Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(47,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.y (of order \(12\), degree \(4\), 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 47.18 | ||
Character | \(\chi\) | \(=\) | 576.47 |
Dual form | 576.2.y.a.527.18 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 1.49488 | − | 0.874828i | 0.863071 | − | 0.505082i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.473330 | − | 1.76649i | 0.211679 | − | 0.789999i | −0.775630 | − | 0.631188i | \(-0.782568\pi\) |
0.987309 | − | 0.158810i | \(-0.0507658\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.40613 | + | 2.43549i | −0.531468 | + | 0.920530i | 0.467857 | + | 0.883804i | \(0.345026\pi\) |
−0.999325 | + | 0.0367260i | \(0.988307\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.46935 | − | 2.61553i | 0.489784 | − | 0.871844i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55262 | − | 5.79446i | −0.468133 | − | 1.74710i | −0.646288 | − | 0.763093i | \(-0.723680\pi\) |
0.178156 | − | 0.984002i | \(-0.442987\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.296913 | − | 1.10810i | 0.0823489 | − | 0.307330i | −0.912450 | − | 0.409188i | \(-0.865812\pi\) |
0.994799 | + | 0.101858i | \(0.0324787\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.837802 | − | 3.05478i | −0.216320 | − | 0.788741i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.699378i | 0.169624i | 0.996397 | + | 0.0848120i | \(0.0270290\pi\) | ||||
−0.996397 | + | 0.0848120i | \(0.972971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.01481 | − | 2.01481i | 0.462228 | − | 0.462228i | −0.437157 | − | 0.899385i | \(-0.644015\pi\) |
0.899385 | + | 0.437157i | \(0.144015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0286324 | + | 4.87090i | 0.00624810 | + | 1.06292i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.91498 | − | 2.83767i | 1.02485 | − | 0.591695i | 0.109341 | − | 0.994004i | \(-0.465126\pi\) |
0.915504 | + | 0.402310i | \(0.131792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.43368 | + | 0.827735i | 0.286736 | + | 0.165547i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.0916271 | − | 5.19534i | −0.0176336 | − | 0.999845i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.45175 | + | 5.41802i | 0.269584 | + | 1.00610i | 0.959385 | + | 0.282101i | \(0.0910315\pi\) |
−0.689801 | + | 0.723999i | \(0.742302\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.15522 | + | 2.97637i | −0.925905 | + | 0.534572i | −0.885514 | − | 0.464612i | \(-0.846194\pi\) |
−0.0403909 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.39014 | − | 7.30377i | −1.28646 | − | 1.27142i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.63671 | + | 3.63671i | 0.614717 | + | 0.614717i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.48490 | − | 3.48490i | 0.572913 | − | 0.572913i | −0.360028 | − | 0.932941i | \(-0.617233\pi\) |
0.932941 | + | 0.360028i | \(0.117233\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.525542 | − | 1.91622i | −0.0841540 | − | 0.306841i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.55998 | − | 2.70196i | −0.243628 | − | 0.421975i | 0.718117 | − | 0.695922i | \(-0.245004\pi\) |
−0.961745 | + | 0.273947i | \(0.911671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.09570 | + | 1.90129i | −1.08208 | + | 0.289944i | −0.755450 | − | 0.655207i | \(-0.772581\pi\) |
−0.326635 | + | 0.945151i | \(0.605915\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.92482 | − | 3.83361i | −0.585078 | − | 0.571480i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.83634 | + | 4.91269i | −0.413723 | + | 0.716589i | −0.995293 | − | 0.0969068i | \(-0.969105\pi\) |
0.581570 | + | 0.813496i | \(0.302438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.454420 | − | 0.787079i | −0.0649172 | − | 0.112440i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.611835 | + | 1.04549i | 0.0856741 | + | 0.146398i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.45605 | + | 4.45605i | 0.612086 | + | 0.612086i | 0.943489 | − | 0.331403i | \(-0.107522\pi\) |
−0.331403 | + | 0.943489i | \(0.607522\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.9708 | −1.47930 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.24929 | − | 4.77451i | 0.165473 | − | 0.632399i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.6570 | + | 3.65938i | 1.77799 | + | 0.476411i | 0.990215 | − | 0.139552i | \(-0.0445663\pi\) |
0.787775 | + | 0.615963i | \(0.211233\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.2354 | + | 3.54643i | −1.69463 | + | 0.454074i | −0.971577 | − | 0.236724i | \(-0.923926\pi\) |
−0.723048 | + | 0.690797i | \(0.757260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.30400 | + | 7.25638i | 0.542253 | + | 0.914219i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.81690 | − | 1.04899i | −0.225359 | − | 0.130111i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8958 | + | 3.45542i | 1.57547 | + | 0.422146i | 0.937520 | − | 0.347930i | \(-0.113115\pi\) |
0.637952 | + | 0.770077i | \(0.279782\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.86486 | − | 8.54175i | 0.585660 | − | 1.02831i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.21910i | − | 0.856749i | −0.903601 | − | 0.428375i | \(-0.859086\pi\) | ||
0.903601 | − | 0.428375i | \(-0.140914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.75535i | 0.439531i | 0.975553 | + | 0.219765i | \(0.0705292\pi\) | ||||
−0.975553 | + | 0.219765i | \(0.929471\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.86731 | − | 0.0168548i | 0.331088 | − | 0.00194622i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.2956 | + | 4.36638i | 1.85705 | + | 0.497596i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.96345 | − | 1.71095i | −0.333415 | − | 0.192497i | 0.323942 | − | 0.946077i | \(-0.394992\pi\) |
−0.657356 | + | 0.753580i | \(0.728325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.68200 | − | 7.68628i | −0.520223 | − | 0.854031i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.15222 | + | 0.308735i | −0.126472 | + | 0.0338881i | −0.321500 | − | 0.946910i | \(-0.604187\pi\) |
0.195028 | + | 0.980798i | \(0.437520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.23544 | + | 0.331036i | 0.134003 | + | 0.0359059i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.91004 | + | 6.82927i | 0.740834 | + | 0.732175i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.391835 | −0.0415344 | −0.0207672 | − | 0.999784i | \(-0.506611\pi\) | ||||
−0.0207672 | + | 0.999784i | \(0.506611\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.28126 | + | 2.28126i | 0.239141 | + | 0.239141i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.10265 | + | 8.95925i | −0.529120 | + | 0.929031i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.60547 | − | 4.51280i | −0.267315 | − | 0.463004i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.875387 | + | 1.51622i | −0.0888821 | + | 0.153948i | −0.907039 | − | 0.421047i | \(-0.861663\pi\) |
0.818157 | + | 0.574995i | \(0.194996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.4369 | − | 4.45318i | −1.75248 | − | 0.447561i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.816427 | + | 0.218761i | −0.0812375 | + | 0.0217675i | −0.299209 | − | 0.954188i | \(-0.596723\pi\) |
0.217971 | + | 0.975955i | \(0.430056\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.30341 | + | 9.18577i | 0.522560 | + | 0.905101i | 0.999655 | + | 0.0262492i | \(0.00835635\pi\) |
−0.477095 | + | 0.878852i | \(0.658310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.61796 | + | 2.25496i | 0.841026 | + | 0.220062i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.39894 | + | 6.39894i | −0.618609 | + | 0.618609i | −0.945174 | − | 0.326566i | \(-0.894109\pi\) |
0.326566 | + | 0.945174i | \(0.394109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.52592 | + | 1.52592i | 0.146157 | + | 0.146157i | 0.776399 | − | 0.630242i | \(-0.217044\pi\) |
−0.630242 | + | 0.776399i | \(0.717044\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.16083 | − | 8.25820i | 0.205097 | − | 0.783834i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.75213 | − | 3.32099i | 0.541115 | − | 0.312413i | −0.204416 | − | 0.978884i | \(-0.565529\pi\) |
