Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1322,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.1322");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 24x^{14} + 212x^{12} + 872x^{10} + 1815x^{8} + 1928x^{6} + 996x^{4} + 200x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1322.15 | ||
Root | \(1.54124i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1322 |
Dual form | 1323.2.c.f.1322.1 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.67093i | 1.88863i | 0.329040 | + | 0.944316i | \(0.393275\pi\) | ||||
−0.329040 | + | 0.944316i | \(0.606725\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.13386 | −2.56693 | ||||||||
\(5\) | −3.20318 | −1.43251 | −0.716253 | − | 0.697840i | \(-0.754144\pi\) | ||||
−0.716253 | + | 0.697840i | \(0.754144\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 8.37032i | − 2.95935i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 8.55547i | − 2.70548i | ||||||||
\(11\) | − 4.06357i | − 1.22521i | −0.790388 | − | 0.612606i | \(-0.790121\pi\) | ||||
0.790388 | − | 0.612606i | \(-0.209879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.99862i | 0.831668i | 0.909441 | + | 0.415834i | \(0.136510\pi\) | ||||
−0.909441 | + | 0.415834i | \(0.863490\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.0888 | 3.02220 | ||||||||
\(17\) | −2.54255 | −0.616659 | −0.308329 | − | 0.951280i | \(-0.599770\pi\) | ||||
−0.308329 | + | 0.951280i | \(0.599770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.165299i | − 0.0379223i | −0.999820 | − | 0.0189611i | \(-0.993964\pi\) | ||||
0.999820 | − | 0.0189611i | \(-0.00603588\pi\) | |||||||
\(20\) | 16.4447 | 3.67714 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.8535 | 2.31398 | ||||||||
\(23\) | − 4.04395i | − 0.843222i | −0.906777 | − | 0.421611i | \(-0.861465\pi\) | ||||
0.906777 | − | 0.421611i | \(-0.138535\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.26038 | 1.05208 | ||||||||
\(26\) | −8.00910 | −1.57071 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.12182i | 0.394013i | 0.980402 | + | 0.197006i | \(0.0631220\pi\) | ||||
−0.980402 | + | 0.197006i | \(0.936878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.70685i | 1.38419i | 0.721806 | + | 0.692095i | \(0.243312\pi\) | ||||
−0.721806 | + | 0.692095i | \(0.756688\pi\) | |||||||
\(32\) | 15.5477i | 2.74847i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 6.79097i | − 1.16464i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.8011 | 1.94009 | 0.970045 | − | 0.242926i | \(-0.0781074\pi\) | ||||
0.970045 | + | 0.242926i | \(0.0781074\pi\) | |||||||
\(38\) | 0.441503 | 0.0716212 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 26.8117i | 4.23929i | ||||||||
\(41\) | 0.629916 | 0.0983763 | 0.0491881 | − | 0.998790i | \(-0.484337\pi\) | ||||
0.0491881 | + | 0.998790i | \(0.484337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.94455 | 0.601539 | 0.300769 | − | 0.953697i | \(-0.402757\pi\) | ||||
0.300769 | + | 0.953697i | \(0.402757\pi\) | |||||||
\(44\) | 20.8618i | 3.14504i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.8011 | 1.59254 | ||||||||
\(47\) | 5.45154 | 0.795188 | 0.397594 | − | 0.917561i | \(-0.369845\pi\) | ||||
0.397594 | + | 0.917561i | \(0.369845\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 14.0501i | 1.98698i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 15.3945i | − 2.13483i | ||||||||
\(53\) | 2.48535i | 0.341389i | 0.985324 | + | 0.170694i | \(0.0546011\pi\) | ||||
−0.985324 | + | 0.170694i | \(0.945399\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.0164i | 1.75513i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.66724 | −0.744145 | ||||||||
\(59\) | −8.84313 | −1.15128 | −0.575639 | − | 0.817704i | \(-0.695247\pi\) | ||||
−0.575639 | + | 0.817704i | \(0.695247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 10.8324i | − 1.38694i | −0.720484 | − | 0.693472i | \(-0.756080\pi\) | ||||
0.720484 | − | 0.693472i | \(-0.243920\pi\) | |||||||
\(62\) | −20.5844 | −2.61423 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −17.3492 | −2.16865 | ||||||||
\(65\) | − 9.60513i | − 1.19137i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.14425 | −0.139792 | −0.0698961 | − | 0.997554i | \(-0.522267\pi\) | ||||
−0.0698961 | + | 0.997554i | \(0.522267\pi\) | |||||||
\(68\) | 13.0531 | 1.58292 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 9.33455i | − 1.10781i | −0.832581 | − | 0.553904i | \(-0.813138\pi\) | ||||
0.832581 | − | 0.553904i | \(-0.186862\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.10764i | − 0.714846i | −0.933943 | − | 0.357423i | \(-0.883656\pi\) | ||||
0.933943 | − | 0.357423i | \(-0.116344\pi\) | |||||||
\(74\) | 31.5199i | 3.66411i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.848624i | 0.0973438i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8712 | −1.44813 | −0.724064 | − | 0.689733i | \(-0.757728\pi\) | ||||
−0.724064 | + | 0.689733i | \(0.757728\pi\) | |||||||
\(80\) | −38.7226 | −4.32932 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.68246i | 0.185797i | ||||||||
\(83\) | −3.76846 | −0.413642 | −0.206821 | − | 0.978379i | \(-0.566312\pi\) | ||||
−0.206821 | + | 0.978379i | \(0.566312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.14425 | 0.883368 | ||||||||
\(86\) | 10.5356i | 1.13609i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −34.0134 | −3.62584 | ||||||||
\(89\) | 18.1382 | 1.92264 | 0.961322 | − | 0.275426i | \(-0.0888188\pi\) | ||||
0.961322 | + | 0.275426i | \(0.0888188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 20.7611i | 2.16449i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.5607i | 1.50182i | ||||||||
\(95\) | 0.529484i | 0.0543239i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1949i | 1.23820i | 0.785311 | + | 0.619101i | \(0.212503\pi\) | ||||
−0.785311 | + | 0.619101i | \(0.787497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −27.0060 | −2.70060 | ||||||||
\(101\) | 14.9295 | 1.48554 | 0.742769 | − | 0.669548i | \(-0.233512\pi\) | ||||
0.742769 | + | 0.669548i | \(0.233512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 11.3531i | − 1.11865i | −0.828947 | − | 0.559327i | \(-0.811060\pi\) | ||||
0.828947 | − | 0.559327i | \(-0.188940\pi\) | |||||||
\(104\) | 25.0994 | 2.46120 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.63819 | −0.644758 | ||||||||
