Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.11337408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 18x^{4} + 81x^{2} + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(2.78499i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.361 |
Dual form | 2520.2.bi.q.1801.3 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64497 | − | 0.0641892i | 0.999706 | − | 0.0242612i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.91187 | − | 5.04351i | 0.877962 | − | 1.52067i | 0.0243876 | − | 0.999703i | \(-0.492236\pi\) |
0.853574 | − | 0.520972i | \(-0.174430\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.75615 | 0.764419 | 0.382209 | − | 0.924076i | \(-0.375163\pi\) | ||||
0.382209 | + | 0.924076i | \(0.375163\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.378076 | + | 0.654846i | 0.0867365 | + | 0.150232i | 0.906130 | − | 0.423000i | \(-0.139023\pi\) |
−0.819393 | + | 0.573232i | \(0.805690\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.266897 | − | 0.462279i | −0.0556518 | − | 0.0963918i | 0.836857 | − | 0.547421i | \(-0.184390\pi\) |
−0.892509 | + | 0.451029i | \(0.851057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.823739 | 0.152964 | 0.0764822 | − | 0.997071i | \(-0.475631\pi\) | ||||
0.0764822 | + | 0.997071i | \(0.475631\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.28995 | − | 2.23425i | 0.231681 | − | 0.401283i | −0.726622 | − | 0.687038i | \(-0.758911\pi\) |
0.958303 | + | 0.285754i | \(0.0922441\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.37808 | + | 2.25852i | 0.232937 | + | 0.381759i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.37808 | − | 4.11895i | −0.390953 | − | 0.677151i | 0.601622 | − | 0.798781i | \(-0.294521\pi\) |
−0.992576 | + | 0.121630i | \(0.961188\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.06759 | −0.947598 | −0.473799 | − | 0.880633i | \(-0.657118\pi\) | ||||
−0.473799 | + | 0.880633i | \(0.657118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.710055 | 0.108282 | 0.0541412 | − | 0.998533i | \(-0.482758\pi\) | ||||
0.0541412 | + | 0.998533i | \(0.482758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.44566 | − | 11.1642i | −0.940197 | − | 1.62847i | −0.765095 | − | 0.643918i | \(-0.777308\pi\) |
−0.175102 | − | 0.984550i | \(-0.556026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99176 | − | 0.339557i | 0.998823 | − | 0.0485082i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.20181 | + | 7.27776i | −0.577164 | + | 0.999677i | 0.418639 | + | 0.908153i | \(0.362507\pi\) |
−0.995803 | + | 0.0915241i | \(0.970826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.82374 | 0.785273 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.70181 | − | 8.14378i | −0.602006 | − | 1.04270i | −0.992517 | − | 0.122106i | \(-0.961035\pi\) |
0.390511 | − | 0.920598i | \(-0.372298\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.37808 | + | 2.38690i | 0.170929 | + | 0.296058i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.93492 | + | 10.2796i | −0.725066 | + | 1.25585i | 0.233881 | + | 0.972265i | \(0.424857\pi\) |
−0.958947 | + | 0.283585i | \(0.908476\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.75615 | + | 3.04174i | −0.205542 | + | 0.356009i | −0.950305 | − | 0.311320i | \(-0.899229\pi\) |
0.744763 | + | 0.667329i | \(0.232562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.37808 | − | 13.5268i | 0.840810 | − | 1.54153i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.75615 | + | 8.23790i | 0.535109 | + | 0.926836i | 0.999158 | + | 0.0410263i | \(0.0130627\pi\) |
−0.464049 | + | 0.885809i | \(0.653604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.71005 | 0.736524 | 0.368262 | − | 0.929722i | \(-0.379953\pi\) | ||||
0.368262 | + | 0.929722i | \(0.379953\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.878076 | + | 1.52087i | 0.0930758 | + | 0.161212i | 0.908804 | − | 0.417223i | \(-0.136997\pi\) |
−0.815728 | + | 0.578436i | \(0.803663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.28995 | − | 0.176915i | 0.764194 | − | 0.0185458i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.378076 | + | 0.654846i | −0.0387898 | + | 0.0671858i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.16802 | − | 2.02307i | 0.116222 | − | 0.201303i | −0.802045 | − | 0.597263i | \(-0.796255\pi\) |
0.918268 | + | 0.395960i | \(0.129588\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.11118 | + | 1.92462i | 0.109488 | + | 0.189638i | 0.915563 | − | 0.402175i | \(-0.131746\pi\) |
−0.806075 | + | 0.591813i | \(0.798412\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.93492 | + | 13.7437i | 0.767097 | + | 1.32865i | 0.939131 | + | 0.343561i | \(0.111633\pi\) |
−0.172033 | + | 0.985091i | \(0.555034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.63423 | − | 2.83056i | 0.156531 | − | 0.271119i | −0.777085 | − | 0.629396i | \(-0.783302\pi\) |
0.933615 | + | 0.358277i | \(0.116636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1598 | 1.23797 | 0.618984 | − | 0.785404i | \(-0.287545\pi\) | ||||
0.618984 | + | 0.785404i | \(0.287545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.266897 | − | 0.462279i | 0.0248883 | − | 0.0431077i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.53379 | − | 4.64542i | 0.232272 | − | 0.425845i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.4580 | − | 19.8458i | −1.04163 | − | 1.80416i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.9159 | 1.05737 | 0.528684 | − | 0.848819i | \(-0.322686\pi\) | ||||
0.528684 | + | 0.848819i | \(0.322686\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7817 | + | 18.6745i | 0.942002 | + | 1.63160i | 0.761646 | + | 0.647994i | \(0.224392\pi\) |
