Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(49,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 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("960.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.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: | \(7.66563859404\) |
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 | 49.14 | ||
Character | \(\chi\) | \(=\) | 960.49 |
Dual form | 960.2.bl.a.529.14 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.15195 | + | 0.607542i | −0.962382 | + | 0.271701i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.25286 | −0.851502 | −0.425751 | − | 0.904840i | \(-0.639990\pi\) | ||||
−0.425751 | + | 0.904840i | \(0.639990\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.66088 | + | 1.66088i | 0.500775 | + | 0.500775i | 0.911679 | − | 0.410904i | \(-0.134787\pi\) |
−0.410904 | + | 0.911679i | \(0.634787\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.76925 | − | 4.76925i | −1.32275 | − | 1.32275i | −0.911540 | − | 0.411212i | \(-0.865106\pi\) |
−0.411212 | − | 0.911540i | \(-0.634894\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.95126 | − | 1.09206i | −0.503812 | − | 0.281969i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.99777i | − | 1.69721i | −0.529028 | − | 0.848604i | \(-0.677443\pi\) | ||
0.529028 | − | 0.848604i | \(-0.322557\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.66634 | − | 2.66634i | 0.611701 | − | 0.611701i | −0.331688 | − | 0.943389i | \(-0.607618\pi\) |
0.943389 | + | 0.331688i | \(0.107618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.59301 | − | 1.59301i | −0.347624 | − | 0.347624i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.41825 | 0.921269 | 0.460634 | − | 0.887590i | \(-0.347622\pi\) | ||||
0.460634 | + | 0.887590i | \(0.347622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.26178 | − | 2.61480i | 0.852357 | − | 0.522960i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.59286 | − | 2.59286i | 0.481481 | − | 0.481481i | −0.424123 | − | 0.905604i | \(-0.639418\pi\) |
0.905604 | + | 0.424123i | \(0.139418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.93331 | 0.706443 | 0.353221 | − | 0.935540i | \(-0.385086\pi\) | ||||
0.353221 | + | 0.935540i | \(0.385086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.34884i | 0.408881i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.84805 | − | 1.36871i | 0.819470 | − | 0.231354i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.01181 | + | 2.01181i | −0.330739 | + | 0.330739i | −0.852867 | − | 0.522128i | \(-0.825138\pi\) |
0.522128 | + | 0.852867i | \(0.325138\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.74474i | − | 1.08002i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.50104i | − | 0.702945i | −0.936198 | − | 0.351472i | \(-0.885681\pi\) | ||
0.936198 | − | 0.351472i | \(-0.114319\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.14876 | + | 7.14876i | −1.09017 | + | 1.09017i | −0.0946658 | + | 0.995509i | \(0.530178\pi\) |
−0.995509 | + | 0.0946658i | \(0.969822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.607542 | − | 2.15195i | −0.0905671 | − | 0.320794i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.1154i | − | 1.47548i | −0.675086 | − | 0.737739i | \(-0.735893\pi\) | ||
0.675086 | − | 0.737739i | \(-0.264107\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.92461 | −0.274945 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.94817 | − | 4.94817i | 0.692883 | − | 0.692883i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.649299 | − | 0.649299i | 0.0891881 | − | 0.0891881i | −0.661105 | − | 0.750293i | \(-0.729912\pi\) |
0.750293 | + | 0.661105i | \(0.229912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.58319 | − | 2.56508i | −0.617997 | − | 0.345875i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.77078 | 0.499452 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.64696 | − | 5.64696i | −0.735172 | − | 0.735172i | 0.236468 | − | 0.971639i | \(-0.424010\pi\) |
−0.971639 | + | 0.236468i | \(0.924010\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00520 | + | 5.00520i | −0.640851 | + | 0.640851i | −0.950765 | − | 0.309914i | \(-0.899700\pi\) |
0.309914 | + | 0.950765i | \(0.399700\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.25286i | − | 0.283834i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.1607 | + | 7.36567i | 1.63239 | + | 0.913599i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.95274 | − | 4.95274i | −0.605074 | − | 0.605074i | 0.336581 | − | 0.941655i | \(-0.390729\pi\) |
−0.941655 | + | 0.336581i | \(0.890729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.12417 | + | 3.12417i | 0.376106 | + | 0.376106i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.33178i | 0.276732i | 0.990381 | + | 0.138366i | \(0.0441850\pi\) | ||||
−0.990381 | + | 0.138366i | \(0.955815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.18275 | −0.255472 | −0.127736 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127736 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.86248 | + | 1.16459i | 0.561471 | + | 0.134476i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.74174 | − | 3.74174i | −0.426410 | − | 0.426410i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.38450 | −0.718312 | −0.359156 | − | 0.933278i | \(-0.616935\pi\) | ||||
−0.359156 | + | 0.933278i | \(0.616935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.25073 | + | 5.25073i | 0.576342 | + | 0.576342i | 0.933894 | − | 0.357551i | \(-0.116388\pi\) |
−0.357551 | + | 0.933894i | \(0.616388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.25144 | + | 15.0589i | 0.461134 | + | 1.63336i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.66685 | 0.393128 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.7100i | − | 1.66525i | −0.553833 | − | 0.832627i | \(-0.686836\pi\) | ||
0.553833 | − | 0.832627i | \(-0.313164\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.7445 | + | 10.7445i | 1.12633 | + | 1.12633i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.78127 | + | 2.78127i | 0.288404 | + | 0.288404i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.11792 | + | 7.35775i | −0.422490 | + | 0.754889i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.61603i | 0.468687i | 0.972154 | + | 0.234343i | \(0.0752940\pi\) | ||||
−0.972154 | + | 0.234343i | \(0.924706\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.66088 | + | 1.66088i | −0.166925 | + | 0.166925i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.13980 | − | 1.13980i | −0.113415 | − | 0.113415i | 0.648122 | − | 0.761537i | \(-0.275555\pi\) |
−0.761537 | + | 0.648122i | \(0.775555\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.11257 | −0.405224 | −0.202612 | − | 0.979259i | \(-0.564943\pi\) | ||||
−0.202612 | + | 0.979259i | \(0.564943\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.39591 | + | 2.46026i | 0.428997 | + | 0.240097i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.98634 | + | 4.98634i | −0.482048 | + | 0.482048i | −0.905785 | − | 0.423737i | \(-0.860718\pi\) |
0.423737 | + | 0.905785i | \(0.360718\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.62560 | − | 3.62560i | 0.347269 | − | 0.347269i | −0.511822 | − | 0.859091i | \(-0.671029\pi\) |
0.859091 | + | 0.511822i | \(0.171029\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.84512 | −0.270047 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.639228i | − | 0.0601335i | −0.999548 | − | 0.0300668i | \(-0.990428\pi\) | ||
