Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1241,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("1380.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.i (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: | \(11.0193554789\) |
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: | \( x^{16} - x^{14} - 4 x^{13} - 2 x^{12} + 12 x^{11} + 17 x^{10} + 16 x^{9} - 110 x^{8} + 48 x^{7} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.9 | ||
Root | \(-0.208374 + 1.71947i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1380.1241 |
Dual form | 1380.2.i.b.1241.10 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.208374 | − | 1.71947i | 0.120305 | − | 0.992737i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.187545i | − | 0.0708855i | −0.999372 | − | 0.0354428i | \(-0.988716\pi\) | ||
0.999372 | − | 0.0354428i | \(-0.0112841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.91316 | − | 0.716587i | −0.971053 | − | 0.238862i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.36350 | −1.31565 | −0.657823 | − | 0.753173i | \(-0.728522\pi\) | ||||
−0.657823 | + | 0.753173i | \(0.728522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.75087 | 1.87235 | 0.936177 | − | 0.351528i | \(-0.114338\pi\) | ||||
0.936177 | + | 0.351528i | \(0.114338\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.208374 | − | 1.71947i | 0.0538020 | − | 0.443965i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.956365 | 0.231953 | 0.115976 | − | 0.993252i | \(-0.463000\pi\) | ||||
0.115976 | + | 0.993252i | \(0.463000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.93504i | − | 1.36159i | −0.732473 | − | 0.680796i | \(-0.761634\pi\) | ||
0.732473 | − | 0.680796i | \(-0.238366\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.322479 | − | 0.0390797i | −0.0703707 | − | 0.00852788i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.02726 | − | 2.60406i | −0.839743 | − | 0.542984i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.83918 | + | 4.85978i | −0.353950 | + | 0.935264i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.44484i | − | 0.825387i | −0.910870 | − | 0.412693i | \(-0.864588\pi\) | ||
0.910870 | − | 0.412693i | \(-0.135412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.97602 | −0.714115 | −0.357057 | − | 0.934082i | \(-0.616220\pi\) | ||||
−0.357057 | + | 0.934082i | \(0.616220\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.909242 | + | 7.50292i | −0.158279 | + | 1.30609i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.187545i | − | 0.0317010i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.51993i | − | 1.56507i | −0.622609 | − | 0.782533i | \(-0.713927\pi\) | ||
0.622609 | − | 0.782533i | \(-0.286073\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.40671 | − | 11.6079i | 0.225254 | − | 1.85876i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.47654i | − | 1.32381i | −0.749586 | − | 0.661907i | \(-0.769748\pi\) | ||
0.749586 | − | 0.661907i | \(-0.230252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.63510i | 1.16434i | 0.813066 | + | 0.582171i | \(0.197797\pi\) | ||||
−0.813066 | + | 0.582171i | \(0.802203\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.91316 | − | 0.716587i | −0.434268 | − | 0.106823i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.92127i | − | 1.15544i | −0.816236 | − | 0.577718i | \(-0.803943\pi\) | ||
0.816236 | − | 0.577718i | \(-0.196057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.96483 | 0.994975 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.199282 | − | 1.64444i | 0.0279051 | − | 0.230268i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.24442 | −0.857737 | −0.428869 | − | 0.903367i | \(-0.641088\pi\) | ||||
−0.428869 | + | 0.903367i | \(0.641088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.36350 | −0.588375 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.2051 | − | 1.23671i | −1.35170 | − | 0.163806i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.525495i | 0.0684136i | 0.999415 | + | 0.0342068i | \(0.0108905\pi\) | ||||
−0.999415 | + | 0.0342068i | \(0.989110\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.02279i | 0.258992i | 0.991580 | + | 0.129496i | \(0.0413359\pi\) | ||||
−0.991580 | + | 0.129496i | \(0.958664\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.134393 | + | 0.546350i | −0.0169319 | + | 0.0688336i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.75087 | 0.837343 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.87613i | 0.962222i | 0.876660 | + | 0.481111i | \(0.159767\pi\) | ||||
−0.876660 | + | 0.481111i | \(0.840233\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.31679 | + | 6.38215i | −0.640066 | + | 0.768320i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.38671i | 0.283251i | 0.989920 | + | 0.141625i | \(0.0452329\pi\) | ||||
−0.989920 | + | 0.141625i | \(0.954767\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.28743 | −0.501806 | −0.250903 | − | 0.968012i | \(-0.580727\pi\) | ||||
−0.250903 | + | 0.968012i | \(0.580727\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.208374 | − | 1.71947i | 0.0240610 | − | 0.198547i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.818355i | 0.0932603i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4888i | 1.51761i | 0.651316 | + | 0.758807i | \(0.274217\pi\) | ||||
−0.651316 | + | 0.758807i | \(0.725783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.97301 | + | 4.17507i | 0.885890 | + | 0.463896i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.08526 | −0.448416 | −0.224208 | − | 0.974541i | \(-0.571979\pi\) | ||||
−0.224208 | + | 0.974541i | \(0.571979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.956365 | 0.103732 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.64278 | − | 0.926191i | −0.819392 | − | 0.0992981i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.73121 | −0.183508 | −0.0917542 | − | 0.995782i | \(-0.529247\pi\) | ||||
−0.0917542 | + | 0.995782i | \(0.529247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.26610i | − | 0.132723i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.828501 | + | 6.83665i | −0.0859116 | + | 0.708928i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.93504i | − | 0.608923i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.4359i | − | 1.26267i | −0.775509 | − | 0.631337i | \(-0.782507\pi\) | ||
0.775509 | − | 0.631337i | \(-0.217493\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.7116 | + | 3.12683i | 1.27756 | + | 0.314258i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.126407i | 0.0125780i | 0.999980 | + | 0.00628900i | \(0.00200186\pi\) | ||||
−0.999980 | + | 0.00628900i | \(0.997998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.2600i | − | 1.10948i | −0.832024 | − | 0.554740i | \(-0.812818\pi\) | ||
0.832024 | − | 0.554740i | \(-0.187182\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.322479 | − | 0.0390797i | −0.0314707 | − | 0.00381378i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.76751 | 0.557566 | 0.278783 | − | 0.960354i | \(-0.410069\pi\) | ||||
0.278783 | + | 0.960354i | \(0.410069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.83222i | 0.462842i | 0.972854 | + | 0.231421i | \(0.0743375\pi\) | ||||