0.180356 | + | 0.983601i | \(0.442275\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.04203 | + | 1.70778i | 0.0903558 | + | 0.148084i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | − | 3.46410i | 0.170872 | − | 0.295958i | −0.767853 | − | 0.640626i | \(-0.778675\pi\) |
0.938725 | + | 0.344668i | \(0.112008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.57989 | 0.558099 | 0.279049 | − | 0.960277i | \(-0.409981\pi\) | ||||
0.279049 | + | 0.960277i | \(0.409981\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.02555 | − | 13.9007i | 0.671130 | − | 1.16243i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.411869 | + | 0.713379i | 0.0342039 | + | 0.0592429i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0543371 | + | 0.0941146i | 0.00445147 | + | 0.00771017i | 0.868243 | − | 0.496140i | \(-0.165250\pi\) |
−0.863791 | + | 0.503850i | \(0.831916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.53379 | − | 11.3169i | 0.531713 | − | 0.920953i | −0.467602 | − | 0.883939i | \(-0.654882\pi\) |
0.999315 | − | 0.0370142i | \(-0.0117847\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.57989 | 0.207222 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.44566 | + | 7.70011i | −0.354803 | + | 0.614536i | −0.987084 | − | 0.160203i | \(-0.948785\pi\) |
0.632282 | + | 0.774739i | \(0.282119\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.735608 | − | 1.20558i | −0.0579740 | − | 0.0950132i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.75615 | + | 9.96995i | 0.450857 | + | 0.780907i | 0.998439 | − | 0.0558449i | \(-0.0177853\pi\) |
−0.547583 | + | 0.836751i | \(0.684452\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.46621 | −0.113458 | −0.0567292 | − | 0.998390i | \(-0.518067\pi\) | ||||
−0.0567292 | + | 0.998390i | \(0.518067\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.40363 | −0.415664 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.62192 | − | 9.73746i | −0.427427 | − | 0.740325i | 0.569217 | − | 0.822188i | \(-0.307247\pi\) |
−0.996644 | + | 0.0818623i | \(0.973913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.26690 | + | 2.32271i | −0.0957684 | + | 0.175580i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.66802 | − | 6.35320i | 0.274161 | − | 0.474860i | −0.695762 | − | 0.718272i | \(-0.744933\pi\) |
0.969923 | + | 0.243412i | \(0.0782666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4712 | −1.37295 | −0.686477 | − | 0.727151i | \(-0.740844\pi\) | ||||
−0.686477 | + | 0.727151i | \(0.740844\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.37808 | − | 4.11895i | 0.174840 | − | 0.302831i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.82374 | − | 10.0870i | −0.425874 | − | 0.737635i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.28995 | + | 12.6266i | 0.527482 | + | 0.913625i | 0.999487 | + | 0.0320296i | \(0.0101971\pi\) |
−0.472005 | + | 0.881596i | \(0.656470\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.40363 | − | 16.2876i | 0.676888 | − | 1.17240i | −0.299025 | − | 0.954245i | \(-0.596661\pi\) |
0.975913 | − | 0.218159i | \(-0.0700052\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.75615 | −0.196368 | −0.0981838 | − | 0.995168i | \(-0.531303\pi\) | ||||
−0.0981838 | + | 0.995168i | \(0.531303\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.51230 | + | 13.0117i | −0.532533 | + | 0.922374i | 0.466745 | + | 0.884392i | \(0.345426\pi\) |
−0.999278 | + | 0.0379825i | \(0.987907\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.17877 | − | 0.0528751i | 0.152919 | − | 0.00371111i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.03379 | − | 5.25468i | −0.211889 | − | 0.367003i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.40363 | 0.304605 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.9159 | −1.50875 | −0.754377 | − | 0.656441i | \(-0.772061\pi\) | ||||
−0.754377 | + | 0.656441i | \(0.772061\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.355027 | + | 0.614926i | 0.0242127 | + | 0.0419376i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.26845 | − | 5.99233i | 0.221877 | − | 0.406786i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.75615 | − | 4.77379i | 0.185399 | − | 0.321120i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.8073 | 1.25943 | 0.629714 | − | 0.776827i | \(-0.283172\pi\) | ||||
0.629714 | + | 0.776827i | \(0.283172\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.33604 | − | 14.4384i | 0.553283 | − | 0.958313i | −0.444752 | − | 0.895654i | \(-0.646708\pi\) |
0.998035 | − | 0.0626599i | \(-0.0199583\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.75615 | − | 16.8982i | −0.644705 | − | 1.11666i | −0.984370 | − | 0.176115i | \(-0.943647\pi\) |
0.339665 | − | 0.940546i | \(-0.389686\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.00000 | + | 15.5885i | 0.589610 | + | 1.02123i | 0.994283 | + | 0.106773i | \(0.0340517\pi\) |
−0.404674 | + | 0.914461i | \(0.632615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.44566 | − | 11.1642i | 0.420469 | − | 0.728273i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0922 | 1.04092 | 0.520459 | − | 0.853887i | \(-0.325761\pi\) | ||||
0.520459 | + | 0.853887i | \(0.325761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.445663 | + | 0.771911i | −0.0287077 | + | 0.0497231i | −0.880022 | − | 0.474932i | \(-0.842473\pi\) |
0.851315 | + | 0.524655i | \(0.175806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.78995 | + | 5.88526i | 0.242131 | + | 0.375996i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.04203 | + | 1.80486i | 0.0663030 | + | 0.114840i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.4712 | −1.10277 | −0.551387 | − | 0.834250i | \(-0.685901\pi\) | ||||
