Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(49,325)]
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([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.m (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.59513806569\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(-1.27597 + 0.609843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.49 |
Dual form | 325.2.m.b.199.3 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.109843 | + | 0.190254i | 0.0776710 | + | 0.134530i | 0.902245 | − | 0.431224i | \(-0.141918\pi\) |
−0.824574 | + | 0.565755i | \(0.808585\pi\) | |||||||
\(3\) | −1.38581 | + | 0.800098i | −0.800098 | + | 0.461937i | −0.843505 | − | 0.537121i | \(-0.819512\pi\) |
0.0434075 | + | 0.999057i | \(0.486179\pi\) | |||||||
\(4\) | 0.975869 | − | 1.69025i | 0.487934 | − | 0.845127i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.304444 | − | 0.175771i | −0.124289 | − | 0.0717582i | ||||
\(7\) | −0.166123 | + | 0.287734i | −0.0627887 | + | 0.108753i | −0.895711 | − | 0.444637i | \(-0.853333\pi\) |
0.832922 | + | 0.553390i | \(0.186666\pi\) | |||||||
\(8\) | 0.868145 | 0.306936 | ||||||||
\(9\) | −0.219687 | + | 0.380509i | −0.0732290 | + | 0.126836i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.65213 | − | 2.68591i | 1.40267 | − | 0.809832i | 0.408004 | − | 0.912980i | \(-0.366225\pi\) |
0.994666 | + | 0.103149i | \(0.0328917\pi\) | |||||||
\(12\) | 3.12316i | 0.901579i | ||||||||
\(13\) | 0.619491 | − | 3.55193i | 0.171816 | − | 0.985129i | ||||
\(14\) | −0.0729902 | −0.0195074 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.85638 | − | 3.21534i | −0.464094 | − | 0.803835i | ||||
\(17\) | 4.38581 | + | 2.53215i | 1.06372 | + | 0.614136i | 0.926458 | − | 0.376399i | \(-0.122838\pi\) |
0.137258 | + | 0.990535i | \(0.456171\pi\) | |||||||
\(18\) | −0.0965246 | −0.0227511 | ||||||||
\(19\) | 1.96410 | + | 1.13397i | 0.450596 | + | 0.260152i | 0.708082 | − | 0.706130i | \(-0.249561\pi\) |
−0.257486 | + | 0.966282i | \(0.582894\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.531659i | − | 0.116018i | ||||||
\(22\) | 1.02201 | + | 0.590059i | 0.217894 | + | 0.125801i | ||||
\(23\) | 2.45880 | − | 1.41959i | 0.512695 | − | 0.296005i | −0.221246 | − | 0.975218i | \(-0.571012\pi\) |
0.733941 | + | 0.679213i | \(0.237679\pi\) | |||||||
\(24\) | −1.20308 | + | 0.694601i | −0.245578 | + | 0.141785i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.743818 | − | 0.272296i | 0.145875 | − | 0.0534016i | ||||
\(27\) | − | 5.50367i | − | 1.05918i | ||||||
\(28\) | 0.324229 | + | 0.561581i | 0.0612735 | + | 0.106129i | ||||
\(29\) | −1.45174 | − | 2.51448i | −0.269581 | − | 0.466928i | 0.699173 | − | 0.714953i | \(-0.253552\pi\) |
−0.968754 | + | 0.248025i | \(0.920219\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46410i | 0.981382i | 0.871334 | + | 0.490691i | \(0.163256\pi\) | ||||
−0.871334 | + | 0.490691i | \(0.836744\pi\) | |||||||
\(32\) | 1.27597 | − | 2.21004i | 0.225561 | − | 0.390683i | ||||
\(33\) | −4.29798 | + | 7.44432i | −0.748182 | + | 1.29589i | ||||
\(34\) | 1.11256i | 0.190802i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.428771 | + | 0.742653i | 0.0714619 | + | 0.123776i | ||||
\(37\) | 2.98601 | + | 5.17191i | 0.490896 | + | 0.850257i | 0.999945 | − | 0.0104803i | \(-0.00333604\pi\) |
