Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} + 28x^{5} + 14x^{4} - 52x^{3} + 306x^{2} + 1052x + 1051 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.3 | ||
Root | \(1.89574 + 2.48951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.865 |
Dual form | 1512.2.s.n.1297.3 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0144658 | − | 0.0250554i | −0.00646928 | − | 0.0112051i | 0.862773 | − | 0.505592i | \(-0.168726\pi\) |
−0.869242 | + | 0.494387i | \(0.835393\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.70811 | + | 2.02048i | −0.645605 | + | 0.763671i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.88127 | + | 3.25845i | −0.567224 | + | 0.982461i | 0.429615 | + | 0.903012i | \(0.358649\pi\) |
−0.996839 | + | 0.0794487i | \(0.974684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.97107 | −0.824026 | −0.412013 | − | 0.911178i | \(-0.635174\pi\) | ||||
−0.412013 | + | 0.911178i | \(0.635174\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.708111 | − | 1.22648i | 0.171742 | − | 0.297466i | −0.767287 | − | 0.641304i | \(-0.778394\pi\) |
0.939029 | + | 0.343838i | \(0.111727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.81196 | − | 6.60250i | −0.874523 | − | 1.51472i | −0.857270 | − | 0.514867i | \(-0.827841\pi\) |
−0.0172529 | − | 0.999851i | \(-0.505492\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.98512 | − | 5.17037i | −0.622440 | − | 1.07810i | −0.989030 | − | 0.147715i | \(-0.952808\pi\) |
0.366590 | − | 0.930382i | \(-0.380525\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.49958 | − | 4.32940i | 0.499916 | − | 0.865880i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.99916 | 1.85680 | 0.928399 | − | 0.371585i | \(-0.121186\pi\) | ||||
0.928399 | + | 0.371585i | \(0.121186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.27700 | − | 7.40799i | 0.768173 | − | 1.33051i | −0.170380 | − | 0.985378i | \(-0.554500\pi\) |
0.938553 | − | 0.345136i | \(-0.112167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0753332 | + | 0.0135696i | 0.0127336 | + | 0.00229368i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.737043 | − | 1.27660i | −0.121169 | − | 0.209871i | 0.799060 | − | 0.601251i | \(-0.205331\pi\) |
−0.920229 | + | 0.391380i | \(0.871998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.38729 | −0.685180 | −0.342590 | − | 0.939485i | \(-0.611304\pi\) | ||||
−0.342590 | + | 0.939485i | \(0.611304\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.76254 | 0.573782 | 0.286891 | − | 0.957963i | \(-0.407378\pi\) | ||||
0.286891 | + | 0.957963i | \(0.407378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.07491 | + | 3.59386i | 0.302657 | + | 0.524218i | 0.976737 | − | 0.214441i | \(-0.0687929\pi\) |
−0.674080 | + | 0.738659i | \(0.735460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.16471 | − | 6.90242i | −0.166388 | − | 0.986060i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.60385 | − | 6.24204i | 0.495026 | − | 0.857411i | −0.504957 | − | 0.863144i | \(-0.668492\pi\) |
0.999984 | + | 0.00573358i | \(0.00182507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.108856 | 0.0146781 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.93027 | + | 12.0036i | −0.902244 | + | 1.56273i | −0.0776699 | + | 0.996979i | \(0.524748\pi\) |
−0.824574 | + | 0.565754i | \(0.808585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.61831 | − | 9.73120i | −0.719351 | − | 1.24595i | −0.961257 | − | 0.275653i | \(-0.911106\pi\) |
0.241906 | − | 0.970300i | \(-0.422227\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0429788 | + | 0.0744414i | 0.00533086 | + | 0.00923332i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.77742 | + | 4.81064i | −0.339316 | + | 0.587713i | −0.984304 | − | 0.176480i | \(-0.943529\pi\) |
0.644988 | + | 0.764193i | \(0.276862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5661 | −1.37264 | −0.686319 | − | 0.727301i | \(-0.740775\pi\) | ||||
−0.686319 | + | 0.727301i | \(0.740775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.17918 | − | 3.77445i | 0.255054 | − | 0.441766i | −0.709856 | − | 0.704346i | \(-0.751240\pi\) |
0.964910 | + | 0.262580i | \(0.0845735\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.37024 | − | 9.36688i | −0.384074 | − | 1.06745i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.04556 | − | 12.2033i | −0.792688 | − | 1.37298i | −0.924297 | − | 0.381674i | \(-0.875348\pi\) |
0.131609 | − | 0.991302i | \(-0.457986\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.62475 | 0.727161 | 0.363580 | − | 0.931563i | \(-0.381554\pi\) | ||||
0.363580 | + | 0.931563i | \(0.381554\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0409735 | −0.00444420 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.14423 | + | 3.71391i | 0.227288 | + | 0.393674i | 0.957003 | − | 0.290077i | \(-0.0936809\pi\) |
−0.729716 | + | 0.683751i | \(0.760348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.07491 | − | 6.00300i | 0.531996 | − | 0.629285i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.110286 | + | 0.191020i | −0.0113151 | + | 0.0195983i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.77458 | −0.687854 | −0.343927 | − | 0.938996i | \(-0.611757\pi\) | ||||
−0.343927 | + | 0.938996i | \(0.611757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.37282 | − | 5.84190i | 0.335609 | − | 0.581291i | −0.647993 | − | 0.761646i | \(-0.724391\pi\) |
0.983602 | + | 0.180355i | \(0.0577247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.38169 | − | 2.39315i | −0.136142 | − | 0.235804i | 0.789891 | − | 0.613247i | \(-0.210137\pi\) |
−0.926033 | + | 0.377442i | \(0.876804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.90134 | + | 15.4176i | 0.860525 | + | 1.49047i | 0.871423 | + | 0.490532i | \(0.163198\pi\) |