−0.972854 | + | 0.231421i | \(0.925662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.3692 | − | 1.98371i | −1.55370 | − | 0.188285i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3323 | 1.25420 | 0.627101 | − | 0.778938i | \(-0.284241\pi\) | ||||
0.627101 | + | 0.778938i | \(0.284241\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.02726 | − | 2.60406i | −0.375544 | − | 0.242830i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.6664 | − | 4.83759i | −1.81816 | − | 0.447235i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.179362i | − | 0.0164421i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.04016 | 0.730924 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.5752 | − | 1.76629i | −1.31420 | − | 0.159261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.62198 | 0.321398 | 0.160699 | − | 0.987003i | \(-0.448625\pi\) | ||||
0.160699 | + | 0.987003i | \(0.448625\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.1283 | + | 1.59096i | 1.15589 | + | 0.140076i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.51312i | 0.219573i | 0.993955 | + | 0.109786i | \(0.0350166\pi\) | ||||
−0.993955 | + | 0.109786i | \(0.964983\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.11309 | −0.0965172 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.83918 | + | 4.85978i | −0.158291 | + | 0.418263i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.4039 | −1.57235 | −0.786176 | − | 0.618003i | \(-0.787942\pi\) | ||||
−0.786176 | + | 0.618003i | \(0.787942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.21774 | 0.103287 | 0.0516436 | − | 0.998666i | \(-0.483554\pi\) | ||||
0.0516436 | + | 0.998666i | \(0.483554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.6204 | − | 1.65059i | −1.14704 | − | 0.139005i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29.4575 | −2.46336 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.44484i | − | 0.369124i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.45129 | − | 11.9758i | 0.119700 | − | 0.987749i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.1340 | 1.32175 | 0.660876 | − | 0.750495i | \(-0.270185\pi\) | ||||
0.660876 | + | 0.750495i | \(0.270185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4844 | −0.934590 | −0.467295 | − | 0.884102i | \(-0.654771\pi\) | ||||
−0.467295 | + | 0.884102i | \(0.654771\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.78605 | − | 0.685319i | −0.225238 | − | 0.0554048i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.97602 | −0.319362 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 22.3016i | − | 1.77986i | −0.456097 | − | 0.889930i | \(-0.650753\pi\) | ||
0.456097 | − | 0.889930i | \(-0.349247\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.30118 | + | 10.7371i | −0.103190 | + | 0.851507i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.488380 | + | 0.755295i | −0.0384897 | + | 0.0595256i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2300 | 0.957928 | 0.478964 | − | 0.877834i | \(-0.341012\pi\) | ||||
0.478964 | + | 0.877834i | \(0.341012\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.909242 | + | 7.50292i | −0.0707844 | + | 0.584101i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 9.12412i | − | 0.706046i | −0.935615 | − | 0.353023i | \(-0.885154\pi\) | ||
0.935615 | − | 0.353023i | \(-0.114846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.5743 | 2.50571 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.25298 | + | 17.2897i | −0.325233 | + | 1.32218i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6174i | 0.959284i | 0.877464 | + | 0.479642i | \(0.159234\pi\) | ||||
−0.877464 | + | 0.479642i | \(0.840766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.187545i | − | 0.0141771i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.903573 | + | 0.109500i | 0.0679167 | + | 0.00823050i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 20.2204i | − | 1.51134i | −0.654951 | − | 0.755671i | \(-0.727311\pi\) | ||
0.654951 | − | 0.755671i | \(-0.272689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.9913i | 1.03996i | 0.854177 | + | 0.519982i | \(0.174061\pi\) | ||||
−0.854177 | + | 0.519982i | \(0.825939\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.47813 | + | 0.421497i | 0.257110 | + | 0.0311580i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.51993i | − | 0.699919i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.17310 | −0.305168 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.911429 | + | 0.344930i | 0.0662967 | + | 0.0250899i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.1977 | 1.02731 | 0.513653 | − | 0.857998i | \(-0.328292\pi\) | ||||
0.513653 | + | 0.857998i | \(0.328292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.1913 | 0.949528 | 0.474764 | − | 0.880113i | \(-0.342533\pi\) | ||||
0.474764 | + | 0.880113i | \(0.342533\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.40671 | − | 11.6079i | 0.100736 | − | 0.831261i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5576i | 1.53592i | 0.640499 | + | 0.767959i | \(0.278728\pi\) | ||||
−0.640499 | + | 0.767959i | \(0.721272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.91585i | − | 0.135811i | −0.997692 | − | 0.0679055i | \(-0.978368\pi\) | ||
0.997692 | − | 0.0679055i | \(-0.0216316\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.5428 | + | 1.64118i | 0.955233 | + | 0.115760i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.833610 | −0.0585080 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 8.47654i | − | 0.592027i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.86603 | + | 10.4719i | 0.685737 | + | 0.727850i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.8976i | 1.79137i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.3873 | 1.40352 | 0.701761 | − | 0.712412i | \(-0.252397\pi\) | ||||
0.701761 | + | 0.712412i | \(0.252397\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.10389 | + | 0.497330i | 0.281194 | + | 0.0340765i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.63510i | 0.520710i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.745685i | 0.0506204i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.893390 | + | 7.37211i | −0.0603697 | + | 0.498161i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.45630 | 0.434298 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.96138 | −0.198309 | −0.0991543 | − | 0.995072i | \(-0.531614\pi\) | ||||
−0.0991543 | + | 0.995072i | \(0.531614\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.91316 | − | 0.716587i | −0.194211 | − | 0.0477725i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.6922 | −1.10790 | −0.553949 | − | 0.832551i | \(-0.686880\pi\) | ||||
−0.553949 | + | 0.832551i | \(0.686880\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.105691i | 0.00698424i | 0.999994 | + | 0.00349212i | \(0.00111158\pi\) | ||||
−0.999994 | + | 0.00349212i | \(0.998888\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.40714 | + | 0.170524i | 0.0925829 | + | 0.0112197i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.0306i | 1.44327i | 0.692273 | + | 0.721636i | \(0.256610\pi\) | ||||
