Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1064,2,Mod(305,1064)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1064, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1064.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1064 = 2^{3} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1064.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.49608277506\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 457.3 | ||
Root | \(-0.456148 - 0.790072i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1064.457 |
Dual form | 1064.2.q.n.305.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(799\) | \(913\) | \(1009\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.456148 | − | 0.790072i | −0.263357 | − | 0.456148i | 0.703775 | − | 0.710423i | \(-0.251496\pi\) |
−0.967132 | + | 0.254275i | \(0.918163\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.832641 | − | 1.44218i | 0.372368 | − | 0.644961i | −0.617561 | − | 0.786523i | \(-0.711879\pi\) |
0.989929 | + | 0.141562i | \(0.0452125\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.462738 | − | 2.60497i | −0.174898 | − | 0.984586i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.08386 | − | 1.87730i | 0.361286 | − | 0.625766i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.121120 | + | 0.209787i | 0.0365192 | + | 0.0632531i | 0.883707 | − | 0.468040i | \(-0.155040\pi\) |
−0.847188 | + | 0.531293i | \(0.821706\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.76999 | −1.60031 | −0.800154 | − | 0.599795i | \(-0.795249\pi\) | ||||
−0.800154 | + | 0.599795i | \(0.795249\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.51923 | −0.392264 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.88319 | − | 4.99382i | −0.699275 | − | 1.21118i | −0.968718 | − | 0.248164i | \(-0.920173\pi\) |
0.269443 | − | 0.963016i | \(-0.413160\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.84704 | + | 1.55385i | −0.403056 | + | 0.339077i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.30773 | + | 5.72915i | −0.689709 | + | 1.19461i | 0.282224 | + | 0.959349i | \(0.408928\pi\) |
−0.971932 | + | 0.235262i | \(0.924405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.11342 | + | 1.92850i | 0.222684 | + | 0.385699i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.71449 | −0.907303 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.91381 | 1.65525 | 0.827627 | − | 0.561279i | \(-0.189690\pi\) | ||||
0.827627 | + | 0.561279i | \(0.189690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.96642 | + | 5.13799i | 0.532785 | + | 0.922810i | 0.999267 | + | 0.0382794i | \(0.0121877\pi\) |
−0.466483 | + | 0.884530i | \(0.654479\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.110498 | − | 0.191388i | 0.0192352 | − | 0.0333163i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.14212 | − | 1.50166i | −0.700147 | − | 0.253826i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.90185 | − | 8.49026i | 0.805860 | − | 1.39579i | −0.109849 | − | 0.993948i | \(-0.535037\pi\) |
0.915709 | − | 0.401842i | \(-0.131630\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.63197 | + | 4.55870i | 0.421452 | + | 0.729977i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.83237 | −1.19443 | −0.597213 | − | 0.802083i | \(-0.703725\pi\) | ||||
−0.597213 | + | 0.802083i | \(0.703725\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.80493 | − | 3.12623i | −0.269063 | − | 0.466031i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.789589 | + | 1.36761i | −0.115173 | + | 0.199486i | −0.917849 | − | 0.396930i | \(-0.870076\pi\) |
0.802676 | + | 0.596416i | \(0.203409\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.57175 | + | 2.41084i | −0.938821 | + | 0.344405i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.63032 | + | 4.55585i | −0.368318 | + | 0.637946i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.24073 | − | 5.61311i | −0.445148 | − | 0.771019i | 0.552914 | − | 0.833238i | \(-0.313516\pi\) |
−0.998063 | + | 0.0622187i | \(0.980182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.403399 | 0.0543944 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.912296 | 0.120837 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.537488 | − | 0.930957i | −0.0699750 | − | 0.121200i | 0.828915 | − | 0.559375i | \(-0.188959\pi\) |
−0.898890 | + | 0.438174i | \(0.855625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55454 | + | 7.88869i | −0.583149 | + | 1.01004i | 0.411955 | + | 0.911204i | \(0.364846\pi\) |
−0.995103 | + | 0.0988387i | \(0.968487\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.39185 | − | 1.95472i | −0.679309 | − | 0.246272i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.80433 | + | 8.32134i | −0.595904 | + | 1.03214i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.01270 | − | 6.95021i | −0.490230 | − | 0.849103i | 0.509707 | − | 0.860348i | \(-0.329754\pi\) |
−0.999937 | + | 0.0112451i | \(0.996421\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.03525 | 0.726559 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.22955 | 0.145921 | 0.0729606 | − | 0.997335i | \(-0.476755\pi\) | ||||
0.0729606 | + | 0.997335i | \(0.476755\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.400685 | − | 0.694007i | −0.0468966 | − | 0.0812274i | 0.841624 | − | 0.540064i | \(-0.181600\pi\) |
−0.888521 | + | 0.458836i | \(0.848266\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.01577 | − | 1.75936i | 0.117291 | − | 0.203153i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.490441 | − | 0.412591i | 0.0558910 | − | 0.0470192i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.79101 | − | 6.56622i | 0.426522 | − | 0.738758i | −0.570039 | − | 0.821617i | \(-0.693072\pi\) |
0.996561 | + | 0.0828597i | \(0.0264053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10107 | − | 1.90711i | −0.122341 | − | 0.211901i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.91292 | −0.978320 | −0.489160 | − | 0.872194i | \(-0.662697\pi\) | ||||
−0.489160 | + | 0.872194i | \(0.662697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.60264 | −1.04155 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.06602 | − | 7.04255i | −0.435923 | − | 0.755041i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.55732 | − | 11.3576i | 0.695074 | − | 1.20390i | −0.275082 | − | 0.961421i | \(-0.588705\pi\) |
0.970156 | − | 0.242483i | \(-0.0779618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.66999 | + | 15.0307i | 0.279891 | + | 1.57564i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.70625 | − | 4.68737i | 0.280625 | − | 0.486057i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.832641 | + | 1.44218i | 0.0854272 | + | 0.147964i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.11664 | 0.113377 | 0.0566886 | − | 0.998392i | \(-0.481946\pi\) | ||||
0.0566886 | + | 0.998392i | \(0.481946\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.525109 | 0.0527755 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.51382 | − | 11.2823i | −0.648149 | − | 1.12263i | −0.983565 | − | 0.180557i | \(-0.942210\pi\) |
0.335416 | − | 0.942070i | \(-0.391123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.86294 | − | 11.8870i | 0.676226 | − | 1.17126i | −0.299883 | − | 0.953976i | \(-0.596948\pi\) |
0.976109 | − | 0.217282i | \(-0.0697190\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.703005 | + | 3.95755i | 0.0686063 | + | 0.386217i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.88424 | + | 3.26359i | −0.182156 | + | 0.315503i | −0.942614 | − | 0.333883i | \(-0.891641\pi\) |
0.760459 | + | 0.649386i | \(0.224974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.337127 | + | 0.583921i | 0.0322909 | + | 0.0559295i | 0.881719 | − | 0.471774i | \(-0.156386\pi\) |
