Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(37,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.p (of order \(4\), 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: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.6 | ||
Root | \(-0.850665 + 0.850665i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.37 |
Dual form | 1710.2.p.c.1063.6 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.23583 | + | 0.0328054i | −0.999892 | + | 0.0146710i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.17648 | − | 3.17648i | −1.20060 | − | 1.20060i | −0.973986 | − | 0.226610i | \(-0.927236\pi\) |
−0.226610 | − | 0.973986i | \(-0.572764\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.55777 | + | 1.60417i | −0.492611 | + | 0.507282i | ||||
\(11\) | −1.49820 | −0.451724 | −0.225862 | − | 0.974159i | \(-0.572520\pi\) | ||||
−0.225862 | + | 0.974159i | \(0.572520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.38967 | + | 2.38967i | 0.662774 | + | 0.662774i | 0.956033 | − | 0.293259i | \(-0.0947398\pi\) |
−0.293259 | + | 0.956033i | \(0.594740\pi\) | |||||||
\(14\) | −4.49222 | −1.20060 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.853306 | − | 0.853306i | −0.206957 | − | 0.206957i | 0.596016 | − | 0.802973i | \(-0.296750\pi\) |
−0.802973 | + | 0.596016i | \(0.796750\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.34485 | + | 0.349716i | 0.996776 | + | 0.0802304i | ||||
\(20\) | 0.0328054 | + | 2.23583i | 0.00733551 | + | 0.499946i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.05939 | + | 1.05939i | −0.225862 | + | 0.225862i | ||||
\(23\) | −4.67468 | + | 4.67468i | −0.974737 | + | 0.974737i | −0.999689 | − | 0.0249512i | \(-0.992057\pi\) |
0.0249512 | + | 0.999689i | \(0.492057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99785 | − | 0.146694i | 0.999570 | − | 0.0293389i | ||||
\(26\) | 3.37950 | 0.662774 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.17648 | + | 3.17648i | −0.600298 | + | 0.600298i | ||||
\(29\) | −5.40423 | −1.00354 | −0.501771 | − | 0.865001i | \(-0.667318\pi\) | ||||
−0.501771 | + | 0.865001i | \(0.667318\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.364245i | − | 0.0654204i | −0.999465 | − | 0.0327102i | \(-0.989586\pi\) | ||
0.999465 | − | 0.0327102i | \(-0.0104138\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.20676 | −0.206957 | ||||||||
\(35\) | 7.20626 | + | 6.99785i | 1.21808 | + | 1.18285i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.29845 | + | 4.29845i | −0.706661 | + | 0.706661i | −0.965832 | − | 0.259170i | \(-0.916551\pi\) |
0.259170 | + | 0.965832i | \(0.416551\pi\) | |||||||
\(38\) | 3.31956 | − | 2.82498i | 0.538503 | − | 0.458273i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.60417 | + | 1.55777i | 0.253641 | + | 0.246305i | ||||
\(41\) | 1.79412i | 0.280194i | 0.990138 | + | 0.140097i | \(0.0447415\pi\) | ||||
−0.990138 | + | 0.140097i | \(0.955259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.623738 | − | 0.623738i | 0.0951192 | − | 0.0951192i | −0.657946 | − | 0.753065i | \(-0.728574\pi\) |
0.753065 | + | 0.657946i | \(0.228574\pi\) | |||||||
\(44\) | 1.49820i | 0.225862i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.61099i | 0.974737i | ||||||||
\(47\) | 5.24209 | + | 5.24209i | 0.764637 | + | 0.764637i | 0.977157 | − | 0.212520i | \(-0.0681670\pi\) |
−0.212520 | + | 0.977157i | \(0.568167\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.1800i | 1.88286i | ||||||||
\(50\) | 3.43028 | − | 3.63774i | 0.485115 | − | 0.514454i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.38967 | − | 2.38967i | 0.331387 | − | 0.331387i | ||||
\(53\) | 5.27391 | + | 5.27391i | 0.724427 | + | 0.724427i | 0.969504 | − | 0.245077i | \(-0.0788132\pi\) |
−0.245077 | + | 0.969504i | \(0.578813\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.34972 | − | 0.0491491i | 0.451676 | − | 0.00662726i | ||||
\(56\) | 4.49222i | 0.600298i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.82137 | + | 3.82137i | −0.501771 | + | 0.501771i | ||||
\(59\) | −1.49134 | −0.194156 | −0.0970781 | − | 0.995277i | \(-0.530950\pi\) | ||||
−0.0970781 | + | 0.995277i | \(0.530950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.2432 | 1.95169 | 0.975844 | − | 0.218468i | \(-0.0701060\pi\) | ||||
0.975844 | + | 0.218468i | \(0.0701060\pi\) | |||||||
\(62\) | −0.257560 | − | 0.257560i | −0.0327102 | − | 0.0327102i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −5.42128 | − | 5.26449i | −0.672426 | − | 0.652979i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.989147 | + | 0.989147i | −0.120844 | + | 0.120844i | −0.764942 | − | 0.644099i | \(-0.777233\pi\) |
0.644099 | + | 0.764942i | \(0.277233\pi\) | |||||||
\(68\) | −0.853306 | + | 0.853306i | −0.103478 | + | 0.103478i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.0438 | − | 0.147369i | 1.20047 | − | 0.0176140i | ||||
\(71\) | − | 8.98443i | − | 1.06626i | −0.846035 | − | 0.533128i | \(-0.821016\pi\) | ||
0.846035 | − | 0.533128i | \(-0.178984\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.2572 | + | 11.2572i | −1.31756 | + | 1.31756i | −0.401850 | + | 0.915706i | \(0.631633\pi\) |
−0.915706 | + | 0.401850i | \(0.868367\pi\) | |||||||
\(74\) | 6.07893i | 0.706661i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.349716 | − | 4.34485i | 0.0401152 | − | 0.498388i | ||||
\(77\) | 4.75900 | + | 4.75900i | 0.542338 | + | 0.542338i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.95317 | −0.894801 | −0.447401 | − | 0.894334i | \(-0.647650\pi\) | ||||
−0.447401 | + | 0.894334i | \(0.647650\pi\) | |||||||
\(80\) | 2.23583 | − | 0.0328054i | 0.249973 | − | 0.00366776i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.26863 | + | 1.26863i | 0.140097 | + | 0.140097i | ||||
\(83\) | −3.94546 | + | 3.94546i | −0.433071 | + | 0.433071i | −0.889672 | − | 0.456601i | \(-0.849067\pi\) |
0.456601 | + | 0.889672i | \(0.349067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.93584 | + | 1.87985i | 0.209971 | + | 0.203898i | ||||
\(86\) | − | 0.882099i | − | 0.0951192i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.05939 | + | 1.05939i | 0.112931 | + | 0.112931i | ||||
\(89\) | 9.30909 | 0.986762 | 0.493381 | − | 0.869813i | \(-0.335761\pi\) | ||||
0.493381 | + | 0.869813i | \(0.335761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15.1814i | − | 1.59145i | ||||||
\(92\) | 4.67468 | + | 4.67468i | 0.487369 | + | 0.487369i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.41343 | 0.764637 | ||||||||
\(95\) | −9.72580 | − | 0.639371i | −0.997846 | − | 0.0655981i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.79952 | + | 8.79952i | −0.893456 | + | 0.893456i | −0.994847 | − | 0.101391i | \(-0.967671\pi\) |
0.101391 | + | 0.994847i | \(0.467671\pi\) | |||||||
\(98\) | 9.31967 | + | 9.31967i | 0.941429 | + | 0.941429i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.146694 | − | 4.99785i | −0.0146694 | − | 0.499785i | ||||
\(101\) | −2.17827 | −0.216746 | −0.108373 | − | 0.994110i | \(-0.534564\pi\) | ||||
−0.108373 | + | 0.994110i | \(0.534564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.44827 | − | 9.44827i | −0.930966 | − | 0.930966i | 0.0668005 | − | 0.997766i | \(-0.478721\pi\) |
−0.997766 | + | 0.0668005i | \(0.978721\pi\) | |||||||
\(104\) | − | 3.37950i | − | 0.331387i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.45843 | 0.724427 | ||||||||
\(107\) | 0.300245 | − | 0.300245i | 0.0290258 | − | 0.0290258i | −0.692445 | − | 0.721471i | \(-0.743466\pi\) |
0.721471 | + | 0.692445i | \(0.243466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.83545 | −0.750500 | −0.375250 | − | 0.926924i | \(-0.622443\pi\) | ||||
−0.375250 | + | 0.926924i | \(0.622443\pi\) | |||||||
\(110\) | 2.33385 | − | 2.40336i | 0.222524 | − | 0.229151i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.17648 | + | 3.17648i | 0.300149 | + | 0.300149i | ||||
\(113\) | 12.3606 | + | 12.3606i | 1.16279 | + | 1.16279i | 0.983862 | + | 0.178928i | \(0.0572631\pi\) |
0.178928 | + | 0.983862i | \(0.442737\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.2984 | − | 10.6051i | 0.960332 | − | 0.988933i | ||||