0.999548 | − | 0.0300668i | \(-0.00957199\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.50786 | + | 2.68427i | −0.886612 | + | 0.250310i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.76925 | − | 4.76925i | 0.440917 | − | 0.440917i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.7650i | 1.44518i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 5.48295i | − | 0.498450i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.18272 | − | 3.18272i | 0.286976 | − | 0.286976i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.58255 | + | 8.21614i | −0.678204 | + | 0.734874i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.5549i | − | 1.55774i | −0.627184 | − | 0.778871i | \(-0.715793\pi\) | ||
0.627184 | − | 0.778871i | \(-0.284207\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.1099 | −0.890124 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.826200 | + | 0.826200i | −0.0721855 | + | 0.0721855i | −0.742278 | − | 0.670092i | \(-0.766255\pi\) |
0.670092 | + | 0.742278i | \(0.266255\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00690 | + | 6.00690i | −0.520864 | + | 0.520864i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.09206 | − | 1.95126i | 0.0939897 | − | 0.167937i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.92457 | 0.762477 | 0.381239 | − | 0.924477i | \(-0.375498\pi\) | ||||
0.381239 | + | 0.924477i | \(0.375498\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.83668 | − | 4.83668i | −0.410242 | − | 0.410242i | 0.471581 | − | 0.881823i | \(-0.343683\pi\) |
−0.881823 | + | 0.471581i | \(0.843683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.15265 | − | 7.15265i | 0.602361 | − | 0.602361i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 15.8423i | − | 1.32480i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00443 | + | 7.15497i | −0.332550 | + | 0.594188i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.36091 | − | 1.36091i | −0.112246 | − | 0.112246i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.49085 | − | 1.49085i | −0.122135 | − | 0.122135i | 0.643397 | − | 0.765533i | \(-0.277524\pi\) |
−0.765533 | + | 0.643397i | \(0.777524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.61540i | − | 0.782490i | −0.920287 | − | 0.391245i | \(-0.872044\pi\) | ||
0.920287 | − | 0.391245i | \(-0.127956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.99777 | 0.565736 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.46429 | + | 2.38965i | −0.679868 | + | 0.191941i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.0158 | − | 16.0158i | −1.27820 | − | 1.27820i | −0.941676 | − | 0.336521i | \(-0.890750\pi\) |
−0.336521 | − | 0.941676i | \(-0.609250\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.918248 | 0.0728218 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.95371 | −0.784462 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.3477 | + | 13.3477i | 1.04547 | + | 1.04547i | 0.998916 | + | 0.0465557i | \(0.0148245\pi\) |
0.0465557 | + | 0.998916i | \(0.485176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.42702 | − | 5.05459i | −0.111093 | − | 0.393499i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.8029 | 0.990720 | 0.495360 | − | 0.868688i | \(-0.335036\pi\) | ||||
0.495360 | + | 0.868688i | \(0.335036\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.4915i | 2.49934i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.66634 | + | 2.66634i | 0.203900 | + | 0.203900i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8300 | + | 12.8300i | 0.975450 | + | 0.975450i | 0.999706 | − | 0.0242559i | \(-0.00772166\pi\) |
−0.0242559 | + | 0.999706i | \(0.507722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.60121 | + | 5.89079i | −0.725784 | + | 0.445302i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 7.98601i | − | 0.600265i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.61252 | + | 4.61252i | −0.344756 | + | 0.344756i | −0.858152 | − | 0.513396i | \(-0.828387\pi\) |
0.513396 | + | 0.858152i | \(0.328387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.12071 | − | 4.12071i | −0.306290 | − | 0.306290i | 0.537179 | − | 0.843468i | \(-0.319490\pi\) |
−0.843468 | + | 0.537179i | \(0.819490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.07843 | −0.523252 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.10705 | − | 5.55156i | 0.228435 | − | 0.408159i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.6225 | − | 11.6225i | 0.849919 | − | 0.849919i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.59301 | − | 1.59301i | 0.115875 | − | 0.115875i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.953399 | 0.0689855 | 0.0344928 | − | 0.999405i | \(-0.489018\pi\) | ||||
0.0344928 | + | 0.999405i | \(0.489018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.82186i | − | 0.347085i | −0.984826 | − | 0.173543i | \(-0.944479\pi\) | ||
0.984826 | − | 0.173543i | \(-0.0555214\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.09771 | + | 14.5143i | 0.293443 | + | 1.03939i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.47660 | + | 2.47660i | −0.176451 | + | 0.176451i | −0.789807 | − | 0.613356i | \(-0.789819\pi\) |
0.613356 | + | 0.789807i | \(0.289819\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.4435i | 1.23654i | 0.785966 | + | 0.618270i | \(0.212166\pi\) | ||||
−0.785966 | + | 0.618270i | \(0.787834\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.00424i | − | 0.494041i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.84135 | + | 5.84135i | −0.409982 | + | 0.409982i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.73457 | + | 9.68602i | 0.190991 | + | 0.676501i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.41825i | 0.307090i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.85695 | 0.612648 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.41135 | + | 5.41135i | −0.372533 | + | 0.372533i | −0.868399 | − | 0.495866i | \(-0.834851\pi\) |
0.495866 | + | 0.868399i | \(0.334851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.64882 | + | 1.64882i | −0.112975 | + | 0.112975i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.0406 | − | 19.7269i | 0.752963 | − | 1.34537i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.86120 | −0.601538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.54344 | − | 1.54344i | −0.104296 | − | 0.104296i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.3741 | + | 33.3741i | −2.24499 | + | 2.24499i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.2634i | 1.22301i | 0.791241 | + | 0.611505i | \(0.209436\pi\) | ||||
−0.791241 | + | 0.611505i | \(0.790564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.61480 | + | 4.26178i | 0.174320 | + | 0.284119i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.23773 | − | 2.23773i | −0.148523 | − | 0.148523i | 0.628935 | − | 0.777458i | \(-0.283491\pi\) |
−0.777458 | + | 0.628935i | \(0.783491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.40974 | + | 6.40974i | 0.423568 | + | 0.423568i | 0.886430 | − | 0.462862i | \(-0.153178\pi\) |
−0.462862 | + | 0.886430i | \(0.653178\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 5.29162i | − | 0.348163i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.67972 | 0.175555 | 0.0877773 | − | 0.996140i | \(-0.472024\pi\) | ||||
0.0877773 | + | 0.996140i | \(0.472024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.14551 | + | 21.7678i | 0.400889 | + | 1.41997i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.51452 | − | 4.51452i | −0.293250 | − | 0.293250i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.0323 | 1.68389 | 0.841946 | − | 0.539562i | \(-0.181410\pi\) | ||||
0.841946 | + | 0.539562i | \(0.181410\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.87408 | 0.378383 | 0.189191 | − | 0.981940i | \(-0.439413\pi\) | ||||