−0.0108984 | + | 0.999941i | \(0.503469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.41622 | + | 9.38117i | −0.518780 | + | 0.898553i | 0.480982 | + | 0.876731i | \(0.340280\pi\) |
−0.999762 | + | 0.0218227i | \(0.993053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.879102 | 0.0826990 | 0.0413495 | − | 0.999145i | \(-0.486834\pi\) | ||||
0.0413495 | + | 0.999145i | \(0.486834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0863639 | + | 0.149587i | −0.00805348 | + | 0.0139490i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.26856 | + | 3.52570i | 0.116289 | + | 0.323200i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.57835 | − | 2.73378i | −0.143486 | − | 0.248526i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.289291 | −0.0258750 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.27156 | −0.112833 | −0.0564165 | − | 0.998407i | \(-0.517967\pi\) | ||||
−0.0564165 | + | 0.998407i | \(0.517967\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.31998 | − | 14.4106i | −0.726920 | − | 1.25906i | −0.958179 | − | 0.286171i | \(-0.907618\pi\) |
0.231258 | − | 0.972892i | \(-0.425716\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.8515 | + | 3.57581i | 1.72134 | + | 0.310062i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.44515 | − | 4.23513i | 0.208904 | − | 0.361832i | −0.742466 | − | 0.669884i | \(-0.766344\pi\) |
0.951369 | + | 0.308052i | \(0.0996772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.61187 | −0.730449 | −0.365225 | − | 0.930919i | \(-0.619008\pi\) | ||||
−0.365225 | + | 0.930919i | \(0.619008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.58938 | − | 9.68109i | 0.467407 | − | 0.809573i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.144645 | − | 0.250533i | −0.0120122 | − | 0.0208057i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.95920 | − | 8.58959i | −0.406274 | − | 0.703686i | 0.588195 | − | 0.808719i | \(-0.299839\pi\) |
−0.994469 | + | 0.105033i | \(0.966505\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.73704 | + | 8.20480i | −0.385495 | + | 0.667697i | −0.991838 | − | 0.127506i | \(-0.959303\pi\) |
0.606343 | + | 0.795203i | \(0.292636\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.247481 | −0.0198781 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.83745 | − | 10.1108i | 0.465880 | − | 0.806927i | −0.533361 | − | 0.845888i | \(-0.679071\pi\) |
0.999241 | + | 0.0389606i | \(0.0124047\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.5456 | + | 2.80019i | 1.22516 | + | 0.220686i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.36680 | − | 11.0276i | −0.498687 | − | 0.863750i | 0.501312 | − | 0.865266i | \(-0.332851\pi\) |
−0.999999 | + | 0.00151597i | \(0.999517\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.8597 | −1.53679 | −0.768395 | − | 0.639976i | \(-0.778944\pi\) | ||||
−0.768395 | + | 0.639976i | \(0.778944\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.17275 | −0.320981 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.55443 | + | 4.42440i | 0.194210 | + | 0.336381i | 0.946641 | − | 0.322290i | \(-0.104452\pi\) |
−0.752432 | + | 0.658670i | \(0.771119\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.47793 | + | 12.4455i | 0.338499 | + | 0.940789i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.98470 | + | 15.5620i | −0.671548 | + | 1.16315i | 0.305917 | + | 0.952058i | \(0.401037\pi\) |
−0.977465 | + | 0.211097i | \(0.932296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.72157 | −0.276622 | −0.138311 | − | 0.990389i | \(-0.544167\pi\) | ||||
−0.138311 | + | 0.990389i | \(0.544167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0213238 | + | 0.0369338i | −0.00156775 | + | 0.00271543i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.66430 | + | 4.61469i | 0.194833 | + | 0.337460i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.88127 | + | 4.99051i | 0.208481 | + | 0.361100i | 0.951236 | − | 0.308463i | \(-0.0998146\pi\) |
−0.742755 | + | 0.669563i | \(0.766481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.80635 | + | 3.12870i | −0.130024 | + | 0.225209i | −0.923686 | − | 0.383151i | \(-0.874839\pi\) |
0.793661 | + | 0.608360i | \(0.208172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.44432 | 0.459139 | 0.229569 | − | 0.973292i | \(-0.426268\pi\) | ||||
0.229569 | + | 0.973292i | \(0.426268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.29147 | − | 2.23689i | 0.0915499 | − | 0.158569i | −0.816614 | − | 0.577185i | \(-0.804151\pi\) |
0.908163 | + | 0.418616i | \(0.137485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.0797 | + | 20.2032i | −1.19876 | + | 1.41798i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0634655 | + | 0.109925i | 0.00443262 | + | 0.00767753i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.6853 | 1.98420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.4162 | 1.33667 | 0.668334 | − | 0.743861i | \(-0.267008\pi\) | ||||
0.668334 | + | 0.743861i | \(0.267008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0544280 | − | 0.0942720i | −0.00371196 | − | 0.00642930i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.66213 | + | 21.2953i | 0.520139 | + | 1.44562i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.10385 | + | 3.64397i | −0.141520 | + | 0.245120i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5074 | 0.770589 | 0.385295 | − | 0.922794i | \(-0.374100\pi\) | ||||
0.385295 | + | 0.922794i | \(0.374100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.48595 | − | 2.57375i | 0.0986261 | − | 0.170826i | −0.812490 | − | 0.582975i | \(-0.801889\pi\) |
0.911116 | + | 0.412150i | \(0.135222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0775 | − | 19.1868i | −0.732023 | − | 1.26790i | −0.956017 | − | 0.293310i | \(-0.905243\pi\) |