0.745531 | + | 0.666471i | \(0.232196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.68630 | − | 10.0254i | −0.250499 | − | 0.934876i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.46199 | − | 2.40477i | −0.227611 | − | 0.222321i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.70333 | − | 0.983418i | −0.156144 | − | 0.0901498i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.6389 | + | 12.4932i | −1.96717 | + | 1.13575i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.69574 | − | 2.67441i | −0.423400 | − | 0.241143i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.60659 | − | 8.60659i | 0.769797 | − | 0.769797i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8224i | 1.22654i | 0.789874 | + | 0.613270i | \(0.210146\pi\) | ||||
−0.789874 | + | 0.613270i | \(0.789854\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.94395 | + | 9.04972i | −0.787471 | + | 0.796784i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.40595 | + | 8.97914i | −0.210209 | + | 0.784511i | 0.777589 | + | 0.628773i | \(0.216442\pi\) |
−0.987798 | + | 0.155739i | \(0.950224\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.07396 | + | 7.74013i | 0.179835 | + | 0.671154i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.22090 | − | 2.29725i | −0.793608 | − | 0.197716i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.96603 | + | 10.3335i | −0.509712 | + | 0.882848i | 0.490224 | + | 0.871596i | \(0.336915\pi\) |
−0.999937 | + | 0.0112514i | \(0.996419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.323448 | − | 1.20712i | 0.0274345 | − | 0.102387i | −0.950851 | − | 0.309649i | \(-0.899789\pi\) |
0.978286 | + | 0.207262i | \(0.0664552\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0577550 | + | 9.82521i | 0.00486385 | + | 0.827432i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.88181 | −0.575486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.2580 | 0.851884 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.36786 | − | 0.779052i | −0.112819 | − | 0.0642551i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.930902 | + | 3.47417i | −0.0762625 | + | 0.284615i | −0.993517 | − | 0.113687i | \(-0.963734\pi\) |
0.917254 | + | 0.398302i | \(0.130401\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.43126 | − | 9.40721i | 0.441989 | − | 0.765548i | −0.555848 | − | 0.831284i | \(-0.687606\pi\) |
0.997837 | + | 0.0657361i | \(0.0209395\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.82924 | + | 1.02763i | 0.147886 | + | 0.0830792i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.81761 | + | 10.5155i | 0.226316 | + | 0.844621i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.55352 | − | 9.52986i | 0.203793 | − | 0.760565i | −0.786021 | − | 0.618199i | \(-0.787862\pi\) |
0.989814 | − | 0.142366i | \(-0.0454709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.5596 | + | 2.76300i | 0.837428 | + | 0.219120i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.9606i | 1.25787i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.66703 | − | 3.66703i | 0.287224 | − | 0.287224i | −0.548758 | − | 0.835981i | \(-0.684899\pi\) |
0.835981 | + | 0.548758i | \(0.184899\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.4000 | + | 9.59752i | −1.27674 | + | 0.747166i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4253 | − | 10.0605i | 1.34841 | − | 0.778505i | 0.360385 | − | 0.932803i | \(-0.382645\pi\) |
0.988024 | + | 0.154299i | \(0.0493118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1186 | + | 5.84198i | 0.778355 | + | 0.449383i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.30932 | − | 8.23025i | −0.176598 | − | 0.629383i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.70826 | − | 10.1074i | −0.205906 | − | 0.768450i | −0.989172 | − | 0.146763i | \(-0.953114\pi\) |
0.783266 | − | 0.621687i | \(-0.213552\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.03189 | + | 2.32781i | −0.304782 | + | 0.175966i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.6169 | − | 6.47717i | 1.77516 | − | 0.486854i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.4542 | + | 12.4542i | 0.930872 | + | 0.930872i | 0.997760 | − | 0.0668885i | \(-0.0213072\pi\) |
−0.0668885 | + | 0.997760i | \(0.521307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.12083 | + | 9.12083i | −0.677946 | + | 0.677946i | −0.959535 | − | 0.281589i | \(-0.909139\pi\) |
0.281589 | + | 0.959535i | \(0.409139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.6829 | + | 16.8802i | −1.23324 | + | 1.24782i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.50653 | − | 7.80554i | −0.331327 | − | 0.573875i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.05252 | − | 1.08587i | 0.296349 | − | 0.0794066i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.7821 | + | 7.08219i | 0.929759 | + | 0.515153i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.76985 | − | 3.06547i | 0.128062 | − | 0.221810i | −0.794864 | − | 0.606788i | \(-0.792458\pi\) |
0.922926 | + | 0.384978i | \(0.125791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.43004 | + | 12.8692i | 0.534826 | + | 0.926346i | 0.999172 | + | 0.0406916i | \(0.0129561\pi\) |
−0.464346 | + | 0.885654i | \(0.653711\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.63374 | + | 0.0213600i | −0.260218 | + | 0.00152962i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9105 | − | 11.9105i | −0.848589 | − | 0.848589i | 0.141368 | − | 0.989957i | \(-0.454850\pi\) |
−0.989957 | + | 0.141368i | \(0.954850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.5983 | −1.10574 | −0.552868 | − | 0.833269i | \(-0.686467\pi\) | ||||
−0.552868 | + | 0.833269i | \(0.686467\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.3006 | − | 6.11615i | 1.57296 | − | 0.431400i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.2369 | − | 4.08272i | −1.06942 | − | 0.286551i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.51137 | + | 1.47677i | −0.384931 | + | 0.103142i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.200159 | − | 17.0248i | −0.0139120 | − | 1.18331i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.8029 | − | 8.54648i | −1.02394 | − | 0.591172i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.6018 | − | 4.18049i | −1.07407 | − | 0.287797i | −0.321907 | − | 0.946771i | \(-0.604324\pi\) |
−0.752165 | + | 0.658975i | \(0.770990\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.31547 | − | 10.7917i | −0.432729 | − | 0.739436i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4344i | 0.916220i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.7407i | − | 1.13643i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.28529 | + | 5.61381i | 0.221999 | + | 0.379346i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.774977 | + | 0.207655i | 0.0521306 | + | 0.0139684i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9254 | + | 8.03982i | 0.932512 | + | 0.538386i | 0.887605 | − | 0.460605i | \(-0.152368\pi\) |
0.0449068 | + | 0.998991i | \(0.485701\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.27155 | − | 2.53360i | 0.284770 | − | 0.168907i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.6697 | + | 2.85895i | −0.708176 | + | 0.189755i | −0.594890 | − | 0.803807i | \(-0.702804\pi\) |
−0.113286 | + | 0.993562i | \(0.536138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.390566 | − | 0.104652i | −0.0258093 | − | 0.00691559i | 0.245891 | − | 0.969297i | \(-0.420919\pi\) |
−0.271701 | + | 0.962382i | \(0.587586\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28.1798 | − | 7.72858i | 1.85409 | − | 0.508503i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.6252 | −0.761590 | −0.380795 | − | 0.924659i | \(-0.624350\pi\) | ||||
−0.380795 | + | 0.924659i | \(0.624350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.33569 | + | 7.33569i | 0.478528 | + | 0.478528i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.92680 | + | 0.0348392i | −0.384987 | + | 0.00226305i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.55685 | − | 2.69654i | −0.100704 | − | 0.174425i | 0.811271 | − | 0.584671i | \(-0.198776\pi\) |