\(116\) | 5.40423i | 0.501771i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.05454 | + | 1.05454i | −0.0970781 | + | 0.0970781i | ||||
\(119\) | 5.42101i | 0.496943i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.75540 | −0.795945 | ||||||||
\(122\) | 10.7786 | − | 10.7786i | 0.975844 | − | 0.975844i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.364245 | −0.0327102 | ||||||||
\(125\) | −11.1695 | + | 0.491940i | −0.999032 | + | 0.0440004i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.31864 | + | 8.31864i | −0.738160 | + | 0.738160i | −0.972222 | − | 0.234062i | \(-0.924798\pi\) |
0.234062 | + | 0.972222i | \(0.424798\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.55598 | + | 0.110866i | −0.662703 | + | 0.00972358i | ||||
\(131\) | −8.07719 | −0.705707 | −0.352854 | − | 0.935679i | \(-0.614789\pi\) | ||||
−0.352854 | + | 0.935679i | \(0.614789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6904 | − | 14.9122i | −1.10040 | − | 1.29305i | ||||
\(134\) | 1.39887i | 0.120844i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.20676i | 0.103478i | ||||||||
\(137\) | −6.99785 | − | 6.99785i | −0.597866 | − | 0.597866i | 0.341878 | − | 0.939744i | \(-0.388937\pi\) |
−0.939744 | + | 0.341878i | \(0.888937\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8866i | 0.923393i | 0.887038 | + | 0.461696i | \(0.152759\pi\) | ||||
−0.887038 | + | 0.461696i | \(0.847241\pi\) | |||||||
\(140\) | 6.99785 | − | 7.20626i | 0.591426 | − | 0.609040i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.35295 | − | 6.35295i | −0.533128 | − | 0.533128i | ||||
\(143\) | −3.58020 | − | 3.58020i | −0.299391 | − | 0.299391i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0829 | − | 0.177288i | 1.00343 | − | 0.0147230i | ||||
\(146\) | 15.9201i | 1.31756i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.29845 | + | 4.29845i | 0.353331 | + | 0.353331i | ||||
\(149\) | 12.6624i | 1.03735i | 0.854972 | + | 0.518674i | \(0.173574\pi\) | ||||
−0.854972 | + | 0.518674i | \(0.826426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.4280i | − | 1.25551i | −0.778411 | − | 0.627755i | \(-0.783974\pi\) | ||
0.778411 | − | 0.627755i | \(-0.216026\pi\) | |||||||
\(152\) | −2.82498 | − | 3.31956i | −0.229136 | − | 0.269252i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.73024 | 0.542338 | ||||||||
\(155\) | 0.0119492 | + | 0.814389i | 0.000959784 | + | 0.0654133i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.2948 | − | 13.2948i | −1.06104 | − | 1.06104i | −0.998012 | − | 0.0630301i | \(-0.979924\pi\) |
−0.0630301 | − | 0.998012i | \(-0.520076\pi\) | |||||||
\(158\) | −5.62374 | + | 5.62374i | −0.447401 | + | 0.447401i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.55777 | − | 1.60417i | 0.123153 | − | 0.126820i | ||||
\(161\) | 29.6980 | 2.34053 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0438073 | − | 0.0438073i | 0.00343125 | − | 0.00343125i | −0.705389 | − | 0.708820i | \(-0.749228\pi\) |
0.708820 | + | 0.705389i | \(0.249228\pi\) | |||||||
\(164\) | 1.79412 | 0.140097 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.57973i | 0.433071i | ||||||||
\(167\) | −6.61861 | + | 6.61861i | −0.512164 | + | 0.512164i | −0.915189 | − | 0.403025i | \(-0.867959\pi\) |
0.403025 | + | 0.915189i | \(0.367959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.57899i | − | 0.121461i | ||||||
\(170\) | 2.69810 | − | 0.0395881i | 0.206935 | − | 0.00303627i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.623738 | − | 0.623738i | −0.0475596 | − | 0.0475596i | ||||
\(173\) | −17.7594 | − | 17.7594i | −1.35022 | − | 1.35022i | −0.885412 | − | 0.464807i | \(-0.846124\pi\) |
−0.464807 | − | 0.885412i | \(-0.653876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.3415 | − | 15.4096i | −1.23530 | − | 1.16485i | ||||
\(176\) | 1.49820 | 0.112931 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.58252 | − | 6.58252i | 0.493381 | − | 0.493381i | ||||
\(179\) | −9.00631 | −0.673164 | −0.336582 | − | 0.941654i | \(-0.609271\pi\) | ||||
−0.336582 | + | 0.941654i | \(0.609271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.7616i | − | 1.39454i | −0.716808 | − | 0.697271i | \(-0.754398\pi\) | ||
0.716808 | − | 0.697271i | \(-0.245602\pi\) | |||||||
\(182\) | −10.7349 | − | 10.7349i | −0.795724 | − | 0.795724i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.61099 | 0.487369 | ||||||||
\(185\) | 9.46959 | − | 9.75161i | 0.696218 | − | 0.716953i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.27842 | + | 1.27842i | 0.0934875 | + | 0.0934875i | ||||
\(188\) | 5.24209 | − | 5.24209i | 0.382319 | − | 0.382319i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.32928 | + | 6.42508i | −0.531722 | + | 0.466124i | ||||
\(191\) | 6.38310 | 0.461865 | 0.230932 | − | 0.972970i | \(-0.425822\pi\) | ||||
0.230932 | + | 0.972970i | \(0.425822\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6976 | + | 15.6976i | 1.12994 | + | 1.12994i | 0.990186 | + | 0.139754i | \(0.0446311\pi\) |
0.139754 | + | 0.990186i | \(0.455369\pi\) | |||||||
\(194\) | 12.4444i | 0.893456i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.1800 | 0.941429 | ||||||||
\(197\) | −2.62159 | − | 2.62159i | −0.186780 | − | 0.186780i | 0.607522 | − | 0.794303i | \(-0.292164\pi\) |
−0.794303 | + | 0.607522i | \(0.792164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.73685i | 0.477563i | 0.971073 | + | 0.238781i | \(0.0767479\pi\) | ||||
−0.971073 | + | 0.238781i | \(0.923252\pi\) | |||||||
\(200\) | −3.63774 | − | 3.43028i | −0.257227 | − | 0.242558i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.54027 | + | 1.54027i | −0.108373 | + | 0.108373i | ||||
\(203\) | 17.1664 | + | 17.1664i | 1.20485 | + | 1.20485i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0588568 | − | 4.01134i | −0.00411073 | − | 0.280164i | ||||
\(206\) | −13.3619 | −0.930966 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.38967 | − | 2.38967i | −0.165694 | − | 0.165694i | ||||
\(209\) | −6.50945 | − | 0.523945i | −0.450268 | − | 0.0362420i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.1654i | − | 1.04403i | −0.852937 | − | 0.522013i | \(-0.825181\pi\) | ||
0.852937 | − | 0.522013i | \(-0.174819\pi\) | |||||||
\(212\) | 5.27391 | − | 5.27391i | 0.362213 | − | 0.362213i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 0.424610i | − | 0.0290258i | ||||||
\(215\) | −1.37411 | + | 1.41503i | −0.0937135 | + | 0.0965045i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.15702 | + | 1.15702i | −0.0785434 | + | 0.0785434i | ||||
\(218\) | −5.54050 | + | 5.54050i | −0.375250 | + | 0.375250i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0491491 | − | 3.34972i | −0.00331363 | − | 0.225838i | ||||
\(221\) | − | 4.07823i | − | 0.274332i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.90756 | + | 1.90756i | 0.127739 | + | 0.127739i | 0.768086 | − | 0.640347i | \(-0.221209\pi\) |
−0.640347 | + | 0.768086i | \(0.721209\pi\) | |||||||
\(224\) | 4.49222 | 0.300149 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.4806 | 1.16279 | ||||||||
\(227\) | 19.8625 | − | 19.8625i | 1.31832 | − | 1.31832i | 0.403212 | − | 0.915106i | \(-0.367894\pi\) |
0.915106 | − | 0.403212i | \(-0.132106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.0279i | 1.25740i | 0.777648 | + | 0.628700i | \(0.216413\pi\) | ||||
−0.777648 | + | 0.628700i | \(0.783587\pi\) | |||||||
\(230\) | −0.216876 | − | 14.7810i | −0.0143004 | − | 0.974633i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.82137 | + | 3.82137i | 0.250885 | + | 0.250885i | ||||
\(233\) | 8.22028 | − | 8.22028i | 0.538529 | − | 0.538529i | −0.384568 | − | 0.923097i | \(-0.625650\pi\) |
0.923097 | + | 0.384568i | \(0.125650\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8924 | − | 11.5484i | −0.775773 | − | 0.753337i | ||||
\(236\) | 1.49134i | 0.0970781i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.83323 | + | 3.83323i | 0.248472 | + | 0.248472i | ||||
\(239\) | − | 5.40164i | − | 0.349403i | −0.984621 | − | 0.174702i | \(-0.944104\pi\) | ||
0.984621 | − | 0.174702i | \(-0.0558961\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.3252i | 1.56692i | 0.621440 | + | 0.783462i | \(0.286548\pi\) | ||||
−0.621440 | + | 0.783462i | \(0.713452\pi\) | |||||||