0.223995 | − | 0.974590i | \(-0.428090\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0056 | − | 17.3302i | −0.655489 | − | 1.13534i | −0.981771 | − | 0.190068i | \(-0.939129\pi\) |
0.326282 | − | 0.945272i | \(-0.394204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0600304 | − | 0.103976i | 0.00391595 | − | 0.00678263i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.6930 | −1.53257 | −0.766286 | − | 0.642500i | \(-0.777897\pi\) | ||||
−0.766286 | + | 0.642500i | \(0.777897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.64983 | + | 9.78579i | −0.363938 | + | 0.630358i | −0.988605 | − | 0.150533i | \(-0.951901\pi\) |
0.624668 | + | 0.780891i | \(0.285234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.156095 | + | 0.129031i | −0.00997253 | + | 0.00824350i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3256 | + | 19.6165i | 0.720630 | + | 1.24817i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.76254 | 0.300609 | 0.150304 | − | 0.988640i | \(-0.451975\pi\) | ||||
0.150304 | + | 0.988640i | \(0.451975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.4632 | 1.41225 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.3230 | − | 21.3440i | −0.768687 | − | 1.33140i | −0.938275 | − | 0.345890i | \(-0.887577\pi\) |
0.169588 | − | 0.985515i | \(-0.445756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.83829 | + | 0.691383i | 0.238500 | + | 0.0429605i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.33787 | − | 9.24547i | 0.329147 | − | 0.570100i | −0.653196 | − | 0.757189i | \(-0.726572\pi\) |
0.982343 | + | 0.187089i | \(0.0599054\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.208530 | −0.0128099 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.653264 | + | 1.13149i | −0.0398302 | + | 0.0689880i | −0.885253 | − | 0.465109i | \(-0.846015\pi\) |
0.845423 | + | 0.534097i | \(0.179348\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.83787 | − | 17.0397i | −0.597608 | − | 1.03509i | −0.993173 | − | 0.116650i | \(-0.962785\pi\) |
0.395565 | − | 0.918438i | \(-0.370549\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.40477 | + | 16.2895i | 0.567129 | + | 0.982296i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3774 | + | 24.9024i | −0.863855 | + | 1.49624i | 0.00432421 | + | 0.999991i | \(0.498624\pi\) |
−0.868179 | + | 0.496250i | \(0.834710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.20853 | 0.549335 | 0.274667 | − | 0.961539i | \(-0.411432\pi\) | ||||
0.274667 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.2613 | + | 19.5051i | −0.669414 | + | 1.15946i | 0.308654 | + | 0.951174i | \(0.400121\pi\) |
−0.978068 | + | 0.208285i | \(0.933212\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.49398 | − | 8.86445i | 0.442356 | − | 0.523252i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.49716 | + | 12.9855i | 0.441009 | + | 0.763850i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.30534 | 0.193100 | 0.0965501 | − | 0.995328i | \(-0.469219\pi\) | ||||
0.0965501 | + | 0.995328i | \(0.469219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.401006 | 0.0233475 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.86898 | + | 15.3615i | 0.512907 | + | 0.888380i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.42683 | + | 7.60215i | −0.370437 | + | 0.438181i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.162546 | + | 0.281538i | −0.00930737 | + | 0.0161208i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.2358 | −0.812479 | −0.406240 | − | 0.913767i | \(-0.633160\pi\) | ||||
−0.406240 | + | 0.913767i | \(0.633160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.9694 | − | 25.9278i | 0.848836 | − | 1.47023i | −0.0334108 | − | 0.999442i | \(-0.510637\pi\) |
0.882247 | − | 0.470786i | \(-0.156030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.47107 | − | 9.47617i | −0.309243 | − | 0.535625i | 0.668954 | − | 0.743304i | \(-0.266742\pi\) |
−0.978197 | + | 0.207679i | \(0.933409\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.27700 | + | 9.14004i | 0.296386 | + | 0.513356i | 0.975306 | − | 0.220856i | \(-0.0708851\pi\) |
−0.678920 | + | 0.734212i | \(0.737552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.8111 | + | 32.5818i | −1.05322 | + | 1.82423i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.7972 | −0.600770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.42643 | + | 12.8630i | −0.411944 | + | 0.713508i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.8055 | − | 1.94638i | −0.595727 | − | 0.107307i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1319 | + | 26.2093i | 0.831727 | + | 1.44059i | 0.896668 | + | 0.442704i | \(0.145981\pi\) |
−0.0649412 | + | 0.997889i | \(0.520686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.160710 | 0.00878053 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.8428 | 1.46222 | 0.731111 | − | 0.682259i | \(-0.239002\pi\) | ||||
0.731111 | + | 0.682259i | \(0.239002\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0924 | + | 27.8728i | 0.871452 | + | 1.50940i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.9357 | + | 9.43682i | 0.860447 | + | 0.509540i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.08938 | − | 15.7433i | 0.487944 | − | 0.845143i | −0.511960 | − | 0.859009i | \(-0.671081\pi\) |
0.999904 | + | 0.0138661i | \(0.00441387\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.15586 | 0.275987 | 0.137993 | − | 0.990433i | \(-0.455935\pi\) | ||||
0.137993 | + | 0.990433i | \(0.455935\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.1838 | + | 24.5670i | −0.754926 | + | 1.30757i | 0.190485 | + | 0.981690i | \(0.438994\pi\) |
−0.945411 | + | 0.325880i | \(0.894339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.167312 | + | 0.289792i | 0.00887998 | + | 0.0153806i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.9793 | − | 22.4808i | −0.685020 | − | 1.18649i | −0.973431 | − | 0.228982i | \(-0.926460\pi\) |