−0.692273 | + | 0.721636i | \(0.743390\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 7.92127i | − | 0.516727i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.1937 | + | 2.81073i | 1.50659 | + | 0.182576i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8622i | 1.22009i | 0.792365 | + | 0.610047i | \(0.208849\pi\) | ||||
−0.792365 | + | 0.610047i | \(0.791151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.1539i | − | 0.911733i | −0.890048 | − | 0.455867i | \(-0.849329\pi\) | ||
0.890048 | − | 0.455867i | \(-0.150671\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.84028 | − | 12.8394i | 0.567104 | − | 0.823646i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.96483 | 0.444966 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 40.0667i | − | 2.54938i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.851264 | + | 7.02449i | −0.0539466 | + | 0.445159i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.81212 | 0.556216 | 0.278108 | − | 0.960550i | \(-0.410293\pi\) | ||||
0.278108 | + | 0.960550i | \(0.410293\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.5730 | + | 11.3628i | 1.10480 | + | 0.714375i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.199282 | − | 1.64444i | 0.0124795 | − | 0.102979i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.7148i | 1.35453i | 0.735739 | + | 0.677265i | \(0.236835\pi\) | ||||
−0.735739 | + | 0.677265i | \(0.763165\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.78542 | −0.110941 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.18512 | + | 12.9485i | −0.197154 | + | 0.801494i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.3401 | 1.87085 | 0.935424 | − | 0.353527i | \(-0.115018\pi\) | ||||
0.935424 | + | 0.353527i | \(0.115018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.24442 | −0.383592 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.360741 | + | 2.97677i | −0.0220770 | + | 0.182176i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 20.9344i | − | 1.27639i | −0.769874 | − | 0.638196i | \(-0.779681\pi\) | ||
0.769874 | − | 0.638196i | \(-0.220319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.6077 | 1.25183 | 0.625915 | − | 0.779891i | \(-0.284726\pi\) | ||||
0.625915 | + | 0.779891i | \(0.284726\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.17701 | − | 0.263822i | −0.131759 | − | 0.0159672i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.36350 | −0.263129 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.09324 | −0.486276 | −0.243138 | − | 0.969992i | \(-0.578177\pi\) | ||||
−0.243138 | + | 0.969992i | \(0.578177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.5828 | + | 2.84917i | 0.693444 | + | 0.170575i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.04239 | −0.360459 | −0.180229 | − | 0.983625i | \(-0.557684\pi\) | ||||
−0.180229 | + | 0.983625i | \(0.557684\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.14109i | 0.365050i | 0.983201 | + | 0.182525i | \(0.0584270\pi\) | ||||
−0.983201 | + | 0.182525i | \(0.941573\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.2051 | − | 1.23671i | −0.604500 | − | 0.0732564i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.58974 | −0.0938392 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0854 | −0.946198 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.3832 | − | 2.59132i | −1.25350 | − | 0.151906i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.7278 | 1.15251 | 0.576255 | − | 0.817270i | \(-0.304514\pi\) | ||||
0.576255 | + | 0.817270i | \(0.304514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.525495i | 0.0305955i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.02526 | − | 21.2056i | 0.465673 | − | 1.23048i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.1875 | − | 17.5797i | −1.57230 | − | 1.01666i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.43193 | 0.0825350 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.217354 | + | 0.0263401i | 0.0124867 | + | 0.00151320i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.02279i | 0.115825i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.60843 | −0.263017 | −0.131509 | − | 0.991315i | \(-0.541982\pi\) | ||||
−0.131509 | + | 0.991315i | \(0.541982\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.3612 | − | 2.34629i | −1.10142 | − | 0.133476i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.8041i | − | 0.669349i | −0.942334 | − | 0.334674i | \(-0.891374\pi\) | ||
0.942334 | − | 0.334674i | \(-0.108626\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.0273i | 1.18853i | 0.804268 | + | 0.594266i | \(0.202557\pi\) | ||||
−0.804268 | + | 0.594266i | \(0.797443\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.134393 | + | 0.546350i | −0.00757217 | + | 0.0307833i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.3475i | 1.53599i | 0.640455 | + | 0.767996i | \(0.278746\pi\) | ||||
−0.640455 | + | 0.767996i | \(0.721254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.3951i | 1.08592i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.20180 | − | 9.91706i | 0.0670779 | − | 0.553516i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.67607i | − | 0.315825i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.75087 | 0.374471 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.30886 | + | 1.00691i | 0.459481 | + | 0.0556822i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.48560 | −0.0819037 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.1655 | 0.888534 | 0.444267 | − | 0.895894i | \(-0.353464\pi\) | ||||
0.444267 | + | 0.895894i | \(0.353464\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.82186 | + | 27.7331i | −0.373836 | + | 1.51976i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.87613i | 0.430319i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4862i | 0.680168i | 0.940395 | + | 0.340084i | \(0.110455\pi\) | ||||
−0.940395 | + | 0.340084i | \(0.889545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.77812 | − | 22.9246i | 0.150887 | − | 1.24509i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.3494 | 0.939522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.61904i | − | 0.141415i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.31679 | + | 6.38215i | −0.286246 | + | 0.343603i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.95560i | − | 0.427079i | −0.976934 | − | 0.213539i | \(-0.931501\pi\) | ||
0.976934 | − | 0.213539i | \(-0.0684992\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.5081 | 0.562487 | 0.281244 | − | 0.959636i | \(-0.409253\pi\) | ||||
0.281244 | + | 0.959636i | \(0.409253\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.4161 | + | 32.8077i | −0.662720 | + | 1.75115i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 14.0694i | − | 0.748839i | −0.927259 | − | 0.374420i | \(-0.877842\pi\) | ||
0.927259 | − | 0.374420i | \(-0.122158\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.38671i | 0.126674i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.308408 | − | 0.0373744i | −0.0163227 | − | 0.00197806i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.4414 | 1.65941 | 0.829707 | − | 0.558198i | \(-0.188507\pi\) | ||||
