Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(251,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.624529833984.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} - 2x^{4} - 18x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.2 | ||
Root | \(0.777403 - 1.54779i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.251 |
Dual form | 525.2.b.h.251.8 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.40651i | − | 1.70166i | −0.525442 | − | 0.850830i | \(-0.676100\pi\) | ||
0.525442 | − | 0.850830i | \(-0.323900\pi\) | |||||||
\(3\) | 0.777403 | + | 1.54779i | 0.448834 | + | 0.893615i | ||||
\(4\) | −3.79129 | −1.89564 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.72476 | − | 1.87083i | 1.52063 | − | 0.763763i | ||||
\(7\) | −1.00000 | + | 2.44949i | −0.377964 | + | 0.925820i | ||||
\(8\) | 4.31075i | 1.52408i | ||||||||
\(9\) | −1.79129 | + | 2.40651i | −0.597096 | + | 0.802170i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.31075i | 1.29974i | 0.760045 | + | 0.649870i | \(0.225177\pi\) | ||||
−0.760045 | + | 0.649870i | \(0.774823\pi\) | |||||||
\(12\) | −2.94736 | − | 5.86811i | −0.850830 | − | 1.69398i | ||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | 5.89472 | + | 2.40651i | 1.57543 | + | 0.643167i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.79129 | 0.697822 | ||||||||
\(17\) | 5.89472 | 1.42968 | 0.714840 | − | 0.699288i | \(-0.246500\pi\) | ||||
0.714840 | + | 0.699288i | \(0.246500\pi\) | |||||||
\(18\) | 5.79129 | + | 4.31075i | 1.36502 | + | 1.01605i | ||||
\(19\) | 6.83723i | 1.56857i | 0.620402 | + | 0.784284i | \(0.286970\pi\) | ||||
−0.620402 | + | 0.784284i | \(0.713030\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.56869 | + | 0.356455i | −0.996970 | + | 0.0777848i | ||||
\(22\) | 10.3739 | 2.21172 | ||||||||
\(23\) | − | 0.502268i | − | 0.104730i | −0.998628 | − | 0.0523650i | \(-0.983324\pi\) | ||
0.998628 | − | 0.0523650i | \(-0.0166759\pi\) | |||||||
\(24\) | −6.67212 | + | 3.35119i | −1.36194 | + | 0.684059i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.89472 | −1.15605 | ||||||||
\(27\) | −5.11732 | − | 0.901703i | −0.984828 | − | 0.173533i | ||||
\(28\) | 3.79129 | − | 9.28672i | 0.716486 | − | 1.75503i | ||||
\(29\) | 0.502268i | 0.0932688i | 0.998912 | + | 0.0466344i | \(0.0148496\pi\) | ||||
−0.998912 | + | 0.0466344i | \(0.985150\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.38774i | 0.788062i | 0.919097 | + | 0.394031i | \(0.128920\pi\) | ||||
−0.919097 | + | 0.394031i | \(0.871080\pi\) | |||||||
\(32\) | 1.90424i | 0.336626i | ||||||||
\(33\) | −6.67212 | + | 3.35119i | −1.16147 | + | 0.583368i | ||||
\(34\) | − | 14.1857i | − | 2.43283i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.79129 | − | 9.12377i | 1.13188 | − | 1.52063i | ||||
\(37\) | −0.582576 | −0.0957749 | −0.0478874 | − | 0.998853i | \(-0.515249\pi\) | ||||
−0.0478874 | + | 0.998853i | \(0.515249\pi\) | |||||||
\(38\) | 16.4539 | 2.66917 | ||||||||
\(39\) | 3.79129 | − | 1.90424i | 0.607092 | − | 0.304923i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.66442 | 0.728460 | 0.364230 | − | 0.931309i | \(-0.381332\pi\) | ||||
0.364230 | + | 0.931309i | \(0.381332\pi\) | |||||||
\(42\) | 0.857812 | + | 10.9946i | 0.132363 | + | 1.69650i | ||||
\(43\) | 2.58258 | 0.393839 | 0.196920 | − | 0.980420i | \(-0.436906\pi\) | ||||
0.196920 | + | 0.980420i | \(0.436906\pi\) | |||||||
\(44\) | − | 16.3433i | − | 2.46384i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.20871 | −0.178215 | ||||||||
\(47\) | 5.89472 | 0.859833 | 0.429917 | − | 0.902869i | \(-0.358543\pi\) | ||||
0.429917 | + | 0.902869i | \(0.358543\pi\) | |||||||
\(48\) | 2.16996 | + | 4.32032i | 0.313206 | + | 0.623584i | ||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.58258 | + | 9.12377i | 0.641689 | + | 1.27758i | ||||
\(52\) | 9.28672i | 1.28784i | ||||||||
\(53\) | − | 13.4345i | − | 1.84537i | −0.385551 | − | 0.922687i | \(-0.625988\pi\) | ||
0.385551 | − | 0.922687i | \(-0.374012\pi\) | |||||||
\(54\) | −2.16996 | + | 12.3149i | −0.295294 | + | 1.67584i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.5591 | − | 4.31075i | −1.41102 | − | 0.576048i | ||||
\(57\) | −10.5826 | + | 5.31529i | −1.40170 | + | 0.704027i | ||||
\(58\) | 1.20871 | 0.158712 | ||||||||
\(59\) | −10.5591 | −1.37468 | −0.687342 | − | 0.726334i | \(-0.741222\pi\) | ||||
−0.687342 | + | 0.726334i | \(0.741222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.38774i | − | 0.561793i | −0.959738 | − | 0.280896i | \(-0.909368\pi\) | ||
0.959738 | − | 0.280896i | \(-0.0906317\pi\) | |||||||
\(62\) | 10.5591 | 1.34101 | ||||||||
\(63\) | −4.10343 | − | 6.79425i | −0.516984 | − | 0.855995i | ||||
\(64\) | 10.1652 | 1.27064 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.06468 | + | 16.0565i | 0.992693 | + | 1.97642i | ||||
\(67\) | −14.1652 | −1.73055 | −0.865274 | − | 0.501299i | \(-0.832856\pi\) | ||||
−0.865274 | + | 0.501299i | \(0.832856\pi\) | |||||||
\(68\) | −22.3486 | −2.71016 | ||||||||
\(69\) | 0.777403 | − | 0.390465i | 0.0935884 | − | 0.0470064i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.31075i | 0.511592i | 0.966731 | + | 0.255796i | \(0.0823375\pi\) | ||||
−0.966731 | + | 0.255796i | \(0.917662\pi\) | |||||||
\(72\) | −10.3739 | − | 7.72180i | −1.22257 | − | 0.910022i | ||||
\(73\) | 6.32599i | 0.740401i | 0.928952 | + | 0.370201i | \(0.120711\pi\) | ||||
−0.928952 | + | 0.370201i | \(0.879289\pi\) | |||||||
\(74\) | 1.40197i | 0.162976i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 25.9219i | − | 2.97345i | ||||||
\(77\) | −10.5591 | − | 4.31075i | −1.20333 | − | 0.491256i | ||||
\(78\) | −4.58258 | − | 9.12377i | −0.518875 | − | 1.03306i | ||||
\(79\) | −8.58258 | −0.965615 | −0.482808 | − | 0.875726i | \(-0.660383\pi\) | ||||
−0.482808 | + | 0.875726i | \(0.660383\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.58258 | − | 8.62150i | −0.286953 | − | 0.957945i | ||||
\(82\) | − | 11.2250i | − | 1.23959i | ||||||
\(83\) | 7.12502 | 0.782073 | 0.391036 | − | 0.920375i | \(-0.372117\pi\) | ||||
0.391036 | + | 0.920375i | \(0.372117\pi\) | |||||||
\(84\) | 17.3212 | − | 1.35142i | 1.88990 | − | 0.147452i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.21499i | − | 0.670180i | ||||||
\(87\) | −0.777403 | + | 0.390465i | −0.0833464 | + | 0.0418622i | ||||
\(88\) | −18.5826 | −1.98091 | ||||||||
\(89\) | 10.5591 | 1.11927 | 0.559633 | − | 0.828740i | \(-0.310942\pi\) | ||||
0.559633 | + | 0.828740i | \(0.310942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 2.44949i | 0.628971 | + | 0.256776i | ||||
\(92\) | 1.90424i | 0.198531i | ||||||||
\(93\) | −6.79129 | + | 3.41105i | −0.704224 | + | 0.353709i | ||||
\(94\) | − | 14.1857i | − | 1.46314i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.94736 | + | 1.48036i | −0.300814 | + | 0.151089i | ||||
\(97\) | 0.511238i | 0.0519084i | 0.999663 | + | 0.0259542i | \(0.00826240\pi\) | ||||
−0.999663 | + | 0.0259542i | \(0.991738\pi\) | |||||||
\(98\) | −11.7894 | + | 12.0325i | −1.19091 | + | 1.21547i | ||||
\(99\) | −10.3739 | − | 7.72180i | −1.04261 | − | 0.776070i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0197 | 1.29551 | 0.647756 | − | 0.761848i | \(-0.275708\pi\) | ||||
0.647756 | + | 0.761848i | \(0.275708\pi\) | |||||||
\(102\) | 21.9564 | − | 11.0280i | 2.17401 | − | 1.09194i | ||||
\(103\) | − | 6.83723i | − | 0.673692i | −0.941560 | − | 0.336846i | \(-0.890640\pi\) | ||
0.941560 | − | 0.336846i | \(-0.109360\pi\) | |||||||
\(104\) | 10.5591 | 1.03541 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −32.3303 | −3.14020 | ||||||||
\(107\) | 1.00454i | 0.0971121i | 0.998820 | + | 0.0485561i | \(0.0154620\pi\) | ||||
−0.998820 | + | 0.0485561i | \(0.984538\pi\) | |||||||
\(108\) | 19.4012 | + | 3.41862i | 1.86688 | + | 0.328956i | ||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.452896 | − | 0.901703i | −0.0429870 | − | 0.0855859i | ||||
\(112\) | −2.79129 | + | 6.83723i | −0.263752 | + | 0.646058i | ||||
\(113\) | 6.31982i | 0.594519i | 0.954797 | + | 0.297259i | \(0.0960726\pi\) | ||||
−0.954797 | + | 0.297259i | \(0.903927\pi\) | |||||||
\(114\) | 12.7913 | + | 25.4671i | 1.19801 | + | 2.38521i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.90424i | − | 0.176804i | ||||||
