Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.110166016.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 729.3 | ||
Root | \(0.360409i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.729 |
Dual form | 1148.2.k.a.337.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.254848 | − | 0.254848i | 0.147136 | − | 0.147136i | −0.629701 | − | 0.776838i | \(-0.716823\pi\) |
0.776838 | + | 0.629701i | \(0.216823\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.56350i | − | 0.699218i | −0.936896 | − | 0.349609i | \(-0.886314\pi\) | ||
0.936896 | − | 0.349609i | \(-0.113686\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.87011i | 0.956702i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.48173 | − | 4.48173i | 1.35129 | − | 1.35129i | 0.467074 | − | 0.884218i | \(-0.345308\pi\) |
0.884218 | − | 0.467074i | \(-0.154692\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.972034 | + | 0.972034i | −0.269594 | + | 0.269594i | −0.828936 | − | 0.559343i | \(-0.811054\pi\) |
0.559343 | + | 0.828936i | \(0.311054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.398455 | − | 0.398455i | −0.102881 | − | 0.102881i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.04523 | − | 4.04523i | −0.981112 | − | 0.981112i | 0.0187126 | − | 0.999825i | \(-0.494043\pi\) |
−0.999825 | + | 0.0187126i | \(0.994043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.81835 | − | 1.81835i | −0.417158 | − | 0.417158i | 0.467065 | − | 0.884223i | \(-0.345311\pi\) |
−0.884223 | + | 0.467065i | \(0.845311\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.360409i | − | 0.0786478i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.75523 | 0.574505 | 0.287253 | − | 0.957855i | \(-0.407258\pi\) | ||||
0.287253 | + | 0.957855i | \(0.407258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.55547 | 0.511094 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.49598 | + | 1.49598i | 0.287902 | + | 0.287902i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.30297 | + | 1.30297i | −0.241956 | + | 0.241956i | −0.817659 | − | 0.575703i | \(-0.804728\pi\) |
0.575703 | + | 0.817659i | \(0.304728\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.14929 | 0.745234 | 0.372617 | − | 0.927985i | \(-0.378461\pi\) | ||||
0.372617 | + | 0.927985i | \(0.378461\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.28432i | − | 0.397649i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.10556 | − | 1.10556i | −0.186874 | − | 0.186874i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.41421 | −0.890091 | −0.445046 | − | 0.895508i | \(-0.646813\pi\) | ||||
−0.445046 | + | 0.895508i | \(0.646813\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.495442i | 0.0793341i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.29857 | − | 6.27006i | 0.202803 | − | 0.979220i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.26203i | 0.649954i | 0.945722 | + | 0.324977i | \(0.105357\pi\) | ||||
−0.945722 | + | 0.324977i | \(0.894643\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.48741 | 0.668943 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0142542 | + | 0.0142542i | 0.00207919 | + | 0.00207919i | 0.708146 | − | 0.706066i | \(-0.249532\pi\) |
−0.706066 | + | 0.708146i | \(0.749532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.06184 | −0.288715 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1645 | − | 10.1645i | 1.39620 | − | 1.39620i | 0.585606 | − | 0.810596i | \(-0.300857\pi\) |
0.810596 | − | 0.585606i | \(-0.199143\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.00718 | − | 7.00718i | −0.944849 | − | 0.944849i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.926804 | −0.122758 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.7696 | −1.92284 | −0.961419 | − | 0.275088i | \(-0.911293\pi\) | ||||
−0.961419 | + | 0.275088i | \(0.911293\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.4610i | − | 1.72351i | −0.507326 | − | 0.861754i | \(-0.669366\pi\) | ||
0.507326 | − | 0.861754i | \(-0.330634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.02947 | + | 2.02947i | 0.255689 | + | 0.255689i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.51978 | + | 1.51978i | 0.188505 | + | 0.188505i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.159366 | + | 0.159366i | 0.0194696 | + | 0.0194696i | 0.716775 | − | 0.697305i | \(-0.245618\pi\) |
−0.697305 | + | 0.716775i | \(0.745618\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.702165 | − | 0.702165i | 0.0845307 | − | 0.0845307i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.37123 | − | 9.37123i | 1.11216 | − | 1.11216i | 0.119302 | − | 0.992858i | \(-0.461934\pi\) |
0.992858 | − | 0.119302i | \(-0.0380656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.11564i | 0.247617i | 0.992306 | + | 0.123809i | \(0.0395109\pi\) | ||||
−0.992306 | + | 0.123809i | \(0.960489\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.651256 | − | 0.651256i | 0.0752005 | − | 0.0752005i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.33812i | − | 0.722296i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.39193 | − | 3.39193i | 0.381622 | − | 0.381622i | −0.490065 | − | 0.871686i | \(-0.663027\pi\) |
0.871686 | + | 0.490065i | \(0.163027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.84782 | −0.871980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.91178 | −1.08796 | −0.543980 | − | 0.839098i | \(-0.683083\pi\) | ||||
−0.543980 | + | 0.839098i | \(0.683083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.32472 | + | 6.32472i | −0.686012 | + | 0.686012i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.664120i | 0.0712011i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.39791 | − | 3.39791i | 0.360178 | − | 0.360178i | −0.503700 | − | 0.863878i | \(-0.668028\pi\) |
0.863878 | + | 0.503700i | \(0.168028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.37466i | 0.144104i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.05744 | − | 1.05744i | 0.109651 | − | 0.109651i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.84299 | + | 2.84299i | −0.291684 | + | 0.291684i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.5392 | + | 11.5392i | 1.17162 | + | 1.17162i | 0.981822 | + | 0.189803i | \(0.0607848\pi\) |
0.189803 | + | 0.981822i | \(0.439215\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.8630 | + | 12.8630i | 1.29278 | + | 1.29278i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3010 | + | 12.3010i | 1.22400 | + | 1.22400i | 0.966198 | + | 0.257801i | \(0.0829980\pi\) |
0.257801 | + | 0.966198i | \(0.417002\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5076i | 1.42947i | 0.699394 | + | 0.714737i | \(0.253453\pi\) | ||||
−0.699394 | + | 0.714737i | \(0.746547\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.563500 | −0.0549920 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.5830 | −1.40979 | −0.704896 | − | 0.709310i | \(-0.749006\pi\) | ||||
−0.704896 | + | 0.709310i | \(0.749006\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.08123 | − | 8.08123i | −0.774041 | − | 0.774041i | 0.204769 | − | 0.978810i | \(-0.434356\pi\) |
−0.978810 | + | 0.204769i | \(0.934356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.37980 | + | 1.37980i | −0.130965 | + | 0.130965i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.9353 | 1.59314 | 0.796568 | − | 0.604549i | \(-0.206647\pi\) | ||||
