Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} + 28 x^{13} + 373 x^{12} - 920 x^{11} + 1088 x^{10} - 168 x^{9} + 16460 x^{8} - 45408 x^{7} + 62624 x^{6} - 18048 x^{5} + 2160 x^{4} - 1664 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.5 | ||
Root | \(-2.64546 - 2.64546i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.b.1471.13 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23448 | 0.466588 | 0.233294 | − | 0.972406i | \(-0.425050\pi\) | ||||
0.233294 | + | 0.972406i | \(0.425050\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.11271 | 1.84305 | 0.921526 | − | 0.388317i | \(-0.126943\pi\) | ||||
0.921526 | + | 0.388317i | \(0.126943\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.591966 | −0.164182 | −0.0820909 | − | 0.996625i | \(-0.526160\pi\) | ||||
−0.0820909 | + | 0.996625i | \(0.526160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.95937i | 1.20282i | 0.798939 | + | 0.601412i | \(0.205395\pi\) | ||||
−0.798939 | + | 0.601412i | \(0.794605\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.62424 | 1.74912 | 0.874560 | − | 0.484917i | \(-0.161150\pi\) | ||||
0.874560 | + | 0.484917i | \(0.161150\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.23448i | − | 0.269385i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.72490 | − | 0.821792i | −0.985209 | − | 0.171356i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.66359 | 0.866007 | 0.433004 | − | 0.901392i | \(-0.357454\pi\) | ||||
0.433004 | + | 0.901392i | \(0.357454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.50734i | 1.34836i | 0.738568 | + | 0.674179i | \(0.235502\pi\) | ||||
−0.738568 | + | 0.674179i | \(0.764498\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.11271i | − | 1.06409i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.23448i | − | 0.208664i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.86288i | − | 0.470654i | −0.971916 | − | 0.235327i | \(-0.924384\pi\) | ||
0.971916 | − | 0.235327i | \(-0.0756162\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.591966i | 0.0947904i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.23178 | 0.660892 | 0.330446 | − | 0.943825i | \(-0.392801\pi\) | ||||
0.330446 | + | 0.943825i | \(0.392801\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.79315 | 0.730948 | 0.365474 | − | 0.930821i | \(-0.380907\pi\) | ||||
0.365474 | + | 0.930821i | \(0.380907\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.19442i | − | 0.757685i | −0.925461 | − | 0.378842i | \(-0.876322\pi\) | ||
0.925461 | − | 0.378842i | \(-0.123678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.47607 | −0.782296 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.95937 | 0.694451 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.65960i | 1.05213i | 0.850445 | + | 0.526064i | \(0.176333\pi\) | ||||
−0.850445 | + | 0.526064i | \(0.823667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.11271i | − | 0.824238i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.62424i | − | 1.00986i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.5061i | 1.49796i | 0.662592 | + | 0.748981i | \(0.269457\pi\) | ||||
−0.662592 | + | 0.748981i | \(0.730543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5924i | 1.48426i | 0.670257 | + | 0.742129i | \(0.266184\pi\) | ||||
−0.670257 | + | 0.742129i | \(0.733816\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.23448 | −0.155529 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.591966i | 0.0734243i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.90488 | −0.354888 | −0.177444 | − | 0.984131i | \(-0.556783\pi\) | ||||
−0.177444 | + | 0.984131i | \(0.556783\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.821792 | + | 4.72490i | −0.0989322 | + | 0.568811i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.7877i | 1.87365i | 0.349796 | + | 0.936826i | \(0.386251\pi\) | ||||
−0.349796 | + | 0.936826i | \(0.613749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.1738 | 1.77596 | 0.887980 | − | 0.459883i | \(-0.152109\pi\) | ||||
0.887980 | + | 0.459883i | \(0.152109\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.54599 | 0.859945 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.6998 | −1.76637 | −0.883183 | − | 0.469028i | \(-0.844604\pi\) | ||||
−0.883183 | + | 0.469028i | \(0.844604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.91936 | 0.430206 | 0.215103 | − | 0.976591i | \(-0.430991\pi\) | ||||
0.215103 | + | 0.976591i | \(0.430991\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.95937 | 0.537920 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.66359i | − | 0.499989i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.663092i | 0.0702876i | 0.999382 | + | 0.0351438i | \(0.0111889\pi\) | ||||
−0.999382 | + | 0.0351438i | \(0.988811\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.730767 | −0.0766052 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.50734 | 0.778475 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 7.62424i | − | 0.782230i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.6244i | 1.18028i | 0.807301 | + | 0.590140i | \(0.200928\pi\) | ||||
−0.807301 | + | 0.590140i | \(0.799072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.11271 | −0.614351 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.20872 | 0.120272 | 0.0601361 | − | 0.998190i | \(-0.480847\pi\) | ||||
0.0601361 | + | 0.998190i | \(0.480847\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.5686 | −1.04136 | −0.520680 | − | 0.853752i | \(-0.674321\pi\) | ||||
−0.520680 | + | 0.853752i | \(0.674321\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.23448 | −0.120472 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.55738 | −0.827274 | −0.413637 | − | 0.910442i | \(-0.635742\pi\) | ||||
−0.413637 | + | 0.910442i | \(0.635742\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.98941i | 0.286334i | 0.989699 | + | 0.143167i | \(0.0457286\pi\) | ||||
−0.989699 | + | 0.143167i | \(0.954271\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.86288 | −0.271732 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 19.9276i | − | 1.87463i | −0.348480 | − | 0.937316i | \(-0.613302\pi\) | ||