−0.911975 | + | 0.410246i | \(0.865443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.16669 | + | 12.4131i | −0.461647 | + | 0.799596i | −0.999043 | − | 0.0437337i | \(-0.986075\pi\) |
0.537396 | + | 0.843330i | \(0.319408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.7232 | − | 7.39414i | −0.880345 | − | 0.474334i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.60546 | + | 0.430181i | −0.102569 | + | 0.0274833i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.63437 | − | 2.83082i | −0.103993 | − | 0.180121i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.45234 | + | 1.46951i | −0.0920382 | + | 0.0931266i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.06176 | − | 3.06176i | 0.193257 | − | 0.193257i | −0.603845 | − | 0.797102i | \(-0.706365\pi\) |
0.797102 | + | 0.603845i | \(0.206365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.0739 | − | 24.0739i | −1.51351 | − | 1.51351i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.13645 | − | 0.585940i | 0.133789 | − | 0.0366930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.78074 | − | 1.60546i | 0.173458 | − | 0.100146i | −0.410757 | − | 0.911745i | \(-0.634736\pi\) |
0.584215 | + | 0.811599i | \(0.301402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.58722 | + | 13.3877i | 0.222899 | + | 0.831870i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.3041 | + | 4.16388i | 1.00920 | + | 0.257737i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.63762 | − | 1.52283i | −0.162643 | − | 0.0939018i | 0.416469 | − | 0.909150i | \(-0.363267\pi\) |
−0.579112 | + | 0.815248i | \(0.696601\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.98076 | − | 5.76240i | 0.613113 | − | 0.353981i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.585748 | + | 0.342788i | −0.0358472 | + | 0.0209783i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.99648 | − | 1.99648i | 0.121727 | − | 0.121727i | −0.643619 | − | 0.765346i | \(-0.722568\pi\) |
0.765346 | + | 0.643619i | \(0.222568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.9357i | − | 0.846534i | −0.906005 | − | 0.423267i | \(-0.860883\pi\) | ||
0.906005 | − | 0.423267i | \(-0.139117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.40593 | + | 1.41451i | 0.327182 | + | 0.0856099i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.57032 | − | 9.59256i | 0.154996 | − | 0.578453i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.09885 | − | 30.2253i | −0.486613 | − | 1.81606i | −0.572686 | − | 0.819774i | \(-0.694099\pi\) |
0.0860738 | − | 0.996289i | \(-0.472568\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.209943 | + | 17.8570i | 0.0125689 | + | 1.06907i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.3745 | − | 19.7012i | 0.678544 | − | 1.17527i | −0.296875 | − | 0.954916i | \(-0.595944\pi\) |
0.975419 | − | 0.220357i | \(-0.0707222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.633463 | + | 2.36412i | −0.0376555 | + | 0.140532i | −0.982194 | − | 0.187867i | \(-0.939843\pi\) |
0.944539 | + | 0.328399i | \(0.106509\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.84279 | − | 4.46678i | −0.464567 | − | 0.264589i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.77415 | 0.517921 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5109 | 0.971228 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0178251 | + | 3.03238i | 0.00104492 | + | 0.177761i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.01774 | − | 7.53030i | 0.117877 | − | 0.439925i | −0.881609 | − | 0.471981i | \(-0.843539\pi\) |
0.999486 | + | 0.0320565i | \(0.0102057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.9285 | − | 22.3929i | 0.752728 | − | 1.30376i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −29.9620 | + | 8.59733i | −1.73857 | + | 0.498868i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.68508 | − | 6.28881i | −0.0974508 | − | 0.363691i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.34693 | − | 19.9550i | 0.308192 | − | 1.15019i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.02908 | + | 1.04125i | −0.0591194 | + | 0.0598185i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.0589i | 1.43487i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0831 | − | 24.0831i | 1.37450 | − | 1.37450i | 0.520843 | − | 0.853652i | \(-0.325618\pi\) |
0.853652 | − | 0.520843i | \(-0.174382\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.9639 | + | 9.09209i | 0.908157 | + | 0.517231i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.09165 | + | 5.24907i | −0.515540 | + | 0.297647i | −0.735108 | − | 0.677950i | \(-0.762869\pi\) |
0.219568 | + | 0.975597i | \(0.429535\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1380 | + | 11.0493i | 1.08174 | + | 0.624544i | 0.931366 | − | 0.364085i | \(-0.118618\pi\) |
0.150376 | + | 0.988629i | \(0.451952\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.8555 | − | 4.16832i | 0.837015 | − | 0.234858i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.71597 | − | 21.3323i | −0.321041 | − | 1.19814i | −0.918232 | − | 0.396042i | \(-0.870383\pi\) |
0.597192 | − | 0.802099i | \(-0.296283\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.1405 | − | 16.8243i | 1.63155 | − | 0.941978i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.96770 | + | 15.1636i | −0.221455 | + | 0.846352i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.40911 | + | 1.40911i | 0.0784050 | + | 0.0784050i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.34289 | − | 1.34289i | 0.0744900 | − | 0.0744900i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.61599 | + | 0.946157i | 0.199965 | + | 0.0523226i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.97655 | − | 13.8158i | −0.439761 | − | 0.761689i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.16734 | + | 0.848686i | −0.174093 | + | 0.0466480i | −0.344812 | − | 0.938672i | \(-0.612057\pi\) |
0.170720 | + | 0.985320i | \(0.445391\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.99431 | − | 14.2354i | −0.218887 | − | 0.780095i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.2079 | − | 21.1447i | 0.666990 | − | 1.15526i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5710 | − | 20.0416i | −0.630315 | − | 1.09174i | −0.987487 | − | 0.157699i | \(-0.949593\pi\) |
0.357172 | − | 0.934038i | \(-0.383741\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.69347 | − | 9.99662i | 0.309227 | − | 0.542942i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.2506 | + | 25.2506i | 1.36739 | + | 1.36739i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.1300 | −0.924931 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.7862 | − | 12.6368i | −0.688388 | − | 0.680342i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.59002 | − | 2.03374i | −0.407454 | − | 0.109177i | 0.0492700 | − | 0.998785i | \(-0.484311\pi\) |
−0.456724 | + | 0.889609i | \(0.650977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9793 | − | 5.62138i | 1.12299 | − | 0.300905i | 0.350900 | − | 0.936413i | \(-0.385876\pi\) |
0.772095 | + | 0.635508i | \(0.219209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.78414 | − | 1.44103i | −0.308735 | − | 0.0769168i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.108858 | − | 0.0628489i | −0.00579390 | − | 0.00334511i | 0.497100 | − | 0.867693i | \(-0.334398\pi\) |
−0.502894 | + | 0.864348i | \(0.667731\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7525 | − | 3.41701i | −0.676831 | − | 0.181356i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.40660 | + | 0.0200249i | −0.180297 | + | 0.00105983i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.07414i | 0.215025i | 0.994204 | + | 0.107512i | \(0.0342886\pi\) | ||||
−0.994204 | + | 0.107512i | \(0.965711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8811i | 0.572691i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.4182 | + | 37.6062i | −1.12416 | + | 1.97381i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.63379 | + | 1.77752i | 0.347229 | + | 0.0930396i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.96310 | − | 2.86545i | −0.259072 | − | 0.149575i | 0.364839 | − | 0.931071i | \(-0.381124\pi\) |