0.829707 | + | 0.558198i | \(0.188507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2247 | −0.853933 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.67536 | − | 13.8248i | 0.0879338 | − | 0.725615i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.28743 | −0.224414 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.5851i | − | 0.761335i | −0.924712 | − | 0.380668i | \(-0.875694\pi\) | ||
0.924712 | − | 0.380668i | \(-0.124306\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.07418 | + | 24.6935i | −0.316209 | + | 1.28549i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.17111i | 0.0608011i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.87471i | 0.148847i | 0.997227 | + | 0.0744234i | \(0.0237116\pi\) | ||||
−0.997227 | + | 0.0744234i | \(0.976288\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.208374 | − | 1.71947i | 0.0107604 | − | 0.0887931i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 30.0066i | − | 1.54542i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.7462i | 1.27113i | 0.772048 | + | 0.635564i | \(0.219232\pi\) | ||||
−0.772048 | + | 0.635564i | \(0.780768\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.754727 | − | 6.22788i | 0.0386658 | − | 0.319064i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.3468 | 1.29516 | 0.647580 | − | 0.761997i | \(-0.275781\pi\) | ||||
0.647580 | + | 0.761997i | \(0.275781\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.818355i | 0.0417073i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.47122 | − | 22.2423i | 0.278118 | − | 1.13064i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.48056 | −0.0750676 | −0.0375338 | − | 0.999295i | \(-0.511950\pi\) | ||||
−0.0375338 | + | 0.999295i | \(0.511950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.85154 | − | 2.49043i | −0.194781 | − | 0.125947i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.32124 | + | 0.523670i | 0.217978 | + | 0.0264157i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.4888i | 0.678697i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.5206 | −1.63216 | −0.816082 | − | 0.577937i | \(-0.803858\pi\) | ||||
−0.816082 | + | 0.577937i | \(0.803858\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.231939 | + | 1.91393i | −0.0116115 | + | 0.0958162i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.9854 | 0.548586 | 0.274293 | − | 0.961646i | \(-0.411556\pi\) | ||||
0.274293 | + | 0.961646i | \(0.411556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.8416 | −1.33708 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.97301 | + | 4.17507i | 0.396182 | + | 0.207461i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.5402i | 2.05907i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.4281 | 0.663978 | 0.331989 | − | 0.943283i | \(-0.392280\pi\) | ||||
0.331989 | + | 0.943283i | \(0.392280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.83490 | + | 31.6450i | −0.189162 | + | 1.56093i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0985542 | 0.00484953 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.08526 | −0.200538 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.253746 | − | 2.09387i | 0.0124260 | − | 0.102537i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.50684 | −0.464440 | −0.232220 | − | 0.972663i | \(-0.574599\pi\) | ||||
−0.232220 | + | 0.972663i | \(0.574599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 28.7212i | − | 1.39978i | −0.714249 | − | 0.699892i | \(-0.753232\pi\) | ||
0.714249 | − | 0.699892i | \(-0.246768\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.67628 | + | 23.0759i | −0.275990 | + | 1.12199i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.956365 | 0.0463905 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.379365 | 0.0183588 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.13818 | + | 50.6512i | −0.296354 | + | 2.44546i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.4182 | 1.17619 | 0.588093 | − | 0.808794i | \(-0.299879\pi\) | ||||
0.588093 | + | 0.808794i | \(0.299879\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.86449i | − | 0.329887i | −0.986303 | − | 0.164943i | \(-0.947256\pi\) | ||
0.986303 | − | 0.164943i | \(-0.0527441\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.64278 | − | 0.926191i | −0.366443 | − | 0.0444075i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.4552 | + | 23.9020i | −0.739323 | + | 1.14339i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.7576 | 1.70662 | 0.853308 | − | 0.521407i | \(-0.174593\pi\) | ||||
0.853308 | + | 0.521407i | \(0.174593\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.2897 | − | 4.99091i | −0.966174 | − | 0.237662i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.12257i | 0.433426i | 0.976235 | + | 0.216713i | \(0.0695336\pi\) | ||||
−0.976235 | + | 0.216713i | \(0.930466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.73121 | −0.0820674 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.36192 | − | 27.7420i | 0.159013 | − | 1.31215i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.7685i | 1.59363i | 0.604221 | + | 0.796817i | \(0.293484\pi\) | ||||
−0.604221 | + | 0.796817i | \(0.706516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.9874i | 1.74167i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.39306 | + | 19.7471i | −0.112436 | + | 0.927802i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.26610i | − | 0.0593555i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.5785i | − | 1.24329i | −0.783299 | − | 0.621645i | \(-0.786465\pi\) | ||
0.783299 | − | 0.621645i | \(-0.213535\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.75893 | + | 4.64772i | −0.0820997 | + | 0.216937i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6065i | 0.540566i | 0.962781 | + | 0.270283i | \(0.0871173\pi\) | ||||
−0.962781 | + | 0.270283i | \(0.912883\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.61792 | 0.168139 | 0.0840695 | − | 0.996460i | \(-0.473208\pi\) | ||||
0.0840695 | + | 0.996460i | \(0.473208\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.828501 | + | 6.83665i | −0.0384208 | + | 0.317042i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.03785 | −0.140575 | −0.0702874 | − | 0.997527i | \(-0.522392\pi\) | ||||
−0.0702874 | + | 0.997527i | \(0.522392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.47713 | 0.0682076 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −38.3469 | − | 4.64708i | −1.76693 | − | 0.214126i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 33.3158i | − | 1.53186i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.93504i | − | 0.272318i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.1910 | + | 4.47467i | 0.832908 | + | 0.204881i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.0908651 | 0.00415173 | 0.00207587 | − | 0.999998i | \(-0.499339\pi\) | ||||
0.00207587 | + | 0.999998i | \(0.499339\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 64.2678i | − | 2.93036i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.19694 | + | 0.997139i | 0.0544628 | + | 0.0453714i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 12.4359i | − | 0.564685i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.2817 | −0.919054 | −0.459527 | − | 0.888164i | \(-0.651981\pi\) | ||||