0.348480 | − | 0.937316i | \(-0.386698\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.821792 | + | 4.72490i | −0.0766325 | + | 0.440599i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.591966 | 0.0547272 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.12222i | 0.561223i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.3652 | 2.39684 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.23178i | − | 0.381566i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.95560i | − | 0.617210i | −0.951190 | − | 0.308605i | \(-0.900138\pi\) | ||
0.951190 | − | 0.308605i | \(-0.0998621\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 4.79315i | − | 0.422013i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.92419i | 0.779710i | 0.920876 | + | 0.389855i | \(0.127475\pi\) | ||||
−0.920876 | + | 0.389855i | \(0.872525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.41193 | 0.816118 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.86465i | − | 0.244744i | −0.992484 | − | 0.122372i | \(-0.960950\pi\) | ||
0.992484 | − | 0.122372i | \(-0.0390501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.7787i | − | 1.25352i | −0.779214 | − | 0.626758i | \(-0.784381\pi\) | ||
0.779214 | − | 0.626758i | \(-0.215619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.19442 | −0.437449 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.61852 | −0.302595 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.66359i | − | 0.387290i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.47607i | 0.451659i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.09665i | − | 0.745227i | −0.927987 | − | 0.372613i | \(-0.878462\pi\) | ||
0.927987 | − | 0.372613i | \(-0.121538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9012i | 0.968508i | 0.874928 | + | 0.484254i | \(0.160909\pi\) | ||||
−0.874928 | + | 0.484254i | \(0.839091\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.95937i | − | 0.400942i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.50734 | 0.603004 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.87561i | − | 0.309307i | −0.987969 | − | 0.154654i | \(-0.950574\pi\) | ||
0.987969 | − | 0.154654i | \(-0.0494262\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.65960 | 0.607446 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.83277 | − | 1.01448i | −0.459687 | − | 0.0799524i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.19414i | − | 0.328510i | −0.986418 | − | 0.164255i | \(-0.947478\pi\) | ||
0.986418 | − | 0.164255i | \(-0.0525221\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.11271 | −0.475874 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.9811i | 0.927128i | 0.886064 | + | 0.463564i | \(0.153430\pi\) | ||||
−0.886064 | + | 0.463564i | \(0.846570\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6496 | −0.973044 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.62424 | −0.583040 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.9589 | −0.909221 | −0.454610 | − | 0.890690i | \(-0.650221\pi\) | ||||
−0.454610 | + | 0.890690i | \(0.650221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.23448 | −0.0933176 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.5061 | 0.864849 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.19461i | 0.463007i | 0.972834 | + | 0.231504i | \(0.0743645\pi\) | ||||
−0.972834 | + | 0.231504i | \(0.925635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.7081i | − | 1.16758i | −0.811906 | − | 0.583788i | \(-0.801570\pi\) | ||
0.811906 | − | 0.583788i | \(-0.198430\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5924 | 0.856937 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.86288 | −0.210483 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.3152i | 2.21687i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.23448i | 0.0897949i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6853 | 1.64145 | 0.820724 | − | 0.571325i | \(-0.193571\pi\) | ||||
0.820724 | + | 0.571325i | \(0.193571\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.5627 | 1.26419 | 0.632095 | − | 0.774891i | \(-0.282195\pi\) | ||||
0.632095 | + | 0.774891i | \(0.282195\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.591966 | 0.0423915 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.4444 | 1.02912 | 0.514559 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514559 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.16919 | −0.153770 | −0.0768850 | − | 0.997040i | \(-0.524497\pi\) | ||||
−0.0768850 | + | 0.997040i | \(0.524497\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.90488i | 0.204894i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.75709 | 0.404068 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.23178i | − | 0.295560i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.72490 | + | 0.821792i | 0.328403 | + | 0.0571185i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 46.6048 | 3.22372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.8897i | − | 1.23158i | −0.787910 | − | 0.615790i | \(-0.788837\pi\) | ||
0.787910 | − | 0.615790i | \(-0.211163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.7877 | 1.08175 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.79315i | − | 0.326890i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.26762i | 0.629127i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 15.1738i | − | 1.02535i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.93578i | − | 0.197482i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.1120i | − | 1.27983i | −0.768445 | − | 0.639916i | \(-0.778969\pi\) | ||
0.768445 | − | 0.639916i | \(-0.221031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.7159 | −0.843984 | −0.421992 | − | 0.906600i | \(-0.638669\pi\) | ||||
−0.421992 | + | 0.906600i | \(0.638669\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 22.2900i | − | 1.47296i | −0.676458 | − | 0.736481i | \(-0.736486\pi\) | ||
0.676458 | − | 0.736481i | \(-0.263514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 7.54599i | − | 0.496490i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.2452 | −1.32631 | −0.663153 | − | 0.748484i | \(-0.730782\pi\) | ||||
−0.663153 | + | 0.748484i | \(0.730782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.19442 | −0.338847 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.6998i | 1.01981i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.08011i | − | 0.393289i | −0.980475 | − | 0.196645i | \(-0.936995\pi\) | ||
0.980475 | − | 0.196645i | \(-0.0630045\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7552i | 0.950465i | 0.879860 | + | 0.475232i | \(0.157636\pi\) | ||||