−0.623911 | + | 0.781495i | \(0.714457\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.35922 | + | 0.110035i | −0.487222 | + | 0.00572822i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.1185 | + | 4.58689i | −0.888748 | + | 0.238139i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.7409 | + | 5.28955i | 1.02214 | + | 0.273882i | 0.730695 | − | 0.682704i | \(-0.239196\pi\) |
0.291448 | + | 0.956587i | \(0.405863\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.33657 | − | 20.3951i | 0.275579 | − | 1.05320i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.43473 | 0.331405 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.85273 | + | 2.85273i | 0.146535 | + | 0.146535i | 0.776568 | − | 0.630033i | \(-0.216959\pi\) |
−0.630033 | + | 0.776568i | \(0.716959\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0922 | + | 20.6629i | 0.619503 | + | 1.05859i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.78731 | − | 13.4880i | −0.397913 | − | 0.689206i | 0.595555 | − | 0.803314i | \(-0.296932\pi\) |
−0.993468 | + | 0.114109i | \(0.963599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.4263 | − | 26.7192i | 0.786200 | − | 1.36174i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.45322 | + | 21.3527i | −0.277203 | + | 1.08542i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.9587 | + | 7.22357i | −1.36686 | + | 0.366250i | −0.866332 | − | 0.499469i | \(-0.833529\pi\) |
−0.500531 | + | 0.865719i | \(0.666862\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.98460 | + | 3.43743i | 0.100366 | + | 0.173838i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.25858 | + | 15.5276i | 0.214817 | + | 0.783262i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.42507 | + | 4.42507i | −0.222649 | + | 0.222649i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.4204 | + | 27.4204i | 1.37619 | + | 1.37619i | 0.850961 | + | 0.525230i | \(0.176021\pi\) |
0.525230 | + | 0.850961i | \(0.323979\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.87161 | + | 9.75623i | 0.494199 | + | 0.488423i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.6316 | + | 8.44757i | −0.730669 | + | 0.421852i | −0.818667 | − | 0.574269i | \(-0.805286\pi\) |
0.0879981 | + | 0.996121i | \(0.471953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.76745 | + | 6.59620i | 0.0880428 | + | 0.328580i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.7939 | + | 4.63257i | −0.784803 | + | 0.230194i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.6038 | − | 14.7824i | −1.26913 | − | 0.732735i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.9737 | + | 8.64508i | −0.740402 | + | 0.427471i | −0.822216 | − | 0.569176i | \(-0.807262\pi\) |
0.0818133 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.121483 | + | 20.6666i | 0.00599233 | + | 1.01941i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.1160 | + | 28.1160i | −1.38350 | + | 1.38350i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.18151i | 0.107086i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.572508 | − | 2.08747i | −0.0280359 | − | 0.102224i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.788205 | + | 2.94162i | −0.0385063 | + | 0.143708i | −0.982503 | − | 0.186248i | \(-0.940367\pi\) |
0.943996 | + | 0.329956i | \(0.107034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.38357 | − | 8.89561i | −0.116168 | − | 0.433546i | 0.883203 | − | 0.468990i | \(-0.155382\pi\) |
−0.999372 | + | 0.0354445i | \(0.988715\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.68170 | + | 14.6370i | 0.422119 | + | 0.711676i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.578900 | + | 1.00268i | −0.0280808 | + | 0.0486373i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.97350 | − | 37.2216i | 0.482651 | − | 1.80128i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.2875 | + | 6.02040i | −0.496685 | + | 0.290667i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.28002 | −0.350666 | −0.175333 | − | 0.984509i | \(-0.556100\pi\) | ||||
−0.175333 | + | 0.984509i | \(0.556100\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.9763 | −0.960002 | −0.480001 | − | 0.877268i | \(-0.659364\pi\) | ||||
−0.480001 | + | 0.877268i | \(0.659364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.3346 | − | 8.97401i | 0.735236 | − | 0.430271i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.18539 | − | 15.6201i | 0.200214 | − | 0.747210i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3133 | + | 26.5235i | −0.730866 | + | 1.26590i | 0.225647 | + | 0.974209i | \(0.427550\pi\) |
−0.956513 | + | 0.291688i | \(0.905783\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.72633 | + | 0.0320532i | −0.129825 | + | 0.00152634i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.70884 | − | 28.7698i | −0.366258 | − | 1.36689i | −0.865708 | − | 0.500550i | \(-0.833131\pi\) |
0.499450 | − | 0.866343i | \(-0.333536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.185467 | + | 0.692173i | −0.00879199 | + | 0.0328121i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.64771 | + | 6.00786i | 0.0779342 | + | 0.284162i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.8028i | − | 1.26490i | −0.774599 | − | 0.632452i | \(-0.782048\pi\) | ||
0.774599 | − | 0.632452i | \(-0.217952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.2344 | + | 13.2344i | −0.623181 | + | 0.623181i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.110594 | − | 18.8141i | −0.00519616 | − | 0.883964i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.10961 | − | 2.95004i | 0.239542 | − | 0.138300i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.25342 | − | 1.87837i | −0.152189 | − | 0.0878662i | 0.421972 | − | 0.906609i | \(-0.361338\pi\) |
−0.574161 | + | 0.818743i | \(0.694671\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.63351 | − | 0.0640819i | 0.169598 | − | 0.00299109i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.05208 | + | 3.92641i | 0.0490002 | + | 0.182871i | 0.986088 | − | 0.166221i | \(-0.0531566\pi\) |
−0.937088 | + | 0.349092i | \(0.886490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.2888 | + | 11.7137i | −0.942899 | + | 0.544383i | −0.890868 | − | 0.454263i | \(-0.849903\pi\) |
−0.0520310 | + | 0.998645i | \(0.516569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.4112 | + | 13.2545i | 0.621930 | + | 0.614661i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.2570 | − | 13.2570i | −0.613463 | − | 0.613463i | 0.330384 | − | 0.943847i | \(-0.392822\pi\) |
−0.943847 | + | 0.330384i | \(0.892822\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.5489 | + | 26.5489i | −1.22591 | + | 1.22591i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.51977 | − | 16.4799i | −0.208260 | − | 0.759354i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.0339 | + | 38.1638i | 1.01312 | + | 1.75477i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.55631 | − | 1.22086i | 0.209058 | − | 0.0560169i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.2025 | − | 5.10743i | 0.833434 | − | 0.233853i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.6429 | + | 30.5584i | −0.806124 | + | 1.39625i | 0.109405 | + | 0.993997i | \(0.465105\pi\) |
−0.915529 | + | 0.402251i | \(0.868228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.82689 | − | 4.89631i | −0.128895 | − | 0.223252i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.9627 | + | 23.8592i | 0.635326 | + | 1.08563i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.26403 | + | 2.26403i | 0.102804 | + | 0.102804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1433 | 0.550266 | 0.275133 | − | 0.961406i | \(-0.411278\pi\) | ||||
0.275133 | + | 0.961406i | \(0.411278\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.27376 | − | 8.68979i | 0.102823 | − | 0.392966i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.746514 | + | 0.200028i | 0.0336897 | + | 0.00902713i | 0.275625 | − | 0.961265i | \(-0.411115\pi\) |
−0.241935 | + | 0.970293i | \(0.577782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.78924 | + | 1.01532i | −0.170659 | + | 0.0457279i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.1199 | + | 28.6944i | −0.724537 | + | 1.28972i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.5821 | + | 10.1510i | 0.788664 | + | 0.455335i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.785369 | − | 0.210439i | −0.0351579 | − | 0.00942054i | 0.241197 | − | 0.970476i | \(-0.422460\pi\) |
