Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, 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("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (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: | \(34.6931230834\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(-1.65506 + 2.86665i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.361 |
Dual form | 588.4.i.l.373.3 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | 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 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.9094 | + | 32.7521i | −0.518310 | + | 0.897739i | 0.481464 | + | 0.876466i | \(0.340105\pi\) |
−0.999774 | + | 0.0212729i | \(0.993228\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −39.9319 | −0.851933 | −0.425966 | − | 0.904739i | \(-0.640066\pi\) | ||||
−0.425966 | + | 0.904739i | \(0.640066\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.5082 | 0.421866 | ||||||||
\(16\) | 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 | \(-0.982800\pi\) |
0.452496 | − | 0.891767i | \(-0.350534\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −59.2973 | − | 102.706i | −0.537580 | − | 0.931116i | −0.999034 | − | 0.0439513i | \(-0.986005\pi\) |
0.461454 | − | 0.887164i | \(-0.347328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.1304 | − | 50.4554i | 0.233043 | − | 0.403643i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −78.4061 | −0.502057 | −0.251028 | − | 0.967980i | \(-0.580769\pi\) | ||||
−0.251028 | + | 0.967980i | \(0.580769\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.0055 | − | 79.6838i | 0.266543 | − | 0.461666i | −0.701424 | − | 0.712744i | \(-0.747452\pi\) |
0.967967 | + | 0.251079i | \(0.0807853\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 56.7283 | + | 98.2563i | 0.299246 | + | 0.518310i | ||||
\(34\) | 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 | ||||||||
\(39\) | −59.8979 | + | 103.746i | −0.245932 | + | 0.425966i | ||||
\(40\) | 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 | ||||||||
\(45\) | 36.7623 | − | 63.6742i | 0.121782 | − | 0.210933i | ||||
\(46\) | 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 | ||||||||
\(51\) | −14.9039 | − | 25.8144i | −0.0409210 | − | 0.0708772i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 201.575 | − | 349.138i | 0.522424 | − | 0.904865i | −0.477236 | − | 0.878775i | \(-0.658361\pi\) |
0.999660 | − | 0.0260895i | \(-0.00830548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −308.958 | −0.757451 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −271.337 | −0.630518 | ||||||||
\(58\) | 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 | 0.986188 | − | 0.165628i | \(-0.0529649\pi\) |
−0.636532 | + | 0.771250i | \(0.719632\pi\) | |||||||
\(62\) | 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 | ||||||||
\(69\) | −355.784 | −0.620744 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −728.272 | −1.21732 | −0.608662 | − | 0.793429i | \(-0.708294\pi\) | ||||
−0.608662 | + | 0.793429i | \(0.708294\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −400.874 | + | 694.335i | −0.642723 | + | 1.11323i | 0.342099 | + | 0.939664i | \(0.388862\pi\) |
−0.984822 | + | 0.173566i | \(0.944471\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −87.3912 | − | 151.366i | −0.134548 | − | 0.233043i | ||||
\(76\) | 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 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 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 | ||||||||
\(87\) | −117.609 | + | 203.705i | −0.144931 | + | 0.251028i | ||||
\(88\) | 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 | ||||||||
\(93\) | −138.016 | − | 239.051i | −0.153889 | − | 0.266543i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 369.444 | − | 639.896i | 0.398991 | − | 0.691073i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1480.94 | −1.55017 | −0.775084 | − | 0.631858i | \(-0.782293\pi\) | ||||
−0.775084 | + | 0.631858i | \(0.782293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 340.370 | 0.345540 | ||||||||
\(100\) | 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 | 0.967364 | − | 0.253392i | \(-0.0815462\pi\) |
−0.703126 | + | 0.711066i | \(0.748213\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −266.902 | − | 462.288i | −0.241144 | − | 0.417674i | 0.719896 | − | 0.694082i | \(-0.244189\pi\) |
−0.961040 | + | 0.276408i | \(0.910856\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | −997.306 | −0.852794 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1425.18 | −1.18646 | −0.593228 | − | 0.805035i | \(-0.702147\pi\) | ||||