−0.551387 | + | 0.834250i | \(0.685901\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.10867 | −0.195441 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.51230 | − | 6.08349i | −0.219091 | − | 0.379478i | 0.735439 | − | 0.677591i | \(-0.236976\pi\) |
−0.954530 | + | 0.298113i | \(0.903643\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.55434 | − | 10.7419i | −0.407267 | − | 0.667467i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.88882 | − | 15.3959i | 0.548108 | − | 0.949351i | −0.450296 | − | 0.892879i | \(-0.648682\pi\) |
0.998404 | − | 0.0564719i | \(-0.0179851\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.40363 | −0.516231 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.70181 | + | 8.14378i | −0.286675 | + | 0.496535i | −0.973014 | − | 0.230746i | \(-0.925883\pi\) |
0.686339 | + | 0.727282i | \(0.259217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.51230 | − | 6.08349i | −0.213357 | − | 0.369546i | 0.739406 | − | 0.673260i | \(-0.235106\pi\) |
−0.952763 | + | 0.303714i | \(0.901773\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.91187 | + | 5.04351i | 0.175592 | + | 0.304135i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.5799 | + | 23.5211i | −0.815937 | + | 1.41324i | 0.0927170 | + | 0.995693i | \(0.470445\pi\) |
−0.908653 | + | 0.417551i | \(0.862889\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.620977 | 0.0370444 | 0.0185222 | − | 0.999828i | \(-0.494104\pi\) | ||||
0.0185222 | + | 0.999828i | \(0.494104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.57989 | + | 2.73645i | −0.0939147 | + | 0.162665i | −0.909155 | − | 0.416458i | \(-0.863271\pi\) |
0.815240 | + | 0.579123i | \(0.196605\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.0486 | + | 0.389474i | −0.947319 | + | 0.0229899i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.2438 | −0.656873 | −0.328436 | − | 0.944526i | \(-0.606522\pi\) | ||||
−0.328436 | + | 0.944526i | \(0.606522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.735608 | − | 1.27411i | −0.0425413 | − | 0.0736837i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.87808 | − | 0.0455779i | 0.108250 | − | 0.00262706i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.70181 | − | 8.14378i | 0.269225 | − | 0.466312i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5173 | 1.34220 | 0.671102 | − | 0.741365i | \(-0.265821\pi\) | ||||
0.671102 | + | 0.741365i | \(0.265821\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.5799 | + | 25.2531i | −0.826750 | + | 1.43197i | 0.0738250 | + | 0.997271i | \(0.476479\pi\) |
−0.900575 | + | 0.434701i | \(0.856854\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.0922 | + | 20.9443i | 0.683491 | + | 1.18384i | 0.973908 | + | 0.226941i | \(0.0728726\pi\) |
−0.290417 | + | 0.956900i | \(0.593794\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.06759 | + | 10.5094i | 0.340790 | + | 0.590265i | 0.984580 | − | 0.174937i | \(-0.0559723\pi\) |
−0.643790 | + | 0.765202i | \(0.722639\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.39862 | − | 4.15453i | 0.134297 | − | 0.232609i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51230 | 0.0841468 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.37808 | + | 2.38690i | −0.0764419 | + | 0.132401i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.7652 | − | 29.1153i | −0.979428 | − | 1.60518i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.911869 | + | 1.57940i | 0.0501209 | + | 0.0868119i | 0.889997 | − | 0.455966i | \(-0.150706\pi\) |
−0.839877 | + | 0.542778i | \(0.817373\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.8698 | −0.648518 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.7827 | −0.968683 | −0.484341 | − | 0.874879i | \(-0.660941\pi\) | ||||
−0.484341 | + | 0.874879i | \(0.660941\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.51230 | − | 13.0117i | −0.406814 | − | 0.704623i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4712 | − | 1.34692i | 0.997352 | − | 0.0727266i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.644973 | + | 1.11713i | −0.0346239 | + | 0.0599704i | −0.882818 | − | 0.469715i | \(-0.844357\pi\) |
0.848194 | + | 0.529685i | \(0.177690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.31144 | 0.0701995 | 0.0350998 | − | 0.999384i | \(-0.488825\pi\) | ||||
0.0350998 | + | 0.999384i | \(0.488825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.51230 | + | 9.54759i | −0.293390 | + | 0.508167i | −0.974609 | − | 0.223913i | \(-0.928117\pi\) |
0.681219 | + | 0.732080i | \(0.261450\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.11368 | + | 8.85716i | 0.269890 | + | 0.467463i | 0.968833 | − | 0.247714i | \(-0.0796794\pi\) |
−0.698943 | + | 0.715177i | \(0.746346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.21412 | − | 15.9593i | 0.484954 | − | 0.839964i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.51230 | −0.183842 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.67053 | + | 15.0178i | −0.452598 | + | 0.783922i | −0.998547 | − | 0.0538962i | \(-0.982836\pi\) |
0.545949 | + | 0.837819i | \(0.316169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.6465 | + | 19.5192i | −0.552740 | + | 1.01339i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.89133 | + | 15.4002i | 0.460375 | + | 0.797394i | 0.998980 | − | 0.0451654i | \(-0.0143815\pi\) |
−0.538604 | + | 0.842559i | \(0.681048\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.27035 | 0.116929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.2109 | −1.70593 | −0.852964 | − | 0.521969i | \(-0.825198\pi\) | ||||
−0.852964 | + | 0.521969i | \(0.825198\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.38058 | + | 12.7835i | 0.377130 | + | 0.653208i | 0.990643 | − | 0.136476i | \(-0.0435776\pi\) |