\(242\) | −6.19100 | + | 6.19100i | −0.397973 | + | 0.397973i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 15.2432i | − | 0.975844i | ||||||
\(245\) | −0.432375 | − | 29.4682i | −0.0276235 | − | 1.88266i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.54703 | + | 11.2184i | 0.607463 | + | 0.713812i | ||||
\(248\) | −0.257560 | + | 0.257560i | −0.0163551 | + | 0.0163551i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.55018 | + | 8.24589i | −0.477516 | + | 0.521516i | ||||
\(251\) | 28.4372 | 1.79494 | 0.897470 | − | 0.441075i | \(-0.145403\pi\) | ||||
0.897470 | + | 0.441075i | \(0.145403\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.00360 | − | 7.00360i | 0.440313 | − | 0.440313i | ||||
\(254\) | 11.7643i | 0.738160i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.1711 | + | 14.1711i | −0.883966 | + | 0.883966i | −0.993935 | − | 0.109969i | \(-0.964925\pi\) |
0.109969 | + | 0.993935i | \(0.464925\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.3079 | 1.69683 | ||||||||
\(260\) | −5.26449 | + | 5.42128i | −0.326490 | + | 0.336213i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.71144 | + | 5.71144i | −0.352854 | + | 0.352854i | ||||
\(263\) | 3.16396 | − | 3.16396i | 0.195098 | − | 0.195098i | −0.602797 | − | 0.797895i | \(-0.705947\pi\) |
0.797895 | + | 0.602797i | \(0.205947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.9646 | − | 11.6185i | −0.734977 | − | 0.713721i | ||||
\(266\) | −19.5180 | − | 1.57100i | −1.19673 | − | 0.0963243i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.989147 | + | 0.989147i | 0.0604218 | + | 0.0604218i | ||||
\(269\) | 5.14967 | 0.313981 | 0.156990 | − | 0.987600i | \(-0.449821\pi\) | ||||
0.156990 | + | 0.987600i | \(0.449821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.33799 | −0.567242 | −0.283621 | − | 0.958936i | \(-0.591536\pi\) | ||||
−0.283621 | + | 0.958936i | \(0.591536\pi\) | |||||||
\(272\) | 0.853306 | + | 0.853306i | 0.0517392 | + | 0.0517392i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.89645 | −0.597866 | ||||||||
\(275\) | −7.48777 | + | 0.219778i | −0.451530 | + | 0.0132531i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.94186 | + | 6.94186i | 0.417096 | + | 0.417096i | 0.884202 | − | 0.467106i | \(-0.154703\pi\) |
−0.467106 | + | 0.884202i | \(0.654703\pi\) | |||||||
\(278\) | 7.69802 | + | 7.69802i | 0.461696 | + | 0.461696i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.147369 | − | 10.0438i | −0.00880698 | − | 0.600233i | ||||
\(281\) | − | 13.9366i | − | 0.831390i | −0.909504 | − | 0.415695i | \(-0.863538\pi\) | ||
0.909504 | − | 0.415695i | \(-0.136462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0086 | + | 13.0086i | −0.773280 | + | 0.773280i | −0.978678 | − | 0.205399i | \(-0.934151\pi\) |
0.205399 | + | 0.978678i | \(0.434151\pi\) | |||||||
\(284\) | −8.98443 | −0.533128 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.06316 | −0.299391 | ||||||||
\(287\) | 5.69897 | − | 5.69897i | 0.336400 | − | 0.336400i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.5437i | − | 0.914338i | ||||||
\(290\) | 8.41856 | − | 8.66929i | 0.494355 | − | 0.509078i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.2572 | + | 11.2572i | 0.658778 | + | 0.658778i | ||||
\(293\) | −11.5186 | − | 11.5186i | −0.672924 | − | 0.672924i | 0.285465 | − | 0.958389i | \(-0.407852\pi\) |
−0.958389 | + | 0.285465i | \(0.907852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.33438 | − | 0.0489241i | 0.194135 | − | 0.00284847i | ||||
\(296\) | 6.07893 | 0.353331 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.95370 | + | 8.95370i | 0.518674 | + | 0.518674i | ||||
\(299\) | −22.3418 | −1.29206 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.96258 | −0.228399 | ||||||||
\(302\) | −10.9092 | − | 10.9092i | −0.627755 | − | 0.627755i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.34485 | − | 0.349716i | −0.249194 | − | 0.0200576i | ||||
\(305\) | −34.0811 | + | 0.500058i | −1.95148 | + | 0.0286333i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8832 | − | 19.8832i | 1.13480 | − | 1.13480i | 0.145427 | − | 0.989369i | \(-0.453545\pi\) |
0.989369 | − | 0.145427i | \(-0.0464555\pi\) | |||||||
\(308\) | 4.75900 | − | 4.75900i | 0.271169 | − | 0.271169i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.584310 | + | 0.567411i | 0.0331866 | + | 0.0322268i | ||||
\(311\) | −25.6191 | −1.45272 | −0.726362 | − | 0.687312i | \(-0.758790\pi\) | ||||
−0.726362 | + | 0.687312i | \(0.758790\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.42367 | + | 1.42367i | −0.0804705 | + | 0.0804705i | −0.746196 | − | 0.665726i | \(-0.768122\pi\) |
0.665726 | + | 0.746196i | \(0.268122\pi\) | |||||||
\(314\) | −18.8017 | −1.06104 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.95317i | 0.447401i | ||||||||
\(317\) | −22.0096 | + | 22.0096i | −1.23618 | + | 1.23618i | −0.274630 | + | 0.961550i | \(0.588555\pi\) |
−0.961550 | + | 0.274630i | \(0.911445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.09662 | 0.453324 | ||||||||
\(320\) | −0.0328054 | − | 2.23583i | −0.00183388 | − | 0.124987i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 20.9997 | − | 20.9997i | 1.17027 | − | 1.17027i | ||||
\(323\) | −3.40907 | − | 4.00590i | −0.189686 | − | 0.222894i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.2937 | + | 11.5926i | 0.681934 | + | 0.643044i | ||||
\(326\) | − | 0.0619528i | − | 0.00343125i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.26863 | − | 1.26863i | 0.0700485 | − | 0.0700485i | ||||
\(329\) | − | 33.3027i | − | 1.83604i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0483i | 1.04699i | 0.852028 | + | 0.523496i | \(0.175372\pi\) | ||||
−0.852028 | + | 0.523496i | \(0.824628\pi\) | |||||||
\(332\) | 3.94546 | + | 3.94546i | 0.216535 | + | 0.216535i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.36013i | 0.512164i | ||||||||
\(335\) | 2.17911 | − | 2.24401i | 0.119058 | − | 0.122603i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.2649 | + | 10.2649i | −0.559164 | + | 0.559164i | −0.929069 | − | 0.369905i | \(-0.879390\pi\) |
0.369905 | + | 0.929069i | \(0.379390\pi\) | |||||||
\(338\) | −1.11651 | − | 1.11651i | −0.0607304 | − | 0.0607304i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.87985 | − | 1.93584i | 0.101949 | − | 0.104985i | ||||
\(341\) | 0.545712i | 0.0295520i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6306 | − | 19.6306i | 1.05996 | − | 1.05996i | ||||
\(344\) | −0.882099 | −0.0475596 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.1155 | −1.35022 | ||||||||
\(347\) | 21.2020 | + | 21.2020i | 1.13818 | + | 1.13818i | 0.988776 | + | 0.149404i | \(0.0477356\pi\) |
0.149404 | + | 0.988776i | \(0.452264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.7333i | 1.05630i | 0.849152 | + | 0.528148i | \(0.177114\pi\) | ||||
−0.849152 | + | 0.528148i | \(0.822886\pi\) | |||||||
\(350\) | −22.4514 | + | 0.658983i | −1.20008 | + | 0.0352241i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.05939 | − | 1.05939i | 0.0564655 | − | 0.0564655i | ||||
\(353\) | −18.4563 | + | 18.4563i | −0.982329 | + | 0.982329i | −0.999847 | − | 0.0175180i | \(-0.994424\pi\) |
0.0175180 | + | 0.999847i | \(0.494424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.294738 | + | 20.0876i | 0.0156431 | + | 1.06614i | ||||
\(356\) | − | 9.30909i | − | 0.493381i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.36843 | + | 6.36843i | −0.336582 | + | 0.336582i | ||||
\(359\) | − | 1.52209i | − | 0.0803327i | −0.999193 | − | 0.0401663i | \(-0.987211\pi\) | ||
0.999193 | − | 0.0401663i | \(-0.0127888\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7554 | + | 3.03893i | 0.987126 | + | 0.159944i | ||||
\(362\) | −13.2665 | − | 13.2665i | −0.697271 | − | 0.697271i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.1814 | −0.795724 | ||||||||
\(365\) | 24.7999 | − | 25.5384i | 1.29808 | − | 1.33674i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.6342 | − | 15.6342i | −0.816099 | − | 0.816099i | 0.169442 | − | 0.985540i | \(-0.445804\pi\) |
−0.985540 | + | 0.169442i | \(0.945804\pi\) | |||||||