−0.593228 | + | 0.805035i | \(0.702147\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 484.423 | − | 839.046i | 0.392806 | − | 0.680360i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 179.694 | + | 311.239i | 0.141989 | + | 0.245932i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.6330 | − | 85.9668i | −0.0372900 | − | 0.0645882i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −107.618 | + | 186.399i | −0.0788907 | + | 0.136643i | ||||
\(124\) | 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 | ||||||||
\(129\) | −173.920 | + | 301.238i | −0.118704 | + | 0.205601i | ||||
\(130\) | 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 | ||||||||
\(135\) | −110.287 | − | 191.023i | −0.0703110 | − | 0.121782i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1181.49 | − | 2046.40i | 0.736798 | − | 1.27617i | −0.217132 | − | 0.976142i | \(-0.569670\pi\) |
0.953930 | − | 0.300029i | \(-0.0969964\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2513.28 | −1.53362 | −0.766811 | − | 0.641873i | \(-0.778158\pi\) | ||||
−0.766811 | + | 0.641873i | \(0.778158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 923.782 | 0.551748 | ||||||||
\(142\) | 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 | \(-0.952621\pi\) |
0.366043 | − | 0.930598i | \(-0.380712\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | −89.4237 | −0.0472515 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 751.675 | 0.389522 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 96.2904 | − | 166.780i | 0.0489478 | − | 0.0847801i | −0.840513 | − | 0.541791i | \(-0.817747\pi\) |
0.889461 | + | 0.457011i | \(0.151080\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −604.725 | − | 1047.41i | −0.301622 | − | 0.522424i | ||||
\(160\) | 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 | ||||||||
\(165\) | −463.436 | + | 802.695i | −0.218657 | + | 0.378726i | ||||
\(166\) | 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 | ||||||||
\(171\) | −407.006 | + | 704.955i | −0.182015 | + | 0.315259i | ||||
\(172\) | 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 | ||||||||
\(177\) | −890.565 | − | 1542.50i | −0.378186 | − | 0.655038i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1232.31 | − | 2134.43i | 0.514566 | − | 0.891255i | −0.485291 | − | 0.874353i | \(-0.661286\pi\) |
0.999857 | − | 0.0169022i | \(-0.00538039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3297.36 | 1.35409 | 0.677047 | − | 0.735940i | \(-0.263259\pi\) | ||||
0.677047 | + | 0.735940i | \(0.263259\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 999.511 | 0.403749 | ||||||||
\(184\) | 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 | \(0.186794\pi\) |
0.0631890 | + | 0.998002i | \(0.479873\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | −978.660 | −0.359402 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3109.06 | −1.12442 | −0.562212 | − | 0.826993i | \(-0.690050\pi\) | ||||
−0.562212 | + | 0.826993i | \(0.690050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −221.756 | + | 384.092i | −0.0789943 | + | 0.136822i | −0.902816 | − | 0.430027i | \(-0.858504\pi\) |
0.823822 | + | 0.566849i | \(0.191838\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1115.27 | − | 1931.70i | −0.391368 | − | 0.677869i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −293.057 | − | 507.590i | −0.0998439 | − | 0.172935i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −533.675 | + | 924.353i | −0.179193 | + | 0.310372i | ||||
\(208\) | 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 | ||||||||
\(213\) | −1092.41 | + | 1892.11i | −0.351411 | + | 0.608662i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −473.607 | − | 820.311i | −0.150231 | − | 0.260208i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1202.62 | + | 2083.00i | 0.371077 | + | 0.642723i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −198.381 | + | 343.606i | −0.0603826 | + | 0.104586i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2778.90 | −0.834481 | −0.417240 | − | 0.908796i | \(-0.637003\pi\) | ||||
−0.417240 | + | 0.908796i | \(0.637003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −524.347 | −0.155362 | ||||||||
\(226\) | 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 | \(-0.985888\pi\) |
0.461126 | − | 0.887335i | \(-0.347446\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1801.76 | + | 3120.73i | 0.506596 | + | 0.877451i | 0.999971 | + | 0.00763377i | \(0.00242993\pi\) |
−0.493374 | + | 0.869817i | \(0.664237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1257.79 | + | 2178.56i | −0.349146 | + | 0.604739i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3203.72 | −0.878075 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2348.76 | 0.635684 | 0.317842 | − | 0.948144i | \(-0.397042\pi\) | ||||
0.317842 | + | 0.948144i | \(0.397042\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2546.70 | + | 4411.01i | −0.680693 | + | 1.17900i | 0.294076 | + | 0.955782i | \(0.404988\pi\) |
