Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(289,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1920.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.bl (of order \(4\), degree \(2\), not 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: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.17 | ||
Character | \(\chi\) | \(=\) | 1920.289 |
Dual form | 1920.2.bl.a.1249.17 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.07735 | + | 1.95942i | −0.481808 | + | 0.876277i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.22137 | −0.461633 | −0.230817 | − | 0.972997i | \(-0.574140\pi\) | ||||
−0.230817 | + | 0.972997i | \(0.574140\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.38208 | + | 1.38208i | −0.416713 | + | 0.416713i | −0.884069 | − | 0.467356i | \(-0.845207\pi\) |
0.467356 | + | 0.884069i | \(0.345207\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.12237 | + | 2.12237i | −0.588641 | + | 0.588641i | −0.937263 | − | 0.348622i | \(-0.886650\pi\) |
0.348622 | + | 0.937263i | \(0.386650\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.623711 | + | 2.14732i | 0.161042 | + | 0.554436i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.00218i | − | 1.45574i | −0.685714 | − | 0.727871i | \(-0.740510\pi\) | ||
0.685714 | − | 0.727871i | \(-0.259490\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.06223 | + | 3.06223i | 0.702525 | + | 0.702525i | 0.964952 | − | 0.262427i | \(-0.0845230\pi\) |
−0.262427 | + | 0.964952i | \(0.584523\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.863636 | + | 0.863636i | −0.188461 | + | 0.188461i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.90813 | 0.606387 | 0.303193 | − | 0.952929i | \(-0.401947\pi\) | ||||
0.303193 | + | 0.952929i | \(0.401947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.67861 | − | 4.22197i | −0.535723 | − | 0.844394i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.18392 | − | 3.18392i | −0.591239 | − | 0.591239i | 0.346727 | − | 0.937966i | \(-0.387293\pi\) |
−0.937966 | + | 0.346727i | \(0.887293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.88079 | −0.697011 | −0.348505 | − | 0.937307i | \(-0.613311\pi\) | ||||
−0.348505 | + | 0.937307i | \(0.613311\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.95456i | 0.340245i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.31584 | − | 2.39316i | 0.222418 | − | 0.404518i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.44376 | − | 2.44376i | −0.401752 | − | 0.401752i | 0.477098 | − | 0.878850i | \(-0.341689\pi\) |
−0.878850 | + | 0.477098i | \(0.841689\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00149i | 0.480623i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.38396i | − | 0.372312i | −0.982520 | − | 0.186156i | \(-0.940397\pi\) | ||
0.982520 | − | 0.186156i | \(-0.0596029\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.00811 | − | 9.00811i | −1.37372 | − | 1.37372i | −0.854852 | − | 0.518871i | \(-0.826352\pi\) |
−0.518871 | − | 0.854852i | \(-0.673648\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.95942 | + | 1.07735i | 0.292092 | + | 0.160603i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.586179i | − | 0.0855030i | −0.999086 | − | 0.0427515i | \(-0.986388\pi\) | ||
0.999086 | − | 0.0427515i | \(-0.0136124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.50826 | −0.786895 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.24418 | − | 4.24418i | −0.594304 | − | 0.594304i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.36822 | + | 2.36822i | 0.325300 | + | 0.325300i | 0.850796 | − | 0.525496i | \(-0.176120\pi\) |
−0.525496 | + | 0.850796i | \(0.676120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.21908 | − | 4.19706i | −0.164381 | − | 0.565931i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.33065 | 0.573609 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.43447 | + | 8.43447i | −1.09807 | + | 1.09807i | −0.103438 | + | 0.994636i | \(0.532984\pi\) |
−0.994636 | + | 0.103438i | \(0.967016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.98062 | − | 9.98062i | −1.27789 | − | 1.27789i | −0.941848 | − | 0.336040i | \(-0.890912\pi\) |
−0.336040 | − | 0.941848i | \(-0.609088\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.22137i | 0.153878i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.87206 | − | 6.44516i | −0.232201 | − | 0.799424i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.82203 | − | 3.82203i | 0.466936 | − | 0.466936i | −0.433985 | − | 0.900920i | \(-0.642893\pi\) |
0.900920 | + | 0.433985i | \(0.142893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.05636 | − | 2.05636i | 0.247556 | − | 0.247556i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5314i | 1.36852i | 0.729238 | + | 0.684260i | \(0.239875\pi\) | ||||
−0.729238 | + | 0.684260i | \(0.760125\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.31108 | 0.153450 | 0.0767250 | − | 0.997052i | \(-0.475554\pi\) | ||||
0.0767250 | + | 0.997052i | \(0.475554\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.87945 | − | 1.09132i | −0.563430 | − | 0.126014i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.68803 | − | 1.68803i | 0.192368 | − | 0.192368i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5967 | −1.41724 | −0.708619 | − | 0.705592i | \(-0.750681\pi\) | ||||
−0.708619 | + | 0.705592i | \(0.750681\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.91633 | − | 2.91633i | 0.320108 | − | 0.320108i | −0.528700 | − | 0.848809i | \(-0.677320\pi\) |
0.848809 | + | 0.528700i | \(0.177320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.7608 | + | 6.46647i | 1.27563 | + | 0.701387i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.50274 | −0.482744 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.58659i | − | 1.01618i | −0.861305 | − | 0.508088i | \(-0.830352\pi\) | ||
0.861305 | − | 0.508088i | \(-0.169648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.59220 | − | 2.59220i | 0.271736 | − | 0.271736i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.74413 | + | 2.74413i | −0.284553 | + | 0.284553i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.29930 | + | 2.70108i | −0.954088 | + | 0.277125i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.45309i | 0.959816i | 0.877319 | + | 0.479908i | \(0.159330\pi\) | ||||
−0.877319 | + | 0.479908i | \(0.840670\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.38208 | + | 1.38208i | 0.138904 | + | 0.138904i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6519 | − | 11.6519i | 1.15940 | − | 1.15940i | 0.174798 | − | 0.984604i | \(-0.444073\pi\) |
0.984604 | − | 0.174798i | \(-0.0559273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.15006 | −0.211852 | −0.105926 | − | 0.994374i | \(-0.533781\pi\) | ||||
−0.105926 | + | 0.994374i | \(0.533781\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.761780 | − | 2.62266i | −0.0743421 | − | 0.255946i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4992 | + | 13.4992i | 1.30501 | + | 1.30501i | 0.924967 | + | 0.380048i | \(0.124092\pi\) |
0.380048 | + | 0.924967i | \(0.375908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7618 | − | 10.7618i | −1.03079 | − | 1.03079i | −0.999511 | − | 0.0312781i | \(-0.990042\pi\) |
−0.0312781 | − | 0.999511i | \(-0.509958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.45601 | −0.328029 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.6206i | − | 1.18725i | −0.804742 | − | 0.593624i | \(-0.797696\pi\) | ||