0.189191 | + | 0.981940i | \(0.439413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.14167 | − | 1.16928i | 0.264602 | − | 0.0747028i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.4329 | −1.61826 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.42565i | 0.470582i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.44080 | − | 8.44080i | −0.532779 | − | 0.532779i | 0.388620 | − | 0.921398i | \(-0.372952\pi\) |
−0.921398 | + | 0.388620i | \(0.872952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.33819 | + | 7.33819i | 0.461348 | + | 0.461348i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.64200 | + | 13.6544i | −0.478561 | + | 0.855075i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.2011i | − | 1.38487i | −0.721480 | − | 0.692435i | \(-0.756538\pi\) | ||
0.721480 | − | 0.692435i | \(-0.243462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.53232 | − | 4.53232i | 0.281625 | − | 0.281625i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.59286 | + | 2.59286i | 0.160494 | + | 0.160494i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.464456 | 0.0286396 | 0.0143198 | − | 0.999897i | \(-0.495442\pi\) | ||||
0.0143198 | + | 0.999897i | \(0.495442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00278 | + | 1.79174i | −0.0616005 | + | 0.110065i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.1086 | − | 11.1086i | 0.679837 | − | 0.679837i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.74205 | − | 4.74205i | 0.289128 | − | 0.289128i | −0.547608 | − | 0.836735i | \(-0.684461\pi\) |
0.836735 | + | 0.547608i | \(0.184461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0417 | −0.731482 | −0.365741 | − | 0.930717i | \(-0.619184\pi\) | ||||
−0.365741 | + | 0.930717i | \(0.619184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.1950i | 0.919641i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.4212 | + | 2.73544i | 0.688724 | + | 0.164953i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.9760 | − | 17.9760i | 1.08007 | − | 1.08007i | 0.0835733 | − | 0.996502i | \(-0.473367\pi\) |
0.996502 | − | 0.0835733i | \(-0.0266333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.93331i | 0.235481i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.58712i | 0.571919i | 0.958242 | + | 0.285960i | \(0.0923123\pi\) | ||||
−0.958242 | + | 0.285960i | \(0.907688\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.09022 | + | 5.09022i | −0.302582 | + | 0.302582i | −0.842023 | − | 0.539441i | \(-0.818636\pi\) |
0.539441 | + | 0.842023i | \(0.318636\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.11453 | + | 2.29091i | −0.480663 | + | 0.135702i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1402i | 0.598559i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.9688 | −1.88052 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.26403 | + | 3.26403i | −0.191341 | + | 0.191341i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.25071 | − | 4.25071i | 0.248329 | − | 0.248329i | −0.571955 | − | 0.820285i | \(-0.693815\pi\) |
0.820285 | + | 0.571955i | \(0.193815\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5827 | + | 8.72121i | 0.907263 | + | 0.507769i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.34884 | −0.136294 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.0717 | − | 21.0717i | −1.21861 | − | 1.21861i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.1052 | − | 16.1052i | 0.928286 | − | 0.928286i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.61193i | − | 0.0926028i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.73008 | − | 13.8118i | 0.442623 | − | 0.790863i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.153856 | + | 0.153856i | 0.00878103 | + | 0.00878103i | 0.711484 | − | 0.702703i | \(-0.248024\pi\) |
−0.702703 | + | 0.711484i | \(0.748024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.90803 | − | 2.90803i | −0.165432 | − | 0.165432i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.8210i | 1.97452i | 0.159115 | + | 0.987260i | \(0.449136\pi\) | ||||
−0.159115 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.3412 | −0.980182 | −0.490091 | − | 0.871671i | \(-0.663036\pi\) | ||||
−0.490091 | + | 0.871671i | \(0.663036\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.36871 | + | 4.84805i | 0.0771180 | + | 0.273157i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.1485 | + | 10.1485i | 0.569999 | + | 0.569999i | 0.932128 | − | 0.362129i | \(-0.117950\pi\) |
−0.362129 | + | 0.932128i | \(0.617950\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.61285 | 0.482227 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.05175 | −0.393591 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.6584 | − | 18.6584i | −1.03818 | − | 1.03818i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.7962 | − | 7.85487i | −1.81920 | − | 0.435710i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.12737 | 0.283544 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.7885i | 1.25637i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.12552 | + | 9.12552i | 0.501584 | + | 0.501584i | 0.911930 | − | 0.410346i | \(-0.134592\pi\) |
−0.410346 | + | 0.911930i | \(0.634592\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.01181 | − | 2.01181i | −0.110246 | − | 0.110246i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.6671 | + | 7.64906i | 0.746711 | + | 0.417913i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.62620i | 0.252005i | 0.992030 | + | 0.126002i | \(0.0402147\pi\) | ||||
−0.992030 | + | 0.126002i | \(0.959785\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.452002 | − | 0.452002i | 0.0245494 | − | 0.0245494i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.53276 | + | 6.53276i | 0.353769 | + | 0.353769i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1059 | 1.08562 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.62114 | − | 4.82500i | −0.464146 | − | 0.259769i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1909 | − | 16.1909i | 0.869173 | − | 0.869173i | −0.123208 | − | 0.992381i | \(-0.539318\pi\) |
0.992381 | + | 0.123208i | \(0.0393182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.6447 | − | 21.6447i | 1.15862 | − | 1.15862i | 0.173842 | − | 0.984774i | \(-0.444382\pi\) |
0.984774 | − | 0.173842i | \(-0.0556182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.74474 | 0.360007 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.1933i | 1.39413i | 0.717009 | + | 0.697064i | \(0.245511\pi\) | ||||
−0.717009 | + | 0.697064i | \(0.754489\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.41666 | − | 5.01788i | −0.0751883 | − | 0.266322i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.1475 | + | 11.1475i | −0.589991 | + | 0.589991i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.73157i | 0.302501i | 0.988495 | + | 0.151250i | \(0.0483300\pi\) | ||||
−0.988495 | + | 0.151250i | \(0.951670\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.78125i | 0.251645i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.87703 | − | 3.87703i | 0.203491 | − | 0.203491i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.69717 | − | 1.32611i | 0.245861 | − | 0.0694119i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.9879i | 1.09556i | 0.836623 | + | 0.547778i | \(0.184526\pi\) | ||||
−0.836623 | + | 0.547778i | \(0.815474\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.50104 | 0.234315 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.46278 | + | 1.46278i | −0.0759438 | + | 0.0759438i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.9141 | − | 12.9141i | 0.668667 | − | 0.668667i | −0.288740 | − | 0.957407i | \(-0.593236\pi\) |