−0.613513 | + | 0.789684i | \(0.710244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.4036 | − | 0.373821i | 0.785042 | − | 0.0190517i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.4036 | + | 19.7517i | −0.578187 | + | 1.00145i | 0.417500 | + | 0.908677i | \(0.362906\pi\) |
−0.995687 | + | 0.0927724i | \(0.970427\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.06759 | −0.0539902 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.75615 | + | 8.23790i | −0.239308 | + | 0.414494i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.13517 | + | 12.3585i | 0.358104 | + | 0.620255i | 0.987644 | − | 0.156714i | \(-0.0500899\pi\) |
−0.629540 | + | 0.776968i | \(0.716757\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.74385 | − | 9.94864i | −0.286834 | − | 0.496811i | 0.686218 | − | 0.727396i | \(-0.259270\pi\) |
−0.973052 | + | 0.230585i | \(0.925936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.55528 | − | 6.15793i | 0.177101 | − | 0.306748i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.6986 | −1.37297 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.899566 | + | 1.55809i | −0.0444807 | + | 0.0770428i | −0.887409 | − | 0.460984i | \(-0.847497\pi\) |
0.842928 | + | 0.538027i | \(0.180830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.1352 | − | 18.5817i | 0.498719 | − | 0.914344i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.35503 | + | 5.81108i | 0.164692 | + | 0.285255i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.4282 | −1.33996 | −0.669978 | − | 0.742381i | \(-0.733697\pi\) | ||||
−0.669978 | + | 0.742381i | \(0.733697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.91593 | 0.142114 | 0.0710569 | − | 0.997472i | \(-0.477363\pi\) | ||||
0.0710569 | + | 0.997472i | \(0.477363\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.9589 | − | 21.2383i | −0.627126 | − | 1.02779i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.28995 | − | 12.6266i | 0.351144 | − | 0.608200i | −0.635306 | − | 0.772261i | \(-0.719126\pi\) |
0.986450 | + | 0.164061i | \(0.0524593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1598 | 1.01687 | 0.508437 | − | 0.861099i | \(-0.330223\pi\) | ||||
0.508437 | + | 0.861099i | \(0.330223\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.201814 | − | 0.349553i | 0.00965409 | − | 0.0167214i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.4712 | + | 26.7969i | 0.738401 | + | 1.27895i | 0.953215 | + | 0.302293i | \(0.0977521\pi\) |
−0.214814 | + | 0.976655i | \(0.568915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.7587 | + | 32.4909i | 0.891251 | + | 1.54369i | 0.838377 | + | 0.545090i | \(0.183505\pi\) |
0.0528732 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.878076 | + | 1.52087i | −0.0416248 | + | 0.0720962i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.0922 | −1.46733 | −0.733666 | − | 0.679511i | \(-0.762192\pi\) | ||||
−0.733666 | + | 0.679511i | \(0.762192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.6680 | + | 30.6019i | −0.831955 | + | 1.44099i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.79819 | + | 6.22482i | 0.178062 | + | 0.291824i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.17626 | + | 3.76940i | 0.101801 | + | 0.176325i | 0.912427 | − | 0.409240i | \(-0.134206\pi\) |
−0.810626 | + | 0.585565i | \(0.800873\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.2950 | −1.73700 | −0.868500 | − | 0.495690i | \(-0.834915\pi\) | ||||
−0.868500 | + | 0.495690i | \(0.834915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.81873 | −0.456315 | −0.228158 | − | 0.973624i | \(-0.573270\pi\) | ||||
−0.228158 | + | 0.973624i | \(0.573270\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.4011 | − | 19.7473i | −0.527581 | − | 0.913797i | −0.999483 | − | 0.0321463i | \(-0.989766\pi\) |
0.471902 | − | 0.881651i | \(-0.343568\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0379 | + | 27.5702i | −0.694384 | + | 1.27307i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.06759 | − | 3.58117i | 0.0950678 | − | 0.164662i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.756152 | −0.0346946 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2224 | + | 17.7056i | −0.467071 | + | 0.808991i | −0.999292 | − | 0.0376140i | \(-0.988024\pi\) |
0.532221 | + | 0.846606i | \(0.321358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.55434 | − | 11.3524i | −0.298852 | − | 0.517627i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.00000 | − | 1.73205i | −0.0454077 | − | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.4036 | − | 37.0722i | 0.969891 | − | 1.67990i | 0.274034 | − | 0.961720i | \(-0.411642\pi\) |
0.695857 | − | 0.718181i | \(-0.255025\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.8502 | 0.850699 | 0.425350 | − | 0.905029i | \(-0.360151\pi\) | ||||
0.425350 | + | 0.905029i | \(0.360151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.823739 | − | 1.42676i | 0.0370993 | − | 0.0642579i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.8698 | − | 24.0233i | −0.620899 | − | 1.07543i | −0.989319 | − | 0.145769i | \(-0.953434\pi\) |
0.368420 | − | 0.929660i | \(-0.379899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.7101 | −0.655889 | −0.327944 | − | 0.944697i | \(-0.606356\pi\) | ||||
−0.327944 | + | 0.944697i | \(0.606356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.33604 | 0.103952 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.99176 | − | 12.1101i | −0.309904 | − | 0.536770i | 0.668437 | − | 0.743769i | \(-0.266964\pi\) |