−0.276355 | + | 0.961056i | \(0.589127\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.2476 | − | 30.2834i | 0.770565 | − | 1.35296i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.40486i | 0.240991i | 0.992714 | + | 0.120495i | \(0.0384483\pi\) | ||||
−0.992714 | + | 0.120495i | \(0.961552\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.54576i | 0.0687852i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.2369 | − | 0.118957i | 0.898751 | − | 0.00528308i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.7030 | − | 7.42301i | −1.22792 | − | 0.329019i | −0.414148 | − | 0.910210i | \(-0.635920\pi\) |
−0.813768 | + | 0.581191i | \(0.802587\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.14614 | − | 5.28052i | −0.404601 | − | 0.233597i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.6522 | − | 10.2830i | −0.470307 | − | 0.454005i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.7368 | − | 5.02052i | 0.825644 | − | 0.221231i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.8701 | + | 8.80753i | 1.44563 | + | 0.387355i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.8908 | − | 12.7401i | −0.565841 | − | 0.559228i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.8208 | −0.561689 | −0.280845 | − | 0.959753i | \(-0.590615\pi\) | ||||
−0.280845 | + | 0.959753i | \(0.590615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.08204 | + | 2.08204i | 0.0910411 | + | 0.0910411i | 0.751161 | − | 0.660120i | \(-0.229494\pi\) |
−0.660120 | + | 0.751161i | \(0.729494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.99077 | + | 7.00701i | −0.174171 | + | 0.305811i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.08161 | − | 3.60545i | −0.0906762 | − | 0.157056i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.60471 | − | 7.97560i | 0.200205 | − | 0.346765i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.6382 | − | 30.3434i | 1.28619 | − | 1.31679i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.45721 | + | 0.926356i | −0.149748 | + | 0.0401249i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.27485 | + | 14.3325i | 0.357753 | + | 0.619647i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.5129 | + | 7.72231i | 1.27358 | + | 0.333242i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.85515 | + | 3.85515i | −0.166053 | + | 0.166053i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.7002 | + | 22.7002i | 0.975956 | + | 0.975956i | 0.999718 | − | 0.0237613i | \(-0.00756417\pi\) |
−0.0237613 | + | 0.999718i | \(0.507564\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.65542 | + | 21.6137i | −0.242697 | + | 0.927534i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.41779 | − | 1.97326i | 0.146402 | − | 0.0845253i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.33444 | + | 19.9084i | 0.228084 | + | 0.851222i | 0.981145 | + | 0.193271i | \(0.0619098\pi\) |
−0.753061 | + | 0.657951i | \(0.771424\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.1718 | + | 39.8287i | −0.434120 | + | 1.69985i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.8413 | + | 7.99125i | 0.589657 | + | 0.340439i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.33402 | − | 4.81165i | 0.354399 | − | 0.204612i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.5652 | − | 7.72594i | −0.575813 | − | 0.327948i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.7551 | + | 10.7551i | −0.455708 | + | 0.455708i | −0.897244 | − | 0.441535i | \(-0.854434\pi\) |
0.441535 | + | 0.897244i | \(0.354434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.42723i | 0.356434i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.10809 | − | 5.16850i | 0.215664 | − | 0.218214i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.56420 | − | 20.7659i | 0.234503 | − | 0.875177i | −0.743869 | − | 0.668325i | \(-0.767012\pi\) |
0.978372 | − | 0.206852i | \(-0.0663218\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.14385 | − | 11.7330i | −0.132263 | − | 0.493611i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.3034 | − | 0.595062i | 1.06264 | − | 0.0249902i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.88272 | − | 3.26097i | 0.0789277 | − | 0.136707i | −0.823860 | − | 0.566794i | \(-0.808184\pi\) |
0.902788 | + | 0.430087i | \(0.141517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.37466 | − | 16.3264i | 0.183074 | − | 0.683241i | −0.811961 | − | 0.583712i | \(-0.801600\pi\) |
0.995035 | − | 0.0995287i | \(-0.0317335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.0360386 | − | 6.13083i | −0.00150553 | − | 0.256119i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.39535 | 0.391813 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.76787 | −0.406642 | −0.203321 | − | 0.979112i | \(-0.565173\pi\) | ||||
−0.203321 | + | 0.979112i | \(0.565173\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.3654 | + | 12.7380i | 0.929473 | + | 0.529371i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.868246 | − | 3.24034i | 0.0360209 | − | 0.134432i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.9019 | − | 32.7390i | 0.782835 | − | 1.35591i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.41333 | + | 3.21083i | −0.223814 | + | 0.132751i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.94132 | + | 22.1733i | 0.245224 | + | 0.915190i | 0.973271 | + | 0.229662i | \(0.0737620\pi\) |
−0.728046 | + | 0.685528i | \(0.759571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.38996 | + | 16.3836i | −0.180885 | + | 0.675073i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.2245 | − | 7.38518i | −1.16100 | − | 0.303786i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.37926i | − | 0.0566394i | −0.999599 | − | 0.0283197i | \(-0.990984\pi\) | ||
0.999599 | − | 0.0283197i | \(-0.00901564\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.54344 | + | 2.54344i | −0.104271 | + | 0.104271i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.3177 | + | 13.6459i | −0.954330 | + | 0.558488i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6820 | + | 15.4049i | −1.09020 | + | 0.629425i | −0.933629 | − | 0.358242i | \(-0.883376\pi\) |
−0.156568 | + | 0.987667i | \(0.550043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.43951 | + | 1.40845i | 0.0995098 | + | 0.0574520i | 0.548929 | − | 0.835869i | \(-0.315036\pi\) |
−0.449419 | + | 0.893321i | \(0.648369\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.9862 | − | 28.6521i | 1.13969 | − | 1.16680i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.8268 | + | 44.1382i | 0.480828 | + | 1.79447i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.2297 | + | 15.1437i | −1.06463 | + | 0.614666i | −0.926710 | − | 0.375777i | \(-0.877376\pi\) |
−0.137922 | + | 0.990443i | \(0.544042\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −26.3491 | + | 7.22648i | −1.06772 | + | 0.292832i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.60158 | + | 4.60158i | 0.186160 | + | 0.186160i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.66344 | − | 3.66344i | 0.147965 | − | 0.147965i | −0.629243 | − | 0.777208i | \(-0.716635\pi\) |
0.777208 | + | 0.629243i | \(0.216635\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.94694 | + | 7.02910i | −0.280128 | + | 0.283441i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2053 | − | 22.8722i | −0.531624 | − | 0.920799i | −0.999319 | − | 0.0369091i | \(-0.988249\pi\) |
0.467695 | − | 0.883890i | \(-0.345085\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.2262 | + | 12.6542i | −1.89818 | + | 0.508617i | −0.900981 | + | 0.433858i | \(0.857152\pi\) |
−0.997202 | + | 0.0747583i | \(0.976181\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.1930 | − | 25.2750i | −0.609674 | − | 1.01425i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.550972 | − | 0.954312i | 0.0220742 | − | 0.0382337i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.99103 | − | 12.1088i | −0.279641 | − | 0.484353i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29.6054 | + | 0.174028i | −1.18232 | + | 0.00695000i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.43726 | + | 2.43726i | 0.0971799 | + | 0.0971799i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.5500 | 1.45503 | 0.727516 | − | 0.686090i | \(-0.240675\pi\) | ||||