−0.849428 | + | 0.527704i | \(0.823053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.94388 | −0.848916 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1480 | 0.954646 | 0.477323 | − | 0.878728i | \(-0.341607\pi\) | ||||
0.477323 | + | 0.878728i | \(0.341607\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.50830 | + | 9.54065i | 0.513651 | + | 0.889670i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.25385 | + | 10.8320i | −0.578169 | + | 1.00142i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.6746 | + | 9.82145i | −1.07021 | + | 0.900330i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.47066 | − | 9.47546i | 0.497333 | − | 0.861406i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.912296 | + | 1.58014i | 0.0822590 | + | 0.142477i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0347 | 1.07642 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.5974 | 1.65025 | 0.825126 | − | 0.564949i | \(-0.191104\pi\) | ||||
0.825126 | + | 0.564949i | \(0.191104\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.57272 | + | 6.18813i | 0.314561 | + | 0.544835i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.98570 | + | 6.90344i | −0.348233 | + | 0.603157i | −0.985936 | − | 0.167126i | \(-0.946551\pi\) |
0.637703 | + | 0.770282i | \(0.279885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.48734 | + | 0.901743i | 0.215680 | + | 0.0781910i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.92548 | + | 6.79912i | −0.337851 | + | 0.585175i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.159382 | + | 0.276057i | 0.0136169 | + | 0.0235852i | 0.872754 | − | 0.488161i | \(-0.162332\pi\) |
−0.859137 | + | 0.511746i | \(0.828999\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.80115 | −0.492047 | −0.246024 | − | 0.969264i | \(-0.579124\pi\) | ||||
−0.246024 | + | 0.969264i | \(0.579124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.44068 | 0.121327 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.698864 | − | 1.21047i | −0.0584419 | − | 0.101224i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.42201 | − | 12.8553i | 0.616364 | − | 1.06757i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.90242 | + | 4.09245i | 0.404345 | + | 0.337540i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.83503 | + | 11.8386i | −0.559948 | + | 0.969858i | 0.437552 | + | 0.899193i | \(0.355845\pi\) |
−0.997500 | + | 0.0706649i | \(0.977488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.51411 | − | 9.55072i | −0.448732 | − | 0.777226i | 0.549572 | − | 0.835446i | \(-0.314791\pi\) |
−0.998304 | + | 0.0582201i | \(0.981457\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.4999 | −1.01055 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.87985 | 0.793568 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.92830 | − | 15.4643i | −0.712556 | − | 1.23418i | −0.963895 | − | 0.266283i | \(-0.914204\pi\) |
0.251339 | − | 0.967899i | \(-0.419129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.95650 | + | 5.12081i | −0.234466 | + | 0.406107i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.4549 | + | 5.96544i | 1.29683 | + | 0.470142i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.59851 | + | 9.69690i | −0.438509 | + | 0.759520i | −0.997575 | − | 0.0696035i | \(-0.977827\pi\) |
0.559066 | + | 0.829123i | \(0.311160\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.184010 | − | 0.318714i | −0.0143251 | − | 0.0248119i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.44712 | 0.111981 | 0.0559906 | − | 0.998431i | \(-0.482168\pi\) | ||||
0.0559906 | + | 0.998431i | \(0.482168\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.2928 | 1.56098 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.08386 | + | 1.87730i | 0.0828847 | + | 0.143560i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.94705 | + | 10.3006i | −0.452146 | + | 0.783140i | −0.998519 | − | 0.0544023i | \(-0.982675\pi\) |
0.546373 | + | 0.837542i | \(0.316008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.50846 | − | 3.79281i | 0.340807 | − | 0.286709i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.490348 | + | 0.849308i | −0.0368568 | + | 0.0638379i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5864 | − | 21.8003i | −0.940751 | − | 1.62943i | −0.764043 | − | 0.645165i | \(-0.776788\pi\) |
−0.176708 | − | 0.984263i | \(-0.556545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7410 | 1.39301 | 0.696503 | − | 0.717554i | \(-0.254738\pi\) | ||||
0.696503 | + | 0.717554i | \(0.254738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.31017 | 0.614305 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.16297 | − | 14.1387i | −0.600154 | − | 1.03950i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.698425 | − | 1.20971i | 0.0510739 | − | 0.0884626i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.18157 | + | 12.2811i | 0.158686 | + | 0.893319i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.178001 | + | 0.308307i | −0.0128797 | + | 0.0223083i | −0.872393 | − | 0.488804i | \(-0.837433\pi\) |
0.859514 | + | 0.511113i | \(0.170767\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.54939 | − | 14.8080i | −0.615398 | − | 1.06590i | −0.990314 | − | 0.138842i | \(-0.955662\pi\) |
0.374916 | − | 0.927059i | \(-0.377671\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.76594 | 0.627742 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1088 | 0.933964 | 0.466982 | − | 0.884267i | \(-0.345341\pi\) | ||||
0.466982 | + | 0.884267i | \(0.345341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.38489 | − | 4.13074i | −0.169060 | − | 0.292821i | 0.769030 | − | 0.639213i | \(-0.220740\pi\) |
−0.938090 | + | 0.346393i | \(0.887407\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.66077 | + | 6.34065i | −0.258211 | + | 0.447235i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.12476 | − | 23.2202i | −0.289501 | − | 1.62974i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.66528 | + | 2.88435i | −0.116308 | + | 0.201452i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.17021 | + | 12.4192i | 0.498364 | + | 0.863192i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.242241 | −0.0167561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0442 | 1.51759 | 0.758794 | − | 0.651331i | \(-0.225789\pi\) | ||||
0.758794 | + | 0.651331i | \(0.225789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.560858 | − | 0.971435i | −0.0384294 | − | 0.0665616i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.52156 | + | 11.2957i | −0.444766 | + | 0.770358i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0116 | − | 10.1050i | 0.815403 | − | 0.685970i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.365543 | + | 0.633140i | −0.0247011 | + | 0.0427836i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.6360 | + | 28.8143i | 1.11906 | + | 1.93826i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.5836 | 1.31142 | 0.655708 | − | 0.755014i | \(-0.272370\pi\) | ||||
0.655708 | + | 0.755014i | \(0.272370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.82715 | 0.321810 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.89414 | + | 5.01280i | 0.192091 | + | 0.332712i | 0.945943 | − | 0.324333i | \(-0.105140\pi\) |
−0.753852 | + | 0.657044i | \(0.771806\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.55372 | − | 16.5475i | 0.631328 | − | 1.09349i | −0.355953 | − | 0.934504i | \(-0.615844\pi\) |
0.987281 | − | 0.158988i | \(-0.0508231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.549691 | − | 0.199281i | −0.0361670 | − | 0.0131117i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.08563 | − | 5.34446i | 0.202146 | − | 0.350127i | −0.747074 | − | 0.664741i | \(-0.768542\pi\) |