0.957407 | + | 0.288740i | \(0.0932365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1714 | + | 0.448018i | −0.576887 | + | 0.0231356i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.7320 | −1.27376 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.07361 | − | 8.07361i | −0.414713 | − | 0.414713i | 0.468663 | − | 0.883377i | \(-0.344736\pi\) |
−0.883377 | + | 0.468663i | \(0.844736\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4132 | − | 12.4132i | 0.635945 | − | 0.635945i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.23276i | 0.471772i | 0.971781 | + | 0.235886i | \(0.0757992\pi\) | ||||
−0.971781 | + | 0.235886i | \(0.924201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3253 | + | 5.77877i | 0.526226 | + | 0.294513i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.14876 | − | 7.14876i | −0.363392 | − | 0.363392i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.32362 | − | 6.32362i | −0.320620 | − | 0.320620i | 0.528385 | − | 0.849005i | \(-0.322798\pi\) |
−0.849005 | + | 0.528385i | \(0.822798\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 30.9179i | − | 1.56359i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.16842 | −0.0589392 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.7391 | − | 3.87885i | 0.691290 | − | 0.195166i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.07806 | + | 1.07806i | 0.0541061 | + | 0.0541061i | 0.733642 | − | 0.679536i | \(-0.237819\pi\) |
−0.679536 | + | 0.733642i | \(0.737819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.49504 | −0.425284 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.0966 | 1.85252 | 0.926258 | − | 0.376891i | \(-0.123007\pi\) | ||||
0.926258 | + | 0.376891i | \(0.123007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.7589 | − | 18.7589i | −0.934449 | − | 0.934449i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.15195 | − | 0.607542i | 0.106931 | − | 0.0301890i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.68274 | −0.331251 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.3422i | − | 0.857518i | −0.903419 | − | 0.428759i | \(-0.858951\pi\) | ||
0.903419 | − | 0.428759i | \(-0.141049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.31062 | + | 6.31062i | 0.311280 | + | 0.311280i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.7218 | + | 12.7218i | 0.626000 | + | 0.626000i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.4894 | − | 8.10927i | −0.711254 | − | 0.398068i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.84010i | − | 0.334961i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.4718 | − | 20.4718i | 1.00011 | − | 1.00011i | 0.000110566 | − | 1.00000i | \(-0.499965\pi\) |
1.00000 | 0.000110566i | \(-3.51942e-5\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.6143 | − | 10.6143i | −0.517308 | − | 0.517308i | 0.399448 | − | 0.916756i | \(-0.369202\pi\) |
−0.916756 | + | 0.399448i | \(0.869202\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.1154 | 0.491826 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.2978 | − | 29.8230i | −0.887573 | − | 1.44663i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.2760 | − | 11.2760i | 0.545685 | − | 0.545685i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.2022 | − | 11.2022i | 0.540848 | − | 0.540848i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.9747 | −0.865812 | −0.432906 | − | 0.901439i | \(-0.642512\pi\) | ||||
−0.432906 | + | 0.901439i | \(0.642512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.1120i | − | 1.11069i | −0.831619 | − | 0.555347i | \(-0.812586\pi\) | ||
0.831619 | − | 0.555347i | \(-0.187414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.89089 | + | 2.22777i | −0.378339 | + | 0.106813i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7806 | − | 11.7806i | 0.563541 | − | 0.563541i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.65049i | 0.126501i | 0.997998 | + | 0.0632505i | \(0.0201467\pi\) | ||||
−0.997998 | + | 0.0632505i | \(0.979853\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1.92461i | − | 0.0916482i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.977227 | + | 0.977227i | −0.0464294 | + | 0.0464294i | −0.729940 | − | 0.683511i | \(-0.760452\pi\) |
0.683511 | + | 0.729940i | \(0.260452\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.54448 | + | 33.8071i | 0.452452 | + | 1.60261i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.10838i | − | 0.0997231i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.6612 | −0.927867 | −0.463934 | − | 0.885870i | \(-0.653562\pi\) | ||||
−0.463934 | + | 0.885870i | \(0.653562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.47570 | − | 7.47570i | 0.352017 | − | 0.352017i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.79911 | − | 6.79911i | 0.319450 | − | 0.319450i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −29.6493 | − | 16.5938i | −1.38998 | − | 0.777931i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.9752 | 1.21507 | 0.607535 | − | 0.794293i | \(-0.292159\pi\) | ||||
0.607535 | + | 0.794293i | \(0.292159\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.94817 | + | 4.94817i | 0.230961 | + | 0.230961i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.94218 | + | 1.94218i | −0.0904565 | + | 0.0904565i | −0.750887 | − | 0.660431i | \(-0.770374\pi\) |
0.660431 | + | 0.750887i | \(0.270374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7805i | 0.593960i | 0.954884 | + | 0.296980i | \(0.0959795\pi\) | ||||
−0.954884 | + | 0.296980i | \(0.904021\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.67489 | − | 4.29541i | −0.355915 | − | 0.199195i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.2154 | − | 28.2154i | −1.30565 | − | 1.30565i | −0.924522 | − | 0.381129i | \(-0.875535\pi\) |
−0.381129 | − | 0.924522i | \(-0.624465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.1578 | + | 11.1578i | 0.515222 | + | 0.515222i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 22.6497i | − | 1.04364i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.7465 | −1.09186 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.39142 | − | 18.3353i | 0.201492 | − | 0.841283i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.649299 | + | 0.649299i | 0.0297294 | + | 0.0297294i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6500 | 1.03490 | 0.517452 | − | 0.855712i | \(-0.326881\pi\) | ||||
0.517452 | + | 0.855712i | \(0.326881\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.1896 | 0.874970 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.03833 | − | 7.03833i | −0.320255 | − | 0.320255i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.80443 | − | 9.93347i | −0.127343 | − | 0.451056i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1202 | −0.911733 | −0.455866 | − | 0.890048i | \(-0.650671\pi\) | ||||
−0.455866 | + | 0.890048i | \(0.650671\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.8765i | 0.853624i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.4434 | − | 20.4434i | −0.922596 | − | 0.922596i | 0.0746163 | − | 0.997212i | \(-0.476227\pi\) |
−0.997212 | + | 0.0746163i | \(0.976227\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.1442 | − | 18.1442i | −0.817174 | − | 0.817174i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.56508 | − | 4.58319i | 0.115292 | − | 0.205999i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.25319i | − | 0.235638i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.7236 | + | 26.7236i | −1.19631 | + | 1.19631i | −0.221052 | + | 0.975262i | \(0.570949\pi\) |
−0.975262 | + | 0.221052i | \(0.929051\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.05304 | + | 9.05304i | 0.404460 | + | 0.404460i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.4692 | −0.778911 | −0.389456 | − | 0.921045i | \(-0.627337\pi\) | ||||
