Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,4,Mod(68,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.68");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(4.07113179040\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-23})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} - 6x + 36 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 68.1 | ||
Root | \(-1.82666 - 1.63197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.4.c.b.68.4 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.99599i | − | 1.76635i | −0.469044 | − | 0.883175i | \(-0.655401\pi\) | ||
0.469044 | − | 0.883175i | \(-0.344599\pi\) | |||||||
\(3\) | −5.15331 | − | 0.665865i | −0.991755 | − | 0.128146i | ||||
\(4\) | −16.9599 | −2.11999 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −3.32666 | + | 25.7459i | −0.226350 | + | 1.75179i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 44.7638i | 1.97830i | ||||||||
\(9\) | 26.1132 | + | 6.86282i | 0.967157 | + | 0.254179i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 87.3998 | + | 11.2930i | 2.10251 | + | 0.271668i | ||||
\(13\) | −86.8397 | −1.85269 | −0.926347 | − | 0.376672i | \(-0.877068\pi\) | ||||
−0.926347 | + | 0.376672i | \(0.877068\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 87.9599 | 1.37437 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 34.2866 | − | 130.462i | 0.448968 | − | 1.70834i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 110.304i | 1.00000i | ||||||||
\(24\) | 29.8066 | − | 230.682i | 0.253510 | − | 1.96199i | ||||
\(25\) | −125.000 | −1.00000 | ||||||||
\(26\) | 433.851i | 3.27250i | ||||||||
\(27\) | −130.000 | − | 52.7541i | −0.926612 | − | 0.376020i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 311.361i | − | 1.99373i | −0.0791039 | − | 0.996866i | \(-0.525206\pi\) | ||
0.0791039 | − | 0.996866i | \(-0.474794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −147.080 | −0.852141 | −0.426070 | − | 0.904690i | \(-0.640102\pi\) | ||||
−0.426070 | + | 0.904690i | \(0.640102\pi\) | |||||||
\(32\) | − | 81.3370i | − | 0.449328i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −442.879 | − | 116.393i | −2.05037 | − | 0.538856i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 447.512 | + | 57.8235i | 1.83742 | + | 0.237415i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 522.393i | − | 1.98986i | −0.100583 | − | 0.994929i | \(-0.532071\pi\) | ||
0.100583 | − | 0.994929i | \(-0.467929\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 551.079 | 1.76635 | ||||||||
\(47\) | 279.751i | 0.868212i | 0.900862 | + | 0.434106i | \(0.142936\pi\) | ||||
−0.900862 | + | 0.434106i | \(0.857064\pi\) | |||||||
\(48\) | −453.285 | − | 58.5694i | −1.36304 | − | 0.176120i | ||||
\(49\) | 343.000 | 1.00000 | ||||||||
\(50\) | 624.499i | 1.76635i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1472.80 | 3.92769 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −263.559 | + | 649.479i | −0.664183 | + | 1.63672i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1555.56 | −3.52163 | ||||||||
\(59\) | − | 815.291i | − | 1.79902i | −0.436905 | − | 0.899508i | \(-0.643925\pi\) | ||
0.436905 | − | 0.899508i | \(-0.356075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 734.811i | 1.50518i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 297.321 | 0.580704 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 73.4477 | − | 568.432i | 0.128146 | − | 0.991755i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 908.142i | 1.51798i | 0.651102 | + | 0.758990i | \(0.274307\pi\) | ||||
−0.651102 | + | 0.758990i | \(0.725693\pi\) | |||||||
\(72\) | −307.206 | + | 1168.93i | −0.502841 | + | 1.91333i | ||||
\(73\) | −812.359 | −1.30246 | −0.651229 | − | 0.758881i | \(-0.725746\pi\) | ||||
−0.651229 | + | 0.758881i | \(0.725746\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 644.164 | + | 83.2331i | 0.991755 | + | 0.128146i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 288.886 | − | 2235.77i | 0.419358 | − | 3.24552i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 634.803 | + | 358.421i | 0.870787 | + | 0.491661i | ||||
\(82\) | −2609.87 | −3.51478 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −207.324 | + | 1604.54i | −0.255488 | + | 1.97730i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1870.75i | − | 2.11999i | ||||||