0.288411 | − | 0.957507i | \(-0.406873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.5620 | + | 33.8824i | −1.02958 | + | 1.78329i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.126094 | −0.00660006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.91062 | − | 17.1657i | 0.517330 | − | 0.896042i | −0.482467 | − | 0.875914i | \(-0.660259\pi\) |
0.999797 | − | 0.0201281i | \(-0.00640740\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.45618 | + | 17.9436i | 0.335188 | + | 0.931586i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.58294 | − | 7.93789i | −0.237296 | − | 0.411008i | 0.722642 | − | 0.691223i | \(-0.242928\pi\) |
−0.959937 | + | 0.280215i | \(0.909594\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.7082 | −1.53005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.12575 | 0.314658 | 0.157329 | − | 0.987546i | \(-0.449712\pi\) | ||||
0.157329 | + | 0.987546i | \(0.449712\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.25795 | − | 7.37498i | −0.217571 | − | 0.376844i | 0.736494 | − | 0.676444i | \(-0.236480\pi\) |
−0.954065 | + | 0.299600i | \(0.903147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.185938 | + | 0.219942i | −0.00947628 | + | 0.0112093i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.16773 | − | 5.48667i | 0.160610 | − | 0.278185i | −0.774477 | − | 0.632602i | \(-0.781987\pi\) |
0.935088 | + | 0.354416i | \(0.115320\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.45517 | −0.427596 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.203839 | + | 0.353059i | −0.0102562 | + | 0.0177643i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.6401 | + | 27.0895i | 0.784956 | + | 1.35958i | 0.929026 | + | 0.370015i | \(0.120648\pi\) |
−0.144070 | + | 0.989567i | \(0.546019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.31454 | + | 2.27686i | 0.0656452 | + | 0.113701i | 0.896980 | − | 0.442071i | \(-0.145756\pi\) |
−0.831335 | + | 0.555772i | \(0.812423\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.7073 | + | 22.0096i | −0.632994 | + | 1.09638i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.54630 | 0.274920 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.89574 | − | 11.9438i | 0.340972 | − | 0.590581i | −0.643641 | − | 0.765327i | \(-0.722577\pi\) |
0.984614 | + | 0.174746i | \(0.0559105\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.4154 | − | 34.5059i | −0.610921 | − | 1.69793i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0958321 | − | 0.165986i | −0.00470421 | − | 0.00814793i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.84532 | 0.139003 | 0.0695016 | − | 0.997582i | \(-0.477859\pi\) | ||||
0.0695016 | + | 0.997582i | \(0.477859\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4374 | 1.43469 | 0.717347 | − | 0.696716i | \(-0.245356\pi\) | ||||
0.717347 | + | 0.696716i | \(0.245356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.53996 | − | 6.13139i | −0.171713 | − | 0.297416i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.2584 | + | 5.27026i | 1.41592 | + | 0.255046i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.36096 | − | 4.08930i | 0.113723 | − | 0.196975i | −0.803545 | − | 0.595243i | \(-0.797056\pi\) |
0.917269 | + | 0.398269i | \(0.130389\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.83813 | −0.184449 | −0.0922243 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922243 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.7583 | + | 39.4185i | −1.08868 | + | 1.88564i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.23018 | − | 15.9871i | −0.440533 | − | 0.763025i | 0.557196 | − | 0.830381i | \(-0.311877\pi\) |
−0.997729 | + | 0.0673558i | \(0.978544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.3001 | + | 19.5723i | 0.536883 | + | 0.929908i | 0.999070 | + | 0.0431258i | \(0.0137316\pi\) |
−0.462187 | + | 0.886783i | \(0.652935\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0620357 | − | 0.107449i | 0.00294078 | − | 0.00509357i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0043 | 0.944063 | 0.472031 | − | 0.881582i | \(-0.343521\pi\) | ||||
0.472031 | + | 0.881582i | \(0.343521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.25368 | − | 14.2958i | 0.388650 | − | 0.673162i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.223820 | − | 0.0403163i | −0.0104929 | − | 0.00189006i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.5196 | − | 23.4167i | −0.632423 | − | 1.09539i | −0.987055 | − | 0.160382i | \(-0.948727\pi\) |
0.354632 | − | 0.935006i | \(-0.384606\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.9557 | −1.44175 | −0.720875 | − | 0.693065i | \(-0.756260\pi\) | ||||
−0.720875 | + | 0.693065i | \(0.756260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.96105 | 0.184086 | 0.0920428 | − | 0.995755i | \(-0.470660\pi\) | ||||
0.0920428 | + | 0.995755i | \(0.470660\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.5834 | + | 23.5271i | 0.628563 | + | 1.08870i | 0.987840 | + | 0.155472i | \(0.0496899\pi\) |
−0.359277 | + | 0.933231i | \(0.616977\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.97567 | − | 13.8288i | −0.229755 | − | 0.638557i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.07835 | + | 12.2601i | −0.325463 | + | 0.563718i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.1132 | −1.74875 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.83788 | − | 15.3077i | 0.403813 | − | 0.699425i | −0.590369 | − | 0.807133i | \(-0.701018\pi\) |
0.994183 | + | 0.107708i | \(0.0343512\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.18980 | + | 3.79285i | 0.0998465 | + | 0.172939i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0979995 | + | 0.169740i | 0.00444993 | + | 0.00770750i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.79665 | − | 11.7722i | 0.307986 | − | 0.533447i | −0.669936 | − | 0.742419i | \(-0.733678\pi\) |
