Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(101,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.n (of order \(6\), 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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 251.3 | ||
Root | \(-1.27597 + 0.609843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.251 |
Dual form | 325.2.n.d.101.3 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.190254 | + | 0.109843i | 0.134530 | + | 0.0776710i | 0.565755 | − | 0.824574i | \(-0.308585\pi\) |
−0.431224 | + | 0.902245i | \(0.641918\pi\) | |||||||
\(3\) | −0.800098 | + | 1.38581i | −0.461937 | + | 0.800098i | −0.999057 | − | 0.0434075i | \(-0.986179\pi\) |
0.537121 | + | 0.843505i | \(0.319512\pi\) | |||||||
\(4\) | −0.975869 | − | 1.69025i | −0.487934 | − | 0.845127i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.304444 | + | 0.175771i | −0.124289 | + | 0.0717582i | ||||
\(7\) | 0.287734 | − | 0.166123i | 0.108753 | − | 0.0627887i | −0.444637 | − | 0.895711i | \(-0.646667\pi\) |
0.553390 | + | 0.832922i | \(0.313334\pi\) | |||||||
\(8\) | − | 0.868145i | − | 0.306936i | ||||||
\(9\) | 0.219687 | + | 0.380509i | 0.0732290 | + | 0.126836i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.65213 | + | 2.68591i | 1.40267 | + | 0.809832i | 0.994666 | − | 0.103149i | \(-0.0328917\pi\) |
0.408004 | + | 0.912980i | \(0.366225\pi\) | |||||||
\(12\) | 3.12316 | 0.901579 | ||||||||
\(13\) | 3.55193 | − | 0.619491i | 0.985129 | − | 0.171816i | ||||
\(14\) | 0.0729902 | 0.0195074 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.85638 | + | 3.21534i | −0.464094 | + | 0.803835i | ||||
\(17\) | 2.53215 | + | 4.38581i | 0.614136 | + | 1.06372i | 0.990535 | + | 0.137258i | \(0.0438288\pi\) |
−0.376399 | + | 0.926458i | \(0.622838\pi\) | |||||||
\(18\) | 0.0965246i | 0.0227511i | ||||||||
\(19\) | −1.96410 | + | 1.13397i | −0.450596 | + | 0.260152i | −0.708082 | − | 0.706130i | \(-0.750439\pi\) |
0.257486 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.531659i | 0.116018i | ||||||||
\(22\) | 0.590059 | + | 1.02201i | 0.125801 | + | 0.217894i | ||||
\(23\) | 1.41959 | − | 2.45880i | 0.296005 | − | 0.512695i | −0.679213 | − | 0.733941i | \(-0.737679\pi\) |
0.975218 | + | 0.221246i | \(0.0710122\pi\) | |||||||
\(24\) | 1.20308 | + | 0.694601i | 0.245578 | + | 0.141785i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.743818 | + | 0.272296i | 0.145875 | + | 0.0534016i | ||||
\(27\) | −5.50367 | −1.05918 | ||||||||
\(28\) | −0.561581 | − | 0.324229i | −0.106129 | − | 0.0612735i | ||||
\(29\) | 1.45174 | − | 2.51448i | 0.269581 | − | 0.466928i | −0.699173 | − | 0.714953i | \(-0.746448\pi\) |
0.968754 | + | 0.248025i | \(0.0797815\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.46410i | − | 0.981382i | −0.871334 | − | 0.490691i | \(-0.836744\pi\) | ||
0.871334 | − | 0.490691i | \(-0.163256\pi\) | |||||||
\(32\) | −2.21004 | + | 1.27597i | −0.390683 | + | 0.225561i | ||||
\(33\) | −7.44432 | + | 4.29798i | −1.29589 | + | 0.748182i | ||||
\(34\) | 1.11256i | 0.190802i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.428771 | − | 0.742653i | 0.0714619 | − | 0.123776i | ||||
\(37\) | 5.17191 | + | 2.98601i | 0.850257 | + | 0.490896i | 0.860738 | − | 0.509049i | \(-0.170003\pi\) |
−0.0104803 | + | 0.999945i | \(0.503336\pi\) | |||||||
\(38\) | −0.498239 | −0.0808250 | ||||||||
\(39\) | −1.98340 | + | 5.41796i | −0.317598 | + | 0.867568i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.23205 | + | 1.86603i | 0.504762 | + | 0.291424i | 0.730678 | − | 0.682723i | \(-0.239204\pi\) |
−0.225916 | + | 0.974147i | \(0.572538\pi\) | |||||||
\(42\) | −0.0583993 | + | 0.101151i | −0.00901121 | + | 0.0156079i | ||||
\(43\) | 2.53215 | + | 4.38581i | 0.386149 | + | 0.668830i | 0.991928 | − | 0.126803i | \(-0.0404717\pi\) |
−0.605779 | + | 0.795633i | \(0.707138\pi\) | |||||||
\(44\) | − | 10.4844i | − | 1.58058i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.540166 | − | 0.311865i | 0.0796432 | − | 0.0459820i | ||||
\(47\) | − | 8.34285i | − | 1.21693i | −0.793581 | − | 0.608465i | \(-0.791786\pi\) | ||
0.793581 | − | 0.608465i | \(-0.208214\pi\) | |||||||
\(48\) | −2.97057 | − | 5.14517i | −0.428764 | − | 0.742642i | ||||
\(49\) | −3.44481 | + | 5.96658i | −0.492115 | + | 0.852368i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.10387 | −1.13477 | ||||||||
\(52\) | −4.51332 | − | 5.39913i | −0.625885 | − | 0.748724i | ||||
\(53\) | 1.56063 | 0.214369 | 0.107184 | − | 0.994239i | \(-0.465817\pi\) | ||||
0.107184 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(54\) | −1.04710 | − | 0.604542i | −0.142492 | − | 0.0822678i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.144219 | − | 0.249795i | −0.0192721 | − | 0.0333802i | ||||
\(57\) | − | 3.62916i | − | 0.480694i | ||||||
\(58\) | 0.552399 | − | 0.318928i | 0.0725335 | − | 0.0418773i | ||||
\(59\) | 2.34461 | − | 1.35366i | 0.305242 | − | 0.176232i | −0.339553 | − | 0.940587i | \(-0.610276\pi\) |
0.644795 | + | 0.764355i | \(0.276943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.05193 | − | 12.2143i | −0.902908 | − | 1.56388i | −0.823702 | − | 0.567023i | \(-0.808095\pi\) |
−0.0792059 | − | 0.996858i | \(-0.525238\pi\) | |||||||
\(62\) | 0.600196 | − | 1.03957i | 0.0762249 | − | 0.132025i | ||||
\(63\) | 0.126423 | + | 0.0729902i | 0.0159278 | + | 0.00919590i | ||||
\(64\) | 6.86488 | 0.858111 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.88842 | −0.232448 | ||||||||
\(67\) | −8.94799 | − | 5.16612i | −1.09317 | − | 0.631142i | −0.158752 | − | 0.987319i | \(-0.550747\pi\) |
−0.934419 | + | 0.356176i | \(0.884080\pi\) | |||||||
\(68\) | 4.94209 | − | 8.55995i | 0.599316 | − | 1.03805i | ||||
\(69\) | 2.27162 | + | 3.93456i | 0.273471 | + | 0.473666i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0828 | + | 6.39866i | −1.31529 | + | 0.759382i | −0.982967 | − | 0.183785i | \(-0.941165\pi\) |
−0.332321 | + | 0.943166i | \(0.607832\pi\) | |||||||
\(72\) | 0.330337 | − | 0.190720i | 0.0389306 | − | 0.0224766i | ||||
\(73\) | 9.68922i | 1.13404i | 0.823705 | + | 0.567019i | \(0.191903\pi\) | ||||
−0.823705 | + | 0.567019i | \(0.808097\pi\) | |||||||
\(74\) | 0.655986 | + | 1.13620i | 0.0762569 | + | 0.132081i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.83341 | + | 2.21322i | 0.439722 | + | 0.253874i | ||||
\(77\) | 1.78477 | 0.203393 | ||||||||
\(78\) | −0.972477 | + | 0.812927i | −0.110111 | + | 0.0920459i | ||||
\(79\) | 4.51851 | 0.508372 | 0.254186 | − | 0.967155i | \(-0.418192\pi\) | ||||
0.254186 | + | 0.967155i | \(0.418192\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.74441 | − | 6.48552i | 0.416046 | − | 0.720613i | ||||
\(82\) | 0.409941 | + | 0.710039i | 0.0452704 | + | 0.0784107i | ||||
\(83\) | − | 4.26371i | − | 0.468003i | −0.972236 | − | 0.234001i | \(-0.924818\pi\) | ||
0.972236 | − | 0.234001i | \(-0.0751821\pi\) | |||||||
\(84\) | 0.898640 | − | 0.518830i | 0.0980496 | − | 0.0566090i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.11256i | 0.119970i | ||||||||
\(87\) | 2.32306 | + | 4.02367i | 0.249059 | + | 0.431382i | ||||
\(88\) | 2.33176 | − | 4.03872i | 0.248566 | − | 0.430529i | ||||
\(89\) | −2.79366 | − | 1.61292i | −0.296127 | − | 0.170969i | 0.344575 | − | 0.938759i | \(-0.388023\pi\) |
−0.640702 | + | 0.767790i | \(0.721356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.919100 | − | 0.768307i | 0.0963478 | − | 0.0805405i | ||||
\(92\) | −5.54133 | −0.577724 | ||||||||
\(93\) | 7.57221 | + | 4.37182i | 0.785201 | + | 0.453336i | ||||
\(94\) | 0.916407 | − | 1.58726i | 0.0945202 | − | 0.163714i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 4.08359i | − | 0.416780i | ||||||
\(97\) | −2.17191 | + | 1.25396i | −0.220524 | + | 0.127320i | −0.606193 | − | 0.795318i | \(-0.707304\pi\) |
0.385669 | + | 0.922637i | \(0.373971\pi\) | |||||||
\(98\) | −1.31078 | + | 0.756779i | −0.132409 | + | 0.0764462i | ||||
\(99\) | 2.36023i | 0.237213i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.22336 | − | 10.7792i | 0.619247 | − | 1.07257i | −0.370376 | − | 0.928882i | \(-0.620771\pi\) |
0.989623 | − | 0.143686i | \(-0.0458955\pi\) | |||||||
\(102\) | −1.54180 | − | 0.890157i | −0.152661 | − | 0.0881386i | ||||
\(103\) | −15.0247 | −1.48043 | −0.740215 | − | 0.672370i | \(-0.765276\pi\) | ||||
−0.740215 | + | 0.672370i | \(0.765276\pi\) | |||||||
\(104\) | −0.537808 | − | 3.08359i | −0.0527364 | − | 0.302371i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.296916 | + | 0.171425i | 0.0288390 | + | 0.0166502i | ||||
\(107\) | −6.53215 | + | 11.3140i | −0.631487 | + | 1.09377i | 0.355761 | + | 0.934577i | \(0.384222\pi\) |
−0.987248 | + | 0.159190i | \(0.949112\pi\) | |||||||
\(108\) | 5.37086 | + | 9.30260i | 0.516811 | + | 0.895144i | ||||
\(109\) | 11.2325i | 1.07587i | 0.842985 | + | 0.537937i | \(0.180796\pi\) | ||||
−0.842985 | + | 0.537937i | \(0.819204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.27607 | + | 4.77819i | −0.785530 | + | 0.453526i | ||||
\(112\) | 1.23355i | 0.116560i | ||||||||
\(113\) | −9.17191 | − | 15.8862i | −0.862821 | − | 1.49445i | −0.869195 | − | 0.494470i | \(-0.835362\pi\) |
0.00637349 | − | 0.999980i | \(-0.497971\pi\) | |||||||