0.949220 | + | 0.314614i | \(0.101875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.31489 | + | 2.27745i | 0.0857739 | + | 0.148565i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.91705 | −0.449311 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1425 | 1.69101 | 0.845507 | − | 0.533964i | \(-0.179298\pi\) | ||||
0.845507 | + | 0.533964i | \(0.179298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.79581 | + | 16.9668i | 0.631003 | + | 1.09293i | 0.987347 | + | 0.158575i | \(0.0506899\pi\) |
−0.356344 | + | 0.934355i | \(0.615977\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.07623 | + | 13.9884i | −0.518091 | + | 0.897359i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.99506 | + | 11.4850i | −0.127459 | + | 0.733749i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.88499 | − | 4.99696i | 0.183568 | − | 0.317949i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.06561 | + | 7.04184i | 0.257647 | + | 0.446259i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.39080 | −0.403384 | −0.201692 | − | 0.979449i | \(-0.564644\pi\) | ||||
−0.201692 | + | 0.979449i | \(0.564644\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.60253 | −0.100750 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.38022 | + | 7.58677i | 0.274300 | + | 0.475102i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.9371 | + | 18.9436i | −0.682238 | + | 1.18167i | 0.292058 | + | 0.956401i | \(0.405660\pi\) |
−0.974296 | + | 0.225271i | \(0.927673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.3852 | − | 8.84043i | −1.51522 | − | 0.549317i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.66131 | − | 16.7339i | 0.598020 | − | 1.03580i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.8618 | + | 25.7414i | 0.916420 | + | 1.58729i | 0.804809 | + | 0.593534i | \(0.202268\pi\) |
0.111611 | + | 0.993752i | \(0.464399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.7935 | −0.663037 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.9644 | −0.732211 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.69279 | − | 11.5923i | −0.408067 | − | 0.706792i | 0.586606 | − | 0.809872i | \(-0.300464\pi\) |
−0.994673 | + | 0.103080i | \(0.967130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8866 | − | 22.3202i | 0.782805 | − | 1.35586i | −0.147496 | − | 0.989063i | \(-0.547121\pi\) |
0.930301 | − | 0.366796i | \(-0.119545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.6574 | − | 8.96569i | 0.645014 | − | 0.542628i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.269715 | + | 0.467161i | −0.0162644 | + | 0.0281708i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.48701 | + | 2.57558i | 0.0893458 | + | 0.154751i | 0.907235 | − | 0.420625i | \(-0.138189\pi\) |
−0.817889 | + | 0.575376i | \(0.804856\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.8607 | 0.769950 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.8947 | −1.12716 | −0.563582 | − | 0.826060i | \(-0.690577\pi\) | ||||
−0.563582 | + | 0.826060i | \(0.690577\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.4150 | − | 19.7713i | −0.678551 | − | 1.17528i | −0.975417 | − | 0.220365i | \(-0.929275\pi\) |
0.296867 | − | 0.954919i | \(-0.404058\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.759615 | − | 1.31569i | 0.0449957 | − | 0.0779349i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.925475 | + | 5.20994i | 0.0546291 | + | 0.307533i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.12552 | + | 14.0738i | −0.477972 | + | 0.827872i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.509351 | − | 0.882222i | −0.0298587 | − | 0.0517168i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.3710 | 0.664299 | 0.332150 | − | 0.943227i | \(-0.392226\pi\) | ||||
0.332150 | + | 0.943227i | \(0.392226\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.79014 | −0.104226 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.571021 | − | 0.989037i | −0.0331340 | − | 0.0573897i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.0855 | − | 33.0571i | 1.10375 | − | 1.91174i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.62433 | + | 20.4031i | 0.208903 | + | 1.17602i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.94253 | + | 10.2928i | −0.341389 | + | 0.591304i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.58459 | + | 13.1369i | 0.434292 | + | 0.752216i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.87636 | −0.221236 | −0.110618 | − | 0.993863i | \(-0.535283\pi\) | ||||
−0.110618 | + | 0.993863i | \(0.535283\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.5221 | −0.712356 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0281 | − | 19.1012i | −0.625344 | − | 1.08313i | −0.988474 | − | 0.151389i | \(-0.951625\pi\) |
0.363130 | − | 0.931738i | \(-0.381708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.5322 | − | 26.9025i | 0.877930 | − | 1.52062i | 0.0243207 | − | 0.999704i | \(-0.492258\pi\) |
0.853609 | − | 0.520914i | \(-0.174409\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.30853 | + | 6.14841i | −0.411789 | + | 0.346424i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.6431 | + | 28.8268i | −0.934772 | + | 1.61907i | −0.159731 | + | 0.987161i | \(0.551063\pi\) |
−0.775040 | + | 0.631912i | \(0.782271\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.07965 | + | 1.87000i | 0.0604485 | + | 0.104700i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.43796 | 0.191888 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.76637 | 0.320850 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.42441 | − | 11.1274i | −0.356362 | − | 0.617237i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.307560 | − | 0.532709i | 0.0170081 | − | 0.0294589i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.92795 | + | 1.42401i | 0.216555 | + | 0.0785084i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.18690 | + | 7.25192i | −0.230133 | + | 0.398601i | −0.957847 | − | 0.287279i | \(-0.907249\pi\) |
0.727714 | + | 0.685880i | \(0.240583\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.6258 | − | 18.4045i | −0.582292 | − | 1.00856i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.3646 | −0.730184 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.87908 | −0.102360 | −0.0511799 | − | 0.998689i | \(-0.516298\pi\) | ||||
−0.0511799 | + | 0.998689i | \(0.516298\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.62900 | − | 8.01767i | −0.251413 | − | 0.435460i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.718588 | + | 1.24463i | −0.0389137 | + | 0.0674005i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.32115 | + | 16.0036i | 0.503295 | + | 0.864115i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.02520 | − | 8.70390i | 0.270548 | − | 0.468602i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.06863 | + | 5.31502i | 0.164733 | + | 0.285325i | 0.936560 | − | 0.350506i | \(-0.113991\pi\) |
−0.771828 | + | 0.635832i | \(0.780657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.9103 | −1.01225 | −0.506123 | − | 0.862461i | \(-0.668922\pi\) | ||||
−0.506123 | + | 0.862461i | \(0.668922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.2025 | 1.45196 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.97227 | + | 8.61222i | 0.264647 | + | 0.458382i | 0.967471 | − | 0.252982i | \(-0.0814112\pi\) |
−0.702824 | + | 0.711364i | \(0.748078\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.02378 | − | 1.77323i | 0.0543364 | − | 0.0941134i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.0850 | + | 4.74374i | 0.692531 | + | 0.251066i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.19502 | + | 15.9262i | −0.485295 | + | 0.840555i | −0.999857 | − | 0.0168977i | \(-0.994621\pi\) |