\(107\) | 4.32637i | 0.418246i | 0.977889 | + | 0.209123i | \(0.0670609\pi\) | ||||
−0.977889 | + | 0.209123i | \(0.932939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.88083 | 0.754847 | 0.377423 | − | 0.926041i | \(-0.376810\pi\) | ||||
0.377423 | + | 0.926041i | \(0.376810\pi\) | |||||||
\(110\) | −34.7658 | −3.31479 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.01207i | 0.471496i | 0.971814 | + | 0.235748i | \(0.0757540\pi\) | ||||
−0.971814 | + | 0.235748i | \(0.924246\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9535i | 1.20792i | ||||||||
\(116\) | − 10.8932i | − 1.01140i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 23.6194i | − 2.17434i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.51261 | −0.501146 | ||||||||
\(122\) | 28.9325 | 2.61943 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 39.5659i | − 3.55312i | ||||||||
\(125\) | −0.834029 | −0.0745978 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.5311 | 1.55564 | 0.777819 | − | 0.628489i | \(-0.216326\pi\) | ||||
0.777819 | + | 0.628489i | \(0.216326\pi\) | |||||||
\(128\) | − 15.2430i | − 1.34731i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 25.6546 | 2.25006 | ||||||||
\(131\) | −4.83988 | −0.422862 | −0.211431 | − | 0.977393i | \(-0.567812\pi\) | ||||
−0.211431 | + | 0.977393i | \(0.567812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 3.05621i | − 0.264016i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.2819i | 1.82491i | ||||||||
\(137\) | 4.04006i | 0.345166i | 0.984995 | + | 0.172583i | \(0.0552113\pi\) | ||||
−0.984995 | + | 0.172583i | \(0.944789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.14265i | − 0.351375i | −0.984446 | − | 0.175687i | \(-0.943785\pi\) | ||||
0.984446 | − | 0.175687i | \(-0.0562148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 24.9319 | 2.09224 | ||||||||
\(143\) | 12.1851 | 1.01897 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 6.79659i | − 0.564426i | ||||||||
\(146\) | 16.3131 | 1.35008 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −60.5852 | −4.98007 | ||||||||
\(149\) | − 5.17025i | − 0.423564i | −0.977317 | − | 0.211782i | \(-0.932073\pi\) | ||||
0.977317 | − | 0.211782i | \(-0.0679266\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.86820 | 0.803063 | 0.401531 | − | 0.915845i | \(-0.368478\pi\) | ||||
0.401531 | + | 0.915845i | \(0.368478\pi\) | |||||||
\(152\) | −1.38361 | −0.112225 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 24.6864i | − 1.98286i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 11.3871i | − 0.908788i | −0.890801 | − | 0.454394i | \(-0.849856\pi\) | ||||
0.890801 | − | 0.454394i | \(-0.150144\pi\) | |||||||
\(158\) | − 34.3782i | − 2.73498i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 49.8021i | − 3.93720i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.94760 | −0.230874 | −0.115437 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115437 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(164\) | −3.23390 | −0.252525 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 10.0653i | − 0.781218i | ||||||||
\(167\) | 17.0818 | 1.32183 | 0.660914 | − | 0.750461i | \(-0.270169\pi\) | ||||
0.660914 | + | 0.750461i | \(0.270169\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00828 | 0.308329 | ||||||||
\(170\) | 21.7527i | 1.66836i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20.2508 | −1.54411 | ||||||||
\(173\) | 13.3937 | 1.01830 | 0.509151 | − | 0.860677i | \(-0.329960\pi\) | ||||
0.509151 | + | 0.860677i | \(0.329960\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 49.1237i | − 3.70284i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 48.4458i | 3.63117i | ||||||||
\(179\) | 8.04603i | 0.601389i | 0.953721 | + | 0.300694i | \(0.0972184\pi\) | ||||
−0.953721 | + | 0.300694i | \(0.902782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.34572i | 0.248686i | 0.992239 | + | 0.124343i | \(0.0396823\pi\) | ||||
−0.992239 | + | 0.124343i | \(0.960318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −33.8492 | −2.49539 | ||||||||
\(185\) | −37.8011 | −2.77919 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.3318i | 0.755538i | ||||||||
\(188\) | −27.9874 | −2.04119 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.41421 | −0.102598 | ||||||||
\(191\) | − 12.9344i | − 0.935898i | −0.883756 | − | 0.467949i | \(-0.844993\pi\) | ||||
0.883756 | − | 0.467949i | \(-0.155007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.2153 | 1.23919 | 0.619593 | − | 0.784923i | \(-0.287298\pi\) | ||||
0.619593 | + | 0.784923i | \(0.287298\pi\) | |||||||
\(194\) | −32.5717 | −2.33851 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 19.3681i | − 1.37992i | −0.723848 | − | 0.689960i | \(-0.757628\pi\) | ||||
0.723848 | − | 0.689960i | \(-0.242372\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0519i | 1.84677i | 0.383874 | + | 0.923385i | \(0.374590\pi\) | ||||
−0.383874 | + | 0.923385i | \(0.625410\pi\) | |||||||
\(200\) | − 44.0310i | − 3.11346i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 39.8756i | 2.80563i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.01773 | −0.140925 | ||||||||
\(206\) | 30.3233 | 2.11272 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 36.2497i | 2.51347i | ||||||||
\(209\) | −0.671705 | −0.0464628 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6672 | 0.940892 | 0.470446 | − | 0.882429i | \(-0.344093\pi\) | ||||
0.470446 | + | 0.882429i | \(0.344093\pi\) | |||||||
\(212\) | − 12.7594i | − 0.876322i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.5554 | −0.789912 | ||||||||
\(215\) | −12.6351 | −0.861708 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 21.0491i | 1.42563i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 66.8242i | − 4.50528i | ||||||||
\(221\) | − 7.62414i | − 0.512855i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 14.7000i | − 0.984387i | −0.870486 | − | 0.492193i | \(-0.836195\pi\) | ||||
0.870486 | − | 0.492193i | \(-0.163805\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.3869 | −0.890483 | ||||||||
\(227\) | −9.40612 | −0.624306 | −0.312153 | − | 0.950032i | \(-0.601050\pi\) | ||||
−0.312153 | + | 0.950032i | \(0.601050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 17.4687i | − 1.15436i | −0.816616 | − | 0.577182i | \(-0.804152\pi\) | ||||