−0.389456 | + | 0.921045i | \(0.627337\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.14528 | + | 1.76032i | 0.139963 | + | 0.0783334i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.9749 | + | 22.9749i | −1.02035 | + | 1.02035i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.1370 | − | 22.1370i | 0.981205 | − | 0.981205i | −0.0186215 | − | 0.999827i | \(-0.505928\pi\) |
0.999827 | + | 0.0186215i | \(0.00592774\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.91744 | 0.217535 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.77078i | 0.166484i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.85005 | − | 2.49856i | 0.389980 | − | 0.110100i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.8004 | − | 16.8004i | 0.738882 | − | 0.738882i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.1444i | 0.796451i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.7634i | 0.909663i | 0.890577 | + | 0.454832i | \(0.150301\pi\) | ||||
−0.890577 | + | 0.454832i | \(0.849699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.9884 | − | 25.9884i | 1.13640 | − | 1.13640i | 0.147304 | − | 0.989091i | \(-0.452941\pi\) |
0.989091 | − | 0.147304i | \(-0.0470595\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.9545 | − | 2.62367i | −0.478094 | − | 0.114506i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 27.5244i | − | 1.19898i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.47907 | −0.151264 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.64696 | − | 5.64696i | 0.245057 | − | 0.245057i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.4666 | + | 21.4666i | −0.929821 | + | 0.929821i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.70095 | − | 13.7598i | 0.332941 | − | 0.594887i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.52309 | −0.281492 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.19655 | − | 3.19655i | −0.137685 | − | 0.137685i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.86704 | − | 4.86704i | 0.209250 | − | 0.209250i | −0.594698 | − | 0.803949i | \(-0.702729\pi\) |
0.803949 | + | 0.594698i | \(0.202729\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 5.82756i | − | 0.250085i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.59940 | + | 10.0048i | −0.239852 | + | 0.428559i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2487 | + | 16.2487i | 0.694742 | + | 0.694742i | 0.963272 | − | 0.268529i | \(-0.0865376\pi\) |
−0.268529 | + | 0.963272i | \(0.586538\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.00520 | − | 5.00520i | −0.213617 | − | 0.213617i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.8269i | − | 0.589045i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.3834 | 0.611644 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.12256 | − | 1.72853i | 0.259888 | − | 0.0733721i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.616853 | − | 0.616853i | −0.0261369 | − | 0.0261369i | 0.693918 | − | 0.720054i | \(-0.255883\pi\) |
−0.720054 | + | 0.693918i | \(0.755883\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 68.1884 | 2.88406 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.4367 | 0.693956 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.4063 | + | 17.4063i | 0.733587 | + | 0.733587i | 0.971328 | − | 0.237742i | \(-0.0764072\pi\) |
−0.237742 | + | 0.971328i | \(0.576407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.388358 | + | 1.37559i | 0.0163383 | + | 0.0578714i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.25286 | 0.0946113 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.57959i | 0.0662197i | 0.999452 | + | 0.0331098i | \(0.0105411\pi\) | ||||
−0.999452 | + | 0.0331098i | \(0.989459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.6949 | − | 24.6949i | −1.03345 | − | 1.03345i | −0.999421 | − | 0.0340299i | \(-0.989166\pi\) |
−0.0340299 | − | 0.999421i | \(-0.510834\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.674155 | + | 0.674155i | 0.0281632 | + | 0.0281632i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.8296 | − | 11.5528i | 0.785250 | − | 0.481787i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.6673i | 1.40159i | 0.713363 | + | 0.700795i | \(0.247171\pi\) | ||||
−0.713363 | + | 0.700795i | \(0.752829\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.40957 | − | 3.40957i | 0.141697 | − | 0.141697i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8292 | − | 11.8292i | −0.490757 | − | 0.490757i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.15682 | 0.0893263 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.36567 | + | 13.1607i | −0.304533 | + | 0.544128i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.6327 | + | 30.6327i | −1.26435 | + | 1.26435i | −0.315385 | + | 0.948964i | \(0.602134\pi\) |
−0.948964 | + | 0.315385i | \(0.897866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.4875 | − | 10.4875i | 0.432132 | − | 0.432132i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.50245 | −0.144071 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.1477i | − | 1.03269i | −0.856380 | − | 0.516347i | \(-0.827292\pi\) | ||
0.856380 | − | 0.516347i | \(-0.172708\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.57791 | − | 33.9255i | −0.392656 | − | 1.39081i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.3344 | + | 12.3344i | −0.504815 | + | 0.504815i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.0767i | 0.738594i | 0.929311 | + | 0.369297i | \(0.120402\pi\) | ||||
−0.929311 | + | 0.369297i | \(0.879598\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26.5291i | − | 1.08214i | −0.840977 | − | 0.541072i | \(-0.818019\pi\) | ||
0.840977 | − | 0.541072i | \(-0.181981\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.95274 | − | 4.95274i | 0.201691 | − | 0.201691i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.33112 | + | 11.7990i | 0.135429 | + | 0.479699i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 28.3496i | − | 1.15068i | −0.817916 | − | 0.575338i | \(-0.804871\pi\) | ||
0.817916 | − | 0.575338i | \(-0.195129\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.26091 | −0.334749 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.2427 | + | 48.2427i | −1.95169 | + | 1.95169i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.24941 | + | 3.24941i | −0.131243 | + | 0.131243i | −0.769677 | − | 0.638434i | \(-0.779583\pi\) |
0.638434 | + | 0.769677i | \(0.279583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.91542 | + | 8.78269i | −0.198209 | + | 0.354152i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.4370 | −0.742245 | −0.371123 | − | 0.928584i | \(-0.621027\pi\) | ||||
−0.371123 | + | 0.928584i | \(0.621027\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.47769 | − | 9.47769i | −0.380941 | − | 0.380941i | 0.490500 | − | 0.871441i | \(-0.336814\pi\) |
−0.871441 | + | 0.490500i | \(0.836814\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.12417 | + | 3.12417i | −0.125369 | + | 0.125369i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.3924i | 1.41797i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.3256 | − | 22.2874i | 0.453025 | − | 0.891498i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.26281 | + | 6.26281i | 0.250113 | + | 0.250113i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.0782 | + | 14.0782i | 0.561333 | + | 0.561333i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.6343i | − | 0.423346i | −0.977341 | − | 0.211673i | \(-0.932109\pi\) | ||