\(114\) | 0.398640 | − | 0.690464i | 0.0373360 | − | 0.0646679i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.66682 | −0.526151 | ||||||||
\(117\) | 1.01603 | + | 1.21545i | 0.0939325 | + | 0.112368i | ||||
\(118\) | 0.594763 | 0.0547524 | ||||||||
\(119\) | 1.45717 | + | 0.841298i | 0.133579 | + | 0.0771216i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.92820 | + | 15.4641i | 0.811655 | + | 1.40583i | ||||
\(122\) | − | 3.09843i | − | 0.280519i | ||||||
\(123\) | −5.17191 | + | 2.98601i | −0.466336 | + | 0.269239i | ||||
\(124\) | −9.23572 | + | 5.33225i | −0.829392 | + | 0.478850i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0160350 | + | 0.0277734i | 0.00142851 | + | 0.00247425i | ||||
\(127\) | −1.61998 | + | 2.80589i | −0.143750 | + | 0.248982i | −0.928906 | − | 0.370316i | \(-0.879249\pi\) |
0.785156 | + | 0.619298i | \(0.212583\pi\) | |||||||
\(128\) | 5.72615 | + | 3.30600i | 0.506125 | + | 0.292212i | ||||
\(129\) | −8.10387 | −0.713506 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.175664 | 0.0153478 | 0.00767390 | − | 0.999971i | \(-0.497557\pi\) | ||||
0.00767390 | + | 0.999971i | \(0.497557\pi\) | |||||||
\(132\) | 14.5294 | + | 8.38853i | 1.26462 | + | 0.730127i | ||||
\(133\) | −0.376759 | + | 0.652566i | −0.0326692 | + | 0.0565846i | ||||
\(134\) | −1.13493 | − | 1.96576i | −0.0980430 | − | 0.169815i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.80752 | − | 2.19827i | 0.326492 | − | 0.188500i | ||||
\(137\) | 15.5736 | − | 8.99144i | 1.33054 | − | 0.768190i | 0.345162 | − | 0.938543i | \(-0.387824\pi\) |
0.985383 | + | 0.170353i | \(0.0544907\pi\) | |||||||
\(138\) | 0.998090i | 0.0849631i | ||||||||
\(139\) | −5.99307 | − | 10.3803i | −0.508325 | − | 0.880445i | −0.999954 | − | 0.00964021i | \(-0.996931\pi\) |
0.491628 | − | 0.870805i | \(-0.336402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5616 | + | 6.67510i | 0.973663 | + | 0.562144i | ||||
\(142\) | −2.81140 | −0.235928 | ||||||||
\(143\) | 18.1879 | + | 6.65821i | 1.52095 | + | 0.556788i | ||||
\(144\) | −1.63129 | −0.135941 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.06430 | + | 1.84342i | −0.0880819 | + | 0.152562i | ||||
\(147\) | −5.51236 | − | 9.54769i | −0.454652 | − | 0.787481i | ||||
\(148\) | − | 11.6558i | − | 0.958101i | ||||||
\(149\) | 2.95350 | − | 1.70520i | 0.241960 | − | 0.139696i | −0.374117 | − | 0.927381i | \(-0.622054\pi\) |
0.616077 | + | 0.787686i | \(0.288721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.96141i | 0.647890i | 0.946076 | + | 0.323945i | \(0.105009\pi\) | ||||
−0.946076 | + | 0.323945i | \(0.894991\pi\) | |||||||
\(152\) | 0.984454 | + | 1.70512i | 0.0798498 | + | 0.138304i | ||||
\(153\) | −1.11256 | + | 1.92701i | −0.0899451 | + | 0.155790i | ||||
\(154\) | 0.339560 | + | 0.196045i | 0.0273625 | + | 0.0157978i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.0933 | − | 1.93477i | 0.888172 | − | 0.154906i | ||||
\(157\) | 16.4329 | 1.31148 | 0.655742 | − | 0.754985i | \(-0.272356\pi\) | ||||
0.655742 | + | 0.754985i | \(0.272356\pi\) | |||||||
\(158\) | 0.859667 | + | 0.496329i | 0.0683914 | + | 0.0394858i | ||||
\(159\) | −1.24865 | + | 2.16273i | −0.0990247 | + | 0.171516i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.943307i | − | 0.0743430i | ||||||
\(162\) | 1.42478 | − | 0.822599i | 0.111942 | − | 0.0646295i | ||||
\(163\) | −15.4215 | + | 8.90361i | −1.20791 | + | 0.697384i | −0.962301 | − | 0.271986i | \(-0.912320\pi\) |
−0.245604 | + | 0.969370i | \(0.578986\pi\) | |||||||
\(164\) | − | 7.28398i | − | 0.568784i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.468341 | − | 0.811190i | 0.0363503 | − | 0.0629605i | ||||
\(167\) | −5.45047 | − | 3.14683i | −0.421770 | − | 0.243509i | 0.274064 | − | 0.961711i | \(-0.411632\pi\) |
−0.695834 | + | 0.718202i | \(0.744965\pi\) | |||||||
\(168\) | 0.461557 | 0.0356099 | ||||||||
\(169\) | 12.2325 | − | 4.40078i | 0.940959 | − | 0.338522i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.862975 | − | 0.498239i | −0.0659933 | − | 0.0381013i | ||||
\(172\) | 4.94209 | − | 8.55995i | 0.376831 | − | 0.652690i | ||||
\(173\) | −7.98756 | − | 13.8349i | −0.607283 | − | 1.05184i | −0.991686 | − | 0.128679i | \(-0.958926\pi\) |
0.384404 | − | 0.923165i | \(-0.374407\pi\) | |||||||
\(174\) | 1.02069i | 0.0773786i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.2722 | + | 9.97212i | −1.30194 | + | 0.751677i | ||||
\(177\) | 4.33225i | 0.325632i | ||||||||
\(178\) | −0.354337 | − | 0.613729i | −0.0265587 | − | 0.0460010i | ||||
\(179\) | 11.8087 | − | 20.4533i | 0.882625 | − | 1.52875i | 0.0342123 | − | 0.999415i | \(-0.489108\pi\) |
0.848412 | − | 0.529336i | \(-0.177559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.62590 | 0.195182 | 0.0975909 | − | 0.995227i | \(-0.468886\pi\) | ||||
0.0975909 | + | 0.995227i | \(0.468886\pi\) | |||||||
\(182\) | 0.259256 | − | 0.0452168i | 0.0192174 | − | 0.00335169i | ||||
\(183\) | 22.5689 | 1.66834 | ||||||||
\(184\) | −2.13459 | − | 1.23241i | −0.157364 | − | 0.0908544i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.960431 | + | 1.66351i | 0.0704222 | + | 0.121975i | ||||
\(187\) | 27.2045i | 1.98939i | ||||||||
\(188\) | −14.1015 | + | 8.14153i | −1.02846 | + | 0.593782i | ||||
\(189\) | −1.58359 | + | 0.914288i | −0.115189 | + | 0.0665046i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.00791 | + | 1.74575i | 0.0729298 | + | 0.126318i | 0.900184 | − | 0.435509i | \(-0.143432\pi\) |
−0.827254 | + | 0.561828i | \(0.810098\pi\) | |||||||
\(192\) | −5.49258 | + | 9.51343i | −0.396393 | + | 0.686572i | ||||
\(193\) | 19.7636 | + | 11.4105i | 1.42262 | + | 0.821348i | 0.996522 | − | 0.0833298i | \(-0.0265555\pi\) |
0.426095 | + | 0.904678i | \(0.359889\pi\) | |||||||
\(194\) | −0.550955 | −0.0395563 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4467 | 0.960480 | ||||||||
\(197\) | 0.556877 | + | 0.321513i | 0.0396758 | + | 0.0229068i | 0.519707 | − | 0.854345i | \(-0.326041\pi\) |
−0.480031 | + | 0.877252i | \(0.659375\pi\) | |||||||
\(198\) | −0.259256 | + | 0.449045i | −0.0184245 | + | 0.0319122i | ||||
\(199\) | 1.53342 | + | 2.65596i | 0.108701 | + | 0.188276i | 0.915244 | − | 0.402899i | \(-0.131997\pi\) |
−0.806543 | + | 0.591175i | \(0.798664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3185 | − | 8.26681i | 1.00995 | − | 0.583096i | ||||
\(202\) | 2.36804 | − | 1.36719i | 0.166615 | − | 0.0961952i | ||||
\(203\) | − | 0.964670i | − | 0.0677065i | ||||||
\(204\) | 7.90831 | + | 13.6976i | 0.553693 | + | 0.959024i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.85852 | − | 1.65037i | −0.199163 | − | 0.114987i | ||||
\(207\) | 1.24746 | 0.0867045 | ||||||||
\(208\) | −4.60185 | + | 12.5707i | −0.319081 | + | 0.871620i | ||||
\(209\) | −12.1830 | −0.842716 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.10020 | − | 7.10175i | 0.282269 | − | 0.488904i | −0.689674 | − | 0.724120i | \(-0.742246\pi\) |
0.971943 | + | 0.235215i | \(0.0755796\pi\) | |||||||
\(212\) | −1.52297 | − | 2.63786i | −0.104598 | − | 0.181169i | ||||
\(213\) | − | 20.4782i | − | 1.40314i | ||||||
\(214\) | −2.48554 | + | 1.43503i | −0.169908 | + | 0.0980964i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.77798i | 0.325101i | ||||||||
\(217\) | −0.907714 | − | 1.57221i | −0.0616197 | − | 0.106728i | ||||
\(218\) | −1.23381 | + | 2.13703i | −0.0835643 | + | 0.144738i | ||||
\(219\) | −13.4274 | − | 7.75232i | −0.907341 | − | 0.523854i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.7110 | + | 14.0095i | 0.787767 | + | 0.942378i | ||||
\(222\) | −2.09941 | −0.140903 | ||||||||
\(223\) | −8.87174 | − | 5.12210i | −0.594095 | − | 0.343001i | 0.172620 | − | 0.984989i | \(-0.444777\pi\) |
−0.766715 | + | 0.641987i | \(0.778110\pi\) | |||||||
\(224\) | −0.423935 | + | 0.734278i | −0.0283254 | + | 0.0490610i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 4.02990i | − | 0.268065i | ||||||
\(227\) | 6.10012 | − | 3.52190i | 0.404879 | − | 0.233757i | −0.283708 | − | 0.958911i | \(-0.591565\pi\) |
0.688587 | + | 0.725154i | \(0.258231\pi\) | |||||||
\(228\) | −6.13421 | + | 3.54159i | −0.406248 | + | 0.234547i | ||||
\(229\) | 1.32899i | 0.0878219i | 0.999035 | + | 0.0439109i | \(0.0139818\pi\) | ||||
−0.999035 | + | 0.0439109i | \(0.986018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.42799 | + | 2.47335i | −0.0939547 | + | 0.162734i | ||||
\(232\) | −2.18294 | − | 1.26032i | −0.143317 | − | 0.0827440i | ||||
\(233\) | −1.24746 | −0.0817238 | −0.0408619 | − | 0.999165i | \(-0.513010\pi\) | ||||
−0.0408619 | + | 0.999165i | \(0.513010\pi\) | |||||||
\(234\) | 0.0597962 | + | 0.342849i | 0.00390900 | + | 0.0224127i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.57606 | − | 2.64199i | −0.297876 | − | 0.171979i | ||||
\(237\) | −3.61525 | + | 6.26180i | −0.234836 | + | 0.406748i | ||||
\(238\) | 0.184822 | + | 0.320121i | 0.0119802 | + | 0.0207504i | ||||
\(239\) | 9.94207i | 0.643099i | 0.946893 | + | 0.321549i | \(0.104204\pi\) | ||||
−0.946893 | + | 0.321549i | \(0.895796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5608 | + | 11.2934i | −1.26002 | + | 0.727475i | −0.973079 | − | 0.230472i | \(-0.925973\pi\) |