−0.459527 | + | 0.888164i | \(0.651981\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.54842 | − | 21.0291i | 0.115244 | − | 0.950971i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 27.9168i | − | 1.25987i | −0.776648 | − | 0.629935i | \(-0.783082\pi\) | ||
0.776648 | − | 0.629935i | \(-0.216918\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.25089i | − | 0.191451i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.7116 | + | 3.12683i | 0.571343 | + | 0.140541i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.447618 | 0.0200784 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.7631 | −1.19808 | −0.599041 | − | 0.800719i | \(-0.704451\pi\) | ||||
−0.599041 | + | 0.800719i | \(0.704451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.6887 | − | 1.90123i | −0.700918 | − | 0.0849408i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.3660 | −0.506784 | −0.253392 | − | 0.967364i | \(-0.581546\pi\) | ||||
−0.253392 | + | 0.967364i | \(0.581546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.126407i | 0.00562506i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.78764 | − | 56.0105i | 0.301450 | − | 2.48751i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.6388i | 1.18074i | 0.807131 | + | 0.590372i | \(0.201019\pi\) | ||||
−0.807131 | + | 0.590372i | \(0.798981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.804088i | 0.0355708i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.8430 | + | 10.9156i | 1.27345 | + | 0.481936i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 11.2600i | − | 0.496175i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.5645i | 1.52014i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.6953 | + | 2.62915i | 0.952317 | + | 0.115407i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.3888 | 1.72565 | 0.862827 | − | 0.505499i | \(-0.168692\pi\) | ||||
0.862827 | + | 0.505499i | \(0.168692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 39.2737i | − | 1.71732i | −0.512545 | − | 0.858661i | \(-0.671297\pi\) | ||
0.512545 | − | 0.858661i | \(-0.328703\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.322479 | − | 0.0390797i | −0.0140741 | − | 0.00170558i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.80253 | −0.165641 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.43773 | + | 20.9745i | 0.410336 | + | 0.911934i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.376563 | − | 1.53085i | 0.0163414 | − | 0.0664333i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 57.2240i | − | 2.47865i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.76751 | 0.249351 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.7683 | − | 4.21341i | −1.50036 | − | 0.181822i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.3910 | −1.30903 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.5155 | −1.52693 | −0.763465 | − | 0.645849i | \(-0.776504\pi\) | ||||
−0.763465 | + | 0.645849i | \(0.776504\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.0576 | + | 2.91543i | 1.03241 | + | 0.125113i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.83222i | 0.206989i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.2488 | −0.523721 | −0.261860 | − | 0.965106i | \(-0.584336\pi\) | ||||
−0.261860 | + | 0.965106i | \(0.584336\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.44950 | − | 5.89271i | 0.0618633 | − | 0.251495i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.3803 | −1.12384 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.52977 | 0.107577 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.3692 | − | 1.98371i | −0.694836 | − | 0.0842038i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.4280 | −1.71299 | −0.856496 | − | 0.516154i | \(-0.827363\pi\) | ||||
−0.856496 | + | 0.516154i | \(0.827363\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.5436i | 2.18006i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.869568 | + | 7.17553i | −0.0367132 | + | 0.302951i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.6387 | −1.24912 | −0.624561 | − | 0.780976i | \(-0.714722\pi\) | ||||
−0.624561 | + | 0.780976i | \(0.714722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.3323 | 0.560896 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.783015 | − | 1.49530i | 0.0328835 | − | 0.0627967i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.1081 | −0.801054 | −0.400527 | − | 0.916285i | \(-0.631173\pi\) | ||||
−0.400527 | + | 0.916285i | \(0.631173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.6457i | 1.53357i | 0.641902 | + | 0.766787i | \(0.278146\pi\) | ||||
−0.641902 | + | 0.766787i | \(0.721854\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.95843 | − | 24.4125i | 0.123590 | − | 1.01985i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.02726 | − | 2.60406i | −0.167949 | − | 0.108597i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.56680 | 0.148488 | 0.0742438 | − | 0.997240i | \(-0.476346\pi\) | ||||
0.0742438 | + | 0.997240i | \(0.476346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.74872 | − | 22.6820i | 0.114233 | − | 0.942631i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.766172i | 0.0317862i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.2475 | 1.12848 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.6664 | − | 4.83759i | −0.813104 | − | 0.200010i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 39.2111i | − | 1.61841i | −0.587524 | − | 0.809207i | \(-0.699897\pi\) | ||
0.587524 | − | 0.809207i | \(-0.300103\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.5979i | 0.972333i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37.0677 | + | 4.49206i | 1.52476 | + | 0.184779i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.6434i | 1.75116i | 0.483076 | + | 0.875578i | \(0.339519\pi\) | ||||
−0.483076 | + | 0.875578i | \(0.660481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.179362i | − | 0.00735312i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.29425 | − | 0.399214i | −0.134825 | − | 0.0163387i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.2440i | 0.949724i | 0.880060 | + | 0.474862i | \(0.157502\pi\) | ||||
−0.880060 | + | 0.474862i | \(0.842498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.3605 | 1.27922 | 0.639610 | − | 0.768699i | \(-0.279096\pi\) | ||||
0.639610 | + | 0.768699i | \(0.279096\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.64393 | − | 22.9444i | 0.229839 | − | 0.934369i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.04016 | 0.326879 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.9418 | −1.70237 | −0.851183 | − | 0.524869i | \(-0.824114\pi\) | ||||
−0.851183 | + | 0.524869i | \(0.824114\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.173703 | + | 1.43337i | −0.00703880 | + | 0.0580830i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 53.4755i | − | 2.16339i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.3655i | 1.79190i | 0.444151 | + | 0.895952i | \(0.353505\pi\) | ||||
−0.444151 | + | 0.895952i | \(0.646495\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.5752 | − | 1.76629i | −0.587727 | − | 0.0712238i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.8190 | −0.475816 | −0.237908 | − | 0.971288i | \(-0.576462\pi\) | ||||