−0.978341 | + | 0.206999i | \(0.933630\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.44973 | + | 8.15805i | −0.196844 | + | 0.360891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.11118 | + | 1.92462i | −0.0489644 | + | 0.0848088i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −75.0757 | −3.30183 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.3616 | − | 17.9468i | 0.453950 | − | 0.786264i | −0.544677 | − | 0.838646i | \(-0.683348\pi\) |
0.998627 | + | 0.0523817i | \(0.0166812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1763 | + | 19.3579i | 0.488704 | + | 0.846460i | 0.999916 | − | 0.0129950i | \(-0.00413655\pi\) |
−0.511212 | + | 0.859455i | \(0.670803\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.57989 | − | 4.46850i | −0.112382 | − | 0.194651i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3575 | − | 19.6718i | 0.493806 | − | 0.855297i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.7232 | −0.724362 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.93492 | + | 13.7437i | −0.343056 | + | 0.594191i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.6465 | − | 36.2517i | 0.803163 | − | 1.56147i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.3278 | − | 28.2806i | −0.701987 | − | 1.21588i | −0.967768 | − | 0.251844i | \(-0.918963\pi\) |
0.265781 | − | 0.964033i | \(-0.414370\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.26845 | 0.140005 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1648 | 1.33251 | 0.666255 | − | 0.745724i | \(-0.267896\pi\) | ||||
0.666255 | + | 0.745724i | \(0.267896\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.311436 | + | 0.539422i | 0.0132676 | + | 0.0229802i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.1087 | + | 21.4837i | 0.557438 | + | 0.913581i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.3616 | + | 38.7314i | −0.947491 | + | 1.64110i | −0.196806 | + | 0.980442i | \(0.563057\pi\) |
−0.750685 | + | 0.660660i | \(0.770276\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.95702 | 0.0827731 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.2464 | + | 28.1395i | −0.684702 | + | 1.18594i | 0.288828 | + | 0.957381i | \(0.406734\pi\) |
−0.973530 | + | 0.228558i | \(0.926599\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.57989 | + | 11.3967i | 0.276818 | + | 0.479463i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.3370 | + | 30.0285i | 0.726804 | + | 1.25886i | 0.958227 | + | 0.286009i | \(0.0923287\pi\) |
−0.231423 | + | 0.972853i | \(0.574338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.55528 | + | 2.69383i | −0.0650866 | + | 0.112733i | −0.896732 | − | 0.442573i | \(-0.854066\pi\) |
0.831646 | + | 0.555306i | \(0.187399\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.533794 | 0.0222607 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.336042 | + | 0.582041i | −0.0139896 | + | 0.0242307i | −0.872935 | − | 0.487836i | \(-0.837787\pi\) |
0.858946 | + | 0.512066i | \(0.171120\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.7479 | − | 0.430713i | 0.736307 | − | 0.0178690i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.4703 | + | 42.3837i | 1.01345 | + | 1.75536i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.67208 | 0.192838 | 0.0964188 | − | 0.995341i | \(-0.469261\pi\) | ||||
0.0964188 | + | 0.995341i | \(0.469261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.95079 | 0.0803808 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.0922 | + | 17.4802i | 0.414437 | + | 0.717825i | 0.995369 | − | 0.0961264i | \(-0.0306453\pi\) |
−0.580932 | + | 0.813952i | \(0.697312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.28995 | − | 0.128378i | 0.216867 | − | 0.00526300i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.7562 | − | 18.6302i | 0.439484 | − | 0.761209i | −0.558165 | − | 0.829730i | \(-0.688494\pi\) |
0.997650 | + | 0.0685204i | \(0.0218278\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.29495 | 0.215986 | 0.107993 | − | 0.994152i | \(-0.465558\pi\) | ||||
0.107993 | + | 0.994152i | \(0.465558\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.4580 | − | 19.8458i | 0.465833 | − | 0.806846i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.3591 | − | 31.7989i | −0.745172 | − | 1.29068i | −0.950114 | − | 0.311902i | \(-0.899034\pi\) |
0.204942 | − | 0.978774i | \(-0.434300\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.7652 | − | 30.7703i | −0.718704 | − | 1.24483i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3616 | + | 35.2673i | −0.822397 | + | 1.42443i | 0.0814954 | + | 0.996674i | \(0.474030\pi\) |
−0.903892 | + | 0.427760i | \(0.859303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.8073 | −0.676635 | −0.338317 | − | 0.941032i | \(-0.609858\pi\) | ||||
−0.338317 | + | 0.941032i | \(0.609858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.8954 | − | 30.9957i | 0.719276 | − | 1.24582i | −0.242010 | − | 0.970274i | \(-0.577807\pi\) |
0.961287 | − | 0.275550i | \(-0.0888598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.42011 | + | 3.96630i | 0.0969597 | + | 0.158907i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.51230 | −0.379280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.4447 | −1.29160 | −0.645802 | − | 0.763505i | \(-0.723477\pi\) | ||||
−0.645802 | + | 0.763505i | \(0.723477\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.95797 | + | 10.3195i | 0.236435 | + | 0.409517i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.2703 | − | 0.935872i | 0.763519 | − | 0.0370806i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.45390 | − | 14.6426i | 0.333909 | − | 0.578348i | −0.649366 | − | 0.760476i | \(-0.724965\pi\) |
0.983275 | + | 0.182129i | \(0.0582988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.135174 | 0.00533075 | 0.00266538 | − | 0.999996i | \(-0.499152\pi\) | ||||
0.00266538 | + | 0.999996i | \(0.499152\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.04454 | + | 3.54125i | −0.0803791 | + | 0.139221i | −0.903413 | − | 0.428772i | \(-0.858946\pi\) |
