Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(361,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.k (of order \(3\), degree \(2\), not 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: | \(104.079369250\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 27x^{6} + 10x^{5} + 446x^{4} + 62x^{3} + 3061x^{2} + 2142x + 14161 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(-1.65506 + 2.86665i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.361 |
Dual form | 1764.4.k.bd.1549.3 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 4.08470 | + | 7.07491i | 0.365347 | + | 0.632799i | 0.988832 | − | 0.149036i | \(-0.0476170\pi\) |
−0.623485 | + | 0.781835i | \(0.714284\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.9094 | − | 32.7521i | 0.518310 | − | 0.897739i | −0.481464 | − | 0.876466i | \(-0.659895\pi\) |
0.999774 | − | 0.0212729i | \(-0.00677189\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 39.9319 | 0.851933 | 0.425966 | − | 0.904739i | \(-0.359934\pi\) | ||||
0.425966 | + | 0.904739i | \(0.359934\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.96798 | − | 8.60480i | 0.0708772 | − | 0.122763i | −0.828409 | − | 0.560124i | \(-0.810753\pi\) |
0.899286 | + | 0.437361i | \(0.144087\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 45.2229 | + | 78.3284i | 0.546045 | + | 0.945777i | 0.998540 | + | 0.0540105i | \(0.0172004\pi\) |
−0.452496 | + | 0.891767i | \(0.649466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 59.2973 | + | 102.706i | 0.537580 | + | 0.931116i | 0.999034 | + | 0.0439513i | \(0.0139947\pi\) |
−0.461454 | + | 0.887164i | \(0.652672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.1304 | − | 50.4554i | 0.233043 | − | 0.403643i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 78.4061 | 0.502057 | 0.251028 | − | 0.967980i | \(-0.419231\pi\) | ||||
0.251028 | + | 0.967980i | \(0.419231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.0055 | + | 79.6838i | −0.266543 | + | 0.461666i | −0.967967 | − | 0.251079i | \(-0.919215\pi\) |
0.701424 | + | 0.712744i | \(0.252548\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −166.218 | − | 287.897i | −0.738541 | − | 1.27919i | −0.953152 | − | 0.302491i | \(-0.902182\pi\) |
0.214611 | − | 0.976700i | \(-0.431152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −71.7451 | −0.273285 | −0.136643 | − | 0.990620i | \(-0.543631\pi\) | ||||
−0.136643 | + | 0.990620i | \(0.543631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −115.947 | −0.411202 | −0.205601 | − | 0.978636i | \(-0.565915\pi\) | ||||
−0.205601 | + | 0.978636i | \(0.565915\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 153.964 | + | 266.673i | 0.477828 | + | 0.827623i | 0.999677 | − | 0.0254154i | \(-0.00809085\pi\) |
−0.521849 | + | 0.853038i | \(0.674758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −201.575 | + | 349.138i | −0.522424 | + | 0.904865i | 0.477236 | + | 0.878775i | \(0.341639\pi\) |
−0.999660 | + | 0.0260895i | \(0.991695\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 308.958 | 0.757451 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 296.855 | − | 514.168i | 0.655038 | − | 1.13456i | −0.326847 | − | 0.945077i | \(-0.605986\pi\) |
0.981884 | − | 0.189481i | \(-0.0606806\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −166.585 | − | 288.534i | −0.349657 | − | 0.605623i | 0.636532 | − | 0.771250i | \(-0.280368\pi\) |
−0.986188 | + | 0.165628i | \(0.947035\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 163.110 | + | 282.515i | 0.311251 | + | 0.539102i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 371.756 | − | 643.900i | 0.677869 | − | 1.17410i | −0.297753 | − | 0.954643i | \(-0.596237\pi\) |
0.975622 | − | 0.219460i | \(-0.0704295\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 728.272 | 1.21732 | 0.608662 | − | 0.793429i | \(-0.291706\pi\) | ||||
0.608662 | + | 0.793429i | \(0.291706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 400.874 | − | 694.335i | 0.642723 | − | 1.11323i | −0.342099 | − | 0.939664i | \(-0.611138\pi\) |
0.984822 | − | 0.173566i | \(-0.0555289\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −533.953 | − | 924.833i | −0.760435 | − | 1.31711i | −0.942626 | − | 0.333849i | \(-0.891652\pi\) |
0.182191 | − | 0.983263i | \(-0.441681\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −906.756 | −1.19915 | −0.599575 | − | 0.800319i | \(-0.704664\pi\) | ||||
−0.599575 | + | 0.800319i | \(0.704664\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 81.1709 | 0.103579 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 556.634 | + | 964.119i | 0.662957 | + | 1.14827i | 0.979835 | + | 0.199808i | \(0.0640320\pi\) |
−0.316878 | + | 0.948466i | \(0.602635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −369.444 | + | 639.896i | −0.398991 | + | 0.691073i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1480.94 | 1.55017 | 0.775084 | − | 0.631858i | \(-0.217707\pi\) | ||||
0.775084 | + | 0.631858i | \(0.217707\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −278.158 | + | 481.784i | −0.274037 | + | 0.474647i | −0.969892 | − | 0.243536i | \(-0.921693\pi\) |
0.695854 | + | 0.718183i | \(0.255026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −276.217 | − | 478.423i | −0.264238 | − | 0.457674i | 0.703126 | − | 0.711066i | \(-0.251787\pi\) |