\(117\) | 5.89472 | + | 4.38774i | 0.544967 | + | 0.405647i | ||||
\(118\) | 25.4107i | 2.33924i | ||||||||
\(119\) | −5.89472 | + | 14.4391i | −0.540368 | + | 1.32363i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.58258 | −0.689325 | ||||||||
\(122\) | −10.5591 | −0.955980 | ||||||||
\(123\) | 3.62614 | + | 7.21953i | 0.326958 | + | 0.650963i | ||||
\(124\) | − | 16.6352i | − | 1.49388i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −16.3504 | + | 9.87495i | −1.45661 | + | 0.879730i | ||||
\(127\) | 10.1652 | 0.902011 | 0.451006 | − | 0.892521i | \(-0.351065\pi\) | ||||
0.451006 | + | 0.892521i | \(0.351065\pi\) | |||||||
\(128\) | − | 20.6540i | − | 1.82558i | ||||||
\(129\) | 2.00770 | + | 3.99728i | 0.176768 | + | 0.351941i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.89472 | −0.515024 | −0.257512 | − | 0.966275i | \(-0.582903\pi\) | ||||
−0.257512 | + | 0.966275i | \(0.582903\pi\) | |||||||
\(132\) | 25.2959 | − | 12.7053i | 2.20173 | − | 1.10586i | ||||
\(133\) | −16.7477 | − | 6.83723i | −1.45221 | − | 0.592863i | ||||
\(134\) | 34.0886i | 2.94480i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 25.4107i | 2.17895i | ||||||||
\(137\) | 1.00454i | 0.0858233i | 0.999079 | + | 0.0429116i | \(0.0136634\pi\) | ||||
−0.999079 | + | 0.0429116i | \(0.986337\pi\) | |||||||
\(138\) | −0.939657 | − | 1.87083i | −0.0799889 | − | 0.159256i | ||||
\(139\) | 2.44949i | 0.207763i | 0.994590 | + | 0.103882i | \(0.0331263\pi\) | ||||
−0.994590 | + | 0.103882i | \(0.966874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.58258 | + | 9.12377i | 0.385922 | + | 0.768360i | ||||
\(142\) | 10.3739 | 0.870555 | ||||||||
\(143\) | 10.5591 | 0.883000 | ||||||||
\(144\) | −5.00000 | + | 6.71726i | −0.416667 | + | 0.559772i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 15.2236 | 1.25991 | ||||||||
\(147\) | 3.69556 | − | 11.5474i | 0.304805 | − | 0.952415i | ||||
\(148\) | 2.20871 | 0.181555 | ||||||||
\(149\) | − | 6.31982i | − | 0.517740i | −0.965912 | − | 0.258870i | \(-0.916650\pi\) | ||
0.965912 | − | 0.258870i | \(-0.0833501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1652 | 1.15274 | 0.576372 | − | 0.817188i | \(-0.304468\pi\) | ||||
0.576372 | + | 0.817188i | \(0.304468\pi\) | |||||||
\(152\) | −29.4736 | −2.39062 | ||||||||
\(153\) | −10.5591 | + | 14.1857i | −0.853656 | + | 1.14685i | ||||
\(154\) | −10.3739 | + | 25.4107i | −0.835950 | + | 2.04765i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.3739 | + | 7.21953i | −1.15083 | + | 0.578025i | ||||
\(157\) | 9.28672i | 0.741161i | 0.928800 | + | 0.370580i | \(0.120841\pi\) | ||||
−0.928800 | + | 0.370580i | \(0.879159\pi\) | |||||||
\(158\) | 20.6540i | 1.64315i | ||||||||
\(159\) | 20.7938 | − | 10.4440i | 1.64905 | − | 0.828266i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.23030 | + | 0.502268i | 0.0969612 | + | 0.0395842i | ||||
\(162\) | −20.7477 | + | 6.21499i | −1.63010 | + | 0.488296i | ||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | −17.6842 | −1.38090 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 17.1464i | − | 1.33082i | ||||||
\(167\) | −13.0197 | −1.00750 | −0.503749 | − | 0.863850i | \(-0.668046\pi\) | ||||
−0.503749 | + | 0.863850i | \(0.668046\pi\) | |||||||
\(168\) | −1.53659 | − | 19.6945i | −0.118550 | − | 1.51946i | ||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.4539 | − | 12.2474i | −1.25826 | − | 0.936586i | ||||
\(172\) | −9.79129 | −0.746579 | ||||||||
\(173\) | 17.6842 | 1.34450 | 0.672251 | − | 0.740323i | \(-0.265328\pi\) | ||||
0.672251 | + | 0.740323i | \(0.265328\pi\) | |||||||
\(174\) | 0.939657 | + | 1.87083i | 0.0712352 | + | 0.141827i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0325i | 0.906987i | ||||||||
\(177\) | −8.20871 | − | 16.3433i | −0.617005 | − | 1.22844i | ||||
\(178\) | − | 25.4107i | − | 1.90461i | ||||||
\(179\) | − | 12.4300i | − | 0.929061i | −0.885557 | − | 0.464530i | \(-0.846223\pi\) | ||
0.885557 | − | 0.464530i | \(-0.153777\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2474i | 0.910346i | 0.890403 | + | 0.455173i | \(0.150423\pi\) | ||||
−0.890403 | + | 0.455173i | \(0.849577\pi\) | |||||||
\(182\) | 5.89472 | − | 14.4391i | 0.436946 | − | 1.07029i | ||||
\(183\) | 6.79129 | − | 3.41105i | 0.502026 | − | 0.252152i | ||||
\(184\) | 2.16515 | 0.159617 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.20871 | + | 16.3433i | 0.601892 | + | 1.19835i | ||||
\(187\) | 25.4107i | 1.85821i | ||||||||
\(188\) | −22.3486 | −1.62994 | ||||||||
\(189\) | 7.32603 | − | 11.6331i | 0.532890 | − | 0.846184i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.4436i | − | 1.11746i | −0.829350 | − | 0.558730i | \(-0.811289\pi\) | ||
0.829350 | − | 0.558730i | \(-0.188711\pi\) | |||||||
\(192\) | 7.90242 | + | 15.7335i | 0.570308 | + | 1.13547i | ||||
\(193\) | −11.0000 | −0.791797 | −0.395899 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395899 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(194\) | 1.23030 | 0.0883304 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.9564 | + | 18.5734i | 1.35403 | + | 1.32667i | ||||
\(197\) | − | 18.7498i | − | 1.33587i | −0.744220 | − | 0.667934i | \(-0.767179\pi\) | ||
0.744220 | − | 0.667934i | \(-0.232821\pi\) | |||||||
\(198\) | −18.5826 | + | 24.9648i | −1.32061 | + | 1.77417i | ||||
\(199\) | 19.0847i | 1.35288i | 0.736499 | + | 0.676439i | \(0.236478\pi\) | ||||
−0.736499 | + | 0.676439i | \(0.763522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.0120 | − | 21.9246i | −0.776729 | − | 1.54644i | ||||
\(202\) | − | 31.3321i | − | 2.20452i | ||||||
\(203\) | −1.23030 | − | 0.502268i | −0.0863501 | − | 0.0352523i | ||||
\(204\) | −17.3739 | − | 34.5908i | −1.21641 | − | 2.42184i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.4539 | −1.14639 | ||||||||
\(207\) | 1.20871 | + | 0.899706i | 0.0840113 | + | 0.0625339i | ||||
\(208\) | − | 6.83723i | − | 0.474077i | ||||||
\(209\) | −29.4736 | −2.03873 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7477 | 0.877590 | 0.438795 | − | 0.898587i | \(-0.355405\pi\) | ||||
0.438795 | + | 0.898587i | \(0.355405\pi\) | |||||||
\(212\) | 50.9341i | 3.49817i | ||||||||
\(213\) | −6.67212 | + | 3.35119i | −0.457166 | + | 0.229620i | ||||
\(214\) | 2.41742 | 0.165252 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.88702 | − | 22.0595i | 0.264478 | − | 1.50096i | ||||
\(217\) | −10.7477 | − | 4.38774i | −0.729603 | − | 0.297859i | ||||
\(218\) | − | 12.0325i | − | 0.814947i | ||||||
\(219\) | −9.79129 | + | 4.91785i | −0.661634 | + | 0.332317i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 14.4391i | − | 0.971276i | ||||||
\(222\) | −2.16996 | + | 1.08990i | −0.145638 | + | 0.0731493i | ||||
\(223\) | − | 2.44949i | − | 0.164030i | −0.996631 | − | 0.0820150i | \(-0.973864\pi\) | ||
0.996631 | − | 0.0820150i | \(-0.0261355\pi\) | |||||||
\(224\) | −4.66442 | − | 1.90424i | −0.311655 | − | 0.127233i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.2087 | 1.01167 | ||||||||
\(227\) | 5.89472 | 0.391246 | 0.195623 | − | 0.980679i | \(-0.437327\pi\) | ||||
0.195623 | + | 0.980679i | \(0.437327\pi\) | |||||||
\(228\) | 40.1216 | − | 20.1518i | 2.65712 | − | 1.33458i | ||||
\(229\) | − | 18.5734i | − | 1.22737i | −0.789552 | − | 0.613684i | \(-0.789687\pi\) | ||
0.789552 | − | 0.613684i | \(-0.210313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.53659 | − | 19.6945i | −0.101100 | − | 1.29580i | ||||
\(232\) | −2.16515 | −0.142149 | ||||||||
\(233\) | − | 0.502268i | − | 0.0329047i | −0.999865 | − | 0.0164523i | \(-0.994763\pi\) | ||
0.999865 | − | 0.0164523i | \(-0.00523717\pi\) | |||||||
\(234\) | 10.5591 | − | 14.1857i | 0.690273 | − | 0.927348i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 40.0327 | 2.60591 | ||||||||
\(237\) | −6.67212 | − | 13.2840i | −0.433401 | − | 0.862888i | ||||
\(238\) | 34.7477 | + | 14.1857i | 2.25236 | + | 0.919522i | ||||
\(239\) | − | 12.4300i | − | 0.804029i | −0.915633 | − | 0.402014i | \(-0.868310\pi\) | ||
0.915633 | − | 0.402014i | \(-0.131690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.85971i | 0.506288i | 0.967429 | + | 0.253144i | \(0.0814647\pi\) | ||||
−0.967429 | + | 0.253144i | \(0.918535\pi\) | |||||||
\(242\) | 18.2475i | 1.17300i | ||||||||