0.796568 | + | 0.604549i | \(0.206647\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.30780i | − | 0.401705i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.78984 | − | 2.78984i | −0.257921 | − | 0.257921i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.72082 | −0.524427 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 29.1718i | − | 2.65198i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.26697 | − | 1.92885i | −0.114239 | − | 0.173919i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.8130i | − | 1.05658i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.10985 | −0.187219 | −0.0936095 | − | 0.995609i | \(-0.529841\pi\) | ||||
−0.0936095 | + | 0.995609i | \(0.529841\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.08617 | + | 1.08617i | 0.0956319 | + | 0.0956319i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4703i | 1.52638i | 0.646172 | + | 0.763192i | \(0.276369\pi\) | ||||
−0.646172 | + | 0.763192i | \(0.723631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.57153 | −0.222980 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.33897 | − | 2.33897i | 0.201307 | − | 0.201307i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.8853 | + | 13.8853i | 1.18630 | + | 1.18630i | 0.978082 | + | 0.208221i | \(0.0667674\pi\) |
0.208221 | + | 0.978082i | \(0.433233\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.29826 | 0.194935 | 0.0974677 | − | 0.995239i | \(-0.468926\pi\) | ||||
0.0974677 | + | 0.995239i | \(0.468926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.00726530 | 0.000611849 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.71279i | 0.728600i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.03720 | + | 2.03720i | 0.169180 | + | 0.169180i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.254848 | − | 0.254848i | −0.0210195 | − | 0.0210195i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.30448 | − | 7.30448i | −0.598406 | − | 0.598406i | 0.341482 | − | 0.939888i | \(-0.389071\pi\) |
−0.939888 | + | 0.341482i | \(0.889071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.04736 | + | 8.04736i | −0.654885 | + | 0.654885i | −0.954165 | − | 0.299280i | \(-0.903253\pi\) |
0.299280 | + | 0.954165i | \(0.403253\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.6102 | − | 11.6102i | 0.938632 | − | 0.938632i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 6.48741i | − | 0.521081i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6499 | + | 12.6499i | −1.00957 | + | 1.00957i | −0.00961539 | + | 0.999954i | \(0.503061\pi\) |
−0.999954 | + | 0.00961539i | \(0.996939\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.18080i | − | 0.410865i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.94824 | − | 1.94824i | 0.153543 | − | 0.153543i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.4762 | 1.36884 | 0.684419 | − | 0.729089i | \(-0.260056\pi\) | ||||
0.684419 | + | 0.729089i | \(0.260056\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.57153 | −0.278043 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.47037 | − | 5.47037i | 0.423310 | − | 0.423310i | −0.463032 | − | 0.886342i | \(-0.653238\pi\) |
0.886342 | + | 0.463032i | \(0.153238\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1103i | 0.854638i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.21885 | − | 5.21885i | 0.399095 | − | 0.399095i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.42858i | − | 0.336699i | −0.985727 | − | 0.168349i | \(-0.946156\pi\) | ||
0.985727 | − | 0.168349i | \(-0.0538437\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.80699 | − | 1.80699i | 0.136595 | − | 0.136595i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.76400 | + | 3.76400i | −0.282920 | + | 0.282920i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.3504 | + | 13.3504i | 0.997859 | + | 0.997859i | 0.999998 | − | 0.00213863i | \(-0.000680749\pi\) |
−0.00213863 | + | 0.999998i | \(0.500681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.94844 | − | 9.94844i | −0.739462 | − | 0.739462i | 0.233012 | − | 0.972474i | \(-0.425142\pi\) |
−0.972474 | + | 0.233012i | \(0.925142\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.43051 | − | 3.43051i | −0.253591 | − | 0.253591i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.46512i | 0.622368i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −36.2593 | −2.65154 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.11564 | 0.153890 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.99711 | + | 5.99711i | 0.433935 | + | 0.433935i | 0.889965 | − | 0.456029i | \(-0.150729\pi\) |
−0.456029 | + | 0.889965i | \(0.650729\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3295 | + | 14.3295i | −1.03146 | + | 1.03146i | −0.0319748 | + | 0.999489i | \(0.510180\pi\) |
−0.999489 | + | 0.0319748i | \(0.989820\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.774623 | 0.0554719 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.3067i | 1.37555i | 0.725925 | + | 0.687773i | \(0.241412\pi\) | ||||
−0.725925 | + | 0.687773i | \(0.758588\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.292893 | − | 0.292893i | −0.0207626 | − | 0.0207626i | 0.696649 | − | 0.717412i | \(-0.254673\pi\) |
−0.717412 | + | 0.696649i | \(0.754673\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.0812280 | 0.00572938 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.84268i | 0.129331i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.80325 | − | 2.03032i | −0.684688 | − | 0.141804i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.90780i | 0.549630i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.2987 | −1.12740 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.80251 | + | 9.80251i | 0.674832 | + | 0.674832i | 0.958826 | − | 0.283994i | \(-0.0916595\pi\) |
−0.283994 | + | 0.958826i | \(0.591659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 4.77647i | − | 0.327279i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.66369 | 0.454460 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.93399 | − | 2.93399i | 0.199172 | − | 0.199172i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.539167 | + | 0.539167i | 0.0364335 | + | 0.0364335i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.86420 | 0.529003 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.52619 | −0.236131 | −0.118066 | − | 0.993006i | \(-0.537669\pi\) | ||||
−0.118066 | + | 0.993006i | \(0.537669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.33446i | 0.488964i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9973 | + | 11.9973i | 0.796291 | + | 0.796291i | 0.982508 | − | 0.186218i | \(-0.0596230\pi\) |
−0.186218 | + | 0.982508i | \(0.559623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.7088 | − | 20.7088i | −1.36848 | − | 1.36848i | −0.862614 | − | 0.505862i | \(-0.831174\pi\) |
−0.505862 | − | 0.862614i | \(-0.668826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.61526 | − | 1.61526i | −0.106276 | − | 0.106276i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8698 | + | 12.8698i | −0.843129 | + | 0.843129i | −0.989265 | − | 0.146136i | \(-0.953316\pi\) |
0.146136 | + | 0.989265i | \(0.453316\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0222864 | − | 0.0222864i | 0.00145381 | − | 0.00145381i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.72885i | − | 0.112301i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7955 | + | 14.7955i | −0.957043 | + | 0.957043i | −0.999115 | − | 0.0420720i | \(-0.986604\pi\) |