−0.967364 | + | 0.253392i | \(0.918454\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 266.902 | + | 462.288i | 0.241144 | + | 0.417674i | 0.961040 | − | 0.276408i | \(-0.0891440\pi\) |
−0.719896 | + | 0.694082i | \(0.755811\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −547.314 | + | 947.976i | −0.480947 | + | 0.833025i | −0.999761 | − | 0.0218626i | \(-0.993040\pi\) |
0.518814 | + | 0.854887i | \(0.326374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1425.18 | 1.18646 | 0.593228 | − | 0.805035i | \(-0.297853\pi\) | ||||
0.593228 | + | 0.805035i | \(0.297853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −484.423 | + | 839.046i | −0.392806 | + | 0.680360i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.6330 | − | 85.9668i | −0.0372900 | − | 0.0645882i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1497.13 | 1.07126 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −786.485 | −0.549522 | −0.274761 | − | 0.961513i | \(-0.588599\pi\) | ||||
−0.274761 | + | 0.961513i | \(0.588599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8651 | − | 24.0151i | −0.00924735 | − | 0.0160169i | 0.861365 | − | 0.507987i | \(-0.169610\pi\) |
−0.870612 | + | 0.491970i | \(0.836277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1181.49 | + | 2046.40i | −0.736798 | + | 1.27617i | 0.217132 | + | 0.976142i | \(0.430330\pi\) |
−0.953930 | + | 0.300029i | \(0.903004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2513.28 | 1.53362 | 0.766811 | − | 0.641873i | \(-0.221842\pi\) | ||||
0.766811 | + | 0.641873i | \(0.221842\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 755.090 | − | 1307.85i | 0.441565 | − | 0.764813i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 320.266 | + | 554.716i | 0.183425 | + | 0.317701i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1132.92 | + | 1962.27i | 0.622900 | + | 1.07889i | 0.988943 | + | 0.148296i | \(0.0473788\pi\) |
−0.366043 | + | 0.930598i | \(0.619288\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −141.573 | + | 245.212i | −0.0762984 | + | 0.132153i | −0.901650 | − | 0.432466i | \(-0.857644\pi\) |
0.825352 | + | 0.564619i | \(0.190977\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −751.675 | −0.389522 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −96.2904 | + | 166.780i | −0.0489478 | + | 0.0847801i | −0.889461 | − | 0.457011i | \(-0.848920\pi\) |
0.840513 | + | 0.541791i | \(0.182253\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 421.417 | + | 729.915i | 0.202502 | + | 0.350744i | 0.949334 | − | 0.314269i | \(-0.101759\pi\) |
−0.746832 | + | 0.665013i | \(0.768426\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3859.21 | 1.78823 | 0.894116 | − | 0.447836i | \(-0.147805\pi\) | ||||
0.894116 | + | 0.447836i | \(0.147805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −602.441 | −0.274211 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 755.329 | + | 1308.27i | 0.331946 | + | 0.574947i | 0.982893 | − | 0.184176i | \(-0.0589616\pi\) |
−0.650948 | + | 0.759123i | \(0.725628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1232.31 | + | 2134.43i | −0.514566 | + | 0.891255i | 0.485291 | + | 0.874353i | \(0.338714\pi\) |
−0.999857 | + | 0.0169022i | \(0.994620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3297.36 | −1.35409 | −0.677047 | − | 0.735940i | \(-0.736741\pi\) | ||||
−0.677047 | + | 0.735940i | \(0.736741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1357.90 | − | 2351.95i | 0.539647 | − | 0.934696i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −187.883 | − | 325.424i | −0.0734727 | − | 0.127258i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2364.85 | − | 4096.05i | −0.895889 | − | 1.55173i | −0.832700 | − | 0.553724i | \(-0.813206\pi\) |
−0.0631890 | − | 0.998002i | \(-0.520127\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2276.59 | + | 3943.17i | −0.849080 | + | 1.47065i | 0.0329498 | + | 0.999457i | \(0.489510\pi\) |
−0.882030 | + | 0.471193i | \(0.843823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3109.06 | 1.12442 | 0.562212 | − | 0.826993i | \(-0.309950\pi\) | ||||
0.562212 | + | 0.826993i | \(0.309950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 221.756 | − | 384.092i | 0.0789943 | − | 0.136822i | −0.823822 | − | 0.566849i | \(-0.808162\pi\) |
0.902816 | + | 0.430027i | \(0.141496\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −293.057 | − | 507.590i | −0.0998439 | − | 0.172935i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3420.56 | 1.13208 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4653.28 | 1.51822 | 0.759112 | − | 0.650960i | \(-0.225633\pi\) | ||||
0.759112 | + | 0.650960i | \(0.225633\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −473.607 | − | 820.311i | −0.150231 | − | 0.260208i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 198.381 | − | 343.606i | 0.0603826 | − | 0.104586i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2778.90 | 0.834481 | 0.417240 | − | 0.908796i | \(-0.362997\pi\) | ||||
0.417240 | + | 0.908796i | \(0.362997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1608.61 | − | 2786.20i | 0.470340 | − | 0.814653i | −0.529084 | − | 0.848569i | \(-0.677464\pi\) |
0.999425 | + | 0.0339159i | \(0.0107978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1864.01 | + | 3228.56i | 0.537891 | + | 0.931655i | 0.999017 | + | 0.0443203i | \(0.0141122\pi\) |