0.816616 | − | 0.577182i | \(-0.195848\pi\) | |||||||
\(230\) | −34.5979 | −2.28132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.7603 | 1.16602 | ||||||||
\(233\) | − 14.8245i | − 0.971185i | −0.874185 | − | 0.485593i | \(-0.838604\pi\) | ||||
0.874185 | − | 0.485593i | \(-0.161396\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.4623 | −1.13911 | ||||||||
\(236\) | 45.3994 | 2.95525 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1924i | 0.853347i | 0.904406 | + | 0.426674i | \(0.140315\pi\) | ||||
−0.904406 | + | 0.426674i | \(0.859685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 26.9521i | − 1.73614i | −0.496442 | − | 0.868070i | \(-0.665361\pi\) | ||||
0.496442 | − | 0.868070i | \(-0.334639\pi\) | |||||||
\(242\) | − 14.7238i | − 0.946480i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 55.6119i | 3.56019i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.495670 | 0.0315387 | ||||||||
\(248\) | 64.5088 | 4.09631 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 2.22763i | − 0.140888i | ||||||||
\(251\) | 8.08092 | 0.510063 | 0.255032 | − | 0.966933i | \(-0.417914\pi\) | ||||
0.255032 | + | 0.966933i | \(0.417914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.4329 | −1.03313 | ||||||||
\(254\) | 46.8244i | 2.93803i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.01469 | 0.375918 | ||||||||
\(257\) | −10.5161 | −0.655975 | −0.327988 | − | 0.944682i | \(-0.606370\pi\) | ||||
−0.327988 | + | 0.944682i | \(0.606370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 49.3114i | 3.05816i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 12.9270i | − 0.798631i | ||||||||
\(263\) | − 14.4891i | − 0.893435i | −0.894675 | − | 0.446717i | \(-0.852593\pi\) | ||||
0.894675 | − | 0.446717i | \(-0.147407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 7.96103i | − 0.489042i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.87441 | 0.358837 | ||||||||
\(269\) | −16.7458 | −1.02101 | −0.510505 | − | 0.859875i | \(-0.670541\pi\) | ||||
−0.510505 | + | 0.859875i | \(0.670541\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 2.57864i | − 0.156641i | −0.996928 | − | 0.0783206i | \(-0.975044\pi\) | ||||
0.996928 | − | 0.0783206i | \(-0.0249558\pi\) | |||||||
\(272\) | −30.7364 | −1.86367 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.7907 | −0.651891 | ||||||||
\(275\) | − 21.3759i | − 1.28902i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.39424 | 0.203940 | 0.101970 | − | 0.994787i | \(-0.467485\pi\) | ||||
0.101970 | + | 0.994787i | \(0.467485\pi\) | |||||||
\(278\) | 11.0647 | 0.663617 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.8408i | 1.42222i | 0.703079 | + | 0.711111i | \(0.251808\pi\) | ||||
−0.703079 | + | 0.711111i | \(0.748192\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 16.0699i | − 0.955255i | −0.878563 | − | 0.477627i | \(-0.841497\pi\) | ||||
0.878563 | − | 0.477627i | \(-0.158503\pi\) | |||||||
\(284\) | 47.9223i | 2.84366i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 32.5455i | 1.92446i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.5354 | −0.619732 | ||||||||
\(290\) | 18.1532 | 1.06599 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 31.3558i | 1.83496i | ||||||||
\(293\) | −10.6137 | −0.620061 | −0.310030 | − | 0.950727i | \(-0.600339\pi\) | ||||
−0.310030 | + | 0.950727i | \(0.600339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.3262 | 1.64921 | ||||||||
\(296\) | − 98.7790i | − 5.74141i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.8094 | 0.799956 | ||||||||
\(299\) | 12.1263 | 0.701280 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 26.3573i | 1.51669i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 1.99827i | − 0.114609i | ||||||||
\(305\) | 34.6981i | 1.98681i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.38473i | − 0.193177i | −0.995324 | − | 0.0965883i | \(-0.969207\pi\) | ||||
0.995324 | − | 0.0965883i | \(-0.0307930\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 65.9357 | 3.74490 | ||||||||
\(311\) | −30.4634 | −1.72742 | −0.863711 | − | 0.503987i | \(-0.831866\pi\) | ||||
−0.863711 | + | 0.503987i | \(0.831866\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1291i | 1.19429i | 0.802134 | + | 0.597144i | \(0.203698\pi\) | ||||
−0.802134 | + | 0.597144i | \(0.796302\pi\) | |||||||
\(314\) | 30.4141 | 1.71637 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 66.0792 | 3.71724 | ||||||||
\(317\) | 2.94574i | 0.165449i | 0.996572 | + | 0.0827247i | \(0.0263622\pi\) | ||||
−0.996572 | + | 0.0827247i | \(0.973638\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.62218 | 0.482750 | ||||||||
\(320\) | 55.5726 | 3.10660 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.420282i | 0.0233851i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.7739i | 0.874977i | ||||||||
\(326\) | − 7.87282i | − 0.436035i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 5.27259i | − 0.291130i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5134 | 0.797729 | 0.398864 | − | 0.917010i | \(-0.369404\pi\) | ||||
0.398864 | + | 0.917010i | \(0.369404\pi\) | |||||||
\(332\) | 19.3468 | 1.06179 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 45.6242i | 2.49645i | ||||||||
\(335\) | 3.66524 | 0.200253 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.40462 | −0.185462 | −0.0927308 | − | 0.995691i | \(-0.529560\pi\) | ||||
−0.0927308 | + | 0.995691i | \(0.529560\pi\) | |||||||
\(338\) | 10.7058i | 0.582320i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −41.8114 | −2.26754 | ||||||||
\(341\) | 31.3173 | 1.69593 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 33.0172i | − 1.78017i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 35.7735i | 1.92320i | ||||||||
\(347\) | − 33.0097i | − 1.77206i | −0.463632 | − | 0.886028i | \(-0.653454\pi\) | ||||
0.463632 | − | 0.886028i | \(-0.346546\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 22.4821i | − 1.20344i | −0.798708 | − | 0.601719i | \(-0.794483\pi\) | ||||
0.798708 | − | 0.601719i | \(-0.205517\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 63.1791 | 3.36746 | ||||||||
\(353\) | 1.31897 | 0.0702018 | 0.0351009 | − | 0.999384i | \(-0.488825\pi\) | ||||
0.0351009 | + | 0.999384i | \(0.488825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.9003i | 1.58694i | ||||||||