0.977922 | + | 0.208972i | \(0.0670117\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.8256 | 0.984974 | 0.492487 | − | 0.870320i | \(-0.336088\pi\) | ||||
0.492487 | + | 0.870320i | \(0.336088\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.08052 | − | 12.2638i | 0.318890 | − | 0.552334i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.7561 | − | 23.3690i | 0.886182 | − | 1.04824i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.6374 | − | 18.4245i | −0.476194 | − | 0.824792i | 0.523434 | − | 0.852066i | \(-0.324651\pi\) |
−0.999628 | + | 0.0272740i | \(0.991317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.2281 | 1.21404 | 0.607020 | − | 0.794687i | \(-0.292365\pi\) | ||||
0.607020 | + | 0.794687i | \(0.292365\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.195162 | −0.00868459 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.23879 | − | 16.0021i | −0.409502 | − | 0.709279i | 0.585332 | − | 0.810794i | \(-0.300964\pi\) |
−0.994834 | + | 0.101515i | \(0.967631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.90394 | + | 10.8502i | 0.172700 | + | 0.479984i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.0399743 | + | 0.0692376i | −0.00176148 | + | 0.00305097i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.6139 | −0.686698 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.93913 | − | 5.09073i | 0.128766 | − | 0.223029i | −0.794433 | − | 0.607352i | \(-0.792232\pi\) |
0.923199 | + | 0.384323i | \(0.125565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.22258 | − | 10.7778i | −0.272094 | − | 0.471281i | 0.697304 | − | 0.716776i | \(-0.254383\pi\) |
−0.969398 | + | 0.245495i | \(0.921050\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.05719 | − | 10.4914i | −0.263855 | − | 0.457011i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.32183 | + | 10.9497i | −0.274862 | + | 0.476075i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.0349 | 0.564606 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.257529 | − | 0.446054i | 0.0111340 | − | 0.0192846i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.6824 | + | 9.19015i | 1.06314 | + | 0.395848i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7362 | + | 18.5957i | 0.461586 | + | 0.799490i | 0.999040 | − | 0.0438031i | \(-0.0139474\pi\) |
−0.537455 | + | 0.843293i | \(0.680614\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.313399 | 0.0134245 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.6741 | 1.31153 | 0.655764 | − | 0.754966i | \(-0.272347\pi\) | ||||
0.655764 | + | 0.754966i | \(0.272347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.1164 | − | 66.0195i | −1.62381 | − | 2.81253i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.6911 | + | 6.60910i | 1.56027 | + | 0.281047i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.5857 | + | 35.6555i | −0.872244 | + | 1.51077i | −0.0125744 | + | 0.999921i | \(0.504003\pi\) |
−0.859670 | + | 0.510850i | \(0.829331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.1788 | −0.472811 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.56848 | + | 7.91283i | −0.192538 | + | 0.333486i | −0.946091 | − | 0.323902i | \(-0.895005\pi\) |
0.753552 | + | 0.657388i | \(0.228339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0127169 | − | 0.0220263i | −0.000535003 | − | 0.000926653i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.7123 | − | 20.2863i | −0.491004 | − | 0.850445i | 0.508942 | − | 0.860801i | \(-0.330037\pi\) |
−0.999946 | + | 0.0103562i | \(0.996703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.91580 | + | 17.1747i | −0.414963 | + | 0.718738i | −0.995425 | − | 0.0955501i | \(-0.969539\pi\) |
0.580461 | + | 0.814288i | \(0.302872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.8462 | −1.24467 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2800 | − | 26.4658i | 0.636116 | − | 1.10178i | −0.350162 | − | 0.936689i | \(-0.613873\pi\) |
0.986278 | − | 0.165095i | \(-0.0527932\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.3158 | + | 13.3852i | −0.469459 | + | 0.555312i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5596 | + | 23.4859i | 0.561582 | + | 0.972688i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.37643 | 0.180635 | 0.0903174 | − | 0.995913i | \(-0.471212\pi\) | ||||
0.0903174 | + | 0.995913i | \(0.471212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −65.2150 | −2.68714 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.2762 | + | 38.5835i | 0.914773 | + | 1.58443i | 0.807234 | + | 0.590232i | \(0.200964\pi\) |
0.107539 | + | 0.994201i | \(0.465703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0699872 | − | 0.0827862i | 0.00286920 | − | 0.00339390i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.85577 | − | 11.8745i | 0.280119 | − | 0.485181i | −0.691295 | − | 0.722573i | \(-0.742959\pi\) |
0.971414 | + | 0.237392i | \(0.0762926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.21373 | −0.0902997 | −0.0451499 | − | 0.998980i | \(-0.514377\pi\) | ||||
−0.0451499 | + | 0.998980i | \(0.514377\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0456641 | + | 0.0790925i | −0.00185651 | + | 0.00321557i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.58980 | + | 2.75361i | 0.0645280 | + | 0.111766i | 0.896484 | − | 0.443075i | \(-0.146113\pi\) |
−0.831957 | + | 0.554841i | \(0.812779\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.16471 | − | 10.6776i | −0.249398 | − | 0.431969i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.15827 | + | 10.6664i | −0.248730 | + | 0.430814i | −0.963174 | − | 0.268880i | \(-0.913347\pi\) |
