Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(61,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.u (of order \(9\), degree \(6\), 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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(-1.37827 - 1.15651i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.61 |
Dual form | 380.2.u.a.81.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.312429 | − | 1.77187i | −0.180381 | − | 1.02299i | −0.931748 | − | 0.363107i | \(-0.881716\pi\) |
0.751366 | − | 0.659885i | \(-0.229395\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.766044 | + | 0.642788i | −0.342585 | + | 0.287463i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.336777 | + | 0.583316i | −0.127290 | + | 0.220473i | −0.922626 | − | 0.385696i | \(-0.873961\pi\) |
0.795336 | + | 0.606169i | \(0.207295\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.222848 | + | 0.0811099i | −0.0742825 | + | 0.0270366i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.21276 | − | 5.56466i | −0.968683 | − | 1.67781i | −0.699376 | − | 0.714754i | \(-0.746539\pi\) |
−0.269307 | − | 0.963054i | \(-0.586795\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.791702 | − | 4.48996i | 0.219579 | − | 1.24529i | −0.653204 | − | 0.757182i | \(-0.726576\pi\) |
0.872782 | − | 0.488110i | \(-0.162313\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.37827 | + | 1.15651i | 0.355869 | + | 0.298609i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.21618 | + | 0.442652i | 0.294966 | + | 0.107359i | 0.485264 | − | 0.874367i | \(-0.338723\pi\) |
−0.190299 | + | 0.981726i | \(0.560946\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.35314 | + | 0.223964i | −0.998679 | + | 0.0513810i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.13878 | + | 0.414482i | 0.248502 | + | 0.0904475i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.04176 | − | 0.874144i | −0.217223 | − | 0.182272i | 0.527683 | − | 0.849442i | \(-0.323061\pi\) |
−0.744906 | + | 0.667170i | \(0.767505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.173648 | − | 0.984808i | 0.0347296 | − | 0.196962i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.48547 | − | 4.30496i | −0.478329 | − | 0.828490i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.80288 | + | 2.47605i | −1.26326 | + | 0.459790i | −0.884863 | − | 0.465852i | \(-0.845748\pi\) |
−0.378400 | + | 0.925642i | \(0.623526\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.97241 | + | 5.14836i | −0.533860 | + | 0.924673i | 0.465358 | + | 0.885123i | \(0.345926\pi\) |
−0.999218 | + | 0.0395498i | \(0.987408\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.85612 | + | 7.43116i | −1.54165 | + | 1.29360i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.116962 | − | 0.663322i | −0.0197701 | − | 0.112122i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.5704 | 1.90216 | 0.951079 | − | 0.308948i | \(-0.0999770\pi\) | ||||
0.951079 | + | 0.308948i | \(0.0999770\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.20300 | −1.31353 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.463683 | − | 2.62968i | −0.0724151 | − | 0.410686i | −0.999369 | − | 0.0355118i | \(-0.988694\pi\) |
0.926954 | − | 0.375175i | \(-0.122417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.31756 | − | 6.14016i | 1.11592 | − | 0.936366i | 0.117526 | − | 0.993070i | \(-0.462504\pi\) |
0.998391 | + | 0.0567043i | \(0.0180592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.118575 | − | 0.205377i | 0.0176761 | − | 0.0306159i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.0445 | − | 4.01987i | 1.61100 | − | 0.586358i | 0.629366 | − | 0.777109i | \(-0.283314\pi\) |
0.981638 | + | 0.190751i | \(0.0610922\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.27316 | + | 5.66928i | 0.467595 | + | 0.809898i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.404354 | − | 2.29321i | 0.0566209 | − | 0.321113i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.74628 | − | 2.30440i | −0.377230 | − | 0.316534i | 0.434384 | − | 0.900728i | \(-0.356966\pi\) |
−0.811614 | + | 0.584194i | \(0.801411\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.03801 | + | 2.19766i | 0.814165 | + | 0.296332i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.75689 | + | 7.64324i | 0.232705 | + | 1.01237i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.150435 | + | 0.0547540i | 0.0195850 | + | 0.00712837i | 0.351794 | − | 0.936077i | \(-0.385572\pi\) |
−0.332209 | + | 0.943206i | \(0.607794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.54965 | + | 4.65671i | 0.710560 | + | 0.596231i | 0.924756 | − | 0.380560i | \(-0.124269\pi\) |
−0.214196 | + | 0.976791i | \(0.568713\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0277374 | − | 0.157306i | 0.00349458 | − | 0.0198187i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.27961 | + | 3.94841i | 0.282751 | + | 0.489740i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.13512 | + | 1.86903i | −0.627354 | + | 0.228338i | −0.636079 | − | 0.771624i | \(-0.719445\pi\) |
0.00872500 | + | 0.999962i | \(0.497223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.22340 | + | 2.11898i | −0.147280 | + | 0.255096i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.00684 | − | 7.55764i | 1.06892 | − | 0.896927i | 0.0739617 | − | 0.997261i | \(-0.476436\pi\) |
0.994954 | + | 0.100334i | \(0.0319913\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.643012 | − | 3.64670i | −0.0752589 | − | 0.426815i | −0.999037 | − | 0.0438852i | \(-0.986026\pi\) |
0.923778 | − | 0.382929i | \(-0.125085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.79921 | −0.207755 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.32794 | 0.493214 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.11567 | − | 6.32728i | −0.125523 | − | 0.711875i | −0.980996 | − | 0.194028i | \(-0.937845\pi\) |
0.855473 | − | 0.517847i | \(-0.173266\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.39632 | + | 6.20625i | −0.821813 | + | 0.689583i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.52251 | + | 4.36912i | −0.276882 | + | 0.479573i | −0.970608 | − | 0.240666i | \(-0.922634\pi\) |
0.693727 | + | 0.720238i | \(0.255968\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.21618 | + | 0.442652i | −0.131913 | + | 0.0480123i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.51266 | + | 11.2803i | 0.698230 | + | 1.20937i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.26006 | − | 7.14615i | 0.133566 | − | 0.757490i | −0.842282 | − | 0.539038i | \(-0.818788\pi\) |
0.975848 | − | 0.218453i | \(-0.0701009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.35244 | + | 1.97393i | 0.246603 | + | 0.206924i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0509 | + | 3.65823i | 1.04223 | + | 0.379341i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.19074 | − | 2.96971i | 0.327363 | − | 0.304686i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.40807 | + | 2.69632i | 0.752176 | + | 0.273770i | 0.689521 | − | 0.724266i | \(-0.257821\pi\) |
0.0626549 | + | 0.998035i | \(0.480043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.16730 | + | 0.979484i | 0.117318 | + | 0.0984419i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.35954 | + | 13.3816i | −0.234783 | + | 1.33152i | 0.608289 | + | 0.793716i | \(0.291856\pi\) |
−0.843071 | + | 0.537802i | \(0.819255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.39106 | + | 9.33758i | 0.531197 | + | 0.920060i | 0.999337 | + | 0.0364055i | \(0.0115908\pi\) |
−0.468140 | + | 0.883654i | \(0.655076\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.13878 | + | 0.414482i | −0.111134 | + | 0.0404493i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.555176 | + | 0.961592i | −0.0536708 | + | 0.0929606i | −0.891613 | − | 0.452799i | \(-0.850426\pi\) |
0.837942 | + | 0.545760i | \(0.183759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.91957 | − | 1.61071i | 0.183862 | − | 0.154278i | −0.546211 | − | 0.837647i | \(-0.683930\pi\) |