\(93\) | 757.950 | + | 97.9355i | 0.845115 | + | 0.109198i | ||||
\(94\) | 1397.64 | 1.53357 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −54.1595 | + | 419.155i | −0.0575794 | + | 0.445623i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 1713.63i | − | 1.76635i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2119.99 | 2.11999 | ||||||||
\(101\) | − | 1246.92i | − | 1.22844i | −0.789133 | − | 0.614222i | \(-0.789470\pi\) | ||
0.789133 | − | 0.614222i | \(-0.210530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | − | 3887.27i | − | 3.66518i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 2204.79 | + | 894.707i | 1.96441 | + | 0.797159i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5280.66i | 4.22670i | ||||||||
\(117\) | −2267.67 | − | 595.965i | −1.79185 | − | 0.470915i | ||||
\(118\) | −4073.19 | −3.17769 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1331.00 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −347.843 | + | 2692.06i | −0.254992 | + | 1.97345i | ||||
\(124\) | 2494.47 | 1.80653 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 282.285 | 0.197234 | 0.0986172 | − | 0.995125i | \(-0.468558\pi\) | ||||
0.0986172 | + | 0.995125i | \(0.468558\pi\) | |||||||
\(128\) | − | 2136.11i | − | 1.47505i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1879.48i | 1.25352i | 0.779213 | + | 0.626759i | \(0.215619\pi\) | ||||
−0.779213 | + | 0.626759i | \(0.784381\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −2839.88 | − | 366.944i | −1.75179 | − | 0.226350i | ||||
\(139\) | −2609.95 | −1.59261 | −0.796305 | − | 0.604896i | \(-0.793215\pi\) | ||||
−0.796305 | + | 0.604896i | \(0.793215\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 186.277 | − | 1441.65i | 0.111258 | − | 0.861054i | ||||
\(142\) | 4537.07 | 2.68128 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2296.92 | + | 603.653i | 1.32924 | + | 0.349336i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4058.54i | 2.30060i | ||||||||
\(147\) | −1767.59 | − | 228.392i | −0.991755 | − | 0.128146i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 415.832 | − | 3218.24i | 0.226350 | − | 1.75179i | ||||
\(151\) | 1085.32 | 0.584917 | 0.292458 | − | 0.956278i | \(-0.405527\pi\) | ||||
0.292458 | + | 0.956278i | \(0.405527\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7589.78 | − | 980.684i | −3.89531 | − | 0.503317i | ||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1790.67 | − | 3171.47i | 0.868446 | − | 1.53811i | ||||
\(163\) | 4132.34 | 1.98571 | 0.992853 | − | 0.119344i | \(-0.0380790\pi\) | ||||
0.992853 | + | 0.119344i | \(0.0380790\pi\) | |||||||
\(164\) | 8859.76i | 4.21848i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3922.99i | − | 1.81778i | −0.417030 | − | 0.908892i | \(-0.636929\pi\) | ||
0.417030 | − | 0.908892i | \(-0.363071\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5344.14 | 2.43247 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2896.68i | 1.27301i | 0.771273 | + | 0.636505i | \(0.219620\pi\) | ||||
−0.771273 | + | 0.636505i | \(0.780380\pi\) | |||||||
\(174\) | 8016.27 | + | 1035.79i | 3.49260 | + | 0.451282i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −542.874 | + | 4201.45i | −0.230536 | + | 1.78418i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 418.343i | − | 0.174684i | −0.996178 | − | 0.0873419i | \(-0.972163\pi\) | ||
0.996178 | − | 0.0873419i | \(-0.0278373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4937.63 | −1.97830 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 489.285 | − | 3786.71i | 0.192882 | − | 1.49277i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 4744.57i | − | 1.84060i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −1532.19 | − | 197.975i | −0.575916 | − | 0.0744148i | ||||
\(193\) | 648.026 | 0.241689 | 0.120844 | − | 0.992671i | \(-0.461440\pi\) | ||||
0.120844 | + | 0.992671i | \(0.461440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5817.26 | −2.11999 | ||||||||
\(197\) | − | 4486.71i | − | 1.62267i | −0.584585 | − | 0.811333i | \(-0.698743\pi\) | ||
0.584585 | − | 0.811333i | \(-0.301257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | − | 5595.47i | − | 1.97830i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6229.58 | −2.16986 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −756.997 | + | 2880.40i | −0.254179 | + | 0.967157i | ||||