\(243\) | 11.3365 | − | 10.6997i | 0.727240 | − | 0.686384i | ||||
\(244\) | 16.6352i | 1.06496i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.3739 | − | 8.72633i | 1.10772 | − | 0.556371i | ||||
\(247\) | 16.7477 | 1.06563 | ||||||||
\(248\) | −18.9145 | −1.20107 | ||||||||
\(249\) | 5.53901 | + | 11.0280i | 0.351021 | + | 0.698872i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.2236 | 0.960903 | 0.480451 | − | 0.877021i | \(-0.340473\pi\) | ||||
0.480451 | + | 0.877021i | \(0.340473\pi\) | |||||||
\(252\) | 15.5573 | + | 25.7590i | 0.980017 | + | 1.62266i | ||||
\(253\) | 2.16515 | 0.136122 | ||||||||
\(254\) | − | 24.4625i | − | 1.53492i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.3739 | −1.83587 | ||||||||
\(257\) | 16.4539 | 1.02636 | 0.513182 | − | 0.858280i | \(-0.328467\pi\) | ||||
0.513182 | + | 0.858280i | \(0.328467\pi\) | |||||||
\(258\) | 9.61948 | − | 4.83156i | 0.598883 | − | 0.300800i | ||||
\(259\) | 0.582576 | − | 1.42701i | 0.0361995 | − | 0.0886703i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.20871 | − | 0.899706i | −0.0748174 | − | 0.0556904i | ||||
\(262\) | 14.1857i | 0.876395i | ||||||||
\(263\) | − | 7.32436i | − | 0.451639i | −0.974169 | − | 0.225820i | \(-0.927494\pi\) | ||
0.974169 | − | 0.225820i | \(-0.0725060\pi\) | |||||||
\(264\) | −14.4462 | − | 28.7619i | −0.889100 | − | 1.77017i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −16.4539 | + | 40.3036i | −1.00885 | + | 2.47117i | ||||
\(267\) | 8.20871 | + | 16.3433i | 0.502365 | + | 1.00019i | ||||
\(268\) | 53.7042 | 3.28050 | ||||||||
\(269\) | 18.9145 | 1.15324 | 0.576618 | − | 0.817014i | \(-0.304372\pi\) | ||||
0.576618 | + | 0.817014i | \(0.304372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.47197i | 0.210907i | 0.994424 | + | 0.105453i | \(0.0336294\pi\) | ||||
−0.994424 | + | 0.105453i | \(0.966371\pi\) | |||||||
\(272\) | 16.4539 | 0.997662 | ||||||||
\(273\) | 0.873133 | + | 11.1910i | 0.0528444 | + | 0.677308i | ||||
\(274\) | 2.41742 | 0.146042 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.94736 | + | 1.48036i | −0.177410 | + | 0.0891074i | ||||
\(277\) | 8.74773 | 0.525600 | 0.262800 | − | 0.964850i | \(-0.415354\pi\) | ||||
0.262800 | + | 0.964850i | \(0.415354\pi\) | |||||||
\(278\) | 5.89472 | 0.353542 | ||||||||
\(279\) | −10.5591 | − | 7.85971i | −0.632159 | − | 0.470548i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.5538i | − | 1.28579i | −0.765955 | − | 0.642895i | \(-0.777733\pi\) | ||
0.765955 | − | 0.642895i | \(-0.222267\pi\) | |||||||
\(282\) | 21.9564 | − | 11.0280i | 1.30749 | − | 0.656709i | ||||
\(283\) | 1.02248i | 0.0607799i | 0.999538 | + | 0.0303900i | \(0.00967491\pi\) | ||||
−0.999538 | + | 0.0303900i | \(0.990325\pi\) | |||||||
\(284\) | − | 16.3433i | − | 0.969796i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 25.4107i | − | 1.50256i | ||||||
\(287\) | −4.66442 | + | 11.4255i | −0.275332 | + | 0.674423i | ||||
\(288\) | −4.58258 | − | 3.41105i | −0.270031 | − | 0.200998i | ||||
\(289\) | 17.7477 | 1.04398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.791288 | + | 0.397438i | −0.0463861 | + | 0.0232983i | ||||
\(292\) | − | 23.9837i | − | 1.40354i | ||||||
\(293\) | −22.3486 | −1.30562 | −0.652809 | − | 0.757523i | \(-0.726410\pi\) | ||||
−0.652809 | + | 0.757523i | \(0.726410\pi\) | |||||||
\(294\) | −27.7890 | − | 8.89340i | −1.62069 | − | 0.518673i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.51134i | − | 0.145969i | ||||||
\(297\) | 3.88702 | − | 22.0595i | 0.225548 | − | 1.28002i | ||||
\(298\) | −15.2087 | −0.881017 | ||||||||
\(299\) | −1.23030 | −0.0711501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.58258 | + | 6.32599i | −0.148857 | + | 0.364624i | ||||
\(302\) | − | 34.0886i | − | 1.96158i | ||||||
\(303\) | 10.1216 | + | 20.1518i | 0.581470 | + | 1.15769i | ||||
\(304\) | 19.0847i | 1.09458i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 34.1380 | + | 25.4107i | 1.95154 | + | 1.45263i | ||||
\(307\) | − | 20.5117i | − | 1.17066i | −0.810794 | − | 0.585332i | \(-0.800964\pi\) | ||
0.810794 | − | 0.585332i | \(-0.199036\pi\) | |||||||
\(308\) | 40.0327 | + | 16.3433i | 2.28108 | + | 0.931246i | ||||
\(309\) | 10.5826 | − | 5.31529i | 0.602022 | − | 0.302376i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.0130 | −1.53177 | −0.765883 | − | 0.642979i | \(-0.777698\pi\) | ||||
−0.765883 | + | 0.642979i | \(0.777698\pi\) | |||||||
\(312\) | 8.20871 | + | 16.3433i | 0.464727 | + | 0.925257i | ||||
\(313\) | 10.7137i | 0.605576i | 0.953058 | + | 0.302788i | \(0.0979174\pi\) | ||||
−0.953058 | + | 0.302788i | \(0.902083\pi\) | |||||||
\(314\) | 22.3486 | 1.26120 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.5390 | 1.83046 | ||||||||
\(317\) | 13.9368i | 0.782768i | 0.920227 | + | 0.391384i | \(0.128004\pi\) | ||||
−0.920227 | + | 0.391384i | \(0.871996\pi\) | |||||||
\(318\) | −25.1337 | − | 50.0404i | −1.40943 | − | 2.80613i | ||||
\(319\) | −2.16515 | −0.121225 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.55481 | + | 0.780929i | −0.0867809 | + | 0.0435872i | ||||
\(322\) | 1.20871 | − | 2.96073i | 0.0673589 | − | 0.164995i | ||||
\(323\) | 40.3036i | 2.24255i | ||||||||
\(324\) | 9.79129 | + | 32.6866i | 0.543960 | + | 1.81592i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 9.62604i | − | 0.533137i | ||||||
\(327\) | 3.88702 | + | 7.73893i | 0.214953 | + | 0.427964i | ||||
\(328\) | 20.1072i | 1.11023i | ||||||||
\(329\) | −5.89472 | + | 14.4391i | −0.324986 | + | 0.796051i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0000 | 0.934405 | 0.467202 | − | 0.884150i | \(-0.345262\pi\) | ||||
0.467202 | + | 0.884150i | \(0.345262\pi\) | |||||||
\(332\) | −27.0130 | −1.48253 | ||||||||
\(333\) | 1.04356 | − | 1.40197i | 0.0571868 | − | 0.0768277i | ||||
\(334\) | 31.3321i | 1.71442i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.7525 | + | 0.994968i | −0.695708 | + | 0.0542800i | ||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | − | 16.8456i | − | 0.916278i | ||||||
\(339\) | −9.78174 | + | 4.91305i | −0.531271 | + | 0.266840i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9145 | −1.02428 | ||||||||
\(342\) | −29.4736 | + | 39.5964i | −1.59375 | + | 2.14113i | ||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 11.1328i | 0.600243i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 42.5571i | − | 2.28788i | ||||||
\(347\) | − | 18.7498i | − | 1.00654i | −0.864129 | − | 0.503271i | \(-0.832130\pi\) | ||
0.864129 | − | 0.503271i | \(-0.167870\pi\) | |||||||
\(348\) | 2.94736 | − | 1.48036i | 0.157995 | − | 0.0793558i | ||||
\(349\) | − | 1.93825i | − | 0.103752i | −0.998654 | − | 0.0518761i | \(-0.983480\pi\) | ||
0.998654 | − | 0.0518761i | \(-0.0165201\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.20871 | + | 12.5348i | −0.117892 | + | 0.669059i | ||||
\(352\) | −8.20871 | −0.437526 | ||||||||
\(353\) | −13.9933 | −0.744786 | −0.372393 | − | 0.928075i | \(-0.621463\pi\) | ||||
−0.372393 | + | 0.928075i | \(0.621463\pi\) | |||||||
\(354\) | −39.3303 | + | 19.7543i | −2.09038 | + | 1.04993i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −40.0327 | −2.12173 | ||||||||
\(357\) | −26.9312 | + | 2.10120i | −1.42535 | + | 0.111207i | ||||
\(358\) | −29.9129 | −1.58094 | ||||||||
\(359\) | − | 6.31982i | − | 0.333547i | −0.985995 | − | 0.166774i | \(-0.946665\pi\) | ||
0.985995 | − | 0.166774i | \(-0.0533349\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −27.7477 | −1.46041 | ||||||||
\(362\) | 29.4736 | 1.54910 | ||||||||
\(363\) | −5.89472 | − | 11.7362i | −0.309393 | − | 0.615991i | ||||
\(364\) | −22.7477 | − | 9.28672i | −1.19230 | − | 0.486756i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.20871 | − | 16.3433i | −0.429076 | − | 0.854278i | ||||
\(367\) | − | 32.7591i | − | 1.71001i | −0.518617 | − | 0.855007i | \(-0.673553\pi\) | ||
0.518617 | − | 0.855007i | \(-0.326447\pi\) | |||||||
\(368\) | − | 1.40197i | − | 0.0730829i | ||||||
\(369\) | −8.35532 | + | 11.2250i | −0.434961 | + | 0.584349i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.9077 | + | 13.4345i | 1.70848 | + | 0.697486i | ||||
\(372\) | 25.7477 | − | 12.9323i | 1.33496 | − | 0.670506i | ||||
\(373\) | −18.9129 | −0.979272 | −0.489636 | − | 0.871927i | \(-0.662870\pi\) | ||||