0.730073 | + | 0.683369i | \(0.239486\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.61492 | − | 20.5012i | −0.343113 | − | 1.94589i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.8298 | −1.39507 | −0.697536 | − | 0.716550i | \(-0.745720\pi\) | ||||
−0.697536 | + | 0.716550i | \(0.745720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.35993 | 0.126814 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.187752 | + | 1.06479i | 0.0173576 | + | 0.0984401i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.667786 | + | 0.560339i | −0.0612158 | + | 0.0513662i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.1436 | + | 26.2295i | −1.37669 | + | 2.38450i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.51459 | + | 1.64317i | −0.407067 | + | 0.148160i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.500000 | + | 0.866025i | 0.0447214 | + | 0.0774597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.01635 | + | 5.76401i | −0.0901865 | + | 0.511473i | 0.905930 | + | 0.423428i | \(0.139173\pi\) |
−0.996116 | + | 0.0880454i | \(0.971938\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.1658 | − | 11.0474i | −1.15918 | − | 0.972671i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.64603 | + | 2.78293i | 0.668037 | + | 0.243146i | 0.653702 | − | 0.756752i | \(-0.273215\pi\) |
0.0143345 | + | 0.999897i | \(0.495437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.33540 | − | 2.61468i | 0.115794 | − | 0.226722i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.67116 | + | 1.70016i | 0.402029 | + | 0.146327i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.81357 | + | 3.19997i | 0.325816 | + | 0.273392i | 0.790992 | − | 0.611826i | \(-0.209565\pi\) |
−0.465177 | + | 0.885218i | \(0.654009\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.364121 | − | 2.06503i | 0.0308843 | − | 0.175154i | −0.965464 | − | 0.260537i | \(-0.916100\pi\) |
0.996348 | + | 0.0853833i | \(0.0272115\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5733 | − | 18.3135i | −0.890434 | − | 1.54228i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.5287 | + | 10.0196i | −2.30206 | + | 0.837882i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.61974 | − | 6.26957i | 0.300603 | − | 0.520659i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.02262 | − | 7.57088i | 0.744173 | − | 0.624436i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.49492 | − | 8.47813i | −0.122469 | − | 0.694556i | −0.982779 | − | 0.184785i | \(-0.940841\pi\) |
0.860310 | − | 0.509771i | \(-0.170270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3265 | 1.49139 | 0.745693 | − | 0.666289i | \(-0.232118\pi\) | ||||
0.745693 | + | 0.666289i | \(0.232118\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.306925 | −0.0248134 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.03231 | − | 5.85450i | −0.0829168 | − | 0.470245i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2264 | − | 8.58096i | 0.816155 | − | 0.684835i | −0.135913 | − | 0.990721i | \(-0.543397\pi\) |
0.952068 | + | 0.305885i | \(0.0989524\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.22509 | + | 5.58602i | −0.255766 | + | 0.443000i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.860745 | − | 0.313285i | 0.0678362 | − | 0.0246904i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7658 | + | 18.6469i | 0.843240 | + | 1.46053i | 0.887141 | + | 0.461498i | \(0.152688\pi\) |
−0.0439014 | + | 0.999036i | \(0.513979\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00752 | − | 11.3852i | 0.156285 | − | 0.886337i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.32714 | − | 7.82640i | −0.721756 | − | 0.605625i | 0.206115 | − | 0.978528i | \(-0.433918\pi\) |
−0.927870 | + | 0.372903i | \(0.878362\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.31698 | − | 2.66316i | −0.562844 | − | 0.204859i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.951921 | − | 0.402993i | 0.0727952 | − | 0.0308176i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.03095 | + | 0.739205i | 0.154410 | + | 0.0562007i | 0.418069 | − | 0.908415i | \(-0.362707\pi\) |
−0.263659 | + | 0.964616i | \(0.584929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.515973 | + | 0.432953i | 0.0390039 | + | 0.0327282i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0500168 | − | 0.283659i | 0.00375949 | − | 0.0213212i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.07390 | − | 15.7164i | −0.678215 | − | 1.17470i | −0.975518 | − | 0.219919i | \(-0.929421\pi\) |
0.297303 | − | 0.954783i | \(-0.403913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.02363 | − | 2.55639i | 0.522062 | − | 0.190015i | −0.0675283 | − | 0.997717i | \(-0.521511\pi\) |
0.589591 | + | 0.807702i | \(0.299289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.51723 | − | 11.2882i | 0.481768 | − | 0.834446i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.86342 | + | 7.43729i | −0.651652 | + | 0.546801i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.44407 | − | 8.18973i | −0.105601 | − | 0.598893i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.34820 | 0.243546 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.9662 | −1.58942 | −0.794710 | − | 0.606990i | \(-0.792377\pi\) | ||||
−0.794710 | + | 0.606990i | \(0.792377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.07436 | − | 11.7643i | −0.149315 | − | 0.846810i | −0.963800 | − | 0.266625i | \(-0.914091\pi\) |
0.814485 | − | 0.580185i | \(-0.197020\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.28386 | − | 5.27279i | 0.449997 | − | 0.377592i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.87650 | − | 6.71430i | 0.276189 | − | 0.478374i | −0.694245 | − | 0.719739i | \(-0.744262\pi\) |
0.970435 | + | 0.241365i | \(0.0775950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.65867 | − | 3.15150i | 0.613797 | − | 0.223404i | −0.0163667 | − | 0.999866i | \(-0.505210\pi\) |
0.630164 | + | 0.776462i | \(0.282988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.91605 | + | 8.51484i | 0.346751 | + | 0.600591i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.846740 | − | 4.80210i | 0.0594295 | − | 0.337042i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.04552 | + | 1.71640i | 0.142866 | + | 0.119879i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.303056 | + | 0.110303i | 0.0210639 | + | 0.00766662i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.2319 | + | 23.5042i | 1.05361 | + | 1.62582i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.3970 | − | 7.05994i | −1.33535 | − | 0.486027i | −0.427003 | − | 0.904250i | \(-0.640431\pi\) |
−0.908344 | + | 0.418224i | \(0.862653\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.2052 | − | 13.5978i | −1.11036 | − | 0.931703i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.65876 | + | 9.40727i | −0.113126 | + | 0.641570i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00208 | − | 3.46770i | −0.135910 | − | 0.235403i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.26061 | + | 2.27867i | −0.423053 | + | 0.153979i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.95034 | − | 5.11013i | 0.198461 | − | 0.343745i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.80840 | + | 1.51742i | −0.121099 | + | 0.101614i | −0.701326 | − | 0.712841i | \(-0.747408\pi\) |
0.580227 | + | 0.814455i | \(0.302964\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0411806 | + | 0.233547i | 0.00274537 | + | 0.0155698i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.3448 | −1.01847 | −0.509236 | − | 0.860627i | \(-0.670072\pi\) | ||||
−0.509236 | + | 0.860627i | \(0.670072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.54861 | 0.630990 | 0.315495 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315495 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.35217 | − | 7.66856i | −0.0889665 | − | 0.504554i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8464 | − | 16.6531i | 1.30018 | − | 1.09098i | 0.310069 | − | 0.950714i | \(-0.399648\pi\) |