−0.286944 | + | 0.957947i | \(0.592640\pi\) | |||||||
\(242\) | 3.92282i | 0.252168i | ||||||||
\(243\) | −2.26371 | − | 3.92086i | −0.145217 | − | 0.251523i | ||||
\(244\) | −13.7635 | + | 23.8391i | −0.881119 | + | 1.52614i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.31197 | −0.0836483 | ||||||||
\(247\) | −6.27387 | + | 5.24455i | −0.399197 | + | 0.333702i | ||||
\(248\) | −4.74363 | −0.301221 | ||||||||
\(249\) | 5.90869 | + | 3.41139i | 0.374448 | + | 0.216188i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.38418 | − | 5.86157i | −0.213608 | − | 0.369979i | 0.739233 | − | 0.673449i | \(-0.235188\pi\) |
−0.952841 | + | 0.303470i | \(0.901855\pi\) | |||||||
\(252\) | − | 0.284915i | − | 0.0179480i | ||||||
\(253\) | 13.2082 | − | 7.62577i | 0.830394 | − | 0.479428i | ||||
\(254\) | −0.616417 | + | 0.355888i | −0.0386774 | + | 0.0223304i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.13860 | − | 10.6324i | −0.383663 | − | 0.664523i | ||||
\(257\) | 5.12691 | − | 8.88007i | 0.319808 | − | 0.553924i | −0.660640 | − | 0.750703i | \(-0.729715\pi\) |
0.980448 | + | 0.196779i | \(0.0630483\pi\) | |||||||
\(258\) | −1.54180 | − | 0.890157i | −0.0959881 | − | 0.0554187i | ||||
\(259\) | 1.98418 | 0.123291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.27571 | 0.0789645 | ||||||||
\(262\) | 0.0334208 | + | 0.0192955i | 0.00206474 | + | 0.00119208i | ||||
\(263\) | 9.32850 | − | 16.1574i | 0.575220 | − | 0.996310i | −0.420798 | − | 0.907154i | \(-0.638250\pi\) |
0.996018 | − | 0.0891555i | \(-0.0284168\pi\) | |||||||
\(264\) | 3.73127 | + | 6.46275i | 0.229644 | + | 0.397754i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.143360 | + | 0.0827690i | −0.00878998 | + | 0.00507489i | ||||
\(267\) | 4.47040 | − | 2.58098i | 0.273584 | − | 0.157954i | ||||
\(268\) | 20.1658i | 1.23182i | ||||||||
\(269\) | −8.97894 | − | 15.5520i | −0.547456 | − | 0.948221i | −0.998448 | − | 0.0556934i | \(-0.982263\pi\) |
0.450992 | − | 0.892528i | \(-0.351070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.7582 | − | 15.4488i | −1.62544 | − | 0.938450i | −0.985429 | − | 0.170086i | \(-0.945595\pi\) |
−0.640014 | − | 0.768363i | \(-0.721071\pi\) | |||||||
\(272\) | −18.8025 | −1.14007 | ||||||||
\(273\) | 0.329358 | + | 1.88842i | 0.0199337 | + | 0.114292i | ||||
\(274\) | 3.95060 | 0.238665 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.43361 | − | 7.67923i | 0.266872 | − | 0.462235i | ||||
\(277\) | −13.2522 | − | 22.9536i | −0.796250 | − | 1.37915i | −0.922042 | − | 0.387089i | \(-0.873481\pi\) |
0.125792 | − | 0.992057i | \(-0.459853\pi\) | |||||||
\(278\) | − | 2.63320i | − | 0.157929i | ||||||
\(279\) | 2.07914 | − | 1.20039i | 0.124475 | − | 0.0718656i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.97766i | 0.296942i | 0.988917 | + | 0.148471i | \(0.0474352\pi\) | ||||
−0.988917 | + | 0.148471i | \(0.952565\pi\) | |||||||
\(282\) | 1.46643 | + | 2.53993i | 0.0873247 | + | 0.151251i | ||||
\(283\) | 6.29317 | − | 10.9001i | 0.374090 | − | 0.647943i | −0.616100 | − | 0.787668i | \(-0.711288\pi\) |
0.990190 | + | 0.139725i | \(0.0446218\pi\) | |||||||
\(284\) | 21.6307 | + | 12.4885i | 1.28355 | + | 0.741057i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.72898 | + | 3.26458i | 0.161368 | + | 0.193039i | ||||
\(287\) | 1.23996 | 0.0731926 | ||||||||
\(288\) | −0.971033 | − | 0.560626i | −0.0572187 | − | 0.0330352i | ||||
\(289\) | −4.32355 | + | 7.48861i | −0.254327 | + | 0.440507i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4.01315i | − | 0.235255i | ||||||
\(292\) | 16.3772 | − | 9.45541i | 0.958406 | − | 0.553336i | ||||
\(293\) | −14.6511 | + | 8.45880i | −0.855925 | + | 0.494168i | −0.862645 | − | 0.505809i | \(-0.831194\pi\) |
0.00672072 | + | 0.999977i | \(0.497861\pi\) | |||||||
\(294\) | − | 2.42199i | − | 0.141253i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.59229 | − | 4.48997i | 0.150674 | − | 0.260974i | ||||
\(297\) | −25.6038 | − | 14.7824i | −1.48568 | − | 0.857759i | ||||
\(298\) | 0.749222 | 0.0434012 | ||||||||
\(299\) | 3.51908 | − | 9.61292i | 0.203514 | − | 0.555929i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.45717 | + | 0.841298i | 0.0839899 | + | 0.0484916i | ||||
\(302\) | −0.874509 | + | 1.51469i | −0.0503223 | + | 0.0871608i | ||||
\(303\) | 9.95859 | + | 17.2488i | 0.572106 | + | 0.990917i | ||||
\(304\) | − | 8.42034i | − | 0.482940i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.423339 | + | 0.244415i | −0.0242007 | + | 0.0139723i | ||||
\(307\) | 4.30426i | 0.245657i | 0.992428 | + | 0.122828i | \(0.0391965\pi\) | ||||
−0.992428 | + | 0.122828i | \(0.960803\pi\) | |||||||
\(308\) | −1.74170 | − | 3.01671i | −0.0992425 | − | 0.171893i | ||||
\(309\) | 12.0213 | − | 20.8214i | 0.683865 | − | 1.18449i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.22512 | 0.126175 | 0.0630875 | − | 0.998008i | \(-0.479905\pi\) | ||||
0.0630875 | + | 0.998008i | \(0.479905\pi\) | |||||||
\(312\) | 4.70357 | + | 1.72188i | 0.266287 | + | 0.0974820i | ||||
\(313\) | −7.20887 | −0.407469 | −0.203735 | − | 0.979026i | \(-0.565308\pi\) | ||||
−0.203735 | + | 0.979026i | \(0.565308\pi\) | |||||||
\(314\) | 3.12642 | + | 1.80504i | 0.176434 | + | 0.101864i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.40948 | − | 7.63744i | −0.248052 | − | 0.429639i | ||||
\(317\) | − | 0.321644i | − | 0.0180653i | −0.999959 | − | 0.00903266i | \(-0.997125\pi\) | ||
0.999959 | − | 0.00903266i | \(-0.00287522\pi\) | |||||||
\(318\) | −0.475124 | + | 0.274313i | −0.0266436 | + | 0.0153827i | ||||
\(319\) | 13.5073 | − | 7.79847i | 0.756266 | − | 0.436630i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.4527 | − | 18.1046i | −0.583414 | − | 1.01050i | ||||
\(322\) | 0.103616 | − | 0.179468i | 0.00577430 | − | 0.0100014i | ||||
\(323\) | −9.94679 | − | 5.74278i | −0.553454 | − | 0.319537i | ||||
\(324\) | −14.6162 | −0.812013 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.91201 | −0.216666 | ||||||||
\(327\) | −15.5661 | − | 8.98707i | −0.860805 | − | 0.496986i | ||||
\(328\) | 1.61998 | − | 2.80589i | 0.0894485 | − | 0.154929i | ||||
\(329\) | −1.38594 | − | 2.40052i | −0.0764094 | − | 0.132345i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4037 | + | 8.31600i | −0.791701 | + | 0.457089i | −0.840561 | − | 0.541717i | \(-0.817775\pi\) |
0.0488600 | + | 0.998806i | \(0.484441\pi\) | |||||||
\(332\) | −7.20676 | + | 4.16082i | −0.395522 | + | 0.228355i | ||||
\(333\) | 2.62395i | 0.143791i | ||||||||
\(334\) | −0.691317 | − | 1.19740i | −0.0378272 | − | 0.0655186i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.70947 | − | 0.986961i | −0.0932590 | − | 0.0538431i | ||||
\(337\) | 24.2186 | 1.31927 | 0.659636 | − | 0.751586i | \(-0.270711\pi\) | ||||
0.659636 | + | 0.751586i | \(0.270711\pi\) | |||||||
\(338\) | 2.81068 | + | 0.506387i | 0.152881 | + | 0.0275438i | ||||
\(339\) | 29.3537 | 1.59427 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.6761 | − | 25.4197i | 0.794754 | − | 1.37655i | ||||
\(342\) | −0.109456 | − | 0.189584i | −0.00591873 | − | 0.0102515i | ||||
\(343\) | 4.61478i | 0.249174i | ||||||||
\(344\) | 3.80752 | − | 2.19827i | 0.205288 | − | 0.118523i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 3.50952i | − | 0.188673i | ||||||
\(347\) | −3.13680 | − | 5.43309i | −0.168392 | − | 0.291664i | 0.769463 | − | 0.638692i | \(-0.220524\pi\) |
−0.937855 | + | 0.347028i | \(0.887191\pi\) | |||||||
\(348\) | 4.53401 | − | 7.85314i | 0.243049 | − | 0.420972i | ||||
\(349\) | −6.12275 | − | 3.53497i | −0.327743 | − | 0.189223i | 0.327095 | − | 0.944991i | \(-0.393930\pi\) |
−0.654839 | + | 0.755769i | \(0.727263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.5487 | + | 3.40948i | −1.04343 | + | 0.181984i | ||||
\(352\) | −13.7085 | −0.730666 | ||||||||
\(353\) | 18.8705 | + | 10.8949i | 1.00438 | + | 0.579878i | 0.909541 | − | 0.415615i | \(-0.136434\pi\) |
0.0948371 | + | 0.995493i | \(0.469767\pi\) | |||||||
\(354\) | −0.475869 | + | 0.824229i | −0.0252921 | + | 0.0438073i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.29598i | 0.333687i | ||||||||
\(357\) | −2.33176 | + | 1.34624i | −0.123410 | + | 0.0712506i | ||||
\(358\) | 4.49332 | − | 2.59422i | 0.237479 | − | 0.137109i | ||||
\(359\) | 23.9737i | 1.26528i | 0.774444 | + | 0.632642i | \(0.218029\pi\) | ||||
−0.774444 | + | 0.632642i | \(0.781971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.92820 | + | 12.0000i | −0.364642 | + | 0.631579i | ||||
\(362\) | 0.499589 | + | 0.288438i | 0.0262578 | + | 0.0151600i | ||||
\(363\) | −28.5737 | −1.49973 | ||||||||
\(364\) | −2.19556 | − | 0.803745i | −0.115078 | − | 0.0421277i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.29384 | + | 2.47905i | 0.224443 | + | 0.129582i | ||||
\(367\) | 3.19566 | − | 5.53505i | 0.166812 | − | 0.288927i | −0.770485 | − | 0.637458i | \(-0.779986\pi\) |
0.937297 | + | 0.348531i | \(0.113319\pi\) | |||||||
\(368\) | 5.27059 | + | 9.12892i | 0.274748 | + | 0.475878i | ||||
\(369\) | 1.63977i | 0.0853628i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.449045 | − | 0.259256i | 0.0233133 | − | 0.0134599i | ||||
\(372\) | − | 17.0653i | − | 0.884793i | ||||||