0.977341 | − | 0.211673i | \(-0.0678912\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.65281 | −0.304172 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.6653 | + | 37.7772i | 0.423240 | + | 1.49914i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.17895 | + | 9.17895i | 0.363683 | + | 0.363683i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.33178 | −0.0922439 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.4256 | −0.846261 | −0.423130 | − | 0.906069i | \(-0.639069\pi\) | ||||
−0.423130 | + | 0.906069i | \(0.639069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7046 | + | 28.7046i | 1.13200 | + | 1.13200i | 0.989845 | + | 0.142152i | \(0.0454022\pi\) |
0.142152 | + | 0.989845i | \(0.454598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.7559 | − | 6.14217i | 0.856639 | − | 0.241848i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.8695 | 1.44949 | 0.724746 | − | 0.689017i | \(-0.241957\pi\) | ||||
0.724746 | + | 0.689017i | \(0.241957\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.7579i | − | 0.736311i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.26582 | − | 6.26582i | −0.245577 | − | 0.245577i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.8096 | − | 27.8096i | −1.08828 | − | 1.08828i | −0.995706 | − | 0.0925688i | \(-0.970492\pi\) |
−0.0925688 | − | 0.995706i | \(-0.529508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.27599 | − | 2.27989i | 0.0498571 | − | 0.0890829i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.18275i | − | 0.0851572i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.6956 | − | 11.6956i | 0.455596 | − | 0.455596i | −0.441611 | − | 0.897207i | \(-0.645593\pi\) |
0.897207 | + | 0.441611i | \(0.145593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7275 | + | 29.7275i | 1.15627 | + | 1.15627i | 0.985272 | + | 0.170994i | \(0.0546979\pi\) |
0.170994 | + | 0.985272i | \(0.445302\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −47.1981 | −1.83302 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.27711 | − | 16.5760i | 0.359751 | − | 0.642790i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.4559 | − | 11.4559i | 0.443574 | − | 0.443574i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9142 | + | 12.9142i | −0.499292 | + | 0.499292i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.6261 | −0.641843 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 19.4197i | − | 0.748575i | −0.927313 | − | 0.374287i | \(-0.877887\pi\) | ||
0.927313 | − | 0.374287i | \(-0.122113\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.16459 | + | 4.86248i | −0.0448252 | + | 0.187157i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.0550 | + | 22.0550i | −0.847643 | + | 0.847643i | −0.989839 | − | 0.142196i | \(-0.954584\pi\) |
0.142196 | + | 0.989839i | \(0.454584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10.3993i | − | 0.399088i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 3.16462i | − | 0.121269i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.95729 | − | 9.95729i | 0.381005 | − | 0.381005i | −0.490459 | − | 0.871464i | \(-0.663171\pi\) |
0.871464 | + | 0.490459i | \(0.163171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.2052 | + | 5.42205i | −0.733794 | + | 0.207166i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.06474i | 0.345842i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.19334 | −0.235947 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.1664 | − | 30.1664i | 1.14758 | − | 1.14758i | 0.160556 | − | 0.987027i | \(-0.448671\pi\) |
0.987027 | − | 0.160556i | \(-0.0513288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.74174 | − | 3.74174i | 0.142137 | − | 0.142137i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.3468 | + | 7.46981i | 0.506272 | + | 0.283346i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.4973 | −1.19304 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.89485 | + | 1.89485i | 0.0716698 | + | 0.0716698i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.10793 | + | 2.10793i | −0.0796155 | + | 0.0796155i | −0.745793 | − | 0.666178i | \(-0.767929\pi\) |
0.666178 | + | 0.745793i | \(0.267929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7283i | 0.404626i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.0466 | + | 19.7377i | −0.416039 | + | 0.743364i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.56782 | + | 2.56782i | 0.0965729 | + | 0.0965729i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.5759 | − | 29.5759i | −1.11075 | − | 1.11075i | −0.993050 | − | 0.117697i | \(-0.962449\pi\) |
−0.117697 | − | 0.993050i | \(-0.537551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 6.38450i | − | 0.239437i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.3783 | 0.650824 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.62488 | + | 34.0919i | 0.359950 | + | 1.27496i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.4076 | + | 18.4076i | 0.687446 | + | 0.687446i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.2528 | −0.568833 | −0.284417 | − | 0.958701i | \(-0.591800\pi\) | ||||
−0.284417 | + | 0.958701i | \(0.591800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.26506 | 0.345049 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.15360 | + | 4.15360i | 0.154474 | + | 0.154474i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.27039 | − | 17.8300i | 0.158598 | − | 0.662190i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5396 | 0.835947 | 0.417973 | − | 0.908459i | \(-0.362740\pi\) | ||||
0.417973 | + | 0.908459i | \(0.362740\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.0254 | + | 50.0254i | 1.85025 | + | 1.85025i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.88368 | + | 8.88368i | 0.328126 | + | 0.328126i | 0.851874 | − | 0.523747i | \(-0.175466\pi\) |
−0.523747 | + | 0.851874i | \(0.675466\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.75541 | + | 2.10180i | 0.138520 | + | 0.0775259i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 16.4518i | − | 0.606011i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.00557 | − | 3.00557i | 0.110562 | − | 0.110562i | −0.649662 | − | 0.760223i | \(-0.725089\pi\) |
0.760223 | + | 0.649662i | \(0.225089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.9838 | − | 17.9838i | −0.660650 | − | 0.660650i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.5808 | −0.534919 | −0.267459 | − | 0.963569i | \(-0.586184\pi\) | ||||
−0.267459 | + | 0.963569i | \(0.586184\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.11399 | + | 2.30248i | 0.150725 | + | 0.0843565i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.25073 | + | 5.25073i | −0.192114 | + | 0.192114i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.2335 | − | 11.2335i | 0.410465 | − | 0.410465i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.92675 | 0.0703083 | 0.0351541 | − | 0.999382i | \(-0.488808\pi\) | ||||
0.0351541 | + | 0.999382i | \(0.488808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 11.9371i | − | 0.435012i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.84176 | + | 20.6919i | 0.212603 | + | 0.753054i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.389306 | − | 0.389306i | 0.0141496 | − | 0.0141496i | −0.699997 | − | 0.714146i | \(-0.746815\pi\) |
0.714146 | + | 0.699997i | \(0.246815\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.3778i | 0.376689i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 18.0200i | − | 0.653223i | −0.945159 | − | 0.326612i | \(-0.894093\pi\) | ||
0.945159 | − | 0.326612i | \(-0.105907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.16797 | + | 8.16797i | −0.295700 | + | 0.295700i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.0589 | + | 4.25144i | −0.544454 | + | 0.153711i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.8635i | 1.94490i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.9422 | −1.26005 | −0.630024 | − | 0.776576i | \(-0.716955\pi\) | ||||