−0.461126 | + | 0.887335i | \(0.652554\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1801.76 | − | 3120.73i | −0.506596 | − | 0.877451i | −0.999971 | − | 0.00763377i | \(-0.997570\pi\) |
0.493374 | − | 0.869817i | \(-0.335763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1257.79 | + | 2178.56i | −0.349146 | + | 0.604739i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2348.76 | −0.635684 | −0.317842 | − | 0.948144i | \(-0.602958\pi\) | ||||
−0.317842 | + | 0.948144i | \(0.602958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2546.70 | − | 4411.01i | 0.680693 | − | 1.17900i | −0.294076 | − | 0.955782i | \(-0.595012\pi\) |
0.974770 | − | 0.223213i | \(-0.0716546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1805.84 | + | 3127.80i | 0.465193 | + | 0.805738i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5939.02 | 1.49350 | 0.746749 | − | 0.665106i | \(-0.231614\pi\) | ||||
0.746749 | + | 0.665106i | \(0.231614\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4485.11 | 1.11453 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −757.944 | − | 1312.80i | −0.183966 | − | 0.318638i | 0.759262 | − | 0.650785i | \(-0.225560\pi\) |
−0.943228 | + | 0.332147i | \(0.892227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3216.96 | + | 5571.94i | −0.754244 | + | 1.30639i | 0.191505 | + | 0.981492i | \(0.438663\pi\) |
−0.945749 | + | 0.324898i | \(0.894670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3293.50 | −0.763464 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3474.90 | + | 6018.69i | −0.787614 | + | 1.36419i | 0.139811 | + | 0.990178i | \(0.455350\pi\) |
−0.927425 | + | 0.374009i | \(0.877983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 480.997 | + | 833.111i | 0.107817 | + | 0.186745i | 0.914886 | − | 0.403713i | \(-0.132281\pi\) |
−0.807068 | + | 0.590458i | \(0.798947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1101.68 | − | 1908.16i | −0.241577 | − | 0.418424i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −380.005 | + | 658.188i | −0.0824271 | + | 0.142768i | −0.904292 | − | 0.426915i | \(-0.859600\pi\) |
0.821865 | + | 0.569682i | \(0.192934\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4412.07 | 0.936662 | 0.468331 | − | 0.883553i | \(-0.344855\pi\) | ||||
0.468331 | + | 0.883553i | \(0.344855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1301.07 | − | 2253.53i | 0.273289 | − | 0.473351i | −0.696413 | − | 0.717641i | \(-0.745222\pi\) |
0.969702 | + | 0.244291i | \(0.0785551\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2407.14 | + | 4169.29i | 0.489953 | + | 0.848623i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9332.18 | 1.86072 | 0.930361 | − | 0.366644i | \(-0.119493\pi\) | ||||
0.930361 | + | 0.366644i | \(0.119493\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4850.26 | 0.957264 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2367.85 | + | 4101.24i | 0.457982 | + | 0.793248i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1360.90 | − | 2357.15i | 0.255492 | − | 0.442525i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4895.51 | 0.910103 | 0.455051 | − | 0.890465i | \(-0.349621\pi\) | ||||
0.455051 | + | 0.890465i | \(0.349621\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3752.64 | − | 6499.77i | 0.684221 | − | 1.18511i | −0.289460 | − | 0.957190i | \(-0.593476\pi\) |
0.973681 | − | 0.227916i | \(-0.0731910\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3174.64 | + | 5498.63i | 0.573294 | + | 0.992974i | 0.996225 | + | 0.0868124i | \(0.0276681\pi\) |
−0.422931 | + | 0.906162i | \(0.638999\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3999.80 | − | 6927.86i | −0.708679 | − | 1.22747i | −0.965347 | − | 0.260968i | \(-0.915958\pi\) |
0.256669 | − | 0.966499i | \(-0.417375\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1482.61 | − | 2567.96i | 0.260221 | − | 0.450716i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 898.666 | 0.154808 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1163.23 | − | 2014.78i | 0.198537 | − | 0.343876i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1060.78 | + | 1837.32i | 0.176150 | + | 0.305101i | 0.940559 | − | 0.339631i | \(-0.110302\pi\) |
−0.764409 | + | 0.644732i | \(0.776969\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6074.05 | 0.990629 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9114.19 | −1.47324 | −0.736620 | − | 0.676307i | \(-0.763579\pi\) | ||||
−0.736620 | + | 0.676307i | \(0.763579\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1739.87 | + | 3013.55i | 0.276303 | + | 0.478572i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −836.534 | + | 1448.92i | −0.129416 | + | 0.224156i | −0.923451 | − | 0.383717i | \(-0.874644\pi\) |
0.794034 | + | 0.607873i | \(0.207977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3467.56 | −0.531845 | −0.265923 | − | 0.963994i | \(-0.585677\pi\) | ||||
−0.265923 | + | 0.963994i | \(0.585677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1992.12 | − | 3450.45i | 0.300368 | − | 0.520252i | −0.675851 | − | 0.737038i | \(-0.736224\pi\) |
0.976219 | + | 0.216785i | \(0.0695572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2974.78 | + | 5152.46i | 0.444746 | + | 0.770322i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1085.47 | + | 1880.08i | 0.159579 | + | 0.276398i | 0.934717 | − | 0.355394i | \(-0.115653\pi\) |