0.804742 | − | 0.593624i | \(-0.202304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.13308 | + | 5.69823i | −0.292162 | + | 0.531363i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.12237 | + | 2.12237i | 0.196214 | + | 0.196214i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.33086i | 0.672018i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.17971i | 0.652701i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.68571 | − | 1.68571i | −0.151996 | − | 0.151996i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1584 | − | 0.699962i | 0.998038 | − | 0.0626065i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.66786i | − | 0.857883i | −0.903332 | − | 0.428942i | \(-0.858887\pi\) | ||
0.903332 | − | 0.428942i | \(-0.141113\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.7394 | −1.12164 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5362 | − | 10.5362i | −0.920553 | − | 0.920553i | 0.0765154 | − | 0.997068i | \(-0.475621\pi\) |
−0.997068 | + | 0.0765154i | \(0.975621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.74011 | − | 3.74011i | −0.324309 | − | 0.324309i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.14732 | − | 0.623711i | 0.184812 | − | 0.0536805i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9189 | 1.10374 | 0.551869 | − | 0.833931i | \(-0.313915\pi\) | ||||
0.551869 | + | 0.833931i | \(0.313915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5153 | + | 11.5153i | −0.976718 | + | 0.976718i | −0.999735 | − | 0.0230167i | \(-0.992673\pi\) |
0.0230167 | + | 0.999735i | \(0.492673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.414491 | − | 0.414491i | −0.0349064 | − | 0.0349064i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.86659i | − | 0.490589i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.66882 | − | 2.80841i | 0.802952 | − | 0.233226i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.89493 | + | 3.89493i | −0.321249 | + | 0.321249i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.8344 | + | 11.8344i | −0.969513 | + | 0.969513i | −0.999549 | − | 0.0300356i | \(-0.990438\pi\) |
0.0300356 | + | 0.999549i | \(0.490438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.240930i | 0.0196066i | 0.999952 | + | 0.00980330i | \(0.00312054\pi\) | ||||
−0.999952 | + | 0.00980330i | \(0.996879\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00218 | −0.485247 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.18099 | − | 7.60408i | 0.335825 | − | 0.610775i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.19573 | − | 7.19573i | 0.574282 | − | 0.574282i | −0.359040 | − | 0.933322i | \(-0.616896\pi\) |
0.933322 | + | 0.359040i | \(0.116896\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.34917 | 0.265606 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.55189 | −0.279928 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7446 | + | 11.7446i | −0.919910 | + | 0.919910i | −0.997022 | − | 0.0771120i | \(-0.975430\pi\) |
0.0771120 | + | 0.997022i | \(0.475430\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.82979 | − | 2.10575i | −0.298149 | − | 0.163932i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.213418 | −0.0165148 | −0.00825739 | − | 0.999966i | \(-0.502628\pi\) | ||||
−0.00825739 | + | 0.999966i | \(0.502628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.99105i | 0.307004i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.06223 | − | 3.06223i | 0.234175 | − | 0.234175i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.36918 | − | 6.36918i | 0.484240 | − | 0.484240i | −0.422243 | − | 0.906483i | \(-0.638757\pi\) |
0.906483 | + | 0.422243i | \(0.138757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.27157 | + | 5.15657i | 0.247307 | + | 0.389800i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.9281i | 0.896574i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.53473 | + | 6.53473i | 0.488428 | + | 0.488428i | 0.907810 | − | 0.419382i | \(-0.137753\pi\) |
−0.419382 | + | 0.907810i | \(0.637753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.23014 | + | 5.23014i | −0.388753 | + | 0.388753i | −0.874242 | − | 0.485490i | \(-0.838641\pi\) |
0.485490 | + | 0.874242i | \(0.338641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.1147 | −1.04339 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.42115 | − | 2.15555i | 0.545614 | − | 0.158479i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.29549 | + | 8.29549i | 0.606626 | + | 0.606626i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.863636 | + | 0.863636i | 0.0628203 | + | 0.0628203i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.1318 | 0.950181 | 0.475090 | − | 0.879937i | \(-0.342415\pi\) | ||||
0.475090 | + | 0.879937i | \(0.342415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0131i | 1.44057i | 0.693676 | + | 0.720287i | \(0.255990\pi\) | ||||
−0.693676 | + | 0.720287i | \(0.744010\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.88117 | − | 3.23367i | −0.421159 | − | 0.231568i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.2424 | − | 19.2424i | −1.37096 | − | 1.37096i | −0.859021 | − | 0.511941i | \(-0.828927\pi\) |
−0.511941 | − | 0.859021i | \(-0.671073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.18227i | 0.367361i | 0.982986 | + | 0.183681i | \(0.0588012\pi\) | ||||
−0.982986 | + | 0.183681i | \(0.941199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.40517i | − | 0.381251i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.88873 | + | 3.88873i | 0.272935 | + | 0.272935i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.67116 | + | 2.56837i | 0.326248 | + | 0.179383i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.90813i | − | 0.202129i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.46451 | −0.585502 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.53295 | + | 5.53295i | 0.380904 | + | 0.380904i | 0.871428 | − | 0.490524i | \(-0.163195\pi\) |
−0.490524 | + | 0.871428i | \(0.663195\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.15390 | + | 8.15390i | 0.558696 | + | 0.558696i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.3555 | − | 7.94570i | 1.86563 | − | 0.541892i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.73987 | 0.321763 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.927072 | − | 0.927072i | 0.0626457 | − | 0.0626457i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.7389 | + | 12.7389i | 0.856909 | + | 0.856909i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.639576i | 0.0428292i | 0.999771 | + | 0.0214146i | \(0.00681700\pi\) | ||||
−0.999771 | + | 0.0214146i | \(0.993183\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.22197 | + | 2.67861i | −0.281465 | + | 0.178574i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.272194 | − | 0.272194i | 0.0180662 | − | 0.0180662i | −0.698016 | − | 0.716082i | \(-0.745934\pi\) |
0.716082 | + | 0.698016i | \(0.245934\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.80055 | + | 4.80055i | −0.317229 | + | 0.317229i | −0.847702 | − | 0.530473i | \(-0.822014\pi\) |
0.530473 | + | 0.847702i | \(0.322014\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.38723i | − | 0.157068i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.8025 | −1.42833 | −0.714166 | − | 0.699977i | \(-0.753194\pi\) | ||||
−0.714166 | + | 0.699977i | \(0.753194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.14857 | + | 0.631522i | 0.0749243 | + | 0.0411960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.90720 | + | 8.90720i | −0.578585 | + | 0.578585i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.01781 | 0.130521 | 0.0652606 | − | 0.997868i | \(-0.479212\pi\) | ||||
0.0652606 | + | 0.997868i | \(0.479212\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.4653 | 0.996209 | 0.498105 | − | 0.867117i | \(-0.334030\pi\) | ||||