\(208\) | −7638.42 | −2.54629 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2468.00 | 0.805233 | 0.402616 | − | 0.915369i | \(-0.368101\pi\) | ||||
0.402616 | + | 0.915369i | \(0.368101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 604.700 | − | 4679.94i | 0.194523 | − | 1.50547i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2361.47 | − | 5819.29i | 0.743880 | − | 1.83311i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4186.34 | + | 540.921i | 1.29172 | + | 0.166904i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4840.00 | −1.45341 | −0.726705 | − | 0.686950i | \(-0.758949\pi\) | ||||
−0.726705 | + | 0.686950i | \(0.758949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3264.16 | − | 857.852i | −0.967157 | − | 0.254179i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13937.7 | 3.94420 | ||||||||
\(233\) | − | 2892.13i | − | 0.813174i | −0.913612 | − | 0.406587i | \(-0.866719\pi\) | ||
0.913612 | − | 0.406587i | \(-0.133281\pi\) | |||||||
\(234\) | −2977.44 | + | 11329.2i | −0.831800 | + | 3.16503i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13827.3i | 3.81390i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6097.92i | 1.65038i | 0.564852 | + | 0.825192i | \(0.308933\pi\) | ||||
−0.564852 | + | 0.825192i | \(0.691067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 6649.67i | 1.76635i | ||||||||
\(243\) | −3032.68 | − | 2269.75i | −0.800603 | − | 0.599195i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13449.5 | + | 1737.82i | 3.48581 | + | 0.450405i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 6583.86i | − | 1.68579i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 1410.29i | − | 0.348385i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8293.41 | −2.02476 | ||||||||
\(257\) | − | 936.820i | − | 0.227382i | −0.993516 | − | 0.113691i | \(-0.963733\pi\) | ||
0.993516 | − | 0.113691i | \(-0.0362674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2136.81 | − | 8130.64i | 0.506764 | − | 1.92825i | ||||
\(262\) | 9389.86 | 2.21415 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5251.15i | − | 1.19022i | −0.803646 | − | 0.595108i | \(-0.797109\pi\) | ||
0.803646 | − | 0.595108i | \(-0.202891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8912.00 | 1.99766 | 0.998829 | − | 0.0483752i | \(-0.0154043\pi\) | ||||
0.998829 | + | 0.0483752i | \(0.0154043\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1245.67 | + | 9640.56i | −0.271668 | + | 2.10251i | ||||
\(277\) | −8743.84 | −1.89663 | −0.948315 | − | 0.317331i | \(-0.897213\pi\) | ||||
−0.948315 | + | 0.317331i | \(0.897213\pi\) | |||||||
\(278\) | 13039.3i | 2.81311i | ||||||||
\(279\) | −3840.74 | − | 1009.38i | −0.824154 | − | 0.216596i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −7202.46 | − | 930.637i | −1.52092 | − | 0.196520i | ||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | − | 15402.0i | − | 3.21811i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 558.201 | − | 2123.97i | 0.114209 | − | 0.434571i | ||||
\(289\) | −4913.00 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13777.6 | 2.76120 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −1141.04 | + | 8830.85i | −0.226350 | + | 1.75179i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 9578.78i | − | 1.85269i | ||||||
\(300\) | −10925.0 | − | 1411.63i | −2.10251 | − | 0.271668i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 5422.27i | − | 1.03317i | ||||||
\(303\) | −830.278 | + | 6425.75i | −0.157420 | + | 1.21832i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10420.0 | −1.93714 | −0.968568 | − | 0.248749i | \(-0.919981\pi\) | ||||
−0.968568 | + | 0.248749i | \(0.919981\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9709.01i | 1.77025i | 0.465354 | + | 0.885125i | \(0.345927\pi\) | ||||
−0.465354 | + | 0.885125i | \(0.654073\pi\) | |||||||
\(312\) | −2588.40 | + | 20032.3i | −0.469677 | + | 3.63496i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11183.9i | 1.98154i | 0.135542 | + | 0.990772i | \(0.456723\pi\) | ||||
−0.135542 | + | 0.990772i | \(0.543277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −10766.2 | − | 6078.80i | −1.84606 | − | 1.04232i | ||||
\(325\) | 10855.0 | 1.85269 | ||||||||
\(326\) | − | 20645.2i | − | 3.50745i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23384.3 | 3.93653 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5997.08 | −0.995859 | −0.497930 | − | 0.867218i | \(-0.665906\pi\) | ||||