−0.775138 | + | 0.631792i | \(0.782320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −660.724 | + | 1144.41i | −0.0963295 | + | 0.166848i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6549.81 | 0.939268 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1796.06 | + | 3110.86i | −0.255459 | + | 0.442468i | −0.965020 | − | 0.262176i | \(-0.915560\pi\) |
0.709561 | + | 0.704644i | \(0.248893\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3719.90 | − | 6443.05i | −0.516378 | − | 0.894393i | −0.999819 | − | 0.0190163i | \(-0.993947\pi\) |
0.483441 | − | 0.875377i | \(-0.339387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3130.91 | 0.427719 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11243.9 | 1.52390 | 0.761951 | − | 0.647635i | \(-0.224242\pi\) | ||||
0.761951 | + | 0.647635i | \(0.224242\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1770.62 | + | 3066.81i | 0.236226 | + | 0.409156i | 0.959628 | − | 0.281271i | \(-0.0907561\pi\) |
−0.723402 | + | 0.690427i | \(0.757423\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5279.10 | + | 9143.66i | −0.688074 | + | 1.19178i | 0.284386 | + | 0.958710i | \(0.408210\pi\) |
−0.972460 | + | 0.233070i | \(0.925123\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1178.35 | 0.152409 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4362.08 | − | 7555.34i | 0.555645 | − | 0.962406i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 270.287 | + | 468.151i | 0.0341696 | + | 0.0591834i | 0.882604 | − | 0.470116i | \(-0.155788\pi\) |
−0.848435 | + | 0.529300i | \(0.822455\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1083.52 | + | 1876.70i | 0.134933 | + | 0.233711i | 0.925572 | − | 0.378572i | \(-0.123585\pi\) |
−0.790639 | + | 0.612283i | \(0.790251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1837.09 | + | 3181.93i | −0.227077 | + | 0.393308i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12572.3 | −1.53117 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 478.845 | − | 829.384i | 0.0578908 | − | 0.100270i | −0.835628 | − | 0.549296i | \(-0.814896\pi\) |
0.893518 | + | 0.449027i | \(0.148229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3703.83 | − | 6415.22i | −0.438105 | − | 0.758821i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6464.42 | −0.753718 | −0.376859 | − | 0.926271i | \(-0.622996\pi\) | ||||
−0.376859 | + | 0.926271i | \(0.622996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6201.23 | −0.717885 | −0.358943 | − | 0.933360i | \(-0.616863\pi\) | ||||
−0.358943 | + | 0.933360i | \(0.616863\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −289.439 | − | 501.322i | −0.0330349 | − | 0.0572181i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 707.796 | − | 1225.94i | 0.0791029 | − | 0.137010i | −0.823760 | − | 0.566938i | \(-0.808128\pi\) |
0.902863 | + | 0.429928i | \(0.141461\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8905.73 | 0.988411 | 0.494206 | − | 0.869345i | \(-0.335459\pi\) | ||||
0.494206 | + | 0.869345i | \(0.335459\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5363.19 | + | 9289.32i | −0.587085 | + | 1.01686i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5438.25 | − | 9419.33i | −0.591238 | − | 1.02405i | −0.994066 | − | 0.108779i | \(-0.965306\pi\) |
0.402828 | − | 0.915276i | \(-0.368027\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5701.48 | + | 9875.25i | 0.611479 | + | 1.05911i | 0.990991 | + | 0.133927i | \(0.0427586\pi\) |
−0.379512 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4547.37 | + | 7876.28i | −0.484418 | + | 0.839037i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12689.0 | 1.33370 | 0.666852 | − | 0.745190i | \(-0.267641\pi\) | ||||
0.666852 | + | 0.745190i | \(0.267641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1356.66 | + | 2349.80i | −0.141646 | + | 0.245339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1135.02 | − | 1965.92i | −0.116180 | − | 0.201229i | 0.802071 | − | 0.597229i | \(-0.203732\pi\) |
−0.918251 | + | 0.395999i | \(0.870398\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10731.2 | −1.08417 | −0.542085 | − | 0.840324i | \(-0.682365\pi\) | ||||
−0.542085 | + | 0.840324i | \(0.682365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3307.74 | −0.332017 | −0.166008 | − | 0.986124i | \(-0.553088\pi\) | ||||
−0.166008 | + | 0.986124i | \(0.553088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4623.35 | − | 8007.87i | −0.458122 | − | 0.793490i | 0.540740 | − | 0.841190i | \(-0.318144\pi\) |
−0.998862 | + | 0.0476996i | \(0.984811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2192.48 | + | 3797.49i | −0.213130 | + | 0.369152i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5269.45 | 0.509008 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7611.66 | − | 13183.8i | 0.726066 | − | 1.25758i | −0.232468 | − | 0.972604i | \(-0.574680\pi\) |
0.958534 | − | 0.284978i | \(-0.0919865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6637.39 | − | 11496.3i | −0.629187 | − | 1.08978i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6049.19 | + | 10477.5i | 0.566349 | + | 0.980946i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3879.36 | − | 6719.25i | 0.360966 | − | 0.625212i | −0.627154 | − | 0.778895i | \(-0.715780\pi\) |
0.988120 | + | 0.153683i | \(0.0491136\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8342.30 | 0.766767 | 0.383384 | − | 0.923589i | \(-0.374759\pi\) | ||||