−0.879860 | + | 0.475232i | \(0.842364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.47607i | 0.349853i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.51329 | −0.287174 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.91936i | − | 0.248379i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.97907 | −0.314276 | −0.157138 | − | 0.987577i | \(-0.550227\pi\) | ||||
−0.157138 | + | 0.987577i | \(0.550227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.8819 | − | 5.02338i | −1.81579 | − | 0.315817i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 4.95937i | − | 0.310568i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.0339 | 1.49919 | 0.749597 | − | 0.661895i | \(-0.230247\pi\) | ||||
0.749597 | + | 0.661895i | \(0.230247\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.53415i | − | 0.219602i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.66359 | −0.288669 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3344 | 0.822232 | 0.411116 | − | 0.911583i | \(-0.365139\pi\) | ||||
0.411116 | + | 0.911583i | \(0.365139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.65960 | 0.470526 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.663092 | 0.0405805 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.3882 | 1.79183 | 0.895916 | − | 0.444222i | \(-0.146520\pi\) | ||||
0.895916 | + | 0.444222i | \(0.146520\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.93152i | 0.299568i | 0.988719 | + | 0.149784i | \(0.0478579\pi\) | ||||
−0.988719 | + | 0.149784i | \(0.952142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.730767i | 0.0442280i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.11271 | −0.368610 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.67570 | 0.100683 | 0.0503415 | − | 0.998732i | \(-0.483969\pi\) | ||||
0.0503415 | + | 0.998732i | \(0.483969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 7.50734i | − | 0.449453i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.09883i | 0.0655510i | 0.999463 | + | 0.0327755i | \(0.0104346\pi\) | ||||
−0.999463 | + | 0.0327755i | \(0.989565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.0056 | −1.30810 | −0.654049 | − | 0.756452i | \(-0.726931\pi\) | ||||
−0.654049 | + | 0.756452i | \(0.726931\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.62424 | −0.451621 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.22402 | 0.308364 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.59538 | −0.446787 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.6244 | 0.681435 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 21.5662i | − | 1.25991i | −0.776632 | − | 0.629955i | \(-0.783073\pi\) | ||
0.776632 | − | 0.629955i | \(-0.216927\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5061 | 0.669909 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.11271i | 0.354695i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.79698 | + | 0.486473i | 0.161753 | + | 0.0281334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.91702 | 0.341052 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.20872i | − | 0.0694392i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.5924 | 0.663780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.70481i | − | 0.154372i | −0.997017 | − | 0.0771859i | \(-0.975407\pi\) | ||
0.997017 | − | 0.0771859i | \(-0.0245935\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.5686i | 0.601229i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 14.5678i | − | 0.826062i | −0.910717 | − | 0.413031i | \(-0.864470\pi\) | ||
0.910717 | − | 0.413031i | \(-0.135530\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.2833i | − | 1.03343i | −0.856156 | − | 0.516717i | \(-0.827154\pi\) | ||
0.856156 | − | 0.516717i | \(-0.172846\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.23448i | 0.0695548i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.2025 | −0.741526 | −0.370763 | − | 0.928728i | \(-0.620904\pi\) | ||||
−0.370763 | + | 0.928728i | \(0.620904\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.5072 | 1.59610 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.55738i | 0.477627i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 37.8114i | 2.10388i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.591966 | 0.0328363 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.98941 | 0.165315 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.41239i | − | 0.353526i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.3479i | − | 1.11842i | −0.829025 | − | 0.559212i | \(-0.811104\pi\) | ||
0.829025 | − | 0.559212i | \(-0.188896\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.86288i | 0.156885i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.90488i | 0.158711i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.8261i | − | 0.589736i | −0.955538 | − | 0.294868i | \(-0.904724\pi\) | ||
0.955538 | − | 0.294868i | \(-0.0952756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.9276 | −1.08232 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 45.8902i | 2.48509i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.4014 | −0.831597 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.72490 | + | 0.821792i | 0.254380 | + | 0.0442438i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.8259i | 1.11799i | 0.829170 | + | 0.558996i | \(0.188813\pi\) | ||||
−0.829170 | + | 0.558996i | \(0.811187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0430 | 0.912289 | 0.456145 | − | 0.889906i | \(-0.349230\pi\) | ||||
0.456145 | + | 0.889906i | \(0.349230\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.591966i | − | 0.0315968i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.1232 | −0.592030 | −0.296015 | − | 0.955183i | \(-0.595658\pi\) | ||||
−0.296015 | + | 0.955183i | \(0.595658\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.7877 | 0.837922 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.12222 | 0.324022 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.33824 | −0.176185 | −0.0880927 | − | 0.996112i | \(-0.528077\pi\) | ||||
−0.0880927 | + | 0.996112i | \(0.528077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.1290 | 2.05942 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 26.3652i | − | 1.38382i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 15.1738i | − | 0.794233i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5263 | −0.810468 | −0.405234 | − | 0.914213i | \(-0.632810\pi\) | ||||