0.514562 | + | 0.857453i | \(0.327954\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.500000 | − | 0.866025i | −0.0263158 | − | 0.0455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.98172 | −0.523905 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.33451 | −0.0698513 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.10761 | + | 12.3107i | 0.371014 | + | 0.642616i | 0.989722 | − | 0.143006i | \(-0.0456767\pi\) |
−0.618707 | + | 0.785621i | \(0.712343\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.16772 | + | 3.75459i | −0.112847 | + | 0.195456i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1224 | + | 11.0394i | −0.681280 | + | 0.573137i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8008 | + | 22.1716i | −0.662800 | + | 1.14800i | 0.317076 | + | 0.948400i | \(0.397299\pi\) |
−0.979877 | + | 0.199604i | \(0.936034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.48961 | − | 9.50829i | −0.283482 | − | 0.491006i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −51.4326 | −2.64891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.51685 | −0.437481 | −0.218741 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218741 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.48316 | − | 14.6933i | −0.434606 | − | 0.752759i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.00847 | − | 8.67492i | 0.255921 | − | 0.443268i | −0.709224 | − | 0.704983i | \(-0.750955\pi\) |
0.965145 | + | 0.261715i | \(0.0842881\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.186668 | − | 1.05084i | −0.00951348 | − | 0.0535559i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.48918 | + | 14.7037i | −0.431529 | + | 0.747431i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.1401 | + | 17.5631i | 0.514123 | + | 0.890487i | 0.999866 | + | 0.0163851i | \(0.00521577\pi\) |
−0.485743 | + | 0.874102i | \(0.661451\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.1472 | 1.92918 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.27229 | 0.366838 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.31310 | − | 10.9346i | −0.317647 | − | 0.550180i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4137 | − | 23.2333i | 0.673216 | − | 1.16604i | −0.303770 | − | 0.952745i | \(-0.598246\pi\) |
0.976987 | − | 0.213300i | \(-0.0684211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.422154 | − | 2.37650i | −0.0211341 | − | 0.118974i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.92911 | − | 12.0016i | 0.346023 | − | 0.599330i | −0.639516 | − | 0.768778i | \(-0.720865\pi\) |
0.985539 | + | 0.169448i | \(0.0541985\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1162 | − | 29.6461i | −0.852619 | − | 1.47678i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.66719 | −0.182224 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.37486 | 0.117717 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.09715 | + | 5.36442i | 0.153144 | + | 0.265253i | 0.932382 | − | 0.361475i | \(-0.117727\pi\) |
−0.779238 | + | 0.626729i | \(0.784393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.145403 | − | 0.251846i | 0.00717222 | − | 0.0124226i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.17640 | + | 1.83093i | −0.107094 | + | 0.0900942i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.42126 | + | 12.8540i | −0.364295 | + | 0.630978i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.64618 | + | 4.58333i | 0.129584 | + | 0.224446i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4938 | 0.708068 | 0.354034 | − | 0.935233i | \(-0.384810\pi\) | ||||
0.354034 | + | 0.935233i | \(0.384810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8753 | 1.45603 | 0.728016 | − | 0.685560i | \(-0.240443\pi\) | ||||
0.728016 | + | 0.685560i | \(0.240443\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.71161 | + | 2.96459i | 0.0832211 | + | 0.144143i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.42038 | − | 11.1204i | 0.311434 | − | 0.539420i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.6574 | + | 8.21404i | 1.09647 | + | 0.397505i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.637570 | + | 1.10430i | −0.0307822 | + | 0.0533163i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.9304 | − | 18.9321i | −0.526501 | − | 0.911926i | −0.999523 | − | 0.0308754i | \(-0.990170\pi\) |
0.473023 | − | 0.881050i | \(-0.343163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.1847 | −0.537500 | −0.268750 | − | 0.963210i | \(-0.586611\pi\) | ||||
−0.268750 | + | 0.963210i | \(0.586611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.5421 | −0.649296 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.30773 | − | 5.72915i | −0.158230 | − | 0.274062i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.70936 | − | 13.3530i | 0.367948 | − | 0.637304i | −0.621297 | − | 0.783575i | \(-0.713394\pi\) |
0.989245 | + | 0.146271i | \(0.0467272\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.59699 | + | 14.9501i | −0.123666 | + | 0.711911i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.469742 | − | 0.813616i | 0.0223181 | − | 0.0386561i | −0.854651 | − | 0.519203i | \(-0.826229\pi\) |
0.876969 | + | 0.480547i | \(0.159562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9198 | − | 18.9136i | −0.517647 | − | 0.896591i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4711 | 0.589865 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.2058 | −1.33112 | −0.665558 | − | 0.746346i | \(-0.731806\pi\) | ||||
−0.665558 | + | 0.746346i | \(0.731806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.242241 | − | 0.419573i | −0.0114067 | − | 0.0197569i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.03050 | + | 8.71308i | −0.236353 | + | 0.409376i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.9000 | + | 8.66454i | 1.12045 | + | 0.406200i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.388913 | + | 0.673617i | −0.0181926 | + | 0.0315105i | −0.874978 | − | 0.484162i | \(-0.839125\pi\) |
0.856786 | + | 0.515672i | \(0.172458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.5927 | + | 23.5433i | 0.634455 | + | 1.09891i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3614 | −0.901751 | −0.450875 | − | 0.892587i | \(-0.648888\pi\) | ||||
−0.450875 | + | 0.892587i | \(0.648888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.5688 | 1.60655 | 0.803275 | − | 0.595608i | \(-0.203089\pi\) | ||||
0.803275 | + | 0.595608i | \(0.203089\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.50667 | − | 7.80579i | −0.208992 | − | 0.361985i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.9272 | − | 25.8547i | 0.690750 | − | 1.19641i | −0.280843 | − | 0.959754i | \(-0.590614\pi\) |
0.971593 | − | 0.236660i | \(-0.0760527\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.2483 | + | 13.6691i | −0.750275 | + | 0.631180i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.14525 | + | 14.1080i | −0.375313 | + | 0.650062i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.948660 | − | 1.64313i | −0.0436194 | − | 0.0755511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.22684 | −0.102174 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.0500 | −0.643303 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.9432 | + | 24.1504i | 0.637082 | + | 1.10346i | 0.986070 | + | 0.166332i | \(0.0531923\pi\) |
−0.348987 | + | 0.937127i | \(0.613474\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.2836 | + | 48.9887i | −1.28962 | + | 2.23369i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.79274 | − | 15.7217i | −0.127074 | − | 0.715360i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.929757 | − | 1.61039i | 0.0422181 | − | 0.0731238i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.81119 | − | 10.0653i | −0.263330 | − | 0.456101i | 0.703795 | − | 0.710404i | \(-0.251488\pi\) |