0.383384 | + | 0.923589i | \(0.374759\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 389.520 | − | 674.668i | 0.0355844 | − | 0.0616340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1293.47 | + | 2240.36i | 0.116040 | + | 0.200987i | 0.918195 | − | 0.396129i | \(-0.129647\pi\) |
−0.802155 | + | 0.597116i | \(0.796313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −409.682 | −0.0363157 | −0.0181578 | − | 0.999835i | \(-0.505780\pi\) | ||||
−0.0181578 | + | 0.999835i | \(0.505780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4544.77 | −0.400475 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2195.25 | + | 3802.29i | 0.191165 | + | 0.331107i | 0.945637 | − | 0.325225i | \(-0.105440\pi\) |
−0.754472 | + | 0.656333i | \(0.772107\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2256.53 | − | 3908.43i | 0.193077 | − | 0.334419i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11645.5 | 0.990652 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9714.76 | + | 16826.5i | −0.816912 | + | 1.41493i | 0.0910341 | + | 0.995848i | \(0.470983\pi\) |
−0.907947 | + | 0.419086i | \(0.862351\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8974.35 | − | 15544.0i | −0.750326 | − | 1.29960i | −0.947664 | − | 0.319268i | \(-0.896563\pi\) |
0.197338 | − | 0.980336i | \(-0.436770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 457.109 | + | 791.735i | 0.0377836 | + | 0.0654431i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −948.833 | + | 1643.43i | −0.0779841 | + | 0.135072i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2864.92 | −0.232821 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2180.43 | + | 3776.62i | −0.176202 | + | 0.305192i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11547.0 | − | 20000.0i | −0.917641 | − | 1.58940i | −0.802989 | − | 0.595994i | \(-0.796758\pi\) |
−0.114652 | − | 0.993406i | \(-0.536575\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8942.47 | −0.702850 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2266.68 | −0.177178 | −0.0885889 | − | 0.996068i | \(-0.528236\pi\) | ||||
−0.0885889 | + | 0.996068i | \(0.528236\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3545.75 | + | 6141.42i | 0.274145 | + | 0.474834i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5519.27 | + | 9559.65i | −0.419854 | + | 0.727209i | −0.995924 | − | 0.0901913i | \(-0.971252\pi\) |
0.576070 | + | 0.817400i | \(0.304585\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4629.97 | −0.350316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3529.68 | + | 6113.58i | −0.264224 | + | 0.457650i | −0.967360 | − | 0.253406i | \(-0.918449\pi\) |
0.703136 | + | 0.711055i | \(0.251783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5821.43 | + | 10083.0i | 0.433468 | + | 0.750788i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −676.403 | − | 1171.56i | −0.0498353 | − | 0.0863172i | 0.840032 | − | 0.542537i | \(-0.182536\pi\) |
−0.889867 | + | 0.456220i | \(0.849203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10419.6 | − | 18047.3i | 0.763655 | − | 1.32269i | −0.177300 | − | 0.984157i | \(-0.556736\pi\) |
0.940955 | − | 0.338532i | \(-0.109930\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6909.42 | 0.501117 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5007.32 | + | 8672.92i | −0.361278 | + | 0.625751i | −0.988171 | − | 0.153353i | \(-0.950993\pi\) |
0.626894 | + | 0.779105i | \(0.284326\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7623.34 | + | 13204.0i | 0.541555 | + | 0.938001i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20864.8 | −1.46709 | −0.733546 | − | 0.679640i | \(-0.762136\pi\) | ||||
−0.733546 | + | 0.679640i | \(0.762136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8322.01 | −0.582177 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8773.84 | + | 15196.7i | 0.607586 | + | 1.05237i | 0.991637 | + | 0.129058i | \(0.0411952\pi\) |
−0.384051 | + | 0.923312i | \(0.625471\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −65.3409 | + | 113.174i | −0.00445703 | + | 0.00771980i | −0.868245 | − | 0.496135i | \(-0.834752\pi\) |
0.863788 | + | 0.503855i | \(0.168085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5964.47 | −0.404818 | −0.202409 | − | 0.979301i | \(-0.564877\pi\) | ||||
−0.202409 | + | 0.979301i | \(0.564877\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 405.472 | − | 702.298i | 0.0272476 | − | 0.0471942i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4955.82 | + | 8583.73i | 0.331384 | + | 0.573975i | 0.982784 | − | 0.184761i | \(-0.0591509\pi\) |
−0.651399 | + | 0.758735i | \(0.725818\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6148.07 | + | 10648.8i | 0.407077 | + | 0.705079i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3241.26 | − | 5614.03i | 0.213562 | − | 0.369900i | −0.739265 | − | 0.673415i | \(-0.764827\pi\) |
0.952827 | + | 0.303515i | \(0.0981602\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7189.36 | −0.469097 | −0.234548 | − | 0.972104i | \(-0.575361\pi\) | ||||
−0.234548 | + | 0.972104i | \(0.575361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −930.696 | + | 1612.01i | −0.0604327 | + | 0.104672i | −0.894659 | − | 0.446750i | \(-0.852581\pi\) |