0.498105 | + | 0.867117i | \(0.334030\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.93435 | − | 10.7930i | 0.379132 | − | 0.689538i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9984 | −0.827069 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.12431i | − | 0.261367i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.43023 | + | 3.43023i | −0.216514 | + | 0.216514i | −0.807028 | − | 0.590514i | \(-0.798925\pi\) |
0.590514 | + | 0.807028i | \(0.298925\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.01927 | + | 4.01927i | −0.252689 | + | 0.252689i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.8886 | − | 3.74362i | 0.807115 | − | 0.234435i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3076i | 1.20437i | 0.798355 | + | 0.602187i | \(0.205704\pi\) | ||||
−0.798355 | + | 0.602187i | \(0.794296\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.98473 | + | 2.98473i | 0.185462 | + | 0.185462i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.18392 | + | 3.18392i | −0.197080 | + | 0.197080i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.26068 | 0.571038 | 0.285519 | − | 0.958373i | \(-0.407834\pi\) | ||||
0.285519 | + | 0.958373i | \(0.407834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.19173 | + | 2.08891i | −0.441785 | + | 0.128321i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.77874 | − | 6.77874i | −0.414852 | − | 0.414852i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.68909 | − | 5.68909i | −0.346870 | − | 0.346870i | 0.512073 | − | 0.858942i | \(-0.328878\pi\) |
−0.858942 | + | 0.512073i | \(0.828878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.56587 | 0.0951199 | 0.0475599 | − | 0.998868i | \(-0.484855\pi\) | ||||
0.0475599 | + | 0.998868i | \(0.484855\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 3.66592i | − | 0.221872i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.53716 | + | 2.13304i | 0.575113 | + | 0.128627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2915 | − | 11.2915i | −0.678441 | − | 0.678441i | 0.281206 | − | 0.959647i | \(-0.409266\pi\) |
−0.959647 | + | 0.281206i | \(0.909266\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.88079i | 0.232337i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8017i | 0.942653i | 0.881959 | + | 0.471326i | \(0.156225\pi\) | ||||
−0.881959 | + | 0.471326i | \(0.843775\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.32452 | − | 2.32452i | −0.138178 | − | 0.138178i | 0.634634 | − | 0.772813i | \(-0.281151\pi\) |
−0.772813 | + | 0.634634i | \(0.781151\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.66565 | + | 8.48555i | −0.276369 | + | 0.502640i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.91169i | 0.171871i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.0261 | −1.11918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.68434 | + | 6.68434i | 0.391843 | + | 0.391843i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.44154 | − | 7.44154i | −0.434739 | − | 0.434739i | 0.455498 | − | 0.890237i | \(-0.349461\pi\) |
−0.890237 | + | 0.455498i | \(0.849461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.43971 | − | 25.6135i | −0.433157 | − | 1.49128i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.95456 | 0.113415 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.17214 | + | 6.17214i | −0.356944 | + | 0.356944i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0022 | + | 11.0022i | 0.634156 | + | 0.634156i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 16.4782i | − | 0.946648i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 30.3088 | − | 8.80351i | 1.73548 | − | 0.504088i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.28621 | + | 3.28621i | −0.187554 | + | 0.187554i | −0.794638 | − | 0.607084i | \(-0.792339\pi\) |
0.607084 | + | 0.794638i | \(0.292339\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.52032 | + | 1.52032i | −0.0864881 | + | 0.0864881i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 29.0235i | − | 1.64577i | −0.568206 | − | 0.822886i | \(-0.692362\pi\) | ||
0.568206 | − | 0.822886i | \(-0.307638\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.50831 | 0.311348 | 0.155674 | − | 0.987808i | \(-0.450245\pi\) | ||||
0.155674 | + | 0.987808i | \(0.450245\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.39316 | − | 1.31584i | −0.134839 | − | 0.0741394i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.6401 | − | 10.6401i | 0.597609 | − | 0.597609i | −0.342067 | − | 0.939676i | \(-0.611127\pi\) |
0.939676 | + | 0.342067i | \(0.111127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.80086 | 0.492754 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.0907 | 1.06554 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.3801 | − | 18.3801i | 1.02269 | − | 1.02269i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.6456 | + | 3.27558i | 0.812393 | + | 0.181696i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.2194 | −0.841636 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.715939i | 0.0394710i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.08181 | − | 8.08181i | 0.444217 | − | 0.444217i | −0.449210 | − | 0.893426i | \(-0.648294\pi\) |
0.893426 | + | 0.449210i | \(0.148294\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.44376 | + | 2.44376i | −0.133917 | + | 0.133917i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.37126 | + | 11.6066i | 0.184192 | + | 0.634138i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.4098i | − | 1.32969i | −0.746983 | − | 0.664843i | \(-0.768498\pi\) | ||
0.746983 | − | 0.664843i | \(-0.231502\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.92413 | − | 8.92413i | −0.484692 | − | 0.484692i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.36357 | − | 5.36357i | 0.290453 | − | 0.290453i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.2772 | 0.824890 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.81383 | + | 6.24468i | 0.0976534 | + | 0.336202i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.40907 | − | 1.40907i | −0.0756427 | − | 0.0756427i | 0.668273 | − | 0.743916i | \(-0.267034\pi\) |
−0.743916 | + | 0.668273i | \(0.767034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.11269 | + | 6.11269i | 0.327205 | + | 0.327205i | 0.851523 | − | 0.524318i | \(-0.175680\pi\) |
−0.524318 | + | 0.851523i | \(0.675680\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.00149 | 0.160208 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.7150i | − | 0.570304i | −0.958482 | − | 0.285152i | \(-0.907956\pi\) | ||
0.958482 | − | 0.285152i | \(-0.0920441\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.5947 | − | 12.4234i | −1.19920 | − | 0.659363i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.18370 | + | 5.18370i | 0.274350 | + | 0.274350i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.7234i | 1.67430i | 0.546975 | + | 0.837149i | \(0.315779\pi\) | ||||
−0.546975 | + | 0.837149i | \(0.684221\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 0.245451i | − | 0.0129185i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.07682 | + | 5.07682i | 0.266464 | + | 0.266464i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.41250 | + | 2.56895i | −0.0739334 | + | 0.134465i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 31.8025i | − | 1.66008i | −0.557707 | − | 0.830038i | \(-0.688319\pi\) | ||
0.557707 | − | 0.830038i | \(-0.311681\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.38396 | −0.124104 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.89246 | − | 2.89246i | −0.150169 | − | 0.150169i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.3861 | + | 17.3861i | 0.900220 | + | 0.900220i | 0.995455 | − | 0.0952347i | \(-0.0303602\pi\) |