−0.497930 | + | 0.867218i | \(0.665906\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19599.2 | −3.21084 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | − | 26699.3i | − | 4.29660i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14471.8 | 2.24858 | ||||||||
\(347\) | − | 9102.49i | − | 1.40821i | −0.710098 | − | 0.704103i | \(-0.751350\pi\) | ||
0.710098 | − | 0.704103i | \(-0.248650\pi\) | |||||||
\(348\) | 3516.21 | − | 27212.9i | 0.541633 | − | 4.19185i | ||||
\(349\) | −12386.8 | −1.89986 | −0.949929 | − | 0.312467i | \(-0.898845\pi\) | ||||
−0.949929 | + | 0.312467i | \(0.898845\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11289.2 | + | 4581.16i | 1.71673 | + | 0.696650i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9374.23i | 1.41343i | 0.707499 | + | 0.706714i | \(0.249823\pi\) | ||||
−0.707499 | + | 0.706714i | \(0.750177\pi\) | |||||||
\(354\) | 20990.4 | + | 2712.19i | 3.15149 | + | 0.407208i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2090.04 | −0.308553 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6859.00 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6859.06 | + | 886.266i | 0.991755 | + | 0.128146i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 9702.34i | 1.37437i | ||||||||
\(369\) | 3585.09 | − | 13641.4i | 0.505779 | − | 1.92451i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −12854.8 | − | 1660.98i | −1.79164 | − | 0.231499i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12522.7 | −1.71758 | ||||||||
\(377\) | 27038.5i | 3.69378i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1454.70 | − | 187.964i | −0.195608 | − | 0.0252748i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | −1422.36 | + | 11008.0i | −0.189022 | + | 1.46289i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3237.53i | − | 0.426907i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15354.0i | 1.97830i | ||||||||
\(393\) | 1251.48 | − | 9685.54i | 0.160633 | − | 1.24318i | ||||
\(394\) | −22415.6 | −2.86620 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11677.7 | 1.47629 | 0.738145 | − | 0.674642i | \(-0.235702\pi\) | ||||
0.738145 | + | 0.674642i | \(0.235702\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10995.0 | −1.37437 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12772.4 | 1.57876 | ||||||||
\(404\) | 21147.6i | 2.60429i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11155.1 | −1.34862 | −0.674308 | − | 0.738451i | \(-0.735558\pi\) | ||||
−0.674308 | + | 0.738451i | \(0.735558\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14390.4 | + | 3781.95i | 1.70834 | + | 0.448968i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7063.28i | 0.832466i | ||||||||
\(417\) | 13449.9 | + | 1737.87i | 1.57948 | + | 0.204086i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | − | 12330.1i | − | 1.42232i | ||||||
\(423\) | −1919.88 | + | 7305.22i | −0.220681 | + | 0.839697i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −23380.9 | − | 3021.08i | −2.65918 | − | 0.343595i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −11434.8 | − | 4640.25i | −1.27351 | − | 0.516792i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2702.44 | − | 20914.9i | 0.294812 | − | 2.28163i | ||||
\(439\) | −10984.0 | −1.19416 | −0.597080 | − | 0.802182i | \(-0.703672\pi\) | ||||
−0.597080 | + | 0.802182i | \(0.703672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8956.84 | + | 2353.95i | 0.967157 | + | 0.254179i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 18198.2i | − | 1.95174i | −0.218352 | − | 0.975870i | \(-0.570068\pi\) | ||
0.218352 | − | 0.975870i | \(-0.429932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24180.6i | 2.56723i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4795.83i | 0.504074i | 0.967718 | + | 0.252037i | \(0.0811005\pi\) | ||||
−0.967718 | + | 0.252037i | \(0.918900\pi\) | |||||||
\(450\) | −4285.82 | + | 16307.7i | −0.448968 | + | 1.70834i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5593.01 | − | 722.679i | −0.580094 | − | 0.0749546i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7066.71i | 0.713947i | 0.934115 | + | 0.356973i | \(0.116191\pi\) | ||||
−0.934115 | + | 0.356973i | \(0.883809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11680.0 | −1.17239 | −0.586194 | − | 0.810171i | \(-0.699374\pi\) | ||||