−0.509049 | + | 0.860738i | \(0.670003\pi\) | |||||||
\(38\) | 0.498239i | 0.0808250i | ||||||||
\(39\) | 1.98340 | + | 5.41796i | 0.317598 | + | 0.867568i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.23205 | − | 1.86603i | 0.504762 | − | 0.291424i | −0.225916 | − | 0.974147i | \(-0.572538\pi\) |
0.730678 | + | 0.682723i | \(0.239204\pi\) | |||||||
\(42\) | 0.101151 | − | 0.0583993i | 0.0156079 | − | 0.00901121i | ||||
\(43\) | −4.38581 | − | 2.53215i | −0.668830 | − | 0.386149i | 0.126803 | − | 0.991928i | \(-0.459528\pi\) |
−0.795633 | + | 0.605779i | \(0.792862\pi\) | |||||||
\(44\) | − | 10.4844i | − | 1.58058i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.540166 | + | 0.311865i | 0.0796432 | + | 0.0459820i | ||||
\(47\) | −8.34285 | −1.21693 | −0.608465 | − | 0.793581i | \(-0.708214\pi\) | ||||
−0.608465 | + | 0.793581i | \(0.708214\pi\) | |||||||
\(48\) | 5.14517 | + | 2.97057i | 0.742642 | + | 0.428764i | ||||
\(49\) | 3.44481 | + | 5.96658i | 0.492115 | + | 0.852368i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.10387 | −1.13477 | ||||||||
\(52\) | −5.39913 | − | 4.51332i | −0.748724 | − | 0.625885i | ||||
\(53\) | − | 1.56063i | − | 0.214369i | −0.994239 | − | 0.107184i | \(-0.965817\pi\) | ||
0.994239 | − | 0.107184i | \(-0.0341835\pi\) | |||||||
\(54\) | 1.04710 | − | 0.604542i | 0.142492 | − | 0.0822678i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.144219 | + | 0.249795i | −0.0192721 | + | 0.0333802i | ||||
\(57\) | −3.62916 | −0.480694 | ||||||||
\(58\) | 0.318928 | − | 0.552399i | 0.0418773 | − | 0.0725335i | ||||
\(59\) | −2.34461 | − | 1.35366i | −0.305242 | − | 0.176232i | 0.339553 | − | 0.940587i | \(-0.389724\pi\) |
−0.644795 | + | 0.764355i | \(0.723057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.05193 | + | 12.2143i | −0.902908 | + | 1.56388i | −0.0792059 | + | 0.996858i | \(0.525238\pi\) |
−0.823702 | + | 0.567023i | \(0.808095\pi\) | |||||||
\(62\) | −1.03957 | + | 0.600196i | −0.132025 | + | 0.0762249i | ||||
\(63\) | −0.0729902 | − | 0.126423i | −0.00919590 | − | 0.0159278i | ||||
\(64\) | −6.86488 | −0.858111 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.88842 | −0.232448 | ||||||||
\(67\) | −5.16612 | − | 8.94799i | −0.631142 | − | 1.09317i | −0.987319 | − | 0.158752i | \(-0.949253\pi\) |
0.356176 | − | 0.934419i | \(-0.384080\pi\) | |||||||
\(68\) | 8.55995 | − | 4.94209i | 1.03805 | − | 0.599316i | ||||
\(69\) | −2.27162 | + | 3.93456i | −0.273471 | + | 0.473666i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0828 | − | 6.39866i | −1.31529 | − | 0.759382i | −0.332321 | − | 0.943166i | \(-0.607832\pi\) |
−0.982967 | + | 0.183785i | \(0.941165\pi\) | |||||||
\(72\) | −0.190720 | + | 0.330337i | −0.0224766 | + | 0.0389306i | ||||
\(73\) | −9.68922 | −1.13404 | −0.567019 | − | 0.823705i | \(-0.691903\pi\) | ||||
−0.567019 | + | 0.823705i | \(0.691903\pi\) | |||||||
\(74\) | −0.655986 | + | 1.13620i | −0.0762569 | + | 0.132081i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.83341 | − | 2.21322i | 0.439722 | − | 0.253874i | ||||
\(77\) | 1.78477i | 0.203393i | ||||||||
\(78\) | −0.812927 | + | 0.972477i | −0.0920459 | + | 0.110111i | ||||
\(79\) | −4.51851 | −0.508372 | −0.254186 | − | 0.967155i | \(-0.581808\pi\) | ||||