−0.974770 | + | 0.223213i | \(0.928345\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1805.84 | + | 3127.80i | 0.465193 | + | 0.805738i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1360.13 | + | 2355.82i | −0.346165 | + | 0.599575i | ||||
\(250\) | 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 | ||||||||
\(255\) | 121.756 | − | 210.888i | 0.0299007 | − | 0.0517895i | ||||
\(256\) | 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 | ||||||||
\(261\) | 352.827 | + | 611.115i | 0.0836761 | + | 0.144931i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3216.96 | − | 5571.94i | 0.754244 | − | 1.30639i | −0.191505 | − | 0.981492i | \(-0.561337\pi\) |
0.945749 | − | 0.324898i | \(-0.105330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3293.50 | 0.763464 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3339.81 | 0.765516 | ||||||||
\(268\) | 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 | 0.807068 | − | 0.590458i | \(-0.201053\pi\) |
−0.914886 | + | 0.403713i | \(0.867719\pi\) | |||||||
\(272\) | 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 | ||||||||
\(279\) | −828.099 | −0.177695 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4412.07 | −0.936662 | −0.468331 | − | 0.883553i | \(-0.655145\pi\) | ||||
−0.468331 | + | 0.883553i | \(0.655145\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1301.07 | + | 2253.53i | −0.273289 | + | 0.473351i | −0.969702 | − | 0.244291i | \(-0.921445\pi\) |
0.696413 | + | 0.717641i | \(0.254778\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1108.33 | − | 1919.69i | −0.230358 | − | 0.398991i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2407.14 | + | 4169.29i | 0.489953 | + | 0.848623i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2221.41 | + | 3847.59i | −0.447495 | + | 0.775084i | ||||
\(292\) | 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 | ||||||||
\(297\) | 510.555 | − | 884.306i | 0.0997488 | − | 0.172770i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2367.85 | + | 4101.24i | 0.457982 | + | 0.793248i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 834.474 | + | 1445.35i | 0.158216 | + | 0.274037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1360.90 | + | 2357.15i | −0.255492 | + | 0.442525i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4895.51 | −0.910103 | −0.455051 | − | 0.890465i | \(-0.650379\pi\) | ||||
−0.455051 | + | 0.890465i | \(0.650379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1657.30 | 0.305116 | ||||||||
\(310\) | 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 | \(-0.972332\pi\) |
0.422931 | − | 0.906162i | \(-0.361001\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3999.80 | + | 6927.86i | 0.708679 | + | 1.22747i | 0.965347 | + | 0.260968i | \(0.0840417\pi\) |
−0.256669 | + | 0.966499i | \(0.582625\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1482.61 | − | 2567.96i | 0.260221 | − | 0.450716i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1601.41 | −0.278449 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −898.666 | −0.154808 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1163.23 | + | 2014.78i | −0.198537 | + | 0.343876i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1641.94 | + | 2843.93i | 0.277675 | + | 0.480947i | ||||
\(328\) | 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 | ||||||||
\(333\) | −1495.96 | + | 2591.08i | −0.246180 | + | 0.426397i | ||||
\(334\) | 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 | ||||||||
\(339\) | −2137.77 | + | 3702.72i | −0.342500 | + | 0.593228i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1739.87 | + | 3013.55i | 0.276303 | + | 0.478572i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1453.27 | − | 2517.14i | −0.226787 | − | 0.392806i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 836.534 | − | 1448.92i | 0.129416 | − | 0.224156i | −0.794034 | − | 0.607873i | \(-0.792023\pi\) |
0.923451 | + | 0.383717i | \(0.125356\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3467.56 | 0.531845 | 0.265923 | − | 0.963994i | \(-0.414323\pi\) | ||||
0.265923 | + | 0.963994i | \(0.414323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1078.16 | 0.163955 | ||||||||
\(352\) | 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 | 0.775138 | − | 0.631792i | \(-0.217680\pi\) |
−0.934717 | + | 0.355394i | \(0.884347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −660.724 | + | 1144.41i | −0.0963295 | + | 0.166848i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −297.798 | −0.0430588 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6549.81 | −0.939268 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1796.06 | − | 3110.86i | 0.255459 | − | 0.442468i | −0.709561 | − | 0.704644i | \(-0.751107\pi\) |