0.0420720 | + | 0.999115i | \(0.486604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.11973i | − | 0.329791i | −0.986311 | − | 0.164896i | \(-0.947271\pi\) | ||
0.986311 | − | 0.164896i | \(-0.0527287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.48795 | + | 6.48795i | −0.416202 | + | 0.416202i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.56350 | −0.0998884 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.53499 | 0.224926 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.52600 | + | 2.52600i | −0.160079 | + | 0.160079i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4051i | 1.09860i | 0.835625 | + | 0.549300i | \(0.185106\pi\) | ||||
−0.835625 | + | 0.549300i | \(0.814894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.3482 | − | 12.3482i | 0.776325 | − | 0.776325i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.22368i | 0.201875i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.694981 | + | 0.694981i | −0.0433517 | + | 0.0433517i | −0.728450 | − | 0.685099i | \(-0.759759\pi\) |
0.685099 | + | 0.728450i | \(0.259759\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.82843 | + | 3.82843i | −0.237887 | + | 0.237887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.73967 | − | 3.73967i | −0.231480 | − | 0.231480i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0938966 | + | 0.0938966i | 0.00578991 | + | 0.00578991i | 0.709996 | − | 0.704206i | \(-0.248697\pi\) |
−0.704206 | + | 0.709996i | \(0.748697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.8922 | − | 15.8922i | −0.976250 | − | 0.976250i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1.73190i | − | 0.105991i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.4227 | 0.757424 | 0.378712 | − | 0.925515i | \(-0.376367\pi\) | ||||
0.378712 | + | 0.925515i | \(0.376367\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.2913 | 0.685898 | 0.342949 | − | 0.939354i | \(-0.388574\pi\) | ||||
0.342949 | + | 0.939354i | \(0.388574\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.350330 | + | 0.350330i | 0.0212029 | + | 0.0212029i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.4529 | − | 11.4529i | 0.690637 | − | 0.690637i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.58880 | −0.0954615 | −0.0477307 | − | 0.998860i | \(-0.515199\pi\) | ||||
−0.0477307 | + | 0.998860i | \(0.515199\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.9089i | 0.712966i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.72951 | + | 7.72951i | 0.461104 | + | 0.461104i | 0.899017 | − | 0.437913i | \(-0.144282\pi\) |
−0.437913 | + | 0.899017i | \(0.644282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2764 | 0.670312 | 0.335156 | − | 0.942163i | \(-0.391211\pi\) | ||||
0.335156 | + | 0.942163i | \(0.391211\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.44906i | 0.0858348i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.51538 | − | 5.35183i | −0.207506 | − | 0.315909i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.7278i | 0.925163i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.88146 | 0.344778 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.41476 | + | 6.41476i | 0.374754 | + | 0.374754i | 0.869205 | − | 0.494451i | \(-0.164631\pi\) |
−0.494451 | + | 0.869205i | \(0.664631\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.0923i | 1.34448i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.4092 | 0.778080 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.67818 | + | 2.67818i | −0.154883 | + | 0.154883i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.01371 | + | 3.01371i | 0.173707 | + | 0.173707i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.26979 | 0.360190 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.0463 | −1.20511 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.1776i | − | 1.20867i | −0.796731 | − | 0.604334i | \(-0.793439\pi\) | ||
0.796731 | − | 0.604334i | \(-0.206561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.69722 | + | 3.69722i | 0.210328 | + | 0.210328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.89100 | + | 1.89100i | 0.107229 | + | 0.107229i | 0.758686 | − | 0.651457i | \(-0.225842\pi\) |
−0.651457 | + | 0.758686i | \(0.725842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.31197 | + | 1.31197i | 0.0741568 | + | 0.0741568i | 0.743212 | − | 0.669056i | \(-0.233301\pi\) |
−0.669056 | + | 0.743212i | \(0.733301\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.17308 | − | 3.17308i | 0.178783 | − | 0.178783i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.5752 | − | 23.5752i | 1.32412 | − | 1.32412i | 0.413703 | − | 0.910412i | \(-0.364235\pi\) |
0.910412 | − | 0.413703i | \(-0.135765\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.6791i | 0.653906i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.71645 | + | 3.71645i | −0.207432 | + | 0.207432i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.7113i | 0.818557i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.48400 | + | 2.48400i | −0.137788 | + | 0.137788i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.11897 | −0.227779 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0201585 | 0.00111137 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3078 | + | 17.3078i | −0.951323 | + | 0.951323i | −0.998869 | − | 0.0475461i | \(-0.984860\pi\) |
0.0475461 | + | 0.998869i | \(0.484860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 15.5394i | − | 0.851552i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.249168 | − | 0.249168i | 0.0136135 | − | 0.0136135i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.9402i | 1.63095i | 0.578795 | + | 0.815473i | \(0.303523\pi\) | ||||
−0.578795 | + | 0.815473i | \(0.696477\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.31592 | − | 4.31592i | 0.234408 | − | 0.234408i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.5960 | − | 18.5960i | 1.00703 | − | 1.00703i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.09783 | − | 1.09783i | −0.0591054 | − | 0.0591054i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.8256 | + | 20.8256i | 1.11798 | + | 1.11798i | 0.992038 | + | 0.125942i | \(0.0401952\pi\) |
0.125942 | + | 0.992038i | \(0.459805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5168i | 1.04471i | 0.852728 | + | 0.522355i | \(0.174946\pi\) | ||||
−0.852728 | + | 0.522355i | \(0.825054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.90829 | −0.155233 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.97149 | 0.211381 | 0.105691 | − | 0.994399i | \(-0.466295\pi\) | ||||
0.105691 | + | 0.994399i | \(0.466295\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.6519 | − | 14.6519i | −0.777643 | − | 0.777643i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.45794 | + | 1.45794i | −0.0771623 | + | 0.0771623i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.8844 | −0.996678 | −0.498339 | − | 0.866982i | \(-0.666057\pi\) | ||||
−0.498339 | + | 0.866982i | \(0.666057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 12.3872i | − | 0.651959i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.43437 | − | 7.43437i | −0.390203 | − | 0.390203i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.30780 | 0.173138 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.2146i | 1.36839i | 0.729300 | + | 0.684195i | \(0.239846\pi\) | ||||