0.990113 | − | 0.140269i | \(-0.0447966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.87665 | + | 10.1787i | −0.383351 | + | 0.663983i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.8626 | + | 3.95365i | −0.705600 | + | 0.256817i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.42312 | − | 12.8572i | −0.480162 | − | 0.831665i | 0.519579 | − | 0.854422i | \(-0.326089\pi\) |
−0.999741 | + | 0.0227574i | \(0.992755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.35050 | − | 19.0016i | 0.215825 | − | 1.22400i | −0.663645 | − | 0.748048i | \(-0.730992\pi\) |
0.879470 | − | 0.475955i | \(-0.157897\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.88363 | + | 1.58055i | 0.120835 | + | 0.101392i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.15153 | − | 2.23897i | −0.393007 | − | 0.143043i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.44080 | + | 19.7228i | −0.155304 | + | 1.25493i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.52963 | + | 3.10453i | 0.540543 | + | 0.196742i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.5731 | + | 12.2283i | 0.919848 | + | 0.771844i | 0.973967 | − | 0.226690i | \(-0.0727905\pi\) |
−0.0541187 | + | 0.998535i | \(0.517235\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.51738 | + | 8.60548i | −0.0953967 | + | 0.541022i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.16429 | + | 2.01661i | 0.0729108 | + | 0.126285i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1329 | + | 4.05205i | −0.694453 | + | 0.252760i | −0.665041 | − | 0.746807i | \(-0.731586\pi\) |
−0.0294123 | + | 0.999567i | \(0.509364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.89664 | + | 6.74918i | −0.242125 | + | 0.419374i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.31517 | − | 1.10356i | 0.0814072 | − | 0.0683087i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.705433 | + | 4.00071i | 0.0434989 | + | 0.246694i | 0.998802 | − | 0.0489336i | \(-0.0155823\pi\) |
−0.955303 | + | 0.295628i | \(0.904471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.58501 | 0.220225 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.0558 | −0.798999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.882623 | + | 5.00561i | 0.0538145 | + | 0.305197i | 0.999820 | − | 0.0189522i | \(-0.00603304\pi\) |
−0.946006 | + | 0.324149i | \(0.894922\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.4535 | + | 9.61062i | −0.695750 | + | 0.583804i | −0.920561 | − | 0.390599i | \(-0.872268\pi\) |
0.224811 | + | 0.974402i | \(0.427824\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.76259 | − | 4.78494i | 0.167199 | − | 0.289598i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.03801 | + | 2.19766i | −0.364106 | + | 0.132524i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.04752 | − | 10.4746i | −0.363361 | − | 0.629359i | 0.625151 | − | 0.780504i | \(-0.285037\pi\) |
−0.988512 | + | 0.151145i | \(0.951704\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.244811 | − | 1.38839i | 0.0146564 | − | 0.0831208i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7076 | + | 14.0193i | 0.996690 | + | 0.836322i | 0.986522 | − | 0.163626i | \(-0.0523190\pi\) |
0.0101678 | + | 0.999948i | \(0.496763\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0489 | + | 5.47733i | 0.894561 | + | 0.325594i | 0.748071 | − | 0.663618i | \(-0.230980\pi\) |
0.146490 | + | 0.989212i | \(0.453202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.25884 | − | 4.72576i | −0.370741 | − | 0.279930i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.69009 | + | 0.615142i | 0.0997628 | + | 0.0363107i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.7396 | − | 9.85071i | −0.690566 | − | 0.579453i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.46304 | − | 13.9686i | 0.144386 | − | 0.818853i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.15924 | − | 5.47196i | −0.184565 | − | 0.319675i | 0.758865 | − | 0.651248i | \(-0.225754\pi\) |
−0.943430 | + | 0.331573i | \(0.892421\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.150435 | + | 0.0547540i | −0.00875869 | + | 0.00318790i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.9704 | + | 27.6616i | −0.926699 | + | 1.60509i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.74964 | + | 3.98542i | −0.274679 | + | 0.230483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.11726 | + | 6.33631i | 0.0643980 | + | 0.365219i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.4477 | 1.40448 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.24456 | −0.414822 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.139362 | − | 0.790360i | −0.00795380 | − | 0.0451082i | 0.980573 | − | 0.196157i | \(-0.0628461\pi\) |
−0.988526 | + | 0.151049i | \(0.951735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.8607 | − | 12.4696i | 0.845396 | − | 0.709371i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.02192 | + | 12.1623i | −0.398176 | + | 0.689662i | −0.993501 | − | 0.113824i | \(-0.963690\pi\) |
0.595325 | + | 0.803485i | \(0.297023\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.5637 | + | 7.48459i | −1.16233 | + | 0.423054i | −0.849930 | − | 0.526896i | \(-0.823356\pi\) |
−0.312402 | + | 0.949950i | \(0.601133\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0798666 | + | 0.138333i | 0.00449997 | + | 0.00779418i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.41832 | − | 30.7288i | 0.304323 | − | 1.72590i | −0.322350 | − | 0.946621i | \(-0.604473\pi\) |
0.626673 | − | 0.779282i | \(-0.284416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.6344 | + | 29.9008i | 1.99514 | + | 1.67412i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.87727 | + | 0.683272i | 0.104779 | + | 0.0381365i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.39332 | − | 1.65454i | −0.300092 | − | 0.0920613i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.28427 | − | 1.55935i | −0.237649 | − | 0.0864971i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.45371 | − | 2.89801i | −0.190991 | − | 0.160260i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.37469 | + | 7.79623i | −0.0757888 | + | 0.429820i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.88658 | − | 10.1959i | −0.323556 | − | 0.560415i | 0.657663 | − | 0.753312i | \(-0.271545\pi\) |
−0.981219 | + | 0.192897i | \(0.938212\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.57843 | + | 0.938471i | −0.141297 | + | 0.0514279i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.73234 | − | 4.73255i | 0.149284 | − | 0.258567i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.27071 | − | 6.10085i | 0.396061 | − | 0.332335i | −0.422908 | − | 0.906173i | \(-0.638991\pi\) |
0.818969 | + | 0.573838i | \(0.194546\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.63327 | + | 26.2766i | 0.251645 | + | 1.42715i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38.1985 | 2.06856 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.12419 | −0.492660 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.424881 | − | 2.40962i | −0.0228748 | − | 0.129730i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.01036 | − | 7.56059i | 0.483701 | − | 0.405874i | −0.368061 | − | 0.929802i | \(-0.619978\pi\) |
0.851763 | + | 0.523928i | \(0.175534\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.21201 | + | 10.7595i | −0.332521 | + | 0.575944i | −0.983006 | − | 0.183576i | \(-0.941233\pi\) |
0.650484 | + | 0.759520i | \(0.274566\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.2969 | + | 7.75143i | −1.13674 | + | 0.413741i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.73224 | − | 9.92852i | −0.305096 | − | 0.528442i | 0.672187 | − | 0.740382i | \(-0.265355\pi\) |
−0.977283 | + | 0.211940i | \(0.932022\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.04169 | + | 11.5790i | −0.108361 | + | 0.614548i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.20149 | + | 1.00817i | 0.0635894 | + | 0.0533578i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1144 | + | 10.5968i | 1.53660 | + | 0.559277i | 0.965227 | − | 0.261413i | \(-0.0841885\pi\) |