0.834226 | + | 0.551422i | \(0.185915\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2474.04 | + | 4285.16i | 0.158338 | + | 0.274250i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3303.06 | −0.209383 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29032.0 | −1.83161 | −0.915803 | − | 0.401627i | \(-0.868445\pi\) | ||||
−0.915803 | + | 0.401627i | \(0.868445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3212.56 | − | 5564.32i | −0.200766 | − | 0.347737i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12228.9 | − | 21181.0i | 0.753527 | − | 1.30515i | −0.192576 | − | 0.981282i | \(-0.561684\pi\) |
0.946103 | − | 0.323866i | \(-0.104983\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10968.2 | 0.672695 | 0.336348 | − | 0.941738i | \(-0.390808\pi\) | ||||
0.336348 | + | 0.941738i | \(0.390808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2742.37 | − | 4749.92i | 0.166636 | − | 0.288622i | −0.770599 | − | 0.637320i | \(-0.780043\pi\) |
0.937235 | + | 0.348698i | \(0.113376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11226.7 | − | 19445.2i | −0.679025 | − | 1.17611i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5164.98 | − | 8946.01i | −0.309527 | − | 0.536117i | 0.668732 | − | 0.743504i | \(-0.266837\pi\) |
−0.978259 | + | 0.207387i | \(0.933504\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 113.270 | − | 196.189i | 0.00675698 | − | 0.0117034i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26822.2 | −1.58550 | −0.792751 | − | 0.609546i | \(-0.791352\pi\) | ||||
−0.792751 | + | 0.609546i | \(0.791352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1249.38 | + | 2163.99i | −0.0735177 | + | 0.127336i | −0.900441 | − | 0.434979i | \(-0.856756\pi\) |
0.826923 | + | 0.562315i | \(0.190089\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4649.27 | + | 8052.77i | 0.269896 | + | 0.467473i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12600.1 | −0.724922 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10092.1 | 0.578044 | 0.289022 | − | 0.957322i | \(-0.406670\pi\) | ||||
0.289022 | + | 0.957322i | \(0.406670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13183.2 | − | 22833.9i | −0.748406 | − | 1.29628i | −0.948586 | − | 0.316518i | \(-0.897486\pi\) |
0.200181 | − | 0.979759i | \(-0.435847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11285.4 | − | 19546.9i | 0.632245 | − | 1.09508i | −0.354847 | − | 0.934924i | \(-0.615467\pi\) |
0.987092 | − | 0.160155i | \(-0.0511996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19304.1 | −1.07675 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8049.28 | + | 13941.8i | −0.445070 | + | 0.770884i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5965.75 | + | 10333.0i | 0.328434 | + | 0.568864i | 0.982201 | − | 0.187832i | \(-0.0601459\pi\) |
−0.653768 | + | 0.756695i | \(0.726813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10266.0 | + | 17781.2i | 0.560304 | + | 0.970475i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −356.428 | + | 617.352i | −0.0193697 | + | 0.0335493i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16592.6 | −0.893997 | −0.446999 | − | 0.894535i | \(-0.647507\pi\) | ||||
−0.446999 | + | 0.894535i | \(0.647507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15033.7 | − | 26039.1i | 0.806553 | − | 1.39699i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9357.00 | − | 16206.8i | −0.495641 | − | 0.858476i | 0.504346 | − | 0.863502i | \(-0.331734\pi\) |
−0.999987 | + | 0.00502575i | \(0.998400\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10912.0 | −0.573152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12337.3 | 0.645298 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12427.4 | − | 21524.9i | −0.644594 | − | 1.11647i | −0.984395 | − | 0.175972i | \(-0.943693\pi\) |
0.339801 | − | 0.940497i | \(-0.389640\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2284.00 | − | 3956.01i | 0.117001 | − | 0.202652i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22506.0 | −1.14814 | −0.574071 | − | 0.818805i | \(-0.694637\pi\) | ||||
−0.574071 | + | 0.818805i | \(0.694637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −576.020 | + | 997.696i | −0.0291448 | + | 0.0504803i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11896.0 | + | 20604.5i | 0.599440 | + | 1.03826i | 0.992904 | + | 0.118920i | \(0.0379432\pi\) |
−0.393464 | + | 0.919340i | \(0.628723\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14059.4 | − | 24351.6i | −0.702692 | − | 1.21710i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2401.62 | + | 4159.72i | −0.119547 | + | 0.207061i | −0.919588 | − | 0.392884i | \(-0.871477\pi\) |
0.800041 | + | 0.599945i | \(0.204811\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5076.10 | −0.250638 | −0.125319 | − | 0.992116i | \(-0.539995\pi\) | ||||
−0.125319 | + | 0.992116i | \(0.539995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9255.24 | + | 16030.6i | −0.455149 | + | 0.788341i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4579.36 | + | 7931.68i | 0.222508 | + | 0.385394i | 0.955569 | − | 0.294768i | \(-0.0952425\pi\) |
−0.733061 | + | 0.680163i | \(0.761909\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2313.14 | −0.111502 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33682.2 | 1.61717 | 0.808587 | − | 0.588377i | \(-0.200233\pi\) | ||||
0.808587 | + | 0.588377i | \(0.200233\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6673.14 | + | 11558.2i | 0.317873 | + | 0.550571i | 0.980044 | − | 0.198781i | \(-0.0636983\pi\) |