−0.630024 | + | 0.776576i | \(0.716955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.6986 | − | 15.6986i | 0.565371 | − | 0.565371i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.83112 | − | 9.83112i | 0.353601 | − | 0.353601i | −0.507847 | − | 0.861447i | \(-0.669558\pi\) |
0.861447 | + | 0.507847i | \(0.169558\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.7629 | − | 10.2848i | 0.602142 | − | 0.369442i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.40967 | 0.229946 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0013 | − | 12.0013i | −0.429992 | − | 0.429992i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.87282 | + | 3.87282i | −0.138580 | + | 0.138580i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.66685i | 0.131043i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.1954 | + | 24.7349i | 1.57740 | + | 0.882826i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.3615 | + | 34.3615i | 1.22486 | + | 1.22486i | 0.965885 | + | 0.258970i | \(0.0833831\pi\) |
0.258970 | + | 0.965885i | \(0.416617\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.328420 | + | 0.328420i | 0.0116921 | + | 0.0116921i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.44009i | 0.0512038i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.7421 | 1.69537 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.97602 | + | 0.557874i | −0.0700823 | + | 0.0197858i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.63103 | + | 3.63103i | 0.128618 | + | 0.128618i | 0.768485 | − | 0.639868i | \(-0.221011\pi\) |
−0.639868 | + | 0.768485i | \(0.721011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −70.7850 | −2.50419 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.7100 | 0.555085 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.62529 | − | 3.62529i | −0.127934 | − | 0.127934i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.4199 | − | 6.04730i | 0.754952 | − | 0.213139i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.70626 | 0.236072 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.9241i | 0.559860i | 0.960020 | + | 0.279930i | \(0.0903113\pi\) | ||||
−0.960020 | + | 0.279930i | \(0.909689\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.6448 | − | 11.6448i | −0.408906 | − | 0.408906i | 0.472451 | − | 0.881357i | \(-0.343369\pi\) |
−0.881357 | + | 0.472451i | \(0.843369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.51477 | − | 8.51477i | −0.298626 | − | 0.298626i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.8328 | − | 20.6143i | −1.29020 | − | 0.722087i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.1220i | 1.33372i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.7445 | + | 10.7445i | −0.375442 | + | 0.375442i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.3703 | + | 24.3703i | 0.850530 | + | 0.850530i | 0.990198 | − | 0.139669i | \(-0.0446037\pi\) |
−0.139669 | + | 0.990198i | \(0.544604\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.2425 | 1.78620 | 0.893101 | − | 0.449856i | \(-0.148525\pi\) | ||||
0.893101 | + | 0.449856i | \(0.148525\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.14176 | + | 10.0103i | 0.213828 | + | 0.348512i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.55201 | + | 9.55201i | −0.332156 | + | 0.332156i | −0.853405 | − | 0.521249i | \(-0.825466\pi\) |
0.521249 | + | 0.853405i | \(0.325466\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.3127 | + | 33.3127i | −1.15700 | + | 1.15700i | −0.171879 | + | 0.985118i | \(0.554984\pi\) |
−0.985118 | + | 0.171879i | \(0.945016\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.4219 | 0.881877 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.4680i | 0.466638i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.5513 | + | 7.77832i | −0.953451 | + | 0.269180i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.78127 | + | 2.78127i | −0.0961347 | + | 0.0961347i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 9.50181i | − | 0.328039i | −0.986457 | − | 0.164019i | \(-0.947554\pi\) | ||
0.986457 | − | 0.164019i | \(-0.0524460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.5542i | 0.536352i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.77911 | + | 6.77911i | −0.233485 | + | 0.233485i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.7399 | − | 69.9200i | −0.679075 | − | 2.40532i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.3523i | 0.424431i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.19866 | −0.247057 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.88866 | + | 8.88866i | −0.304699 | + | 0.304699i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.2909 | + | 14.2909i | −0.489310 | + | 0.489310i | −0.908089 | − | 0.418778i | \(-0.862458\pi\) |
0.418778 | + | 0.908089i | \(0.362458\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.35775 | − | 4.11792i | −0.251630 | − | 0.140830i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4246 | 0.834327 | 0.417164 | − | 0.908831i | \(-0.363024\pi\) | ||||
0.417164 | + | 0.908831i | \(0.363024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.3398 | − | 21.3398i | −0.728105 | − | 0.728105i | 0.242137 | − | 0.970242i | \(-0.422152\pi\) |
−0.970242 | + | 0.242137i | \(0.922152\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.17022 | + | 7.17022i | −0.244361 | + | 0.244361i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 54.8339i | − | 1.86657i | −0.359138 | − | 0.933284i | \(-0.616929\pi\) | ||
0.359138 | − | 0.933284i | \(-0.383071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.4044 | − | 19.8148i | −1.20379 | − | 0.673724i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.6054 | − | 22.6054i | −0.767718 | − | 0.767718i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.6039 | − | 10.6039i | −0.359712 | − | 0.359712i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47.2417i | 1.60072i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.61603 | −0.156229 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.0824 | − | 18.5098i | 0.577492 | − | 0.625747i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.43052 | + | 8.43052i | 0.284678 | + | 0.284678i | 0.834972 | − | 0.550293i | \(-0.185484\pi\) |
−0.550293 | + | 0.834972i | \(0.685484\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.01142 | 0.202760 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.7215 | −1.13611 | −0.568053 | − | 0.822992i | \(-0.692303\pi\) | ||||
−0.568053 | + | 0.822992i | \(0.692303\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.5737 | − | 33.5737i | −1.12984 | − | 1.12984i | −0.990202 | − | 0.139642i | \(-0.955405\pi\) |
−0.139642 | − | 0.990202i | \(-0.544595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.85184 | + | 17.1855i | 0.163093 | + | 0.577684i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.09705 | 0.238295 | 0.119148 | − | 0.992877i | \(-0.461984\pi\) | ||||
0.119148 | + | 0.992877i | \(0.461984\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.5487i | 1.32642i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.66088 | − | 1.66088i | −0.0556416 | − | 0.0556416i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.9710 | − | 26.9710i | −0.902551 | − | 0.902551i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.12362 | − | 12.7282i | 0.238116 | − | 0.425457i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 29.7999i | − | 0.994991i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.1985 | − | 10.1985i | 0.340139 | − | 0.340139i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.54365 | − | 4.54365i | −0.151371 | − | 0.151371i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.7761 | 0.757942 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.3711 | + | 6.36405i | 0.377987 | + | 0.211548i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.37877 | + | 4.37877i | −0.145395 | + | 0.145395i | −0.776057 | − | 0.630662i | \(-0.782783\pi\) |