0.965020 | + | 0.262176i | \(0.0844400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 322.853 | + | 559.197i | 0.0455475 | + | 0.0788907i | ||||
\(370\) | 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 | ||||||||
\(375\) | 2245.70 | − | 3889.66i | 0.309246 | − | 0.535630i | ||||
\(376\) | 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 | ||||||||
\(381\) | −1179.73 | + | 2043.35i | −0.158633 | + | 0.274761i | ||||
\(382\) | 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 | ||||||||
\(387\) | 521.759 | + | 903.714i | 0.0685336 | + | 0.118704i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5279.10 | − | 9143.66i | 0.688074 | − | 1.19178i | −0.284386 | − | 0.958710i | \(-0.591790\pi\) |
0.972460 | − | 0.233070i | \(-0.0748770\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1178.35 | −0.152409 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −83.1908 | −0.0106779 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4362.08 | − | 7555.34i | 0.555645 | − | 0.962406i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −270.287 | − | 468.151i | −0.0341696 | − | 0.0591834i | 0.848435 | − | 0.529300i | \(-0.177545\pi\) |
−0.882604 | + | 0.470116i | \(0.844212\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1083.52 | − | 1876.70i | −0.134933 | − | 0.233711i | 0.790639 | − | 0.612283i | \(-0.209749\pi\) |
−0.925572 | + | 0.378572i | \(0.876415\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1837.09 | + | 3181.93i | −0.227077 | + | 0.393308i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −661.722 | −0.0811882 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12572.3 | 1.53117 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −478.845 | + | 829.384i | −0.0578908 | + | 0.100270i | −0.893518 | − | 0.449027i | \(-0.851771\pi\) |
0.835628 | + | 0.549296i | \(0.185104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3544.46 | − | 6139.19i | −0.425390 | − | 0.736798i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3703.83 | − | 6415.22i | −0.438105 | − | 0.758821i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3769.92 | + | 6529.69i | −0.442719 | + | 0.766811i | ||||
\(418\) | 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 | ||||||||
\(423\) | 1385.67 | − | 2400.06i | 0.159276 | − | 0.275874i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −289.439 | − | 501.322i | −0.0330349 | − | 0.0572181i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2265.27 | − | 3923.56i | −0.254938 | − | 0.441565i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −707.796 | + | 1225.94i | −0.0791029 | + | 0.137010i | −0.902863 | − | 0.429928i | \(-0.858539\pi\) |
0.823760 | + | 0.566938i | \(0.191872\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8905.73 | −0.988411 | −0.494206 | − | 0.869345i | \(-0.664541\pi\) | ||||
−0.494206 | + | 0.869345i | \(0.664541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1921.59 | −0.211801 | ||||||||
\(436\) | 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 | \(0.0346940\pi\) |
−0.402828 | + | 0.915276i | \(0.631973\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5701.48 | − | 9875.25i | −0.611479 | − | 1.05911i | −0.990991 | − | 0.133927i | \(-0.957241\pi\) |
0.379512 | − | 0.925187i | \(-0.376092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4547.37 | + | 7876.28i | −0.484418 | + | 0.839037i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6797.49 | −0.719262 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12689.0 | −1.33370 | −0.666852 | − | 0.745190i | \(-0.732359\pi\) | ||||
−0.666852 | + | 0.745190i | \(0.732359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1356.66 | − | 2349.80i | 0.141646 | − | 0.245339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 424.720 | + | 735.636i | 0.0440509 | + | 0.0762984i | ||||
\(454\) | 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 | ||||||||
\(459\) | −134.135 | + | 232.329i | −0.0136403 | + | 0.0236257i | ||||
\(460\) | 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 | ||||||||
\(465\) | 1127.51 | − | 1952.91i | 0.112445 | − | 0.194761i | ||||
\(466\) | 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 | ||||||||
\(471\) | −288.871 | − | 500.339i | −0.0282600 | − | 0.0489478i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2192.48 | − | 3797.49i | 0.213130 | − | 0.369152i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5269.45 | −0.509008 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3628.35 | −0.348283 | ||||||||
\(478\) | 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 | ||||||||
\(489\) | 2528.50 | 0.233830 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8342.30 | −0.766767 | −0.383384 | − | 0.923589i | \(-0.625241\pi\) | ||||