\(356\) | −93.1190 | −4.93529 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.4904 | −1.13580 | ||||||||
\(359\) | 15.5097i | 0.818572i | 0.912406 | + | 0.409286i | \(0.134222\pi\) | ||||
−0.912406 | + | 0.409286i | \(0.865778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9727 | 0.998562 | ||||||||
\(362\) | −8.93619 | −0.469676 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.5639i | 1.02402i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 20.6751i | − 1.07923i | −0.841911 | − | 0.539617i | \(-0.818569\pi\) | ||||
0.841911 | − | 0.539617i | \(-0.181431\pi\) | |||||||
\(368\) | − 48.8865i | − 2.54839i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 100.964i | − 5.24887i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6559 | 0.655299 | 0.327649 | − | 0.944799i | \(-0.393743\pi\) | ||||
0.327649 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(374\) | −27.5956 | −1.42693 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 45.6311i | − 2.35324i | ||||||||
\(377\) | −6.36255 | −0.327688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.1126 | −1.80361 | −0.901806 | − | 0.432142i | \(-0.857758\pi\) | ||||
−0.901806 | + | 0.432142i | \(0.857758\pi\) | |||||||
\(380\) | − 2.71830i | − 0.139446i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 34.5468 | 1.76757 | ||||||||
\(383\) | −5.18897 | −0.265144 | −0.132572 | − | 0.991173i | \(-0.542324\pi\) | ||||
−0.132572 | + | 0.991173i | \(0.542324\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 45.9809i | 2.34037i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 62.6068i | − 3.17838i | ||||||||
\(389\) | 23.3663i | 1.18472i | 0.805674 | + | 0.592359i | \(0.201803\pi\) | ||||
−0.805674 | + | 0.592359i | \(0.798197\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2819i | 0.519980i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 51.7308 | 2.60616 | ||||||||
\(395\) | 41.2289 | 2.07445 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 24.5539i | − 1.23233i | −0.787618 | − | 0.616164i | \(-0.788686\pi\) | ||||
0.787618 | − | 0.616164i | \(-0.211314\pi\) | |||||||
\(398\) | −69.5828 | −3.48787 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 63.5916 | 3.17958 | ||||||||
\(401\) | 21.4007i | 1.06870i | 0.845264 | + | 0.534349i | \(0.179443\pi\) | ||||
−0.845264 | + | 0.534349i | \(0.820557\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.1099 | −1.15119 | ||||||||
\(404\) | −76.6458 | −3.81327 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 47.9546i | − 2.37702i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.8267i | 0.832026i | 0.909359 | + | 0.416013i | \(0.136573\pi\) | ||||
−0.909359 | + | 0.416013i | \(0.863427\pi\) | |||||||
\(410\) | − 5.38922i | − 0.266155i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 58.2852i | 2.87151i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0711 | 0.592545 | ||||||||
\(416\) | −46.6216 | −2.28581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 1.79408i | − 0.0877512i | ||||||||
\(419\) | 32.3652 | 1.58115 | 0.790573 | − | 0.612368i | \(-0.209783\pi\) | ||||
0.790573 | + | 0.612368i | \(0.209783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5354 | −0.513466 | −0.256733 | − | 0.966482i | \(-0.582646\pi\) | ||||
−0.256733 | + | 0.966482i | \(0.582646\pi\) | |||||||
\(422\) | 36.5042i | 1.77700i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 20.8032 | 1.01029 | ||||||||
\(425\) | −13.3748 | −0.648771 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 22.2110i | − 1.07361i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 33.7475i | − 1.62745i | ||||||||
\(431\) | 1.20142i | 0.0578702i | 0.999581 | + | 0.0289351i | \(0.00921162\pi\) | ||||
−0.999581 | + | 0.0289351i | \(0.990788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.1553i | 1.40111i | 0.713596 | + | 0.700557i | \(0.247065\pi\) | ||||
−0.713596 | + | 0.700557i | \(0.752935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −40.4591 | −1.93764 | ||||||||
\(437\) | −0.668462 | −0.0319769 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9225i | 0.521301i | 0.965433 | + | 0.260651i | \(0.0839370\pi\) | ||||
−0.965433 | + | 0.260651i | \(0.916063\pi\) | |||||||
\(440\) | 108.951 | 5.19404 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.3635 | 0.968595 | ||||||||
\(443\) | − 4.49622i | − 0.213622i | −0.994279 | − | 0.106811i | \(-0.965936\pi\) | ||||
0.994279 | − | 0.106811i | \(-0.0340639\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −58.0999 | −2.75420 | ||||||||
\(446\) | 39.2627 | 1.85914 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 13.3794i | − 0.631414i | −0.948857 | − | 0.315707i | \(-0.897758\pi\) | ||||
0.948857 | − | 0.315707i | \(-0.102242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.55971i | − 0.120532i | ||||||||
\(452\) | − 25.7313i | − 1.21030i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 25.1231i | − 1.17908i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.1243 | −1.31560 | −0.657799 | − | 0.753194i | \(-0.728512\pi\) | ||||
−0.657799 | + | 0.753194i | \(0.728512\pi\) | |||||||
\(458\) | 46.6576 | 2.18017 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 66.5015i | − 3.10065i | ||||||||
\(461\) | −19.1329 | −0.891108 | −0.445554 | − | 0.895255i | \(-0.646993\pi\) | ||||
−0.445554 | + | 0.895255i | \(0.646993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.3116 | −0.665119 | −0.332559 | − | 0.943082i | \(-0.607912\pi\) | ||||
−0.332559 | + | 0.943082i | \(0.607912\pi\) | |||||||
\(464\) | 25.6503i | 1.19079i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 39.5952 | 1.83421 | ||||||||
\(467\) | 1.43785 | 0.0665360 | 0.0332680 | − | 0.999446i | \(-0.489409\pi\) | ||||
0.0332680 | + | 0.999446i | \(0.489409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 46.6405i | − 2.15136i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 74.0198i | 3.40704i | ||||||||
\(473\) | − 16.0290i | − 0.737013i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.869536i | − 0.0398971i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −35.2360 | −1.61166 | ||||||||
\(479\) | −4.31575 | −0.197192 | −0.0985958 | − | 0.995128i | \(-0.531435\pi\) | ||||
−0.0985958 | + | 0.995128i | \(0.531435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.3870i | 1.61351i | ||||||||