0.630662 | + | 0.776057i | \(0.282783\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.13980 | − | 1.13980i | 0.0378049 | − | 0.0378049i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.7307 | −0.885627 | −0.442814 | − | 0.896614i | \(-0.646020\pi\) | ||||
−0.442814 | + | 0.896614i | \(0.646020\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.4417i | 0.577235i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.2324 | − | 4.30044i | 0.503568 | − | 0.142168i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.86132 | − | 1.86132i | 0.0614661 | − | 0.0614661i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.5598i | 0.810154i | 0.914282 | + | 0.405077i | \(0.132755\pi\) | ||||
−0.914282 | + | 0.405077i | \(0.867245\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.217585i | 0.00716968i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.1209 | − | 11.1209i | 0.366047 | − | 0.366047i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.31341 | + | 13.8344i | −0.108944 | + | 0.454871i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 4.11257i | − | 0.135075i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.25552 | 0.205237 | 0.102619 | − | 0.994721i | \(-0.467278\pi\) | ||||
0.102619 | + | 0.994721i | \(0.467278\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.13167 | + | 5.13167i | −0.168184 | + | 0.168184i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.6222 | + | 24.6222i | −0.806095 | + | 0.806095i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.9498 | + | 32.0721i | −0.587023 | + | 1.04887i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0332 | 1.07915 | 0.539574 | − | 0.841938i | \(-0.318585\pi\) | ||||
0.539574 | + | 0.841938i | \(0.318585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.2621 | − | 12.2621i | −0.400158 | − | 0.400158i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.4774 | + | 24.4774i | −0.797941 | + | 0.797941i | −0.982771 | − | 0.184830i | \(-0.940827\pi\) |
0.184830 | + | 0.982771i | \(0.440827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 19.8867i | − | 0.647601i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.46026 | + | 4.39591i | −0.0800324 | + | 0.142999i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.7666 | + | 34.7666i | 1.12976 | + | 1.12976i | 0.990216 | + | 0.139546i | \(0.0445643\pi\) |
0.139546 | + | 0.990216i | \(0.455436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4101 | + | 10.4101i | 0.337925 | + | 0.337925i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.3522i | 0.465402i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.9913 | 0.550403 | 0.275201 | − | 0.961387i | \(-0.411255\pi\) | ||||
0.275201 | + | 0.961387i | \(0.411255\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.05167 | + | 0.579230i | −0.0663904 | + | 0.0187434i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.09021 | + | 6.09021i | 0.196868 | + | 0.196868i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.1058 | −0.649251 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5291 | −0.500938 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.98634 | − | 4.98634i | −0.160683 | − | 0.160683i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.92948 | + | 10.3764i | 0.0943034 | + | 0.334028i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.8174 | −1.85928 | −0.929641 | − | 0.368467i | \(-0.879883\pi\) | ||||
−0.929641 | + | 0.368467i | \(0.879883\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 26.3870i | − | 0.847674i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.9663 | + | 39.9663i | 1.28258 | + | 1.28258i | 0.939196 | + | 0.343383i | \(0.111573\pi\) |
0.343383 | + | 0.939196i | \(0.388427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.8964 | + | 10.8964i | 0.349322 | + | 0.349322i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.6362 | − | 28.7446i | −0.564809 | − | 0.920564i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.3797i | 1.77175i | 0.463921 | + | 0.885877i | \(0.346442\pi\) | ||||
−0.463921 | + | 0.885877i | \(0.653558\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.0924 | − | 26.0924i | 0.833917 | − | 0.833917i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.62560 | + | 3.62560i | 0.115756 | + | 0.115756i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.19883 | 0.102027 | 0.0510134 | − | 0.998698i | \(-0.483755\pi\) | ||||
0.0510134 | + | 0.998698i | \(0.483755\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.82489 | − | 6.83417i | 0.121871 | − | 0.217755i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.1139 | + | 16.1139i | −0.512912 | + | 0.512912i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.5850 | + | 31.5850i | −1.00434 | + | 1.00434i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.5891 | −0.336373 | −0.168186 | − | 0.985755i | \(-0.553791\pi\) | ||||
−0.168186 | + | 0.985755i | \(0.553791\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.9054i | 0.409541i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.5977 | − | 37.5376i | −0.335969 | − | 1.19002i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.1735 | + | 18.1735i | −0.575559 | + | 0.575559i | −0.933677 | − | 0.358117i | \(-0.883419\pi\) |
0.358117 | + | 0.933677i | \(0.383419\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 2.84512i | − | 0.0900157i |
(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 | 960.2.bl.a.49.14 | 48 | ||
4.3 | odd | 2 | 240.2.bl.a.229.4 | yes | 48 | ||
5.4 | even | 2 | inner | 960.2.bl.a.49.8 | 48 | ||
8.3 | odd | 2 | 1920.2.bl.a.1249.16 | 48 | |||
8.5 | even | 2 | 1920.2.bl.b.1249.9 | 48 | |||
12.11 | even | 2 | 720.2.bm.h.469.21 | 48 | |||
16.3 | odd | 4 | 240.2.bl.a.109.21 | yes | 48 | ||
16.5 | even | 4 | 1920.2.bl.b.289.16 | 48 | |||
16.11 | odd | 4 | 1920.2.bl.a.289.9 | 48 | |||
16.13 | even | 4 | inner | 960.2.bl.a.529.8 | 48 | ||
20.19 | odd | 2 | 240.2.bl.a.229.21 | yes | 48 | ||
40.19 | odd | 2 | 1920.2.bl.a.1249.9 | 48 | |||
40.29 | even | 2 | 1920.2.bl.b.1249.16 | 48 | |||
48.35 | even | 4 | 720.2.bm.h.109.4 | 48 | |||
60.59 | even | 2 | 720.2.bm.h.469.4 | 48 | |||
80.19 | odd | 4 | 240.2.bl.a.109.4 | ✓ | 48 | ||
80.29 | even | 4 | inner | 960.2.bl.a.529.14 | 48 | ||
80.59 | odd | 4 | 1920.2.bl.a.289.16 | 48 | |||
80.69 | even | 4 | 1920.2.bl.b.289.9 | 48 | |||
240.179 | even | 4 | 720.2.bm.h.109.21 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.bl.a.109.4 | ✓ | 48 | 80.19 | odd | 4 | ||
240.2.bl.a.109.21 | yes | 48 | 16.3 | odd | 4 | ||
240.2.bl.a.229.4 | yes | 48 | 4.3 | odd | 2 | ||
240.2.bl.a.229.21 | yes | 48 | 20.19 | odd | 2 | ||
720.2.bm.h.109.4 | 48 | 48.35 | even | 4 | |||
720.2.bm.h.109.21 | 48 | 240.179 | even | 4 | |||
720.2.bm.h.469.4 | 48 | 60.59 | even | 2 | |||
720.2.bm.h.469.21 | 48 | 12.11 | even | 2 | |||
960.2.bl.a.49.8 | 48 | 5.4 | even | 2 | inner | ||
960.2.bl.a.49.14 | 48 | 1.1 | even | 1 | trivial | ||
960.2.bl.a.529.8 | 48 | 16.13 | even | 4 | inner | ||
960.2.bl.a.529.14 | 48 | 80.29 | even | 4 | inner | ||
1920.2.bl.a.289.9 | 48 | 16.11 | odd | 4 | |||
1920.2.bl.a.289.16 | 48 | 80.59 | odd | 4 | |||
1920.2.bl.a.1249.9 | 48 | 40.19 | odd | 2 | |||
1920.2.bl.a.1249.16 | 48 | 8.3 | odd | 2 | |||
1920.2.bl.b.289.9 | 48 | 80.69 | even | 4 | |||
1920.2.bl.b.289.16 | 48 | 16.5 | even | 4 | |||
1920.2.bl.b.1249.9 | 48 | 8.5 | even | 2 | |||
1920.2.bl.b.1249.16 | 48 | 40.29 | even | 2 |