\(373\) | −10.0401 | − | 17.3899i | −0.519855 | − | 0.900414i | −0.999734 | − | 0.0230798i | \(-0.992653\pi\) |
0.479879 | − | 0.877335i | \(-0.340681\pi\) | |||||||
\(374\) | −2.98823 | + | 5.17577i | −0.154518 | + | 0.267633i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.24280 | −0.373519 | ||||||||
\(377\) | 3.59878 | − | 9.83062i | 0.185346 | − | 0.506302i | ||||
\(378\) | −0.401714 | −0.0206619 | ||||||||
\(379\) | −4.73007 | − | 2.73091i | −0.242968 | − | 0.140277i | 0.373572 | − | 0.927601i | \(-0.378133\pi\) |
−0.616540 | + | 0.787324i | \(0.711466\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.59229 | − | 4.48997i | −0.132807 | − | 0.230028i | ||||
\(382\) | 0.442849i | 0.0226581i | ||||||||
\(383\) | −4.90842 | + | 2.83388i | −0.250808 | + | 0.144804i | −0.620134 | − | 0.784496i | \(-0.712922\pi\) |
0.369326 | + | 0.929300i | \(0.379589\pi\) | |||||||
\(384\) | −9.16297 | + | 5.29024i | −0.467596 | + | 0.269966i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.50675 | + | 4.34181i | 0.127590 | + | 0.220992i | ||||
\(387\) | −1.11256 | + | 1.92701i | −0.0565546 | + | 0.0979554i | ||||
\(388\) | 4.23901 | + | 2.44739i | 0.215203 | + | 0.124247i | ||||
\(389\) | −10.6174 | −0.538325 | −0.269162 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269162 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3784 | 0.727149 | ||||||||
\(392\) | 5.17986 | + | 2.99059i | 0.261622 | + | 0.151048i | ||||
\(393\) | −0.140548 | + | 0.243436i | −0.00708971 | + | 0.0122797i | ||||
\(394\) | 0.0706321 | + | 0.122338i | 0.00355840 | + | 0.00616332i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.98940 | − | 2.30328i | 0.200475 | − | 0.115744i | ||||
\(397\) | −24.2780 | + | 14.0169i | −1.21848 | + | 0.703487i | −0.964592 | − | 0.263748i | \(-0.915041\pi\) |
−0.253884 | + | 0.967235i | \(0.581708\pi\) | |||||||
\(398\) | 0.673745i | 0.0337718i | ||||||||
\(399\) | −0.602888 | − | 1.04423i | −0.0301822 | − | 0.0522770i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.4979 | + | 11.2571i | 0.973680 | + | 0.562155i | 0.900356 | − | 0.435154i | \(-0.143306\pi\) |
0.0733241 | + | 0.997308i | \(0.476639\pi\) | |||||||
\(402\) | 3.63222 | 0.181159 | ||||||||
\(403\) | −3.38496 | − | 19.4081i | −0.168617 | − | 0.966788i | ||||
\(404\) | −24.2927 | −1.20861 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.105963 | − | 0.183533i | 0.00525884 | − | 0.00910857i | ||||
\(407\) | 16.0403 | + | 27.7826i | 0.795087 | + | 1.37713i | ||||
\(408\) | 7.03533i | 0.348301i | ||||||||
\(409\) | −3.71328 | + | 2.14386i | −0.183610 | + | 0.106007i | −0.588988 | − | 0.808142i | \(-0.700473\pi\) |
0.405378 | + | 0.914149i | \(0.367140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.7761i | 1.41942i | ||||||||
\(412\) | 14.6622 | + | 25.3956i | 0.722353 | + | 1.25115i | ||||
\(413\) | 0.449749 | − | 0.778989i | 0.0221307 | − | 0.0383315i | ||||
\(414\) | 0.237335 | + | 0.137025i | 0.0116644 | + | 0.00673443i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.05946 | + | 5.90125i | −0.346119 | + | 0.289333i | ||||
\(417\) | 19.1802 | 0.939257 | ||||||||
\(418\) | −2.31787 | − | 1.33822i | −0.113371 | − | 0.0654546i | ||||
\(419\) | −8.85578 | + | 15.3387i | −0.432633 | + | 0.749343i | −0.997099 | − | 0.0761137i | \(-0.975749\pi\) |
0.564466 | + | 0.825456i | \(0.309082\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.8787i | − | 0.627672i | −0.949477 | − | 0.313836i | \(-0.898386\pi\) | ||
0.949477 | − | 0.313836i | \(-0.101614\pi\) | |||||||
\(422\) | 1.56016 | − | 0.900759i | 0.0759474 | − | 0.0438483i | ||||
\(423\) | 3.17453 | − | 1.83281i | 0.154351 | − | 0.0891145i | ||||
\(424\) | − | 1.35485i | − | 0.0657973i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.24940 | − | 3.89607i | 0.108984 | − | 0.188765i | ||||
\(427\) | −4.05816 | − | 2.34298i | −0.196388 | − | 0.113385i | ||||
\(428\) | 25.4981 | 1.23250 | ||||||||
\(429\) | −23.7792 | + | 19.8778i | −1.14807 | + | 0.959710i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.22590 | + | 4.74923i | 0.396228 | + | 0.228762i | 0.684855 | − | 0.728679i | \(-0.259866\pi\) |
−0.288627 | + | 0.957442i | \(0.593199\pi\) | |||||||
\(432\) | 10.2169 | − | 17.6962i | 0.491560 | − | 0.851408i | ||||
\(433\) | 0.698141 | + | 1.20922i | 0.0335505 | + | 0.0581112i | 0.882313 | − | 0.470663i | \(-0.155985\pi\) |
−0.848763 | + | 0.528774i | \(0.822652\pi\) | |||||||
\(434\) | − | 0.398826i | − | 0.0191443i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.9857 | − | 10.9614i | 0.909251 | − | 0.524956i | ||||
\(437\) | 6.43911i | 0.308024i | ||||||||
\(438\) | −1.70308 | − | 2.94983i | −0.0813765 | − | 0.140948i | ||||
\(439\) | 2.08090 | − | 3.60422i | 0.0993159 | − | 0.172020i | −0.812086 | − | 0.583538i | \(-0.801668\pi\) |
0.911402 | + | 0.411518i | \(0.135001\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.02711 | −0.144148 | ||||||||
\(442\) | 0.689221 | + | 3.95174i | 0.0327829 | + | 0.187965i | ||||
\(443\) | −9.54563 | −0.453526 | −0.226763 | − | 0.973950i | \(-0.572814\pi\) | ||||
−0.226763 | + | 0.973950i | \(0.572814\pi\) | |||||||
\(444\) | 16.1527 | + | 9.32578i | 0.766574 | + | 0.442582i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.12526 | − | 1.94900i | −0.0532825 | − | 0.0922880i | ||||
\(447\) | 5.45732i | 0.258122i | ||||||||
\(448\) | 1.97526 | − | 1.14042i | 0.0933223 | − | 0.0538796i | ||||
\(449\) | 18.8075 | − | 10.8585i | 0.887582 | − | 0.512446i | 0.0144310 | − | 0.999896i | \(-0.495406\pi\) |
0.873151 | + | 0.487450i | \(0.162073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0239 | + | 17.3620i | 0.472009 | + | 0.817544i | ||||
\(452\) | −17.9012 | + | 31.0057i | −0.842000 | + | 1.45839i | ||||
\(453\) | −11.0330 | − | 6.36991i | −0.518376 | − | 0.299284i | ||||
\(454\) | 1.54743 | 0.0726246 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.15064 | −0.147542 | ||||||||
\(457\) | −4.08989 | − | 2.36130i | −0.191317 | − | 0.110457i | 0.401282 | − | 0.915955i | \(-0.368565\pi\) |
−0.592599 | + | 0.805498i | \(0.701898\pi\) | |||||||
\(458\) | −0.145980 | + | 0.252845i | −0.00682122 | + | 0.0118147i | ||||
\(459\) | −13.9361 | − | 24.1381i | −0.650482 | − | 1.12667i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.54283 | − | 0.890753i | 0.0718568 | − | 0.0414865i | −0.463641 | − | 0.886023i | \(-0.653457\pi\) |
0.535498 | + | 0.844537i | \(0.320124\pi\) | |||||||
\(462\) | −0.543362 | + | 0.313710i | −0.0252795 | + | 0.0145951i | ||||
\(463\) | − | 6.80200i | − | 0.316116i | −0.987430 | − | 0.158058i | \(-0.949477\pi\) | ||
0.987430 | − | 0.158058i | \(-0.0505232\pi\) | |||||||
\(464\) | 5.38995 | + | 9.33566i | 0.250222 | + | 0.433397i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.237335 | − | 0.137025i | −0.0109943 | − | 0.00634758i | ||||
\(467\) | 18.2374 | 0.843927 | 0.421963 | − | 0.906613i | \(-0.361341\pi\) | ||||
0.421963 | + | 0.906613i | \(0.361341\pi\) | |||||||
\(468\) | 1.06290 | − | 2.90348i | 0.0491325 | − | 0.134213i | ||||
\(469\) | −3.43285 | −0.158514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.1479 | + | 22.7728i | −0.605823 | + | 1.04932i | ||||
\(472\) | −1.17517 | − | 2.03546i | −0.0540918 | − | 0.0936897i | ||||
\(473\) | 27.2045i | 1.25086i | ||||||||
\(474\) | −1.37564 | + | 0.794223i | −0.0631850 | + | 0.0364799i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 3.28398i | − | 0.150521i | ||||||
\(477\) | 0.342849 | + | 0.593832i | 0.0156980 | + | 0.0271897i | ||||
\(478\) | −1.09207 | + | 1.89152i | −0.0499502 | + | 0.0865162i | ||||
\(479\) | 30.4674 | + | 17.5904i | 1.39209 | + | 0.803724i | 0.993547 | − | 0.113425i | \(-0.0361821\pi\) |
0.398544 | + | 0.917149i | \(0.369515\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2201 | + | 7.40214i | 0.921957 | + | 0.337508i | ||||
\(482\) | −4.96204 | −0.226015 | ||||||||
\(483\) | 1.30724 | + | 0.754738i | 0.0594817 | + | 0.0343418i | ||||
\(484\) | 17.4255 | − | 30.1819i | 0.792069 | − | 1.37190i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 0.994615i | − | 0.0451166i | ||||||
\(487\) | −8.92352 | + | 5.15200i | −0.404363 | + | 0.233459i | −0.688365 | − | 0.725364i | \(-0.741671\pi\) |
0.284002 | + | 0.958824i | \(0.408338\pi\) | |||||||
\(488\) | −10.6038 | + | 6.12210i | −0.480011 | + | 0.277134i | ||||
\(489\) | − | 28.4950i | − | 1.28859i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.66599 | − | 8.08174i | 0.210573 | − | 0.364724i | −0.741321 | − | 0.671151i | \(-0.765800\pi\) |
0.951894 | + | 0.306427i | \(0.0991336\pi\) | |||||||
\(492\) | 10.0942 | + | 5.82790i | 0.455083 | + | 0.262742i | ||||
\(493\) | 14.7041 | 0.662238 | ||||||||
\(494\) | −1.76971 | + | 0.308654i | −0.0796230 | + | 0.0138870i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.5689 | + | 10.1434i | 0.788869 | + | 0.455454i | ||||
\(497\) | −2.12593 | + | 3.68222i | −0.0953611 | + | 0.165170i | ||||
\(498\) | 0.749437 | + | 1.29806i | 0.0335831 | + | 0.0581676i | ||||
\(499\) | − | 23.9421i | − | 1.07179i | −0.844283 | − | 0.535897i | \(-0.819974\pi\) | ||
0.844283 | − | 0.535897i | \(-0.180026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.72181 | − | 5.03554i | 0.389662 | − | 0.224971i | ||||
\(502\) | − | 1.48692i | − | 0.0663645i | ||||||