\(368\) | 4.67468 | − | 4.67468i | 0.243684 | − | 0.243684i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.199422 | − | 13.5914i | −0.0103674 | − | 0.706585i | ||||
\(371\) | − | 33.5049i | − | 1.73949i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.2074 | − | 10.2074i | −0.528520 | − | 0.528520i | 0.391611 | − | 0.920131i | \(-0.371918\pi\) |
−0.920131 | + | 0.391611i | \(0.871918\pi\) | |||||||
\(374\) | 1.80796 | 0.0934875 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 7.41343i | − | 0.382319i | ||||||
\(377\) | −12.9143 | − | 12.9143i | −0.665121 | − | 0.665121i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3997 | −0.893762 | −0.446881 | − | 0.894593i | \(-0.647465\pi\) | ||||
−0.446881 | + | 0.894593i | \(0.647465\pi\) | |||||||
\(380\) | −0.639371 | + | 9.72580i | −0.0327990 | + | 0.498923i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.51353 | − | 4.51353i | 0.230932 | − | 0.230932i | ||||
\(383\) | 14.2959 | + | 14.2959i | 0.730485 | + | 0.730485i | 0.970716 | − | 0.240231i | \(-0.0772230\pi\) |
−0.240231 | + | 0.970716i | \(0.577223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.7964 | − | 10.4842i | −0.550236 | − | 0.534323i | ||||
\(386\) | 22.1998 | 1.12994 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.79952 | + | 8.79952i | 0.446728 | + | 0.446728i | ||||
\(389\) | 11.0275i | 0.559116i | 0.960129 | + | 0.279558i | \(0.0901879\pi\) | ||||
−0.960129 | + | 0.279558i | \(0.909812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.97786 | 0.403457 | ||||||||
\(392\) | 9.31967 | − | 9.31967i | 0.470715 | − | 0.470715i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.70748 | −0.186780 | ||||||||
\(395\) | 17.7819 | − | 0.260907i | 0.894705 | − | 0.0131276i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.09266 | − | 1.09266i | −0.0548392 | − | 0.0548392i | 0.679155 | − | 0.733995i | \(-0.262346\pi\) |
−0.733995 | + | 0.679155i | \(0.762346\pi\) | |||||||
\(398\) | 4.76367 | + | 4.76367i | 0.238781 | + | 0.238781i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.99785 | + | 0.146694i | −0.249892 | + | 0.00733472i | ||||
\(401\) | 13.6821i | 0.683249i | 0.939836 | + | 0.341625i | \(0.110977\pi\) | ||||
−0.939836 | + | 0.341625i | \(0.889023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.870424 | − | 0.870424i | 0.0433589 | − | 0.0433589i | ||||
\(404\) | 2.17827i | 0.108373i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.2770 | 1.20485 | ||||||||
\(407\) | 6.43994 | − | 6.43994i | 0.319216 | − | 0.319216i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.9275 | −0.688673 | −0.344336 | − | 0.938846i | \(-0.611896\pi\) | ||||
−0.344336 | + | 0.938846i | \(0.611896\pi\) | |||||||
\(410\) | −2.87806 | − | 2.79483i | −0.142137 | − | 0.138027i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.44827 | + | 9.44827i | −0.465483 | + | 0.465483i | ||||
\(413\) | 4.73721 | + | 4.73721i | 0.233103 | + | 0.233103i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.69194 | − | 8.95080i | 0.426670 | − | 0.439378i | ||||
\(416\) | −3.37950 | −0.165694 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.97336 | + | 4.23239i | −0.243255 | + | 0.207013i | ||||
\(419\) | − | 31.7859i | − | 1.55284i | −0.630215 | − | 0.776421i | \(-0.717033\pi\) | ||
0.630215 | − | 0.776421i | \(-0.282967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.9617i | 1.46025i | 0.683316 | + | 0.730123i | \(0.260537\pi\) | ||||
−0.683316 | + | 0.730123i | \(0.739463\pi\) | |||||||
\(422\) | −10.7235 | − | 10.7235i | −0.522013 | − | 0.522013i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 7.45843i | − | 0.362213i | ||||||
\(425\) | −4.38987 | − | 4.13952i | −0.212940 | − | 0.200796i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.4196 | − | 48.4196i | −2.34319 | − | 2.34319i | ||||
\(428\) | −0.300245 | − | 0.300245i | −0.0145129 | − | 0.0145129i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0289376 | + | 1.97222i | 0.00139550 | + | 0.0951090i | ||||
\(431\) | 19.4154i | 0.935207i | 0.883938 | + | 0.467603i | \(0.154882\pi\) | ||||
−0.883938 | + | 0.467603i | \(0.845118\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.53848 | − | 5.53848i | −0.266162 | − | 0.266162i | 0.561390 | − | 0.827552i | \(-0.310267\pi\) |
−0.827552 | + | 0.561390i | \(0.810267\pi\) | |||||||
\(434\) | 1.63627i | 0.0785434i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.83545i | 0.375250i | ||||||||
\(437\) | −21.9456 | + | 18.6759i | −1.04980 | + | 0.893392i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.2533 | −0.918908 | −0.459454 | − | 0.888202i | \(-0.651955\pi\) | ||||
−0.459454 | + | 0.888202i | \(0.651955\pi\) | |||||||
\(440\) | −2.40336 | − | 2.33385i | −0.114576 | − | 0.111262i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.88374 | − | 2.88374i | −0.137166 | − | 0.137166i | ||||
\(443\) | 0.822360 | − | 0.822360i | 0.0390715 | − | 0.0390715i | −0.687301 | − | 0.726373i | \(-0.741205\pi\) |
0.726373 | + | 0.687301i | \(0.241205\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.8135 | + | 0.305388i | −0.986655 | + | 0.0144768i | ||||
\(446\) | 2.69769 | 0.127739 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.17648 | − | 3.17648i | 0.150074 | − | 0.150074i | ||||
\(449\) | 34.0243 | 1.60570 | 0.802852 | − | 0.596178i | \(-0.203315\pi\) | ||||
0.802852 | + | 0.596178i | \(0.203315\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.68795i | − | 0.126570i | ||||||
\(452\) | 12.3606 | − | 12.3606i | 0.581395 | − | 0.581395i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 28.0898i | − | 1.31832i | ||||||
\(455\) | 0.498033 | + | 33.9431i | 0.0233482 | + | 1.59128i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.2360 | + | 26.2360i | 1.22727 | + | 1.22727i | 0.964994 | + | 0.262273i | \(0.0844722\pi\) |
0.262273 | + | 0.964994i | \(0.415528\pi\) | |||||||
\(458\) | 13.4548 | + | 13.4548i | 0.628700 | + | 0.628700i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.6051 | − | 10.2984i | −0.494466 | − | 0.480166i | ||||
\(461\) | 26.7535 | 1.24604 | 0.623018 | − | 0.782207i | \(-0.285906\pi\) | ||||
0.623018 | + | 0.782207i | \(0.285906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5215 | + | 16.5215i | −0.767820 | + | 0.767820i | −0.977722 | − | 0.209902i | \(-0.932685\pi\) |
0.209902 | + | 0.977722i | \(0.432685\pi\) | |||||||
\(464\) | 5.40423 | 0.250885 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 11.6252i | − | 0.538529i | ||||||
\(467\) | −6.89955 | − | 6.89955i | −0.319273 | − | 0.319273i | 0.529215 | − | 0.848488i | \(-0.322487\pi\) |
−0.848488 | + | 0.529215i | \(0.822487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.28401 | 0.290168 | ||||||||
\(470\) | −16.5752 | + | 0.243201i | −0.764555 | + | 0.0112180i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.05454 | + | 1.05454i | 0.0485391 | + | 0.0485391i | ||||
\(473\) | −0.934485 | + | 0.934485i | −0.0429677 | + | 0.0429677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.7662 | + | 1.11046i | 0.998701 | + | 0.0509516i | ||||
\(476\) | 5.42101 | 0.248472 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.81954 | − | 3.81954i | −0.174702 | − | 0.174702i | ||||
\(479\) | 10.1104i | 0.461958i | 0.972959 | + | 0.230979i | \(0.0741929\pi\) | ||||
−0.972959 | + | 0.230979i | \(0.925807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.5437 | −0.936714 | ||||||||
\(482\) | 17.2005 | + | 17.2005i | 0.783462 | + | 0.783462i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.75540i | 0.397973i | ||||||||
\(485\) | 19.3855 | − | 19.9629i | 0.880252 | − | 0.906468i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.5066 | + | 19.5066i | −0.883928 | + | 0.883928i | −0.993931 | − | 0.110003i | \(-0.964914\pi\) |
0.110003 | + | 0.993931i | \(0.464914\pi\) | |||||||
\(488\) | −10.7786 | − | 10.7786i | −0.487922 | − | 0.487922i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.1429 | − | 20.5314i | −0.955140 | − | 0.927516i | ||||
\(491\) | 14.0700 | 0.634970 | 0.317485 | − | 0.948263i | \(-0.397162\pi\) | ||||
0.317485 | + | 0.948263i | \(0.397162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.61146 | + | 4.61146i | 0.207690 | + | 0.207690i | ||||
\(494\) | 14.6834 | + | 1.18187i | 0.660638 | + | 0.0531747i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.364245i | 0.0163551i | ||||||||