−0.586194 | + | 0.810171i | \(0.699374\pi\) | |||||||
\(464\) | − | 27387.3i | − | 2.74013i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14449.0 | −1.43635 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 38459.5 | + | 10107.5i | 3.79870 | + | 0.998336i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36495.5 | 3.55899 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 30465.2 | 2.91516 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22573.7 | 2.11999 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11339.6 | + | 15151.2i | −1.05839 | + | 1.41414i | ||||
\(487\) | 17336.9 | 1.61316 | 0.806580 | − | 0.591125i | \(-0.201316\pi\) | ||||
0.806580 | + | 0.591125i | \(0.201316\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21295.3 | − | 2751.58i | −1.96933 | − | 0.254460i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21296.6i | − | 1.95744i | −0.205206 | − | 0.978719i | \(-0.565786\pi\) | ||
0.205206 | − | 0.978719i | \(-0.434214\pi\) | |||||||
\(492\) | 5899.40 | − | 45657.1i | 0.540581 | − | 4.18370i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12937.2 | −1.17116 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5737.17 | 0.514691 | 0.257346 | − | 0.966319i | \(-0.417152\pi\) | ||||
0.257346 | + | 0.966319i | \(0.417152\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2612.18 | + | 20216.4i | −0.232941 | + | 1.80280i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −27540.0 | − | 3558.48i | −2.41242 | − | 0.311711i | ||||
\(508\) | −4787.54 | −0.418135 | ||||||||
\(509\) | − | 3876.14i | − | 0.337538i | −0.985656 | − | 0.168769i | \(-0.946021\pi\) | ||
0.985656 | − | 0.168769i | \(-0.0539792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24344.9i | 2.10138i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4680.34 | −0.401636 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1928.80 | − | 14927.5i | 0.163131 | − | 1.26251i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | −40620.6 | − | 10675.5i | −3.40597 | − | 0.895123i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | − | 31875.8i | − | 2.65745i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5595.20 | − | 21289.9i | 0.457271 | − | 1.73993i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45364.5i | 3.68659i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −278.560 | + | 2155.85i | −0.0223850 | + | 0.173244i | ||||
\(538\) | −26234.7 | −2.10234 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22247.0 | 1.76797 | 0.883985 | − | 0.467515i | \(-0.154851\pi\) | ||||
0.883985 | + | 0.467515i | \(0.154851\pi\) | |||||||
\(542\) | − | 44524.3i | − | 3.52856i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22901.7 | −1.79014 | −0.895068 | − | 0.445930i | \(-0.852873\pi\) | ||||
−0.895068 | + | 0.445930i | \(0.852873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 25445.1 | + | 3287.79i | 1.96199 | + | 0.253510i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 43684.2i | 3.35011i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 44264.5 | 3.37632 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | −5042.88 | + | 19188.3i | −0.382584 | + | 1.45575i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | −3159.24 | + | 24450.2i | −0.235865 | + | 1.82543i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −40651.8 | −3.00302 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 13788.0i | − | 1.00000i | ||||||
\(576\) | 7764.00 | + | 2040.46i | 0.561632 | + | 0.147603i | ||||
\(577\) | −3963.24 | −0.285948 | −0.142974 | − | 0.989726i | \(-0.545667\pi\) | ||||
−0.142974 | + | 0.989726i | \(0.545667\pi\) | |||||||
\(578\) | 24545.3i | 1.76635i | ||||||||
\(579\) | −3339.48 | − | 431.498i | −0.239696 | − | 0.0309714i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 36364.2i | − | 2.57665i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12321.1i | − | 0.866344i | −0.901311 | − | 0.433172i | \(-0.857394\pi\) | ||
0.901311 | − | 0.433172i | \(-0.142606\pi\) | |||||||
\(588\) | 29978.1 | + | 3873.51i | 2.10251 | + | 0.271668i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2987.55 | + | 23121.4i | −0.207938 | + | 1.60929i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11778.6i | − | 0.815662i | −0.913057 | − | 0.407831i | \(-0.866285\pi\) | ||