\(482\) | 71.9872 | 3.27893 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.3009 | 1.28641 | ||||||||
\(485\) | − 39.0624i | − 1.77373i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.7443 | −1.71036 | −0.855180 | − | 0.518332i | \(-0.826553\pi\) | ||||
−0.855180 | + | 0.518332i | \(0.826553\pi\) | |||||||
\(488\) | −90.6704 | −4.10446 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 25.3545i | − 1.14423i | −0.820173 | − | 0.572116i | \(-0.806123\pi\) | ||||
0.820173 | − | 0.572116i | \(-0.193877\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.39484i | − 0.242972i | ||||||||
\(494\) | 1.32390i | 0.0595650i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 93.1666i | 4.18330i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.0116489 | 0.000521477 0 | 0.000260738 | − | 1.00000i | \(-0.499917\pi\) | ||||
0.000260738 | 1.00000i | \(0.499917\pi\) | ||||||||
\(500\) | 4.28179 | 0.191487 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.5836i | 0.963322i | ||||||||
\(503\) | 24.9237 | 1.11129 | 0.555646 | − | 0.831419i | \(-0.312471\pi\) | ||||
0.555646 | + | 0.831419i | \(0.312471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.8218 | −2.12804 | ||||||||
\(506\) | − 43.8910i | − 1.95119i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −90.0024 | −3.99321 | ||||||||
\(509\) | 21.3672 | 0.947084 | 0.473542 | − | 0.880771i | \(-0.342975\pi\) | ||||
0.473542 | + | 0.880771i | \(0.342975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 14.4212i | − 0.637335i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 28.0877i | − 1.23890i | ||||||||
\(515\) | 36.3660i | 1.60248i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 22.1527i | − 0.974275i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −80.3980 | −3.52568 | ||||||||
\(521\) | 10.0430 | 0.439990 | 0.219995 | − | 0.975501i | \(-0.429396\pi\) | ||||
0.219995 | + | 0.975501i | \(0.429396\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5654i | 0.680628i | 0.940312 | + | 0.340314i | \(0.110533\pi\) | ||||
−0.940312 | + | 0.340314i | \(0.889467\pi\) | |||||||
\(524\) | 24.8473 | 1.08546 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 38.6993 | 1.68737 | ||||||||
\(527\) | − 19.5950i | − 0.853573i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.64647 | 0.288977 | ||||||||
\(530\) | 21.2633 | 0.923620 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.88888i | 0.0818164i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 13.8581i | − 0.599140i | ||||||||
\(536\) | 9.57773i | 0.413695i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 44.7269i | − 1.92831i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.8241 | 1.23924 | 0.619622 | − | 0.784901i | \(-0.287286\pi\) | ||||
0.619622 | + | 0.784901i | \(0.287286\pi\) | |||||||
\(542\) | 6.88736 | 0.295838 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 39.5308i | − 1.69487i | ||||||||
\(545\) | −25.2437 | −1.08132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.3469 | −1.04100 | −0.520500 | − | 0.853862i | \(-0.674254\pi\) | ||||
−0.520500 | + | 0.853862i | \(0.674254\pi\) | |||||||
\(548\) | − 20.7411i | − 0.886016i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 57.0935 | 2.43448 | ||||||||
\(551\) | 0.350736 | 0.0149419 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.06576i | 0.385167i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.2678i | 0.901954i | ||||||||
\(557\) | − 8.26112i | − 0.350035i | −0.984565 | − | 0.175017i | \(-0.944002\pi\) | ||||
0.984565 | − | 0.175017i | \(-0.0559982\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.8282i | 0.500280i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −63.6771 | −2.68605 | ||||||||
\(563\) | −0.276886 | −0.0116694 | −0.00583468 | − | 0.999983i | \(-0.501857\pi\) | ||||
−0.00583468 | + | 0.999983i | \(0.501857\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 16.0546i | − 0.675421i | ||||||||
\(566\) | 42.9215 | 1.80412 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −78.1332 | −3.27839 | ||||||||
\(569\) | 36.4807i | 1.52935i | 0.644415 | + | 0.764676i | \(0.277101\pi\) | ||||
−0.644415 | + | 0.764676i | \(0.722899\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.4091 | 0.435605 | 0.217803 | − | 0.975993i | \(-0.430111\pi\) | ||||
0.217803 | + | 0.975993i | \(0.430111\pi\) | |||||||
\(572\) | −62.5566 | −2.61562 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 21.2727i | − 0.887133i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.0368i | 0.459467i | 0.973254 | + | 0.229734i | \(0.0737855\pi\) | ||||
−0.973254 | + | 0.229734i | \(0.926215\pi\) | |||||||
\(578\) | − 28.1394i | − 1.17045i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 34.8927i | 1.44884i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0994 | 0.418274 | ||||||||
\(584\) | −51.1229 | −2.11548 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 28.3485i | − 1.17107i | ||||||||
\(587\) | 19.3497 | 0.798649 | 0.399324 | − | 0.916810i | \(-0.369245\pi\) | ||||
0.399324 | + | 0.916810i | \(0.369245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.27394 | 0.0524916 | ||||||||
\(590\) | 75.6571i | 3.11476i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 142.661 | 5.86334 | ||||||||
\(593\) | 33.4553 | 1.37385 | 0.686923 | − | 0.726730i | \(-0.258961\pi\) | ||||
0.686923 | + | 0.726730i | \(0.258961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.5434i | 1.08726i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.3884i | 1.32446i | ||||||||
\(599\) | − 7.34670i | − 0.300178i | −0.988672 | − | 0.150089i | \(-0.952044\pi\) | ||||
0.988672 | − | 0.150089i | \(-0.0479560\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 26.5631i | − 1.08353i | −0.840530 | − | 0.541766i | \(-0.817756\pi\) | ||||
0.840530 | − | 0.541766i | \(-0.182244\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −50.6620 | −2.06141 | ||||||||
\(605\) | 17.6579 | 0.717895 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 21.3489i | − 0.866527i | −0.901267 | − | 0.433263i | \(-0.857362\pi\) | ||||
0.901267 | − | 0.433263i | \(-0.142638\pi\) | |||||||
\(608\) | 2.57002 | 0.104228 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −92.6761 | −3.75234 | ||||||||
\(611\) | 16.3471i | 0.661332i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.4572 | −0.705088 | −0.352544 | − | 0.935795i | \(-0.614683\pi\) | ||||