0.714443 | + | 0.699693i | \(0.246680\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.9405 | 1.84949 | 0.924747 | − | 0.380583i | \(-0.124277\pi\) | ||||
0.924747 | + | 0.380583i | \(0.124277\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.79648 | − | 11.7718i | 0.273174 | − | 0.473151i | −0.696499 | − | 0.717558i | \(-0.745260\pi\) |
0.969673 | + | 0.244407i | \(0.0785933\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.1665 | − | 2.01139i | −0.447375 | − | 0.0805848i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4937 | − | 21.6398i | −0.499749 | − | 0.865590i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.08763 | −0.0832393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.682615 | 0.0271745 | 0.0135872 | − | 0.999908i | \(-0.495675\pi\) | ||||
0.0135872 | + | 0.999908i | \(0.495675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0183941 | + | 0.0318596i | 0.000729949 | + | 0.00126431i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.46044 | + | 20.5076i | 0.137108 | + | 0.812540i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.7325 | + | 41.1059i | −0.937378 | + | 1.62359i | −0.167042 | + | 0.985950i | \(0.553421\pi\) |
−0.770337 | + | 0.637637i | \(0.779912\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.4928 | 1.36026 | 0.680132 | − | 0.733090i | \(-0.261923\pi\) | ||||
0.680132 | + | 0.733090i | \(0.261923\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.6587 | − | 21.9255i | 0.497665 | − | 0.861980i | −0.502332 | − | 0.864675i | \(-0.667524\pi\) |
0.999996 | + | 0.00269463i | \(0.000857729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.0754 | − | 45.1639i | −1.02355 | − | 1.77284i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.19122 | + | 7.25941i | 0.164015 | + | 0.284083i | 0.936305 | − | 0.351188i | \(-0.114222\pi\) |
−0.772290 | + | 0.635270i | \(0.780889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.240710 | + | 0.416922i | −0.00940531 | + | 0.0162905i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4114 | −0.756160 | −0.378080 | − | 0.925773i | \(-0.623416\pi\) | ||||
−0.378080 | + | 0.925773i | \(0.623416\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.39833 | − | 9.35019i | 0.209971 | − | 0.363680i | −0.741734 | − | 0.670694i | \(-0.765996\pi\) |
0.951705 | + | 0.307014i | \(0.0993298\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.197574 | − | 0.549115i | −0.00766158 | − | 0.0212938i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.8487 | − | 51.6994i | −1.15574 | − | 2.00181i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.2782 | 1.63213 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.07074 | −0.195463 | −0.0977314 | − | 0.995213i | \(-0.531159\pi\) | ||||
−0.0977314 | + | 0.995213i | \(0.531159\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.2737 | + | 31.6511i | 0.702317 | + | 1.21645i | 0.967651 | + | 0.252292i | \(0.0811844\pi\) |
−0.265334 | + | 0.964157i | \(0.585482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.5717 | − | 13.6879i | 0.444082 | − | 0.525295i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.34590 | − | 9.25937i | 0.204555 | − | 0.354300i | −0.745436 | − | 0.666577i | \(-0.767759\pi\) |
0.949991 | + | 0.312278i | \(0.101092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.141484 | −0.00540583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.7073 | + | 18.5455i | −0.407915 | + | 0.706529i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4686 | − | 19.8643i | −0.436288 | − | 0.755673i | 0.561112 | − | 0.827740i | \(-0.310374\pi\) |
−0.997400 | + | 0.0720673i | \(0.977040\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.124577 | + | 0.215774i | 0.00472549 | + | 0.00818478i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.10669 | + | 5.38094i | −0.117674 | + | 0.203818i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.9789 | −1.81214 | −0.906069 | − | 0.423129i | \(-0.860932\pi\) | ||||
−0.906069 | + | 0.423129i | \(0.860932\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.61915 | + | 9.73265i | −0.211930 | + | 0.367074i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.04232 | + | 16.7934i | 0.227245 | + | 0.631579i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.3095 | − | 17.8566i | −0.387183 | − | 0.670620i | 0.604887 | − | 0.796312i | \(-0.293218\pi\) |
−0.992069 | + | 0.125692i | \(0.959885\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −51.0694 | −1.91256 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.323419 | −0.0120952 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.59498 | − | 4.49464i | −0.0967765 | − | 0.167622i | 0.813572 | − | 0.581464i | \(-0.197520\pi\) |
−0.910349 | + | 0.413842i | \(0.864187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.19541 | + | 1.29609i | 0.267971 | + | 0.0482690i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.9937 | − | 43.2904i | 0.928244 | − | 1.60776i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.9339 | −1.48107 | −0.740534 | − | 0.672019i | \(-0.765427\pi\) | ||||
−0.740534 | + | 0.672019i | \(0.765427\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.66430 | − | 4.61469i | 0.0985425 | − | 0.170681i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.6661 | − | 42.7229i | −0.911062 | − | 1.57800i | −0.812567 | − | 0.582867i | \(-0.801931\pi\) |
−0.0984942 | − | 0.995138i | \(-0.531403\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.4502 | − | 18.1002i | −0.384937 | − | 0.666730i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5576 | + | 28.6786i | −0.609081 | + | 1.05496i | 0.382311 | + | 0.924034i | \(0.375128\pi\) |
−0.991392 | + | 0.130926i | \(0.958205\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.4157 | 0.859040 | 0.429520 | − | 0.903057i | \(-0.358683\pi\) | ||||