−0.383384 | + | 0.923589i | \(0.625241\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −389.520 | + | 674.668i | −0.0355844 | + | 0.0616340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1390.31 | + | 2408.09i | 0.126242 | + | 0.218657i | ||||
\(496\) | 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 | ||||||||
\(501\) | 5788.82 | − | 10026.5i | 0.516218 | − | 0.894116i | ||||
\(502\) | 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 | ||||||||
\(507\) | −903.662 | + | 1565.19i | −0.0791578 | + | 0.137105i | ||||
\(508\) | 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 | ||||||||
\(513\) | 1221.02 | + | 2114.87i | 0.105086 | + | 0.182015i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2256.53 | + | 3908.43i | −0.193077 | + | 0.334419i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11645.5 | −0.990652 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4531.98 | 0.383298 | ||||||||
\(520\) | 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 | \(0.103437\pi\) |
−0.197338 | + | 0.980336i | \(0.563230\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | −5343.39 | −0.436692 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2864.92 | 0.232821 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2180.43 | − | 3776.62i | 0.176202 | − | 0.305192i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3696.94 | − | 6403.28i | −0.297085 | − | 0.514566i | ||||
\(538\) | 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 | ||||||||
\(543\) | 4946.04 | − | 8566.80i | 0.390893 | − | 0.677047i | ||||
\(544\) | 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 | ||||||||
\(549\) | 1499.27 | − | 2596.81i | 0.116552 | − | 0.201874i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3545.75 | + | 6141.42i | 0.274145 | + | 0.474834i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4073.70 | − | 7055.85i | −0.311565 | − | 0.539647i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5519.27 | − | 9559.65i | 0.419854 | − | 0.727209i | −0.576070 | − | 0.817400i | \(-0.695415\pi\) |
0.995924 | + | 0.0901913i | \(0.0287478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4629.97 | 0.350316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1127.30 | 0.0848390 | ||||||||
\(562\) | 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 | 0.889867 | − | 0.456220i | \(-0.150797\pi\) |
−0.840032 | + | 0.542537i | \(0.817464\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 14189.1 | 1.03448 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6909.42 | −0.501117 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5007.32 | − | 8672.92i | 0.361278 | − | 0.625751i | −0.626894 | − | 0.779105i | \(-0.715674\pi\) |
0.988171 | + | 0.153353i | \(0.0490073\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6829.77 | + | 11829.5i | 0.490217 | + | 0.849080i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7623.34 | + | 13204.0i | 0.541555 | + | 0.938001i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1467.99 | + | 2542.63i | −0.103750 | + | 0.179701i | ||||
\(586\) | 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 | ||||||||
\(591\) | −4663.60 | + | 8077.59i | −0.324593 | + | 0.562212i | ||||
\(592\) | 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 | ||||||||
\(597\) | 665.268 | + | 1152.28i | 0.0456074 | + | 0.0789943i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 65.3409 | − | 113.174i | 0.00445703 | − | 0.00771980i | −0.863788 | − | 0.503855i | \(-0.831915\pi\) |
0.868245 | + | 0.496135i | \(0.165248\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5964.47 | 0.404818 | 0.202409 | − | 0.979301i | \(-0.435123\pi\) | ||||
0.202409 | + | 0.979301i | \(0.435123\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6691.60 | −0.451912 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 405.472 | − | 702.298i | 0.0272476 | − | 0.0471942i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4955.82 | − | 8583.73i | −0.331384 | − | 0.573975i | 0.651399 | − | 0.758735i | \(-0.274182\pi\) |
−0.982784 | + | 0.184761i | \(0.940849\pi\) | |||||||
\(608\) | 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 | ||||||||
\(615\) | −1758.34 | −0.115290 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7189.36 | 0.469097 | 0.234548 | − | 0.972104i | \(-0.424639\pi\) | ||||
0.234548 | + | 0.972104i | \(0.424639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 930.696 | − | 1612.01i | 0.0604327 | − | 0.104672i | −0.834226 | − | 0.551422i | \(-0.814085\pi\) |
0.894659 | + | 0.446750i | \(0.147419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1601.03 | + | 2773.06i | 0.103457 | + | 0.179193i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2474.04 | + | 4285.16i | 0.158338 | + | 0.274250i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5130.84 | − | 8886.87i | 0.326804 | − | 0.566041i | ||||
\(628\) | 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 | ||||||||