0.823034 | + | 0.567993i | \(0.192280\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.2950 | − | 40.3480i | −0.914407 | − | 1.58380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.9580 | + | 27.6400i | 0.624483 | + | 1.08164i | 0.988641 | + | 0.150300i | \(0.0480238\pi\) |
−0.364157 | + | 0.931338i | \(0.618643\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7817 | + | 18.6745i | −0.421276 | + | 0.729672i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.70505 | −0.183283 | −0.0916413 | − | 0.995792i | \(-0.529211\pi\) | ||||
−0.0916413 | + | 0.995792i | \(0.529211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.25710 | + | 3.90941i | −0.0877910 | + | 0.152058i | −0.906577 | − | 0.422040i | \(-0.861314\pi\) |
0.818786 | + | 0.574099i | \(0.194647\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.957966 | + | 1.75632i | −0.0371483 | + | 0.0681071i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.219853 | − | 0.380797i | −0.00851275 | − | 0.0147445i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −54.7643 | −2.11415 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.9424 | 1.80950 | 0.904749 | − | 0.425945i | \(-0.140058\pi\) | ||||
0.904749 | + | 0.425945i | \(0.140058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.20181 | − | 9.00981i | −0.199922 | − | 0.346275i | 0.748581 | − | 0.663043i | \(-0.230736\pi\) |
−0.948503 | + | 0.316768i | \(0.897402\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.28995 | + | 0.128378i | −0.203009 | + | 0.00492671i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.53129 | − | 4.38432i | 0.0968571 | − | 0.167761i | −0.813525 | − | 0.581530i | \(-0.802454\pi\) |
0.910382 | + | 0.413768i | \(0.135788\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | 0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.5808 | + | 20.0586i | −0.441195 | + | 0.764172i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.22236 | + | 3.84924i | 0.0845425 | + | 0.146432i | 0.905196 | − | 0.424994i | \(-0.139724\pi\) |
−0.820654 | + | 0.571426i | \(0.806390\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.28995 | + | 5.69835i | 0.124795 | + | 0.216151i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.06759 | + | 10.5094i | −0.229826 | + | 0.398071i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.7562 | −0.821719 | −0.410859 | − | 0.911699i | \(-0.634771\pi\) | ||||
−0.410859 | + | 0.911699i | \(0.634771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.79819 | − | 3.11455i | 0.0678199 | − | 0.117467i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.95952 | − | 5.42594i | 0.111304 | − | 0.204064i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.5041 | + | 35.5141i | 0.770046 | + | 1.33376i | 0.937537 | + | 0.347886i | \(0.113100\pi\) |
−0.167491 | + | 0.985874i | \(0.553566\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.37713 | −0.0515739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0511 | 0.600277 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.8698 | + | 20.5592i | 0.442670 | + | 0.766727i | 0.997887 | − | 0.0649787i | \(-0.0206979\pi\) |
−0.555216 | + | 0.831706i | \(0.687365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.06258 | + | 5.01924i | 0.114056 | + | 0.186926i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.411869 | + | 0.713379i | −0.0152964 | + | 0.0264942i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.8534 | −1.07011 | −0.535056 | − | 0.844817i | \(-0.679709\pi\) | ||||
−0.535056 | + | 0.844817i | \(0.679709\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.710055 | − | 1.22985i | 0.0262623 | − | 0.0454877i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.4292 | − | 40.5805i | −0.865377 | − | 1.49888i | −0.866673 | − | 0.498877i | \(-0.833746\pi\) |
0.00129620 | − | 0.999999i | \(-0.499587\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.5634 | + | 59.8656i | 1.27316 | + | 2.20518i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.07165 | + | 13.9805i | −0.296920 | + | 0.514281i | −0.975430 | − | 0.220310i | \(-0.929293\pi\) |
0.678509 | + | 0.734592i | \(0.262626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.2243 | 0.595210 | 0.297605 | − | 0.954689i | \(-0.403812\pi\) | ||||
0.297605 | + | 0.954689i | \(0.403812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0543371 | + | 0.0941146i | −0.00199076 | + | 0.00344809i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.8698 | + | 35.8423i | 0.799106 | + | 1.30965i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.7562 | − | 18.6302i | −0.392498 | − | 0.679826i | 0.600281 | − | 0.799789i | \(-0.295056\pi\) |
−0.992778 | + | 0.119964i | \(0.961722\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.0676 | 0.475578 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.840220 | 0.0305383 | 0.0152692 | − | 0.999883i | \(-0.495139\pi\) | ||||
0.0152692 | + | 0.999883i | \(0.495139\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.4457 | − | 25.0206i | −0.523655 | − | 0.906997i | −0.999621 | − | 0.0275332i | \(-0.991235\pi\) |
0.475966 | − | 0.879464i | \(-0.342099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.14079 | − | 7.59167i | 0.149907 | − | 0.274837i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.0246 | − | 19.0952i | 0.398075 | − | 0.689487i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.3790 | −0.987313 | −0.493656 | − | 0.869657i | \(-0.664340\pi\) | ||||
−0.493656 | + | 0.869657i | \(0.664340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.1177 | + | 33.1129i | −0.687618 | + | 1.19099i | 0.284989 | + | 0.958531i | \(0.408010\pi\) |