0.913057 | − | 0.407831i | \(-0.133715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −47855.5 | −3.27250 | ||||||||
\(599\) | − | 16353.8i | − | 1.11552i | −0.830002 | − | 0.557761i | \(-0.811661\pi\) | ||
0.830002 | − | 0.557761i | \(-0.188339\pi\) | |||||||
\(600\) | −3725.83 | + | 28835.2i | −0.253510 | + | 1.96199i | ||||
\(601\) | 25354.9 | 1.72088 | 0.860441 | − | 0.509550i | \(-0.170188\pi\) | ||||
0.860441 | + | 0.509550i | \(0.170188\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18407.0 | −1.24002 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 32103.0 | + | 4148.06i | 2.15197 | + | 0.278059i | ||||
\(607\) | 8840.00 | 0.591111 | 0.295556 | − | 0.955326i | \(-0.404495\pi\) | ||||
0.295556 | + | 0.955326i | \(0.404495\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 24293.5i | − | 1.60853i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 52058.2i | 3.42166i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5819.00 | − | 14339.5i | 0.376020 | − | 0.926612i | ||||
\(622\) | 48506.2 | 3.12688 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 39363.2 | + | 5086.16i | 2.52530 | + | 0.326297i | ||||
\(625\) | 15625.0 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12718.4 | − | 1643.35i | −0.798594 | − | 0.103187i | ||||
\(634\) | 55874.6 | 3.50010 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29786.0 | −1.85269 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6232.41 | + | 23714.5i | −0.385838 | + | 1.46813i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16636.7i | 1.01091i | 0.862854 | + | 0.505454i | \(0.168675\pi\) | ||||
−0.862854 | + | 0.505454i | \(0.831325\pi\) | |||||||
\(648\) | −16044.3 | + | 28416.2i | −0.972652 | + | 1.72268i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 54231.3i | − | 3.27250i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −70084.3 | −4.20968 | ||||||||
\(653\) | − | 6538.77i | − | 0.391856i | −0.980618 | − | 0.195928i | \(-0.937228\pi\) | ||
0.980618 | − | 0.195928i | \(-0.0627719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 45949.7i | − | 2.73481i | ||||||
\(657\) | −21213.3 | − | 5575.07i | −1.25968 | − | 0.331057i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 29961.4i | 1.75904i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34344.4 | 1.99373 | ||||||||
\(668\) | 66533.7i | 3.85369i | ||||||||
\(669\) | 24942.0 | + | 3222.79i | 1.44143 | + | 0.186248i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8519.60 | 0.487974 | 0.243987 | − | 0.969778i | \(-0.421545\pi\) | ||||
0.243987 | + | 0.969778i | \(0.421545\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16250.0 | + | 6594.27i | 0.926612 | + | 0.376020i | ||||
\(676\) | −90636.3 | −5.15682 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33067.2i | − | 1.85253i | −0.376867 | − | 0.926267i | \(-0.622999\pi\) | ||
0.376867 | − | 0.926267i | \(-0.377001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6028.00 | −0.331861 | −0.165930 | − | 0.986137i | \(-0.553063\pi\) | ||||
−0.165930 | + | 0.986137i | \(0.553063\pi\) | |||||||
\(692\) | − | 49127.5i | − | 2.69877i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −45476.0 | −2.48738 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −71825.2 | − | 9280.61i | −3.91168 | − | 0.505432i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 61884.4i | 3.35581i | ||||||||
\(699\) | −1925.77 | + | 14904.0i | −0.104205 | + | 0.806470i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 22887.4 | − | 56400.6i | 1.23053 | − | 3.03234i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 46833.6 | 2.49661 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9207.11 | − | 71256.3i | 0.488735 | − | 3.78245i | ||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16223.5i | − | 0.852141i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7095.07i | 0.370328i | ||||||||
\(717\) | 4060.39 | − | 31424.5i | 0.211490 | − | 1.63678i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 6858.04i | − | 0.355719i | −0.984056 | − | 0.177859i | \(-0.943083\pi\) | ||
0.984056 | − | 0.177859i | \(-0.0569172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 34267.5i | − | 1.76635i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38920.1i | 1.99373i | ||||||||