−0.489636 | + | 0.871927i | \(0.662870\pi\) | |||||||
\(374\) | 61.1510 | 3.16204 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.4107i | 1.31046i | ||||||||
\(377\) | 1.23030 | 0.0633637 | ||||||||
\(378\) | −27.9952 | − | 17.6302i | −1.43992 | − | 0.906797i | ||||
\(379\) | −19.3303 | −0.992931 | −0.496465 | − | 0.868056i | \(-0.665369\pi\) | ||||
−0.496465 | + | 0.868056i | \(0.665369\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.90242 | + | 15.7335i | 0.404853 | + | 0.806051i | ||||
\(382\) | −37.1652 | −1.90153 | ||||||||
\(383\) | 19.8880 | 1.01623 | 0.508114 | − | 0.861290i | \(-0.330343\pi\) | ||||
0.508114 | + | 0.861290i | \(0.330343\pi\) | |||||||
\(384\) | 31.9681 | − | 16.0565i | 1.63136 | − | 0.819381i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.4716i | 1.34737i | ||||||||
\(387\) | −4.62614 | + | 6.21499i | −0.235160 | + | 0.315926i | ||||
\(388\) | − | 1.93825i | − | 0.0983998i | ||||||
\(389\) | 26.3668i | 1.33685i | 0.743780 | + | 0.668424i | \(0.233031\pi\) | ||||
−0.743780 | + | 0.668424i | \(0.766969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.96073i | − | 0.149730i | ||||||
\(392\) | 21.1183 | − | 21.5538i | 1.06663 | − | 1.08863i | ||||
\(393\) | −4.58258 | − | 9.12377i | −0.231160 | − | 0.460233i | ||||
\(394\) | −45.1216 | −2.27319 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 39.3303 | + | 29.2756i | 1.97642 | + | 1.47115i | ||||
\(397\) | 13.6745i | 0.686302i | 0.939280 | + | 0.343151i | \(0.111494\pi\) | ||||
−0.939280 | + | 0.343151i | \(0.888506\pi\) | |||||||
\(398\) | 45.9275 | 2.30214 | ||||||||
\(399\) | −2.43716 | − | 31.2372i | −0.122011 | − | 1.56382i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1328i | 0.555948i | 0.960589 | + | 0.277974i | \(0.0896628\pi\) | ||||
−0.960589 | + | 0.277974i | \(0.910337\pi\) | |||||||
\(402\) | −52.7618 | + | 26.5006i | −2.63152 | + | 1.32173i | ||||
\(403\) | 10.7477 | 0.535382 | ||||||||
\(404\) | −49.3616 | −2.45583 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.20871 | + | 2.96073i | −0.0599874 | + | 0.146938i | ||||
\(407\) | − | 2.51134i | − | 0.124482i | ||||||
\(408\) | −39.3303 | + | 19.7543i | −1.94714 | + | 0.977986i | ||||
\(409\) | 24.3882i | 1.20592i | 0.797772 | + | 0.602959i | \(0.206012\pi\) | ||||
−0.797772 | + | 0.602959i | \(0.793988\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.55481 | + | 0.780929i | −0.0766930 | + | 0.0385204i | ||||
\(412\) | 25.9219i | 1.27708i | ||||||||
\(413\) | 10.5591 | − | 25.8645i | 0.519581 | − | 1.27271i | ||||
\(414\) | 2.16515 | − | 2.90878i | 0.106411 | − | 0.142959i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.66442 | 0.228692 | ||||||||
\(417\) | −3.79129 | + | 1.90424i | −0.185660 | + | 0.0932511i | ||||
\(418\) | 70.9285i | 3.46923i | ||||||||
\(419\) | 18.9145 | 0.924032 | 0.462016 | − | 0.886872i | \(-0.347126\pi\) | ||||
0.462016 | + | 0.886872i | \(0.347126\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.1652 | −0.495419 | −0.247710 | − | 0.968834i | \(-0.579678\pi\) | ||||
−0.247710 | + | 0.968834i | \(0.579678\pi\) | |||||||
\(422\) | − | 30.6775i | − | 1.49336i | ||||||
\(423\) | −10.5591 | + | 14.1857i | −0.513403 | + | 0.689732i | ||||
\(424\) | 57.9129 | 2.81250 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.06468 | + | 16.0565i | 0.390735 | + | 0.777941i | ||||
\(427\) | 10.7477 | + | 4.38774i | 0.520119 | + | 0.212338i | ||||
\(428\) | − | 3.80848i | − | 0.184090i | ||||||
\(429\) | 8.20871 | + | 16.3433i | 0.396320 | + | 0.789062i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.8872i | 1.48778i | 0.668300 | + | 0.743892i | \(0.267022\pi\) | ||||
−0.668300 | + | 0.743892i | \(0.732978\pi\) | |||||||
\(432\) | −14.2839 | − | 2.51691i | −0.687235 | − | 0.121095i | ||||
\(433\) | − | 23.4724i | − | 1.12801i | −0.825770 | − | 0.564006i | \(-0.809259\pi\) | ||
0.825770 | − | 0.564006i | \(-0.190741\pi\) | |||||||
\(434\) | −10.5591 | + | 25.8645i | −0.506855 | + | 1.24154i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.9564 | −0.907849 | ||||||||
\(437\) | 3.43412 | 0.164276 | ||||||||
\(438\) | 11.8348 | + | 23.5628i | 0.565491 | + | 1.12588i | ||||
\(439\) | 26.9444i | 1.28599i | 0.765872 | + | 0.642993i | \(0.222307\pi\) | ||||
−0.765872 | + | 0.642993i | \(0.777693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.7459 | − | 3.25706i | 0.987899 | − | 0.155098i | ||||
\(442\) | −34.7477 | −1.65278 | ||||||||
\(443\) | − | 13.4345i | − | 0.638293i | −0.947705 | − | 0.319147i | \(-0.896604\pi\) | ||
0.947705 | − | 0.319147i | \(-0.103396\pi\) | |||||||
\(444\) | 1.71706 | + | 3.41862i | 0.0814881 | + | 0.162240i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.89472 | −0.279123 | ||||||||
\(447\) | 9.78174 | − | 4.91305i | 0.462660 | − | 0.232379i | ||||
\(448\) | −10.1652 | + | 24.8994i | −0.480258 | + | 1.17639i | ||||
\(449\) | 19.5447i | 0.922371i | 0.887304 | + | 0.461185i | \(0.152576\pi\) | ||||
−0.887304 | + | 0.461185i | \(0.847424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.1072i | 0.946809i | ||||||||
\(452\) | − | 23.9603i | − | 1.12700i | ||||||
\(453\) | 11.0120 | + | 21.9246i | 0.517391 | + | 1.03011i | ||||
\(454\) | − | 14.1857i | − | 0.665768i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −22.9129 | − | 45.6189i | −1.07299 | − | 2.13630i | ||||
\(457\) | 15.8348 | 0.740723 | 0.370361 | − | 0.928888i | \(-0.379234\pi\) | ||||
0.370361 | + | 0.928888i | \(0.379234\pi\) | |||||||
\(458\) | −44.6972 | −2.08856 | ||||||||
\(459\) | −30.1652 | − | 5.31529i | −1.40799 | − | 0.248096i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.09854 | −0.377187 | −0.188593 | − | 0.982055i | \(-0.560393\pi\) | ||||
−0.188593 | + | 0.982055i | \(0.560393\pi\) | |||||||
\(462\) | −47.3950 | + | 3.69781i | −2.20501 | + | 0.172038i | ||||
\(463\) | 14.7477 | 0.685385 | 0.342693 | − | 0.939448i | \(-0.388661\pi\) | ||||
0.342693 | + | 0.939448i | \(0.388661\pi\) | |||||||
\(464\) | 1.40197i | 0.0650850i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.20871 | −0.0559925 | ||||||||
\(467\) | 35.3683 | 1.63665 | 0.818325 | − | 0.574755i | \(-0.194903\pi\) | ||||
0.818325 | + | 0.574755i | \(0.194903\pi\) | |||||||
\(468\) | −22.3486 | − | 16.6352i | −1.03306 | − | 0.768962i | ||||
\(469\) | 14.1652 | − | 34.6974i | 0.654086 | − | 1.60218i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.3739 | + | 7.21953i | −0.662313 | + | 0.332658i | ||||
\(472\) | − | 45.5178i | − | 2.09513i | ||||||
\(473\) | 11.1328i | 0.511889i | ||||||||
\(474\) | −31.9681 | + | 16.0565i | −1.46834 | + | 0.737501i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.3486 | − | 54.7426i | 1.02435 | − | 2.50912i | ||||
\(477\) | 32.3303 | + | 24.0651i | 1.48030 | + | 1.10186i | ||||
\(478\) | −29.9129 | −1.36818 | ||||||||
\(479\) | −10.5591 | −0.482459 | −0.241230 | − | 0.970468i | \(-0.577551\pi\) | ||||
−0.241230 | + | 0.970468i | \(0.577551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.42701i | 0.0650662i | ||||||||
\(482\) | 18.9145 | 0.861530 | ||||||||
\(483\) | 0.179036 | + | 2.29471i | 0.00814641 | + | 0.104413i | ||||
\(484\) | 28.7477 | 1.30671 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −25.7488 | − | 27.2815i | −1.16799 | − | 1.23751i | ||||
\(487\) | 40.1652 | 1.82006 | 0.910028 | − | 0.414546i | \(-0.136060\pi\) | ||||
0.910028 | + | 0.414546i | \(0.136060\pi\) | |||||||
\(488\) | 18.9145 | 0.856217 | ||||||||
\(489\) | 3.10961 | + | 6.19115i | 0.140622 | + | 0.279973i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.51134i | − | 0.113335i | −0.998393 | − | 0.0566676i | \(-0.981952\pi\) | ||
0.998393 | − | 0.0566676i | \(-0.0180475\pi\) | |||||||
\(492\) | −13.7477 | − | 27.3713i | −0.619795 | − | 1.23399i | ||||
\(493\) | 2.96073i | 0.133344i | ||||||||
\(494\) | − | 40.3036i | − | 1.81334i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.2474i | 0.549927i | ||||||||
\(497\) | −10.5591 | − | 4.31075i | −0.473642 | − | 0.193364i | ||||
\(498\) | 26.5390 | − | 13.3297i | 1.18924 | − | 0.597318i | ||||
\(499\) | 30.7477 | 1.37646 | 0.688229 | − | 0.725494i | \(-0.258389\pi\) | ||||
0.688229 | + | 0.725494i | \(0.258389\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.1216 | − | 20.1518i | −0.452199 | − | 0.900315i | ||||