−0.967125 | + | 0.254302i | \(0.918154\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.2150 | 0.461938 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.4037 | −1.14645 | −0.573225 | − | 0.819398i | \(-0.694308\pi\) | ||||
−0.573225 | + | 0.819398i | \(0.694308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.7002 | − | 44.5140i | −1.15748 | − | 2.00481i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.437228 | − | 0.757300i | 0.0196519 | − | 0.0340381i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.568961 | − | 3.20295i | −0.0255214 | − | 0.143672i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.33920 | + | 2.31956i | −0.0599509 | + | 0.103838i | −0.894443 | − | 0.447182i | \(-0.852428\pi\) |
0.834492 | + | 0.551020i | \(0.185761\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.660099 | − | 1.14333i | −0.0294911 | − | 0.0510800i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.0893 | −1.65373 | −0.826866 | − | 0.562399i | \(-0.809879\pi\) | ||||
−0.826866 | + | 0.562399i | \(0.809879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.6947 | −0.965401 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.25651 | − | 16.0327i | −0.411096 | − | 0.712039i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.41214 | + | 12.8382i | −0.328537 | + | 0.569043i | −0.982222 | − | 0.187724i | \(-0.939889\pi\) |
0.653685 | + | 0.756767i | \(0.273222\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.62246 | + | 1.36492i | −0.0717732 | + | 0.0603803i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.35724 | − | 4.08287i | 0.104075 | − | 0.180263i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.4287 | − | 19.7951i | −0.503610 | − | 0.872279i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.382542 | −0.0168242 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.8509 | 0.476303 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.24608 | + | 9.08648i | 0.229835 | + | 0.398086i | 0.957759 | − | 0.287572i | \(-0.0928480\pi\) |
−0.727924 | + | 0.685658i | \(0.759515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.73787 | − | 13.4024i | 0.338353 | − | 0.586045i | −0.645770 | − | 0.763532i | \(-0.723463\pi\) |
0.984123 | + | 0.177487i | \(0.0567968\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.05311 | − | 1.83192i | −0.220536 | − | 0.0799516i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.1055 | − | 29.6275i | 0.745126 | − | 1.29060i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.3821 | − | 17.9823i | −0.451396 | − | 0.781840i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.33024 | −0.101124 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.5400 | 0.499852 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.13778 | + | 5.43480i | 0.135658 | + | 0.234967i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.4825 | + | 19.8883i | −0.495507 | + | 0.858243i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.30173 | − | 1.08666i | −0.0560697 | − | 0.0468059i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.39634 | − | 16.2749i | 0.403980 | − | 0.699715i | −0.590222 | − | 0.807241i | \(-0.700960\pi\) |
0.994202 | + | 0.107527i | \(0.0342931\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.54865 | − | 14.8067i | −0.366858 | − | 0.635416i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.12282 | 0.0480965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.809060 | −0.0345929 | −0.0172965 | − | 0.999850i | \(-0.505506\pi\) | ||||
−0.0172965 | + | 0.999850i | \(0.505506\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.87294 | + | 17.1004i | 0.421367 | + | 0.729829i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.45691 | + | 7.71959i | −0.189871 | + | 0.328866i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.8591 | − | 6.83703i | −0.801969 | − | 0.290740i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.44705 | + | 12.8987i | −0.316109 | + | 0.547518i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.72680 | + | 15.1153i | 0.369767 | + | 0.640455i | 0.989529 | − | 0.144335i | \(-0.0461043\pi\) |
−0.619762 | + | 0.784790i | \(0.712771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.1927 | 1.91145 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.27434 | −0.0538027 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.84187 | + | 3.19022i | 0.0776257 | + | 0.134452i | 0.902225 | − | 0.431265i | \(-0.141933\pi\) |
−0.824599 | + | 0.565717i | \(0.808599\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.44967 | − | 14.6353i | 0.355480 | − | 0.615710i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.45846 | + | 3.75075i | −0.187238 | + | 0.157517i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.56612 | − | 7.90875i | 0.191422 | − | 0.331552i | −0.754300 | − | 0.656530i | \(-0.772024\pi\) |
0.945722 | + | 0.324978i | \(0.105357\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5623 | − | 18.2945i | −0.442020 | − | 0.765601i | 0.555820 | − | 0.831303i | \(-0.312405\pi\) |
−0.997839 | + | 0.0657023i | \(0.979071\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.324779 | 0.0135678 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.7315 | −0.614347 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.62137 | − | 4.54035i | −0.109129 | − | 0.189017i | 0.806289 | − | 0.591522i | \(-0.201473\pi\) |
−0.915418 | + | 0.402505i | \(0.868140\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.79957 | + | 13.5093i | −0.324139 | + | 0.561425i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.12434 | + | 23.2179i | 0.171106 | + | 0.963240i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.785037 | − | 1.35972i | 0.0325129 | − | 0.0563140i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.4144 | + | 18.0383i | 0.430583 | + | 0.745792i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.26045 | −0.134573 | −0.0672865 | − | 0.997734i | \(-0.521434\pi\) | ||||
−0.0672865 | + | 0.997734i | \(0.521434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.93284 | −0.244458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.97956 | − | 10.3569i | −0.245966 | − | 0.426026i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.96152 | + | 17.2539i | −0.409070 | + | 0.708531i | −0.994786 | − | 0.101986i | \(-0.967480\pi\) |
0.585715 | + | 0.810517i | \(0.300814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.44350 | + | 25.0146i | 0.182166 | + | 1.02550i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.17572 | + | 3.76846i | −0.0890464 | + | 0.154233i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.2325 | − | 38.5077i | −0.908394 | − | 1.57338i | −0.816296 | − | 0.577634i | \(-0.803976\pi\) |
−0.0920976 | − | 0.995750i | \(-0.529357\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3392 | 0.911233 | 0.455617 | − | 0.890176i | \(-0.349419\pi\) | ||||
0.455617 | + | 0.890176i | \(0.349419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.3968 | −0.708453 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.11019 | − | 15.7793i | −0.370382 | − | 0.641520i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.2044 | + | 29.7989i | −0.698306 | + | 1.20950i | 0.270747 | + | 0.962651i | \(0.412729\pi\) |
−0.969053 | + | 0.246851i | \(0.920604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.4641 | + | 13.8507i | −0.667161 | + | 0.561259i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.55592 | − | 7.89109i | 0.184313 | − | 0.319239i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.1470 | + | 21.0392i | 0.490613 | + | 0.849766i | 0.999942 | − | 0.0108056i | \(-0.00343961\pi\) |