\(633\) | 6979.93 | − | 12089.6i | 0.438274 | − | 0.759112i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3212.56 | − | 5564.32i | −0.200766 | − | 0.347737i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3277.23 | + | 5676.32i | 0.202887 | + | 0.351411i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12228.9 | + | 21181.0i | −0.753527 | + | 1.30515i | 0.192576 | + | 0.981282i | \(0.438316\pi\) |
−0.946103 | + | 0.323866i | \(0.895017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10968.2 | −0.672695 | −0.336348 | − | 0.941738i | \(-0.609192\pi\) | ||||
−0.336348 | + | 0.941738i | \(0.609192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2841.64 | −0.173472 | ||||||||
\(646\) | 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 | 0.978259 | − | 0.207387i | \(-0.0664959\pi\) |
−0.668732 | + | 0.743504i | \(0.733163\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 113.270 | − | 196.189i | 0.00675698 | − | 0.0117034i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7215.74 | 0.428482 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26822.2 | 1.58550 | 0.792751 | − | 0.609546i | \(-0.208648\pi\) | ||||
0.792751 | + | 0.609546i | \(0.208648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1249.38 | − | 2163.99i | 0.0735177 | − | 0.127336i | −0.826923 | − | 0.562315i | \(-0.809911\pi\) |
0.900441 | + | 0.434979i | \(0.143244\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 595.143 | + | 1030.82i | 0.0348619 | + | 0.0603826i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4649.27 | + | 8052.77i | 0.269896 | + | 0.467473i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4168.36 | + | 7219.81i | −0.240894 | + | 0.417240i | ||||
\(670\) | 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 | ||||||||
\(675\) | −786.521 | + | 1362.29i | −0.0448492 | + | 0.0776811i | ||||
\(676\) | 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 | ||||||||
\(681\) | −4825.83 | − | 8358.59i | −0.271551 | − | 0.470340i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11285.4 | + | 19546.9i | −0.632245 | + | 1.09508i | 0.354847 | + | 0.934924i | \(0.384533\pi\) |
−0.987092 | + | 0.160155i | \(0.948800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19304.1 | 1.07675 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11184.0 | −0.621103 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8049.28 | + | 13941.8i | −0.445070 | + | 0.770884i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5965.75 | − | 10333.0i | −0.328434 | − | 0.568864i | 0.653768 | − | 0.756695i | \(-0.273187\pi\) |
−0.982201 | + | 0.187832i | \(0.939854\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 10810.5 | 0.584967 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16592.6 | 0.893997 | 0.446999 | − | 0.894535i | \(-0.352493\pi\) | ||||
0.446999 | + | 0.894535i | \(0.352493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15033.7 | + | 26039.1i | −0.806553 | + | 1.39699i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3773.38 | + | 6535.68i | 0.201580 | + | 0.349146i | ||||
\(706\) | 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 | ||||||||
\(711\) | −4805.57 | + | 8323.50i | −0.253478 | + | 0.439037i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10912.0 | −0.573152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12337.3 | 0.645298 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3523.14 | − | 6102.25i | 0.183506 | − | 0.317842i | ||||
\(718\) | 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 | ||||||||
\(723\) | 7640.09 | + | 13233.0i | 0.392998 | + | 0.680693i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2284.00 | + | 3956.01i | −0.117001 | + | 0.202652i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22506.0 | 1.14814 | 0.574071 | − | 0.818805i | \(-0.305363\pi\) | ||||
0.574071 | + | 0.818805i | \(0.305363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 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 | \(-0.962057\pi\) |
0.393464 | − | 0.919340i | \(-0.371277\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | 10835.0 | 0.537159 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5076.10 | 0.250638 | 0.125319 | − | 0.992116i | \(-0.460005\pi\) | ||||
0.125319 | + | 0.992116i | \(0.460005\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9255.24 | − | 16030.6i | 0.455149 | − | 0.788341i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4080.40 | + | 7067.46i | 0.199858 | + | 0.346165i | ||||
\(748\) | 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 | ||||||||
\(753\) | 8908.54 | − | 15430.0i | 0.431136 | − | 0.746749i | ||||
\(754\) | 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 | ||||||||
\(759\) | 6727.67 | − | 11652.7i | 0.321738 | − | 0.557266i | ||||
\(760\) | 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 | ||||||||