\(497\) | −28.5388 | + | 28.5388i | −1.28014 | + | 1.28014i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.43607i | − | 0.198586i | −0.995058 | − | 0.0992929i | \(-0.968342\pi\) | ||
0.995058 | − | 0.0992929i | \(-0.0316581\pi\) | |||||||
\(500\) | 0.491940 | + | 11.1695i | 0.0220002 | + | 0.499516i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.1081 | − | 20.1081i | 0.897470 | − | 0.897470i | ||||
\(503\) | 3.35985 | − | 3.35985i | 0.149808 | − | 0.149808i | −0.628224 | − | 0.778032i | \(-0.716218\pi\) |
0.778032 | + | 0.628224i | \(0.216218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.87023 | − | 0.0714589i | 0.216722 | − | 0.00317988i | ||||
\(506\) | − | 9.90459i | − | 0.440313i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.31864 | + | 8.31864i | 0.369080 | + | 0.369080i | ||||
\(509\) | −37.6552 | −1.66904 | −0.834519 | − | 0.550979i | \(-0.814254\pi\) | ||||
−0.834519 | + | 0.550979i | \(0.814254\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 71.5164 | 3.16370 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.0409i | 0.883966i | ||||||||
\(515\) | 21.4347 | + | 20.8147i | 0.944524 | + | 0.917207i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.85370 | − | 7.85370i | −0.345405 | − | 0.345405i | ||||
\(518\) | 19.3096 | − | 19.3096i | 0.848414 | − | 0.848414i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.110866 | + | 7.55598i | 0.00486179 | + | 0.331351i | ||||
\(521\) | − | 27.2139i | − | 1.19226i | −0.802887 | − | 0.596131i | \(-0.796704\pi\) | ||
0.802887 | − | 0.596131i | \(-0.203296\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9984 | − | 11.9984i | −0.524655 | − | 0.524655i | 0.394319 | − | 0.918974i | \(-0.370981\pi\) |
−0.918974 | + | 0.394319i | \(0.870981\pi\) | |||||||
\(524\) | 8.07719i | 0.352854i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 4.47451i | − | 0.195098i | ||||||
\(527\) | −0.310812 | + | 0.310812i | −0.0135392 | + | 0.0135392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 20.7052i | − | 0.900226i | ||||||
\(530\) | −16.6758 | + | 0.244677i | −0.724349 | + | 0.0106281i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.9122 | + | 12.6904i | −0.646525 | + | 0.550200i | ||||
\(533\) | −4.28734 | + | 4.28734i | −0.185705 | + | 0.185705i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.661446 | + | 0.681146i | −0.0285968 | + | 0.0294485i | ||||
\(536\) | 1.39887 | 0.0604218 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.64136 | − | 3.64136i | 0.156990 | − | 0.156990i | ||||
\(539\) | − | 19.7463i | − | 0.850533i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.33439 | −0.100363 | −0.0501816 | − | 0.998740i | \(-0.515980\pi\) | ||||
−0.0501816 | + | 0.998740i | \(0.515980\pi\) | |||||||
\(542\) | −6.60295 | + | 6.60295i | −0.283621 | + | 0.283621i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.20676 | 0.0517392 | ||||||||
\(545\) | 17.5187 | − | 0.257045i | 0.750420 | − | 0.0110106i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.46036 | − | 8.46036i | 0.361739 | − | 0.361739i | −0.502714 | − | 0.864453i | \(-0.667665\pi\) |
0.864453 | + | 0.502714i | \(0.167665\pi\) | |||||||
\(548\) | −6.99785 | + | 6.99785i | −0.298933 | + | 0.298933i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.13925 | + | 5.45006i | −0.219138 | + | 0.232391i | ||||
\(551\) | −23.4806 | − | 1.88995i | −1.00031 | − | 0.0805145i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.2630 | + | 25.2630i | 1.07429 | + | 1.07429i | ||||
\(554\) | 9.81727 | 0.417096 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.8866 | 0.461696 | ||||||||
\(557\) | −14.2030 | − | 14.2030i | −0.601801 | − | 0.601801i | 0.338989 | − | 0.940790i | \(-0.389915\pi\) |
−0.940790 | + | 0.338989i | \(0.889915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.98105 | 0.126085 | ||||||||
\(560\) | −7.20626 | − | 6.99785i | −0.304520 | − | 0.295713i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.85468 | − | 9.85468i | −0.415695 | − | 0.415695i | ||||
\(563\) | −30.8429 | − | 30.8429i | −1.29987 | − | 1.29987i | −0.928472 | − | 0.371401i | \(-0.878877\pi\) |
−0.371401 | − | 0.928472i | \(-0.621123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.0417 | − | 27.2307i | −1.17972 | − | 1.14561i | ||||
\(566\) | 18.3969i | 0.773280i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.35295 | + | 6.35295i | −0.266564 | + | 0.266564i | ||||
\(569\) | 13.5457 | 0.567864 | 0.283932 | − | 0.958844i | \(-0.408361\pi\) | ||||
0.283932 | + | 0.958844i | \(0.408361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5825 | 0.442863 | 0.221431 | − | 0.975176i | \(-0.428927\pi\) | ||||
0.221431 | + | 0.975176i | \(0.428927\pi\) | |||||||
\(572\) | −3.58020 | + | 3.58020i | −0.149696 | + | 0.149696i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 8.05956i | − | 0.336400i | ||||||
\(575\) | −22.6776 | + | 24.0491i | −0.945720 | + | 1.00292i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.85640 | − | 4.85640i | −0.202175 | − | 0.202175i | 0.598757 | − | 0.800931i | \(-0.295662\pi\) |
−0.800931 | + | 0.598757i | \(0.795662\pi\) | |||||||
\(578\) | −10.9911 | − | 10.9911i | −0.457169 | − | 0.457169i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.177288 | − | 12.0829i | −0.00736149 | − | 0.501717i | ||||
\(581\) | 25.0653 | 1.03989 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.90137 | − | 7.90137i | −0.327241 | − | 0.327241i | ||||
\(584\) | 15.9201 | 0.658778 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.2898 | −0.672924 | ||||||||
\(587\) | −7.59468 | − | 7.59468i | −0.313466 | − | 0.313466i | 0.532785 | − | 0.846251i | \(-0.321146\pi\) |
−0.846251 | + | 0.532785i | \(0.821146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.127383 | − | 1.58259i | 0.00524870 | − | 0.0652095i | ||||
\(590\) | 2.32317 | − | 2.39236i | 0.0956434 | − | 0.0984919i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.29845 | − | 4.29845i | 0.176665 | − | 0.176665i | ||||
\(593\) | −16.8852 | + | 16.8852i | −0.693392 | + | 0.693392i | −0.962977 | − | 0.269585i | \(-0.913114\pi\) |
0.269585 | + | 0.962977i | \(0.413114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.177838 | − | 12.1204i | −0.00729066 | − | 0.496890i | ||||
\(596\) | 12.6624 | 0.518674 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.7981 | + | 15.7981i | −0.646031 | + | 0.646031i | ||||
\(599\) | 40.3029 | 1.64673 | 0.823365 | − | 0.567512i | \(-0.192094\pi\) | ||||
0.823365 | + | 0.567512i | \(0.192094\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 37.1125i | − | 1.51385i | −0.653503 | − | 0.756924i | \(-0.726701\pi\) | ||
0.653503 | − | 0.756924i | \(-0.273299\pi\) | |||||||
\(602\) | −2.80197 | + | 2.80197i | −0.114200 | + | 0.114200i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.4280 | −0.627755 | ||||||||
\(605\) | 19.5756 | − | 0.287224i | 0.795860 | − | 0.0116773i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.9049 | − | 21.9049i | 0.889091 | − | 0.889091i | −0.105345 | − | 0.994436i | \(-0.533595\pi\) |
0.994436 | + | 0.105345i | \(0.0335945\pi\) | |||||||
\(608\) | −3.31956 | + | 2.82498i | −0.134626 | + | 0.114568i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.7454 | + | 24.4526i | −0.961422 | + | 0.990056i | ||||
\(611\) | 25.0537i | 1.01356i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.66633 | − | 3.66633i | 0.148082 | − | 0.148082i | −0.629179 | − | 0.777261i | \(-0.716609\pi\) |
0.777261 | + | 0.629179i | \(0.216609\pi\) | |||||||
\(614\) | − | 28.1191i | − | 1.13480i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 6.73024i | − | 0.271169i | ||||||
\(617\) | 21.5484 | + | 21.5484i | 0.867507 | + | 0.867507i | 0.992196 | − | 0.124689i | \(-0.0397932\pi\) |
−0.124689 | + | 0.992196i | \(0.539793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.0888i | 0.928017i | 0.885831 | + | 0.464008i | \(0.153589\pi\) | ||||
−0.885831 | + | 0.464008i | \(0.846411\pi\) | |||||||
\(620\) | 0.814389 | − | 0.0119492i | 0.0327067 | − | 0.000479892i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.1154 | + | 18.1154i | −0.726362 | + | 0.726362i | ||||