0.727516 | + | 0.686090i | \(0.240675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.9801 | + | 7.39954i | −1.07236 | + | 0.294105i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.4171 | + | 6.54255i | 0.968964 | + | 0.259633i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00708 | + | 0.269847i | −0.0399020 | + | 0.0106917i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.8818 | − | 10.6074i | −0.746952 | − | 0.419623i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.95425 | − | 3.43769i | −0.235179 | − | 0.135780i | 0.377780 | − | 0.925895i | \(-0.376688\pi\) |
−0.612959 | + | 0.790115i | \(0.710021\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.3564 | − | 7.59808i | −1.11827 | − | 0.299639i | −0.348086 | − | 0.937463i | \(-0.613168\pi\) |
−0.770183 | + | 0.637823i | \(0.779835\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.7528 | + | 20.0829i | 0.462766 | + | 0.790764i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.90726i | − | 0.0749821i | −0.999297 | − | 0.0374911i | \(-0.988063\pi\) | ||
0.999297 | − | 0.0374911i | \(-0.0119366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 84.8166i | − | 3.32934i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.6452 | − | 25.0254i | −0.573991 | − | 0.980821i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.1710 | − | 5.94070i | −0.867618 | − | 0.232478i | −0.202560 | − | 0.979270i | \(-0.564926\pi\) |
−0.665057 | + | 0.746792i | \(0.731593\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.7228 | + | 8.50019i | 0.575266 | + | 0.332130i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.82224 | + | 5.51794i | 0.383202 | + | 0.215275i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.4059 | − | 3.86006i | 0.561175 | − | 0.150366i | 0.0329291 | − | 0.999458i | \(-0.489516\pi\) |
0.528246 | + | 0.849091i | \(0.322850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.4336 | − | 9.76236i | −1.41710 | − | 0.379712i | −0.532648 | − | 0.846337i | \(-0.678803\pi\) |
−0.884455 | + | 0.466625i | \(0.845470\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.34016 | − | 0.367552i | 0.0520476 | − | 0.0142745i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.6545 | 0.568278 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.5099 | + | 22.5099i | 0.871586 | + | 0.871586i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.8503 | − | 0.163711i | 1.07675 | − | 0.00632943i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.0993 | + | 71.1860i | 1.58662 | + | 2.74811i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2966 | + | 19.5664i | −0.435454 | + | 0.754228i | −0.997333 | − | 0.0729916i | \(-0.976745\pi\) |
0.561879 | + | 0.827220i | \(0.310079\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.16901 | − | 7.52430i | 0.160465 | − | 0.289611i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.3860 | − | 8.14191i | 1.16783 | − | 0.312919i | 0.377741 | − | 0.925911i | \(-0.376701\pi\) |
0.790089 | + | 0.612992i | \(0.210034\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.46182 | − | 4.26400i | −0.0944760 | − | 0.163637i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.4489 | + | 13.6080i | −0.515365 | + | 0.521459i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.1502 | − | 24.1502i | 0.924081 | − | 0.924081i | −0.0732336 | − | 0.997315i | \(-0.523332\pi\) |
0.997315 | + | 0.0732336i | \(0.0233319\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4301 | + | 15.4301i | 0.589553 | + | 0.589553i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.675403 | + | 0.185236i | −0.0257682 | + | 0.00706718i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.26079 | − | 3.61467i | 0.238517 | − | 0.137708i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.7138 | + | 39.9843i | 0.407571 | + | 1.52108i | 0.799264 | + | 0.600980i | \(0.205223\pi\) |
−0.391693 | + | 0.920096i | \(0.628111\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 35.3643 | − | 36.2058i | 1.34338 | − | 1.37534i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.97928 | − | 1.14273i | −0.0750782 | − | 0.0433464i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.88969 | − | 1.09101i | 0.0715772 | − | 0.0413251i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.3783 | + | 10.1700i | −0.657307 | + | 0.384666i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.1814 | − | 21.1814i | 0.800009 | − | 0.800009i | −0.183088 | − | 0.983097i | \(-0.558609\pi\) |
0.983097 | + | 0.183088i | \(0.0586092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 14.0428i | − | 0.529633i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.3835 | + | 4.54854i | 0.654699 | + | 0.171308i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.615214 | − | 2.29601i | 0.0231375 | − | 0.0863503i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.24787 | + | 15.8532i | 0.159532 | + | 0.595381i | 0.998675 | + | 0.0514698i | \(0.0163906\pi\) |
−0.839143 | + | 0.543911i | \(0.816943\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.82940 | + | 5.23701i | −0.331128 | + | 0.196403i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.8919 | + | 29.2576i | −0.632606 | + | 1.09571i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.25736 | + | 12.1566i | −0.121819 | + | 0.454633i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.68631 | − | 2.66904i | −0.175014 | − | 0.0996771i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.3461 | −0.870664 | −0.435332 | − | 0.900270i | \(-0.643369\pi\) | ||||
−0.435332 | + | 0.900270i | \(0.643369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.8292 | −1.11090 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.145932 | + | 24.8257i | 0.00542726 | + | 0.923278i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.40334 | + | 8.96937i | −0.0892576 | + | 0.333114i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.90255 | − | 5.02736i | 0.107650 | − | 0.186454i | −0.807168 | − | 0.590322i | \(-0.799001\pi\) |
0.914818 | + | 0.403867i | \(0.132334\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9832 | + | 0.952068i | −0.999378 | + | 0.0352618i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.32972 | − | 4.96258i | −0.0491814 | − | 0.183548i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.240792 | + | 0.898647i | −0.00889384 | + | 0.0331923i | −0.970230 | − | 0.242185i | \(-0.922136\pi\) |
0.961336 | + | 0.275377i | \(0.0888027\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.02364 | + | 2.04757i | −0.0746430 | + | 0.0755257i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 80.0891i | − | 2.95012i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.91328 | + | 5.91328i | −0.217523 | + | 0.217523i | −0.807454 | − | 0.589931i | \(-0.799155\pi\) |
0.589931 | + | 0.807454i | \(0.299155\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.91968 | − | 2.80195i | −0.180729 | − | 0.102932i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.3899 | + | 11.7721i | −0.748032 | + | 0.431876i | −0.824982 | − | 0.565158i | \(-0.808815\pi\) |
0.0769504 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.69647 | + | 3.28886i | 0.208703 | + | 0.120494i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.885505 | + | 3.46730i | −0.0323989 | + | 0.126862i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.58682 | − | 24.5823i | −0.240677 | − | 0.898219i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0649 | − | 7.54301i | 0.476744 | − | 0.275248i | −0.242315 | − | 0.970198i | \(-0.577907\pi\) |
0.719059 | + | 0.694949i | \(0.244573\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.89846 | − | 7.25549i | 0.0691838 | − | 0.264405i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.0470 | − | 14.0470i | −0.511222 | − | 0.511222i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.48920 | − | 4.48920i | 0.163163 | − | 0.163163i | −0.620803 | − | 0.783966i | \(-0.713193\pi\) |