−0.0952347 | + | 0.995455i | \(0.530360\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.39524 | − | 8.38513i | 0.381888 | − | 0.433006i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.5149 | 0.696054 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.4215 | − | 16.4215i | 0.843513 | − | 0.843513i | −0.145801 | − | 0.989314i | \(-0.546576\pi\) |
0.989314 | + | 0.145801i | \(0.0465758\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.83621 | − | 6.83621i | −0.350229 | − | 0.350229i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.00561i | 0.460165i | 0.973171 | + | 0.230083i | \(0.0738997\pi\) | ||||
−0.973171 | + | 0.230083i | \(0.926100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.48894 | + | 5.12615i | 0.0758835 | + | 0.261253i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.00811 | + | 9.00811i | −0.457908 | + | 0.457908i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.84497 | + | 1.84497i | −0.0935438 | + | 0.0935438i | −0.752330 | − | 0.658786i | \(-0.771070\pi\) |
0.658786 | + | 0.752330i | \(0.271070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.4551i | − | 0.882742i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.9005 | −0.751628 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.5711 | − | 24.6821i | 0.682836 | − | 1.24189i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0894 | + | 24.0894i | −1.20901 | + | 1.20901i | −0.237663 | + | 0.971348i | \(0.576381\pi\) |
−0.971348 | + | 0.237663i | \(0.923619\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.28931 | −0.264797 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4494 | −0.521817 | −0.260909 | − | 0.965364i | \(-0.584022\pi\) | ||||
−0.260909 | + | 0.965364i | \(0.584022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.23650 | − | 8.23650i | 0.410289 | − | 0.410289i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.07735 | − | 1.95942i | 0.0535342 | − | 0.0973641i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.75496 | 0.334831 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.67465i | − | 0.330040i | −0.986290 | − | 0.165020i | \(-0.947231\pi\) | ||
0.986290 | − | 0.165020i | \(-0.0527689\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.13506 | − | 9.13506i | 0.450599 | − | 0.450599i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.3016 | − | 10.3016i | 0.506907 | − | 0.506907i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.57238 | + | 8.85621i | 0.126273 | + | 0.434734i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.2851i | 0.797487i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8121 | + | 15.8121i | 0.772472 | + | 0.772472i | 0.978538 | − | 0.206066i | \(-0.0660663\pi\) |
−0.206066 | + | 0.978538i | \(0.566066\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.69730 | − | 1.69730i | 0.0827211 | − | 0.0827211i | −0.664536 | − | 0.747257i | \(-0.731371\pi\) |
0.747257 | + | 0.664536i | \(0.231371\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.586179 | −0.0285010 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.3410 | + | 16.0775i | −1.22922 | + | 0.779874i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.1900 | + | 12.1900i | 0.589915 | + | 0.589915i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.14830 | − | 4.14830i | −0.200282 | − | 0.200282i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.28686 | 0.350996 | 0.175498 | − | 0.984480i | \(-0.443847\pi\) | ||||
0.175498 | + | 0.984480i | \(0.443847\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.13785i | 0.102738i | 0.998680 | + | 0.0513692i | \(0.0163585\pi\) | ||||
−0.998680 | + | 0.0513692i | \(0.983641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.85105 | − | 8.82274i | 0.232590 | − | 0.423018i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.90537 | + | 8.90537i | 0.426002 | + | 0.426002i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.2103i | 1.58504i | 0.609846 | + | 0.792520i | \(0.291231\pi\) | ||||
−0.609846 | + | 0.792520i | \(0.708769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50826i | 0.262298i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.4343 | + | 12.4343i | 0.590771 | + | 0.590771i | 0.937840 | − | 0.347068i | \(-0.112823\pi\) |
−0.347068 | + | 0.937840i | \(0.612823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.7841 | + | 10.3282i | 0.890452 | + | 0.489602i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.7364i | 0.791604i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.8408 | 0.511607 | 0.255803 | − | 0.966729i | \(-0.417660\pi\) | ||||
0.255803 | + | 0.966729i | \(0.417660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.29482 | + | 3.29482i | 0.155147 | + | 0.155147i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.170363 | + | 0.170363i | 0.00800436 | + | 0.00800436i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.28648 | + | 7.87190i | 0.107192 | + | 0.369041i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.6178 | −1.52580 | −0.762899 | − | 0.646518i | \(-0.776224\pi\) | ||||
−0.762899 | + | 0.646518i | \(0.776224\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.24418 | + | 4.24418i | −0.198101 | + | 0.198101i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.9449 | + | 18.9449i | 0.882353 | + | 0.882353i | 0.993773 | − | 0.111421i | \(-0.0355401\pi\) |
−0.111421 | + | 0.993773i | \(0.535540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.7663i | 1.75515i | 0.479441 | + | 0.877574i | \(0.340840\pi\) | ||||
−0.479441 | + | 0.877574i | \(0.659160\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.42049 | − | 8.33330i | −0.112248 | − | 0.386448i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.10601 | − | 3.10601i | 0.143729 | − | 0.143729i | −0.631581 | − | 0.775310i | \(-0.717594\pi\) |
0.775310 | + | 0.631581i | \(0.217594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.66810 | + | 4.66810i | −0.215553 | + | 0.215553i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 10.1763i | − | 0.468899i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.8999 | 1.14490 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.72611 | − | 21.1312i | 0.216849 | − | 0.969566i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.36822 | − | 2.36822i | 0.108433 | − | 0.108433i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.23987 | −0.376489 | −0.188245 | − | 0.982122i | \(-0.560280\pi\) | ||||
−0.188245 | + | 0.982122i | \(0.560280\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3732 | 0.472976 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.51157 | + | 2.51157i | −0.114280 | + | 0.114280i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.5225 | − | 10.1843i | −0.841064 | − | 0.462446i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.7527 | 0.713822 | 0.356911 | − | 0.934138i | \(-0.383830\pi\) | ||||
0.356911 | + | 0.934138i | \(0.383830\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.6094i | 0.751104i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.14298 | − | 9.14298i | 0.412617 | − | 0.412617i | −0.470032 | − | 0.882649i | \(-0.655758\pi\) |
0.882649 | + | 0.470032i | \(0.155758\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.1104 | + | 19.1104i | −0.860691 | + | 0.860691i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.19706 | + | 1.21908i | −0.188644 | + | 0.0547935i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 14.0840i | − | 0.631754i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.93929 | + | 5.93929i | 0.265879 | + | 0.265879i | 0.827437 | − | 0.561558i | \(-0.189798\pi\) |
−0.561558 | + | 0.827437i | \(0.689798\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.150909 | + | 0.150909i | −0.00674213 | + | 0.00674213i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.53406 | 0.157576 | 0.0787879 | − | 0.996891i | \(-0.474895\pi\) | ||||