−0.405234 | + | 0.914213i | \(0.632810\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.23178 | −0.220297 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.45559i | 0.490910i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 28.8438i | − | 1.49347i | −0.665120 | − | 0.746737i | \(-0.731619\pi\) | ||
0.665120 | − | 0.746737i | \(-0.268381\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.76069 | −0.142183 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.77317 | −0.296548 | −0.148274 | − | 0.988946i | \(-0.547372\pi\) | ||||
−0.148274 | + | 0.988946i | \(0.547372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.95560 | −0.356346 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.4701 | 1.45475 | 0.727376 | − | 0.686239i | \(-0.240740\pi\) | ||||
0.727376 | + | 0.686239i | \(0.240740\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 7.54599i | − | 0.384579i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.79315 | −0.243649 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.4547i | 1.44271i | 0.692564 | + | 0.721356i | \(0.256481\pi\) | ||||
−0.692564 | + | 0.721356i | \(0.743519\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.07557 | − | 23.4325i | 0.206111 | − | 1.18503i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.92419 | 0.450166 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.6998i | 0.789943i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.4303 | 0.975181 | 0.487590 | − | 0.873073i | \(-0.337876\pi\) | ||||
0.487590 | + | 0.873073i | \(0.337876\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 9.41193i | − | 0.471186i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.04759i | − | 0.0523141i | −0.999658 | − | 0.0261571i | \(-0.991673\pi\) | ||
0.999658 | − | 0.0261571i | \(-0.00832700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.44409i | − | 0.221376i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 17.4999i | − | 0.867440i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.6624 | −1.12058 | −0.560292 | − | 0.828295i | \(-0.689311\pi\) | ||||
−0.560292 | + | 0.828295i | \(0.689311\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.86465 | −0.141303 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.2040i | 0.698931i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.91936i | − | 0.192394i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.7787 | −0.723718 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.2006 | −0.547184 | −0.273592 | − | 0.961846i | \(-0.588212\pi\) | ||||
−0.273592 | + | 0.961846i | \(0.588212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.6665i | − | 0.568591i | −0.958737 | − | 0.284295i | \(-0.908240\pi\) | ||
0.958737 | − | 0.284295i | \(-0.0917596\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.19442i | 0.252562i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4.95937i | − | 0.240565i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.3106i | 0.692537i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.61852i | 0.174704i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.6855 | −0.707374 | −0.353687 | − | 0.935364i | \(-0.615072\pi\) | ||||
−0.353687 | + | 0.935364i | \(0.615072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.7196i | − | 1.42823i | −0.700027 | − | 0.714116i | \(-0.746829\pi\) | ||
0.700027 | − | 0.714116i | \(-0.253171\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.66359 | −0.223602 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −36.0237 | − | 6.26554i | −1.72325 | − | 0.299721i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.5496i | − | 0.789870i | −0.918709 | − | 0.394935i | \(-0.870767\pi\) | ||
0.918709 | − | 0.394935i | \(-0.129233\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.47607 | 0.260765 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.9462i | 1.37528i | 0.726054 | + | 0.687638i | \(0.241352\pi\) | ||||
−0.726054 | + | 0.687638i | \(0.758648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.663092 | 0.0314336 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.09665 | −0.430257 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.6399 | 1.82353 | 0.911765 | − | 0.410713i | \(-0.134720\pi\) | ||||
0.911765 | + | 0.410713i | \(0.134720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.8676 | 1.21806 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.9012 | 0.559168 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.730767i | 0.0342589i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.7846i | 1.01904i | 0.860458 | + | 0.509521i | \(0.170177\pi\) | ||||
−0.860458 | + | 0.509521i | \(0.829823\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.95937 | −0.231484 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.04092 | −0.141630 | −0.0708150 | − | 0.997489i | \(-0.522560\pi\) | ||||
−0.0708150 | + | 0.997489i | \(0.522560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.10105i | 0.422962i | 0.977382 | + | 0.211481i | \(0.0678286\pi\) | ||||
−0.977382 | + | 0.211481i | \(0.932171\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 7.50734i | − | 0.348144i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.3771 | 1.91470 | 0.957352 | − | 0.288925i | \(-0.0932980\pi\) | ||||
0.957352 | + | 0.288925i | \(0.0932980\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.58600 | −0.165586 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.87561 | −0.178579 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.2991 | 1.34718 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.62424 | −0.349824 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 7.65960i | − | 0.350709i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.89200 | −0.360595 | −0.180297 | − | 0.983612i | \(-0.557706\pi\) | ||||
−0.180297 | + | 0.983612i | \(0.557706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.69473i | 0.0772728i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.01448 | + | 5.83277i | −0.0461605 | + | 0.265400i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.6244 | 0.527837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.3469i | − | 1.64704i | −0.567291 | − | 0.823518i | \(-0.692008\pi\) | ||
0.567291 | − | 0.823518i | \(-0.307992\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.19414 | −0.189666 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 39.3024i | − | 1.77369i | −0.462065 | − | 0.886846i | \(-0.652891\pi\) | ||