−0.352544 | + | 0.935795i | \(0.614683\pi\) | |||||||
\(614\) | 9.04036 | 0.364839 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.7469i | 1.60015i | 0.599901 | + | 0.800074i | \(0.295207\pi\) | ||||
−0.599901 | + | 0.800074i | \(0.704793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.35594i | 0.376047i | 0.982165 | + | 0.188023i | \(0.0602081\pi\) | ||||
−0.982165 | + | 0.188023i | \(0.939792\pi\) | |||||||
\(620\) | 126.737i | 5.08987i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 81.3656i | − 3.26246i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.6303 | −0.945213 | ||||||||
\(626\) | −56.4343 | −2.25557 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 58.4597i | 2.33279i | ||||||||
\(629\) | −30.0049 | −1.19637 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.1161 | −0.681382 | −0.340691 | − | 0.940175i | \(-0.610661\pi\) | ||||
−0.340691 | + | 0.940175i | \(0.610661\pi\) | |||||||
\(632\) | 107.736i | 4.28552i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.86787 | −0.312473 | ||||||||
\(635\) | −56.1554 | −2.22846 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 23.0292i | 0.911736i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 48.8262i | 1.93002i | ||||||||
\(641\) | 6.26895i | 0.247609i | 0.992307 | + | 0.123804i | \(0.0395095\pi\) | ||||
−0.992307 | + | 0.123804i | \(0.960490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 37.8182i | − 1.49141i | −0.666279 | − | 0.745703i | \(-0.732114\pi\) | ||||
0.666279 | − | 0.745703i | \(-0.267886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.12254 | −0.0441658 | ||||||||
\(647\) | 26.0490 | 1.02409 | 0.512045 | − | 0.858958i | \(-0.328888\pi\) | ||||
0.512045 | + | 0.858958i | \(0.328888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.9347i | 1.41056i | ||||||||
\(650\) | −42.1309 | −1.65251 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.1325 | 0.592636 | ||||||||
\(653\) | − 26.8906i | − 1.05231i | −0.850388 | − | 0.526156i | \(-0.823633\pi\) | ||||
0.850388 | − | 0.526156i | \(-0.176367\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.5030 | 0.605753 | ||||||||
\(656\) | 7.61493 | 0.297313 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.10738i | 0.315819i | 0.987454 | + | 0.157909i | \(0.0504754\pi\) | ||||
−0.987454 | + | 0.157909i | \(0.949525\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.4100i | 1.14392i | 0.820283 | + | 0.571958i | \(0.193816\pi\) | ||||
−0.820283 | + | 0.571958i | \(0.806184\pi\) | |||||||
\(662\) | 38.7643i | 1.50662i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.5432i | 1.22411i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.58055 | 0.332240 | ||||||||
\(668\) | −87.6955 | −3.39304 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.78959i | 0.378205i | ||||||||
\(671\) | −44.0181 | −1.69930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.3797 | −0.592843 | −0.296421 | − | 0.955057i | \(-0.595793\pi\) | ||||
−0.296421 | + | 0.955057i | \(0.595793\pi\) | |||||||
\(674\) | − 9.09351i | − 0.350269i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.5779 | −0.791459 | ||||||||
\(677\) | 24.7993 | 0.953114 | 0.476557 | − | 0.879143i | \(-0.341885\pi\) | ||||
0.476557 | + | 0.879143i | \(0.341885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 68.1700i | − 2.61420i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 83.6463i | 3.20298i | ||||||||
\(683\) | − 39.8402i | − 1.52444i | −0.647316 | − | 0.762222i | \(-0.724108\pi\) | ||||
0.647316 | − | 0.762222i | \(-0.275892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12.9411i | − 0.494452i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 47.6849 | 1.81797 | ||||||||
\(689\) | −7.45262 | −0.283922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 12.7920i | − 0.486631i | −0.969947 | − | 0.243316i | \(-0.921765\pi\) | ||||
0.969947 | − | 0.243316i | \(-0.0782351\pi\) | |||||||
\(692\) | −68.7612 | −2.61391 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 88.1666 | 3.34676 | ||||||||
\(695\) | 13.2696i | 0.503346i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.60159 | −0.0606646 | ||||||||
\(698\) | 60.0480 | 2.27285 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.7936i | 1.23860i | 0.785155 | + | 0.619299i | \(0.212583\pi\) | ||||
−0.785155 | + | 0.619299i | \(0.787417\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.95071i | − 0.0735726i | ||||||||
\(704\) | 70.4996i | 2.65705i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.52288i | 0.132585i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.3711 | 0.990387 | 0.495193 | − | 0.868783i | \(-0.335097\pi\) | ||||
0.495193 | + | 0.868783i | \(0.335097\pi\) | |||||||
\(710\) | −79.8615 | −2.99715 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 151.822i | − 5.68979i | ||||||||
\(713\) | 31.1661 | 1.16718 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39.0311 | −1.45968 | ||||||||
\(716\) | − 41.3072i | − 1.54372i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −41.4253 | −1.54598 | ||||||||
\(719\) | −33.9578 | −1.26641 | −0.633207 | − | 0.773983i | \(-0.718262\pi\) | ||||
−0.633207 | + | 0.773983i | \(0.718262\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 50.6747i | 1.88592i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 17.1765i | − 0.638359i | ||||||||
\(725\) | 11.1616i | 0.414531i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3061i | 0.530583i | 0.964168 | + | 0.265292i | \(0.0854682\pi\) | ||||
−0.964168 | + | 0.265292i | \(0.914532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −52.2538 | −1.93400 | ||||||||
\(731\) | −10.0292 | −0.370944 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1450i | 0.781009i | 0.920601 | + | 0.390504i | \(0.127699\pi\) | ||||
−0.920601 | + | 0.390504i | \(0.872301\pi\) | |||||||
\(734\) | 55.2218 | 2.03828 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 62.8741 | 2.31757 | ||||||||
\(737\) | 4.64974i | 0.171275i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.5709 | 1.05100 | 0.525499 | − | 0.850794i | \(-0.323879\pi\) | ||||
0.525499 | + | 0.850794i | \(0.323879\pi\) | |||||||
\(740\) | 194.065 | 7.13399 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.925908i | 0.0339683i | 0.999856 | + | 0.0169841i | \(0.00540648\pi\) | ||||