0.0787879 | + | 0.996891i | \(0.474895\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2776 | + | 35.3840i | 0.457349 | + | 1.57457i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.82210 | + | 2.82210i | 0.125334 | + | 0.125334i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.43955 | − | 8.43955i | −0.374076 | − | 0.374076i | 0.494883 | − | 0.868960i | \(-0.335211\pi\) |
−0.868960 | + | 0.494883i | \(0.835211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.60131 | −0.0708376 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.33065i | − | 0.191203i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.31638 | − | 4.21286i | 0.102072 | − | 0.185641i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.810146 | + | 0.810146i | 0.0356302 | + | 0.0356302i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.00739i | − | 0.395380i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.64810i | − | 0.422691i | −0.977411 | − | 0.211345i | \(-0.932216\pi\) | ||
0.977411 | − | 0.211345i | \(-0.0677845\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.7409 | − | 25.7409i | −1.12557 | − | 1.12557i | −0.990889 | − | 0.134683i | \(-0.956998\pi\) |
−0.134683 | − | 0.990889i | \(-0.543002\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.95959 | + | 1.33290i | 0.260098 | + | 0.0581724i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.2932i | 1.01467i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.5428 | −0.632295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.43447 | + | 8.43447i | 0.366025 | + | 0.366025i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.05965 | + | 5.05965i | 0.219158 | + | 0.219158i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.9939 | + | 11.9071i | −1.77232 | + | 0.514788i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.24150 | 0.398800 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.61287 | − | 7.61287i | 0.327909 | − | 0.327909i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.2087 | + | 19.2087i | 0.825846 | + | 0.825846i | 0.986939 | − | 0.161093i | \(-0.0515021\pi\) |
−0.161093 | + | 0.986939i | \(0.551502\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.39653i | 0.317415i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 32.6810 | − | 9.49252i | 1.39990 | − | 0.406615i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.9722 | − | 27.9722i | 1.19600 | − | 1.19600i | 0.220652 | − | 0.975353i | \(-0.429181\pi\) |
0.975353 | − | 0.220652i | \(-0.0708185\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.98062 | + | 9.98062i | −0.425963 | + | 0.425963i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 19.4998i | − | 0.830719i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.3852 | 0.654244 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.72334 | − | 6.77175i | 0.158047 | − | 0.287445i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.4266 | + | 15.4266i | −0.653647 | + | 0.653647i | −0.953869 | − | 0.300222i | \(-0.902939\pi\) |
0.300222 | + | 0.953869i | \(0.402939\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.2372 | 1.61726 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.7316 | 0.495308 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2389 | + | 18.2389i | −0.768676 | + | 0.768676i | −0.977874 | − | 0.209197i | \(-0.932915\pi\) |
0.209197 | + | 0.977874i | \(0.432915\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.7290 | + | 13.5969i | 1.04036 | + | 0.572025i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.22137 | 0.0512926 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.0254i | 1.42642i | 0.700950 | + | 0.713210i | \(0.252760\pi\) | ||||
−0.700950 | + | 0.713210i | \(0.747240\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9297 | − | 17.9297i | 0.750335 | − | 0.750335i | −0.224207 | − | 0.974542i | \(-0.571979\pi\) |
0.974542 | + | 0.224207i | \(0.0719790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.28556 | − | 9.28556i | 0.387910 | − | 0.387910i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.78976 | − | 12.2780i | −0.324855 | − | 0.512029i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.122769i | − | 0.00511093i | −0.999997 | − | 0.00255547i | \(-0.999187\pi\) | ||
0.999997 | − | 0.00255547i | \(-0.000813431\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1514 | + | 14.1514i | 0.588112 | + | 0.588112i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.56190 | + | 3.56190i | −0.147773 | + | 0.147773i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.54614 | −0.271113 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.44516 | + | 1.87206i | −0.266475 | + | 0.0774003i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.93139 | − | 6.93139i | −0.286089 | − | 0.286089i | 0.549443 | − | 0.835531i | \(-0.314840\pi\) |
−0.835531 | + | 0.549443i | \(0.814840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8839 | − | 11.8839i | −0.489667 | − | 0.489667i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.2128 | −1.11939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 21.4611i | − | 0.881303i | −0.897678 | − | 0.440652i | \(-0.854747\pi\) | ||
0.897678 | − | 0.440652i | \(-0.145253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.3642 | − | 7.89793i | −0.588874 | − | 0.323784i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.66442 | + | 3.66442i | 0.149975 | + | 0.149975i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.94482i | 0.202040i | 0.994884 | + | 0.101020i | \(0.0322106\pi\) | ||||
−0.994884 | + | 0.101020i | \(0.967789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.1862i | − | 0.823414i | −0.911316 | − | 0.411707i | \(-0.864933\pi\) | ||
0.911316 | − | 0.411707i | \(-0.135067\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.82203 | − | 3.82203i | −0.155645 | − | 0.155645i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.0680 | − | 7.73509i | −0.571947 | − | 0.314476i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.8529i | 0.968161i | 0.875024 | + | 0.484080i | \(0.160846\pi\) | ||||
−0.875024 | + | 0.484080i | \(0.839154\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.49949 | 0.222851 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.24409 | + | 1.24409i | 0.0503305 | + | 0.0503305i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.1159 | − | 24.1159i | −0.974031 | − | 0.974031i | 0.0256404 | − | 0.999671i | \(-0.491838\pi\) |
−0.999671 | + | 0.0256404i | \(0.991838\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.11912 | − | 1.48690i | 0.206423 | − | 0.0599576i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.63876 | −0.347783 | −0.173892 | − | 0.984765i | \(-0.555634\pi\) | ||||
−0.173892 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.3601 | + | 32.3601i | −1.30066 | + | 1.30066i | −0.372716 | + | 0.927945i | \(0.621573\pi\) |
−0.927945 | + | 0.372716i | \(0.878427\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.05636 | − | 2.05636i | −0.0825188 | − | 0.0825188i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.7087i | 0.469101i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.6500 | + | 22.6181i | −0.426002 | + | 0.904722i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.98531 | + | 5.98531i | −0.239030 | + | 0.239030i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.6679 | + | 14.6679i | −0.584848 | + | 0.584848i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.3652i | − | 0.452443i | −0.974076 | − | 0.226222i | \(-0.927363\pi\) | ||