\(503\) | 21.0721 | + | 36.4980i | 0.939560 | + | 1.62737i | 0.766294 | + | 0.642490i | \(0.222099\pi\) |
0.173266 | + | 0.984875i | \(0.444568\pi\) | |||||||
\(504\) | 0.0633661 | − | 0.109753i | 0.00282255 | − | 0.00488880i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.35056 | 0.148951 | ||||||||
\(507\) | −3.68852 | + | 20.4729i | −0.163813 | + | 0.909235i | ||||
\(508\) | 6.32355 | 0.280562 | ||||||||
\(509\) | −29.0640 | − | 16.7801i | −1.28824 | − | 0.743765i | −0.309899 | − | 0.950770i | \(-0.600295\pi\) |
−0.978340 | + | 0.207005i | \(0.933629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.60960 | + | 2.78792i | 0.0712047 | + | 0.123330i | ||||
\(512\) | − | 15.9211i | − | 0.703621i | ||||||
\(513\) | 10.8098 | − | 6.24102i | 0.477263 | − | 0.275548i | ||||
\(514\) | 1.95084 | − | 1.12632i | 0.0860477 | − | 0.0496796i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.90831 | + | 13.6976i | 0.348144 | + | 0.603003i | ||||
\(517\) | 22.4081 | − | 38.8120i | 0.985508 | − | 1.70695i | ||||
\(518\) | 0.377499 | + | 0.217949i | 0.0165864 | + | 0.00957614i | ||||
\(519\) | 25.5633 | 1.12210 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4649 | 0.546098 | 0.273049 | − | 0.962000i | \(-0.411968\pi\) | ||||
0.273049 | + | 0.962000i | \(0.411968\pi\) | |||||||
\(522\) | 0.242710 | + | 0.140128i | 0.0106231 | + | 0.00613326i | ||||
\(523\) | −2.82978 | + | 4.90132i | −0.123738 | + | 0.214320i | −0.921239 | − | 0.388998i | \(-0.872821\pi\) |
0.797501 | + | 0.603317i | \(0.206155\pi\) | |||||||
\(524\) | −0.171425 | − | 0.296916i | −0.00748872 | − | 0.0129708i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.54958 | − | 2.04935i | 0.154769 | − | 0.0893558i | ||||
\(527\) | 23.9645 | − | 13.8359i | 1.04391 | − | 0.602702i | ||||
\(528\) | − | 31.9147i | − | 1.38891i | ||||||
\(529\) | 7.46953 | + | 12.9376i | 0.324762 | + | 0.562505i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.03016 | + | 0.594763i | 0.0447051 | + | 0.0258105i | ||||
\(532\) | 1.47067 | 0.0637616 | ||||||||
\(533\) | 12.6360 | + | 4.62577i | 0.547327 | + | 0.200364i | ||||
\(534\) | 1.13402 | 0.0490737 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.48494 | + | 7.76815i | −0.193720 | + | 0.335533i | ||||
\(537\) | 18.8963 | + | 32.7293i | 0.815433 | + | 1.41237i | ||||
\(538\) | − | 3.94511i | − | 0.170086i | ||||||
\(539\) | −32.0514 | + | 18.5049i | −1.38055 | + | 0.797061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15.4750i | − | 0.665321i | −0.943047 | − | 0.332660i | \(-0.892054\pi\) | ||
0.943047 | − | 0.332660i | \(-0.107946\pi\) | |||||||
\(542\) | −3.39391 | − | 5.87842i | −0.145781 | − | 0.252500i | ||||
\(543\) | −2.10098 | + | 3.63900i | −0.0901616 | + | 0.156165i | ||||
\(544\) | −11.1923 | − | 6.46187i | −0.479866 | − | 0.277051i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.144769 | + | 0.395458i | −0.00619552 | + | 0.0169240i | ||||
\(547\) | −25.1765 | −1.07647 | −0.538234 | − | 0.842795i | \(-0.680908\pi\) | ||||
−0.538234 | + | 0.842795i | \(0.680908\pi\) | |||||||
\(548\) | −30.3956 | − | 17.5489i | −1.29844 | − | 0.749653i | ||||
\(549\) | 3.09843 | − | 5.36665i | 0.132238 | − | 0.229043i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.58493i | 0.280528i | ||||||||
\(552\) | 3.41577 | − | 1.97210i | 0.145385 | − | 0.0839380i | ||||
\(553\) | 1.30013 | − | 0.750630i | 0.0552871 | − | 0.0319200i | ||||
\(554\) | − | 5.82269i | − | 0.247382i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.6969 | + | 20.2596i | −0.496059 | + | 0.859199i | ||||
\(557\) | 36.6752 | + | 21.1744i | 1.55398 | + | 0.897190i | 0.997812 | + | 0.0661194i | \(0.0210618\pi\) |
0.556167 | + | 0.831071i | \(0.312272\pi\) | |||||||
\(558\) | 0.527420 | 0.0223275 | ||||||||
\(559\) | 11.7110 | + | 14.0095i | 0.495322 | + | 0.592537i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.7002 | − | 21.7662i | −1.59171 | − | 0.918971i | ||||
\(562\) | −0.546763 | + | 0.947022i | −0.0230638 | + | 0.0399477i | ||||
\(563\) | −11.8953 | − | 20.6032i | −0.501326 | − | 0.868322i | −0.999999 | − | 0.00153173i | \(-0.999512\pi\) |
0.498673 | − | 0.866790i | \(-0.333821\pi\) | |||||||
\(564\) | − | 26.0561i | − | 1.09716i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.39461 | − | 1.38253i | 0.100653 | − | 0.0581119i | ||||
\(567\) | − | 2.48814i | − | 0.104492i | ||||||
\(568\) | 5.55497 | + | 9.62148i | 0.233081 | + | 0.403709i | ||||
\(569\) | −13.3710 | + | 23.1593i | −0.560543 | + | 0.970889i | 0.436906 | + | 0.899507i | \(0.356074\pi\) |
−0.997449 | + | 0.0713817i | \(0.977259\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.7159 | 0.699539 | 0.349769 | − | 0.936836i | \(-0.386260\pi\) | ||||
0.349769 | + | 0.936836i | \(0.386260\pi\) | |||||||
\(572\) | −6.49498 | − | 37.2398i | −0.271569 | − | 1.55707i | ||||
\(573\) | −3.22571 | −0.134756 | ||||||||
\(574\) | 0.235908 | + | 0.136202i | 0.00984661 | + | 0.00568494i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50812 | + | 2.61215i | 0.0628385 | + | 0.108840i | ||||
\(577\) | − | 20.6768i | − | 0.860786i | −0.902642 | − | 0.430393i | \(-0.858375\pi\) | ||
0.902642 | − | 0.430393i | \(-0.141625\pi\) | |||||||
\(578\) | −1.64515 | + | 0.949828i | −0.0684292 | + | 0.0395076i | ||||
\(579\) | −31.6257 | + | 18.2591i | −1.31432 | + | 0.758822i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.708301 | − | 1.22681i | −0.0293853 | − | 0.0508968i | ||||
\(582\) | 0.440818 | − | 0.763519i | 0.0182725 | − | 0.0316489i | ||||
\(583\) | 7.26023 | + | 4.19170i | 0.300688 | + | 0.173602i | ||||
\(584\) | 8.41165 | 0.348076 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.71657 | −0.153530 | ||||||||
\(587\) | −18.0109 | − | 10.3986i | −0.743388 | − | 0.429196i | 0.0799116 | − | 0.996802i | \(-0.474536\pi\) |
−0.823300 | + | 0.567606i | \(0.807870\pi\) | |||||||
\(588\) | −10.7587 | + | 18.6346i | −0.443681 | + | 0.768478i | ||||
\(589\) | 6.19615 | + | 10.7321i | 0.255308 | + | 0.442206i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.891111 | + | 0.514483i | −0.0366554 | + | 0.0211630i | ||||
\(592\) | −19.2021 | + | 11.0863i | −0.789199 | + | 0.455644i | ||||
\(593\) | 21.8475i | 0.897169i | 0.893740 | + | 0.448585i | \(0.148072\pi\) | ||||
−0.893740 | + | 0.448585i | \(0.851928\pi\) | |||||||
\(594\) | −3.24749 | − | 5.62482i | −0.133246 | − | 0.230789i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.76446 | − | 3.32811i | −0.236121 | − | 0.136325i | ||||
\(597\) | −4.90755 | −0.200853 | ||||||||
\(598\) | 1.72544 | − | 1.44235i | 0.0705583 | − | 0.0589822i | ||||
\(599\) | −3.58040 | −0.146291 | −0.0731456 | − | 0.997321i | \(-0.523304\pi\) | ||||
−0.0731456 | + | 0.997321i | \(0.523304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6743 | + | 18.4885i | −0.435414 | + | 0.754160i | −0.997329 | − | 0.0730352i | \(-0.976731\pi\) |
0.561915 | + | 0.827195i | \(0.310065\pi\) | |||||||
\(602\) | 0.184822 | + | 0.320121i | 0.00753278 | + | 0.0130472i | ||||
\(603\) | − | 4.53972i | − | 0.184872i | ||||||
\(604\) | 13.4568 | − | 7.76929i | 0.547550 | − | 0.316128i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.37554i | 0.177744i | ||||||||
\(607\) | −1.64988 | − | 2.85767i | −0.0669665 | − | 0.115989i | 0.830598 | − | 0.556872i | \(-0.187999\pi\) |
−0.897565 | + | 0.440883i | \(0.854665\pi\) | |||||||
\(608\) | 2.89383 | − | 5.01226i | 0.117360 | − | 0.203274i | ||||
\(609\) | 1.33685 | + | 0.771830i | 0.0541718 | + | 0.0312761i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.16832 | − | 29.6332i | −0.209088 | − | 1.19883i | ||||
\(612\) | 4.34285 | 0.175549 | ||||||||
\(613\) | −8.56183 | − | 4.94318i | −0.345809 | − | 0.199653i | 0.317029 | − | 0.948416i | \(-0.397315\pi\) |
−0.662838 | + | 0.748763i | \(0.730648\pi\) | |||||||
\(614\) | −0.472795 | + | 0.818904i | −0.0190804 | + | 0.0330483i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1.54944i | − | 0.0624286i | ||||||
\(617\) | −39.5920 | + | 22.8584i | −1.59391 | + | 0.920246i | −0.601287 | + | 0.799033i | \(0.705345\pi\) |
−0.992626 | + | 0.121213i | \(0.961321\pi\) | |||||||
\(618\) | 4.57419 | − | 2.64091i | 0.184001 | − | 0.106233i | ||||
\(619\) | 19.9143i | 0.800425i | 0.916422 | + | 0.400212i | \(0.131064\pi\) | ||||
−0.916422 | + | 0.400212i | \(0.868936\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.81295 | + | 13.5324i | −0.313523 | + | 0.543038i | ||||
\(622\) | 0.423339 | + | 0.244415i | 0.0169743 | + | 0.00980014i | ||||
\(623\) | −1.07177 | −0.0429397 | ||||||||
\(624\) | −13.7386 | − | 16.4351i | −0.549986 | − | 0.657930i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.37152 | − | 0.791847i | −0.0548169 | − | 0.0316486i | ||||
\(627\) | 9.74760 | − | 16.8833i | 0.389282 | − | 0.674255i | ||||
\(628\) | −16.0363 | − | 27.7757i | −0.639918 | − | 1.10837i | ||||
\(629\) | 30.2440i | 1.20591i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6403 | − | 7.29790i | 0.503204 | − | 0.290525i | −0.226832 | − | 0.973934i | \(-0.572837\pi\) |
0.730036 | + | 0.683409i | \(0.239503\pi\) | |||||||
\(632\) | − | 3.92272i | − | 0.156038i | ||||||
\(633\) | 6.56112 | + | 11.3642i | 0.260781 | + | 0.451686i | ||||