−0.972607 | + | 0.232458i | \(0.925323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.28995 | + | 2.23425i | 0.0463362 | + | 0.0802566i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.29401 | − | 3.97334i | −0.0821914 | − | 0.142360i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.89133 | −0.317345 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.66646 | + | 6.35050i | −0.130695 | + | 0.226371i | −0.923945 | − | 0.382526i | \(-0.875054\pi\) |
0.793249 | + | 0.608897i | \(0.208388\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.8073 | − | 0.844716i | 1.23760 | − | 0.0300346i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.9589 | − | 22.4455i | −0.460184 | − | 0.797063i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.4877 | −0.513181 | −0.256590 | − | 0.966520i | \(-0.582599\pi\) | ||||
−0.256590 | + | 0.966520i | \(0.582599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.7827 | −0.912125 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.2274 | + | 17.7143i | 0.360916 | + | 0.625125i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.676261 | − | 1.23985i | 0.0238351 | − | 0.0436989i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.67626 | + | 9.83157i | −0.199567 | + | 0.345660i | −0.948388 | − | 0.317112i | \(-0.897287\pi\) |
0.748821 | + | 0.662772i | \(0.230620\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.7662 | −1.01012 | −0.505058 | − | 0.863085i | \(-0.668529\pi\) | ||||
−0.505058 | + | 0.863085i | \(0.668529\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.75615 | + | 9.96995i | −0.201629 | + | 0.349232i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.268455 | + | 0.464977i | 0.00939204 | + | 0.0162675i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.02461 | − | 13.8990i | −0.280061 | − | 0.485079i | 0.691339 | − | 0.722531i | \(-0.257021\pi\) |
−0.971399 | + | 0.237451i | \(0.923688\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00250 | + | 12.1287i | −0.244092 | + | 0.422780i | −0.961876 | − | 0.273486i | \(-0.911823\pi\) |
0.717784 | + | 0.696266i | \(0.245157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.2899 | −0.531683 | −0.265842 | − | 0.964017i | \(-0.585650\pi\) | ||||
−0.265842 | + | 0.964017i | \(0.585650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.6475 | − | 18.4420i | 0.369802 | − | 0.640516i | −0.619732 | − | 0.784813i | \(-0.712759\pi\) |
0.989534 | + | 0.144297i | \(0.0460921\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.40363 | − | 12.4496i | 0.221873 | − | 0.431354i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.733103 | − | 1.26977i | −0.0253701 | − | 0.0439423i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.2274 | −1.45785 | −0.728925 | − | 0.684593i | \(-0.759980\pi\) | ||||
−0.728925 | + | 0.684593i | \(0.759980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3215 | −0.976602 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.70181 | − | 4.67968i | −0.0929452 | − | 0.160986i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.5799 | − | 51.7561i | −1.08510 | − | 1.77836i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.26940 | + | 2.19867i | −0.0435145 | + | 0.0753694i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.2931 | −0.455146 | −0.227573 | − | 0.973761i | \(-0.573079\pi\) | ||||
−0.227573 | + | 0.973761i | \(0.573079\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.2274 | − | 33.3028i | 0.656794 | − | 1.13760i | −0.324646 | − | 0.945835i | \(-0.605245\pi\) |
0.981441 | − | 0.191766i | \(-0.0614214\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | − | 6.92820i | −0.136478 | − | 0.236387i | 0.789683 | − | 0.613515i | \(-0.210245\pi\) |
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.5404 | − | 40.7731i | −0.801323 | − | 1.38793i | −0.918745 | − | 0.394850i | \(-0.870796\pi\) |
0.117422 | − | 0.993082i | \(-0.462537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.62192 | − | 9.73746i | 0.191151 | − | 0.331084i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 55.3972 | 1.87922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.3575 | + | 28.3321i | −0.554254 | + | 0.959996i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.64497 | + | 0.0641892i | −0.0894164 | + | 0.00216999i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.28588 | + | 3.95926i | 0.0771888 | + | 0.133695i | 0.902036 | − | 0.431661i | \(-0.142072\pi\) |
−0.824847 | + | 0.565356i | \(0.808739\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.2849 | 0.481272 | 0.240636 | − | 0.970615i | \(-0.422644\pi\) | ||||
0.240636 | + | 0.970615i | \(0.422644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9670 | −0.537334 | −0.268667 | − | 0.963233i | \(-0.586583\pi\) | ||||
−0.268667 | + | 0.963233i | \(0.586583\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.58239 | − | 6.20489i | −0.120285 | − | 0.208340i | 0.799595 | − | 0.600540i | \(-0.205048\pi\) |
−0.919880 | + | 0.392200i | \(0.871714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.5173 | − | 0.764874i | 1.05706 | − | 0.0256531i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.87390 | − | 8.44184i | 0.163099 | − | 0.282495i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.33604 | 0.245217 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.06258 | − | 1.84044i | 0.0354389 | − | 0.0613821i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.40363 | + | 14.5555i | 0.279965 | + | 0.484914i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.23561 | − | 15.9965i | −0.307002 | − | 0.531743i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.13267 | + | 7.15799i | −0.137223 | + | 0.237677i | −0.926444 | − | 0.376431i | \(-0.877151\pi\) |
0.789221 | + | 0.614109i | \(0.210484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.2274 | −0.868951 | −0.434476 | − | 0.900684i | \(-0.643066\pi\) | ||||