\(726\) | 4427.78 | − | 34267.8i | 0.226350 | − | 1.75179i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14117.0 | + | 13716.1i | 0.717218 | + | 0.696849i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8971.81 | 0.449328 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −68152.3 | − | 17911.1i | −3.39935 | − | 0.893383i | ||||
\(739\) | 7328.32 | 0.364786 | 0.182393 | − | 0.983226i | \(-0.441616\pi\) | ||||
0.182393 | + | 0.983226i | \(0.441616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | −4383.96 | + | 33928.7i | −0.216027 | + | 1.67189i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 24606.9i | 1.19325i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 135084. | 6.52450 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26268.3i | − | 1.25128i | −0.780111 | − | 0.625641i | \(-0.784837\pi\) | ||
0.780111 | − | 0.625641i | \(-0.215163\pi\) | |||||||
\(762\) | −939.066 | + | 7267.69i | −0.0446441 | + | 0.345513i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 70799.7i | 3.33302i | ||||||||
\(768\) | 42738.5 | + | 5522.29i | 2.00806 | + | 0.259464i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −623.796 | + | 4827.72i | −0.0291381 | + | 0.225507i | ||||
\(772\) | −10990.5 | −0.512378 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18385.0 | 0.852141 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16425.6 | + | 40476.9i | −0.749683 | + | 1.84742i | ||||
\(784\) | 30170.3 | 1.37437 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −48388.9 | − | 6252.38i | −2.19590 | − | 0.283734i | ||||
\(787\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(788\) | 76094.4i | 3.44004i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | − | 58341.7i | − | 2.60764i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 10167.1i | 0.449328i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 63810.8i | − | 2.78864i | ||||||
\(807\) | −3496.56 | + | 27060.8i | −0.152521 | + | 1.18040i | ||||
\(808\) | 55816.7 | 2.43023 | ||||||||
\(809\) | − | 36640.2i | − | 1.59234i | −0.605076 | − | 0.796168i | \(-0.706857\pi\) | ||
0.605076 | − | 0.796168i | \(-0.293143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38214.7 | −1.65462 | −0.827312 | − | 0.561743i | \(-0.810131\pi\) | ||||
−0.827312 | + | 0.561743i | \(0.810131\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −45926.3 | − | 5934.19i | −1.98119 | − | 0.255991i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 55730.7i | 2.38213i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40189.1i | 1.70841i | 0.519933 | + | 0.854207i | \(0.325957\pi\) | ||||
−0.519933 | + | 0.854207i | \(0.674043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29161.0 | −1.23510 | −0.617550 | − | 0.786532i | \(-0.711875\pi\) | ||||
−0.617550 | + | 0.786532i | \(0.711875\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 12838.6 | − | 48851.4i | 0.538856 | − | 2.05037i | ||||
\(829\) | −4966.00 | −0.208053 | −0.104027 | − | 0.994575i | \(-0.533173\pi\) | ||||
−0.104027 | + | 0.994575i | \(0.533173\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 45059.7 | + | 5822.22i | 1.88099 | + | 0.243045i | ||||
\(832\) | −25819.2 | −1.07587 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8682.39 | − | 67195.4i | 0.360488 | − | 2.78991i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19120.4 | + | 7759.09i | 0.789604 | + | 0.320422i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −72556.6 | −2.97497 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −41857.1 | −1.70709 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 36496.8 | + | 9591.73i | 1.48320 | + | 0.389799i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −10255.7 | + | 79371.4i | −0.412387 | + | 3.19157i | ||||
\(853\) | 24590.0 | 0.987041 | 0.493520 | − | 0.869734i | \(-0.335710\pi\) | ||||
0.493520 | + | 0.869734i | \(0.335710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 44702.2i | − | 1.78179i | −0.454205 | − | 0.890897i | \(-0.650077\pi\) | ||
0.454205 | − | 0.890897i | \(-0.349923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25747.2 | −1.02268 | −0.511340 | − | 0.859379i | \(-0.670851\pi\) | ||||
−0.511340 | + | 0.859379i | \(0.670851\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20690.6i | 0.816125i | 0.912954 | + | 0.408063i | \(0.133795\pi\) | ||||
−0.912954 | + | 0.408063i | \(0.866205\pi\) | |||||||
\(864\) | −4290.86 | + | 10573.8i | −0.168956 | + | 0.416352i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25318.2 | + | 3271.39i | 0.991755 | + | 0.128146i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −71000.0 | − | 9173.99i | −2.73844 | − | 0.353836i | ||||