−0.509329 | + | 0.860572i | \(0.670106\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.03846 | 0.122523 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.0255 | −0.685422 | −0.342711 | − | 0.939441i | \(-0.611345\pi\) | ||||
−0.342711 | + | 0.939441i | \(0.611345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.3397 | − | 24.8372i | −0.576363 | − | 0.998290i | −0.995892 | − | 0.0905479i | \(-0.971138\pi\) |
0.419529 | − | 0.907742i | \(-0.362195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.5942 | − | 27.0100i | 0.625775 | − | 1.08387i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.6205 | − | 11.8260i | −1.30691 | − | 0.473800i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.45351 | − | 7.71371i | 0.178141 | − | 0.308548i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.110498 | + | 0.191388i | 0.00441285 | + | 0.00764328i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −56.5318 | −2.25407 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4675 | −1.17308 | −0.586542 | − | 0.809919i | \(-0.699511\pi\) | ||||
−0.586542 | + | 0.809919i | \(0.699511\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.0554 | − | 17.4165i | −0.399668 | − | 0.692244i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.4849 | − | 26.8207i | 0.614501 | − | 1.06435i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.9189 | − | 13.9105i | 1.50240 | − | 0.551154i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.33266 | − | 2.30824i | 0.0527193 | − | 0.0913124i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.06837 | + | 13.9748i | 0.318681 | + | 0.551972i | 0.980213 | − | 0.197945i | \(-0.0634266\pi\) |
−0.661532 | + | 0.749917i | \(0.730093\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8353 | 0.900535 | 0.450267 | − | 0.892894i | \(-0.351329\pi\) | ||||
0.450267 | + | 0.892894i | \(0.351329\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.8992 | 0.468530 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.3699 | − | 17.9613i | −0.407685 | − | 0.706131i | 0.586945 | − | 0.809627i | \(-0.300330\pi\) |
−0.994630 | + | 0.103496i | \(0.966997\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.130202 | − | 0.225516i | 0.00511086 | − | 0.00885227i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.4627 | − | 4.88069i | −0.527646 | − | 0.191289i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.68834 | − | 16.7807i | 0.379134 | − | 0.656679i | −0.611802 | − | 0.791011i | \(-0.709555\pi\) |
0.990936 | + | 0.134331i | \(0.0428886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.63732 | + | 11.4962i | 0.259342 | + | 0.449193i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.73714 | −0.0677724 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.33347 | 0.285672 | 0.142836 | − | 0.989746i | \(-0.454378\pi\) | ||||
0.142836 | + | 0.989746i | \(0.454378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.8535 | + | 32.6552i | 0.733315 | + | 1.27014i | 0.955459 | + | 0.295124i | \(0.0953611\pi\) |
−0.222144 | + | 0.975014i | \(0.571306\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.1769 | − | 26.2872i | 0.589422 | − | 1.02091i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.37153 | − | 2.83636i | 0.130742 | − | 0.109989i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.4845 | + | 51.0686i | −1.14164 | + | 1.97738i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.93303 | − | 15.4725i | −0.345371 | − | 0.598200i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.20659 | −0.0851844 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.4005 | 1.86570 | 0.932851 | − | 0.360263i | \(-0.117313\pi\) | ||||
0.932851 | + | 0.360263i | \(0.117313\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.24919 | − | 9.09187i | −0.202042 | − | 0.349946i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.93290 | + | 13.7402i | −0.304886 | + | 0.528078i | −0.977236 | − | 0.212155i | \(-0.931952\pi\) |
0.672350 | + | 0.740233i | \(0.265285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.516709 | − | 2.90880i | −0.0198295 | − | 0.111630i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.64032 | − | 4.57316i | 0.101177 | − | 0.175244i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.63354 | − | 14.9537i | −0.330353 | − | 0.572189i | 0.652228 | − | 0.758023i | \(-0.273835\pi\) |
−0.982581 | + | 0.185834i | \(0.940501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.530831 | 0.0202820 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.4316 | −0.665059 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.6990 | + | 32.3876i | 0.712374 | + | 1.23387i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.6306 | − | 42.6614i | 0.936992 | − | 1.62292i | 0.165949 | − | 0.986134i | \(-0.446931\pi\) |
0.771043 | − | 0.636783i | \(-0.219735\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.242988 | − | 1.36789i | −0.00923034 | − | 0.0519620i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.83028 | + | 8.36629i | −0.183223 | + | 0.317351i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.76637 | + | 9.98765i | 0.218417 | + | 0.378309i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.63001 | −0.212947 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.1609 | 0.383770 | 0.191885 | − | 0.981417i | \(-0.438540\pi\) | ||||
0.191885 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.90185 | + | 8.49026i | 0.184877 | + | 0.320216i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.19957 | − | 2.07771i | 0.0451784 | − | 0.0782512i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.3758 | + | 22.1890i | −0.991963 | + | 0.834504i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.86510 | + | 6.69454i | −0.145157 | + | 0.251419i | −0.929431 | − | 0.368995i | \(-0.879702\pi\) |
0.784275 | + | 0.620414i | \(0.213035\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.21783 | − | 14.2337i | −0.308193 | − | 0.533806i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.2484 | −1.46986 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.32761 | −0.0870477 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.9248 | − | 20.6544i | −0.445341 | − | 0.771353i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.6604 | + | 21.9284i | −0.472152 | + | 0.817791i | −0.999492 | − | 0.0318632i | \(-0.989856\pi\) |
0.527340 | + | 0.849654i | \(0.323189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.1409 | − | 12.3772i | −1.27148 | − | 0.460952i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.93667 | − | 15.4788i | 0.332358 | − | 0.575662i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.92480 | + | 17.1903i | 0.368598 | + | 0.638430i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.5601 | 0.910884 | 0.455442 | − | 0.890266i | \(-0.349481\pi\) | ||||
0.455442 | + | 0.890266i | \(0.349481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.12941 | 0.301089 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.5822 | + | 39.1135i | 0.835232 | + | 1.44666i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.6516 | − | 23.6453i | 0.504235 | − | 0.873361i | −0.495753 | − | 0.868464i | \(-0.665108\pi\) |
0.999988 | − | 0.00489700i | \(-0.00155877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.98400 | − | 3.66261i | 0.368265 | − | 0.135098i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.972041 | − | 1.68362i | 0.0358056 | − | 0.0620171i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.0188 | − | 41.6017i | −0.883544 | − | 1.53034i | −0.847373 | − | 0.530998i | \(-0.821817\pi\) |
−0.0361706 | − | 0.999346i | \(-0.511516\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.26394 | −0.193376 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.8539 | 0.398190 | 0.199095 | − | 0.979980i | \(-0.436200\pi\) | ||||