0.429520 | + | 0.903057i | \(0.358683\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.143477 | + | 0.248510i | −0.00525660 | + | 0.00910470i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.3554 | − | 8.34991i | −1.69379 | − | 0.305099i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.41364 | − | 16.3049i | −0.343508 | − | 0.594974i | 0.641573 | − | 0.767062i | \(-0.278282\pi\) |
−0.985082 | + | 0.172088i | \(0.944949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.274100 | 0.00997551 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.0156 | 0.981897 | 0.490949 | − | 0.871188i | \(-0.336650\pi\) | ||||
0.490949 | + | 0.871188i | \(0.336650\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.64356 | + | 16.7031i | 0.349579 | + | 0.605488i | 0.986175 | − | 0.165709i | \(-0.0529913\pi\) |
−0.636596 | + | 0.771198i | \(0.719658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.70300 | − | 26.9675i | −0.351272 | − | 0.976288i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.5903 | − | 35.6635i | 0.743473 | − | 1.28773i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.26639 | −0.117789 | −0.0588946 | − | 0.998264i | \(-0.518758\pi\) | ||||
−0.0588946 | + | 0.998264i | \(0.518758\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.9963 | − | 19.0462i | 0.395510 | − | 0.685044i | −0.597656 | − | 0.801753i | \(-0.703901\pi\) |
0.993166 | + | 0.116709i | \(0.0372345\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.3814 | − | 37.0337i | −0.768044 | − | 1.33029i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.7242 | + | 28.9671i | 0.599205 | + | 1.03785i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.7589 | − | 37.6875i | 0.778593 | − | 1.34856i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.337773 | −0.0120556 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.64724 | + | 8.04926i | −0.165656 | + | 0.286925i | −0.936888 | − | 0.349629i | \(-0.886308\pi\) |
0.771232 | + | 0.636554i | \(0.219641\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.50160 | + | 1.77621i | −0.0533909 | + | 0.0631548i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.6924 | + | 28.9121i | 0.592764 | + | 1.02670i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.4137 | 1.00647 | 0.503233 | − | 0.864151i | \(-0.332144\pi\) | ||||
0.503233 | + | 0.864151i | \(0.332144\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.87708 | 0.207916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.19925 | + | 14.2015i | 0.289345 | + | 0.501161i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.154718 | − | 0.430008i | −0.00545311 | − | 0.0151558i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.2425 | + | 24.6687i | −0.500739 | + | 0.867305i | 0.499261 | + | 0.866452i | \(0.333605\pi\) |
−1.00000 | 0.000853079i | \(0.999728\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.5507 | 1.70484 | 0.852422 | − | 0.522854i | \(-0.175133\pi\) | ||||
0.852422 | + | 0.522854i | \(0.175133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.184201 | + | 0.319046i | −0.00645229 | + | 0.0111757i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.3426 | − | 24.8422i | −0.501785 | − | 0.869118i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.56647 | − | 9.64141i | −0.194271 | − | 0.336487i | 0.752390 | − | 0.658718i | \(-0.228901\pi\) |
−0.946661 | + | 0.322230i | \(0.895567\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5218 | − | 33.8128i | 0.680488 | − | 1.17864i | −0.294344 | − | 0.955699i | \(-0.595101\pi\) |
0.974832 | − | 0.222940i | \(-0.0715654\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.0851 | −1.67208 | −0.836042 | − | 0.548666i | \(-0.815136\pi\) | ||||
−0.836042 | + | 0.548666i | \(0.815136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.64180 | + | 2.84369i | −0.0570222 | + | 0.0987653i | −0.893127 | − | 0.449804i | \(-0.851494\pi\) |
0.836105 | + | 0.548569i | \(0.184827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.29046 | − | 3.45918i | −0.321895 | − | 0.119853i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.287286 | + | 0.497593i | 0.00994193 | + | 0.0172199i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.1274 | 0.487733 | 0.243866 | − | 0.969809i | \(-0.421584\pi\) | ||||
0.243866 | + | 0.969809i | \(0.421584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 70.9833 | 2.44770 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.0603620 | + | 0.104550i | 0.00207652 | + | 0.00359663i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.21956 | + | 1.48057i | 0.282427 | + | 0.0508731i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.40031 | + | 7.62157i | −0.150841 | + | 0.261264i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5850 | 0.636337 | 0.318169 | − | 0.948034i | \(-0.396932\pi\) | ||||
0.318169 | + | 0.948034i | \(0.396932\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.4244 | + | 26.7159i | −0.526888 | + | 0.912597i | 0.472621 | + | 0.881266i | \(0.343308\pi\) |
−0.999509 | + | 0.0313313i | \(0.990025\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.1410 | − | 31.4211i | −0.618962 | − | 1.07207i | −0.989675 | − | 0.143327i | \(-0.954220\pi\) |
0.370713 | − | 0.928747i | \(-0.379113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.2584 | + | 36.8207i | 0.723646 | + | 1.25339i | 0.959529 | + | 0.281610i | \(0.0908684\pi\) |
−0.235883 | + | 0.971781i | \(0.575798\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0739035 | − | 0.128005i | 0.00251279 | − | 0.00435229i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.0184 | 1.79853 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.25191 | − | 14.2927i | 0.279605 | − | 0.484291i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.494141 | − | 0.584508i | 0.0167050 | − | 0.0197600i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.35752 | − | 16.2077i | −0.315981 | − | 0.547295i | 0.663664 | − | 0.748030i | \(-0.269000\pi\) |