\(502\) | − | 36.6356i | − | 1.63513i | ||||||
\(503\) | −11.7894 | −0.525665 | −0.262833 | − | 0.964841i | \(-0.584657\pi\) | ||||
−0.262833 | + | 0.964841i | \(0.584657\pi\) | |||||||
\(504\) | 29.2883 | − | 17.6889i | 1.30461 | − | 0.787925i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 5.21046i | − | 0.231633i | ||||||
\(507\) | 5.44182 | + | 10.8345i | 0.241680 | + | 0.481177i | ||||
\(508\) | −38.5390 | −1.70989 | ||||||||
\(509\) | 31.6774 | 1.40408 | 0.702039 | − | 0.712139i | \(-0.252273\pi\) | ||||
0.702039 | + | 0.712139i | \(0.252273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4955 | − | 6.32599i | −0.685479 | − | 0.279845i | ||||
\(512\) | 29.3804i | 1.29844i | ||||||||
\(513\) | 6.16515 | − | 34.9883i | 0.272198 | − | 1.54477i | ||||
\(514\) | − | 39.5964i | − | 1.74652i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.61178 | − | 15.1548i | −0.335090 | − | 0.667154i | ||||
\(517\) | 25.4107i | 1.11756i | ||||||||
\(518\) | −3.43412 | − | 1.40197i | −0.150887 | − | 0.0615992i | ||||
\(519\) | 13.7477 | + | 27.3713i | 0.603458 | + | 1.20147i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.3683 | −1.54951 | −0.774757 | − | 0.632259i | \(-0.782128\pi\) | ||||
−0.774757 | + | 0.632259i | \(0.782128\pi\) | |||||||
\(522\) | −2.16515 | + | 2.90878i | −0.0947661 | + | 0.127314i | ||||
\(523\) | − | 14.6969i | − | 0.642652i | −0.946969 | − | 0.321326i | \(-0.895871\pi\) | ||
0.946969 | − | 0.321326i | \(-0.104129\pi\) | |||||||
\(524\) | 22.3486 | 0.976302 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.6261 | −0.768536 | ||||||||
\(527\) | 25.8645i | 1.12668i | ||||||||
\(528\) | −18.6238 | + | 9.35414i | −0.810498 | + | 0.407087i | ||||
\(529\) | 22.7477 | 0.989032 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.9145 | − | 25.4107i | 0.820818 | − | 1.10273i | ||||
\(532\) | 63.4955 | + | 25.9219i | 2.75288 | + | 1.12386i | ||||
\(533\) | − | 11.4255i | − | 0.494891i | ||||||
\(534\) | 39.3303 | − | 19.7543i | 1.70199 | − | 0.854854i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 61.0624i | − | 2.63750i | ||||||
\(537\) | 19.2390 | − | 9.66311i | 0.830223 | − | 0.416994i | ||||
\(538\) | − | 45.5178i | − | 1.96241i | ||||||
\(539\) | 21.1183 | − | 21.5538i | 0.909629 | − | 0.928386i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.582576 | 0.0250469 | 0.0125234 | − | 0.999922i | \(-0.496014\pi\) | ||||
0.0125234 | + | 0.999922i | \(0.496014\pi\) | |||||||
\(542\) | 8.35532 | 0.358892 | ||||||||
\(543\) | −18.9564 | + | 9.52121i | −0.813499 | + | 0.408594i | ||||
\(544\) | 11.2250i | 0.481267i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 26.9312 | − | 2.10120i | 1.15255 | − | 0.0899231i | ||||
\(547\) | −41.3303 | −1.76716 | −0.883578 | − | 0.468284i | \(-0.844872\pi\) | ||||
−0.883578 | + | 0.468284i | \(0.844872\pi\) | |||||||
\(548\) | − | 3.80848i | − | 0.162690i | ||||||
\(549\) | 10.5591 | + | 7.85971i | 0.450653 | + | 0.335444i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.43412 | −0.146298 | ||||||||
\(552\) | 1.68320 | + | 3.35119i | 0.0716416 | + | 0.142636i | ||||
\(553\) | 8.58258 | − | 21.0229i | 0.364968 | − | 0.893986i | ||||
\(554\) | − | 21.0515i | − | 0.894392i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.28672i | − | 0.393845i | ||||||
\(557\) | 46.6234i | 1.97550i | 0.156056 | + | 0.987748i | \(0.450122\pi\) | ||||
−0.156056 | + | 0.987748i | \(0.549878\pi\) | |||||||
\(558\) | −18.9145 | + | 25.4107i | −0.800713 | + | 1.07572i | ||||
\(559\) | − | 6.32599i | − | 0.267561i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.3303 | + | 19.7543i | −1.66053 | + | 0.834029i | ||||
\(562\) | −51.8693 | −2.18798 | ||||||||
\(563\) | −32.9077 | −1.38690 | −0.693448 | − | 0.720507i | \(-0.743909\pi\) | ||||
−0.693448 | + | 0.720507i | \(0.743909\pi\) | |||||||
\(564\) | −17.3739 | − | 34.5908i | −0.731572 | − | 1.45654i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.46060 | 0.103427 | ||||||||
\(567\) | 23.7009 | + | 2.29551i | 0.995342 | + | 0.0964023i | ||||
\(568\) | −18.5826 | −0.779708 | ||||||||
\(569\) | − | 32.1843i | − | 1.34924i | −0.738166 | − | 0.674619i | \(-0.764308\pi\) | ||
0.738166 | − | 0.674619i | \(-0.235692\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.25227 | −0.0942547 | −0.0471273 | − | 0.998889i | \(-0.515007\pi\) | ||||
−0.0471273 | + | 0.998889i | \(0.515007\pi\) | |||||||
\(572\) | −40.0327 | −1.67385 | ||||||||
\(573\) | 23.9034 | − | 12.0059i | 0.998578 | − | 0.501554i | ||||
\(574\) | 27.4955 | + | 11.2250i | 1.14764 | + | 0.468521i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −18.2087 | + | 24.4625i | −0.758696 | + | 1.01927i | ||||
\(577\) | 12.7587i | 0.531151i | 0.964090 | + | 0.265576i | \(0.0855620\pi\) | ||||
−0.964090 | + | 0.265576i | \(0.914438\pi\) | |||||||
\(578\) | − | 42.7101i | − | 1.77650i | ||||||
\(579\) | −8.55144 | − | 17.0257i | −0.355386 | − | 0.707562i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.12502 | + | 17.4527i | −0.295596 | + | 0.724058i | ||||
\(582\) | 0.956439 | + | 1.90424i | 0.0396457 | + | 0.0789334i | ||||
\(583\) | 57.9129 | 2.39851 | ||||||||
\(584\) | −27.2698 | −1.12843 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 53.7821i | 2.22172i | ||||||||
\(587\) | −34.1380 | −1.40903 | −0.704513 | − | 0.709691i | \(-0.748835\pi\) | ||||
−0.704513 | + | 0.709691i | \(0.748835\pi\) | |||||||
\(588\) | −14.0109 | + | 43.7796i | −0.577801 | + | 1.80544i | ||||
\(589\) | −30.0000 | −1.23613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.0207 | − | 14.5762i | 1.19375 | − | 0.599583i | ||||
\(592\) | −1.62614 | −0.0668338 | ||||||||
\(593\) | −11.7894 | −0.484134 | −0.242067 | − | 0.970259i | \(-0.577825\pi\) | ||||
−0.242067 | + | 0.970259i | \(0.577825\pi\) | |||||||
\(594\) | −53.0863 | − | 9.35414i | −2.17816 | − | 0.383805i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.9603i | 0.981451i | ||||||||
\(597\) | −29.5390 | + | 14.8365i | −1.20895 | + | 0.607217i | ||||
\(598\) | 2.96073i | 0.121073i | ||||||||
\(599\) | 19.5447i | 0.798574i | 0.916826 | + | 0.399287i | \(0.130742\pi\) | ||||
−0.916826 | + | 0.399287i | \(0.869258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.0459i | 1.71509i | 0.514412 | + | 0.857543i | \(0.328010\pi\) | ||||
−0.514412 | + | 0.857543i | \(0.671990\pi\) | |||||||
\(602\) | 15.2236 | + | 6.21499i | 0.620466 | + | 0.253304i | ||||
\(603\) | 25.3739 | − | 34.0886i | 1.03330 | − | 1.38819i | ||||
\(604\) | −53.7042 | −2.18519 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 48.4955 | − | 24.3577i | 1.96999 | − | 0.989464i | ||||
\(607\) | 1.42701i | 0.0579207i | 0.999581 | + | 0.0289603i | \(0.00921965\pi\) | ||||
−0.999581 | + | 0.0289603i | \(0.990780\pi\) | |||||||
\(608\) | −13.0197 | −0.528020 | ||||||||
\(609\) | −0.179036 | − | 2.29471i | −0.00725490 | − | 0.0929862i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14.4391i | − | 0.584142i | ||||||
\(612\) | 40.0327 | − | 53.7821i | 1.61823 | − | 2.17401i | ||||
\(613\) | −27.4174 | −1.10738 | −0.553690 | − | 0.832723i | \(-0.686781\pi\) | ||||
−0.553690 | + | 0.832723i | \(0.686781\pi\) | |||||||
\(614\) | −49.3616 | −1.99207 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.5826 | − | 45.5178i | 0.748713 | − | 1.83397i | ||||
\(617\) | 13.9368i | 0.561074i | 0.959843 | + | 0.280537i | \(0.0905125\pi\) | ||||
−0.959843 | + | 0.280537i | \(0.909487\pi\) | |||||||
\(618\) | −12.7913 | − | 25.4671i | −0.514541 | − | 1.02444i | ||||
\(619\) | 35.7199i | 1.43570i | 0.696196 | + | 0.717851i | \(0.254874\pi\) | ||||
−0.696196 | + | 0.717851i | \(0.745126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.452896 | + | 2.57026i | −0.0181741 | + | 0.103141i | ||||
\(622\) | 65.0070i | 2.60655i | ||||||||
\(623\) | −10.5591 | + | 25.8645i | −0.423043 | + | 1.03624i | ||||
\(624\) | 10.5826 | − | 5.31529i | 0.423642 | − | 0.212782i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25.7827 | 1.03048 | ||||||||
\(627\) | −22.9129 | − | 45.6189i | −0.915052 | − | 1.82184i | ||||
\(628\) | − | 35.2086i | − | 1.40498i | ||||||
\(629\) | −3.43412 | −0.136927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.25227 | 0.248899 | 0.124450 | − | 0.992226i | \(-0.460284\pi\) | ||||
0.124450 | + | 0.992226i | \(0.460284\pi\) | |||||||