0.571374 | + | 0.820690i | \(0.306411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8997 | − | 1.94990i | 0.994720 | − | 0.102626i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 51.2067 | + | 18.6377i | 2.68766 | + | 0.978227i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.83663 | + | 2.38022i | 0.148476 | + | 0.124586i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.782062 | + | 4.43529i | −0.0408233 | + | 0.231520i | −0.998392 | − | 0.0566842i | \(-0.981947\pi\) |
0.957569 | + | 0.288205i | \(0.0930583\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.316623 | + | 0.548407i | 0.0164827 | + | 0.0285490i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.26908 | − | 0.825877i | 0.117805 | − | 0.0428774i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.56116 | − | 16.5604i | 0.495058 | − | 0.857466i | −0.504926 | − | 0.863163i | \(-0.668480\pi\) |
0.999984 | + | 0.00569689i | \(0.00181339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.37827 | − | 1.15651i | 0.0711737 | − | 0.0597218i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.73150 | + | 32.5050i | 0.295187 | + | 1.67409i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.21152 | −0.0622314 | −0.0311157 | − | 0.999516i | \(-0.509906\pi\) | ||||
−0.0311157 | + | 0.999516i | \(0.509906\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.5306 | 0.539501 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.06603 | + | 6.04574i | 0.0544715 | + | 0.308923i | 0.999855 | − | 0.0170375i | \(-0.00542347\pi\) |
−0.945383 | + | 0.325960i | \(0.894312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.31539 | + | 2.78194i | −0.168968 | + | 0.141781i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.13267 | + | 1.96185i | −0.0575769 | + | 0.0997262i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.111964 | − | 0.0407516i | 0.00567680 | − | 0.00206619i | −0.339180 | − | 0.940721i | \(-0.610150\pi\) |
0.344857 | + | 0.938655i | \(0.387927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.880027 | − | 1.52425i | −0.0445049 | − | 0.0770847i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.54215 | − | 14.4173i | 0.128235 | − | 0.727255i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.92175 | + | 4.12984i | 0.247640 | + | 0.207795i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.58876 | + | 0.942231i | 0.129926 | + | 0.0472892i | 0.406165 | − | 0.913800i | \(-0.366866\pi\) |
−0.276239 | + | 0.961089i | \(0.589088\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.05010 | − | 1.54925i | −0.252821 | − | 0.0775597i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.4922 | − | 7.45853i | −1.02333 | − | 0.372461i | −0.224792 | − | 0.974407i | \(-0.572170\pi\) |
−0.798537 | + | 0.601945i | \(0.794392\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.7627 | + | 17.4220i | 1.03426 | + | 0.867850i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.67661 | − | 9.50852i | 0.0833114 | − | 0.472482i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.1728 | − | 64.3852i | −1.84259 | − | 3.19146i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.6340 | + | 5.32635i | −0.723605 | + | 0.263371i | −0.677456 | − | 0.735564i | \(-0.736917\pi\) |
−0.0461499 | + | 0.998935i | \(0.514695\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.47847 | − | 7.75694i | 0.220907 | − | 0.382622i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.0826022 | + | 0.0693114i | −0.00406459 | + | 0.00341059i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.876059 | − | 4.96838i | −0.0430040 | − | 0.243888i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.77274 | −0.184752 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.2596 | −0.745479 | −0.372739 | − | 0.927936i | \(-0.621581\pi\) | ||||
−0.372739 | + | 0.927936i | \(0.621581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.42403 | + | 8.07607i | 0.0694029 | + | 0.393603i | 0.999645 | + | 0.0266562i | \(0.00848593\pi\) |
−0.930242 | + | 0.366947i | \(0.880403\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.13519 | + | 1.79163i | −0.103816 | + | 0.0871123i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.647113 | − | 1.12083i | 0.0313896 | − | 0.0543684i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.58533 | + | 1.66892i | −0.221900 | + | 0.0807649i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.3543 | + | 45.6469i | 1.27240 | + | 2.20385i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.44591 | + | 8.20017i | −0.0696471 | + | 0.394988i | 0.929978 | + | 0.367615i | \(0.119825\pi\) |
−0.999625 | + | 0.0273736i | \(0.991286\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0125 | + | 21.8271i | 1.25008 | + | 1.04894i | 0.996666 | + | 0.0815863i | \(0.0259986\pi\) |
0.253416 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.2398 | − | 4.45492i | −0.586853 | − | 0.213597i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.73072 | + | 3.57195i | 0.226301 | + | 0.170870i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.7612 | + | 4.28073i | 0.561331 | + | 0.204308i | 0.607074 | − | 0.794645i | \(-0.292343\pi\) |
−0.0457426 | + | 0.998953i | \(0.514565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18925 | − | 0.997900i | −0.0566310 | − | 0.0475190i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.04892 | + | 22.9625i | −0.192370 | + | 1.09098i | 0.723745 | + | 0.690068i | \(0.242419\pi\) |
−0.916115 | + | 0.400916i | \(0.868692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.62820 | + | 6.28422i | 0.171993 | + | 0.297901i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.5551 | + | 5.29763i | −0.688434 | + | 0.250569i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.7619 | − | 18.6402i | 0.507887 | − | 0.879686i | −0.492072 | − | 0.870555i | \(-0.663760\pi\) |
0.999958 | − | 0.00913096i | \(-0.00290651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.1436 | + | 11.0287i | −0.618906 | + | 0.519324i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.72572 | − | 32.4722i | −0.269018 | − | 1.52568i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.07089 | −0.143966 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.0765 | −1.40692 | −0.703459 | − | 0.710735i | \(-0.748362\pi\) | ||||
−0.703459 | + | 0.710735i | \(0.748362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.11717 | − | 6.33579i | −0.0521450 | − | 0.295729i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5942 | − | 12.2459i | 0.679717 | − | 0.570351i | −0.236206 | − | 0.971703i | \(-0.575904\pi\) |
0.915924 | + | 0.401352i | \(0.131460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2775 | − | 17.8012i | 0.477637 | − | 0.827292i | −0.522034 | − | 0.852925i | \(-0.674827\pi\) |
0.999671 | + | 0.0256324i | \(0.00815994\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.0509 | + | 3.65823i | −0.466100 | + | 0.169646i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.2855 | + | 35.1354i | 0.938699 | + | 1.62587i | 0.767901 | + | 0.640568i | \(0.221301\pi\) |
0.170798 | + | 0.985306i | \(0.445366\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.639157 | − | 3.62484i | 0.0295135 | − | 0.167380i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.3994 | − | 15.4389i | −0.847800 | − | 0.711389i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −57.6774 | − | 20.9929i | −2.65201 | − | 0.965253i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.535353 | + | 4.32590i | −0.0245637 | + | 0.198486i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.798911 | + | 0.290780i | 0.0365796 | + | 0.0133139i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.78854 | + | 8.21356i | 0.447250 | + | 0.375287i | 0.838414 | − | 0.545034i | \(-0.183483\pi\) |
−0.391164 | + | 0.920321i | \(0.627928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.16028 | − | 51.9506i | 0.417673 | − | 2.36874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.824024 | − | 1.42725i | −0.0374944 | − | 0.0649422i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.40807 | + | 2.69632i | −0.336383 | + | 0.122434i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.754890 | − | 1.30751i | 0.0342074 | − | 0.0592489i | −0.848415 | − | 0.529332i | \(-0.822443\pi\) |