0.974076 | − | 0.226222i | \(-0.0726373\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.82477 | 0.311007 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.9433 | + | 10.4157i | 0.751744 | + | 0.413335i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.6906 | − | 11.6906i | 0.463199 | − | 0.463199i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.5314 | 0.456173 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.9081 | −0.549336 | −0.274668 | − | 0.961539i | \(-0.588568\pi\) | ||||
−0.274668 | + | 0.961539i | \(0.588568\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.4850 | + | 18.4850i | −0.728977 | + | 0.728977i | −0.970416 | − | 0.241439i | \(-0.922381\pi\) |
0.241439 | + | 0.970416i | \(0.422381\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.7248 | − | 24.9618i | 0.540415 | − | 0.982868i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.15900 | 0.0455649 | 0.0227825 | − | 0.999740i | \(-0.492747\pi\) | ||||
0.0227825 | + | 0.999740i | \(0.492747\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 23.3142i | − | 0.915163i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.35159 | − | 3.35159i | 0.131359 | − | 0.131359i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.8412 | + | 11.8412i | −0.463383 | + | 0.463383i | −0.899763 | − | 0.436380i | \(-0.856260\pi\) |
0.436380 | + | 0.899763i | \(0.356260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.9960 | − | 9.29358i | 1.25019 | − | 0.363130i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.31108i | − | 0.0511500i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.22941 | + | 1.22941i | 0.0478909 | + | 0.0478909i | 0.730647 | − | 0.682756i | \(-0.239219\pi\) |
−0.682756 | + | 0.730647i | \(0.739219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2100 | + | 13.2100i | −0.513810 | + | 0.513810i | −0.915692 | − | 0.401882i | \(-0.868356\pi\) |
0.401882 | + | 0.915692i | \(0.368356\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.0155 | 0.699663 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3578 | − | 3.29900i | 0.440438 | − | 0.127930i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.25924 | − | 9.25924i | −0.358519 | − | 0.358519i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.452248 | + | 0.452248i | 0.0174849 | + | 0.0174849i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.5880 | 1.06502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.69175i | 0.180854i | 0.995903 | + | 0.0904268i | \(0.0288231\pi\) | ||||
−0.995903 | + | 0.0904268i | \(0.971177\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.09132 | + | 4.87945i | −0.0420048 | + | 0.187810i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.1893 | + | 36.1893i | 1.39087 | + | 1.39087i | 0.823385 | + | 0.567483i | \(0.192083\pi\) |
0.567483 | + | 0.823385i | \(0.307917\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 11.5457i | − | 0.443083i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 0.384941i | − | 0.0147510i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.7839 | + | 18.7839i | 0.718744 | + | 0.718744i | 0.968348 | − | 0.249604i | \(-0.0803004\pi\) |
−0.249604 | + | 0.968348i | \(0.580300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.9183 | + | 25.3135i | −0.531790 | + | 0.967181i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.78901i | 0.259017i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.0525 | −0.382969 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0077 | − | 12.0077i | −0.456795 | − | 0.456795i | 0.440807 | − | 0.897602i | \(-0.354692\pi\) |
−0.897602 | + | 0.440807i | \(0.854692\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.68803 | − | 1.68803i | −0.0641228 | − | 0.0641228i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.1572 | − | 34.9694i | −0.385286 | − | 1.32647i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.3089 | −0.541990 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.4167 | + | 15.4167i | −0.583114 | + | 0.583114i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.6671 | + | 18.6671i | 0.705046 | + | 0.705046i | 0.965489 | − | 0.260443i | \(-0.0838686\pi\) |
−0.260443 | + | 0.965489i | \(0.583869\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 14.9668i | − | 0.564482i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.25871 | − | 0.365606i | 0.0474059 | − | 0.0137695i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.2312 | + | 14.2312i | −0.535219 | + | 0.535219i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.320563 | − | 0.320563i | 0.0120390 | − | 0.0120390i | −0.701062 | − | 0.713101i | \(-0.747290\pi\) |
0.713101 | + | 0.701062i | \(0.247290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.5967i | 0.472413i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.2858 | −0.422658 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.4951 | + | 6.32039i | 0.429892 | + | 0.236369i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.42681 | − | 1.42681i | 0.0532850 | − | 0.0532850i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.8907 | −1.82332 | −0.911658 | − | 0.410951i | \(-0.865197\pi\) | ||||
−0.911658 | + | 0.410951i | \(0.865197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.62601 | 0.0977977 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.9356 | − | 10.9356i | 0.406701 | − | 0.406701i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.91391 | + | 21.9709i | −0.182498 | + | 0.815978i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.5201 | 0.909401 | 0.454700 | − | 0.890644i | \(-0.349746\pi\) | ||||
0.454700 | + | 0.890644i | \(0.349746\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.0683 | + | 54.0683i | −1.99979 | + | 1.99979i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.3958 | − | 27.3958i | 1.01189 | − | 1.01189i | 0.0119594 | − | 0.999928i | \(-0.496193\pi\) |
0.999928 | − | 0.0119594i | \(-0.00380688\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.43557 | − | 11.8280i | −0.126723 | − | 0.436283i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5647i | 0.389156i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.1011 | − | 19.1011i | −0.702644 | − | 0.702644i | 0.262333 | − | 0.964977i | \(-0.415508\pi\) |
−0.964977 | + | 0.262333i | \(0.915508\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.19127 | + | 9.19127i | −0.337650 | + | 0.337650i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.305994 | 0.0112258 | 0.00561291 | − | 0.999984i | \(-0.498213\pi\) | ||||
0.00561291 | + | 0.999984i | \(0.498213\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.4387 | − | 35.9384i | −0.382443 | − | 1.31668i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.91633 | − | 2.91633i | −0.106703 | − | 0.106703i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.4874 | − | 16.4874i | −0.602438 | − | 0.602438i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.13631 | −0.260408 | −0.130204 | − | 0.991487i | \(-0.541563\pi\) | ||||
−0.130204 | + | 0.991487i | \(0.541563\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.85108i | 0.176783i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.472082 | − | 0.259567i | −0.0171808 | − | 0.00944660i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.8469 | − | 25.8469i | −0.939422 | − | 0.939422i | 0.0588455 | − | 0.998267i | \(-0.481258\pi\) |
−0.998267 | + | 0.0588455i | \(0.981258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.68410i | 0.206320i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 11.9718i | − | 0.433979i | −0.976174 | − | 0.216989i | \(-0.930376\pi\) | ||
0.976174 | − | 0.216989i | \(-0.0696237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.1440 | + | 13.1440i | 0.475846 | + | 0.475846i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.46647 | − | 11.7608i | 0.233796 | − | 0.425211i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 35.8022i | − | 1.29274i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.2266 | −0.981816 | −0.490908 | − | 0.871211i | \(-0.663335\pi\) | ||||