\(623\) | −29.5701 | − | 29.5701i | −1.18470 | − | 1.18470i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9570 | − | 1.46631i | 0.998278 | − | 0.0586525i | ||||
\(626\) | 2.01337i | 0.0804705i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.2948 | + | 13.2948i | −0.530521 | + | 0.530521i | ||||
\(629\) | 7.33579 | 0.292497 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.3658 | 1.48751 | 0.743754 | − | 0.668453i | \(-0.233043\pi\) | ||||
0.743754 | + | 0.668453i | \(0.233043\pi\) | |||||||
\(632\) | 5.62374 | + | 5.62374i | 0.223700 | + | 0.223700i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.1262i | 1.23618i | ||||||||
\(635\) | 18.3262 | − | 18.8719i | 0.727251 | − | 0.748910i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.4958 | + | 31.4958i | −1.24791 | + | 1.24791i | ||||
\(638\) | 5.72518 | − | 5.72518i | 0.226662 | − | 0.226662i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.60417 | − | 1.55777i | −0.0634102 | − | 0.0615763i | ||||
\(641\) | 35.6140i | 1.40667i | 0.710859 | + | 0.703335i | \(0.248307\pi\) | ||||
−0.710859 | + | 0.703335i | \(0.751693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.3543 | + | 35.3543i | −1.39424 | + | 1.39424i | −0.578694 | + | 0.815545i | \(0.696437\pi\) |
−0.815545 | + | 0.578694i | \(0.803563\pi\) | |||||||
\(644\) | − | 29.6980i | − | 1.17027i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.24317 | − | 0.422022i | −0.206290 | − | 0.0166042i | ||||
\(647\) | −20.9716 | − | 20.9716i | −0.824480 | − | 0.824480i | 0.162267 | − | 0.986747i | \(-0.448120\pi\) |
−0.986747 | + | 0.162267i | \(0.948120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.23433 | 0.0877051 | ||||||||
\(650\) | 16.8902 | − | 0.495754i | 0.662489 | − | 0.0194451i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0438073 | − | 0.0438073i | −0.00171563 | − | 0.00171563i | ||||
\(653\) | −31.2511 | + | 31.2511i | −1.22295 | + | 1.22295i | −0.256372 | + | 0.966578i | \(0.582527\pi\) |
−0.966578 | + | 0.256372i | \(0.917473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.0592 | − | 0.264975i | 0.705631 | − | 0.0103534i | ||||
\(656\) | − | 1.79412i | − | 0.0700485i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −23.5486 | − | 23.5486i | −0.918020 | − | 0.918020i | ||||
\(659\) | 32.1135 | 1.25097 | 0.625483 | − | 0.780238i | \(-0.284902\pi\) | ||||
0.625483 | + | 0.780238i | \(0.284902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.31818i | 0.0512712i | 0.999671 | + | 0.0256356i | \(0.00816097\pi\) | ||||
−0.999671 | + | 0.0256356i | \(0.991839\pi\) | |||||||
\(662\) | 13.4692 | + | 13.4692i | 0.523496 | + | 0.523496i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.57973 | 0.216535 | ||||||||
\(665\) | 28.8628 | + | 32.9247i | 1.11925 | + | 1.27677i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.2630 | − | 25.2630i | 0.978189 | − | 0.978189i | ||||
\(668\) | 6.61861 | + | 6.61861i | 0.256082 | + | 0.256082i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.0458903 | − | 3.12762i | −0.00177290 | − | 0.120831i | ||||
\(671\) | −22.8373 | −0.881625 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.51419 | − | 2.51419i | −0.0969147 | − | 0.0969147i | 0.656987 | − | 0.753902i | \(-0.271831\pi\) |
−0.753902 | + | 0.656987i | \(0.771831\pi\) | |||||||
\(674\) | 14.5167i | 0.559164i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.57899 | −0.0607304 | ||||||||
\(677\) | −18.7510 | + | 18.7510i | −0.720658 | + | 0.720658i | −0.968739 | − | 0.248081i | \(-0.920200\pi\) |
0.248081 | + | 0.968739i | \(0.420200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 55.9030 | 2.14536 | ||||||||
\(680\) | −0.0395881 | − | 2.69810i | −0.00151814 | − | 0.103467i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.385877 | + | 0.385877i | 0.0147760 | + | 0.0147760i | ||||
\(683\) | −17.3262 | − | 17.3262i | −0.662968 | − | 0.662968i | 0.293110 | − | 0.956079i | \(-0.405310\pi\) |
−0.956079 | + | 0.293110i | \(0.905310\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.8755 | + | 15.4164i | 0.606573 | + | 0.589031i | ||||
\(686\) | − | 27.7619i | − | 1.05996i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.623738 | + | 0.623738i | −0.0237798 | + | 0.0237798i | ||||
\(689\) | 25.2058i | 0.960263i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.3859 | −0.395097 | −0.197549 | − | 0.980293i | \(-0.563298\pi\) | ||||
−0.197549 | + | 0.980293i | \(0.563298\pi\) | |||||||
\(692\) | −17.7594 | + | 17.7594i | −0.675110 | + | 0.675110i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 29.9841 | 1.13818 | ||||||||
\(695\) | −0.357141 | − | 24.3406i | −0.0135471 | − | 0.923293i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.53093 | − | 1.53093i | 0.0579881 | − | 0.0579881i | ||||
\(698\) | 13.9535 | + | 13.9535i | 0.528148 | + | 0.528148i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15.4096 | + | 16.3415i | −0.582427 | + | 0.617651i | ||||
\(701\) | −31.8741 | −1.20387 | −0.601934 | − | 0.798546i | \(-0.705603\pi\) | ||||
−0.601934 | + | 0.798546i | \(0.705603\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.1794 | + | 17.1729i | −0.761079 | + | 0.647688i | ||||
\(704\) | − | 1.49820i | − | 0.0564655i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.1011i | 0.982329i | ||||||||
\(707\) | 6.91921 | + | 6.91921i | 0.260224 | + | 0.260224i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.1134i | 0.492483i | 0.969209 | + | 0.246241i | \(0.0791956\pi\) | ||||
−0.969209 | + | 0.246241i | \(0.920804\pi\) | |||||||
\(710\) | 14.4125 | + | 13.9957i | 0.540892 | + | 0.525249i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.58252 | − | 6.58252i | −0.246690 | − | 0.246690i | ||||
\(713\) | 1.70273 | + | 1.70273i | 0.0637677 | + | 0.0637677i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.12215 | + | 7.88725i | 0.303751 | + | 0.294967i | ||||
\(716\) | 9.00631i | 0.336582i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.07628 | − | 1.07628i | −0.0401663 | − | 0.0401663i | ||||
\(719\) | 16.8894i | 0.629869i | 0.949113 | + | 0.314935i | \(0.101983\pi\) | ||||
−0.949113 | + | 0.314935i | \(0.898017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 60.0244i | 2.23543i | ||||||||
\(722\) | 15.4109 | − | 11.1132i | 0.573535 | − | 0.413591i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.7616 | −0.697271 | ||||||||
\(725\) | −27.0095 | + | 0.792771i | −1.00311 | + | 0.0294428i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7209 | + | 10.7209i | 0.397617 | + | 0.397617i | 0.877392 | − | 0.479775i | \(-0.159282\pi\) |
−0.479775 | + | 0.877392i | \(0.659282\pi\) | |||||||
\(728\) | −10.7349 | + | 10.7349i | −0.397862 | + | 0.397862i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.522265 | − | 35.5946i | −0.0193299 | − | 1.31741i | ||||
\(731\) | −1.06448 | −0.0393712 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.7783 | + | 24.7783i | −0.915207 | + | 0.915207i | −0.996676 | − | 0.0814690i | \(-0.974039\pi\) |
0.0814690 | + | 0.996676i | \(0.474039\pi\) | |||||||
\(734\) | −22.1101 | −0.816099 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.61099i | − | 0.243684i | ||||||
\(737\) | 1.48194 | − | 1.48194i | 0.0545880 | − | 0.0545880i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 0.497280i | − | 0.0182928i | −0.999958 | − | 0.00914638i | \(-0.997089\pi\) | ||
0.999958 | − | 0.00914638i | \(-0.00291142\pi\) | |||||||
\(740\) | −9.75161 | − | 9.46959i | −0.358476 | − | 0.348109i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.6915 | − | 23.6915i | −0.869743 | − | 0.869743i | ||||
\(743\) | −15.6060 | − | 15.6060i | −0.572529 | − | 0.572529i | 0.360305 | − | 0.932835i | \(-0.382673\pi\) |
−0.932835 | + | 0.360305i | \(0.882673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.415396 | − | 28.3110i | −0.0152189 | − | 1.03724i | ||||
\(746\) | −14.4355 | −0.528520 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.27842 | − | 1.27842i | 0.0467438 | − | 0.0467438i | ||||
\(749\) | −1.90744 | −0.0696964 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5.39804i | − | 0.196977i | −0.995138 | − | 0.0984887i | \(-0.968599\pi\) | ||
0.995138 | − | 0.0984887i | \(-0.0314008\pi\) | |||||||