\(632\) | − | 36.9973i | − | 1.47168i | ||||||
\(633\) | 9.91013 | + | 19.7308i | 0.393892 | + | 0.784227i | ||||
\(634\) | 33.5390 | 1.33200 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −78.8352 | + | 39.5964i | −3.12602 | + | 1.57010i | ||||
\(637\) | −12.0000 | + | 12.2474i | −0.475457 | + | 0.485262i | ||||
\(638\) | 5.21046i | 0.206284i | ||||||||
\(639\) | −10.3739 | − | 7.72180i | −0.410384 | − | 0.305470i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.9973i | 1.46131i | 0.682748 | + | 0.730654i | \(0.260785\pi\) | ||||
−0.682748 | + | 0.730654i | \(0.739215\pi\) | |||||||
\(642\) | 1.87931 | + | 3.74166i | 0.0741706 | + | 0.147671i | ||||
\(643\) | 43.0683i | 1.69845i | 0.528032 | + | 0.849225i | \(0.322930\pi\) | ||||
−0.528032 | + | 0.849225i | \(0.677070\pi\) | |||||||
\(644\) | −4.66442 | − | 1.90424i | −0.183804 | − | 0.0750376i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 96.9909 | 3.81606 | ||||||||
\(647\) | 18.6577 | 0.733509 | 0.366755 | − | 0.930318i | \(-0.380469\pi\) | ||||
0.366755 | + | 0.930318i | \(0.380469\pi\) | |||||||
\(648\) | 37.1652 | − | 11.1328i | 1.45999 | − | 0.437339i | ||||
\(649\) | − | 45.5178i | − | 1.78673i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.56403 | − | 20.0462i | −0.0612992 | − | 0.785674i | ||||
\(652\) | −15.1652 | −0.593913 | ||||||||
\(653\) | 12.4300i | 0.486423i | 0.969973 | + | 0.243211i | \(0.0782009\pi\) | ||||
−0.969973 | + | 0.243211i | \(0.921799\pi\) | |||||||
\(654\) | 18.6238 | − | 9.35414i | 0.728249 | − | 0.365776i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 13.0197 | 0.508335 | ||||||||
\(657\) | −15.2236 | − | 11.3317i | −0.593928 | − | 0.442091i | ||||
\(658\) | 34.7477 | + | 14.1857i | 1.35461 | + | 0.553016i | ||||
\(659\) | − | 12.4300i | − | 0.484203i | −0.970251 | − | 0.242102i | \(-0.922163\pi\) | ||
0.970251 | − | 0.242102i | \(-0.0778368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.3546i | − | 1.25845i | −0.777224 | − | 0.629224i | \(-0.783373\pi\) | ||
0.777224 | − | 0.629224i | \(-0.216627\pi\) | |||||||
\(662\) | − | 40.9107i | − | 1.59004i | ||||||
\(663\) | 22.3486 | − | 11.2250i | 0.867947 | − | 0.435942i | ||||
\(664\) | 30.7142i | 1.19194i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.37386 | − | 2.51134i | −0.130735 | − | 0.0973124i | ||||
\(667\) | 0.252273 | 0.00976805 | ||||||||
\(668\) | 49.3616 | 1.90986 | ||||||||
\(669\) | 3.79129 | − | 1.90424i | 0.146580 | − | 0.0736222i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.9145 | 0.730185 | ||||||||
\(672\) | −0.678776 | − | 8.69989i | −0.0261844 | − | 0.335606i | ||||
\(673\) | −47.4955 | −1.83082 | −0.915408 | − | 0.402528i | \(-0.868132\pi\) | ||||
−0.915408 | + | 0.402528i | \(0.868132\pi\) | |||||||
\(674\) | 4.81302i | 0.185391i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.5390 | −1.02073 | ||||||||
\(677\) | −23.5789 | −0.906210 | −0.453105 | − | 0.891457i | \(-0.649684\pi\) | ||||
−0.453105 | + | 0.891457i | \(0.649684\pi\) | |||||||
\(678\) | 11.8233 | + | 23.5398i | 0.454071 | + | 0.904042i | ||||
\(679\) | −1.25227 | − | 0.511238i | −0.0480578 | − | 0.0196195i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.58258 | + | 9.12377i | 0.175605 | + | 0.349624i | ||||
\(682\) | 45.5178i | 1.74297i | ||||||||
\(683\) | − | 33.1889i | − | 1.26994i | −0.772538 | − | 0.634968i | \(-0.781013\pi\) | ||
0.772538 | − | 0.634968i | \(-0.218987\pi\) | |||||||
\(684\) | 62.3813 | + | 46.4336i | 2.38521 | + | 1.77543i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.6842 | − | 40.9107i | −0.675184 | − | 1.56198i | ||||
\(687\) | 28.7477 | − | 14.4391i | 1.09679 | − | 0.550884i | ||||
\(688\) | 7.20871 | 0.274830 | ||||||||
\(689\) | −32.9077 | −1.25368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 4.38774i | − | 0.166918i | −0.996511 | − | 0.0834588i | \(-0.973403\pi\) | ||
0.996511 | − | 0.0834588i | \(-0.0265967\pi\) | |||||||
\(692\) | −67.0457 | −2.54870 | ||||||||
\(693\) | 29.2883 | − | 17.6889i | 1.11257 | − | 0.671945i | ||||
\(694\) | −45.1216 | −1.71279 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.68320 | − | 3.35119i | −0.0638014 | − | 0.127027i | ||||
\(697\) | 27.4955 | 1.04146 | ||||||||
\(698\) | −4.66442 | −0.176551 | ||||||||
\(699\) | 0.777403 | − | 0.390465i | 0.0294041 | − | 0.0147687i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.4436i | − | 0.583296i | −0.956526 | − | 0.291648i | \(-0.905796\pi\) | ||
0.956526 | − | 0.291648i | \(-0.0942037\pi\) | |||||||
\(702\) | 30.1652 | + | 5.31529i | 1.13851 | + | 0.200613i | ||||
\(703\) | − | 3.98320i | − | 0.150229i | ||||||
\(704\) | 43.8194i | 1.65151i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.6749i | 1.26737i | ||||||||
\(707\) | −13.0197 | + | 31.8917i | −0.489658 | + | 1.19941i | ||||
\(708\) | 31.1216 | + | 61.9621i | 1.16962 | + | 2.32868i | ||||
\(709\) | −31.4955 | −1.18284 | −0.591418 | − | 0.806365i | \(-0.701432\pi\) | ||||
−0.591418 | + | 0.806365i | \(0.701432\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.3739 | − | 20.6540i | 0.576565 | − | 0.774587i | ||||
\(712\) | 45.5178i | 1.70585i | ||||||||
\(713\) | 2.20382 | 0.0825337 | ||||||||
\(714\) | 5.05656 | + | 64.8101i | 0.189237 | + | 2.42546i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 47.1257i | 1.76117i | ||||||||
\(717\) | 19.2390 | − | 9.66311i | 0.718492 | − | 0.360876i | ||||
\(718\) | −15.2087 | −0.567584 | ||||||||
\(719\) | 40.0327 | 1.49297 | 0.746485 | − | 0.665403i | \(-0.231740\pi\) | ||||
0.746485 | + | 0.665403i | \(0.231740\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.7477 | + | 6.83723i | 0.623718 | + | 0.254632i | ||||
\(722\) | 66.7752i | 2.48511i | ||||||||
\(723\) | −12.1652 | + | 6.11016i | −0.452427 | + | 0.227239i | ||||
\(724\) | − | 46.4336i | − | 1.72569i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −28.2433 | + | 14.1857i | −1.04821 | + | 0.526481i | ||||
\(727\) | − | 45.0066i | − | 1.66920i | −0.550855 | − | 0.834601i | \(-0.685698\pi\) | ||
0.550855 | − | 0.834601i | \(-0.314302\pi\) | |||||||
\(728\) | −10.5591 | + | 25.8645i | −0.391348 | + | 0.958602i | ||||
\(729\) | 25.3739 | + | 9.22860i | 0.939773 | + | 0.341800i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.2236 | 0.563064 | ||||||||
\(732\) | −25.7477 | + | 12.9323i | −0.951663 | + | 0.477990i | ||||
\(733\) | − | 32.2479i | − | 1.19110i | −0.803317 | − | 0.595552i | \(-0.796933\pi\) | ||
0.803317 | − | 0.595552i | \(-0.203067\pi\) | |||||||
\(734\) | −78.8352 | −2.90986 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.956439 | 0.0352548 | ||||||||
\(737\) | − | 61.0624i | − | 2.24926i | ||||||
\(738\) | 27.0130 | + | 20.1072i | 0.994362 | + | 0.740155i | ||||
\(739\) | −40.8258 | −1.50180 | −0.750900 | − | 0.660416i | \(-0.770380\pi\) | ||||
−0.750900 | + | 0.660416i | \(0.770380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.0197 | + | 25.9219i | 0.478292 | + | 0.952265i | ||||
\(742\) | 32.3303 | − | 79.1927i | 1.18688 | − | 2.90726i | ||||
\(743\) | 12.4300i | 0.456012i | 0.973660 | + | 0.228006i | \(0.0732206\pi\) | ||||
−0.973660 | + | 0.228006i | \(0.926779\pi\) | |||||||
\(744\) | −14.7042 | − | 29.2756i | −0.539081 | − | 1.07329i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 45.5140i | 1.66639i | ||||||||
\(747\) | −12.7630 | + | 17.1464i | −0.466972 | + | 0.627355i | ||||
\(748\) | − | 96.3392i | − | 3.52251i | ||||||
\(749\) | −2.46060 | − | 1.00454i | −0.0899083 | − | 0.0367049i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.7477 | −1.41392 | −0.706962 | − | 0.707251i | \(-0.749935\pi\) | ||||
−0.706962 | + | 0.707251i | \(0.749935\pi\) | |||||||
\(752\) | 16.4539 | 0.600011 | ||||||||
\(753\) | 11.8348 | + | 23.5628i | 0.431286 | + | 0.858677i | ||||
\(754\) | − | 2.96073i | − | 0.107823i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −27.7751 | + | 44.1045i | −1.01017 | + | 1.60406i | ||||
\(757\) | −6.25227 | −0.227243 | −0.113621 | − | 0.993524i | \(-0.536245\pi\) | ||||
−0.113621 | + | 0.993524i | \(0.536245\pi\) | |||||||
\(758\) | 46.5186i | 1.68963i | ||||||||
\(759\) | 1.68320 | + | 3.35119i | 0.0610961 | + | 0.121641i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.6972 | 1.62027 | 0.810135 | − | 0.586243i | \(-0.199394\pi\) | ||||