0.462065 | − | 0.886846i | \(-0.347109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.1285i | 1.04165i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.11271i | 0.274746i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.4895i | 0.874223i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 15.2335i | − | 0.681946i | −0.940073 | − | 0.340973i | \(-0.889243\pi\) | ||
0.940073 | − | 0.340973i | \(-0.110757\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.9811 | 0.535277 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.2999 | −0.726776 | −0.363388 | − | 0.931638i | \(-0.618380\pi\) | ||||
−0.363388 | + | 0.931638i | \(0.618380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.20872i | − | 0.0537874i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.6496i | 0.561787i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.6751 | −1.40397 | −0.701987 | − | 0.712189i | \(-0.747704\pi\) | ||||
−0.701987 | + | 0.712189i | \(0.747704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.7317 | 0.828641 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.62424i | 0.336618i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.5686i | 0.465710i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 31.7520i | − | 1.39645i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9589i | 0.524939i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.8736i | 1.08973i | 0.838524 | + | 0.544865i | \(0.183419\pi\) | ||||
−0.838524 | + | 0.544865i | \(0.816581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.37517 | −0.235040 | −0.117520 | − | 0.993071i | \(-0.537494\pi\) | ||||
−0.117520 | + | 0.993071i | \(0.537494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.23448i | 0.0538769i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37.2317 | −1.62184 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6493 | + | 7.76577i | 0.941275 | + | 0.337642i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 11.5061i | − | 0.499321i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.50507 | −0.108506 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.55738i | 0.369968i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.19461 | 0.267317 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.4736 | −1.44181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.7344 | −1.32137 | −0.660687 | − | 0.750662i | \(-0.729735\pi\) | ||||
−0.660687 | + | 0.750662i | \(0.729735\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.7081 | −0.674100 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.98941 | 0.128052 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 34.5025i | − | 1.47522i | −0.675226 | − | 0.737611i | \(-0.735954\pi\) | ||
0.675226 | − | 0.737611i | \(-0.264046\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 11.5924i | − | 0.494753i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.5563 | 1.51475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.3810 | −0.824165 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.86288i | 0.121522i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.2831i | 0.520452i | 0.965548 | + | 0.260226i | \(0.0837971\pi\) | ||||
−0.965548 | + | 0.260226i | \(0.916203\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.83738 | −0.120008 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.3152 | 1.27991 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.0000 | −1.51722 | −0.758610 | − | 0.651545i | \(-0.774121\pi\) | ||||
−0.758610 | + | 0.651545i | \(0.774121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.9276 | −0.838361 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.23448 | 0.0518431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 36.4118i | − | 1.52646i | −0.646126 | − | 0.763231i | \(-0.723612\pi\) | ||
0.646126 | − | 0.763231i | \(-0.276388\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.29464 | −0.0541789 | −0.0270895 | − | 0.999633i | \(-0.508624\pi\) | ||||
−0.0270895 | + | 0.999633i | \(0.508624\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 22.6853i | − | 0.947690i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.72490 | + | 0.821792i | 0.197042 | + | 0.0342711i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.3549 | 1.34695 | 0.673476 | − | 0.739209i | \(-0.264800\pi\) | ||||
0.673476 | + | 0.739209i | \(0.264800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 17.5627i | − | 0.729880i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.83836 | 0.200729 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.8209i | 1.93912i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.591966i | − | 0.0244748i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.4859i | 1.01064i | 0.862932 | + | 0.505320i | \(0.168626\pi\) | ||||
−0.862932 | + | 0.505320i | \(0.831374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.2377i | 2.35844i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 14.4444i | − | 0.594161i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.5612 | −0.515826 | −0.257913 | − | 0.966168i | \(-0.583035\pi\) | ||||
−0.257913 | + | 0.966168i | \(0.583035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.12222 | 0.250987 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.16919i | 0.0887792i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.7320i | 1.86856i | 0.356541 | + | 0.934280i | \(0.383956\pi\) | ||||
−0.356541 | + | 0.934280i | \(0.616044\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.449630 | −0.0183408 | −0.00917039 | − | 0.999958i | \(-0.502919\pi\) | ||||
−0.00917039 | + | 0.999958i | \(0.502919\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.90488 | 0.118296 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 26.3652i | − | 1.07190i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.2249i | − | 1.02385i | −0.859031 | − | 0.511924i | \(-0.828933\pi\) | ||
0.859031 | − | 0.511924i | \(-0.171067\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 5.75709i | − | 0.233289i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.07492i | 0.124398i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.6265i | − | 0.954264i | −0.878832 | − | 0.477132i | \(-0.841676\pi\) | ||
0.878832 | − | 0.477132i | \(-0.158324\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.23178 | −0.170642 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 31.3914i | − | 1.26377i | −0.775063 | − | 0.631884i | \(-0.782282\pi\) | ||
0.775063 | − | 0.631884i | \(-0.217718\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.1598 | 0.609322 | 0.304661 | − | 0.952461i | \(-0.401457\pi\) | ||||