\(634\) | 0.0353305 | − | 0.0611942i | 0.00140315 | − | 0.00243033i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.87409 | 0.193270 | ||||||||
\(637\) | −8.53948 | + | 23.3269i | −0.338346 | + | 0.924246i | ||||
\(638\) | 3.42644 | 0.135654 | ||||||||
\(639\) | −4.86950 | − | 2.81140i | −0.192634 | − | 0.111217i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.08183 | − | 12.2661i | −0.279716 | − | 0.484482i | 0.691598 | − | 0.722282i | \(-0.256907\pi\) |
−0.971314 | + | 0.237801i | \(0.923573\pi\) | |||||||
\(642\) | − | 4.59265i | − | 0.181257i | ||||||
\(643\) | 14.5246 | − | 8.38581i | 0.572796 | − | 0.330704i | −0.185469 | − | 0.982650i | \(-0.559380\pi\) |
0.758265 | + | 0.651946i | \(0.226047\pi\) | |||||||
\(644\) | −1.59443 | + | 0.920544i | −0.0628293 | + | 0.0362745i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.26161 | − | 2.18518i | −0.0496376 | − | 0.0859748i | ||||
\(647\) | 1.49584 | − | 2.59087i | 0.0588075 | − | 0.101858i | −0.835123 | − | 0.550063i | \(-0.814604\pi\) |
0.893930 | + | 0.448206i | \(0.147937\pi\) | |||||||
\(648\) | −5.63037 | − | 3.25069i | −0.221182 | − | 0.127699i | ||||
\(649\) | 14.5432 | 0.570872 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.90504 | 0.113858 | ||||||||
\(652\) | 30.0987 | + | 17.3775i | 1.17876 | + | 0.680556i | ||||
\(653\) | −5.83217 | + | 10.1016i | −0.228230 | + | 0.395307i | −0.957284 | − | 0.289150i | \(-0.906627\pi\) |
0.729053 | + | 0.684457i | \(0.239961\pi\) | |||||||
\(654\) | −1.97434 | − | 3.41966i | −0.0772028 | − | 0.133719i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.9998 | + | 6.92810i | −0.468514 | + | 0.270497i | ||||
\(657\) | −3.68683 | + | 2.12859i | −0.143837 | + | 0.0830444i | ||||
\(658\) | − | 0.608946i | − | 0.0237392i | ||||||
\(659\) | 0.905237 | + | 1.56792i | 0.0352630 | + | 0.0610773i | 0.883118 | − | 0.469150i | \(-0.155440\pi\) |
−0.847855 | + | 0.530228i | \(0.822106\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6872 | + | 6.17028i | 0.415686 | + | 0.239996i | 0.693230 | − | 0.720717i | \(-0.256187\pi\) |
−0.277544 | + | 0.960713i | \(0.589520\pi\) | |||||||
\(662\) | −3.65383 | −0.142010 | ||||||||
\(663\) | −28.7844 | + | 5.02027i | −1.11789 | + | 0.194971i | ||||
\(664\) | −3.70152 | −0.143647 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.288223 | + | 0.499217i | −0.0111684 | + | 0.0193443i | ||||
\(667\) | −4.12174 | − | 7.13907i | −0.159594 | − | 0.276426i | ||||
\(668\) | 12.2836i | 0.475265i | ||||||||
\(669\) | 14.1965 | − | 8.19636i | 0.548869 | − | 0.316890i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 75.7634i | − | 2.92481i | ||||||
\(672\) | −0.678380 | − | 1.17499i | −0.0261691 | − | 0.0453262i | ||||
\(673\) | −4.63313 | + | 8.02481i | −0.178594 | + | 0.309334i | −0.941399 | − | 0.337295i | \(-0.890488\pi\) |
0.762805 | + | 0.646628i | \(0.223822\pi\) | |||||||
\(674\) | 4.60770 | + | 2.66025i | 0.177482 | + | 0.102469i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.3757 | − | 16.3814i | −0.745220 | − | 0.630053i | ||||
\(677\) | −13.8984 | −0.534158 | −0.267079 | − | 0.963675i | \(-0.586059\pi\) | ||||
−0.267079 | + | 0.963675i | \(0.586059\pi\) | |||||||
\(678\) | 5.58467 | + | 3.22431i | 0.214478 | + | 0.123829i | ||||
\(679\) | −0.416622 | + | 0.721611i | −0.0159885 | + | 0.0276929i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.2715i | 0.431924i | ||||||||
\(682\) | 5.58438 | − | 3.22414i | 0.213837 | − | 0.123459i | ||||
\(683\) | 32.6935 | − | 18.8756i | 1.25098 | − | 0.722255i | 0.279678 | − | 0.960094i | \(-0.409772\pi\) |
0.971305 | + | 0.237838i | \(0.0764388\pi\) | |||||||
\(684\) | 1.94486i | 0.0743637i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.506903 | + | 0.877981i | −0.0193536 | + | 0.0335215i | ||||
\(687\) | −1.84172 | − | 1.06332i | −0.0702661 | − | 0.0405681i | ||||
\(688\) | −18.8025 | −0.716838 | ||||||||
\(689\) | 5.54324 | − | 0.966794i | 0.211181 | − | 0.0368319i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.43146 | − | 0.826456i | −0.0544554 | − | 0.0314399i | 0.472525 | − | 0.881317i | \(-0.343343\pi\) |
−0.526981 | + | 0.849877i | \(0.676676\pi\) | |||||||
\(692\) | −15.5896 | + | 27.0020i | −0.592628 | + | 1.02646i | ||||
\(693\) | 0.392090 | + | 0.679120i | 0.0148943 | + | 0.0257976i | ||||
\(694\) | − | 1.37823i | − | 0.0523168i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.49312 | − | 2.01676i | 0.132407 | − | 0.0764450i | ||||
\(697\) | 18.9002i | 0.715897i | ||||||||
\(698\) | −0.776587 | − | 1.34509i | −0.0293943 | − | 0.0509123i | ||||
\(699\) | 0.998090 | − | 1.72874i | 0.0377512 | − | 0.0653871i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4819 | −0.773590 | −0.386795 | − | 0.922166i | \(-0.626418\pi\) | ||||
−0.386795 | + | 0.922166i | \(0.626418\pi\) | |||||||
\(702\) | −4.09373 | − | 1.49863i | −0.154508 | − | 0.0565620i | ||||
\(703\) | −13.5442 | −0.510830 | ||||||||
\(704\) | 31.9363 | + | 18.4384i | 1.20365 | + | 0.694925i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.39347 | + | 4.14561i | 0.0900794 | + | 0.156022i | ||||
\(707\) | − | 4.13538i | − | 0.155527i | ||||||
\(708\) | 7.32260 | − | 4.22770i | 0.275200 | − | 0.158887i | ||||
\(709\) | 19.0021 | − | 10.9709i | 0.713639 | − | 0.412020i | −0.0987679 | − | 0.995110i | \(-0.531490\pi\) |
0.812407 | + | 0.583091i | \(0.198157\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.992658 | + | 1.71933i | 0.0372276 | + | 0.0644801i | ||||
\(712\) | −1.40025 | + | 2.42530i | −0.0524764 | + | 0.0908919i | ||||
\(713\) | −13.4351 | − | 7.75678i | −0.503150 | − | 0.290494i | ||||
\(714\) | −0.591503 | −0.0221364 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −46.0950 | −1.72265 | ||||||||
\(717\) | −13.7778 | − | 7.95463i | −0.514542 | − | 0.297071i | ||||
\(718\) | −2.63335 | + | 4.56110i | −0.0982759 | + | 0.170219i | ||||
\(719\) | 19.4237 | + | 33.6429i | 0.724384 | + | 1.25467i | 0.959227 | + | 0.282636i | \(0.0912089\pi\) |
−0.234844 | + | 0.972033i | \(0.575458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.32312 | + | 2.49596i | −0.161002 | + | 0.0929543i | ||||
\(722\) | −2.63624 | + | 1.52204i | −0.0981108 | + | 0.0566443i | ||||
\(723\) | − | 36.1434i | − | 1.34419i | ||||||
\(724\) | −2.56254 | − | 4.43844i | −0.0952359 | − | 0.164953i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.43628 | − | 3.13864i | −0.201759 | − | 0.116486i | ||||
\(727\) | −30.6598 | −1.13711 | −0.568555 | − | 0.822645i | \(-0.692497\pi\) | ||||
−0.568555 | + | 0.822645i | \(0.692497\pi\) | |||||||
\(728\) | −0.667002 | − | 0.797912i | −0.0247207 | − | 0.0295726i | ||||
\(729\) | 29.7112 | 1.10042 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.8236 | + | 22.2110i | −0.474296 | + | 0.821505i | ||||
\(732\) | −22.0243 | − | 38.1473i | −0.814043 | − | 1.40996i | ||||
\(733\) | 24.3858i | 0.900709i | 0.892850 | + | 0.450355i | \(0.148702\pi\) | ||||
−0.892850 | + | 0.450355i | \(0.851298\pi\) | |||||||
\(734\) | 1.21598 | − | 0.702045i | 0.0448826 | − | 0.0259130i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.24539i | 0.267069i | ||||||||
\(737\) | −27.7515 | − | 48.0669i | −1.02224 | − | 1.77057i | ||||
\(738\) | −0.180117 | + | 0.311973i | −0.00663021 | + | 0.0114839i | ||||
\(739\) | −33.1504 | − | 19.1394i | −1.21946 | − | 0.704054i | −0.254656 | − | 0.967032i | \(-0.581962\pi\) |
−0.964802 | + | 0.262977i | \(0.915296\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.24823 | − | 12.8905i | −0.0825909 | − | 0.473546i | ||||
\(742\) | 0.113910 | 0.00418178 | ||||||||
\(743\) | 34.6479 | + | 20.0040i | 1.27111 | + | 0.733874i | 0.975196 | − | 0.221342i | \(-0.0710437\pi\) |
0.295910 | + | 0.955216i | \(0.404377\pi\) | |||||||
\(744\) | 3.79537 | − | 6.57377i | 0.139145 | − | 0.241006i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 4.41134i | − | 0.161511i | ||||||
\(747\) | 1.62238 | − | 0.936681i | 0.0593598 | − | 0.0342714i | ||||
\(748\) | 45.9825 | − | 26.5480i | 1.68129 | − | 0.970691i | ||||
\(749\) | 4.34057i | 0.158601i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8010 | − | 22.1720i | 0.467115 | − | 0.809067i | −0.532179 | − | 0.846632i | \(-0.678627\pi\) |
0.999294 | + | 0.0375648i | \(0.0119601\pi\) | |||||||
\(752\) | 26.8251 | + | 15.4875i | 0.978211 | + | 0.564770i | ||||
\(753\) | 10.8307 | 0.394693 | ||||||||
\(754\) | 1.76451 | − | 1.47502i | 0.0642597 | − | 0.0537169i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.09076 | + | 1.78445i | 0.112410 | + | 0.0648998i | ||||
\(757\) | −0.924239 | + | 1.60083i | −0.0335920 | + | 0.0581831i | −0.882333 | − | 0.470626i | \(-0.844028\pi\) |
0.848741 | + | 0.528809i | \(0.177361\pi\) | |||||||
\(758\) | −0.599945 | − | 1.03914i | −0.0217910 | − | 0.0377431i | ||||
\(759\) | 24.4055i | 0.885862i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.7006 | − | 13.1062i | 0.822896 | − | 0.475099i | −0.0285179 | − | 0.999593i | \(-0.509079\pi\) |
0.851414 | + | 0.524494i | \(0.175745\pi\) | |||||||
\(762\) | − | 1.13898i | − | 0.0412610i | ||||||
\(763\) | 1.86597 | + | 3.23196i | 0.0675528 | + | 0.117005i | ||||
\(764\) | 1.96718 | − | 3.40725i | 0.0711699 | − | 0.123270i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.24513 | −0.0449884 | ||||||||