0.810135 | + | 0.586243i | \(0.199394\pi\) | |||||||
\(762\) | 37.8628 | − | 19.0173i | 1.37162 | − | 0.688923i | ||||
\(763\) | −5.00000 | + | 12.2474i | −0.181012 | + | 0.443387i | ||||
\(764\) | 58.5511i | 2.11830i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 47.8606i | − | 1.72927i | ||||||
\(767\) | 25.8645i | 0.933913i | ||||||||
\(768\) | −22.8353 | − | 45.4645i | −0.823999 | − | 1.64056i | ||||
\(769\) | 3.36526i | 0.121355i | 0.998157 | + | 0.0606773i | \(0.0193260\pi\) | ||||
−0.998157 | + | 0.0606773i | \(0.980674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.7913 | + | 25.4671i | 0.460667 | + | 0.917174i | ||||
\(772\) | 41.7042 | 1.50097 | ||||||||
\(773\) | 7.12502 | 0.256269 | 0.128135 | − | 0.991757i | \(-0.459101\pi\) | ||||
0.128135 | + | 0.991757i | \(0.459101\pi\) | |||||||
\(774\) | 14.9564 | + | 11.1328i | 0.537598 | + | 0.400162i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.20382 | −0.0791126 | ||||||||
\(777\) | 2.66161 | − | 0.207662i | 0.0954847 | − | 0.00744983i | ||||
\(778\) | 63.4519 | 2.27486 | ||||||||
\(779\) | 31.8917i | 1.14264i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.5826 | −0.664937 | ||||||||
\(782\) | −7.12502 | −0.254790 | ||||||||
\(783\) | 0.452896 | − | 2.57026i | 0.0161852 | − | 0.0918537i | ||||
\(784\) | −13.9564 | − | 13.6745i | −0.498444 | − | 0.488374i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.9564 | + | 11.0280i | −0.783160 | + | 0.393356i | ||||
\(787\) | − | 16.1240i | − | 0.574757i | −0.957817 | − | 0.287378i | \(-0.907216\pi\) | ||
0.957817 | − | 0.287378i | \(-0.0927837\pi\) | |||||||
\(788\) | 71.0859i | 2.53233i | ||||||||
\(789\) | 11.3365 | − | 5.69398i | 0.403592 | − | 0.202711i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.4803 | − | 6.31982i | −0.550418 | − | 0.224707i | ||||
\(792\) | 33.2867 | − | 44.7191i | 1.18279 | − | 1.58903i | ||||
\(793\) | −10.7477 | −0.381663 | ||||||||
\(794\) | 32.9077 | 1.16785 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 72.3555i | − | 2.56457i | ||||||
\(797\) | −15.2236 | −0.539246 | −0.269623 | − | 0.962966i | \(-0.586899\pi\) | ||||
−0.269623 | + | 0.962966i | \(0.586899\pi\) | |||||||
\(798\) | −75.1726 | + | 5.86506i | −2.66108 | + | 0.207621i | ||||
\(799\) | 34.7477 | 1.22929 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.9145 | + | 25.4107i | −0.668310 | + | 0.897842i | ||||
\(802\) | 26.7913 | 0.946033 | ||||||||
\(803\) | −27.2698 | −0.962330 | ||||||||
\(804\) | 41.7498 | + | 83.1226i | 1.47240 | + | 2.93151i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 25.8645i | − | 0.911038i | ||||||
\(807\) | 14.7042 | + | 29.2756i | 0.517611 | + | 1.03055i | ||||
\(808\) | 56.1249i | 1.97447i | ||||||||
\(809\) | 7.32436i | 0.257511i | 0.991676 | + | 0.128755i | \(0.0410982\pi\) | ||||
−0.991676 | + | 0.128755i | \(0.958902\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.77548i | − | 0.308149i | −0.988059 | − | 0.154074i | \(-0.950760\pi\) | ||
0.988059 | − | 0.154074i | \(-0.0492396\pi\) | |||||||
\(812\) | 4.66442 | + | 1.90424i | 0.163689 | + | 0.0668258i | ||||
\(813\) | −5.37386 | + | 2.69912i | −0.188470 | + | 0.0946622i | ||||
\(814\) | −6.04356 | −0.211827 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.7913 | + | 25.4671i | 0.447785 | + | 0.891526i | ||||
\(817\) | 17.6577i | 0.617764i | ||||||||
\(818\) | 58.6904 | 2.05206 | ||||||||
\(819\) | −16.6424 | + | 10.0513i | −0.581534 | + | 0.351221i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 15.4436i | − | 0.538985i | −0.963002 | − | 0.269493i | \(-0.913144\pi\) | ||
0.963002 | − | 0.269493i | \(-0.0868560\pi\) | |||||||
\(822\) | 1.87931 | + | 3.74166i | 0.0655486 | + | 0.130505i | ||||
\(823\) | 29.7477 | 1.03694 | 0.518470 | − | 0.855096i | \(-0.326502\pi\) | ||||
0.518470 | + | 0.855096i | \(0.326502\pi\) | |||||||
\(824\) | 29.4736 | 1.02676 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −62.2432 | − | 25.4107i | −2.16572 | − | 0.884150i | ||||
\(827\) | − | 44.6143i | − | 1.55139i | −0.631107 | − | 0.775696i | \(-0.717399\pi\) | ||
0.631107 | − | 0.775696i | \(-0.282601\pi\) | |||||||
\(828\) | −4.58258 | − | 3.41105i | −0.159256 | − | 0.118542i | ||||
\(829\) | − | 26.4331i | − | 0.918061i | −0.888420 | − | 0.459031i | \(-0.848197\pi\) | ||
0.888420 | − | 0.459031i | \(-0.151803\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.80051 | + | 13.5396i | 0.235907 | + | 0.469684i | ||||
\(832\) | − | 24.8994i | − | 0.863233i | ||||||
\(833\) | −29.4736 | − | 28.8781i | −1.02120 | − | 1.00057i | ||||
\(834\) | 4.58258 | + | 9.12377i | 0.158682 | + | 0.315930i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 111.743 | 3.86471 | ||||||||
\(837\) | 3.95644 | − | 22.4535i | 0.136755 | − | 0.776105i | ||||
\(838\) | − | 45.5178i | − | 1.57239i | ||||||
\(839\) | −10.5591 | −0.364542 | −0.182271 | − | 0.983248i | \(-0.558345\pi\) | ||||
−0.182271 | + | 0.983248i | \(0.558345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7477 | 0.991301 | ||||||||
\(842\) | 24.4625i | 0.843035i | ||||||||
\(843\) | 33.3606 | − | 16.7560i | 1.14900 | − | 0.577106i | ||||
\(844\) | −48.3303 | −1.66360 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 34.1380 | + | 25.4107i | 1.17369 | + | 0.873637i | ||||
\(847\) | 7.58258 | − | 18.5734i | 0.260540 | − | 0.638191i | ||||
\(848\) | − | 37.4996i | − | 1.28774i | ||||||
\(849\) | −1.58258 | + | 0.794877i | −0.0543139 | + | 0.0272801i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.292609i | 0.0100305i | ||||||||
\(852\) | 25.2959 | − | 12.7053i | 0.866625 | − | 0.435278i | ||||
\(853\) | 27.3489i | 0.936409i | 0.883620 | + | 0.468205i | \(0.155099\pi\) | ||||
−0.883620 | + | 0.468205i | \(0.844901\pi\) | |||||||
\(854\) | 10.5591 | − | 25.8645i | 0.361326 | − | 0.885065i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.33030 | −0.148007 | ||||||||
\(857\) | −21.3751 | −0.730158 | −0.365079 | − | 0.930977i | \(-0.618958\pi\) | ||||
−0.365079 | + | 0.930977i | \(0.618958\pi\) | |||||||
\(858\) | 39.3303 | − | 19.7543i | 1.34271 | − | 0.674402i | ||||
\(859\) | − | 25.5174i | − | 0.870642i | −0.900275 | − | 0.435321i | \(-0.856635\pi\) | ||
0.900275 | − | 0.435321i | \(-0.143365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.3103 | + | 1.66266i | −0.726253 | + | 0.0566632i | ||||
\(862\) | 74.3303 | 2.53170 | ||||||||
\(863\) | 39.0064i | 1.32779i | 0.747824 | + | 0.663897i | \(0.231099\pi\) | ||||
−0.747824 | + | 0.663897i | \(0.768901\pi\) | |||||||
\(864\) | 1.71706 | − | 9.74461i | 0.0584156 | − | 0.331518i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −56.4866 | −1.91949 | ||||||||
\(867\) | 13.7971 | + | 27.4697i | 0.468576 | + | 0.932920i | ||||
\(868\) | 40.7477 | + | 16.6352i | 1.38307 | + | 0.564635i | ||||
\(869\) | − | 36.9973i | − | 1.25505i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.6974i | 1.17568i | ||||||||
\(872\) | 21.5538i | 0.729902i | ||||||||
\(873\) | −1.23030 | − | 0.915775i | −0.0416393 | − | 0.0309943i | ||||
\(874\) | − | 8.26424i | − | 0.279542i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 37.1216 | − | 18.6450i | 1.25422 | − | 0.629955i | ||||
\(877\) | −23.4955 | −0.793385 | −0.396693 | − | 0.917952i | \(-0.629842\pi\) | ||||
−0.396693 | + | 0.917952i | \(0.629842\pi\) | |||||||
\(878\) | 64.8419 | 2.18831 | ||||||||
\(879\) | −17.3739 | − | 34.5908i | −0.586006 | − | 1.16672i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −58.6904 | −1.97733 | −0.988665 | − | 0.150136i | \(-0.952029\pi\) | ||||
−0.988665 | + | 0.150136i | \(0.952029\pi\) | |||||||
\(882\) | −7.83816 | − | 49.9252i | −0.263924 | − | 1.68107i | ||||
\(883\) | −24.5826 | −0.827270 | −0.413635 | − | 0.910443i | \(-0.635741\pi\) | ||||
−0.413635 | + | 0.910443i | \(0.635741\pi\) | |||||||
\(884\) | 54.7426i | 1.84119i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.3303 | −1.08616 | ||||||||
\(887\) | −46.9010 | −1.57478 | −0.787390 | − | 0.616455i | \(-0.788568\pi\) | ||||
−0.787390 | + | 0.616455i | \(0.788568\pi\) | |||||||
\(888\) | 3.88702 | − | 1.95232i | 0.130440 | − | 0.0655157i | ||||
\(889\) | −10.1652 | + | 24.8994i | −0.340928 | + | 0.835100i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.1652 | − | 11.1328i | 1.24508 | − | 0.372964i | ||||
\(892\) | 9.28672i | 0.310942i | ||||||||