0.304661 | + | 0.952461i | \(0.401457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.821792 | − | 4.72490i | 0.0329774 | − | 0.189604i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.818570i | 0.0327953i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 46.6048i | − | 1.86122i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.1981 | 0.566115 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.7377 | −1.34308 | −0.671538 | − | 0.740970i | \(-0.734366\pi\) | ||||
−0.671538 | + | 0.740970i | \(0.734366\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.8897 | −0.711053 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.95560 | −0.276025 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.24165 | 0.128439 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 15.7877i | − | 0.624551i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.8579i | − | 0.823837i | −0.911221 | − | 0.411918i | \(-0.864859\pi\) | ||
0.911221 | − | 0.411918i | \(-0.135141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.3538 | 1.59140 | 0.795700 | − | 0.605692i | \(-0.207103\pi\) | ||||
0.795700 | + | 0.605692i | \(0.207103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.79315 | −0.188730 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 11.2696i | − | 0.443054i | −0.975154 | − | 0.221527i | \(-0.928896\pi\) | ||
0.975154 | − | 0.221527i | \(-0.0711041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 70.3332i | 2.76082i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.26762 | 0.363227 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.7439 | −0.537842 | −0.268921 | − | 0.963162i | \(-0.586667\pi\) | ||||
−0.268921 | + | 0.963162i | \(0.586667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.92419 | 0.348697 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.1738 | −0.591986 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1309 | 0.394645 | 0.197322 | − | 0.980339i | \(-0.436775\pi\) | ||||
0.197322 | + | 0.980339i | \(0.436775\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.1223i | 1.40499i | 0.711686 | + | 0.702497i | \(0.247932\pi\) | ||||
−0.711686 | + | 0.702497i | \(0.752068\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.93578 | −0.114016 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9.41193i | − | 0.364979i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.0350 | − | 3.83250i | −0.853198 | − | 0.148395i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.1120 | −0.738912 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.8611i | 2.73556i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.2950 | 1.16779 | 0.583893 | − | 0.811831i | \(-0.301529\pi\) | ||||
0.583893 | + | 0.811831i | \(0.301529\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.2931i | 1.77919i | 0.456751 | + | 0.889594i | \(0.349013\pi\) | ||||
−0.456751 | + | 0.889594i | \(0.650987\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.3501i | 0.550704i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.7159i | 0.487274i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.7794i | 0.527256i | 0.964624 | + | 0.263628i | \(0.0849191\pi\) | ||||
−0.964624 | + | 0.263628i | \(0.915081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.86465 | −0.109453 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.2900 | −0.850415 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4.53422i | − | 0.172740i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 28.6475i | − | 1.08980i | −0.838500 | − | 0.544902i | \(-0.816567\pi\) | ||
0.838500 | − | 0.544902i | \(-0.183433\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.54599 | −0.286648 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.7787 | −0.560589 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.9870i | 0.794938i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.2452i | 0.765743i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.6434i | 0.666381i | 0.942859 | + | 0.333191i | \(0.108125\pi\) | ||||
−0.942859 | + | 0.333191i | \(0.891875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 21.8273i | − | 0.823231i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.19442i | 0.195633i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.49214 | 0.0561176 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 14.2902i | − | 0.536679i | −0.963324 | − | 0.268339i | \(-0.913525\pi\) | ||
0.963324 | − | 0.268339i | \(-0.0864749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.6998 | 0.588789 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.16947 | − | 35.4714i | 0.231049 | − | 1.32841i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.61852i | 0.135325i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.08011 | −0.227066 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.3841i | 0.760200i | 0.924945 | + | 0.380100i | \(0.124110\pi\) | ||||
−0.924945 | + | 0.380100i | \(0.875890\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.0467 | −0.485886 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.7552 | 0.548751 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.66359 | −0.173201 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.5609 | −1.05926 | −0.529632 | − | 0.848228i | \(-0.677670\pi\) | ||||
−0.529632 | + | 0.848228i | \(0.677670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.7710i | 0.879203i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.55848i | 0.0575639i | 0.999586 | + | 0.0287819i | \(0.00916284\pi\) | ||||
−0.999586 | + | 0.0287819i | \(0.990837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.47607 | 0.201988 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.7567 | −0.654076 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.69465i | 0.283052i | 0.989935 | + | 0.141526i | \(0.0452009\pi\) | ||||
−0.989935 | + | 0.141526i | \(0.954799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.51329i | 0.165800i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.862609 | 0.0316461 | 0.0158230 | − | 0.999875i | \(-0.494963\pi\) | ||||
0.0158230 | + | 0.999875i | \(0.494963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.09665 | −0.333276 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.91936 | −0.143402 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.5639 | −0.385996 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.83821 | −0.140058 | −0.0700292 | − | 0.997545i | \(-0.522309\pi\) | ||||