−0.254186 | + | 0.967155i | \(0.581808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.74441 | + | 6.48552i | 0.416046 | + | 0.720613i | ||||
\(82\) | 0.710039 | + | 0.409941i | 0.0784107 | + | 0.0452704i | ||||
\(83\) | 4.26371 | 0.468003 | 0.234001 | − | 0.972236i | \(-0.424818\pi\) | ||||
0.234001 | + | 0.972236i | \(0.424818\pi\) | |||||||
\(84\) | −0.898640 | − | 0.518830i | −0.0980496 | − | 0.0566090i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.11256i | − | 0.119970i | ||||||
\(87\) | 4.02367 | + | 2.32306i | 0.431382 | + | 0.249059i | ||||
\(88\) | 4.03872 | − | 2.33176i | 0.430529 | − | 0.248566i | ||||
\(89\) | 2.79366 | − | 1.61292i | 0.296127 | − | 0.170969i | −0.344575 | − | 0.938759i | \(-0.611977\pi\) |
0.640702 | + | 0.767790i | \(0.278644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.919100 | + | 0.768307i | 0.0963478 | + | 0.0805405i | ||||
\(92\) | − | 5.54133i | − | 0.577724i | ||||||
\(93\) | −4.37182 | − | 7.57221i | −0.453336 | − | 0.785201i | ||||
\(94\) | −0.916407 | − | 1.58726i | −0.0945202 | − | 0.163714i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.08359i | 0.416780i | ||||||||
\(97\) | 1.25396 | − | 2.17191i | 0.127320 | − | 0.220524i | −0.795318 | − | 0.606193i | \(-0.792696\pi\) |
0.922637 | + | 0.385669i | \(0.126029\pi\) | |||||||
\(98\) | −0.756779 | + | 1.31078i | −0.0764462 | + | 0.132409i | ||||
\(99\) | 2.36023i | 0.237213i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.22336 | + | 10.7792i | 0.619247 | + | 1.07257i | 0.989623 | + | 0.143686i | \(0.0458955\pi\) |
−0.370376 | + | 0.928882i | \(0.620771\pi\) | |||||||
\(102\) | −0.890157 | − | 1.54180i | −0.0881386 | − | 0.152661i | ||||
\(103\) | 15.0247i | 1.48043i | 0.672370 | + | 0.740215i | \(0.265276\pi\) | ||||
−0.672370 | + | 0.740215i | \(0.734724\pi\) | |||||||
\(104\) | 0.537808 | − | 3.08359i | 0.0527364 | − | 0.302371i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.296916 | − | 0.171425i | 0.0288390 | − | 0.0166502i | ||||
\(107\) | 11.3140 | − | 6.53215i | 1.09377 | − | 0.631487i | 0.159190 | − | 0.987248i | \(-0.449112\pi\) |
0.934577 | + | 0.355761i | \(0.115778\pi\) | |||||||
\(108\) | −9.30260 | − | 5.37086i | −0.895144 | − | 0.516811i | ||||
\(109\) | 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 | ||||
\(112\) | 1.23355 | 0.116560 | ||||||||
\(113\) | 15.8862 | + | 9.17191i | 1.49445 | + | 0.862821i | 0.999980 | − | 0.00637349i | \(-0.00202876\pi\) |
0.494470 | + | 0.869195i | \(0.335362\pi\) | |||||||
\(114\) | −0.398640 | − | 0.690464i | −0.0373360 | − | 0.0646679i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.66682 | −0.526151 | ||||||||
\(117\) | 1.21545 | + | 1.01603i | 0.112368 | + | 0.0939325i | ||||
\(118\) | − | 0.594763i | − | 0.0547524i | ||||||
\(119\) | −1.45717 | + | 0.841298i | −0.133579 | + | 0.0771216i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.92820 | − | 15.4641i | 0.811655 | − | 1.40583i | ||||
\(122\) | −3.09843 | −0.280519 | ||||||||
\(123\) | −2.98601 | + | 5.17191i | −0.269239 | + | 0.466336i | ||||
\(124\) | 9.23572 | + | 5.33225i | 0.829392 | + | 0.478850i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0160350 | − | 0.0277734i | 0.00142851 | − | 0.00247425i | ||||
\(127\) | 2.80589 | − | 1.61998i | 0.248982 | − | 0.143750i | −0.370316 | − | 0.928906i | \(-0.620751\pi\) |