−0.729300 | + | 0.684195i | \(0.760154\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.9957 | + | 3.72704i | 0.936821 | + | 0.194022i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 14.3748i | − | 0.746301i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0195 | −0.777681 | −0.388840 | − | 0.921305i | \(-0.627124\pi\) | ||||
−0.388840 | + | 0.921305i | \(0.627124\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.01051 | − | 3.01051i | −0.155462 | − | 0.155462i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.53307i | − | 0.130460i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.80687 | 0.298279 | 0.149139 | − | 0.988816i | \(-0.452350\pi\) | ||||
0.149139 | + | 0.988816i | \(0.452350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.537691 | + | 0.537691i | −0.0275467 | + | 0.0275467i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.4288 | − | 24.4288i | −1.24825 | − | 1.24825i | −0.956491 | − | 0.291763i | \(-0.905758\pi\) |
−0.291763 | − | 0.956491i | \(-0.594242\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.90966 | −0.505043 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.2325 | −0.621812 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 28.3372i | − | 1.43675i | −0.695656 | − | 0.718375i | \(-0.744886\pi\) | ||
0.695656 | − | 0.718375i | \(-0.255114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.1455 | − | 11.1455i | −0.563654 | − | 0.563654i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.45226 | + | 4.45226i | 0.224587 | + | 0.224587i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.30328 | − | 5.30328i | −0.266837 | − | 0.266837i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.8306 | − | 19.8306i | 0.995269 | − | 0.995269i | −0.00472015 | − | 0.999989i | \(-0.501502\pi\) |
0.999989 | + | 0.00472015i | \(0.00150248\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.655350 | + | 0.655350i | −0.0328085 | + | 0.0328085i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5160i | 0.974584i | 0.873239 | + | 0.487292i | \(0.162015\pi\) | ||||
−0.873239 | + | 0.487292i | \(0.837985\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.03325 | + | 4.03325i | −0.200910 | + | 0.200910i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.2701i | 0.609704i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.2650 | + | 24.2650i | −1.20277 | + | 1.20277i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.13126 | 0.303171 | 0.151586 | − | 0.988444i | \(-0.451562\pi\) | ||||
0.151586 | + | 0.988444i | \(0.451562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.07729 | 0.349097 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.4437 | + | 10.4437i | −0.513900 | + | 0.513900i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4971i | 0.760721i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.585705 | − | 0.585705i | 0.0286821 | − | 0.0286821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.75478i | 0.183433i | 0.995785 | + | 0.0917166i | \(0.0292354\pi\) | ||||
−0.995785 | + | 0.0917166i | \(0.970765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.66007 | − | 1.66007i | 0.0809067 | − | 0.0809067i | −0.665495 | − | 0.746402i | \(-0.731780\pi\) |
0.746402 | + | 0.665495i | \(0.231780\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.0409110 | + | 0.0409110i | −0.00198916 | + | 0.00198916i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.3375 | − | 10.3375i | −0.501440 | − | 0.501440i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.51838 | − | 9.51838i | −0.460627 | − | 0.460627i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.22044 | + | 2.22044i | 0.107204 | + | 0.107204i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.73186i | 0.420599i | 0.977637 | + | 0.210299i | \(0.0674439\pi\) | ||||
−0.977637 | + | 0.210299i | \(0.932556\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.23449 | −0.155440 | −0.0777199 | − | 0.996975i | \(-0.524764\pi\) | ||||
−0.0777199 | + | 0.996975i | \(0.524764\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.03835 | 0.0497851 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.00997 | − | 5.00997i | −0.239659 | − | 0.239659i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2187 | + | 11.2187i | −0.535441 | + | 0.535441i | −0.922186 | − | 0.386746i | \(-0.873599\pi\) |
0.386746 | + | 0.922186i | \(0.373599\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.87011 | 0.136672 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.5388i | 0.595735i | 0.954607 | + | 0.297867i | \(0.0962753\pi\) | ||||
−0.954607 | + | 0.297867i | \(0.903725\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.31264 | − | 5.31264i | −0.251843 | − | 0.251843i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.72306 | −0.176095 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 23.1930i | − | 1.09455i | −0.836954 | − | 0.547274i | \(-0.815666\pi\) | ||
0.836954 | − | 0.547274i | \(-0.184334\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.2809 | − | 33.9206i | −1.04917 | − | 1.59726i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.10170i | 0.192715i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.14929 | 0.100760 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.50478 | + | 5.50478i | 0.257503 | + | 0.257503i | 0.824038 | − | 0.566535i | \(-0.191716\pi\) |
−0.566535 | + | 0.824038i | \(0.691716\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 12.1032i | − | 0.564929i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.9113 | −0.787638 | −0.393819 | − | 0.919188i | \(-0.628846\pi\) | ||||
−0.393819 | + | 0.919188i | \(0.628846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.01712 | − | 2.01712i | 0.0937435 | − | 0.0937435i | −0.658680 | − | 0.752423i | \(-0.728885\pi\) |
0.752423 | + | 0.658680i | \(0.228885\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.65330 | − | 1.65330i | −0.0766701 | − | 0.0766701i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.8616 | 1.61320 | 0.806600 | − | 0.591097i | \(-0.201305\pi\) | ||||
0.806600 | + | 0.591097i | \(0.201305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.225377 | 0.0104069 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.44758i | 0.297089i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.1013 | + | 19.1013i | 0.878278 | + | 0.878278i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.64673 | − | 4.64673i | −0.213207 | − | 0.213207i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.1732 | + | 29.1732i | 1.33575 | + | 1.33575i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.4086 | − | 30.4086i | 1.38941 | − | 1.38941i | 0.562838 | − | 0.826567i | \(-0.309709\pi\) |
0.826567 | − | 0.562838i | \(-0.190291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.26280 | − | 5.26280i | 0.239963 | − | 0.239963i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.993011i | − | 0.0451836i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.0415 | − | 18.0415i | 0.819222 | − | 0.819222i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.7055i | − | 0.711685i | −0.934546 | − | 0.355843i | \(-0.884194\pi\) | ||
0.934546 | − | 0.355843i | \(-0.115806\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.45376 | − | 4.45376i | 0.201406 | − | 0.201406i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4699 | −0.517631 | −0.258816 | − | 0.965927i | \(-0.583332\pi\) | ||||