−0.0700292 | + | 0.997545i | \(0.522309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.97907i | 0.181447i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.9012 | 0.433130 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.5793i | 0.929696i | 0.885391 | + | 0.464848i | \(0.153891\pi\) | ||||
−0.885391 | + | 0.464848i | \(0.846109\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.02338 | + | 28.8819i | −0.182337 | + | 1.04835i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.4410 | −0.704735 | −0.352367 | − | 0.935862i | \(-0.614623\pi\) | ||||
−0.352367 | + | 0.935862i | \(0.614623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.69036i | 0.133600i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.95937 | −0.179307 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.81119i | − | 0.245938i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 36.0564i | − | 1.30023i | −0.759838 | − | 0.650113i | \(-0.774722\pi\) | ||
0.759838 | − | 0.650113i | \(-0.225278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 24.0339i | − | 0.865560i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 16.6369i | − | 0.598389i | −0.954192 | − | 0.299194i | \(-0.903282\pi\) | ||
0.954192 | − | 0.299194i | \(-0.0967179\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.50734i | − | 0.269672i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.53415 | −0.126787 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.2641 | 1.15598 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 96.5055i | 3.45324i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.66359i | 0.166663i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.87561 | −0.138327 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.5394 | −0.482628 | −0.241314 | − | 0.970447i | \(-0.577578\pi\) | ||||
−0.241314 | + | 0.970447i | \(0.577578\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 13.3344i | − | 0.474716i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 24.6001i | − | 0.874681i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.86232i | − | 0.243688i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 7.65960i | − | 0.271658i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 24.8048i | − | 0.878633i | −0.898332 | − | 0.439316i | \(-0.855221\pi\) | ||
0.898332 | − | 0.439316i | \(-0.144779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.7611 | 0.911362 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 0.663092i | − | 0.0234292i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 92.7531 | 3.27318 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.01448 | + | 5.83277i | −0.0357558 | + | 0.205578i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 29.3882i | − | 1.03452i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.57360 | 0.336590 | 0.168295 | − | 0.985737i | \(-0.446174\pi\) | ||||
0.168295 | + | 0.985737i | \(0.446174\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2723i | 0.992776i | 0.868101 | + | 0.496388i | \(0.165341\pi\) | ||||
−0.868101 | + | 0.496388i | \(0.834659\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.93152 | 0.172956 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.19414 | −0.146914 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.5441 | 1.27852 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.730767 | 0.0255351 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.41542 | 0.189000 | 0.0944998 | − | 0.995525i | \(-0.469875\pi\) | ||||
0.0944998 | + | 0.995525i | \(0.469875\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.9798i | 0.557022i | 0.960433 | + | 0.278511i | \(0.0898408\pi\) | ||||
−0.960433 | + | 0.278511i | \(0.910159\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.11271i | 0.212817i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.60684 | 0.194969 | 0.0974845 | − | 0.995237i | \(-0.468920\pi\) | ||||
0.0974845 | + | 0.995237i | \(0.468920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.6944 | −1.03133 | −0.515665 | − | 0.856790i | \(-0.672455\pi\) | ||||
−0.515665 | + | 0.856790i | \(0.672455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.67570i | − | 0.0581293i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 27.1579i | − | 0.940965i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.9811 | 0.414624 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.50734 | −0.259492 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.84512 | 0.270844 | 0.135422 | − | 0.990788i | \(-0.456761\pi\) | ||||
0.135422 | + | 0.990788i | \(0.456761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.25092 | −0.250032 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.09883 | 0.0378459 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6496i | 0.435159i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.5472 | 1.11834 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.0056i | 0.755231i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.35269 | + | 13.5268i | −0.0806492 | + | 0.463693i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.6885 | −1.01652 | −0.508258 | − | 0.861205i | \(-0.669710\pi\) | ||||
−0.508258 | + | 0.861205i | \(0.669710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.62424i | 0.260743i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.6320 | 1.21717 | 0.608583 | − | 0.793490i | \(-0.291738\pi\) | ||||
0.608583 | + | 0.793490i | \(0.291738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 0.919485i | − | 0.0313724i | −0.999877 | − | 0.0156862i | \(-0.995007\pi\) | ||
0.999877 | − | 0.0156862i | \(-0.00499328\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 5.22402i | − | 0.178034i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 20.4788i | − | 0.697105i | −0.937289 | − | 0.348553i | \(-0.886673\pi\) | ||
0.937289 | − | 0.348553i | \(-0.113327\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.9589i | 0.406616i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.59538i | 0.257953i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −95.9684 | −3.25551 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.71959 | 0.0582660 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 11.6244i | − | 0.393427i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.23448i | 0.0417329i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.6713 | −1.06946 | −0.534731 | − | 0.845022i | \(-0.679587\pi\) | ||||
−0.534731 | + | 0.845022i | \(0.679587\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.5662 | −0.727409 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.9512i | 0.638482i | 0.947674 | + | 0.319241i | \(0.103428\pi\) | ||||