0.199095 | + | 0.979980i | \(0.436200\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.3823 | + | 19.7146i | 0.417014 | + | 0.722289i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.66033 | + | 16.7322i | −0.353453 | + | 0.612199i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.37347 | + | 3.39819i | 0.342499 | + | 0.124167i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.95718 | + | 15.5143i | −0.326852 | + | 0.566125i | −0.981885 | − | 0.189475i | \(-0.939321\pi\) |
0.655033 | + | 0.755600i | \(0.272655\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.91515 | + | 5.04919i | 0.106234 | + | 0.184003i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.3651 | −0.668374 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.7888 | 0.719235 | 0.359617 | − | 0.933100i | \(-0.382907\pi\) | ||||
0.359617 | + | 0.933100i | \(0.382907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.730992 | + | 1.26612i | 0.0265333 | + | 0.0459571i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.7301 | + | 44.5659i | −0.932717 | + | 1.61551i | −0.154062 | + | 0.988061i | \(0.549235\pi\) |
−0.778655 | + | 0.627452i | \(0.784098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.36510 | − | 1.14841i | 0.0494198 | − | 0.0415752i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.4079 | + | 18.0270i | −0.376298 | + | 0.651768i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.10130 | + | 5.37161i | 0.111981 | + | 0.193958i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.2468 | −0.946485 | −0.473243 | − | 0.880932i | \(-0.656917\pi\) | ||||
−0.473243 | + | 0.880932i | \(0.656917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.9558 | 0.718689 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.02611 | − | 5.24138i | −0.108842 | − | 0.188519i | 0.806460 | − | 0.591289i | \(-0.201381\pi\) |
−0.915301 | + | 0.402770i | \(0.868048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.60573 | + | 11.4415i | −0.237285 | + | 0.410989i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.13867 | + | 23.2986i | 0.148474 | + | 0.835831i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00000 | − | 1.73205i | 0.0358287 | − | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.148924 | + | 0.257944i | 0.00532892 | + | 0.00922996i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.0241 | −1.50182 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.7363 | −1.06133 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.22879 | + | 10.7886i | 0.222032 | + | 0.384571i | 0.955425 | − | 0.295234i | \(-0.0953976\pi\) |
−0.733393 | + | 0.679805i | \(0.762064\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.5584 | − | 23.4838i | 0.482691 | − | 0.836046i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.69587 | − | 26.4353i | −0.166966 | − | 0.939932i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.2796 | − | 45.5176i | 0.933217 | − | 1.61638i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.92341 | + | 8.52760i | 0.174615 | + | 0.302443i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.13423 | 0.252707 | 0.126354 | − | 0.991985i | \(-0.459673\pi\) | ||||
0.126354 | + | 0.991985i | \(0.459673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.10613 | 0.322152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.2144 | − | 24.6201i | −0.502241 | − | 0.869907i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0970623 | − | 0.168117i | 0.00342525 | − | 0.00593271i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.3042 | − | 18.7638i | 0.786121 | − | 0.661336i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.10581 | + | 10.5756i | −0.214935 | + | 0.372278i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.87901 | − | 8.45069i | −0.171537 | − | 0.297110i | 0.767421 | − | 0.641144i | \(-0.221540\pi\) |
−0.938957 | + | 0.344034i | \(0.888207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.23879 | −0.0434998 | −0.0217499 | − | 0.999763i | \(-0.506924\pi\) | ||||
−0.0217499 | + | 0.999763i | \(0.506924\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.5128 | −0.824630 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.32310 | + | 16.1481i | 0.326574 | + | 0.565642i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.91619 | − | 6.78303i | 0.137010 | − | 0.237308i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 31.1109 | + | 11.2787i | 1.08710 | + | 0.394111i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4406 | + | 37.1361i | −0.748281 | + | 1.29606i | 0.200365 | + | 0.979721i | \(0.435787\pi\) |
−0.948646 | + | 0.316339i | \(0.897546\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.37704 | + | 11.0454i | 0.222290 | + | 0.385017i | 0.955503 | − | 0.294982i | \(-0.0953136\pi\) |
−0.733213 | + | 0.679999i | \(0.761980\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.492120 | 0.0171334 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.6536 | 1.83095 | 0.915473 | − | 0.402380i | \(-0.131817\pi\) | ||||
0.915473 | + | 0.402380i | \(0.131817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.0607719 | + | 0.105260i | 0.00211070 | + | 0.00365583i | 0.867079 | − | 0.498171i | \(-0.165995\pi\) |
−0.864968 | + | 0.501827i | \(0.832661\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.35659 | − | 2.34969i | 0.0470597 | − | 0.0815098i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.9869 | + | 25.8673i | 1.07363 | + | 0.896248i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.20493 | − | 2.08700i | 0.0416983 | − | 0.0722235i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.9851 | − | 24.2230i | −0.483397 | − | 0.837268i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.8707 | 1.58363 | 0.791816 | − | 0.610759i | \(-0.209136\pi\) | ||||
0.791816 | + | 0.610759i | \(0.209136\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.4561 | 1.73987 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.61878 | + | 14.9282i | 0.296847 | + | 0.514153i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.8966 | − | 29.2658i | 0.581261 | − | 1.00677i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.2148 | − | 9.86626i | −0.935111 | − | 0.339009i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.4138 | + | 18.0373i | −0.357402 | + | 0.619039i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.4280 | + | 56.1669i | 1.11162 | + | 1.92538i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.8106 | −0.644064 | −0.322032 | − | 0.946729i | \(-0.604366\pi\) | ||||
−0.322032 | + | 0.946729i | \(0.604366\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.60986 | 0.123455 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.9968 | + | 19.0470i | 0.375644 | + | 0.650635i | 0.990423 | − | 0.138065i | \(-0.0440882\pi\) |
−0.614779 | + | 0.788699i | \(0.710755\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9879 | + | 29.4238i | −0.579619 | + | 1.00393i | 0.415904 | + | 0.909408i | \(0.363465\pi\) |
−0.995523 | + | 0.0945204i | \(0.969868\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.69407 | − | 3.10770i | 0.125894 | − | 0.105910i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.5221 | − | 28.6171i | 0.562419 | − | 0.974139i | −0.434865 | − | 0.900496i | \(-0.643204\pi\) |
0.997285 | − | 0.0736435i | \(-0.0234627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.90352 | + | 17.1534i | 0.336730 | + | 0.583233i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.8258 | 0.503509 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.83668 | 0.0623049 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.1533 | + | 40.1026i | 0.784518 | + | 1.35883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.21027 | − | 2.09626i | 0.0409616 | − | 0.0709475i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.56892 | − | 31.3501i | −0.188264 | − | 1.05983i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.3633 | − | 23.1459i | 0.451247 | − | 0.781583i | −0.547217 | − | 0.836991i | \(-0.684313\pi\) |