−0.979646 | + | 0.200735i | \(0.935667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.832933 | −0.0280622 | −0.0140311 | − | 0.999902i | \(-0.504466\pi\) | ||||
−0.0140311 | + | 0.999902i | \(0.504466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.67225 | −0.0562756 | −0.0281378 | − | 0.999604i | \(-0.508958\pi\) | ||||
−0.0281378 | + | 0.999604i | \(0.508958\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.0691 | − | 46.8850i | −0.908890 | − | 1.57424i | −0.815608 | − | 0.578605i | \(-0.803597\pi\) |
−0.0932821 | − | 0.995640i | \(-0.529736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.17197 | − | 2.56918i | 0.0728456 | − | 0.0861674i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.8190 | − | 27.3993i | 0.529362 | − | 0.916881i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.519882 | 0.0173777 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42.7665 | − | 74.0737i | 1.42634 | − | 2.47050i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.10385 | − | 8.84012i | −0.170034 | − | 0.294507i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0538353 | + | 0.0932454i | 0.00178955 | + | 0.00309958i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.74481 | − | 15.1465i | 0.290367 | − | 0.502930i | −0.683530 | − | 0.729923i | \(-0.739556\pi\) |
0.973896 | + | 0.226993i | \(0.0728894\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.7838 | −1.05304 | −0.526522 | − | 0.850162i | \(-0.676504\pi\) | ||||
−0.526522 | + | 0.850162i | \(0.676504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4629 | + | 21.5865i | −0.412463 | + | 0.714407i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.3279 | + | 7.80457i | 1.43081 | + | 0.257729i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.2038 | − | 31.5300i | −0.600489 | − | 1.04008i | −0.992747 | − | 0.120223i | \(-0.961639\pi\) |
0.392258 | − | 0.919855i | \(-0.371694\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.3635 | 1.13109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.36919 | −0.242298 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.9728 | − | 38.0581i | −0.720905 | − | 1.24864i | −0.960637 | − | 0.277805i | \(-0.910393\pi\) |
0.239732 | − | 0.970839i | \(-0.422940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.1334 | + | 34.0018i | −1.34809 | + | 1.11436i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0770821 | − | 0.133510i | 0.00252085 | − | 0.00436625i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.0774 | −1.66863 | −0.834313 | − | 0.551291i | \(-0.814135\pi\) | ||||
−0.834313 | + | 0.551291i | \(0.814135\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.0898 | + | 38.2607i | −0.720107 | + | 1.24726i | 0.240850 | + | 0.970562i | \(0.422574\pi\) |
−0.960957 | + | 0.276699i | \(0.910759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.0966 | + | 22.6839i | 0.426483 | + | 0.738690i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.16730 | + | 10.6821i | 0.200410 | + | 0.347121i | 0.948661 | − | 0.316296i | \(-0.102439\pi\) |
−0.748250 | + | 0.663416i | \(0.769106\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.47449 | + | 11.2141i | −0.210171 | + | 0.364027i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.4140 | −1.30914 | −0.654570 | − | 0.756002i | \(-0.727150\pi\) | ||||
−0.654570 | + | 0.756002i | \(0.727150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0833595 | − | 0.144383i | 0.00269745 | − | 0.00467212i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.38042 | + | 12.1745i | 0.141451 | + | 0.393134i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0855 | − | 36.5212i | −0.680179 | − | 1.17810i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.104521 | 0.00336466 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.69549 | −0.183155 | −0.0915774 | − | 0.995798i | \(-0.529191\pi\) | ||||
−0.0915774 | + | 0.995798i | \(0.529191\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.52609 | + | 13.0356i | 0.241524 | + | 0.418331i | 0.961149 | − | 0.276032i | \(-0.0890195\pi\) |
−0.719625 | + | 0.694363i | \(0.755686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.7100 | − | 17.4002i | 0.471582 | − | 0.557823i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.01262 | + | 15.6103i | −0.288339 | + | 0.499418i | −0.973413 | − | 0.229055i | \(-0.926436\pi\) |
0.685074 | + | 0.728473i | \(0.259770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.1355 | −0.515692 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.99700 | − | 3.45890i | 0.0636943 | − | 0.110322i | −0.832420 | − | 0.554146i | \(-0.813045\pi\) |
0.896114 | + | 0.443824i | \(0.146378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0932219 | − | 0.161465i | −0.00297030 | − | 0.00514471i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.2316 | − | 19.4537i | −0.357145 | − | 0.618593i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.18202 | − | 7.24347i | 0.132846 | − | 0.230097i | −0.791926 | − | 0.610617i | \(-0.790922\pi\) |
0.924773 | + | 0.380520i | \(0.124255\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.0747284 | −0.00236905 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0375384 | − | 0.0650184i | 0.00118885 | − | 0.00205915i | −0.865430 | − | 0.501029i | \(-0.832955\pi\) |
0.866619 | + | 0.498970i | \(0.166288\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1512.2.s.n.865.3 | ✓ | 8 | |
3.2 | odd | 2 | 1512.2.s.o.865.2 | yes | 8 | ||
7.2 | even | 3 | inner | 1512.2.s.n.1297.3 | yes | 8 | |
21.2 | odd | 6 | 1512.2.s.o.1297.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.n.865.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1512.2.s.n.1297.3 | yes | 8 | 7.2 | even | 3 | inner | |
1512.2.s.o.865.2 | yes | 8 | 3.2 | odd | 2 | ||
1512.2.s.o.1297.2 | yes | 8 | 21.2 | odd | 6 |