\(752\) | −5.24209 | − | 5.24209i | −0.191159 | − | 0.191159i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.2636 | −0.665121 | ||||||||
\(755\) | 0.506121 | + | 34.4943i | 0.0184196 | + | 1.25538i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.00432 | − | 3.00432i | −0.109194 | − | 0.109194i | 0.650399 | − | 0.759593i | \(-0.274602\pi\) |
−0.759593 | + | 0.650399i | \(0.774602\pi\) | |||||||
\(758\) | −12.3034 | + | 12.3034i | −0.446881 | + | 0.446881i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.42508 | + | 7.32928i | 0.233062 | + | 0.265861i | ||||
\(761\) | 9.42821 | 0.341772 | 0.170886 | − | 0.985291i | \(-0.445337\pi\) | ||||
0.170886 | + | 0.985291i | \(0.445337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.8891 | + | 24.8891i | 0.901047 | + | 0.901047i | ||||
\(764\) | − | 6.38310i | − | 0.230932i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.2174 | 0.730485 | ||||||||
\(767\) | −3.56381 | − | 3.56381i | −0.128682 | − | 0.128682i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.1986i | − | 0.908683i | −0.890828 | − | 0.454342i | \(-0.849875\pi\) | ||
0.890828 | − | 0.454342i | \(-0.150125\pi\) | |||||||
\(770\) | −15.0477 | + | 0.220788i | −0.542280 | + | 0.00795665i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.6976 | − | 15.6976i | 0.564970 | − | 0.564970i | ||||
\(773\) | −8.32250 | − | 8.32250i | −0.299340 | − | 0.299340i | 0.541416 | − | 0.840755i | \(-0.317889\pi\) |
−0.840755 | + | 0.541416i | \(0.817889\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0534327 | − | 1.82044i | −0.00191936 | − | 0.0653922i | ||||
\(776\) | 12.4444 | 0.446728 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.79761 | + | 7.79761i | 0.279558 | + | 0.279558i | ||||
\(779\) | −0.627432 | + | 7.79517i | −0.0224801 | + | 0.279291i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.4605i | 0.481654i | ||||||||
\(782\) | 5.64120 | − | 5.64120i | 0.201729 | − | 0.201729i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 13.1800i | − | 0.470715i | ||||||
\(785\) | 30.1611 | + | 29.2888i | 1.07649 | + | 1.04536i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.1356 | − | 33.1356i | 1.18116 | − | 1.18116i | 0.201710 | − | 0.979445i | \(-0.435350\pi\) |
0.979445 | − | 0.201710i | \(-0.0646498\pi\) | |||||||
\(788\) | −2.62159 | + | 2.62159i | −0.0933901 | + | 0.0933901i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.3892 | − | 12.7582i | 0.440789 | − | 0.453916i | ||||
\(791\) | − | 78.5265i | − | 2.79208i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.4261 | + | 36.4261i | 1.29353 | + | 1.29353i | ||||
\(794\) | −1.54526 | −0.0548392 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.73685 | 0.238781 | ||||||||
\(797\) | 10.3195 | − | 10.3195i | 0.365534 | − | 0.365534i | −0.500311 | − | 0.865846i | \(-0.666781\pi\) |
0.865846 | + | 0.500311i | \(0.166781\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.94620i | − | 0.316494i | ||||||
\(800\) | −3.43028 | + | 3.63774i | −0.121279 | + | 0.128614i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.67468 | + | 9.67468i | 0.341625 | + | 0.341625i | ||||
\(803\) | 16.8655 | − | 16.8655i | 0.595172 | − | 0.595172i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −66.3996 | + | 0.974255i | −2.34028 | + | 0.0343380i | ||||
\(806\) | − | 1.23097i | − | 0.0433589i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.54027 | + | 1.54027i | 0.0541864 | + | 0.0541864i | ||||
\(809\) | 27.5401i | 0.968260i | 0.874996 | + | 0.484130i | \(0.160864\pi\) | ||||
−0.874996 | + | 0.484130i | \(0.839136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 39.9597i | − | 1.40318i | −0.712583 | − | 0.701588i | \(-0.752475\pi\) | ||
0.712583 | − | 0.701588i | \(-0.247525\pi\) | |||||||
\(812\) | 17.1664 | − | 17.1664i | 0.602423 | − | 0.602423i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 9.10745i | − | 0.319216i | ||||||
\(815\) | −0.0965084 | + | 0.0993826i | −0.00338054 | + | 0.00348122i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.92818 | − | 2.49192i | 0.102444 | − | 0.0871811i | ||||
\(818\) | −9.84826 | + | 9.84826i | −0.344336 | + | 0.344336i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.01134 | + | 0.0588568i | −0.140082 | + | 0.00205537i | ||||
\(821\) | −23.0062 | −0.802922 | −0.401461 | − | 0.915876i | \(-0.631498\pi\) | ||||
−0.401461 | + | 0.915876i | \(0.631498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.1426 | − | 15.1426i | 0.527839 | − | 0.527839i | −0.392088 | − | 0.919928i | \(-0.628247\pi\) |
0.919928 | + | 0.392088i | \(0.128247\pi\) | |||||||
\(824\) | 13.3619i | 0.465483i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.69943 | 0.233103 | ||||||||
\(827\) | 30.6119 | − | 30.6119i | 1.06448 | − | 1.06448i | 0.0667089 | − | 0.997772i | \(-0.478750\pi\) |
0.997772 | − | 0.0667089i | \(-0.0212499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.6550 | −0.717377 | −0.358688 | − | 0.933457i | \(-0.616776\pi\) | ||||
−0.358688 | + | 0.933457i | \(0.616776\pi\) | |||||||
\(830\) | −0.183045 | − | 12.4753i | −0.00635359 | − | 0.433024i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.38967 | + | 2.38967i | −0.0828468 | + | 0.0828468i | ||||
\(833\) | 11.2466 | − | 11.2466i | 0.389671 | − | 0.389671i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.5809 | − | 15.0152i | 0.504595 | − | 0.519622i | ||||
\(836\) | −0.523945 | + | 6.50945i | −0.0181210 | + | 0.225134i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.4760 | − | 22.4760i | −0.776421 | − | 0.776421i | ||||
\(839\) | 14.8706 | 0.513391 | 0.256696 | − | 0.966492i | \(-0.417366\pi\) | ||||
0.256696 | + | 0.966492i | \(0.417366\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.205753 | 0.00709491 | ||||||||
\(842\) | 21.1861 | + | 21.1861i | 0.730123 | + | 0.730123i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.1654 | −0.522013 | ||||||||
\(845\) | 0.0517994 | + | 3.53035i | 0.00178195 | + | 0.121448i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.8113 | + | 27.8113i | 0.955608 | + | 0.955608i | ||||
\(848\) | −5.27391 | − | 5.27391i | −0.181107 | − | 0.181107i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.03118 | + | 0.177024i | −0.206868 | + | 0.00607189i | ||||
\(851\) | − | 40.1878i | − | 1.37762i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.8845 | − | 18.8845i | 0.646592 | − | 0.646592i | −0.305576 | − | 0.952168i | \(-0.598849\pi\) |
0.952168 | + | 0.305576i | \(0.0988490\pi\) | |||||||
\(854\) | −68.4756 | −2.34319 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.424610 | −0.0145129 | ||||||||
\(857\) | −3.38649 | + | 3.38649i | −0.115680 | + | 0.115680i | −0.762577 | − | 0.646897i | \(-0.776066\pi\) |
0.646897 | + | 0.762577i | \(0.276066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.3135i | 0.693089i | 0.938034 | + | 0.346544i | \(0.112645\pi\) | ||||
−0.938034 | + | 0.346544i | \(0.887355\pi\) | |||||||
\(860\) | 1.41503 | + | 1.37411i | 0.0482522 | + | 0.0468567i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.7288 | + | 13.7288i | 0.467603 | + | 0.467603i | ||||
\(863\) | −20.2596 | − | 20.2596i | −0.689645 | − | 0.689645i | 0.272508 | − | 0.962153i | \(-0.412147\pi\) |
−0.962153 | + | 0.272508i | \(0.912147\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.2895 | + | 39.1243i | 1.36988 | + | 1.33026i | ||||
\(866\) | −7.83259 | −0.266162 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.15702 | + | 1.15702i | 0.0392717 | + | 0.0392717i | ||||
\(869\) | 11.9154 | 0.404203 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.72746 | −0.160184 | ||||||||
\(872\) | 5.54050 | + | 5.54050i | 0.187625 | + | 0.187625i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.31197 | + | 28.7237i | −0.0782036 | + | 0.971595i | ||||
\(875\) | 37.0423 | + | 33.9171i | 1.25226 | + | 1.14661i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.8421 | − | 22.8421i | 0.771322 | − | 0.771322i | −0.207016 | − | 0.978338i | \(-0.566375\pi\) |
0.978338 | + | 0.207016i | \(0.0663752\pi\) | |||||||
\(878\) | −13.6141 | + | 13.6141i | −0.459454 | + | 0.459454i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.34972 | + | 0.0491491i | −0.112919 | + | 0.00165681i | ||||
\(881\) | 43.2232 | 1.45623 | 0.728113 | − | 0.685457i | \(-0.240397\pi\) | ||||