\(877\) | −34090.0 | −1.31259 | −0.656293 | − | 0.754506i | \(-0.727876\pi\) | ||||
−0.656293 | + | 0.754506i | \(0.727876\pi\) | |||||||
\(878\) | 54875.8i | 2.10930i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 11760.3 | − | 44748.3i | 0.448968 | − | 1.70834i | ||||
\(883\) | −2860.00 | −0.109000 | −0.0544998 | − | 0.998514i | \(-0.517356\pi\) | ||||
−0.0544998 | + | 0.998514i | \(0.517356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −90917.9 | −3.44746 | ||||||||
\(887\) | 28407.6i | 1.07535i | 0.843153 | + | 0.537673i | \(0.180697\pi\) | ||||
−0.843153 | + | 0.537673i | \(0.819303\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 82086.1 | 3.08122 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6378.18 | + | 49362.5i | −0.237415 | + | 1.83742i | ||||
\(898\) | 23959.9 | 0.890371 | ||||||||
\(899\) | 45795.0i | 1.69894i | ||||||||
\(900\) | 55359.9 | + | 14549.1i | 2.05037 | + | 0.538856i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3610.50 | + | 27942.6i | −0.132396 | + | 1.02465i | ||||
\(907\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8557.36 | − | 32561.0i | 0.312244 | − | 1.18810i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53697.5 | + | 6938.31i | 1.92117 | + | 0.248236i | ||||
\(922\) | 35305.2 | 1.26108 | ||||||||
\(923\) | − | 78862.8i | − | 2.81235i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 58353.2i | 2.07085i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25325.2 | −0.895839 | ||||||||
\(929\) | − | 56624.7i | − | 1.99978i | −0.0148179 | − | 0.999890i | \(-0.504717\pi\) | ||
0.0148179 | − | 0.999890i | \(-0.495283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 49050.3i | 1.72392i | ||||||||
\(933\) | 6464.89 | − | 50033.6i | 0.226850 | − | 1.75565i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 26677.7 | − | 101509.i | 0.931610 | − | 3.54480i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57622.2 | 1.98986 | ||||||||
\(944\) | − | 71713.0i | − | 2.47252i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44151.8i | 1.51504i | 0.652814 | + | 0.757518i | \(0.273588\pi\) | ||||
−0.652814 | + | 0.757518i | \(0.726412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 70545.0 | 2.41305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7446.95 | − | 57634.0i | 0.253926 | − | 1.96521i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 103420.i | − | 3.49880i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8158.44 | −0.273856 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47303.2 | −1.57308 | −0.786540 | − | 0.617539i | \(-0.788130\pi\) | ||||
−0.786540 | + | 0.617539i | \(0.788130\pi\) | |||||||
\(968\) | − | 59580.6i | − | 1.97830i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 51434.1 | + | 38494.8i | 1.69727 | + | 1.27029i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 86614.9i | − | 2.84941i | ||||||
\(975\) | −55939.0 | − | 7227.94i | −1.83742 | − | 0.237415i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | −13746.9 | + | 106391.i | −0.449465 | + | 3.47853i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −106398. | −3.45752 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | −120507. | − | 15570.8i | −3.90407 | − | 0.504450i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9128.00 | 0.292594 | 0.146297 | − | 0.989241i | \(-0.453265\pi\) | ||||
0.146297 | + | 0.989241i | \(0.453265\pi\) | |||||||
\(992\) | 11963.1i | 0.382891i | ||||||||
\(993\) | 30904.8 | + | 3993.25i | 0.987649 | + | 0.127615i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60190.0 | −1.91197 | −0.955986 | − | 0.293412i | \(-0.905209\pi\) | ||||
−0.955986 | + | 0.293412i | \(0.905209\pi\) | |||||||
\(998\) | − | 28662.9i | − | 0.909125i | ||||||
\(999\) | 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 | 69.4.c.b.68.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 69.4.c.b.68.4 | yes | 4 | |
23.22 | odd | 2 | CM | 69.4.c.b.68.1 | ✓ | 4 | |
69.68 | even | 2 | inner | 69.4.c.b.68.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.4.c.b.68.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
69.4.c.b.68.1 | ✓ | 4 | 23.22 | odd | 2 | CM | |
69.4.c.b.68.4 | yes | 4 | 3.2 | odd | 2 | inner | |
69.4.c.b.68.4 | yes | 4 | 69.68 | even | 2 | inner |