0.783966 | + | 0.620803i | \(0.213193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −57.0481 | − | 14.9271i | −2.07071 | − | 0.541821i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0628 | + | 33.0177i | 0.691025 | + | 1.19689i | 0.971502 | + | 0.237030i | \(0.0761739\pi\) |
−0.280477 | + | 0.959861i | \(0.590493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.86202 | + | 1.57072i | −0.212219 | + | 0.0568640i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.68114 | − | 2.74493i | 0.0969368 | − | 0.0992433i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.10989 | − | 14.0467i | 0.292831 | − | 0.507198i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5683 | + | 30.4291i | 0.633528 | + | 1.09730i | 0.986825 | + | 0.161791i | \(0.0517271\pi\) |
−0.353297 | + | 0.935511i | \(0.614940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.75238 | − | 4.83265i | 0.0991247 | − | 0.174044i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.4773 | − | 23.4773i | −0.844420 | − | 0.844420i | 0.145010 | − | 0.989430i | \(-0.453678\pi\) |
−0.989430 | + | 0.145010i | \(0.953678\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.85458 | −0.353987 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.0744 | + | 16.8748i | 0.612540 | + | 0.605381i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.58698 | − | 2.30087i | −0.307660 | − | 0.0824374i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.8308 | + | 11.2085i | −1.49682 | + | 0.401073i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.0155 | − | 8.03880i | 1.00119 | − | 0.287283i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.6257 | − | 9.02153i | −0.557707 | − | 0.321992i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.208763 | + | 0.0559379i | 0.00744160 | + | 0.00199397i | 0.262538 | − | 0.964922i | \(-0.415441\pi\) |
−0.255096 | + | 0.966916i | \(0.582107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.27515 | + | 0.0310087i | −0.187800 | + | 0.00110394i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.6790i | 0.664150i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7191i | 0.558202i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.87897 | − | 17.3456i | 0.350371 | − | 0.615183i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.95273 | − | 0.791183i | −0.104591 | − | 0.0280251i | 0.206144 | − | 0.978522i | \(-0.433909\pi\) |
−0.310735 | + | 0.950497i | \(0.600575\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.43583 | − | 1.98367i | −0.121551 | − | 0.0701774i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.575744 | + | 1.02486i | −0.0203429 | + | 0.0362115i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.7602 | − | 5.83064i | 0.767902 | − | 0.205759i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.1942 | + | 7.55460i | 0.993714 | + | 0.266265i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.23793 | − | 4.73107i | 0.0435771 | − | 0.166542i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.5506 | 1.49600 | 0.748000 | − | 0.663699i | \(-0.231014\pi\) | ||||
0.748000 | + | 0.663699i | \(0.231014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.1448 | − | 15.1448i | −0.531806 | − | 0.531806i | 0.389304 | − | 0.921109i | \(-0.372716\pi\) |
−0.921109 | + | 0.389304i | \(0.872716\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.1913 | − | 20.8323i | −0.427569 | − | 0.730619i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.74206 | − | 8.21348i | −0.166107 | − | 0.287706i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4657 | + | 18.1272i | −0.366150 | + | 0.634190i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.31868 | − | 2.61473i | 0.325621 | − | 0.0913660i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.6973 | − | 7.15352i | 0.931742 | − | 0.249660i | 0.239145 | − | 0.970984i | \(-0.423133\pi\) |
0.692598 | + | 0.721324i | \(0.256466\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.1921 | + | 17.6532i | 0.355273 | + | 0.615350i | 0.987165 | − | 0.159706i | \(-0.0510547\pi\) |
−0.631892 | + | 0.775057i | \(0.717721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.54951 | − | 16.5883i | −0.158394 | − | 0.577532i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.34698 | + | 8.34698i | −0.290253 | + | 0.290253i | −0.837180 | − | 0.546927i | \(-0.815797\pi\) |
0.546927 | + | 0.837180i | \(0.315797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.48126 | − | 2.48126i | −0.0861778 | − | 0.0861778i | 0.662704 | − | 0.748882i | \(-0.269409\pi\) |
−0.748882 | + | 0.662704i | \(0.769409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.5488 | − | 38.0982i | −1.33724 | − | 1.32161i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.550465 | − | 0.317811i | 0.0190725 | − | 0.0110115i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.52386 | − | 35.5435i | −0.329587 | − | 1.23004i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.9356 | + | 26.5104i | 0.550815 | + | 0.916335i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.7430 | + | 10.2439i | 0.612558 | + | 0.353660i | 0.773966 | − | 0.633227i | \(-0.218270\pi\) |
−0.161408 | + | 0.986888i | \(0.551604\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.13260 | + | 1.23126i | −0.0735380 | + | 0.0424572i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.231613 | − | 39.4017i | −0.00797717 | − | 1.35707i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.1092 | − | 15.1092i | 0.519774 | − | 0.519774i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 70.2684i | − | 2.41445i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.12124 | + | 4.08825i | 0.0384809 | + | 0.140308i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.23923 | − | 27.0172i | 0.248158 | − | 0.926137i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.06296 | + | 15.1632i | 0.139113 | + | 0.519177i | 0.999947 | + | 0.0102909i | \(0.00327574\pi\) |
−0.860834 | + | 0.508886i | \(0.830058\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.6317 | + | 0.183781i | −0.534594 | + | 0.00628517i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.102894 | − | 0.178217i | 0.00351478 | − | 0.00608778i | −0.864263 | − | 0.503041i | \(-0.832215\pi\) |
0.867777 | + | 0.496953i | \(0.165548\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.733242 | − | 2.73650i | 0.0250179 | − | 0.0933681i | −0.952288 | − | 0.305201i | \(-0.901276\pi\) |
0.977306 | + | 0.211833i | \(0.0679431\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.1163 | − | 7.67587i | 0.447003 | − | 0.261593i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.9928 | 0.918846 | 0.459423 | − | 0.888218i | \(-0.348056\pi\) | ||||
0.459423 | + | 0.888218i | \(0.348056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1365 | −0.650660 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.6818 | − | 14.4442i | 0.838239 | − | 0.490550i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.31292 | + | 19.8281i | −0.180228 | + | 0.672621i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.65786 | − | 13.2638i | 0.259477 | − | 0.449427i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.67945 | + | 4.51746i | 0.0906858 | + | 0.152893i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.85929 | + | 33.0633i | 0.299499 | + | 1.11774i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9344 | + | 52.0038i | −0.470531 | + | 1.75604i | 0.167338 | + | 0.985900i | \(0.446483\pi\) |
−0.637869 | + | 0.770145i | \(0.720184\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.57143 | − | 13.0221i | −0.120461 | − | 0.439224i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.9049i | 0.940139i | 0.882629 | + | 0.470069i | \(0.155771\pi\) | ||||
−0.882629 | + | 0.470069i | \(0.844229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.83601 | + | 3.83601i | −0.129092 | + | 0.129092i | −0.768701 | − | 0.639609i | \(-0.779096\pi\) |
0.639609 | + | 0.768701i | \(0.279096\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.263257 | − | 44.7850i | −0.00884929 | − | 1.50543i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.3036 | − | 25.5787i | 1.48757 | − | 0.858849i | 0.487671 | − | 0.873028i | \(-0.337847\pi\) |