−0.999856 | + | 0.0169841i | \(0.994594\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.5613i | 0.606758i | ||||||||
\(746\) | 33.8031i | 1.23762i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 53.0422i | − 1.93941i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.07444 | −0.258150 | −0.129075 | − | 0.991635i | \(-0.541201\pi\) | ||||
−0.129075 | + | 0.991635i | \(0.541201\pi\) | |||||||
\(752\) | 65.9025 | 2.40322 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 16.9939i | − 0.618882i | ||||||||
\(755\) | −31.6096 | −1.15039 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.3950 | 0.523196 | 0.261598 | − | 0.965177i | \(-0.415750\pi\) | ||||
0.261598 | + | 0.965177i | \(0.415750\pi\) | |||||||
\(758\) | − 93.7832i | − 3.40636i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.43195 | 0.160764 | ||||||||
\(761\) | −19.7726 | −0.716757 | −0.358378 | − | 0.933576i | \(-0.616670\pi\) | ||||
−0.358378 | + | 0.933576i | \(0.616670\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 66.4032i | 2.40238i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 13.8594i | − 0.500759i | ||||||||
\(767\) | − 26.5172i | − 0.957480i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.3584i | 0.517779i | 0.965907 | + | 0.258889i | \(0.0833565\pi\) | ||||
−0.965907 | + | 0.258889i | \(0.916643\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −88.3810 | −3.18090 | ||||||||
\(773\) | −16.2164 | −0.583263 | −0.291632 | − | 0.956531i | \(-0.594198\pi\) | ||||
−0.291632 | + | 0.956531i | \(0.594198\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.5409i | 1.45627i | ||||||||
\(776\) | 102.075 | 3.66428 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −62.4097 | −2.23750 | ||||||||
\(779\) | − 0.104125i | − 0.00373065i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.9316 | −1.35730 | ||||||||
\(782\) | −27.4623 | −0.982051 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.4749i | 1.30184i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 49.9936i | − 1.78208i | −0.453927 | − | 0.891039i | \(-0.649977\pi\) | ||||
0.453927 | − | 0.891039i | \(-0.350023\pi\) | |||||||
\(788\) | 99.4331i | 3.54216i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 110.120i | 3.91788i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.4822 | 1.15348 | ||||||||
\(794\) | 65.5818 | 2.32741 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 133.747i | − 4.74053i | ||||||||
\(797\) | −10.9957 | −0.389488 | −0.194744 | − | 0.980854i | \(-0.562388\pi\) | ||||
−0.194744 | + | 0.980854i | \(0.562388\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.8608 | −0.490360 | ||||||||
\(800\) | 81.7867i | 2.89160i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −57.1597 | −2.01838 | ||||||||
\(803\) | −24.8188 | −0.875838 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 61.7249i | − 2.17417i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 124.964i | − 4.39623i | ||||||||
\(809\) | 35.3075i | 1.24135i | 0.784069 | + | 0.620674i | \(0.213141\pi\) | ||||
−0.784069 | + | 0.620674i | \(0.786859\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7045i | 0.727034i | 0.931588 | + | 0.363517i | \(0.118424\pi\) | ||||
−0.931588 | + | 0.363517i | \(0.881576\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 128.083 | 4.48932 | ||||||||
\(815\) | 9.44169 | 0.330728 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 0.652032i | − 0.0228117i | ||||||||
\(818\) | −44.9429 | −1.57139 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.3588 | 0.361744 | ||||||||
\(821\) | 11.6830i | 0.407739i | 0.978998 | + | 0.203869i | \(0.0653518\pi\) | ||||
−0.978998 | + | 0.203869i | \(0.934648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.2902 | 0.916420 | 0.458210 | − | 0.888844i | \(-0.348491\pi\) | ||||
0.458210 | + | 0.888844i | \(0.348491\pi\) | |||||||
\(824\) | −95.0290 | −3.31049 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.4447i | 1.05867i | 0.848414 | + | 0.529333i | \(0.177558\pi\) | ||||
−0.848414 | + | 0.529333i | \(0.822442\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 29.8109i | − 1.03537i | −0.855570 | − | 0.517687i | \(-0.826793\pi\) | ||||
0.855570 | − | 0.517687i | \(-0.173207\pi\) | |||||||
\(830\) | 32.2410i | 1.11910i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 52.0236i | − 1.80359i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54.7161 | −1.89353 | ||||||||
\(836\) | 3.44844 | 0.119267 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 86.4453i | 2.98620i | ||||||||
\(839\) | 20.1662 | 0.696215 | 0.348107 | − | 0.937455i | \(-0.386824\pi\) | ||||
0.348107 | + | 0.937455i | \(0.386824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.4979 | 0.844754 | ||||||||
\(842\) | − 28.1394i | − 0.969748i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −70.1657 | −2.41520 | ||||||||
\(845\) | −12.8392 | −0.441683 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 30.0449i | 1.03175i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 35.7230i | − 1.22529i | ||||||||
\(851\) | − 47.7231i | − 1.63593i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 35.2714i | − 1.20767i | −0.797109 | − | 0.603835i | \(-0.793639\pi\) | ||||
0.797109 | − | 0.603835i | \(-0.206361\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.2131 | 1.23774 | ||||||||
\(857\) | −42.9336 | −1.46658 | −0.733291 | − | 0.679915i | \(-0.762017\pi\) | ||||
−0.733291 | + | 0.679915i | \(0.762017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 39.9956i | − 1.36463i | −0.731057 | − | 0.682317i | \(-0.760973\pi\) | ||||
0.731057 | − | 0.682317i | \(-0.239027\pi\) | |||||||
\(860\) | 64.8670 | 2.21194 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.20890 | −0.109296 | ||||||||
\(863\) | 48.2349i | 1.64194i | 0.570975 | + | 0.820968i | \(0.306565\pi\) | ||||
−0.570975 | + | 0.820968i | \(0.693435\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.9024 | −1.45872 | ||||||||
\(866\) | −77.8718 | −2.64619 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.3032i | 1.77426i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 3.43117i | − 0.116261i | ||||||||
\(872\) | − 65.9651i | − 2.23386i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 1.78542i | − 0.0603926i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.3378 | −1.39588 | −0.697939 | − | 0.716157i | \(-0.745899\pi\) | ||||
−0.697939 | + | 0.716157i | \(0.745899\pi\) | |||||||