−0.258816 | + | 0.965927i | \(0.583332\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.5416 | 0.474772 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.1114 | − | 20.1114i | 0.903938 | − | 0.903938i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 13.2529i | − | 0.594475i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.31496 | − | 4.31496i | 0.193164 | − | 0.193164i | −0.603898 | − | 0.797062i | \(-0.706387\pi\) |
0.797062 | + | 0.603898i | \(0.206387\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 2.78822i | − | 0.124569i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.95360 | − | 7.95360i | 0.354634 | − | 0.354634i | −0.507197 | − | 0.861830i | \(-0.669318\pi\) |
0.861830 | + | 0.507197i | \(0.169318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.2327 | − | 19.2327i | 0.855843 | − | 0.855843i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.83144 | + | 2.83144i | 0.125749 | + | 0.125749i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.886631 | − | 0.886631i | −0.0392992 | − | 0.0392992i | 0.687184 | − | 0.726483i | \(-0.258847\pi\) |
−0.726483 | + | 0.687184i | \(0.758847\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.49598 | + | 1.49598i | 0.0661784 | + | 0.0661784i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.44044i | − | 0.240201i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.6826 | 0.999514 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.127767 | 0.00561918 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.12861 | − | 1.12861i | −0.0495407 | − | 0.0495407i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.46171 | + | 7.46171i | −0.326904 | + | 0.326904i | −0.851408 | − | 0.524504i | \(-0.824251\pi\) |
0.524504 | + | 0.851408i | \(0.324251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9101 | −0.520792 | −0.260396 | − | 0.965502i | \(-0.583853\pi\) | ||||
−0.260396 | + | 0.965502i | \(0.583853\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 0.921014i | − | 0.0401964i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.7848 | − | 16.7848i | −0.731158 | − | 0.731158i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.4087 | −0.669943 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 42.3903i | − | 1.83958i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.83246 | + | 7.35697i | 0.209317 | + | 0.318666i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.8005i | 0.985753i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.80467 | 0.293643 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.48173 | − | 4.48173i | −0.193042 | − | 0.193042i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 29.4589i | − | 1.26654i | −0.773932 | − | 0.633269i | \(-0.781713\pi\) | ||
0.773932 | − | 0.633269i | \(-0.218287\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.07068 | −0.217604 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.6350 | + | 12.6350i | −0.541224 | + | 0.541224i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2371 | + | 11.2371i | 0.480463 | + | 0.480463i | 0.905279 | − | 0.424817i | \(-0.139661\pi\) |
−0.424817 | + | 0.905279i | \(0.639661\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 38.6346 | 1.64888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.73851 | 0.201868 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.79691i | − | 0.203985i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.15732 | + | 2.15732i | 0.0915731 | + | 0.0915731i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.4187 | + | 13.4187i | 0.568570 | + | 0.568570i | 0.931728 | − | 0.363158i | \(-0.118301\pi\) |
−0.363158 | + | 0.931728i | \(0.618301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.14284 | − | 4.14284i | −0.175223 | − | 0.175223i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.24059 | + | 9.24059i | −0.390138 | + | 0.390138i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.7624 | + | 22.7624i | −0.959320 | + | 0.959320i | −0.999204 | − | 0.0398841i | \(-0.987301\pi\) |
0.0398841 | + | 0.999204i | \(0.487301\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 26.4783i | − | 1.11395i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.54925 | + | 5.54925i | −0.233046 | + | 0.233046i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.44661i | − | 0.270256i | −0.990828 | − | 0.135128i | \(-0.956855\pi\) | ||
0.990828 | − | 0.135128i | \(-0.0431446\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.3652 | + | 10.3652i | −0.433771 | + | 0.433771i | −0.889909 | − | 0.456138i | \(-0.849232\pi\) |
0.456138 | + | 0.889909i | \(0.349232\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.05670 | 0.127695 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.04090 | 0.293626 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.989459 | − | 0.989459i | 0.0411917 | − | 0.0411917i | −0.686211 | − | 0.727403i | \(-0.740727\pi\) |
0.727403 | + | 0.686211i | \(0.240727\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.30371i | 0.303532i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.00869 | + | 7.00869i | −0.290769 | + | 0.290769i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 91.1091i | − | 3.77335i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.36191 | + | 4.36191i | −0.180343 | + | 0.180343i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.5081 | − | 11.5081i | 0.474989 | − | 0.474989i | −0.428536 | − | 0.903525i | \(-0.640970\pi\) |
0.903525 | + | 0.428536i | \(0.140970\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.54485 | − | 7.54485i | −0.310880 | − | 0.310880i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.92028 | + | 4.92028i | 0.202393 | + | 0.202393i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.3684 | − | 31.3684i | −1.28815 | − | 1.28815i | −0.935912 | − | 0.352233i | \(-0.885422\pi\) |
−0.352233 | − | 0.935912i | \(-0.614578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.94450i | 0.366689i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.149286 | −0.00610989 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.2661 | 1.03235 | 0.516173 | − | 0.856484i | \(-0.327356\pi\) | ||||
0.516173 | + | 0.856484i | \(0.327356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.12731 | + | 3.12731i | 0.127565 | + | 0.127565i | 0.768007 | − | 0.640442i | \(-0.221249\pi\) |
−0.640442 | + | 0.768007i | \(0.721249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.457396 | + | 0.457396i | −0.0186266 | + | 0.0186266i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −45.6101 | −1.85431 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19.6679i | − | 0.798295i | −0.916887 | − | 0.399148i | \(-0.869306\pi\) | ||
0.916887 | − | 0.399148i | \(-0.130694\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.469603 | + | 0.469603i | 0.0190293 | + | 0.0190293i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0277111 | −0.00112107 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.92464i | − | 0.158515i | −0.996854 | − | 0.0792573i | \(-0.974745\pi\) | ||
0.996854 | − | 0.0792573i | \(-0.0252549\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.01576 | + | 1.98091i | −0.121607 | + | 0.0798782i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14.9036i | − | 0.599996i | −0.953940 | − | 0.299998i | \(-0.903014\pi\) | ||