−0.237908 | + | 0.971288i | \(0.576462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 43.3150i | − | 1.74098i | −0.492188 | − | 0.870489i | \(-0.663803\pi\) | ||
0.492188 | − | 0.870489i | \(-0.336197\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.0620 | − | 14.7823i | 0.805061 | − | 0.593192i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.324681i | 0.0130081i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 44.5301 | + | 5.39639i | 1.77836 | + | 0.215511i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.10453i | − | 0.363021i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.77912i | − | 0.230063i | −0.993362 | − | 0.115032i | \(-0.963303\pi\) | ||
0.993362 | − | 0.115032i | \(-0.0366969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.24820 | − | 35.0554i | 0.168851 | − | 1.39333i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.62198 | 0.143734 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.0187 | 1.86295 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.71029 | − | 6.95288i | 0.0676580 | − | 0.275052i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.52676 | −0.0603036 | −0.0301518 | − | 0.999545i | \(-0.509599\pi\) | ||||
−0.0301518 | + | 0.999545i | \(0.509599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.6023i | − | 0.457551i | −0.973479 | − | 0.228776i | \(-0.926528\pi\) | ||
0.973479 | − | 0.228776i | \(-0.0734722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.1283 | + | 1.59096i | 0.516928 | + | 0.0626440i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.9339i | − | 0.508485i | −0.967141 | − | 0.254242i | \(-0.918174\pi\) | ||
0.967141 | − | 0.254242i | \(-0.0818261\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.29300i | − | 0.0900081i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.28218 | + | 0.155382i | 0.0502527 | + | 0.00608989i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.54433i | 0.138700i | 0.997592 | + | 0.0693502i | \(0.0220926\pi\) | ||||
−0.997592 | + | 0.0693502i | \(0.977907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.51312i | 0.0981958i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.4900 | + | 3.07232i | 0.487280 | + | 0.119863i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.8500 | 1.16279 | 0.581395 | − | 0.813622i | \(-0.302507\pi\) | ||||
0.581395 | + | 0.813622i | \(0.302507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0421i | 1.20740i | 0.797212 | + | 0.603700i | \(0.206307\pi\) | ||||
−0.797212 | + | 0.603700i | \(0.793693\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.34533 | − | 11.1014i | 0.0522482 | − | 0.431143i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.11309 | −0.0431638 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.5746 | + | 17.9006i | −0.448172 | + | 0.693112i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.617076 | + | 5.09201i | −0.0238575 | + | 0.196868i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.82645i | − | 0.340741i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.14264 | 0.352423 | 0.176211 | − | 0.984352i | \(-0.443616\pi\) | ||||
0.176211 | + | 0.984352i | \(0.443616\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.83918 | + | 4.85978i | −0.0707900 | + | 0.187053i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.0265 | −0.385350 | −0.192675 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192675 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.33230 | −0.0895053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.47822 | + | 28.7017i | −0.133286 | + | 1.09985i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 14.7246i | − | 0.563421i | −0.959499 | − | 0.281710i | \(-0.909098\pi\) | ||
0.959499 | − | 0.281710i | \(-0.0909018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.4039 | −0.703177 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.181732 | + | 0.0220232i | 0.00693351 | + | 0.000840239i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.1553 | −1.60599 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.4472 | −0.473515 | −0.236757 | − | 0.971569i | \(-0.576085\pi\) | ||||
−0.236757 | + | 0.971569i | \(0.576085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.586423 | − | 2.38400i | 0.0222764 | − | 0.0905607i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.21774 | 0.0461915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.10667i | − | 0.307062i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 37.8810 | + | 4.59061i | 1.43279 | + | 0.173633i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.8908 | 1.65773 | 0.828867 | − | 0.559446i | \(-0.188986\pi\) | ||||
0.828867 | + | 0.559446i | \(0.188986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −56.5012 | −2.13098 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.6204 | − | 1.65059i | −0.512974 | − | 0.0621648i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0237071 | 0.000891599 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 49.5649i | − | 1.86145i | −0.365720 | − | 0.930725i | \(-0.619177\pi\) | ||
0.365720 | − | 0.930725i | \(-0.380823\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.66593 | − | 39.2952i | 0.362501 | − | 1.47368i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.0125 | + | 10.3538i | 0.599673 | + | 0.387753i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.4575 | −1.10165 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.4330 | + | 3.93040i | 1.21123 | + | 0.146783i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.72405i | 0.325352i | 0.986680 | + | 0.162676i | \(0.0520125\pi\) | ||||
−0.986680 | + | 0.162676i | \(0.947987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.11176 | −0.0786461 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.3372 | − | 2.94931i | −0.905111 | − | 0.109686i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 4.44484i | − | 0.165077i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.5678i | 0.466113i | 0.972463 | + | 0.233057i | \(0.0748727\pi\) | ||||
−0.972463 | + | 0.233057i | \(0.925127\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.2348 | − | 17.8760i | −0.749439 | − | 0.662074i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.30194i | 0.270072i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5708i | 0.390440i | 0.980759 | + | 0.195220i | \(0.0625421\pi\) | ||||
−0.980759 | + | 0.195220i | \(0.937458\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.45129 | − | 11.9758i | 0.0535317 | − | 0.441735i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 34.3675i | − | 1.26594i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.3127 | −1.44614 | −0.723070 | − | 0.690774i | \(-0.757270\pi\) | ||||
−0.723070 | + | 0.690774i | \(0.757270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −68.8935 | − | 8.34887i | −2.53087 | − | 0.306704i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.69891 | 0.209073 | 0.104536 | − | 0.994521i | \(-0.466664\pi\) | ||||