−0.662171 | + | 0.749352i | \(0.730365\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11854.0 | − | 20531.7i | 0.558048 | − | 0.966568i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15530.6 | −0.728281 | −0.364140 | − | 0.931344i | \(-0.618637\pi\) | ||||
−0.364140 | + | 0.931344i | \(0.618637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5507.62 | + | 9539.47i | −0.256268 | + | 0.443869i | −0.965239 | − | 0.261368i | \(-0.915826\pi\) |
0.708971 | + | 0.705238i | \(0.249160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2680.32 | + | 4642.45i | 0.124232 | + | 0.215176i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3244.52 | − | 5619.67i | −0.149226 | − | 0.258467i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13771.2 | − | 23852.4i | 0.630951 | − | 1.09284i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1573.27 | −0.0715317 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10596.3 | + | 18353.3i | −0.479946 | + | 0.831291i | −0.999735 | − | 0.0230036i | \(-0.992677\pi\) |
0.519789 | + | 0.854294i | \(0.326010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6652.07 | − | 11521.7i | −0.297884 | − | 0.515950i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18189.9 | −0.808432 | −0.404216 | − | 0.914663i | \(-0.632456\pi\) | ||||
−0.404216 | + | 0.914663i | \(0.632456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3059.56 | 0.135468 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15160.6 | − | 26259.0i | −0.666260 | − | 1.15400i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22758.3 | − | 39418.5i | 0.989045 | − | 1.71308i | 0.366688 | − | 0.930344i | \(-0.380492\pi\) |
0.622358 | − | 0.782733i | \(-0.286175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42099.9 | −1.82285 | −0.911423 | − | 0.411472i | \(-0.865015\pi\) | ||||
−0.911423 | + | 0.411472i | \(0.865015\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3442.72 | + | 5962.97i | −0.147967 | + | 0.256287i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5243.44 | − | 9081.90i | −0.224535 | − | 0.388905i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13278.0 | − | 22998.1i | −0.564439 | − | 0.977637i | −0.997102 | − | 0.0760810i | \(-0.975759\pi\) |
0.432663 | − | 0.901556i | \(-0.357574\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 777.124 | − | 1346.02i | 0.0329147 | − | 0.0570100i | −0.849099 | − | 0.528234i | \(-0.822854\pi\) |
0.882014 | + | 0.471224i | \(0.156188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10548.3 | 0.443531 | 0.221766 | − | 0.975100i | \(-0.428818\pi\) | ||||
0.221766 | + | 0.975100i | \(0.428818\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2165.63 | + | 3750.98i | −0.0907303 | + | 0.157150i | −0.907819 | − | 0.419363i | \(-0.862253\pi\) |
0.817088 | + | 0.576513i | \(0.195587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15763.7 | + | 27303.6i | 0.653325 | + | 1.13159i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23557.7 | 0.969369 | 0.484685 | − | 0.874689i | \(-0.338934\pi\) | ||||
0.484685 | + | 0.874689i | \(0.338934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18241.5 | −0.747939 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2460.79 | − | 4262.22i | −0.100182 | − | 0.173520i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19712.5 | − | 34143.1i | 0.794049 | − | 1.37533i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11493.6 | −0.461350 | −0.230675 | − | 0.973031i | \(-0.574093\pi\) | ||||
−0.230675 | + | 0.973031i | \(0.574093\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1267.11 | + | 2194.71i | −0.0505062 | + | 0.0874792i | −0.890173 | − | 0.455622i | \(-0.849417\pi\) |
0.839667 | + | 0.543101i | \(0.182750\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1563.54 | − | 2708.14i | −0.0621041 | − | 0.107567i | 0.833302 | − | 0.552819i | \(-0.186448\pi\) |
−0.895406 | + | 0.445251i | \(0.853114\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7654.94 | + | 13258.7i | 0.301943 | + | 0.522981i | 0.976576 | − | 0.215172i | \(-0.0690313\pi\) |
−0.674633 | + | 0.738153i | \(0.735698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6170.59 | + | 10687.8i | −0.242551 | + | 0.420110i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40387.0 | −1.57656 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14844.9 | − | 25712.2i | 0.577498 | − | 1.00026i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21210.3 | + | 36737.4i | 0.816673 | + | 1.41452i | 0.908120 | + | 0.418710i | \(0.137518\pi\) |
−0.0914467 | + | 0.995810i | \(0.529149\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10060.8 | −0.384740 | −0.192370 | − | 0.981322i | \(-0.561617\pi\) | ||||
−0.192370 | + | 0.981322i | \(0.561617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17437.8 | 0.664585 | 0.332293 | − | 0.943176i | \(-0.392178\pi\) | ||||
0.332293 | + | 0.943176i | \(0.392178\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8008.33 | − | 13870.8i | −0.303149 | − | 0.525070i | 0.673698 | − | 0.739007i | \(-0.264705\pi\) |