\(893\) | 40.3036i | 1.34871i | ||||||||
\(894\) | −11.8233 | − | 23.5398i | −0.395430 | − | 0.787290i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50.5919 | + | 20.6540i | 1.69016 | + | 0.690003i | ||||
\(897\) | −0.956439 | − | 1.90424i | −0.0319346 | − | 0.0635808i | ||||
\(898\) | 47.0345 | 1.56956 | ||||||||
\(899\) | −2.20382 | −0.0735015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 79.1927i | − | 2.63829i | ||||||
\(902\) | 48.3881 | 1.61115 | ||||||||
\(903\) | −11.7990 | + | 0.920572i | −0.392646 | + | 0.0306347i | ||||
\(904\) | −27.2432 | −0.906095 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 52.7618 | − | 26.5006i | 1.75289 | − | 0.880423i | ||||
\(907\) | −53.4955 | −1.77629 | −0.888144 | − | 0.459566i | \(-0.848005\pi\) | ||||
−0.888144 | + | 0.459566i | \(0.848005\pi\) | |||||||
\(908\) | −22.3486 | −0.741664 | ||||||||
\(909\) | −23.3221 | + | 31.3321i | −0.773545 | + | 1.03922i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 54.2404i | − | 1.79706i | −0.438909 | − | 0.898532i | \(-0.644635\pi\) | ||
0.438909 | − | 0.898532i | \(-0.355365\pi\) | |||||||
\(912\) | −29.5390 | + | 14.8365i | −0.978135 | + | 0.491285i | ||||
\(913\) | 30.7142i | 1.01649i | ||||||||
\(914\) | − | 38.1067i | − | 1.26046i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 70.4173i | 2.32665i | ||||||||
\(917\) | 5.89472 | − | 14.4391i | 0.194661 | − | 0.476820i | ||||
\(918\) | −12.7913 | + | 72.5927i | −0.422175 | + | 2.39592i | ||||
\(919\) | 40.0780 | 1.32205 | 0.661026 | − | 0.750363i | \(-0.270121\pi\) | ||||
0.661026 | + | 0.750363i | \(0.270121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.7477 | − | 15.9459i | 1.04612 | − | 0.525434i | ||||
\(922\) | 19.4892i | 0.641843i | ||||||||
\(923\) | 10.5591 | 0.347558 | ||||||||
\(924\) | 5.82565 | + | 74.6675i | 0.191650 | + | 2.45638i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 35.4905i | − | 1.16629i | ||||||
\(927\) | 16.4539 | + | 12.2474i | 0.540416 | + | 0.402259i | ||||
\(928\) | −0.956439 | −0.0313967 | ||||||||
\(929\) | 10.5591 | 0.346434 | 0.173217 | − | 0.984884i | \(-0.444584\pi\) | ||||
0.173217 | + | 0.984884i | \(0.444584\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.4955 | − | 34.1862i | 1.09777 | − | 1.12041i | ||||
\(932\) | 1.90424i | 0.0623755i | ||||||||
\(933\) | −21.0000 | − | 41.8104i | −0.687509 | − | 1.36881i | ||||
\(934\) | − | 85.1142i | − | 2.78502i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.9145 | + | 25.4107i | −0.618238 | + | 0.830574i | ||||
\(937\) | 25.0061i | 0.816915i | 0.912777 | + | 0.408457i | \(0.133933\pi\) | ||||
−0.912777 | + | 0.408457i | \(0.866067\pi\) | |||||||
\(938\) | −83.4996 | − | 34.0886i | −2.72636 | − | 1.11303i | ||||
\(939\) | −16.5826 | + | 8.32889i | −0.541152 | + | 0.271803i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.7827 | 0.840492 | 0.420246 | − | 0.907410i | \(-0.361944\pi\) | ||||
0.420246 | + | 0.907410i | \(0.361944\pi\) | |||||||
\(942\) | 17.3739 | + | 34.5908i | 0.566071 | + | 1.12703i | ||||
\(943\) | − | 2.34279i | − | 0.0762917i | ||||||
\(944\) | −29.4736 | −0.959284 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.7913 | 0.871060 | ||||||||
\(947\) | − | 24.8600i | − | 0.807841i | −0.914794 | − | 0.403920i | \(-0.867647\pi\) | ||
0.914794 | − | 0.403920i | \(-0.132353\pi\) | |||||||
\(948\) | 25.2959 | + | 50.3635i | 0.821574 | + | 1.63573i | ||||
\(949\) | 15.4955 | 0.503004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.5712 | + | 10.8345i | −0.699493 | + | 0.351333i | ||||
\(952\) | −62.2432 | − | 25.4107i | −2.01731 | − | 0.823565i | ||||
\(953\) | − | 0.502268i | − | 0.0162700i | −0.999967 | − | 0.00813502i | \(-0.997411\pi\) | ||
0.999967 | − | 0.00813502i | \(-0.00258949\pi\) | |||||||
\(954\) | 57.9129 | − | 77.8032i | 1.87500 | − | 2.51897i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 47.1257i | 1.52415i | ||||||||
\(957\) | −1.68320 | − | 3.35119i | −0.0544100 | − | 0.108329i | ||||
\(958\) | 25.4107i | 0.820982i | ||||||||
\(959\) | −2.46060 | − | 1.00454i | −0.0794569 | − | 0.0324381i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.7477 | 0.378959 | ||||||||
\(962\) | 3.43412 | 0.110720 | ||||||||
\(963\) | −2.41742 | − | 1.79941i | −0.0779004 | − | 0.0579853i | ||||
\(964\) | − | 29.7984i | − | 0.959742i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.52223 | − | 0.430851i | 0.177675 | − | 0.0138624i | ||||
\(967\) | −12.7477 | −0.409939 | −0.204970 | − | 0.978768i | \(-0.565710\pi\) | ||||
−0.204970 | + | 0.978768i | \(0.565710\pi\) | |||||||
\(968\) | − | 32.6866i | − | 1.05059i | ||||||
\(969\) | −62.3813 | + | 31.3321i | −2.00398 | + | 1.00653i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.1313 | −1.54461 | −0.772303 | − | 0.635254i | \(-0.780895\pi\) | ||||
−0.772303 | + | 0.635254i | \(0.780895\pi\) | |||||||
\(972\) | −42.9801 | + | 40.5655i | −1.37859 | + | 1.30114i | ||||
\(973\) | −6.00000 | − | 2.44949i | −0.192351 | − | 0.0785270i | ||||
\(974\) | − | 96.6578i | − | 3.09712i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 12.2474i | − | 0.392031i | ||||||
\(977\) | 13.9368i | 0.445877i | 0.974832 | + | 0.222939i | \(0.0715650\pi\) | ||||
−0.974832 | + | 0.222939i | \(0.928435\pi\) | |||||||
\(978\) | 14.8991 | − | 7.48331i | 0.476419 | − | 0.239290i | ||||
\(979\) | 45.5178i | 1.45476i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.95644 | + | 12.0325i | −0.285957 | + | 0.384170i | ||||
\(982\) | −6.04356 | −0.192858 | ||||||||
\(983\) | 7.12502 | 0.227253 | 0.113626 | − | 0.993524i | \(-0.463753\pi\) | ||||
0.113626 | + | 0.993524i | \(0.463753\pi\) | |||||||
\(984\) | −31.1216 | + | 15.6314i | −0.992120 | + | 0.498310i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.12502 | 0.226907 | ||||||||
\(987\) | −26.9312 | + | 2.10120i | −0.857228 | + | 0.0668820i | ||||
\(988\) | −63.4955 | −2.02006 | ||||||||
\(989\) | − | 1.29714i | − | 0.0412468i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.0780 | 0.701332 | 0.350666 | − | 0.936501i | \(-0.385955\pi\) | ||||
0.350666 | + | 0.936501i | \(0.385955\pi\) | |||||||
\(992\) | −8.35532 | −0.265282 | ||||||||
\(993\) | 13.2159 | + | 26.3124i | 0.419393 | + | 0.834998i | ||||
\(994\) | −10.3739 | + | 25.4107i | −0.329039 | + | 0.805978i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.0000 | − | 41.8104i | −0.665410 | − | 1.32481i | ||||
\(997\) | − | 36.2311i | − | 1.14745i | −0.819048 | − | 0.573725i | \(-0.805498\pi\) | ||
0.819048 | − | 0.573725i | \(-0.194502\pi\) | |||||||
\(998\) | − | 73.9947i | − | 2.34226i | ||||||
\(999\) | 2.98122 | + | 0.525310i | 0.0943218 | + | 0.0166201i |
(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 | 525.2.b.h.251.2 | yes | 8 | |
3.2 | odd | 2 | inner | 525.2.b.h.251.7 | yes | 8 | |
5.2 | odd | 4 | 525.2.g.f.524.15 | 16 | |||
5.3 | odd | 4 | 525.2.g.f.524.2 | 16 | |||
5.4 | even | 2 | 525.2.b.i.251.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 525.2.b.h.251.1 | ✓ | 8 | |
15.2 | even | 4 | 525.2.g.f.524.4 | 16 | |||
15.8 | even | 4 | 525.2.g.f.524.13 | 16 | |||
15.14 | odd | 2 | 525.2.b.i.251.2 | yes | 8 | ||
21.20 | even | 2 | inner | 525.2.b.h.251.8 | yes | 8 | |
35.13 | even | 4 | 525.2.g.f.524.3 | 16 | |||
35.27 | even | 4 | 525.2.g.f.524.14 | 16 | |||
35.34 | odd | 2 | 525.2.b.i.251.8 | yes | 8 | ||
105.62 | odd | 4 | 525.2.g.f.524.1 | 16 | |||
105.83 | odd | 4 | 525.2.g.f.524.16 | 16 | |||
105.104 | even | 2 | 525.2.b.i.251.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.b.h.251.1 | ✓ | 8 | 7.6 | odd | 2 | inner | |
525.2.b.h.251.2 | yes | 8 | 1.1 | even | 1 | trivial | |
525.2.b.h.251.7 | yes | 8 | 3.2 | odd | 2 | inner | |
525.2.b.h.251.8 | yes | 8 | 21.20 | even | 2 | inner | |
525.2.b.i.251.1 | yes | 8 | 105.104 | even | 2 | ||
525.2.b.i.251.2 | yes | 8 | 15.14 | odd | 2 | ||
525.2.b.i.251.7 | yes | 8 | 5.4 | even | 2 | ||
525.2.b.i.251.8 | yes | 8 | 35.34 | odd | 2 | ||
525.2.g.f.524.1 | 16 | 105.62 | odd | 4 | |||
525.2.g.f.524.2 | 16 | 5.3 | odd | 4 | |||
525.2.g.f.524.3 | 16 | 35.13 | even | 4 | |||
525.2.g.f.524.4 | 16 | 15.2 | even | 4 | |||
525.2.g.f.524.13 | 16 | 15.8 | even | 4 | |||
525.2.g.f.524.14 | 16 | 35.27 | even | 4 | |||
525.2.g.f.524.15 | 16 | 5.2 | odd | 4 | |||
525.2.g.f.524.16 | 16 | 105.83 | odd | 4 |