0.998464 | + | 0.0554081i | \(0.0176460\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.18685 | − | 8.98388i | −0.174948 | − | 0.303019i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.6752 | 1.13454 | 0.567272 | − | 0.823530i | \(-0.307999\pi\) | ||||
0.567272 | + | 0.823530i | \(0.307999\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6753 | −0.527516 | −0.263758 | − | 0.964589i | \(-0.584962\pi\) | ||||
−0.263758 | + | 0.964589i | \(0.584962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.816568 | + | 1.41434i | 0.0274486 | + | 0.0475424i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.59856 | + | 4.50083i | −0.0872510 | + | 0.151123i | −0.906348 | − | 0.422532i | \(-0.861142\pi\) |
0.819097 | + | 0.573655i | \(0.194475\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.60571 | − | 48.4457i | −0.288626 | − | 1.62482i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.266724 | − | 0.461980i | 0.00893560 | − | 0.0154769i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.789589 | − | 1.36761i | −0.0264226 | − | 0.0457653i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.9198 | −1.40122 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.8233 | −1.16272 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.4421 | + | 45.7991i | 0.881894 | + | 1.52748i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.6872 | + | 32.3673i | −0.622562 | + | 1.07831i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.4667 | − | 12.1703i | 0.481421 | − | 0.405003i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.6045 | − | 27.0278i | 0.518711 | − | 0.898434i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.7915 | + | 32.5478i | 0.623962 | + | 1.08073i | 0.988741 | + | 0.149639i | \(0.0478113\pi\) |
−0.364779 | + | 0.931094i | \(0.618855\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.2402 | −0.936669 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.9982 | 0.662571 | 0.331286 | − | 0.943530i | \(-0.392518\pi\) | ||||
0.331286 | + | 0.943530i | \(0.392518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.07954 | − | 1.86981i | −0.0357274 | − | 0.0618817i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.91939 | − | 11.9847i | 0.228748 | − | 0.396203i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.8276 | + | 7.18816i | 0.654765 | + | 0.237374i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.8126 | − | 36.0484i | 0.686543 | − | 1.18913i | −0.286406 | − | 0.958108i | \(-0.592461\pi\) |
0.972949 | − | 0.231019i | \(-0.0742061\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.76819 | + | 3.06260i | 0.0582640 | + | 0.100916i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.09451 | −0.233519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.8312 | 0.717807 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.8769 | − | 25.7676i | −0.488622 | − | 0.846318i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.1611 | − | 27.9919i | 0.530229 | − | 0.918384i | −0.469149 | − | 0.883119i | \(-0.655439\pi\) |
0.999378 | − | 0.0352650i | \(-0.0112275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.19803 | − | 6.89672i | 0.0392638 | − | 0.226031i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.0609 | + | 17.4259i | −0.329378 | + | 0.570499i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.16308 | − | 2.01451i | −0.0380366 | − | 0.0658814i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.8754 | −0.779975 | −0.389988 | − | 0.920820i | \(-0.627521\pi\) | ||||
−0.389988 | + | 0.920820i | \(0.627521\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.3399 | −0.924836 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.3481 | + | 26.5837i | 0.500334 | + | 0.866603i | 1.00000 | 0.000385246i | \(0.000122628\pi\) | |
−0.499666 | + | 0.866218i | \(0.666544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.61545 | − | 11.4583i | 0.215429 | − | 0.373134i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 19.5280 | + | 7.07954i | 0.635245 | + | 0.230297i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.8689 | + | 24.0216i | −0.450678 | + | 0.780598i | −0.998428 | − | 0.0560442i | \(-0.982151\pi\) |
0.547750 | + | 0.836642i | \(0.315485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.31195 | + | 4.00441i | 0.0750490 | + | 0.129989i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.3669 | 0.984715 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.9634 | −0.970611 | −0.485305 | − | 0.874345i | \(-0.661292\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.296422 | + | 0.513418i | 0.00959198 | + | 0.0166138i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.984956 | − | 1.70599i | 0.0318391 | − | 0.0551469i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.645369 | − | 0.542927i | 0.0208401 | − | 0.0175320i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09928 | + | 3.63606i | −0.0677187 | + | 0.117292i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.08449 | + | 7.07454i | 0.131621 | + | 0.227974i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.4743 | −0.916619 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.2270 | −0.618299 | −0.309150 | − | 0.951013i | \(-0.600044\pi\) | ||||
−0.309150 | + | 0.951013i | \(0.600044\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.63032 | − | 4.55585i | −0.0844980 | − | 0.146355i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.14680 | + | 14.1107i | −0.261443 | + | 0.452833i | −0.966626 | − | 0.256193i | \(-0.917532\pi\) |
0.705182 | + | 0.709026i | \(0.250865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.68441 | + | 15.1118i | 0.0860583 | + | 0.484463i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.86096 | + | 10.1515i | −0.187701 | + | 0.325108i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6532 | + | 18.4520i | 0.340828 | + | 0.590331i | 0.984587 | − | 0.174898i | \(-0.0559594\pi\) |
−0.643759 | + | 0.765228i | \(0.722626\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.17690 | 0.101534 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.46159 | 0.0466650 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.63704 | + | 6.29954i | 0.116004 | + | 0.200924i | 0.918181 | − | 0.396162i | \(-0.129658\pi\) |
−0.802177 | + | 0.597087i | \(0.796325\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.9149 | − | 18.9052i | 0.347779 | − | 0.602371i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.666656 | − | 3.75293i | −0.0212199 | − | 0.119457i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.9073 | − | 44.8728i | 0.823806 | − | 1.42687i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.6379 | + | 34.0138i | 0.623818 | + | 1.08048i | 0.988768 | + | 0.149458i | \(0.0477528\pi\) |
−0.364950 | + | 0.931027i | \(0.618914\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.63938 | 0.242428 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.94301 | −0.251811 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.48646 | − | 7.77078i | −0.142088 | − | 0.246103i | 0.786195 | − | 0.617979i | \(-0.212048\pi\) |
−0.928283 | + | 0.371876i | \(0.878715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.1097 | + | 40.0272i | −0.731159 | + | 1.26641i |
(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 | 1064.2.q.n.457.3 | yes | 16 | |
7.2 | even | 3 | 7448.2.a.bq.1.6 | 8 | |||
7.4 | even | 3 | inner | 1064.2.q.n.305.3 | ✓ | 16 | |
7.5 | odd | 6 | 7448.2.a.br.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.q.n.305.3 | ✓ | 16 | 7.4 | even | 3 | inner | |
1064.2.q.n.457.3 | yes | 16 | 1.1 | even | 1 | trivial | |
7448.2.a.bq.1.6 | 8 | 7.2 | even | 3 | |||
7448.2.a.br.1.3 | 8 | 7.5 | odd | 6 |