0.728113 | + | 0.685457i | \(0.240397\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.6956 | + | 33.6956i | −1.13395 | + | 1.13395i | −0.144431 | + | 0.989515i | \(0.546135\pi\) |
−0.989515 | + | 0.144431i | \(0.953865\pi\) | |||||||
\(884\) | −4.07823 | −0.137166 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 1.16299i | − | 0.0390715i | ||||||
\(887\) | −22.5354 | + | 22.5354i | −0.756666 | + | 0.756666i | −0.975714 | − | 0.219048i | \(-0.929705\pi\) |
0.219048 | + | 0.975714i | \(0.429705\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 52.8480 | 1.77246 | ||||||||
\(890\) | −14.5014 | + | 14.9333i | −0.486089 | + | 0.500566i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.90756 | − | 1.90756i | 0.0638697 | − | 0.0638697i | ||||
\(893\) | 20.9428 | + | 24.6093i | 0.700825 | + | 0.823519i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.1366 | − | 0.295456i | 0.673091 | − | 0.00987600i | ||||
\(896\) | − | 4.49222i | − | 0.150074i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.0588 | − | 24.0588i | 0.802852 | − | 0.802852i | ||||
\(899\) | 1.96847i | 0.0656520i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 9.00051i | − | 0.299850i | ||||||
\(902\) | −1.90067 | − | 1.90067i | −0.0632852 | − | 0.0632852i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 17.4806i | − | 0.581395i | ||||||
\(905\) | 0.615483 | + | 41.9478i | 0.0204593 | + | 1.39439i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4318 | − | 16.4318i | 0.545611 | − | 0.545611i | −0.379558 | − | 0.925168i | \(-0.623924\pi\) |
0.925168 | + | 0.379558i | \(0.123924\pi\) | |||||||
\(908\) | −19.8625 | − | 19.8625i | −0.659159 | − | 0.659159i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 24.3535 | + | 23.6492i | 0.807312 | + | 0.783964i | ||||
\(911\) | − | 12.8284i | − | 0.425024i | −0.977158 | − | 0.212512i | \(-0.931836\pi\) | ||
0.977158 | − | 0.212512i | \(-0.0681644\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.91109 | − | 5.91109i | 0.195629 | − | 0.195629i | ||||
\(914\) | 37.1033 | 1.22727 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.0279 | 0.628700 | ||||||||
\(917\) | 25.6570 | + | 25.6570i | 0.847269 | + | 0.847269i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.1134i | 0.498544i | 0.968434 | + | 0.249272i | \(0.0801913\pi\) | ||||
−0.968434 | + | 0.249272i | \(0.919809\pi\) | |||||||
\(920\) | −14.7810 | + | 0.216876i | −0.487316 | + | 0.00715020i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.9176 | − | 18.9176i | 0.623018 | − | 0.623018i | ||||
\(923\) | 21.4698 | − | 21.4698i | 0.706687 | − | 0.706687i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.8525 | + | 22.1136i | −0.685625 | + | 0.727090i | ||||
\(926\) | 23.3650i | 0.767820i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.82137 | − | 3.82137i | 0.125443 | − | 0.125443i | ||||
\(929\) | 54.6979i | 1.79458i | 0.441442 | + | 0.897290i | \(0.354467\pi\) | ||||
−0.441442 | + | 0.897290i | \(0.645533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.60926 | + | 57.2651i | −0.151063 | + | 1.87679i | ||||
\(932\) | −8.22028 | − | 8.22028i | −0.269264 | − | 0.269264i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.75744 | −0.319273 | ||||||||
\(935\) | −2.90027 | − | 2.81639i | −0.0948490 | − | 0.0921059i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.3024 | + | 19.3024i | 0.630582 | + | 0.630582i | 0.948214 | − | 0.317632i | \(-0.102888\pi\) |
−0.317632 | + | 0.948214i | \(0.602888\pi\) | |||||||
\(938\) | 4.44346 | − | 4.44346i | 0.145084 | − | 0.145084i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −11.5484 | + | 11.8924i | −0.376668 | + | 0.387886i | ||||
\(941\) | − | 3.83170i | − | 0.124910i | −0.998048 | − | 0.0624549i | \(-0.980107\pi\) | ||
0.998048 | − | 0.0624549i | \(-0.0198930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.38692 | − | 8.38692i | −0.273116 | − | 0.273116i | ||||
\(944\) | 1.49134 | 0.0485391 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.32156i | 0.0429677i | ||||||||
\(947\) | 22.3934 | + | 22.3934i | 0.727689 | + | 0.727689i | 0.970159 | − | 0.242470i | \(-0.0779575\pi\) |
−0.242470 | + | 0.970159i | \(0.577958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.8019 | −1.74648 | ||||||||
\(950\) | 16.1762 | − | 14.6058i | 0.524826 | − | 0.473875i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.83323 | − | 3.83323i | 0.124236 | − | 0.124236i | ||||
\(953\) | −0.832761 | − | 0.832761i | −0.0269758 | − | 0.0269758i | 0.693490 | − | 0.720466i | \(-0.256072\pi\) |
−0.720466 | + | 0.693490i | \(0.756072\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.2715 | + | 0.209400i | −0.461815 | + | 0.00677603i | ||||
\(956\) | −5.40164 | −0.174702 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.14916 | + | 7.14916i | 0.230979 | + | 0.230979i | ||||
\(959\) | 44.4570i | 1.43559i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8673 | 0.995720 | ||||||||
\(962\) | −14.5266 | + | 14.5266i | −0.468357 | + | 0.468357i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.3252 | 0.783462 | ||||||||
\(965\) | −35.6122 | − | 34.5822i | −1.14640 | − | 1.11324i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.69878 | − | 8.69878i | −0.279734 | − | 0.279734i | 0.553269 | − | 0.833003i | \(-0.313380\pi\) |
−0.833003 | + | 0.553269i | \(0.813380\pi\) | |||||||
\(968\) | 6.19100 | + | 6.19100i | 0.198986 | + | 0.198986i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.408244 | − | 27.8235i | −0.0131079 | − | 0.893360i | ||||
\(971\) | 27.6771i | 0.888202i | 0.895977 | + | 0.444101i | \(0.146477\pi\) | ||||
−0.895977 | + | 0.444101i | \(0.853523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.5812 | − | 34.5812i | 1.10862 | − | 1.10862i | ||||
\(974\) | 27.5865i | 0.883928i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.2432 | −0.487922 | ||||||||
\(977\) | 14.3182 | − | 14.3182i | 0.458079 | − | 0.458079i | −0.439946 | − | 0.898024i | \(-0.645002\pi\) |
0.898024 | + | 0.439946i | \(0.145002\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.9469 | −0.445744 | ||||||||
\(980\) | −29.4682 | + | 0.432375i | −0.941328 | + | 0.0138117i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.94898 | − | 9.94898i | 0.317485 | − | 0.317485i | ||||
\(983\) | 32.4108 | + | 32.4108i | 1.03374 | + | 1.03374i | 0.999410 | + | 0.0343335i | \(0.0109308\pi\) |
0.0343335 | + | 0.999410i | \(0.489069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.94742 | + | 5.77541i | 0.189500 | + | 0.184020i | ||||
\(986\) | 6.52159 | 0.207690 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.2184 | − | 9.54703i | 0.356906 | − | 0.303731i | ||||
\(989\) | 5.83155i | 0.185433i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 26.7718i | − | 0.850435i | −0.905091 | − | 0.425218i | \(-0.860198\pi\) | ||
0.905091 | − | 0.425218i | \(-0.139802\pi\) | |||||||
\(992\) | 0.257560 | + | 0.257560i | 0.00817755 | + | 0.00817755i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 40.3600i | 1.28014i | ||||||||
\(995\) | −0.221005 | − | 15.0624i | −0.00700633 | − | 0.477511i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.08169 | − | 3.08169i | −0.0975982 | − | 0.0975982i | 0.656622 | − | 0.754220i | \(-0.271985\pi\) |
−0.754220 | + | 0.656622i | \(0.771985\pi\) | |||||||
\(998\) | −3.13678 | − | 3.13678i | −0.0992929 | − | 0.0992929i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1710.2.p.c.37.6 | 20 | ||
3.2 | odd | 2 | 570.2.m.b.37.5 | ✓ | 20 | ||
5.3 | odd | 4 | inner | 1710.2.p.c.1063.1 | 20 | ||
15.8 | even | 4 | 570.2.m.b.493.10 | yes | 20 | ||
19.18 | odd | 2 | inner | 1710.2.p.c.37.1 | 20 | ||
57.56 | even | 2 | 570.2.m.b.37.10 | yes | 20 | ||
95.18 | even | 4 | inner | 1710.2.p.c.1063.6 | 20 | ||
285.113 | odd | 4 | 570.2.m.b.493.5 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.b.37.5 | ✓ | 20 | 3.2 | odd | 2 | ||
570.2.m.b.37.10 | yes | 20 | 57.56 | even | 2 | ||
570.2.m.b.493.5 | yes | 20 | 285.113 | odd | 4 | ||
570.2.m.b.493.10 | yes | 20 | 15.8 | even | 4 | ||
1710.2.p.c.37.1 | 20 | 19.18 | odd | 2 | inner | ||
1710.2.p.c.37.6 | 20 | 1.1 | even | 1 | trivial | ||
1710.2.p.c.1063.1 | 20 | 5.3 | odd | 4 | inner | ||
1710.2.p.c.1063.6 | 20 | 95.18 | even | 4 | inner |