0.882622 | + | 0.470083i | \(0.155776\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.6763 | − | 24.9014i | 1.34201 | − | 1.12608i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.10731 | + | 28.9650i | 0.230490 | + | 1.30717i | 0.851907 | + | 0.523693i | \(0.175446\pi\) |
−0.621417 | + | 0.783480i | \(0.713443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.36952 | −0.421982 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.52381 | −0.0684900 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.37519 | + | 7.79907i | 0.0616856 | + | 0.349836i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7504 | − | 11.5379i | 0.615551 | − | 0.516509i | −0.280850 | − | 0.959752i | \(-0.590616\pi\) |
0.896402 | + | 0.443243i | \(0.146172\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.9533 | + | 18.9717i | −0.489358 | + | 0.847594i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.63252 | + | 2.41404i | −0.295730 | + | 0.107637i | −0.485624 | − | 0.874168i | \(-0.661408\pi\) |
0.189895 | + | 0.981804i | \(0.439185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.79401 | − | 11.7676i | −0.302330 | − | 0.523650i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.43275 | + | 13.7968i | −0.108042 | + | 0.612738i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.30918 | − | 4.45493i | −0.235325 | − | 0.197461i | 0.517497 | − | 0.855685i | \(-0.326864\pi\) |
−0.752823 | + | 0.658224i | \(0.771308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.34373 | + | 0.853049i | 0.103681 | + | 0.0377367i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.7838 | + | 18.1835i | 0.520266 | + | 0.802819i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.1319 | − | 3.68770i | −0.446464 | − | 0.162499i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.8525 | − | 48.5440i | −2.54435 | − | 2.13496i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.675251 | − | 3.82954i | 0.0296402 | − | 0.168098i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3552 | + | 31.7921i | 0.804155 | + | 1.39284i | 0.916860 | + | 0.399208i | \(0.130715\pi\) |
−0.112705 | + | 0.993628i | \(0.535952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.83828 | − | 1.39702i | 0.167836 | − | 0.0610874i | −0.256736 | − | 0.966482i | \(-0.582647\pi\) |
0.424572 | + | 0.905394i | \(0.360425\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.605933 | − | 1.04951i | 0.0264451 | − | 0.0458042i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.89390 | + | 4.94557i | −0.256742 | + | 0.215432i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.67276 | − | 20.8293i | −0.159685 | − | 0.905621i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0379653 | −0.00164755 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.1742 | −0.527325 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.192810 | − | 1.09348i | −0.00833592 | − | 0.0472754i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.0126 | + | 20.9881i | −1.07937 | + | 0.905702i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.0318 | − | 36.4281i | 0.905902 | − | 1.56907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.7657 | + | 11.9257i | −1.40871 | + | 0.512727i | −0.930750 | − | 0.365657i | \(-0.880844\pi\) |
−0.477956 | + | 0.878384i | \(0.658622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.72399 | − | 11.6463i | −0.288554 | − | 0.499790i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.435132 | + | 2.46776i | −0.0186390 | + | 0.105707i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1746 | − | 10.2157i | −0.520548 | − | 0.436792i | 0.344275 | − | 0.938869i | \(-0.388125\pi\) |
−0.864823 | + | 0.502077i | \(0.832569\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.61443 | − | 0.587605i | −0.0689022 | − | 0.0250784i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.0594 | − | 12.3022i | 1.23797 | − | 0.524090i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.06654 | + | 1.48010i | 0.172927 | + | 0.0629402i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.9471 | + | 13.3812i | 0.676918 | + | 0.568002i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.82337 | + | 10.3409i | −0.0772588 | + | 0.438156i | 0.921501 | + | 0.388375i | \(0.126963\pi\) |
−0.998760 | + | 0.0497811i | \(0.984148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.7758 | − | 37.7167i | −0.921017 | − | 1.59525i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.0600 | + | 5.11742i | −0.593614 | + | 0.216058i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.48851 | + | 6.04227i | −0.147023 | + | 0.254651i | −0.930126 | − | 0.367241i | \(-0.880302\pi\) |
0.783103 | + | 0.621892i | \(0.213636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.3603 | − | 9.53242i | 0.477931 | − | 0.401032i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.12929 | − | 6.40451i | −0.0474257 | − | 0.268964i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.5455 | −1.07092 | −0.535461 | − | 0.844560i | \(-0.679862\pi\) | ||||
−0.535461 | + | 0.844560i | \(0.679862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.23193 | −0.0515548 | −0.0257774 | − | 0.999668i | \(-0.508206\pi\) | ||||
−0.0257774 | + | 0.999668i | \(0.508206\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.86289 | + | 38.9214i | 0.286701 | + | 1.62596i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.04176 | + | 0.874144i | −0.0434446 | + | 0.0364543i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.53389 | + | 4.38883i | −0.105487 | + | 0.182710i | −0.913937 | − | 0.405856i | \(-0.866974\pi\) |
0.808450 | + | 0.588565i | \(0.200307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.1967 | + | 7.35100i | −0.839346 | + | 0.305497i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.69905 | − | 2.94284i | −0.0704885 | − | 0.122090i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.00008 | + | 22.6856i | −0.165666 | + | 0.939541i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.828261 | − | 0.694994i | −0.0342444 | − | 0.0287344i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.1177 | + | 8.41416i | 0.954170 | + | 0.347290i | 0.771746 | − | 0.635930i | \(-0.219384\pi\) |
0.182424 | + | 0.983220i | \(0.441606\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.7863 | − | 23.0772i | 0.485644 | − | 0.950881i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.1080 | − | 4.77093i | −0.539192 | − | 0.196250i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.6285 | + | 13.9530i | 0.682852 | + | 0.572981i | 0.916838 | − | 0.399259i | \(-0.130733\pi\) |
−0.233986 | + | 0.972240i | \(0.575177\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.151375 | − | 0.858489i | 0.00620576 | − | 0.0351946i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.28928 | − | 14.3575i | −0.339258 | − | 0.587612i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.2847 | − | 12.8426i | 1.44169 | − | 0.524734i | 0.501435 | − | 0.865195i | \(-0.332806\pi\) |
0.940258 | + | 0.340461i | \(0.110583\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.31628 | + | 16.1363i | −0.380019 | + | 0.658212i | −0.991065 | − | 0.133383i | \(-0.957416\pi\) |
0.611046 | + | 0.791595i | \(0.290749\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.992751 | − | 0.833017i | 0.0404280 | − | 0.0339231i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.25933 | − | 29.8271i | −0.213822 | − | 1.21264i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.4925 | −1.76531 | −0.882653 | − | 0.470025i | \(-0.844245\pi\) | ||||
−0.882653 | + | 0.470025i | \(0.844245\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.77327 | −0.355511 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.30511 | − | 52.7719i | −0.376444 | − | 2.13492i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.0997 | − | 31.1304i | 1.49844 | − | 1.25734i | 0.615253 | − | 0.788330i | \(-0.289054\pi\) |
0.883191 | − | 0.469014i | \(-0.155391\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.40216 | − | 4.16066i | 0.0968645 | − | 0.167774i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.8080 | − | 7.93747i | 0.877957 | − | 0.319550i | 0.136572 | − | 0.990630i | \(-0.456391\pi\) |