\(878\) | −29.1731 | −0.984546 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 157.352i | 5.30434i | ||||||||
\(881\) | 43.3796 | 1.46150 | 0.730749 | − | 0.682647i | \(-0.239171\pi\) | ||||
0.730749 | + | 0.682647i | \(0.239171\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.4836 | 0.420105 | 0.210053 | − | 0.977690i | \(-0.432637\pi\) | ||||
0.210053 | + | 0.977690i | \(0.432637\pi\) | |||||||
\(884\) | 39.1413i | 1.31646i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0091 | 0.403453 | ||||||||
\(887\) | 26.8236 | 0.900649 | 0.450325 | − | 0.892865i | \(-0.351308\pi\) | ||||
0.450325 | + | 0.892865i | \(0.351308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 155.181i | − 5.20167i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 75.4679i | 2.52685i | ||||||||
\(893\) | − 0.901135i | − 0.0301553i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 25.7729i | − 0.861493i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 35.7355 | 1.19251 | ||||||||
\(899\) | −16.3526 | −0.545389 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 6.31912i | − 0.210521i | ||||||||
\(902\) | 6.83679 | 0.227640 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.9526 | 1.39532 | ||||||||
\(905\) | − 10.7170i | − 0.356244i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.7707 | −0.490454 | −0.245227 | − | 0.969466i | \(-0.578863\pi\) | ||||
−0.245227 | + | 0.969466i | \(0.578863\pi\) | |||||||
\(908\) | 48.2897 | 1.60255 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 25.1293i | − 0.832571i | −0.909234 | − | 0.416286i | \(-0.863332\pi\) | ||||
0.909234 | − | 0.416286i | \(-0.136668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3134i | 0.506800i | ||||||||
\(914\) | − 75.1179i | − 2.48468i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 89.6818i | 2.96317i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.2856 | 1.36189 | 0.680943 | − | 0.732337i | \(-0.261570\pi\) | ||||
0.680943 | + | 0.732337i | \(0.261570\pi\) | |||||||
\(920\) | 108.425 | 3.57467 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 51.1026i | − 1.68297i | ||||||||
\(923\) | 27.9908 | 0.921328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62.0782 | 2.04112 | ||||||||
\(926\) | − 38.2254i | − 1.25616i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32.9895 | −1.08293 | ||||||||
\(929\) | −1.85221 | −0.0607690 | −0.0303845 | − | 0.999538i | \(-0.509673\pi\) | ||||
−0.0303845 | + | 0.999538i | \(0.509673\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 76.1069i | 2.49297i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.84041i | 0.125662i | ||||||||
\(935\) | − 33.0947i | − 1.08231i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.2417i | 1.54332i | 0.636036 | + | 0.771659i | \(0.280573\pi\) | ||||
−0.636036 | + | 0.771659i | \(0.719427\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 89.6488 | 2.92402 | ||||||||
\(941\) | 40.7764 | 1.32927 | 0.664636 | − | 0.747168i | \(-0.268587\pi\) | ||||
0.664636 | + | 0.747168i | \(0.268587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2.54735i | − 0.0829530i | ||||||||
\(944\) | −106.903 | −3.47939 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42.8122 | 1.39195 | ||||||||
\(947\) | − 12.8681i | − 0.418159i | −0.977899 | − | 0.209079i | \(-0.932953\pi\) | ||||
0.977899 | − | 0.209079i | \(-0.0670467\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.3145 | 0.594514 | ||||||||
\(950\) | 2.32247 | 0.0753509 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 35.7507i | − 1.15808i | −0.815300 | − | 0.579039i | \(-0.803428\pi\) | ||||
0.815300 | − | 0.579039i | \(-0.196572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.4311i | 1.34068i | ||||||||
\(956\) | − 67.7281i | − 2.19048i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 11.5271i | − 0.372422i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3955 | −0.915984 | ||||||||
\(962\) | −94.5162 | −3.04733 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 138.368i | 4.45655i | ||||||||
\(965\) | −55.1438 | −1.77514 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.2307 | −1.10078 | −0.550392 | − | 0.834906i | \(-0.685522\pi\) | ||||
−0.550392 | + | 0.834906i | \(0.685522\pi\) | |||||||
\(968\) | 46.1423i | 1.48307i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 104.333 | 3.34993 | ||||||||
\(971\) | −3.99904 | −0.128335 | −0.0641677 | − | 0.997939i | \(-0.520439\pi\) | ||||
−0.0641677 | + | 0.997939i | \(0.520439\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 100.812i | − 3.23024i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 130.950i | − 4.19162i | ||||||||
\(977\) | 43.4806i | 1.39107i | 0.718493 | + | 0.695535i | \(0.244832\pi\) | ||||
−0.718493 | + | 0.695535i | \(0.755168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 73.7058i | − 2.35565i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 67.7200 | 2.16103 | ||||||||
\(983\) | 31.2017 | 0.995179 | 0.497589 | − | 0.867413i | \(-0.334219\pi\) | ||||
0.497589 | + | 0.867413i | \(0.334219\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 62.0395i | 1.97674i | ||||||||
\(986\) | 14.4092 | 0.458884 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.54470 | −0.0809577 | ||||||||
\(989\) | − 15.9516i | − 0.507231i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4989 | 0.841766 | 0.420883 | − | 0.907115i | \(-0.361720\pi\) | ||||
0.420883 | + | 0.907115i | \(0.361720\pi\) | |||||||
\(992\) | −119.824 | −3.80441 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 83.4490i | − 2.64551i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 18.8775i | − 0.597857i | −0.954276 | − | 0.298928i | \(-0.903371\pi\) | ||||
0.954276 | − | 0.298928i | \(-0.0966292\pi\) | |||||||
\(998\) | 0.0311134i | 0 0.000984877i | ||||||||
\(999\) | 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 | 1323.2.c.f.1322.15 | yes | 16 | |
3.2 | odd | 2 | inner | 1323.2.c.f.1322.2 | yes | 16 | |
7.6 | odd | 2 | inner | 1323.2.c.f.1322.16 | yes | 16 | |
21.20 | even | 2 | inner | 1323.2.c.f.1322.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.2.c.f.1322.1 | ✓ | 16 | 21.20 | even | 2 | inner | |
1323.2.c.f.1322.2 | yes | 16 | 3.2 | odd | 2 | inner | |
1323.2.c.f.1322.15 | yes | 16 | 1.1 | even | 1 | trivial | |
1323.2.c.f.1322.16 | yes | 16 | 7.6 | odd | 2 | inner |