\(767\) | 7.48932 | − | 6.26058i | 0.270424 | − | 0.226056i | ||||
\(768\) | 19.6459 | 0.708911 | ||||||||
\(769\) | −38.4078 | − | 22.1747i | −1.38502 | − | 0.799641i | −0.392271 | − | 0.919850i | \(-0.628310\pi\) |
−0.992749 | + | 0.120208i | \(0.961644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.20406 | + | 14.2099i | 0.295462 | + | 0.511755i | ||||
\(772\) | − | 44.5408i | − | 1.60306i | ||||||
\(773\) | −20.1471 | + | 11.6319i | −0.724640 | + | 0.418371i | −0.816458 | − | 0.577405i | \(-0.804065\pi\) |
0.0918181 | + | 0.995776i | \(0.470732\pi\) | |||||||
\(774\) | −0.423339 | + | 0.244415i | −0.0152166 | + | 0.00878531i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.08861 | + | 1.88554i | 0.0390790 | + | 0.0676868i | ||||
\(777\) | −1.58754 | + | 2.74970i | −0.0569526 | + | 0.0986448i | ||||
\(778\) | −2.02001 | − | 1.16625i | −0.0724209 | − | 0.0418122i | ||||
\(779\) | −8.46410 | −0.303258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −68.7449 | −2.45989 | ||||||||
\(782\) | 2.73556 | + | 1.57938i | 0.0978235 | + | 0.0564784i | ||||
\(783\) | −7.98989 | + | 13.8389i | −0.285535 | + | 0.494562i | ||||
\(784\) | −12.7897 | − | 22.1524i | −0.456776 | − | 0.791159i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.0534798 | + | 0.0308766i | −0.00190756 | + | 0.00110133i | ||||
\(787\) | 41.4942 | − | 23.9567i | 1.47911 | − | 0.853963i | 0.479387 | − | 0.877604i | \(-0.340859\pi\) |
0.999721 | + | 0.0236408i | \(0.00752582\pi\) | |||||||
\(788\) | − | 1.25502i | − | 0.0447081i | ||||||
\(789\) | 14.9274 | + | 25.8551i | 0.531430 | + | 0.920464i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.27814 | − | 3.04734i | −0.187669 | − | 0.108351i | ||||
\(792\) | 2.04903 | 0.0728090 | ||||||||
\(793\) | −32.6147 | − | 39.0158i | −1.15818 | − | 1.38549i | ||||
\(794\) | −6.15865 | −0.218562 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.99284 | − | 5.18374i | 0.106078 | − | 0.183733i | ||||
\(797\) | 10.3476 | + | 17.9225i | 0.366530 | + | 0.634849i | 0.989020 | − | 0.147779i | \(-0.0472124\pi\) |
−0.622490 | + | 0.782627i | \(0.713879\pi\) | |||||||
\(798\) | − | 0.264893i | − | 0.00937712i | ||||||
\(799\) | 36.5902 | − | 21.1253i | 1.29447 | − | 0.747361i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.41735i | − | 0.0500795i | ||||||
\(802\) | 2.47305 | + | 4.28344i | 0.0873263 | + | 0.151254i | ||||
\(803\) | −26.0244 | + | 45.0755i | −0.918380 | + | 1.59068i | ||||
\(804\) | −27.9460 | − | 16.1346i | −0.985580 | − | 0.569025i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.48785 | − | 4.06430i | 0.0524073 | − | 0.143159i | ||||
\(807\) | 28.7361 | 1.01156 | ||||||||
\(808\) | −9.35788 | − | 5.40278i | −0.329209 | − | 0.190069i | ||||
\(809\) | −7.94574 | + | 13.7624i | −0.279357 | + | 0.483861i | −0.971225 | − | 0.238163i | \(-0.923455\pi\) |
0.691868 | + | 0.722024i | \(0.256788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.8796i | 0.838525i | 0.907865 | + | 0.419263i | \(0.137711\pi\) | ||||
−0.907865 | + | 0.419263i | \(0.862289\pi\) | |||||||
\(812\) | −1.63054 | + | 0.941391i | −0.0572206 | + | 0.0330363i | ||||
\(813\) | 42.8183 | − | 24.7212i | 1.50170 | − | 0.867009i | ||||
\(814\) | 7.04768i | 0.247021i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15.0438 | − | 26.0567i | 0.526640 | − | 0.912167i | ||||
\(817\) | −9.94679 | − | 5.74278i | −0.347994 | − | 0.200915i | ||||
\(818\) | −0.941956 | −0.0329347 | ||||||||
\(819\) | 0.494262 | + | 0.180939i | 0.0172709 | + | 0.00632250i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7782 | + | 7.95484i | 0.480862 | + | 0.277626i | 0.720776 | − | 0.693169i | \(-0.243786\pi\) |
−0.239914 | + | 0.970794i | \(0.577119\pi\) | |||||||
\(822\) | −3.16087 | + | 5.47478i | −0.110248 | + | 0.190955i | ||||
\(823\) | 7.40573 | + | 12.8271i | 0.258147 | + | 0.447124i | 0.965746 | − | 0.259491i | \(-0.0835547\pi\) |
−0.707598 | + | 0.706615i | \(0.750221\pi\) | |||||||
\(824\) | 13.0436i | 0.454397i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.171134 | − | 0.0988040i | 0.00595450 | − | 0.00343783i | ||||
\(827\) | − | 33.9498i | − | 1.18055i | −0.807202 | − | 0.590275i | \(-0.799019\pi\) | ||
0.807202 | − | 0.590275i | \(-0.200981\pi\) | |||||||
\(828\) | −1.21736 | − | 2.10853i | −0.0423061 | − | 0.0732763i | ||||
\(829\) | 11.6573 | − | 20.1910i | 0.404875 | − | 0.701264i | −0.589432 | − | 0.807818i | \(-0.700648\pi\) |
0.994307 | + | 0.106554i | \(0.0339818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.4124 | 1.47127 | ||||||||
\(832\) | 24.3836 | − | 4.25274i | 0.845350 | − | 0.147437i | ||||
\(833\) | −34.8910 | −1.20890 | ||||||||
\(834\) | 3.64911 | + | 2.10682i | 0.126358 | + | 0.0729530i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.8890 | + | 20.5924i | 0.411190 | + | 0.712202i | ||||
\(837\) | 30.0726i | 1.03946i | ||||||||
\(838\) | −3.36970 | + | 1.94550i | −0.116404 | + | 0.0672061i | ||||
\(839\) | −12.8111 | + | 7.39649i | −0.442288 | + | 0.255355i | −0.704568 | − | 0.709637i | \(-0.748859\pi\) |
0.262280 | + | 0.964992i | \(0.415526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.2849 | + | 17.8140i | 0.354652 | + | 0.614276i | ||||
\(842\) | 1.41465 | − | 2.45024i | 0.0487519 | − | 0.0844408i | ||||
\(843\) | −6.89809 | − | 3.98261i | −0.237583 | − | 0.137169i | ||||
\(844\) | −16.0050 | −0.550915 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.805291 | 0.0276865 | ||||||||
\(847\) | 5.13789 | + | 2.96636i | 0.176540 | + | 0.101925i | ||||
\(848\) | −2.89711 | + | 5.01794i | −0.0994872 | + | 0.172317i | ||||
\(849\) | 10.0703 | + | 17.4423i | 0.345612 | + | 0.598617i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6840 | − | 8.47780i | 0.503360 | − | 0.290615i | ||||
\(852\) | −34.6134 | + | 19.9841i | −1.18584 | + | 0.684643i | ||||
\(853\) | 16.3452i | 0.559650i | 0.960051 | + | 0.279825i | \(0.0902765\pi\) | ||||
−0.960051 | + | 0.279825i | \(0.909724\pi\) | |||||||
\(854\) | −0.514722 | − | 0.891525i | −0.0176134 | − | 0.0305073i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.82220 | + | 5.67085i | 0.335716 | + | 0.193826i | ||||
\(857\) | −34.1418 | −1.16626 | −0.583132 | − | 0.812378i | \(-0.698173\pi\) | ||||
−0.583132 | + | 0.812378i | \(0.698173\pi\) | |||||||
\(858\) | −6.70754 | + | 1.16986i | −0.228992 | + | 0.0399383i | ||||
\(859\) | −45.1996 | −1.54219 | −0.771096 | − | 0.636719i | \(-0.780291\pi\) | ||||
−0.771096 | + | 0.636719i | \(0.780291\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.992090 | + | 1.71835i | −0.0338103 | + | 0.0585612i | ||||
\(862\) | 1.04334 | + | 1.80712i | 0.0355364 | + | 0.0615508i | ||||
\(863\) | 4.75058i | 0.161712i | 0.996726 | + | 0.0808559i | \(0.0257653\pi\) | ||||
−0.996726 | + | 0.0808559i | \(0.974235\pi\) | |||||||
\(864\) | 12.1633 | − | 7.02250i | 0.413805 | − | 0.238910i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.306745i | 0.0104236i | ||||||||
\(867\) | −6.91853 | − | 11.9832i | −0.234966 | − | 0.406972i | ||||
\(868\) | −1.77162 | + | 3.06854i | −0.0601327 | + | 0.104153i | ||||
\(869\) | 21.0207 | + | 12.1363i | 0.713079 | + | 0.411696i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.9830 | − | 12.8065i | −1.18535 | − | 0.433933i | ||||
\(872\) | 9.75140 | 0.330224 | ||||||||
\(873\) | −0.954282 | − | 0.550955i | −0.0322975 | − | 0.0186470i | ||||
\(874\) | −0.707294 | + | 1.22507i | −0.0239246 | + | 0.0414386i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 30.2610i | 1.02242i | ||||||||
\(877\) | 1.95294 | − | 1.12753i | 0.0659462 | − | 0.0380741i | −0.466664 | − | 0.884434i | \(-0.654544\pi\) |
0.532611 | + | 0.846360i | \(0.321211\pi\) | |||||||
\(878\) | 0.791801 | − | 0.457146i | 0.0267220 | − | 0.0154279i | ||||
\(879\) | − | 27.0715i | − | 0.913098i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.49152 | + | 2.58339i | −0.0502507 | + | 0.0870367i | −0.890057 | − | 0.455850i | \(-0.849335\pi\) |
0.839806 | + | 0.542887i | \(0.182669\pi\) | |||||||
\(882\) | −0.575922 | − | 0.332509i | −0.0193923 | − | 0.0111961i | ||||
\(883\) | 28.2874 | 0.951947 | 0.475973 | − | 0.879460i | \(-0.342096\pi\) | ||||
0.475973 | + | 0.879460i | \(0.342096\pi\) | |||||||
\(884\) | 12.2512 | − | 33.4660i | 0.412051 | − | 1.12558i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.81610 | − | 1.04852i | −0.0610130 | − | 0.0352259i | ||||
\(887\) | −13.9908 | + | 24.2328i | −0.469766 | + | 0.813658i | −0.999402 | − | 0.0345665i | \(-0.988995\pi\) |
0.529637 | + | 0.848225i | \(0.322328\pi\) | |||||||
\(888\) | 4.14816 | + | 7.18483i | 0.139203 | + | 0.241107i | ||||
\(889\) | 1.07647i | 0.0361035i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34.8390 | − | 20.1143i | 1.16715 | − | 0.673855i | ||||
\(892\) | 19.9940i | 0.669448i | ||||||||
\(893\) | 9.46058 | + | 16.3862i | 0.316586 | + | 0.548343i | ||||
\(894\) | −0.599451 | + | 1.03828i | −0.0200486 | + | 0.0347252i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.19681 | 0.0733903 | ||||||||
\(897\) | 10.5061 | + | 12.5681i | 0.350787 | + | 0.419635i | ||||
\(898\) | 4.77095 | 0.159209 | ||||||||
\(899\) | −13.7394 | − | 7.93244i | −0.458234 | − | 0.264562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.95174 | + | 6.84461i | 0.131651 | + | 0.228027i | ||||