0.953940 | − | 0.299998i | \(-0.0969860\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.3485 | −1.05904 | −0.529518 | − | 0.848299i | \(-0.677627\pi\) | ||||
−0.529518 | + | 0.848299i | \(0.677627\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.12178 | + | 4.12178i | 0.165401 | + | 0.165401i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 4.80537i | − | 0.192523i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.69225 | −0.227690 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.15369 | + | 4.15369i | −0.165882 | + | 0.165882i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.9017 | + | 21.9017i | 0.873279 | + | 0.873279i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.2937 | 0.807880 | 0.403940 | − | 0.914785i | \(-0.367640\pi\) | ||||
0.403940 | + | 0.914785i | \(0.367640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.99630 | 0.198585 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.29875i | 0.130907i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.972034 | + | 0.972034i | 0.0385134 | + | 0.0385134i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.8964 | + | 26.8964i | 1.06401 | + | 1.06401i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.35473 | − | 8.35473i | −0.329992 | − | 0.329992i | 0.522591 | − | 0.852583i | \(-0.324965\pi\) |
−0.852583 | + | 0.522591i | \(0.824965\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.44242 | − | 3.44242i | 0.135756 | − | 0.135756i | −0.635963 | − | 0.771719i | \(-0.719397\pi\) |
0.771719 | + | 0.635963i | \(0.219397\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.69823 | − | 1.69823i | 0.0668676 | − | 0.0668676i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.9293i | 1.09801i | 0.835817 | + | 0.549007i | \(0.184994\pi\) | ||||
−0.835817 | + | 0.549007i | \(0.815006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −66.1934 | + | 66.1934i | −2.59832 | + | 2.59832i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.49544i | − | 0.0586110i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.04040 | + | 1.04040i | −0.0407139 | + | 0.0407139i | −0.727171 | − | 0.686457i | \(-0.759165\pi\) |
0.686457 | + | 0.727171i | \(0.259165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.3148 | 1.06728 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.07211 | −0.236896 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.2088 | − | 25.2088i | 0.981994 | − | 0.981994i | −0.0178465 | − | 0.999841i | \(-0.505681\pi\) |
0.999841 | + | 0.0178465i | \(0.00568101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.62851i | 0.296715i | 0.988934 | + | 0.148357i | \(0.0473986\pi\) | ||||
−0.988934 | + | 0.148357i | \(0.952601\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.00417 | − | 2.00417i | 0.0778357 | − | 0.0778357i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.02059i | 0.155912i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.58999 | + | 3.58999i | −0.139005 | + | 0.139005i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.898643 | + | 0.898643i | −0.0347435 | + | 0.0347435i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.3287 | − | 60.3287i | −2.32896 | − | 2.32896i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.2048 | − | 31.2048i | −1.20286 | − | 1.20286i | −0.973294 | − | 0.229562i | \(-0.926271\pi\) |
−0.229562 | − | 0.973294i | \(-0.573729\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.82294 | + | 3.82294i | 0.147145 | + | 0.147145i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 33.8516i | − | 1.30102i | −0.759497 | − | 0.650511i | \(-0.774555\pi\) | ||
0.759497 | − | 0.650511i | \(-0.225445\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.3188 | 0.626260 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.11499 | 0.234327 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.24531 | + | 8.24531i | 0.315498 | + | 0.315498i | 0.847035 | − | 0.531537i | \(-0.178385\pi\) |
−0.531537 | + | 0.847035i | \(0.678385\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.7097 | − | 21.7097i | 0.829485 | − | 0.829485i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.5552 | −0.402706 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.7605i | 0.752814i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3595 | − | 18.3595i | −0.698427 | − | 0.698427i | 0.265644 | − | 0.964071i | \(-0.414415\pi\) |
−0.964071 | + | 0.265644i | \(0.914415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.1911 | 0.691022 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.59332i | − | 0.136302i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.6169 | + | 20.1108i | −1.15970 | + | 0.761752i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.55968i | 0.248110i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.6033 | 0.853714 | 0.426857 | − | 0.904319i | \(-0.359621\pi\) | ||||
0.426857 | + | 0.904319i | \(0.359621\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.84492 | + | 9.84492i | 0.371308 | + | 0.371308i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 0.0113593i | − | 0.000427816i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.3963 | 0.654255 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.664120 | − | 0.664120i | 0.0249415 | − | 0.0249415i | −0.694526 | − | 0.719468i | \(-0.744386\pi\) |
0.719468 | + | 0.694526i | \(0.244386\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.73519 | + | 9.73519i | 0.365098 | + | 0.365098i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.4322 | 0.428141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.6224 | 0.509450 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.54121i | 0.281632i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.92610 | + | 8.92610i | 0.332887 | + | 0.332887i | 0.853682 | − | 0.520795i | \(-0.174364\pi\) |
−0.520795 | + | 0.853682i | \(0.674364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2584 | + | 10.2584i | 0.382043 | + | 0.382043i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.30475 | − | 1.30475i | −0.0485243 | − | 0.0485243i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.32970 | + | 3.32970i | −0.123662 | + | 0.123662i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8758 | − | 19.8758i | 0.737153 | − | 0.737153i | −0.234873 | − | 0.972026i | \(-0.575467\pi\) |
0.972026 | + | 0.234873i | \(0.0754674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 20.2366i | − | 0.749503i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.2409 | − | 17.2409i | 0.637678 | − | 0.637678i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.9920i | 1.73569i | 0.496834 | + | 0.867845i | \(0.334496\pi\) | ||||
−0.496834 | + | 0.867845i | \(0.665504\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.398455 | + | 0.398455i | −0.0146972 | + | 0.0146972i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.42847 | 0.0526183 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.7510 | 0.652980 | 0.326490 | − | 0.945201i | \(-0.394134\pi\) | ||||
0.326490 | + | 0.945201i | \(0.394134\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.900885 | − | 0.900885i | 0.0330948 | − | 0.0330948i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.6333i | 0.867022i | 0.901148 | + | 0.433511i | \(0.142726\pi\) | ||||