0.999899 | + | 0.0141788i | \(0.00451340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.6644 | − | 19.4361i | −1.12907 | − | 0.651867i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.2685 | + | 39.0636i | −1.24854 | + | 1.30868i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.18343 | + | 15.6128i | 0.139993 | + | 0.522462i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.8952 | − | 16.1053i | 0.932434 | − | 0.538341i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.02063 | − | 7.92688i | −0.267801 | − | 0.264671i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.6101 | − | 23.6101i | −0.787442 | − | 0.787442i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.11647 | + | 3.11647i | −0.103825 | + | 0.103825i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.46416 | − | 34.5081i | −0.314947 | − | 1.14836i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.7947 | + | 20.4290i | 0.392069 | + | 0.679084i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.99802 | − | 2.67896i | 0.331979 | − | 0.0889535i | −0.0889794 | − | 0.996033i | \(-0.528361\pi\) |
0.420958 | + | 0.907080i | \(0.361694\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.627443 | + | 2.45683i | −0.0208110 | + | 0.0814878i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.69107 | − | 9.85722i | 0.188553 | − | 0.326584i | −0.756215 | − | 0.654324i | \(-0.772953\pi\) |
0.944768 | + | 0.327739i | \(0.106287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.57791 | + | 6.19712i | 0.118411 | + | 0.205095i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.9222 | + | 37.4602i | 0.724727 | + | 1.23839i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.4856 | − | 18.4856i | −0.610447 | − | 0.610447i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.8316 | −0.390288 | −0.195144 | − | 0.980775i | \(-0.562517\pi\) | ||||
−0.195144 | + | 0.980775i | \(0.562517\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.9329 | − | 57.0700i | 0.492055 | − | 1.88052i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.99945 | − | 2.14345i | −0.263305 | − | 0.0705524i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.88080 | − | 2.11165i | 0.259119 | − | 0.0694307i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.8182 | − | 0.374084i | 1.04505 | − | 0.0122865i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.7139 | + | 20.6194i | 1.17174 | + | 0.676502i | 0.954088 | − | 0.299525i | \(-0.0968284\pi\) |
0.217647 | + | 0.976027i | \(0.430162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.50138 | − | 0.670242i | −0.0819794 | − | 0.0219663i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.99893 | + | 15.8004i | −0.294612 | + | 0.517281i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7.67271i | − | 0.250924i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.6750i | − | 0.512081i | −0.966666 | − | 0.256041i | \(-0.917582\pi\) | ||
0.966666 | − | 0.256041i | \(-0.0824181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.2753 | − | 0.224992i | 1.24907 | − | 0.00734233i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.63753 | + | 2.58237i | 0.314174 | + | 0.0841828i | 0.412461 | − | 0.910975i | \(-0.364669\pi\) |
−0.0982863 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.3345 | − | 8.85340i | −0.499361 | − | 0.288306i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.5608 | − | 19.2272i | 0.603781 | − | 0.625461i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.28712 | − | 0.612832i | 0.0743214 | − | 0.0199144i | −0.221467 | − | 0.975168i | \(-0.571084\pi\) |
0.295788 | + | 0.955254i | \(0.404418\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.16129 | + | 1.11501i | 0.135081 | + | 0.0361949i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.2068 | − | 26.8888i | −0.882240 | − | 0.871929i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.1152 | 1.39664 | 0.698320 | − | 0.715786i | \(-0.253931\pi\) | ||||
0.698320 | + | 0.715786i | \(0.253931\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.57740 | − | 4.57740i | −0.148121 | − | 0.148121i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.8433 | − | 50.6432i | 0.932371 | − | 1.63706i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.7781 | − | 29.0605i | −0.541792 | − | 0.938411i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.21754 | − | 3.84089i | 0.0715334 | − | 0.123900i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.33432 | + | 26.1389i | 0.236345 | + | 0.842315i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.2502 | − | 7.03372i | 0.845023 | − | 0.226423i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.1271 | + | 36.5932i | 0.679401 | + | 1.17676i | 0.975162 | + | 0.221495i | \(0.0710936\pi\) |
−0.295761 | + | 0.955262i | \(0.595573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.33918 | + | 0.873727i | 0.107270 | + | 0.0280682i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.0093 | + | 11.0093i | −0.353305 | + | 0.353305i | −0.861338 | − | 0.508033i | \(-0.830373\pi\) |
0.508033 | + | 0.861338i | \(0.330373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.48513 | + | 2.48513i | 0.0796697 | + | 0.0796697i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.832665 | − | 3.18226i | 0.0266666 | − | 0.101914i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.5197 | − | 17.6206i | 0.976413 | − | 0.563732i | 0.0752275 | − | 0.997166i | \(-0.476032\pi\) |
0.901185 | + | 0.433434i | \(0.142698\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.608371 | + | 2.27047i | 0.0194436 | + | 0.0725646i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.23321 | − | 1.74898i | 0.199011 | − | 0.0558406i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.9109 | + | 19.5785i | 1.08159 | + | 0.624456i | 0.931325 | − | 0.364190i | \(-0.118654\pi\) |
0.150264 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.6774 | + | 15.4022i | −0.850013 | + | 0.490755i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.0104 | − | 13.6749i | −0.764261 | − | 0.435276i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.4801 | + | 29.4801i | −0.937411 | + | 0.937411i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.1164i | 0.480188i | 0.970750 | + | 0.240094i | \(0.0771783\pi\) | ||||
−0.970750 | + | 0.240094i | \(0.922822\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.99235 | + | 4.03956i | −0.126693 | + | 0.128192i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.38315 | + | 27.5543i | −0.234062 | + | 0.873530i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3875 | − | 38.7668i | −0.328976 | − | 1.22776i | −0.910254 | − | 0.414051i | \(-0.864113\pi\) |
0.581277 | − | 0.813706i | \(-0.302553\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.4245 | − | 17.7859i | −0.582927 | − | 0.562722i |
(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 | 576.2.y.a.47.18 | 88 | ||
3.2 | odd | 2 | 1728.2.z.a.1007.6 | 88 | |||
4.3 | odd | 2 | 144.2.u.a.83.17 | yes | 88 | ||
9.4 | even | 3 | 1728.2.z.a.1583.6 | 88 | |||
9.5 | odd | 6 | inner | 576.2.y.a.239.16 | 88 | ||
12.11 | even | 2 | 432.2.v.a.35.6 | 88 | |||
16.5 | even | 4 | 144.2.u.a.11.10 | ✓ | 88 | ||
16.11 | odd | 4 | inner | 576.2.y.a.335.16 | 88 | ||
36.23 | even | 6 | 144.2.u.a.131.10 | yes | 88 | ||
36.31 | odd | 6 | 432.2.v.a.179.13 | 88 | |||
48.5 | odd | 4 | 432.2.v.a.251.13 | 88 | |||
48.11 | even | 4 | 1728.2.z.a.143.6 | 88 | |||
144.5 | odd | 12 | 144.2.u.a.59.17 | yes | 88 | ||
144.59 | even | 12 | inner | 576.2.y.a.527.18 | 88 | ||
144.85 | even | 12 | 432.2.v.a.395.6 | 88 | |||
144.139 | odd | 12 | 1728.2.z.a.719.6 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.10 | ✓ | 88 | 16.5 | even | 4 | ||
144.2.u.a.59.17 | yes | 88 | 144.5 | odd | 12 | ||
144.2.u.a.83.17 | yes | 88 | 4.3 | odd | 2 | ||
144.2.u.a.131.10 | yes | 88 | 36.23 | even | 6 | ||
432.2.v.a.35.6 | 88 | 12.11 | even | 2 | |||
432.2.v.a.179.13 | 88 | 36.31 | odd | 6 | |||
432.2.v.a.251.13 | 88 | 48.5 | odd | 4 | |||
432.2.v.a.395.6 | 88 | 144.85 | even | 12 | |||
576.2.y.a.47.18 | 88 | 1.1 | even | 1 | trivial | ||
576.2.y.a.239.16 | 88 | 9.5 | odd | 6 | inner | ||
576.2.y.a.335.16 | 88 | 16.11 | odd | 4 | inner | ||
576.2.y.a.527.18 | 88 | 144.59 | even | 12 | inner | ||
1728.2.z.a.143.6 | 88 | 48.11 | even | 4 | |||
1728.2.z.a.719.6 | 88 | 144.139 | odd | 12 | |||
1728.2.z.a.1007.6 | 88 | 3.2 | odd | 2 | |||
1728.2.z.a.1583.6 | 88 | 9.4 | even | 3 |