
\(952\) | 28.0249i | 0.908291i | ||||||||
\(953\) | − | 37.8748i | − | 1.22688i | −0.789740 | − | 0.613442i | \(-0.789784\pi\) | ||
0.789740 | − | 0.613442i | \(-0.210216\pi\) | |||||||
\(954\) | −4.23992 | −0.137273 | ||||||||
\(955\) | −0.586253 | − | 0.913125i | −0.0189707 | − | 0.0295480i | ||||
\(956\) | 0.807106 | 0.0261037 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.7482i | 0.347260i | ||||||||
\(959\) | −66.3964 | −2.14405 | ||||||||
\(960\) | 11.4373 | − | 7.34307i | 0.369137 | − | 0.236997i | ||||
\(961\) | −30.3867 | −0.980216 | ||||||||
\(962\) | 30.0376i | 0.968450i | ||||||||
\(963\) | 5.42307i | 0.174756i | ||||||||
\(964\) | 2.96557 | 0.0955144 | ||||||||
\(965\) | −23.6831 | + | 15.2052i | −0.762385 | + | 0.489474i | ||||
\(966\) | −26.5369 | −0.853811 | ||||||||
\(967\) | 43.6845i | 1.40480i | 0.711783 | + | 0.702400i | \(0.247888\pi\) | ||||
−0.711783 | + | 0.702400i | \(0.752112\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.0703 | −0.741125 | ||||||||
\(970\) | −16.6249 | − | 25.8943i | −0.533793 | − | 0.831415i | ||||
\(971\) | −2.73545 | −0.0877848 | −0.0438924 | − | 0.999036i | \(-0.513976\pi\) | ||||
−0.0438924 | + | 0.999036i | \(0.513976\pi\) | |||||||
\(972\) | − | 0.361523i | − | 0.0115959i | ||||||
\(973\) | − | 39.6057i | − | 1.26970i | ||||||
\(974\) | 9.35220 | 0.299664 | ||||||||
\(975\) | −5.06963 | + | 11.0747i | −0.162358 | + | 0.354674i | ||||
\(976\) | −63.3292 | −2.02712 | ||||||||
\(977\) | − | 36.5804i | − | 1.17031i | −0.810921 | − | 0.585156i | \(-0.801033\pi\) | ||
0.810921 | − | 0.585156i | \(-0.198967\pi\) | |||||||
\(978\) | 26.1427i | 0.835950i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.527769 | + | 0.822033i | 0.0168590 | + | 0.0262589i | ||||
\(981\) | −2.29776 | −0.0733618 | ||||||||
\(982\) | 7.03919i | 0.224630i | ||||||||
\(983\) | 6.44168i | 0.205458i | 0.994709 | + | 0.102729i | \(0.0327574\pi\) | ||||
−0.994709 | + | 0.102729i | \(0.967243\pi\) | |||||||
\(984\) | −18.9898 | −0.605372 | ||||||||
\(985\) | −29.9070 | + | 19.2011i | −0.952916 | + | 0.611799i | ||||
\(986\) | 24.1007 | 0.767523 | ||||||||
\(987\) | − | 1.57893i | − | 0.0502578i | ||||||
\(988\) | − | 5.22981i | − | 0.166382i | ||||||
\(989\) | 59.7050 | 1.89851 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.5718 | −0.431123 | −0.215561 | − | 0.976490i | \(-0.569158\pi\) | ||||
−0.215561 | + | 0.976490i | \(0.569158\pi\) | |||||||
\(992\) | − | 1.58301i | − | 0.0502607i | ||||||
\(993\) | 24.9385i | 0.791398i | ||||||||
\(994\) | −40.8256 | −1.29491 | ||||||||
\(995\) | 6.06558 | + | 9.44752i | 0.192292 | + | 0.299506i | ||||
\(996\) | −4.22249 | −0.133795 | ||||||||
\(997\) | − | 1.84851i | − | 0.0585429i | −0.999571 | − | 0.0292715i | \(-0.990681\pi\) | ||
0.999571 | − | 0.0292715i | \(-0.00931873\pi\) | |||||||
\(998\) | − | 32.5823i | − | 1.03138i | ||||||
\(999\) | −8.02406 | −0.253870 |
(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 | 1815.2.c.i.364.4 | yes | 12 | |
5.2 | odd | 4 | 9075.2.a.ds.1.5 | 6 | |||
5.3 | odd | 4 | 9075.2.a.do.1.2 | 6 | |||
5.4 | even | 2 | inner | 1815.2.c.i.364.9 | yes | 12 | |
11.10 | odd | 2 | 1815.2.c.h.364.9 | yes | 12 | ||
55.32 | even | 4 | 9075.2.a.dp.1.2 | 6 | |||
55.43 | even | 4 | 9075.2.a.dr.1.5 | 6 | |||
55.54 | odd | 2 | 1815.2.c.h.364.4 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.c.h.364.4 | ✓ | 12 | 55.54 | odd | 2 | ||
1815.2.c.h.364.9 | yes | 12 | 11.10 | odd | 2 | ||
1815.2.c.i.364.4 | yes | 12 | 1.1 | even | 1 | trivial | |
1815.2.c.i.364.9 | yes | 12 | 5.4 | even | 2 | inner | |
9075.2.a.do.1.2 | 6 | 5.3 | odd | 4 | |||
9075.2.a.dp.1.2 | 6 | 55.32 | even | 4 | |||
9075.2.a.dr.1.5 | 6 | 55.43 | even | 4 | |||
9075.2.a.ds.1.5 | 6 | 5.2 | odd | 4 |