0.741385 | + | 0.671080i | \(0.234169\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.33161 | + | 4.03847i | 0.0937154 | + | 0.162320i | 0.909072 | − | 0.416640i | \(-0.136792\pi\) |
−0.815356 | + | 0.578959i | \(0.803459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.17388 | + | 6.65742i | −0.0471063 | + | 0.267153i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.74410 | + | 3.14167i | 0.150004 | + | 0.125869i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.939693 | − | 0.342020i | −0.0375877 | − | 0.0136808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 36.8876 | − | 34.3324i | 1.47315 | − | 1.37110i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.0716 | + | 5.12164i | 0.561071 | + | 0.204213i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.92604 | + | 5.81163i | 0.275721 | + | 0.231357i | 0.770153 | − | 0.637859i | \(-0.220180\pi\) |
−0.494432 | + | 0.869216i | \(0.664624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.44913 | + | 36.5748i | −0.256330 | + | 1.45372i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.92646 | − | 5.06878i | −0.116133 | − | 0.201149i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0462 | − | 10.2080i | 1.11123 | − | 0.404456i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.39415 | + | 2.41474i | −0.0551519 | + | 0.0955258i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.88738 | − | 4.10100i | 0.193040 | − | 0.161980i | −0.541145 | − | 0.840929i | \(-0.682009\pi\) |
0.734185 | + | 0.678950i | \(0.237565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.28320 | − | 41.3051i | −0.287221 | − | 1.62891i | −0.697241 | − | 0.716837i | \(-0.745589\pi\) |
0.410020 | − | 0.912077i | \(-0.365522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.1867 | 0.676727 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.4481 | 1.11841 | 0.559205 | − | 0.829030i | \(-0.311107\pi\) | ||||
0.559205 | + | 0.829030i | \(0.311107\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.178625 | − | 1.01303i | −0.00701165 | − | 0.0397651i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.51882 | + | 4.63084i | −0.216300 | + | 0.181497i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.5691 | + | 25.2345i | −0.570134 | + | 0.987501i | 0.426418 | + | 0.904526i | \(0.359775\pi\) |
−0.996552 | + | 0.0829744i | \(0.973558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.64603 | + | 2.78293i | −0.298755 | + | 0.108738i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.439077 | + | 0.760504i | 0.0171300 | + | 0.0296701i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.78347 | + | 10.1145i | −0.0694740 | + | 0.394006i | 0.930165 | + | 0.367141i | \(0.119664\pi\) |
−0.999639 | + | 0.0268649i | \(0.991448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4375 | + | 11.2754i | 0.522658 | + | 0.438562i | 0.865557 | − | 0.500810i | \(-0.166965\pi\) |
−0.342899 | + | 0.939372i | \(0.611409\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.97628 | − | 3.63107i | −0.387447 | − | 0.141019i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.657711 | + | 2.86134i | 0.0255049 | + | 0.110958i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.25142 | + | 3.36724i | 0.358216 | + | 0.130380i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.25368 | + | 2.73016i | 0.125795 | + | 0.105554i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.08332 | − | 45.8428i | 0.312053 | − | 1.76974i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.8057 | − | 32.5724i | −0.724906 | − | 1.25557i | −0.959012 | − | 0.283364i | \(-0.908550\pi\) |
0.234106 | − | 0.972211i | \(-0.424784\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.67116 | + | 1.70016i | −0.179793 | + | 0.0654393i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.73960 | − | 4.74513i | 0.105291 | − | 0.182370i | −0.808566 | − | 0.588406i | \(-0.799756\pi\) |
0.913857 | + | 0.406036i | \(0.133089\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.06768 | + | 3.41319i | −0.156103 | + | 0.130986i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.79417 | + | 27.1891i | 0.183713 | + | 1.04189i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.75347 | −0.296678 | −0.148339 | − | 0.988937i | \(-0.547393\pi\) | ||||
−0.148339 | + | 0.988937i | \(0.547393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.97827 | −0.190210 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.98326 | − | 16.9189i | −0.113819 | − | 0.645498i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.5209 | + | 10.5063i | −0.477009 | + | 0.400258i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.8718 | + | 39.6151i | −0.870084 | + | 1.50703i | −0.00817434 | + | 0.999967i | \(0.502602\pi\) |
−0.861909 | + | 0.507062i | \(0.830731\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.964470 | + | 0.351038i | −0.0366372 | + | 0.0133348i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.04844 | + | 1.81596i | 0.0397698 | + | 0.0688833i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.600111 | − | 3.40340i | 0.0227308 | − | 0.128913i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35.7078 | − | 29.9624i | −1.35059 | − | 1.13328i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.17535 | + | 3.33956i | 0.346548 | + | 0.126133i | 0.509429 | − | 0.860512i | \(-0.329856\pi\) |
−0.162881 | + | 0.986646i | \(0.552079\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.3675 | + | 2.59135i | −1.89965 | + | 0.0977347i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.8713 | + | 7.23258i | 0.748398 | + | 0.272395i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.01105 | − | 5.88297i | −0.263678 | − | 0.221252i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.49893 | + | 31.1860i | −0.206517 | + | 1.17121i | 0.688518 | + | 0.725219i | \(0.258261\pi\) |
−0.895035 | + | 0.445996i | \(0.852850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.761829 | + | 1.31953i | 0.0285708 | + | 0.0494861i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.59695 | − | 2.76507i | 0.284508 | − | 0.103553i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.6477 | − | 25.3706i | 0.547793 | − | 0.948805i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.4622 | + | 17.1698i | −0.764174 | + | 0.641218i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.66644 | + | 32.1360i | 0.211322 | + | 1.19847i | 0.887175 | + | 0.461433i | \(0.152664\pi\) |
−0.675853 | + | 0.737037i | \(0.736225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.26235 | −0.270464 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −34.7153 | −1.29108 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.25712 | + | 7.12949i | 0.0466883 | + | 0.264783i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.4241 | − | 21.3333i | 0.942927 | − | 0.791210i | −0.0351651 | − | 0.999382i | \(-0.511196\pi\) |
0.978092 | + | 0.208172i | \(0.0667513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2708 | + | 21.2536i | −0.454473 | + | 0.787171i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.6174 | − | 4.22838i | 0.429684 | − | 0.156392i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.60440 | + | 6.24300i | 0.133132 | + | 0.230591i | 0.924882 | − | 0.380254i | \(-0.124163\pi\) |
−0.791751 | + | 0.610845i | \(0.790830\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.04526 | + | 11.5993i | −0.0754406 | + | 0.427845i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8984 | + | 22.5704i | 0.990815 | + | 0.831393i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.3257 | − | 8.48987i | −0.858051 | − | 0.312305i | −0.124733 | − | 0.992190i | \(-0.539807\pi\) |
−0.733318 | + | 0.679885i | \(0.762030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.7088 | − | 1.83718i | 1.31180 | − | 0.0674905i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.6624 | + | 10.0683i | 1.01483 | + | 0.369370i | 0.795288 | − | 0.606232i | \(-0.207320\pi\) |