0.104536 | + | 0.994521i | \(0.466664\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.1340 | 0.591105 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.9010 | + | 2.92745i | 0.435436 | + | 0.107110i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.08167i | − | 0.0395234i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.2980i | 1.39751i | 0.715359 | + | 0.698757i | \(0.246263\pi\) | ||||
−0.715359 | + | 0.698757i | \(0.753737\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.83622 | − | 15.1522i | 0.0669156 | − | 0.552176i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.4844 | −0.417961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 13.1087i | − | 0.476444i | −0.971211 | − | 0.238222i | \(-0.923435\pi\) | ||
0.971211 | − | 0.238222i | \(-0.0765645\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.1998 | − | 27.8485i | 0.842100 | − | 1.01084i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 39.6953i | − | 1.43895i | −0.694516 | − | 0.719477i | \(-0.744381\pi\) | ||
0.694516 | − | 0.719477i | \(-0.255619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.906260 | 0.0328088 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.78605 | − | 0.685319i | −0.100730 | − | 0.0247778i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.54755i | 0.128095i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 11.0014i | − | 0.396719i | −0.980129 | − | 0.198360i | \(-0.936439\pi\) | ||
0.980129 | − | 0.198360i | \(-0.0635614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.3379 | + | 4.52480i | 1.34469 | + | 0.162957i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.1581 | −1.55229 | −0.776144 | − | 0.630556i | \(-0.782827\pi\) | ||||
−0.776144 | + | 0.630556i | \(0.782827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.97602 | −0.142823 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.372036 | + | 3.06998i | −0.0133467 | + | 0.110135i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −50.3086 | −1.80249 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 10.4144i | − | 0.372658i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.6009 | + | 8.17486i | 0.771955 | + | 0.292146i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 22.3016i | − | 0.795978i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33.8343i | − | 1.20606i | −0.797717 | − | 0.603031i | \(-0.793959\pi\) | ||
0.797717 | − | 0.603031i | \(-0.206041\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.32209 | − | 52.1689i | 0.225072 | − | 1.85726i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.50042i | − | 0.0889048i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.6556i | 0.484924i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.30118 | + | 10.7371i | −0.0461480 | + | 0.380806i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.52419 | −0.160255 | −0.0801275 | − | 0.996785i | \(-0.525533\pi\) | ||||
−0.0801275 | + | 0.996785i | \(0.525533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.57563i | − | 0.268006i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.04331 | + | 1.24057i | 0.178196 | + | 0.0438333i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.7082 | 0.660199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.488380 | + | 0.755295i | −0.0172131 | + | 0.0266207i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.9961 | − | 4.36219i | −1.26712 | − | 0.153556i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.57880i | − | 0.0555077i | −0.999615 | − | 0.0277539i | \(-0.991165\pi\) | ||
0.999615 | − | 0.0277539i | \(-0.00883546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.58195 | −0.125779 | −0.0628897 | − | 0.998020i | \(-0.520032\pi\) | ||||
−0.0628897 | + | 0.998020i | \(0.520032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.29412 | − | 35.4344i | 0.150601 | − | 1.24274i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.2300 | 0.428399 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.3146 | 1.58536 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.907268 | + | 3.68834i | −0.0317025 | + | 0.128881i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 25.4983i | − | 0.889898i | −0.895556 | − | 0.444949i | \(-0.853222\pi\) | ||
0.895556 | − | 0.444949i | \(-0.146778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.365706 | 0.0127477 | 0.00637386 | − | 0.999980i | \(-0.497971\pi\) | ||||
0.00637386 | + | 0.999980i | \(0.497971\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.909242 | + | 7.50292i | −0.0316557 | + | 0.261218i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7234 | 0.720623 | 0.360311 | − | 0.932832i | \(-0.382670\pi\) | ||||
0.360311 | + | 0.932832i | \(0.382670\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.7977 | −0.513946 | −0.256973 | − | 0.966419i | \(-0.582725\pi\) | ||||
−0.256973 | + | 0.966419i | \(0.582725\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.68642 | + | 13.9161i | −0.0585014 | + | 0.482744i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.66092 | 0.230787 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 9.12412i | − | 0.315753i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.31262 | − | 19.3226i | 0.252761 | − | 0.667886i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.8342 | −0.684754 | −0.342377 | − | 0.939563i | \(-0.611232\pi\) | ||||
−0.342377 | + | 0.939563i | \(0.611232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.24337 | 0.318737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.25908 | + | 10.3897i | −0.0433650 | + | 0.357841i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.5743 | 1.12059 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.50790i | − | 0.0518119i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.5594 | + | 1.27965i | 0.362399 | + | 0.0439173i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.7905 | + | 38.3393i | −0.849807 | + | 1.31425i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.7004 | −0.537572 | −0.268786 | − | 0.963200i | \(-0.586623\pi\) | ||||
−0.268786 | + | 0.963200i | \(0.586623\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.25298 | + | 17.2897i | −0.145449 | + | 0.591296i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 15.5570i | − | 0.531418i | −0.964053 | − | 0.265709i | \(-0.914394\pi\) | ||
0.964053 | − | 0.265709i | \(-0.0856061\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.1242 | −0.618390 | −0.309195 | − | 0.950999i | \(-0.600060\pi\) | ||||
−0.309195 | + | 0.950999i | \(0.600060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.331260 | + | 2.73351i | −0.0112893 | + | 0.0931577i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.51915i | − | 0.0857527i | −0.999080 | − | 0.0428764i | \(-0.986348\pi\) | ||
0.999080 | − | 0.0428764i | \(-0.0136522\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.6174i | 0.429005i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.35178 | + | 27.6583i | −0.113832 | + | 0.939326i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 58.8586i | − | 1.99664i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.1707i | 1.80162i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.91140 | + | 36.2277i | −0.301605 | + | 1.22612i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 0.187545i | − | 0.00634019i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.5977 | −0.627999 | −0.313999 | − | 0.949423i | \(-0.601669\pi\) | ||||