−0.947674 | + | 0.319241i | \(0.896572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.88729i | − | 0.130818i | −0.997859 | − | 0.0654089i | \(-0.979165\pi\) | ||
0.997859 | − | 0.0654089i | \(-0.0208352\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 11.5061i | − | 0.386772i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 14.2199i | − | 0.477459i | −0.971086 | − | 0.238729i | \(-0.923269\pi\) | ||
0.971086 | − | 0.238729i | \(-0.0767309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.58652i | − | 0.287982i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.11271 | 0.204784 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 39.6035i | − | 1.32528i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.19461 | 0.207063 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.486473 | − | 2.79698i | 0.0162429 | − | 0.0933883i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.0112i | 1.16769i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.9868 | −1.26552 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 5.91702i | − | 0.196906i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.7081 | −0.522156 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.8964 | 0.859876 | 0.429938 | − | 0.902858i | \(-0.358535\pi\) | ||||
0.429938 | + | 0.902858i | \(0.358535\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.20872 | −0.0400908 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.4760 | −1.14224 | −0.571120 | − | 0.820867i | \(-0.693491\pi\) | ||||
−0.571120 | + | 0.820867i | \(0.693491\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.9579 | 0.792892 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 11.5924i | − | 0.383234i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.0167i | 0.363803i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.0066 | 1.45164 | 0.725822 | − | 0.687882i | \(-0.241459\pi\) | ||||
0.725822 | + | 0.687882i | \(0.241459\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.70481 | −0.0891266 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 9.34576i | − | 0.307619i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.86288i | 0.0941309i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.5686 | 0.347120 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.44279 | 0.211381 | 0.105691 | − | 0.994399i | \(-0.466295\pi\) | ||||
0.105691 | + | 0.994399i | \(0.466295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.7509 | −1.36833 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.5678 | −0.476927 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.3152 | 0.991413 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.82216i | 0.0921959i | 0.998937 | + | 0.0460980i | \(0.0146786\pi\) | ||||
−0.998937 | + | 0.0460980i | \(0.985321\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.2833 | −0.596653 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.2138i | − | 1.37613i | −0.725649 | − | 0.688065i | \(-0.758460\pi\) | ||
0.725649 | − | 0.688065i | \(-0.241540\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.9947 | − | 3.47764i | −0.651117 | − | 0.113248i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.23448 | 0.0401575 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.3580i | 1.14898i | 0.818511 | + | 0.574491i | \(0.194800\pi\) | ||||
−0.818511 | + | 0.574491i | \(0.805200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.98237 | −0.291580 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.2025i | 0.428120i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 19.2667i | − | 0.624108i | −0.950064 | − | 0.312054i | \(-0.898983\pi\) | ||
0.950064 | − | 0.312054i | \(-0.101017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 22.6853i | − | 0.734077i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 28.5072i | − | 0.921506i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 3.53634i | − | 0.114194i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.3601 | −0.818069 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.55738 | 0.275758 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 17.5627i | − | 0.565363i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 0.779855i | − | 0.0250785i | −0.999921 | − | 0.0125392i | \(-0.996009\pi\) | ||
0.999921 | − | 0.0125392i | \(-0.00399147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.8114 | 1.21468 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.9761 | 0.833612 | 0.416806 | − | 0.908996i | \(-0.363150\pi\) | ||||
0.416806 | + | 0.908996i | \(0.363150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 18.2440i | − | 0.584875i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 0.591966i | − | 0.0189581i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.4340i | 1.22961i | 0.788678 | + | 0.614806i | \(0.210766\pi\) | ||||
−0.788678 | + | 0.614806i | \(0.789234\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.05329i | 0.129544i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.98941i | − | 0.0954446i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.1045 | −1.18345 | −0.591724 | − | 0.806141i | \(-0.701553\pi\) | ||||
−0.591724 | + | 0.806141i | \(0.701553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 14.4444i | − | 0.460235i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.41239 | −0.204109 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.6471 | − | 3.93897i | −0.720137 | − | 0.125252i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 50.5058i | − | 1.60437i | −0.597076 | − | 0.802185i | \(-0.703671\pi\) | ||
0.597076 | − | 0.802185i | \(-0.296329\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.3479 | −0.645722 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.16919i | 0.0687681i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7293 | 0.561492 | 0.280746 | − | 0.959782i | \(-0.409418\pi\) | ||||
0.280746 | + | 0.959782i | \(0.409418\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.86288 | 0.0905775 |
(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 | 5520.2.be.b.1471.5 | yes | 16 | |
4.3 | odd | 2 | 5520.2.be.a.1471.12 | yes | 16 | ||
23.22 | odd | 2 | 5520.2.be.a.1471.4 | ✓ | 16 | ||
92.91 | even | 2 | inner | 5520.2.be.b.1471.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.a.1471.4 | ✓ | 16 | 23.22 | odd | 2 | ||
5520.2.be.a.1471.12 | yes | 16 | 4.3 | odd | 2 | ||
5520.2.be.b.1471.5 | yes | 16 | 1.1 | even | 1 | trivial | |
5520.2.be.b.1471.13 | yes | 16 | 92.91 | even | 2 | inner |