0.219547 | + | 0.975602i | \(0.429542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.59482 | + | 5.53371i | 0.241615 | + | 0.202739i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.207757 | − | 1.17825i | 0.00760142 | − | 0.0431098i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.373941 | − | 0.647685i | −0.0136635 | − | 0.0236659i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.6975 | + | 11.1730i | −1.12017 | + | 0.407707i | −0.834713 | − | 0.550685i | \(-0.814366\pi\) |
−0.285453 | + | 0.958393i | \(0.592144\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.1140 | − | 29.6422i | 0.623667 | − | 1.08022i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.0389 | + | 11.7800i | −0.510927 | + | 0.428719i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00156 | + | 51.0504i | 0.327167 | + | 1.85546i | 0.493986 | + | 0.869470i | \(0.335539\pi\) |
−0.166819 | + | 0.985988i | \(0.553349\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.7219 | 0.570669 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.7963 | 1.08011 | 0.540057 | − | 0.841628i | \(-0.318403\pi\) | ||||
0.540057 | + | 0.841628i | \(0.318403\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.293085 | + | 1.66217i | 0.0106104 | + | 0.0601746i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.235118 | − | 0.197288i | 0.00850072 | − | 0.00713295i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.364944 | − | 0.632101i | 0.0131774 | − | 0.0228238i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.7119 | − | 4.26278i | 0.422342 | − | 0.153720i | −0.122101 | − | 0.992518i | \(-0.538963\pi\) |
0.544443 | + | 0.838798i | \(0.316741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6580 | + | 18.4602i | 0.383838 | + | 0.664827i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.08078 | + | 28.8145i | −0.182743 | + | 1.03639i | 0.746078 | + | 0.665858i | \(0.231934\pi\) |
−0.928821 | + | 0.370528i | \(0.879177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.55399 | + | 3.82125i | 0.163584 | + | 0.137263i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.1761 | + | 4.79572i | 0.472691 | + | 0.172045i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.60743 | + | 11.3435i | 0.0934209 | + | 0.406423i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −70.9925 | − | 25.8392i | −2.54031 | − | 0.924598i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.5676 | + | 23.1320i | 0.985187 | + | 0.826670i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.31814 | + | 13.1468i | −0.0827378 | + | 0.469229i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1220 | + | 27.9240i | 0.574686 | + | 0.995385i | 0.996076 | + | 0.0885051i | \(0.0282090\pi\) |
−0.421390 | + | 0.906879i | \(0.638458\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.86836 | − | 2.49988i | 0.244520 | − | 0.0889980i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.99435 | − | 8.65047i | 0.177579 | − | 0.307575i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.3021 | − | 21.2310i | 0.898505 | − | 0.753935i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.12006 | − | 6.35219i | −0.0397245 | − | 0.225289i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.58966 | 0.0917304 | 0.0458652 | − | 0.998948i | \(-0.485396\pi\) | ||||
0.0458652 | + | 0.998948i | \(0.485396\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.2114 | 0.538142 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.298822 | + | 1.69470i | 0.0105584 | + | 0.0598795i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.2268 | + | 15.2941i | −0.643211 | + | 0.539718i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.457993 | + | 0.793267i | −0.0161421 | + | 0.0279590i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.59355 | − | 3.12780i | 0.302507 | − | 0.110104i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.3087 | − | 17.8552i | −0.362435 | − | 0.627756i | 0.625926 | − | 0.779883i | \(-0.284721\pi\) |
−0.988361 | + | 0.152126i | \(0.951388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.10908 | − | 11.9612i | 0.0740600 | − | 0.420015i | −0.925126 | − | 0.379661i | \(-0.876040\pi\) |
0.999185 | − | 0.0403535i | \(-0.0128484\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.6072 | + | 17.2915i | 0.722727 | + | 0.606440i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.2330 | − | 7.36422i | −0.708732 | − | 0.257957i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.4792 | + | 28.3679i | −1.06633 | + | 0.992466i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.684340 | − | 0.249080i | −0.0239128 | − | 0.00870354i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.05042 | + | 2.55961i | 0.106460 | + | 0.0893309i | 0.694464 | − | 0.719527i | \(-0.255642\pi\) |
−0.588004 | + | 0.808858i | \(0.700086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.228416 | − | 1.29541i | 0.00796207 | − | 0.0451551i | −0.980568 | − | 0.196180i | \(-0.937146\pi\) |
0.988530 | + | 0.151025i | \(0.0482574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.78042 | + | 10.0120i | 0.201248 | + | 0.348572i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.87578 | − | 1.04670i | 0.100001 | − | 0.0363972i | −0.291535 | − | 0.956560i | \(-0.594166\pi\) |
0.391536 | + | 0.920163i | \(0.371944\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.6472 | + | 44.4222i | −0.890763 | + | 1.54285i | −0.0518002 | + | 0.998657i | \(0.516496\pi\) |
−0.838963 | + | 0.544189i | \(0.816837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.6703 | + | 13.9880i | −0.578286 | + | 0.485239i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.47122 | + | 8.34371i | 0.0509748 | + | 0.289092i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.1757 | 0.421358 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.5513 | 1.02144 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.38236 | + | 13.5110i | 0.0822482 | + | 0.466453i | 0.997917 | + | 0.0645179i | \(0.0205510\pi\) |
−0.915668 | + | 0.401935i | \(0.868338\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.9331 | − | 15.0476i | 0.618382 | − | 0.518884i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.6205 | − | 33.9838i | 0.675767 | − | 1.17046i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.31698 | − | 2.66316i | 0.251712 | − | 0.0916155i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.2001 | − | 17.6670i | −0.350478 | − | 0.607046i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.00344 | − | 28.3759i | 0.171718 | − | 0.973860i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0536 | − | 10.1142i | −0.413192 | − | 0.346709i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.4590 | − | 16.9097i | −1.59072 | − | 0.578976i | −0.613224 | − | 0.789909i | \(-0.710128\pi\) |
−0.977501 | + | 0.210933i | \(0.932350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.470175 | + | 0.920593i | −0.0160797 | + | 0.0314836i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.4491 | + | 3.80315i | 0.356933 | + | 0.129913i | 0.514262 | − | 0.857633i | \(-0.328066\pi\) |
−0.157329 | + | 0.987546i | \(0.550288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.5108 | − | 24.7625i | −1.00690 | − | 0.844886i | −0.0189707 | − | 0.999820i | \(-0.506039\pi\) |
−0.987925 | + | 0.154934i | \(0.950483\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.561921 | − | 3.18681i | 0.0191502 | − | 0.108606i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.92961 | + | 6.80628i | 0.133765 | + | 0.231688i | 0.925125 | − | 0.379662i | \(-0.123960\pi\) |
−0.791360 | + | 0.611351i | \(0.790626\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.03095 | + | 0.739205i | −0.0690544 | + | 0.0251337i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.7864 | + | 23.8788i | −0.468211 | + | 0.810965i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.6248 | + | 26.5363i | −1.07280 | + | 0.900184i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.32639 | + | 24.5362i | 0.146594 | + | 0.831377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.86957 | −0.0632753 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.673555 | −0.0227703 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.02596 | + | 39.8462i | 0.237250 | + | 1.34551i | 0.837823 | + | 0.545941i | \(0.183828\pi\) |