0.619298 | + | 0.785156i | \(0.287417\pi\) | |||||||
\(128\) | −3.30600 | − | 5.72615i | −0.292212 | − | 0.506125i | ||||
\(129\) | 8.10387 | 0.713506 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.175664 | 0.0153478 | 0.00767390 | − | 0.999971i | \(-0.497557\pi\) | ||||
0.00767390 | + | 0.999971i | \(0.497557\pi\) | |||||||
\(132\) | 8.38853 | + | 14.5294i | 0.730127 | + | 1.26462i | ||||
\(133\) | −0.652566 | + | 0.376759i | −0.0565846 | + | 0.0326692i | ||||
\(134\) | 1.13493 | − | 1.96576i | 0.0980430 | − | 0.169815i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.80752 | + | 2.19827i | 0.326492 | + | 0.188500i | ||||
\(137\) | −8.99144 | + | 15.5736i | −0.768190 | + | 1.33054i | 0.170353 | + | 0.985383i | \(0.445509\pi\) |
−0.938543 | + | 0.345162i | \(0.887824\pi\) | |||||||
\(138\) | −0.998090 | −0.0849631 | ||||||||
\(139\) | 5.99307 | − | 10.3803i | 0.508325 | − | 0.880445i | −0.491628 | − | 0.870805i | \(-0.663598\pi\) |
0.999954 | − | 0.00964021i | \(-0.00306862\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5616 | − | 6.67510i | 0.973663 | − | 0.562144i | ||||
\(142\) | − | 2.81140i | − | 0.235928i | ||||||
\(143\) | −6.65821 | − | 18.1879i | −0.556788 | − | 1.52095i | ||||
\(144\) | 1.63129 | 0.135941 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.06430 | − | 1.84342i | −0.0880819 | − | 0.152562i | ||||
\(147\) | −9.54769 | − | 5.51236i | −0.787481 | − | 0.454652i | ||||
\(148\) | 11.6558 | 0.958101 | ||||||||
\(149\) | −2.95350 | − | 1.70520i | −0.241960 | − | 0.139696i | 0.374117 | − | 0.927381i | \(-0.377946\pi\) |
−0.616077 | + | 0.787686i | \(0.711279\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.96141i | − | 0.647890i | −0.946076 | − | 0.323945i | \(-0.894991\pi\) | ||
0.946076 | − | 0.323945i | \(-0.105009\pi\) | |||||||
\(152\) | 1.70512 | + | 0.984454i | 0.138304 | + | 0.0798498i | ||||
\(153\) | −1.92701 | + | 1.11256i | −0.155790 | + | 0.0899451i | ||||
\(154\) | −0.339560 | + | 0.196045i | −0.0273625 | + | 0.0157978i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.0933 | + | 1.93477i | 0.888172 | + | 0.154906i | ||||
\(157\) | 16.4329i | 1.31148i | 0.754985 | + | 0.655742i | \(0.227644\pi\) | ||||
−0.754985 | + | 0.655742i | \(0.772356\pi\) | |||||||
\(158\) | −0.496329 | − | 0.859667i | −0.0394858 | − | 0.0683914i | ||||
\(159\) | 1.24865 | + | 2.16273i | 0.0990247 | + | 0.171516i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.943307i | 0.0743430i | ||||||||
\(162\) | −0.822599 | + | 1.42478i | −0.0646295 | + | 0.111942i | ||||
\(163\) | −8.90361 | + | 15.4215i | −0.697384 | + | 1.20791i | 0.271986 | + | 0.962301i | \(0.412320\pi\) |
−0.969370 | + | 0.245604i | \(0.921014\pi\) | |||||||
\(164\) | − | 7.28398i | − | 0.568784i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.468341 | + | 0.811190i | 0.0363503 | + | 0.0629605i | ||||
\(167\) | −3.14683 | − | 5.45047i | −0.243509 | − | 0.421770i | 0.718202 | − | 0.695834i | \(-0.244965\pi\) |
−0.961711 | + | 0.274064i | \(0.911632\pi\) | |||||||
\(168\) | − | 0.461557i | − | 0.0356099i | ||||||
\(169\) | −12.2325 | − | 4.40078i | −0.940959 | − | 0.338522i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.862975 | + | 0.498239i | −0.0659933 | + | 0.0381013i | ||||