−0.490908 | + | 0.871211i | \(0.663335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.6525 | + | 13.6525i | 0.491684 | + | 0.491684i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.83729 | − | 8.83729i | −0.317855 | − | 0.317855i | 0.530088 | − | 0.847943i | \(-0.322159\pi\) |
−0.847943 | + | 0.530088i | \(0.822159\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3951 | + | 16.3846i | 0.373405 | + | 0.588552i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.22105 | 0.151429 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.30024 | − | 7.30024i | 0.261558 | − | 0.261558i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.9373 | − | 15.9373i | −0.570280 | − | 0.570280i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.50274i | 0.160915i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.34707 | + | 21.8518i | 0.226537 | + | 0.779923i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.7150 | − | 21.7150i | 0.774058 | − | 0.774058i | −0.204755 | − | 0.978813i | \(-0.565640\pi\) |
0.978813 | + | 0.204755i | \(0.0656399\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.54829 | − | 6.54829i | 0.233125 | − | 0.233125i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4144i | 0.548073i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.3652 | 1.50443 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.60824 | + | 6.56241i | −0.127971 | + | 0.232745i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.4134 | − | 28.4134i | 1.00645 | − | 1.00645i | 0.00647582 | − | 0.999979i | \(-0.497939\pi\) |
0.999979 | − | 0.00647582i | \(-0.00206133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.51835 | −0.124470 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.58659 | −0.338726 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.81201 | + | 1.81201i | −0.0639446 | + | 0.0639446i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.82664 | − | 6.95963i | 0.134871 | − | 0.245295i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.04558 | −0.283218 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 26.4356i | − | 0.929426i | −0.885461 | − | 0.464713i | \(-0.846158\pi\) | ||
0.885461 | − | 0.464713i | \(-0.153842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.0962 | + | 15.0962i | −0.530100 | + | 0.530100i | −0.920602 | − | 0.390502i | \(-0.872301\pi\) |
0.390502 | + | 0.920602i | \(0.372301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.10724 | − | 1.10724i | 0.0388325 | − | 0.0388325i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.3595 | − | 35.6657i | −0.362877 | − | 1.24932i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 55.1699i | − | 1.93015i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.59220 | − | 2.59220i | −0.0905787 | − | 0.0905787i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.4997 | − | 29.4997i | 1.02955 | − | 1.02955i | 0.0299962 | − | 0.999550i | \(-0.490450\pi\) |
0.999550 | − | 0.0299962i | \(-0.00954951\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.2908 | −0.742152 | −0.371076 | − | 0.928602i | \(-0.621011\pi\) | ||||
−0.371076 | + | 0.928602i | \(0.621011\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.25208 | − | 5.23551i | 0.287301 | − | 0.182277i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.4619 | − | 14.4619i | −0.502888 | − | 0.502888i | 0.409446 | − | 0.912334i | \(-0.365722\pi\) |
−0.912334 | + | 0.409446i | \(0.865722\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.64651 | − | 5.64651i | −0.196111 | − | 0.196111i | 0.602219 | − | 0.798331i | \(-0.294283\pi\) |
−0.798331 | + | 0.602219i | \(0.794283\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.9686 | −0.553945 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.0616i | 1.14552i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.229927 | − | 0.418175i | 0.00795695 | − | 0.0144715i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.74413 | + | 2.74413i | 0.0948512 | + | 0.0948512i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 21.4686i | − | 0.741178i | −0.928797 | − | 0.370589i | \(-0.879156\pi\) | ||
0.928797 | − | 0.370589i | \(-0.120844\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 8.72534i | − | 0.300874i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.1735 | + | 11.1735i | 0.384836 | + | 0.384836i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.82012 | − | 4.29977i | −0.269020 | − | 0.147917i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.76905i | − | 0.301308i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.28736 | −0.112822 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.10678 | − | 7.10678i | −0.243617 | − | 0.243617i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.10917 | + | 5.10917i | 0.174935 | + | 0.174935i | 0.789143 | − | 0.614209i | \(-0.210525\pi\) |
−0.614209 | + | 0.789143i | \(0.710525\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.70108 | + | 9.29930i | 0.0923748 | + | 0.318029i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.14205 | −0.243968 | −0.121984 | − | 0.992532i | \(-0.538926\pi\) | ||||
−0.121984 | + | 0.992532i | \(0.538926\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9070 | + | 12.9070i | −0.440381 | + | 0.440381i | −0.892140 | − | 0.451759i | \(-0.850797\pi\) |
0.451759 | + | 0.892140i | \(0.350797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.05887 | + | 2.05887i | 0.0701662 | + | 0.0701662i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 34.4382i | − | 1.17229i | −0.810206 | − | 0.586145i | \(-0.800645\pi\) | ||
0.810206 | − | 0.586145i | \(-0.199355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.61801 | + | 19.3417i | 0.191018 | + | 0.657639i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.4535 | + | 13.4535i | −0.456905 | + | 0.456905i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.4096 | − | 17.4096i | 0.590581 | − | 0.590581i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2236i | 0.549715i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.45309 | 0.319939 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.6285 | + | 0.854909i | −0.460727 | + | 0.0289012i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.5999 | − | 20.5999i | 0.695609 | − | 0.695609i | −0.267851 | − | 0.963460i | \(-0.586314\pi\) |
0.963460 | + | 0.267851i | \(0.0863136\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.5239 | −0.354963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.0289 | 0.742171 | 0.371086 | − | 0.928599i | \(-0.378986\pi\) | ||||
0.371086 | + | 0.928599i | \(0.378986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.2149 | + | 15.2149i | −0.512022 | + | 0.512022i | −0.915146 | − | 0.403123i | \(-0.867925\pi\) |
0.403123 | + | 0.915146i | \(0.367925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.3722 | − | 12.8508i | −0.785647 | − | 0.431976i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.6823 | −1.39956 | −0.699778 | − | 0.714361i | \(-0.746718\pi\) | ||||
−0.699778 | + | 0.714361i | \(0.746718\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8080i | 0.396027i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.38208 | − | 1.38208i | 0.0463014 | − | 0.0463014i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.79502 | − | 1.79502i | 0.0600679 | − | 0.0600679i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.8445 | + | 5.76403i | −0.663327 | + | 0.192670i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.72872i | 0.291444i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.3561 | + | 12.3561i | 0.412100 | + | 0.412100i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.2145 | − | 14.2145i | 0.473552 | − | 0.473552i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.5595 | 0.517786 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.61330 | − | 15.8827i | −0.153351 | − | 0.527959i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.7322 | − | 27.7322i | −0.920834 | − | 0.920834i | 0.0762544 | − | 0.997088i | \(-0.475704\pi\) |