\(765\) | −365.269 | − | 632.665i | −0.0172632 | − | 0.0299007i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11854.0 | + | 20531.7i | −0.558048 | + | 0.966568i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15530.6 | 0.728281 | 0.364140 | − | 0.931344i | \(-0.381363\pi\) | ||||
0.364140 | + | 0.931344i | \(0.381363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4547.66 | −0.212425 | ||||||||
\(772\) | 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 | ||||||||
\(783\) | 2116.96 | 0.0966209 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1573.27 | 0.0715317 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10596.3 | − | 18353.3i | 0.479946 | − | 0.831291i | −0.519789 | − | 0.854294i | \(-0.673990\pi\) |
0.999735 | + | 0.0230036i | \(0.00732292\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9650.88 | − | 16715.8i | −0.435463 | − | 0.754244i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6652.07 | − | 11521.7i | −0.297884 | − | 0.515950i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4940.25 | − | 8556.76i | 0.220393 | − | 0.381732i | ||||
\(796\) | 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 | ||||||||
\(801\) | 5009.71 | − | 8677.07i | 0.220986 | − | 0.382758i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15160.6 | − | 26259.0i | −0.666260 | − | 1.15400i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10424.7 | + | 18056.1i | 0.454729 | + | 0.787614i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22758.3 | + | 39418.5i | −0.989045 | + | 1.71308i | −0.366688 | + | 0.930344i | \(0.619508\pi\) |
−0.622358 | + | 0.782733i | \(0.713825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42099.9 | 1.82285 | 0.911423 | − | 0.411472i | \(-0.134985\pi\) | ||||
0.911423 | + | 0.411472i | \(0.134985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2885.98 | −0.124497 | ||||||||
\(814\) | 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 | \(0.0242408\pi\) |
−0.432663 | + | 0.901556i | \(0.642426\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 6610.07 | 0.278949 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10548.3 | −0.443531 | −0.221766 | − | 0.975100i | \(-0.571182\pi\) | ||||
−0.221766 | + | 0.975100i | \(0.571182\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2165.63 | − | 3750.98i | 0.0907303 | − | 0.157150i | −0.817088 | − | 0.576513i | \(-0.804413\pi\) |
0.907819 | + | 0.419363i | \(0.137747\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1140.02 | + | 1974.56i | 0.0475893 | + | 0.0824271i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15763.7 | + | 27303.6i | 0.653325 | + | 1.13159i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1242.15 | + | 2151.46i | −0.0512962 | + | 0.0888476i | ||||
\(838\) | 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 | ||||||||
\(843\) | −6618.11 | + | 11462.9i | −0.270391 | + | 0.468331i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2460.79 | − | 4262.22i | −0.100182 | − | 0.173520i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3903.22 | + | 6760.58i | 0.157784 | + | 0.273289i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19712.5 | + | 34143.1i | −0.794049 | + | 1.37533i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11493.6 | 0.461350 | 0.230675 | − | 0.973031i | \(-0.425907\pi\) | ||||
0.230675 | + | 0.973031i | \(0.425907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6650.00 | −0.265994 | ||||||||
\(856\) | 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 | 0.895406 | − | 0.445251i | \(-0.146886\pi\) |
−0.833302 | + | 0.552819i | \(0.813552\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7654.94 | − | 13258.7i | −0.301943 | − | 0.522981i | 0.674633 | − | 0.738153i | \(-0.264302\pi\) |
−0.976576 | + | 0.215172i | \(0.930969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6170.59 | + | 10687.8i | −0.242551 | + | 0.420110i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14442.8 | 0.565749 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40387.0 | 1.57656 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14844.9 | + | 25712.2i | −0.577498 | + | 1.00026i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6664.22 | + | 11542.8i | 0.258361 | + | 0.447495i | ||||
\(874\) | 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 | ||||||||
\(879\) | 13998.3 | − | 24245.7i | 0.537144 | − | 0.930361i | ||||
\(880\) | 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 | ||||||||
\(885\) | 7275.39 | − | 12601.3i | 0.276338 | − | 0.478632i | ||||
\(886\) | 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 | ||||||||
\(891\) | −1531.66 | − | 2652.92i | −0.0575900 | − | 0.0997488i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13925.4 | − | 24119.5i | 0.521831 | − | 0.903838i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20134.5 | 0.751981 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14207.1 | 0.528832 | ||||||||