−0.600573 | + | 0.799570i | \(0.705061\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.70858 | + | 7.30737i | −0.293733 | + | 0.246471i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.248999 | − | 0.431278i | 0.00838898 | − | 0.0145301i | −0.861800 | − | 0.507247i | \(-0.830663\pi\) |
0.870189 | + | 0.492717i | \(0.163996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.9080 | − | 15.2533i | 1.41032 | − | 0.513314i | 0.479095 | − | 0.877763i | \(-0.340965\pi\) |
0.931223 | + | 0.364449i | \(0.118743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.144018 | + | 0.249446i | 0.00484110 | + | 0.00838503i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.46596 | + | 30.9990i | −0.183529 | + | 1.04084i | 0.744302 | + | 0.667843i | \(0.232782\pi\) |
−0.927831 | + | 0.373001i | \(0.878329\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.01995 | − | 2.53404i | −0.101286 | − | 0.0849890i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 58.2982 | + | 21.2188i | 1.95306 | + | 0.710857i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −47.1779 | + | 19.9726i | −1.57875 | + | 0.668358i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.0533 | + | 6.20691i | 0.570030 | + | 0.207474i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.54559 | + | 7.17060i | 0.285329 | + | 0.239419i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.47335 | − | 42.3835i | 0.249250 | − | 1.41357i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.31991 | − | 4.01820i | −0.0772874 | − | 0.133866i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.8781 | − | 3.95930i | 0.362000 | − | 0.131757i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.73720 | + | 6.47301i | −0.124229 | + | 0.215170i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.3861 | − | 24.6578i | 0.975748 | − | 0.818750i | −0.00769425 | − | 0.999970i | \(-0.502449\pi\) |
0.983443 | + | 0.181220i | \(0.0580047\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.559562 | − | 3.17344i | −0.0185595 | − | 0.105256i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.1083 | 1.59390 | 0.796949 | − | 0.604046i | \(-0.206446\pi\) | ||||
0.796949 | + | 0.604046i | \(0.206446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.4169 | 1.07284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.26341 | + | 12.8364i | 0.0748260 | + | 0.424360i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.19834 | + | 3.52282i | −0.138641 | + | 0.116334i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.30053 | − | 7.44874i | 0.141861 | − | 0.245711i | −0.786336 | − | 0.617799i | \(-0.788025\pi\) |
0.928198 | + | 0.372088i | \(0.121358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.35688 | + | 0.493863i | −0.0447106 | + | 0.0162733i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.8028 | − | 46.4238i | −0.882224 | − | 1.52806i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00917 | − | 11.3946i | 0.0660612 | − | 0.374652i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.95875 | − | 1.64359i | −0.0643339 | − | 0.0539826i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.4554 | + | 13.9966i | 1.26168 | + | 0.459214i | 0.884332 | − | 0.466858i | \(-0.154614\pi\) |
0.377348 | + | 0.926072i | \(0.376836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.5183 | − | 23.9461i | −0.508590 | − | 0.784802i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.7439 | + | 8.64209i | 0.777342 | + | 0.282929i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.37048 | + | 5.34547i | 0.208337 | + | 0.174816i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.06308 | − | 28.7142i | 0.165404 | − | 0.938051i | −0.783244 | − | 0.621715i | \(-0.786436\pi\) |
0.948647 | − | 0.316336i | \(-0.102453\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.6865 | + | 34.0979i | 0.642443 | + | 1.11274i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.6205 | − | 14.4207i | 1.29159 | − | 0.470100i | 0.397342 | − | 0.917671i | \(-0.369933\pi\) |
0.894249 | + | 0.447570i | \(0.147711\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.81567 | + | 3.14483i | −0.0591263 | + | 0.102410i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.56487 | + | 2.15218i | −0.0834353 | + | 0.0700105i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.78955 | − | 21.4916i | −0.123144 | − | 0.698383i | −0.982393 | − | 0.186826i | \(-0.940180\pi\) |
0.859249 | − | 0.511557i | \(-0.170931\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.8826 | −0.548034 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −56.1404 | −1.82048 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.49487 | − | 42.5055i | −0.242783 | − | 1.37689i | −0.825587 | − | 0.564276i | \(-0.809156\pi\) |
0.582804 | − | 0.812613i | \(-0.301956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.8271 | − | 14.1196i | 0.544512 | − | 0.456900i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 41.8472 | − | 72.4815i | 1.35273 | − | 2.34299i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.15092 | + | 1.14684i | −0.101748 | + | 0.0370334i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.17040 | − | 3.75924i | −0.0700129 | − | 0.121266i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0457249 | − | 0.259319i | 0.00147346 | − | 0.00835643i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.15097 | + | 7.67857i | 0.294580 | + | 0.247182i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.0667 | + | 19.6787i | 1.73867 | + | 0.632823i | 0.999185 | − | 0.0403543i | \(-0.0128487\pi\) |
0.739481 | + | 0.673177i | \(0.235071\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.24661 | + | 10.0732i | −0.0400470 | + | 0.323598i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.4251 | − | 8.16206i | −0.719655 | − | 0.261933i | −0.0438756 | − | 0.999037i | \(-0.513971\pi\) |
−0.675779 | + | 0.737104i | \(0.736193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.08194 | + | 0.907854i | 0.0346854 | + | 0.0291045i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.42444 | + | 8.07838i | −0.0456185 | + | 0.258715i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.3169 | + | 33.4578i | 0.618002 | + | 1.07041i | 0.989850 | + | 0.142118i | \(0.0453911\pi\) |
−0.371847 | + | 0.928294i | \(0.621276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.8142 | + | 15.9470i | −1.40031 | + | 0.509670i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.297127 | + | 0.514640i | −0.00948655 | + | 0.0164312i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.7057 | + | 9.82225i | −0.373354 | + | 0.313281i | −0.810087 | − | 0.586310i | \(-0.800580\pi\) |
0.436733 | + | 0.899591i | \(0.356136\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.34630 | + | 7.63522i | 0.0428965 | + | 0.243278i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.2434 | 0.453373 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.9906 | −0.413076 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.957751 | + | 5.43167i | 0.0304240 | + | 0.172543i | 0.996234 | − | 0.0867092i | \(-0.0276351\pi\) |
−0.965810 | + | 0.259252i | \(0.916524\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.2266 | + | 13.6158i | −0.514936 | + | 0.432083i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.60718 | + | 7.97988i | −0.146058 | + | 0.252979i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1034 | − | 10.2288i | 0.890044 | − | 0.323949i | 0.143788 | − | 0.989609i | \(-0.454072\pi\) |
0.746256 | + | 0.665659i | \(0.231850\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.7578 | − | 49.8100i | −0.909858 | − | 1.57592i |
(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 | 380.2.u.a.61.1 | ✓ | 18 | |
19.5 | even | 9 | inner | 380.2.u.a.81.1 | yes | 18 | |
19.9 | even | 9 | 7220.2.a.v.1.3 | 9 | |||
19.10 | odd | 18 | 7220.2.a.x.1.7 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.u.a.61.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
380.2.u.a.81.1 | yes | 18 | 19.5 | even | 9 | inner | |
7220.2.a.v.1.3 | 9 | 19.9 | even | 9 | |||
7220.2.a.x.1.7 | 9 | 19.10 | odd | 18 |