\(902\) | 4.40426i | 0.146646i | ||||||||
\(903\) | −2.33176 | + | 1.34624i | −0.0775960 | + | 0.0448001i | ||||
\(904\) | −13.7915 | + | 7.96255i | −0.458700 | + | 0.264830i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.39938 | − | 2.42381i | −0.0464914 | − | 0.0805255i | ||||
\(907\) | −8.27600 | + | 14.3344i | −0.274800 | + | 0.475967i | −0.970085 | − | 0.242767i | \(-0.921945\pi\) |
0.695285 | + | 0.718734i | \(0.255278\pi\) | |||||||
\(908\) | −11.9058 | − | 6.87383i | −0.395109 | − | 0.228116i | ||||
\(909\) | 5.46876 | 0.181387 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.04863 | 0.233532 | 0.116766 | − | 0.993159i | \(-0.462747\pi\) | ||||
0.116766 | + | 0.993159i | \(0.462747\pi\) | |||||||
\(912\) | 11.6690 | + | 6.73710i | 0.386399 | + | 0.223088i | ||||
\(913\) | 11.4519 | − | 19.8353i | 0.379004 | − | 0.656454i | ||||
\(914\) | −0.518746 | − | 0.898494i | −0.0171586 | − | 0.0297196i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.24632 | − | 1.29692i | 0.0742206 | − | 0.0428513i | ||||
\(917\) | 0.0505443 | − | 0.0291818i | 0.00166912 | − | 0.000963668i | ||||
\(918\) | − | 6.12316i | − | 0.202094i | ||||||
\(919\) | −8.27188 | − | 14.3273i | −0.272864 | − | 0.472615i | 0.696730 | − | 0.717334i | \(-0.254638\pi\) |
−0.969594 | + | 0.244719i | \(0.921304\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.96488 | − | 3.44383i | −0.196550 | − | 0.113478i | ||||
\(922\) | 0.391374 | 0.0128892 | ||||||||
\(923\) | −35.4015 | + | 29.5933i | −1.16525 | + | 0.974076i | ||||
\(924\) | 5.57412 | 0.183375 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.747155 | − | 1.29411i | 0.0245530 | − | 0.0425271i | ||||
\(927\) | −3.30074 | − | 5.71704i | −0.108410 | − | 0.187772i | ||||
\(928\) | 7.40948i | 0.243228i | ||||||||
\(929\) | −29.3035 | + | 16.9184i | −0.961416 | + | 0.555074i | −0.896609 | − | 0.442824i | \(-0.853977\pi\) |
−0.0648073 | + | 0.997898i | \(0.520643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 15.6253i | − | 0.512098i | ||||||
\(932\) | 1.21736 | + | 2.10853i | 0.0398759 | + | 0.0690670i | ||||
\(933\) | −1.78031 | + | 3.08359i | −0.0582848 | + | 0.100952i | ||||
\(934\) | 3.46975 | + | 2.00326i | 0.113534 | + | 0.0655487i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.05518 | − | 0.882066i | 0.0344898 | − | 0.0288312i | ||||
\(937\) | 30.4606 | 0.995104 | 0.497552 | − | 0.867434i | \(-0.334232\pi\) | ||||
0.497552 | + | 0.867434i | \(0.334232\pi\) | |||||||
\(938\) | −0.653115 | − | 0.377076i | −0.0213250 | − | 0.0123120i | ||||
\(939\) | 5.76780 | − | 9.99012i | 0.188225 | − | 0.326015i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.2101i | 1.24561i | 0.782375 | + | 0.622807i | \(0.214008\pi\) | ||||
−0.782375 | + | 0.622807i | \(0.785992\pi\) | |||||||
\(942\) | −5.00289 | + | 2.88842i | −0.163003 | + | 0.0941098i | ||||
\(943\) | 9.17637 | − | 5.29798i | 0.298824 | − | 0.172526i | ||||
\(944\) | 10.0516i | 0.327153i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.98823 | + | 5.17577i | −0.0971558 | + | 0.168279i | ||||
\(947\) | 45.4215 | + | 26.2241i | 1.47600 | + | 0.852169i | 0.999633 | − | 0.0270773i | \(-0.00862003\pi\) |
0.476367 | + | 0.879247i | \(0.341953\pi\) | |||||||
\(948\) | 14.1120 | 0.458338 | ||||||||
\(949\) | 6.00239 | + | 34.4155i | 0.194846 | + | 1.11717i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.445737 | + | 0.257347i | 0.0144540 | + | 0.00834504i | ||||
\(952\) | 0.730368 | − | 1.26503i | 0.0236714 | − | 0.0410000i | ||||
\(953\) | −19.8750 | − | 34.4245i | −0.643814 | − | 1.11512i | −0.984574 | − | 0.174969i | \(-0.944018\pi\) |
0.340760 | − | 0.940150i | \(-0.389316\pi\) | |||||||
\(954\) | 0.150639i | 0.00487711i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.8046 | − | 9.70215i | 0.543500 | − | 0.313790i | ||||
\(957\) | 24.9581i | 0.806782i | ||||||||
\(958\) | 3.86437 | + | 6.69329i | 0.124852 | + | 0.216250i | ||||
\(959\) | 2.98737 | − | 5.17428i | 0.0964673 | − | 0.167086i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.14359 | 0.0368901 | ||||||||
\(962\) | 3.03389 | + | 3.62933i | 0.0978164 | + | 0.117014i | ||||
\(963\) | −5.74011 | −0.184972 | ||||||||
\(964\) | 38.1776 | + | 22.0418i | 1.22962 | + | 0.709920i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.165806 | + | 0.287184i | 0.00533472 | + | 0.00924001i | ||||
\(967\) | 25.7857i | 0.829214i | 0.910001 | + | 0.414607i | \(0.136081\pi\) | ||||
−0.910001 | + | 0.414607i | \(0.863919\pi\) | |||||||
\(968\) | 13.4251 | − | 7.75097i | 0.431498 | − | 0.249126i | ||||
\(969\) | 15.9168 | − | 9.18958i | 0.511322 | − | 0.295212i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.7626 | + | 48.0863i | 0.890945 | + | 1.54316i | 0.838744 | + | 0.544525i | \(0.183290\pi\) |
0.0522005 | + | 0.998637i | \(0.483377\pi\) | |||||||
\(972\) | −4.41817 | + | 7.65249i | −0.141713 | + | 0.245454i | ||||
\(973\) | −3.44882 | − | 1.99118i | −0.110564 | − | 0.0638342i | ||||
\(974\) | −2.26365 | −0.0725321 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.3642 | 1.67614 | ||||||||
\(977\) | 35.0879 | + | 20.2580i | 1.12256 | + | 0.648112i | 0.942054 | − | 0.335461i | \(-0.108892\pi\) |
0.180509 | + | 0.983573i | \(0.442226\pi\) | |||||||
\(978\) | 3.12999 | − | 5.42130i | 0.100086 | − | 0.173354i | ||||
\(979\) | −8.66430 | − | 15.0070i | −0.276912 | − | 0.479626i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.27405 | + | 2.46762i | −0.136460 | + | 0.0787852i | ||||
\(982\) | 1.77545 | − | 1.02506i | 0.0566569 | − | 0.0327109i | ||||
\(983\) | − | 34.8059i | − | 1.11014i | −0.831805 | − | 0.555068i | \(-0.812692\pi\) | ||
0.831805 | − | 0.555068i | \(-0.187308\pi\) | |||||||
\(984\) | 2.59229 | + | 4.48997i | 0.0826390 | + | 0.143135i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.79751 | + | 1.61514i | 0.0890910 | + | 0.0514367i | ||||
\(987\) | 4.43555 | 0.141185 | ||||||||
\(988\) | 14.9871 | + | 5.48645i | 0.476803 | + | 0.174547i | ||||
\(989\) | 14.3784 | 0.457208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.9427 | + | 38.0059i | −0.697034 | + | 1.20730i | 0.272456 | + | 0.962168i | \(0.412164\pi\) |
−0.969490 | + | 0.245130i | \(0.921169\pi\) | |||||||
\(992\) | 6.97201 | + | 12.0759i | 0.221362 | + | 0.383410i | ||||
\(993\) | − | 26.6145i | − | 0.844584i | ||||||
\(994\) | −0.808936 | + | 0.467040i | −0.0256579 | + | 0.0148136i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 13.3163i | − | 0.421942i | ||||||
\(997\) | −2.74569 | − | 4.75567i | −0.0869568 | − | 0.150614i | 0.819267 | − | 0.573413i | \(-0.194381\pi\) |
−0.906223 | + | 0.422799i | \(0.861048\pi\) | |||||||
\(998\) | 2.62988 | − | 4.55508i | 0.0832474 | − | 0.144189i | ||||
\(999\) | −28.4645 | − | 16.4340i | −0.900577 | − | 0.519949i |
(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 | 325.2.n.d.251.3 | 8 | ||
5.2 | odd | 4 | 325.2.m.c.199.2 | 8 | |||
5.3 | odd | 4 | 325.2.m.b.199.3 | 8 | |||
5.4 | even | 2 | 65.2.m.a.56.2 | yes | 8 | ||
13.6 | odd | 12 | 4225.2.a.bl.1.2 | 4 | |||
13.7 | odd | 12 | 4225.2.a.bi.1.3 | 4 | |||
13.10 | even | 6 | inner | 325.2.n.d.101.3 | 8 | ||
15.14 | odd | 2 | 585.2.bu.c.316.3 | 8 | |||
20.19 | odd | 2 | 1040.2.da.b.641.2 | 8 | |||
65.4 | even | 6 | 845.2.c.g.506.4 | 8 | |||
65.9 | even | 6 | 845.2.c.g.506.5 | 8 | |||
65.19 | odd | 12 | 845.2.a.l.1.3 | 4 | |||
65.23 | odd | 12 | 325.2.m.c.49.2 | 8 | |||
65.24 | odd | 12 | 845.2.e.m.146.3 | 8 | |||
65.29 | even | 6 | 845.2.m.g.361.3 | 8 | |||
65.34 | odd | 4 | 845.2.e.m.191.3 | 8 | |||
65.44 | odd | 4 | 845.2.e.n.191.2 | 8 | |||
65.49 | even | 6 | 65.2.m.a.36.2 | ✓ | 8 | ||
65.54 | odd | 12 | 845.2.e.n.146.2 | 8 | |||
65.59 | odd | 12 | 845.2.a.m.1.2 | 4 | |||
65.62 | odd | 12 | 325.2.m.b.49.3 | 8 | |||
65.64 | even | 2 | 845.2.m.g.316.3 | 8 | |||
195.59 | even | 12 | 7605.2.a.cf.1.3 | 4 | |||
195.149 | even | 12 | 7605.2.a.cj.1.2 | 4 | |||
195.179 | odd | 6 | 585.2.bu.c.361.3 | 8 | |||
260.179 | odd | 6 | 1040.2.da.b.881.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.2 | ✓ | 8 | 65.49 | even | 6 | ||
65.2.m.a.56.2 | yes | 8 | 5.4 | even | 2 | ||
325.2.m.b.49.3 | 8 | 65.62 | odd | 12 | |||
325.2.m.b.199.3 | 8 | 5.3 | odd | 4 | |||
325.2.m.c.49.2 | 8 | 65.23 | odd | 12 | |||
325.2.m.c.199.2 | 8 | 5.2 | odd | 4 | |||
325.2.n.d.101.3 | 8 | 13.10 | even | 6 | inner | ||
325.2.n.d.251.3 | 8 | 1.1 | even | 1 | trivial | ||
585.2.bu.c.316.3 | 8 | 15.14 | odd | 2 | |||
585.2.bu.c.361.3 | 8 | 195.179 | odd | 6 | |||
845.2.a.l.1.3 | 4 | 65.19 | odd | 12 | |||
845.2.a.m.1.2 | 4 | 65.59 | odd | 12 | |||
845.2.c.g.506.4 | 8 | 65.4 | even | 6 | |||
845.2.c.g.506.5 | 8 | 65.9 | even | 6 | |||
845.2.e.m.146.3 | 8 | 65.24 | odd | 12 | |||
845.2.e.m.191.3 | 8 | 65.34 | odd | 4 | |||
845.2.e.n.146.2 | 8 | 65.54 | odd | 12 | |||
845.2.e.n.191.2 | 8 | 65.44 | odd | 4 | |||
845.2.m.g.316.3 | 8 | 65.64 | even | 2 | |||
845.2.m.g.361.3 | 8 | 65.29 | even | 6 | |||
1040.2.da.b.641.2 | 8 | 20.19 | odd | 2 | |||
1040.2.da.b.881.2 | 8 | 260.179 | odd | 6 | |||
4225.2.a.bi.1.3 | 4 | 13.7 | odd | 12 | |||
4225.2.a.bl.1.2 | 4 | 13.6 | odd | 12 | |||
7605.2.a.cf.1.3 | 4 | 195.59 | even | 12 | |||
7605.2.a.cj.1.2 | 4 | 195.149 | even | 12 |