−0.901148 | + | 0.433511i | \(0.857274\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.4206 | + | 11.4206i | −0.418417 | + | 0.418417i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 28.4479i | − | 1.04085i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.3117 | + | 10.3117i | −0.376783 | + | 0.376783i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.9429 | − | 13.9429i | 0.508783 | − | 0.508783i | −0.405370 | − | 0.914153i | \(-0.632857\pi\) |
0.914153 | + | 0.405370i | \(0.132857\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.43565 | + | 4.43565i | 0.161644 | + | 0.161644i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5820 | + | 12.5820i | 0.457907 | + | 0.457907i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.25553 | + | 3.25553i | 0.118324 | + | 0.118324i | 0.763790 | − | 0.645465i | \(-0.223336\pi\) |
−0.645465 | + | 0.763790i | \(0.723336\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 6.29383i | − | 0.228451i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.17017 | 0.151169 | 0.0755843 | − | 0.997139i | \(-0.475918\pi\) | ||||
0.0755843 | + | 0.997139i | \(0.475918\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.4286 | −0.413742 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.1526 | − | 18.1526i | −0.656309 | − | 0.656309i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.3566 | − | 14.3566i | 0.518385 | − | 0.518385i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.37265 | 0.265865 | 0.132932 | − | 0.991125i | \(-0.457561\pi\) | ||||
0.132932 | + | 0.991125i | \(0.457561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.354229i | 0.0127572i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.31710 | + | 6.31710i | 0.227210 | + | 0.227210i | 0.811526 | − | 0.584316i | \(-0.198637\pi\) |
−0.584316 | + | 0.811526i | \(0.698637\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.6034 | 0.380884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.95133i | 0.0700037i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.7624 | + | 9.03990i | −0.493090 | + | 0.323888i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 83.9986i | − | 3.00571i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.89845 | −0.139319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.7781 | + | 19.7781i | 0.705909 | + | 0.705909i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.5407i | − | 1.05301i | −0.850171 | − | 0.526507i | \(-0.823501\pi\) | ||
0.850171 | − | 0.526507i | \(-0.176499\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.0478587 | 0.00170381 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.9750 | − | 11.9750i | 0.425784 | − | 0.425784i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.0846 | + | 13.0846i | 0.464647 | + | 0.464647i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.10019 | −0.287284 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.1515 | 0.890911 | 0.445456 | − | 0.895304i | \(-0.353042\pi\) | ||||
0.445456 | + | 0.895304i | \(0.353042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.115323i | − | 0.00407984i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.75237 | + | 9.75237i | 0.344583 | + | 0.344583i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.48173 | + | 9.48173i | 0.334603 | + | 0.334603i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.04608 | − | 3.04608i | −0.107360 | − | 0.107360i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.16589 | − | 3.16589i | 0.111445 | − | 0.111445i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.9213 | + | 22.9213i | −0.805868 | + | 0.805868i | −0.984006 | − | 0.178137i | \(-0.942993\pi\) |
0.178137 | + | 0.984006i | \(0.442993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.09001i | − | 0.108505i | −0.998527 | − | 0.0542525i | \(-0.982722\pi\) | ||
0.998527 | − | 0.0542525i | \(-0.0172776\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.87757 | − | 2.87757i | 0.100921 | − | 0.100921i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 27.3240i | − | 0.957117i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.74986 | − | 7.74986i | 0.271133 | − | 0.271133i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.94543 | −0.137864 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.8825 | 0.449603 | 0.224801 | − | 0.974405i | \(-0.427827\pi\) | ||||
0.224801 | + | 0.974405i | \(0.427827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.0156 | + | 27.0156i | −0.941703 | + | 0.941703i | −0.998392 | − | 0.0566888i | \(-0.981946\pi\) |
0.0566888 | + | 0.998392i | \(0.481946\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.83750i | − | 0.203236i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.2793 | + | 25.2793i | −0.879049 | + | 0.879049i | −0.993436 | − | 0.114387i | \(-0.963510\pi\) |
0.114387 | + | 0.993436i | \(0.463510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.638230i | 0.0221666i | 0.999939 | + | 0.0110833i | \(0.00352800\pi\) | ||||
−0.999939 | + | 0.0110833i | \(0.996472\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.404901 | + | 0.404901i | −0.0140459 | + | 0.0140459i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.04523 | + | 4.04523i | −0.140159 | + | 0.140159i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.55292 | − | 8.55292i | −0.295986 | − | 0.295986i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.20727 | + | 6.20727i | 0.214554 | + | 0.214554i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.5218 | + | 11.5218i | 0.397777 | + | 0.397777i | 0.877448 | − | 0.479671i | \(-0.159244\pi\) |
−0.479671 | + | 0.877448i | \(0.659244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6045i | 0.882915i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.93970 | 0.135690 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.3710 | 0.597579 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.6276 | − | 20.6276i | −0.708772 | − | 0.708772i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.87377 | − | 2.87377i | 0.0986274 | − | 0.0986274i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.9174 | −0.511362 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.1139i | − | 0.928364i | −0.885740 | − | 0.464182i | \(-0.846348\pi\) | ||
0.885740 | − | 0.464182i | \(-0.153652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.15967 | − | 8.15967i | −0.279055 | − | 0.279055i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.1588 | 0.551974 | 0.275987 | − | 0.961161i | \(-0.410995\pi\) | ||||
0.275987 | + | 0.961161i | \(0.410995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.8872i | 0.439705i | 0.975533 | + | 0.219853i | \(0.0705577\pi\) | ||||
−0.975533 | + | 0.219853i | \(0.929442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.25979 | − | 0.468018i | −0.0770134 | − | 0.0159500i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.8684i | − | 0.642289i | −0.947030 | − | 0.321144i | \(-0.895933\pi\) | ||
0.947030 | − | 0.321144i | \(-0.104067\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.92409 | −0.235426 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.00819 | + | 4.00819i | 0.136125 | + | 0.136125i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 30.4034i | − | 1.03136i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.309818 | −0.0104978 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −33.1186 | + | 33.1186i | −1.12090 | + | 1.12090i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.35303 | − | 8.35303i | −0.282384 | − | 0.282384i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.0659 | −0.981485 | −0.490742 | − | 0.871305i | \(-0.663274\pi\) | ||||