−0.434476 | + | 0.900684i | \(0.643066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.5388 | − | 33.8422i | 0.646640 | − | 1.12001i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.7160 | + | 48.7014i | 0.981309 | + | 1.60826i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.37902 | + | 16.2449i | 0.309385 | + | 0.535871i | 0.978228 | − | 0.207533i | \(-0.0665434\pi\) |
−0.668843 | + | 0.743404i | \(0.733210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.75615 | 0.156381 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.45390 | − | 11.1785i | −0.211746 | − | 0.366754i | 0.740515 | − | 0.672040i | \(-0.234582\pi\) |
−0.952261 | + | 0.305285i | \(0.901248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.86577 | + | 4.45015i | 0.0939219 | + | 0.145848i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.82374 | − | 10.0870i | 0.190457 | − | 0.329881i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.78265 | 0.0582367 | 0.0291183 | − | 0.999576i | \(-0.490730\pi\) | ||||
0.0291183 | + | 0.999576i | \(0.490730\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.5634 | + | 39.0810i | −0.735546 | + | 1.27400i | 0.218937 | + | 0.975739i | \(0.429741\pi\) |
−0.954483 | + | 0.298264i | \(0.903592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.61942 | + | 2.80492i | 0.0527356 | + | 0.0913407i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.0436 | + | 19.1281i | 0.358869 | + | 0.621579i | 0.987772 | − | 0.155905i | \(-0.0498293\pi\) |
−0.628904 | + | 0.777483i | \(0.716496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.84022 | + | 8.38351i | −0.157120 | + | 0.272140i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.3442 | 1.46884 | 0.734421 | − | 0.678694i | \(-0.237454\pi\) | ||||
0.734421 | + | 0.678694i | \(0.237454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.28995 | + | 12.6266i | −0.235897 | + | 0.408586i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.06759 | − | 9.29083i | 0.163641 | − | 0.300017i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.1721 | + | 21.0827i | 0.392648 | + | 0.680086i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.8073 | 0.605427 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.0296 | −0.547636 | −0.273818 | − | 0.961782i | \(-0.588287\pi\) | ||||
−0.273818 | + | 0.961782i | \(0.588287\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.6054 | − | 25.2974i | −0.468711 | − | 0.811831i | 0.530649 | − | 0.847591i | \(-0.321948\pi\) |
−0.999360 | + | 0.0357602i | \(0.988615\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.4036 | − | 0.422358i | 0.557935 | − | 0.0135402i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.420110 | − | 0.727652i | 0.0134405 | − | 0.0232796i | −0.859227 | − | 0.511595i | \(-0.829055\pi\) |
0.872667 | + | 0.488315i | \(0.162388\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.2274 | 0.326868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.15822 | − | 7.20225i | 0.132627 | − | 0.229716i | −0.792062 | − | 0.610441i | \(-0.790992\pi\) |
0.924688 | + | 0.380725i | \(0.124326\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.37808 | − | 2.38690i | −0.0439091 | − | 0.0760529i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.189511 | − | 0.328243i | −0.00602611 | − | 0.0104375i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1302 | − | 17.5460i | 0.321795 | − | 0.557366i | −0.659063 | − | 0.752088i | \(-0.729047\pi\) |
0.980859 | + | 0.194722i | \(0.0623804\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.0246 | −0.476312 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5388 | − | 45.9666i | 0.840492 | − | 1.45578i | −0.0489867 | − | 0.998799i | \(-0.515599\pi\) |
0.889479 | − | 0.456976i | \(-0.151067\pi\) | |||||||
\(998\) | 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 | 2520.2.bi.q.361.3 | 6 | ||
3.2 | odd | 2 | 280.2.q.e.81.3 | ✓ | 6 | ||
7.2 | even | 3 | inner | 2520.2.bi.q.1801.3 | 6 | ||
12.11 | even | 2 | 560.2.q.l.81.1 | 6 | |||
15.2 | even | 4 | 1400.2.bh.i.249.1 | 12 | |||
15.8 | even | 4 | 1400.2.bh.i.249.6 | 12 | |||
15.14 | odd | 2 | 1400.2.q.j.1201.1 | 6 | |||
21.2 | odd | 6 | 280.2.q.e.121.3 | yes | 6 | ||
21.5 | even | 6 | 1960.2.q.w.961.1 | 6 | |||
21.11 | odd | 6 | 1960.2.a.w.1.1 | 3 | |||
21.17 | even | 6 | 1960.2.a.v.1.3 | 3 | |||
21.20 | even | 2 | 1960.2.q.w.361.1 | 6 | |||
84.11 | even | 6 | 3920.2.a.cc.1.3 | 3 | |||
84.23 | even | 6 | 560.2.q.l.401.1 | 6 | |||
84.59 | odd | 6 | 3920.2.a.cb.1.1 | 3 | |||
105.2 | even | 12 | 1400.2.bh.i.849.6 | 12 | |||
105.23 | even | 12 | 1400.2.bh.i.849.1 | 12 | |||
105.44 | odd | 6 | 1400.2.q.j.401.1 | 6 | |||
105.59 | even | 6 | 9800.2.a.cf.1.1 | 3 | |||
105.74 | odd | 6 | 9800.2.a.ce.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.e.81.3 | ✓ | 6 | 3.2 | odd | 2 | ||
280.2.q.e.121.3 | yes | 6 | 21.2 | odd | 6 | ||
560.2.q.l.81.1 | 6 | 12.11 | even | 2 | |||
560.2.q.l.401.1 | 6 | 84.23 | even | 6 | |||
1400.2.q.j.401.1 | 6 | 105.44 | odd | 6 | |||
1400.2.q.j.1201.1 | 6 | 15.14 | odd | 2 | |||
1400.2.bh.i.249.1 | 12 | 15.2 | even | 4 | |||
1400.2.bh.i.249.6 | 12 | 15.8 | even | 4 | |||
1400.2.bh.i.849.1 | 12 | 105.23 | even | 12 | |||
1400.2.bh.i.849.6 | 12 | 105.2 | even | 12 | |||
1960.2.a.v.1.3 | 3 | 21.17 | even | 6 | |||
1960.2.a.w.1.1 | 3 | 21.11 | odd | 6 | |||
1960.2.q.w.361.1 | 6 | 21.20 | even | 2 | |||
1960.2.q.w.961.1 | 6 | 21.5 | even | 6 | |||
2520.2.bi.q.361.3 | 6 | 1.1 | even | 1 | trivial | ||
2520.2.bi.q.1801.3 | 6 | 7.2 | even | 3 | inner | ||
3920.2.a.cb.1.1 | 3 | 84.59 | odd | 6 | |||
3920.2.a.cc.1.3 | 3 | 84.11 | even | 6 | |||
9800.2.a.ce.1.3 | 3 | 105.74 | odd | 6 | |||
9800.2.a.cf.1.1 | 3 | 105.59 | even | 6 |