−0.997088 | + | 0.0762544i | \(0.975704\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.6519 | − | 11.6519i | −0.386468 | − | 0.386468i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3043 | 1.07029 | 0.535145 | − | 0.844760i | \(-0.320257\pi\) | ||||
0.535145 | + | 0.844760i | \(0.320257\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.06119i | 0.266787i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.2066 | − | 27.6566i | 0.502714 | − | 0.914299i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.8686 | + | 12.8686i | 0.424958 | + | 0.424958i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.5387i | 1.79907i | 0.436853 | + | 0.899533i | \(0.356093\pi\) | ||||
−0.436853 | + | 0.899533i | \(0.643907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.64740i | 0.153137i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.4739 | − | 24.4739i | −0.805567 | − | 0.805567i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.77159 | + | 16.8634i | −0.124009 | + | 0.554465i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.15006i | 0.0706172i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.8714 | −1.37375 | −0.686877 | − | 0.726773i | \(-0.741019\pi\) | ||||
−0.686877 | + | 0.726773i | \(0.741019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.8676 | − | 16.8676i | −0.552813 | − | 0.552813i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.5227 | − | 20.5227i | −0.671884 | − | 0.671884i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.1915 | + | 7.31713i | −0.823850 | + | 0.239296i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.5314 | −0.409384 | −0.204692 | − | 0.978826i | \(-0.565619\pi\) | ||||
−0.204692 | + | 0.978826i | \(0.565619\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.89496 | − | 3.89496i | 0.127107 | − | 0.127107i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.1881 | − | 40.1881i | −1.31009 | − | 1.31009i | −0.921343 | − | 0.388751i | \(-0.872907\pi\) |
−0.388751 | − | 0.921343i | \(-0.627093\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.93285i | − | 0.225765i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.62266 | + | 0.761780i | −0.0853153 | + | 0.0247807i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.2243 | + | 26.2243i | −0.852174 | + | 0.852174i | −0.990401 | − | 0.138227i | \(-0.955860\pi\) |
0.138227 | + | 0.990401i | \(0.455860\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.78260 | + | 2.78260i | −0.0903270 | + | 0.0903270i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 15.0474i | − | 0.487945i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.51475 | −0.0814607 | −0.0407304 | − | 0.999170i | \(-0.512968\pi\) | ||||
−0.0407304 | + | 0.999170i | \(0.512968\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.1476 | + | 25.7306i | −0.457804 | + | 0.832622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.22315 | − | 6.22315i | 0.201166 | − | 0.201166i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.7787 | −0.509522 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.9395 | −0.514176 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.4992 | − | 13.4992i | 0.435005 | − | 0.435005i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.2139 | − | 21.5612i | −1.26234 | − | 0.694079i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.5088 | 1.65641 | 0.828205 | − | 0.560425i | \(-0.189362\pi\) | ||||
0.828205 | + | 0.560425i | \(0.189362\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 25.9933i | − | 0.835026i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.0586 | − | 26.0586i | 0.836259 | − | 0.836259i | −0.152105 | − | 0.988364i | \(-0.548605\pi\) |
0.988364 | + | 0.152105i | \(0.0486053\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0644 | − | 14.0644i | 0.450885 | − | 0.450885i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.6722 | − | 8.03984i | 0.405835 | − | 0.257481i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.6258i | 0.563899i | 0.959429 | + | 0.281950i | \(0.0909811\pi\) | ||||
−0.959429 | + | 0.281950i | \(0.909019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.2494 | + | 13.2494i | 0.423454 | + | 0.423454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.7618 | + | 10.7618i | −0.343596 | + | 0.343596i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.64257 | 0.0523899 | 0.0261949 | − | 0.999657i | \(-0.491661\pi\) | ||||
0.0261949 | + | 0.999657i | \(0.491661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 58.4346 | − | 16.9729i | 1.86188 | − | 0.540803i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.506245 | + | 0.506245i | 0.0161140 | + | 0.0161140i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.1967 | − | 26.1967i | −0.833008 | − | 0.833008i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.3434 | −1.98040 | −0.990202 | − | 0.139642i | \(-0.955405\pi\) | ||||
−0.990202 | + | 0.139642i | \(0.955405\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 11.4294i | − | 0.362701i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.1542 | − | 5.58314i | −0.321910 | − | 0.176997i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.0563 | − | 30.0563i | −0.951891 | − | 0.951891i | 0.0470037 | − | 0.998895i | \(-0.485033\pi\) |
−0.998895 | + | 0.0470037i | \(0.985033\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.45601i | 0.109343i |
(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 | 1920.2.bl.a.289.17 | 48 | ||
4.3 | odd | 2 | 1920.2.bl.b.289.8 | 48 | |||
5.4 | even | 2 | inner | 1920.2.bl.a.289.8 | 48 | ||
8.3 | odd | 2 | 960.2.bl.a.529.20 | 48 | |||
8.5 | even | 2 | 240.2.bl.a.109.8 | ✓ | 48 | ||
16.3 | odd | 4 | 960.2.bl.a.49.11 | 48 | |||
16.5 | even | 4 | inner | 1920.2.bl.a.1249.8 | 48 | ||
16.11 | odd | 4 | 1920.2.bl.b.1249.17 | 48 | |||
16.13 | even | 4 | 240.2.bl.a.229.17 | yes | 48 | ||
20.19 | odd | 2 | 1920.2.bl.b.289.17 | 48 | |||
24.5 | odd | 2 | 720.2.bm.h.109.17 | 48 | |||
40.19 | odd | 2 | 960.2.bl.a.529.11 | 48 | |||
40.29 | even | 2 | 240.2.bl.a.109.17 | yes | 48 | ||
48.29 | odd | 4 | 720.2.bm.h.469.8 | 48 | |||
80.19 | odd | 4 | 960.2.bl.a.49.20 | 48 | |||
80.29 | even | 4 | 240.2.bl.a.229.8 | yes | 48 | ||
80.59 | odd | 4 | 1920.2.bl.b.1249.8 | 48 | |||
80.69 | even | 4 | inner | 1920.2.bl.a.1249.17 | 48 | ||
120.29 | odd | 2 | 720.2.bm.h.109.8 | 48 | |||
240.29 | odd | 4 | 720.2.bm.h.469.17 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.bl.a.109.8 | ✓ | 48 | 8.5 | even | 2 | ||
240.2.bl.a.109.17 | yes | 48 | 40.29 | even | 2 | ||
240.2.bl.a.229.8 | yes | 48 | 80.29 | even | 4 | ||
240.2.bl.a.229.17 | yes | 48 | 16.13 | even | 4 | ||
720.2.bm.h.109.8 | 48 | 120.29 | odd | 2 | |||
720.2.bm.h.109.17 | 48 | 24.5 | odd | 2 | |||
720.2.bm.h.469.8 | 48 | 48.29 | odd | 4 | |||
720.2.bm.h.469.17 | 48 | 240.29 | odd | 4 | |||
960.2.bl.a.49.11 | 48 | 16.3 | odd | 4 | |||
960.2.bl.a.49.20 | 48 | 80.19 | odd | 4 | |||
960.2.bl.a.529.11 | 48 | 40.19 | odd | 2 | |||
960.2.bl.a.529.20 | 48 | 8.3 | odd | 2 | |||
1920.2.bl.a.289.8 | 48 | 5.4 | even | 2 | inner | ||
1920.2.bl.a.289.17 | 48 | 1.1 | even | 1 | trivial | ||
1920.2.bl.a.1249.8 | 48 | 16.5 | even | 4 | inner | ||
1920.2.bl.a.1249.17 | 48 | 80.69 | even | 4 | inner | ||
1920.2.bl.b.289.8 | 48 | 4.3 | odd | 2 | |||
1920.2.bl.b.289.17 | 48 | 20.19 | odd | 2 | |||
1920.2.bl.b.1249.8 | 48 | 80.59 | odd | 4 | |||
1920.2.bl.b.1249.17 | 48 | 16.11 | odd | 4 |