\(898\) | 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 | ||||||||
\(909\) | 5006.85 | 0.182692 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1320.58 | 0.0480273 | 0.0240137 | − | 0.999712i | \(-0.492355\pi\) | ||||
0.0240137 | + | 0.999712i | \(0.492355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17146.2 | − | 29698.2i | 0.621531 | − | 1.07652i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4082.71 | + | 7071.45i | 0.147508 | + | 0.255492i | ||||
\(916\) | 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 | ||||||||
\(921\) | −7343.26 | + | 12718.9i | −0.262724 | + | 0.455051i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29081.3 | 1.03708 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19368.0 | −0.688448 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2485.96 | − | 4305.80i | 0.0880793 | − | 0.152558i | ||||
\(928\) | 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 | ||||||||
\(933\) | −11257.9 | − | 19499.3i | −0.395035 | − | 0.684221i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1534.90 | + | 2658.52i | −0.0536860 | + | 0.0929869i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8853.60 | 0.308682 | 0.154341 | − | 0.988018i | \(-0.450675\pi\) | ||||
0.154341 | + | 0.988018i | \(0.450675\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19047.8 | −0.661983 | ||||||||
\(940\) | 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 | 0.788990 | − | 0.614407i | \(-0.210604\pi\) |
−0.926586 | + | 0.376082i | \(0.877271\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16007.7 | − | 27726.1i | 0.547557 | − | 0.948397i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23998.8 | 0.818312 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42628.0 | 1.44896 | 0.724479 | − | 0.689297i | \(-0.242080\pi\) | ||||
0.724479 | + | 0.689297i | \(0.242080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19319.5 | + | 33462.3i | −0.654621 | + | 1.13384i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4447.84 | − | 7703.89i | −0.150239 | − | 0.260221i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10662.5 | + | 18468.0i | 0.357910 | + | 0.619918i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2402.12 | + | 4160.59i | −0.0803813 | + | 0.139225i | ||||
\(964\) | 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 | ||||||||
\(969\) | −1348.00 | + | 2334.80i | −0.0446894 | + | 0.0774042i | ||||
\(970\) | 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 | ||||||||
\(975\) | 3489.70 | + | 6044.34i | 0.114625 | + | 0.198537i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13329.0 | − | 23086.6i | 0.436472 | − | 0.755992i | −0.560942 | − | 0.827855i | \(-0.689561\pi\) |
0.997415 | + | 0.0718626i | \(0.0228943\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42102.6 | −1.37447 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9851.66 | 0.320631 | ||||||||
\(982\) | 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 | ||||||||
\(993\) | 6364.68 | 0.203401 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3623.23 | −0.115441 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13558.2 | − | 23483.5i | 0.430685 | − | 0.745968i | −0.566247 | − | 0.824235i | \(-0.691605\pi\) |
0.996932 | + | 0.0782670i | \(0.0249387\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4487.88 | + | 7773.23i | 0.142132 | + | 0.246180i |
(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 | 588.4.i.l.361.3 | 8 | ||
3.2 | odd | 2 | 1764.4.k.bb.361.2 | 8 | |||
7.2 | even | 3 | inner | 588.4.i.l.373.3 | 8 | ||
7.3 | odd | 6 | 588.4.a.k.1.3 | yes | 4 | ||
7.4 | even | 3 | 588.4.a.j.1.2 | ✓ | 4 | ||
7.5 | odd | 6 | 588.4.i.k.373.2 | 8 | |||
7.6 | odd | 2 | 588.4.i.k.361.2 | 8 | |||
21.2 | odd | 6 | 1764.4.k.bb.1549.2 | 8 | |||
21.5 | even | 6 | 1764.4.k.bd.1549.3 | 8 | |||
21.11 | odd | 6 | 1764.4.a.bc.1.3 | 4 | |||
21.17 | even | 6 | 1764.4.a.ba.1.2 | 4 | |||
21.20 | even | 2 | 1764.4.k.bd.361.3 | 8 | |||
28.3 | even | 6 | 2352.4.a.cl.1.3 | 4 | |||
28.11 | 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 | 7.4 | even | 3 | ||
588.4.a.k.1.3 | yes | 4 | 7.3 | odd | 6 | ||
588.4.i.k.361.2 | 8 | 7.6 | odd | 2 | |||
588.4.i.k.373.2 | 8 | 7.5 | odd | 6 | |||
588.4.i.l.361.3 | 8 | 1.1 | even | 1 | trivial | ||
588.4.i.l.373.3 | 8 | 7.2 | even | 3 | inner | ||
1764.4.a.ba.1.2 | 4 | 21.17 | even | 6 | |||
1764.4.a.bc.1.3 | 4 | 21.11 | odd | 6 | |||
1764.4.k.bb.361.2 | 8 | 3.2 | odd | 2 | |||
1764.4.k.bb.1549.2 | 8 | 21.2 | odd | 6 | |||
1764.4.k.bd.361.3 | 8 | 21.20 | even | 2 | |||
1764.4.k.bd.1549.3 | 8 | 21.5 | even | 6 | |||
2352.4.a.cl.1.3 | 4 | 28.3 | even | 6 | |||
2352.4.a.cq.1.2 | 4 | 28.11 | odd | 6 |