−0.976848 | + | 0.213937i | \(0.931371\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13925.4 | + | 24119.5i | −0.521831 | + | 0.903838i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20134.5 | −0.751981 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3607.11 | + | 6247.70i | −0.133820 | + | 0.231782i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2002.84 | + | 3469.03i | 0.0740559 | + | 0.128269i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13468.7 | − | 23328.5i | −0.494714 | − | 0.856870i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5065.50 | − | 8773.70i | 0.185443 | − | 0.321197i | −0.758282 | − | 0.651926i | \(-0.773961\pi\) |
0.943726 | + | 0.330729i | \(0.107295\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1320.58 | −0.0480273 | −0.0240137 | − | 0.999712i | \(-0.507645\pi\) | ||||
−0.0240137 | + | 0.999712i | \(0.507645\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17146.2 | + | 29698.2i | −0.621531 | + | 1.07652i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3642.88 | + | 6309.66i | 0.130759 | + | 0.226481i | 0.923969 | − | 0.382466i | \(-0.124925\pi\) |
−0.793210 | + | 0.608948i | \(0.791592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29081.3 | 1.03708 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19368.0 | −0.688448 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11854.0 | + | 20531.7i | 0.418640 | + | 0.725106i | 0.995803 | − | 0.0915233i | \(-0.0291736\pi\) |
−0.577163 | + | 0.816629i | \(0.695840\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1534.90 | − | 2658.52i | 0.0536860 | − | 0.0929869i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8853.60 | −0.308682 | −0.154341 | − | 0.988018i | \(-0.549325\pi\) | ||||
−0.154341 | + | 0.988018i | \(0.549325\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26985.8 | + | 46740.7i | −0.934869 | + | 1.61924i | −0.160000 | + | 0.987117i | \(0.551150\pi\) |
−0.774868 | + | 0.632123i | \(0.782184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4254.29 | − | 7368.64i | −0.146913 | − | 0.254460i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4009.90 | + | 6945.35i | 0.137597 | + | 0.238325i | 0.926586 | − | 0.376082i | \(-0.122729\pi\) |
−0.788990 | + | 0.614407i | \(0.789396\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16007.7 | − | 27726.1i | 0.547557 | − | 0.948397i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42628.0 | −1.44896 | −0.724479 | − | 0.689297i | \(-0.757920\pi\) | ||||
−0.724479 | + | 0.689297i | \(0.757920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19319.5 | − | 33462.3i | 0.654621 | − | 1.13384i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10662.5 | + | 18468.0i | 0.357910 | + | 0.619918i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37196.8 | −1.24084 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43161.7 | −1.43535 | −0.717676 | − | 0.696377i | \(-0.754794\pi\) | ||||
−0.717676 | + | 0.696377i | \(0.754794\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19887.7 | − | 34446.5i | −0.657288 | − | 1.13846i | −0.981315 | − | 0.192408i | \(-0.938370\pi\) |
0.324027 | − | 0.946048i | \(-0.394963\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13329.0 | + | 23086.6i | −0.436472 | + | 0.755992i | −0.997415 | − | 0.0718626i | \(-0.977106\pi\) |
0.560942 | + | 0.827855i | \(0.310439\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42102.6 | 1.37447 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1471.21 | + | 2548.22i | −0.0477359 | + | 0.0826810i | −0.888906 | − | 0.458089i | \(-0.848534\pi\) |
0.841170 | + | 0.540771i | \(0.181867\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12699.6 | + | 21996.4i | 0.410805 | + | 0.711535i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6875.31 | − | 11908.4i | −0.221054 | − | 0.382876i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22484.9 | + | 38945.0i | −0.720743 | + | 1.24836i | 0.239960 | + | 0.970783i | \(0.422866\pi\) |
−0.960703 | + | 0.277580i | \(0.910468\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3623.23 | 0.115441 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13558.2 | + | 23483.5i | −0.430685 | + | 0.745968i | −0.996932 | − | 0.0782670i | \(-0.975061\pi\) |
0.566247 | + | 0.824235i | \(0.308395\pi\) | |||||||
\(998\) | 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 | 1764.4.k.bd.361.3 | 8 | ||
3.2 | odd | 2 | 588.4.i.k.361.2 | 8 | |||
7.2 | even | 3 | inner | 1764.4.k.bd.1549.3 | 8 | ||
7.3 | odd | 6 | 1764.4.a.bc.1.3 | 4 | |||
7.4 | even | 3 | 1764.4.a.ba.1.2 | 4 | |||
7.5 | odd | 6 | 1764.4.k.bb.1549.2 | 8 | |||
7.6 | odd | 2 | 1764.4.k.bb.361.2 | 8 | |||
21.2 | odd | 6 | 588.4.i.k.373.2 | 8 | |||
21.5 | even | 6 | 588.4.i.l.373.3 | 8 | |||
21.11 | odd | 6 | 588.4.a.k.1.3 | yes | 4 | ||
21.17 | even | 6 | 588.4.a.j.1.2 | ✓ | 4 | ||
21.20 | even | 2 | 588.4.i.l.361.3 | 8 | |||
84.11 | even | 6 | 2352.4.a.cl.1.3 | 4 | |||
84.59 | odd | 6 | 2352.4.a.cq.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.j.1.2 | ✓ | 4 | 21.17 | even | 6 | ||
588.4.a.k.1.3 | yes | 4 | 21.11 | odd | 6 | ||
588.4.i.k.361.2 | 8 | 3.2 | odd | 2 | |||
588.4.i.k.373.2 | 8 | 21.2 | odd | 6 | |||
588.4.i.l.361.3 | 8 | 21.20 | even | 2 | |||
588.4.i.l.373.3 | 8 | 21.5 | even | 6 | |||
1764.4.a.ba.1.2 | 4 | 7.4 | even | 3 | |||
1764.4.a.bc.1.3 | 4 | 7.3 | odd | 6 | |||
1764.4.k.bb.361.2 | 8 | 7.6 | odd | 2 | |||
1764.4.k.bb.1549.2 | 8 | 7.5 | odd | 6 | |||
1764.4.k.bd.361.3 | 8 | 1.1 | even | 1 | trivial | ||
1764.4.k.bd.1549.3 | 8 | 7.2 | even | 3 | inner | ||
2352.4.a.cl.1.3 | 4 | 84.11 | even | 6 | |||
2352.4.a.cq.1.2 | 4 | 84.59 | odd | 6 |