−0.490742 | + | 0.871305i | \(0.663274\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.26957 | 0.110280 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.3751i | 1.09075i | 0.838194 | + | 0.545373i | \(0.183612\pi\) | ||||
−0.838194 | + | 0.545373i | \(0.816388\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.2872 | − | 16.2872i | −0.548110 | − | 0.548110i | 0.377784 | − | 0.925894i | \(-0.376686\pi\) |
−0.925894 | + | 0.377784i | \(0.876686\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.88502 | + | 5.88502i | 0.197823 | + | 0.197823i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.3493 | + | 34.3493i | 1.15334 | + | 1.15334i | 0.985879 | + | 0.167456i | \(0.0535554\pi\) |
0.167456 | + | 0.985879i | \(0.446445\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.49189 | + | 1.49189i | −0.0500364 | + | 0.0500364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.1718 | + | 35.1718i | −1.17830 | + | 1.17830i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 0.0518382i | − | 0.00173470i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.8734 | − | 20.8734i | 0.697721 | − | 0.697721i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.36506i | 0.0455779i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.40641 | + | 5.40641i | −0.180314 | + | 0.180314i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −82.2355 | −2.73966 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.53608 | 0.0511174 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.5544 | + | 15.5544i | −0.517045 | + | 0.517045i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.9735i | 1.12807i | 0.825751 | + | 0.564035i | \(0.190752\pi\) | ||||
−0.825751 | + | 0.564035i | \(0.809248\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.3053 | + | 35.3053i | −1.17100 | + | 1.17100i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.2317i | − | 0.802831i | −0.915896 | − | 0.401416i | \(-0.868518\pi\) | ||
0.915896 | − | 0.401416i | \(-0.131482\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.4219 | + | 44.4219i | −1.47015 | + | 1.47015i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.36361 | + | 5.36361i | −0.177315 | + | 0.177315i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.3533 | + | 12.3533i | 0.407943 | + | 0.407943i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.1571 | + | 26.1571i | 0.862843 | + | 0.862843i | 0.991667 | − | 0.128825i | \(-0.0411205\pi\) |
−0.128825 | + | 0.991667i | \(0.541120\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.39706 | − | 5.39706i | −0.177839 | − | 0.177839i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.2183i | 0.599663i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8358 | −0.454920 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.6382 | −1.36758 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.22797 | + | 9.22797i | 0.302760 | + | 0.302760i | 0.842093 | − | 0.539333i | \(-0.181324\pi\) |
−0.539333 | + | 0.842093i | \(0.681324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.81835 | + | 1.81835i | −0.0595939 | + | 0.0595939i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.963835 | 0.0315546 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 56.6913i | 1.85401i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.55404 | + | 1.55404i | 0.0507684 | + | 0.0507684i | 0.732035 | − | 0.681267i | \(-0.238571\pi\) |
−0.681267 | + | 0.732035i | \(0.738571\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.668704 | 0.0218223 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 34.2396i | − | 1.11618i | −0.829781 | − | 0.558089i | \(-0.811535\pi\) | ||
0.829781 | − | 0.558089i | \(-0.188465\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.57787 | − | 17.2755i | 0.116511 | − | 0.562567i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 3.30780i | − | 0.107603i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.0556 | −1.36662 | −0.683311 | − | 0.730127i | \(-0.739461\pi\) | ||||
−0.683311 | + | 0.730127i | \(0.739461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.05647 | − | 2.05647i | −0.0667560 | − | 0.0667560i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 12.0162i | − | 0.389651i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.29357 | 0.171475 | 0.0857377 | − | 0.996318i | \(-0.472675\pi\) | ||||
0.0857377 | + | 0.996318i | \(0.472675\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.37647 | − | 9.37647i | 0.303416 | − | 0.303416i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.97640 | + | 2.97640i | 0.0962135 | + | 0.0962135i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.6368 | 0.634106 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7834 | −0.444627 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 41.8548i | − | 1.34875i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.4042 | + | 22.4042i | 0.721218 | + | 0.721218i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.26902 | + | 1.26902i | 0.0408090 | + | 0.0408090i | 0.727217 | − | 0.686408i | \(-0.240813\pi\) |
−0.686408 | + | 0.727217i | \(0.740813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.74914 | + | 3.74914i | 0.120440 | + | 0.120440i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.24821 | − | 3.24821i | 0.104240 | − | 0.104240i | −0.653063 | − | 0.757303i | \(-0.726516\pi\) |
0.757303 | + | 0.653063i | \(0.226516\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.62511 | − | 1.62511i | 0.0520987 | − | 0.0520987i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.26608i | 0.0405472i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.99196 | − | 3.99196i | 0.127714 | − | 0.127714i | −0.640361 | − | 0.768074i | \(-0.721215\pi\) |
0.768074 | + | 0.640361i | \(0.221215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30.4570i | − | 0.973412i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.1940 | − | 23.1940i | 0.740527 | − | 0.740527i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.8434 | −0.601011 | −0.300506 | − | 0.953780i | \(-0.597155\pi\) | ||||
−0.300506 | + | 0.953780i | \(0.597155\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.1861 | 0.961808 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.00513735 | − | 0.00513735i | 0.000163524 | − | 0.000163524i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.7429i | 0.373402i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.6867 | + | 17.6867i | −0.561838 | + | 0.561838i | −0.929829 | − | 0.367991i | \(-0.880046\pi\) |
0.367991 | + | 0.929829i | \(0.380046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.82171i | 0.279949i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.457939 | + | 0.457939i | −0.0145176 | + | 0.0145176i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.0055 | + | 29.0055i | −0.918615 | + | 0.918615i | −0.996929 | − | 0.0783141i | \(-0.975046\pi\) |
0.0783141 | + | 0.996929i | \(0.475046\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.09958 | − | 8.09958i | −0.256259 | − | 0.256259i |
(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 | 1148.2.k.a.729.3 | yes | 8 | |
41.9 | even | 4 | inner | 1148.2.k.a.337.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.a.337.3 | ✓ | 8 | 41.9 | even | 4 | inner | |
1148.2.k.a.729.3 | yes | 8 | 1.1 | even | 1 | trivial |