−0.313999 | + | 0.949423i | \(0.601669\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.11076 | − | 33.9213i | 0.138653 | − | 1.14414i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.8225 | −0.600456 | −0.300228 | − | 0.953868i | \(-0.597063\pi\) | ||||
−0.300228 | + | 0.953868i | \(0.597063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.1025 | −0.676502 | −0.338251 | − | 0.941056i | \(-0.609835\pi\) | ||||
−0.338251 | + | 0.941056i | \(0.609835\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.903573 | + | 0.109500i | 0.0303733 | + | 0.00368079i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.9425i | 1.20683i | 0.797427 | + | 0.603416i | \(0.206194\pi\) | ||||
−0.797427 | + | 0.603416i | \(0.793806\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.679285i | − | 0.0227825i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.7902 | − | 18.2179i | −1.16552 | − | 0.610323i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −47.0131 | −1.57323 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 20.2204i | − | 0.675893i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35.8929 | + | 43.0850i | −1.19843 | + | 1.43857i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.6728i | 0.589421i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.97195 | −0.198954 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.298377 | − | 2.46216i | 0.00992937 | − | 0.0819355i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.9913i | 0.465086i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.2167i | 1.46819i | 0.679046 | + | 0.734096i | \(0.262394\pi\) | ||||
−0.679046 | + | 0.734096i | \(0.737606\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.0905819 | − | 0.368245i | 0.00300441 | − | 0.0122139i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0784 | 1.32786 | 0.663928 | − | 0.747797i | \(-0.268888\pi\) | ||||
0.663928 | + | 0.747797i | \(0.268888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.8261 | 0.589956 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.47813 | + | 0.421497i | 0.114983 | + | 0.0139343i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.471325 | 0.0155645 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.8185i | 0.917649i | 0.888527 | + | 0.458825i | \(0.151729\pi\) | ||||
−0.888527 | + | 0.458825i | \(0.848271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.960279 | + | 7.92407i | −0.0316423 | + | 0.261107i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.1124i | 0.530346i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 9.51993i | − | 0.313013i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.06877 | + | 32.8022i | −0.265013 | + | 1.07736i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.55183i | 0.280576i | 0.990111 | + | 0.140288i | \(0.0448029\pi\) | ||||
−0.990111 | + | 0.140288i | \(0.955197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 41.3365i | − | 1.35475i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.2968 | − | 2.45967i | −0.664487 | − | 0.0805260i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.17310 | −0.136475 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 30.7135i | − | 1.00337i | −0.865051 | − | 0.501684i | \(-0.832714\pi\) | ||
0.865051 | − | 0.501684i | \(-0.167286\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.1558 | + | 4.38155i | 1.17990 | + | 0.142986i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.5302 | −0.799661 | −0.399831 | − | 0.916589i | \(-0.630931\pi\) | ||||
−0.399831 | + | 0.916589i | \(0.630931\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.0734 | + | 34.1373i | −0.718810 | + | 1.11166i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.911429 | + | 0.344930i | 0.0296488 | + | 0.0112206i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.96398i | 0.258795i | 0.991593 | + | 0.129397i | \(0.0413043\pi\) | ||||
−0.991593 | + | 0.129397i | \(0.958696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.9439 | −0.939558 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.0233 | + | 5.69853i | 1.52484 | + | 0.184787i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0590 | −1.13567 | −0.567836 | − | 0.823142i | \(-0.692219\pi\) | ||||
−0.567836 | + | 0.823142i | \(0.692219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.1977 | 0.459425 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.3493 | + | 4.04144i | 1.07803 | + | 0.130641i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.45157i | 0.111457i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1912 | −0.490040 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.8017 | − | 4.13292i | −0.541426 | − | 0.133182i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.1913 | 0.424642 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.2914 | 1.68158 | 0.840789 | − | 0.541363i | \(-0.182091\pi\) | ||||
0.840789 | + | 0.541363i | \(0.182091\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.75983 | − | 1.18275i | −0.313531 | − | 0.0379953i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.2490 | 1.19538 | 0.597689 | − | 0.801728i | \(-0.296086\pi\) | ||||
0.597689 | + | 0.801728i | \(0.296086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 0.228381i | − | 0.00732157i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.40671 | − | 11.6079i | 0.0450507 | − | 0.371751i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.9791 | 0.735167 | 0.367583 | − | 0.929991i | \(-0.380185\pi\) | ||||
0.367583 | + | 0.929991i | \(0.380185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.55416 | 0.241432 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.46270 | − | 14.0770i | 0.110556 | − | 0.449445i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.9968 | 1.46707 | 0.733536 | − | 0.679651i | \(-0.237869\pi\) | ||||
0.733536 | + | 0.679651i | \(0.237869\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.5576i | 0.686884i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.309561 | + | 2.55444i | −0.00985343 | + | 0.0813089i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.8823 | − | 30.7486i | 0.632220 | − | 0.977748i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.8353 | −1.51954 | −0.759768 | − | 0.650194i | \(-0.774688\pi\) | ||||
−0.759768 | + | 0.650194i | \(0.774688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.36847 | − | 27.7960i | 0.106895 | − | 0.882081i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.91585i | − | 0.0607365i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.1839 | −1.01927 | −0.509637 | − | 0.860390i | \(-0.670220\pi\) | ||||
−0.509637 | + | 0.860390i | \(0.670220\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 46.2647 | + | 17.5089i | 1.46375 | + | 0.553956i |
(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 | 1380.2.i.b.1241.9 | yes | 16 | |
3.2 | odd | 2 | 1380.2.i.a.1241.10 | yes | 16 | ||
23.22 | odd | 2 | 1380.2.i.a.1241.9 | ✓ | 16 | ||
69.68 | even | 2 | inner | 1380.2.i.b.1241.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.i.a.1241.9 | ✓ | 16 | 23.22 | odd | 2 | ||
1380.2.i.a.1241.10 | yes | 16 | 3.2 | odd | 2 | ||
1380.2.i.b.1241.9 | yes | 16 | 1.1 | even | 1 | trivial | |
1380.2.i.b.1241.10 | yes | 16 | 69.68 | even | 2 | inner |