\(172\) | −8.55995 | + | 4.94209i | −0.652690 | + | 0.376831i | ||||
\(173\) | 13.8349 | + | 7.98756i | 1.05184 | + | 0.607283i | 0.923165 | − | 0.384404i | \(-0.125593\pi\) |
0.128679 | + | 0.991686i | \(0.458926\pi\) | |||||||
\(174\) | 1.02069i | 0.0773786i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.2722 | − | 9.97212i | −1.30194 | − | 0.751677i | ||||
\(177\) | 4.33225 | 0.325632 | ||||||||
\(178\) | 0.613729 | + | 0.354337i | 0.0460010 | + | 0.0265587i | ||||
\(179\) | −11.8087 | − | 20.4533i | −0.882625 | − | 1.52875i | −0.848412 | − | 0.529336i | \(-0.822441\pi\) |
−0.0342123 | − | 0.999415i | \(-0.510892\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.62590 | 0.195182 | 0.0975909 | − | 0.995227i | \(-0.468886\pi\) | ||||
0.0975909 | + | 0.995227i | \(0.468886\pi\) | |||||||
\(182\) | −0.0452168 | + | 0.259256i | −0.00335169 | + | 0.0192174i | ||||
\(183\) | − | 22.5689i | − | 1.66834i | ||||||
\(184\) | 2.13459 | − | 1.23241i | 0.157364 | − | 0.0908544i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.960431 | − | 1.66351i | 0.0704222 | − | 0.121975i | ||||
\(187\) | 27.2045 | 1.98939 | ||||||||
\(188\) | −8.14153 | + | 14.1015i | −0.593782 | + | 1.02846i | ||||
\(189\) | 1.58359 | + | 0.914288i | 0.115189 | + | 0.0665046i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.00791 | − | 1.74575i | 0.0729298 | − | 0.126318i | −0.827254 | − | 0.561828i | \(-0.810098\pi\) |
0.900184 | + | 0.435509i | \(0.143432\pi\) | |||||||
\(192\) | 9.51343 | − | 5.49258i | 0.686572 | − | 0.396393i | ||||
\(193\) | −11.4105 | − | 19.7636i | −0.821348 | − | 1.42262i | −0.904678 | − | 0.426095i | \(-0.859889\pi\) |
0.0833298 | − | 0.996522i | \(-0.473445\pi\) | |||||||
\(194\) | 0.550955 | 0.0395563 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4467 | 0.960480 | ||||||||
\(197\) | 0.321513 | + | 0.556877i | 0.0229068 | + | 0.0396758i | 0.877252 | − | 0.480031i | \(-0.159375\pi\) |
−0.854345 | + | 0.519707i | \(0.826041\pi\) | |||||||
\(198\) | −0.449045 | + | 0.259256i | −0.0319122 | + | 0.0184245i | ||||
\(199\) | −1.53342 | + | 2.65596i | −0.108701 | + | 0.188276i | −0.915244 | − | 0.402899i | \(-0.868003\pi\) |
0.806543 | + | 0.591175i | \(0.201336\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3185 | + | 8.26681i | 1.00995 | + | 0.583096i | ||||
\(202\) | −1.36719 | + | 2.36804i | −0.0961952 | + | 0.166615i | ||||
\(203\) | 0.964670 | 0.0677065 | ||||||||
\(204\) | −7.90831 | + | 13.6976i | −0.553693 | + | 0.959024i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.85852 | + | 1.65037i | −0.199163 | + | 0.114987i | ||||
\(207\) | 1.24746i | 0.0867045i | ||||||||
\(208\) | −12.5707 | + | 4.60185i | −0.871620 | + | 0.319081i | ||||
\(209\) | 12.1830 | 0.842716 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.10020 | + | 7.10175i | 0.282269 | + | 0.488904i | 0.971943 | − | 0.235215i | \(-0.0755796\pi\) |
−0.689674 | + | 0.724120i | \(0.742246\pi\) | |||||||
\(212\) | −2.63786 | − | 1.52297i | −0.181169 | − | 0.104598i | ||||
\(213\) | 20.4782 | 1.40314 | ||||||||
\(214\) | 2.48554 | + | 1.43503i | 0.169908 | + | 0.0980964i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 4.77798i | − | 0.325101i | ||||||
\(217\) | −1.57221 | − | 0.907714i | −0.106728 | − | 0.0616197i | ||||
\(218\) | −2.13703 | + | 1.23381i | −0.144738 | + | 0.0835643i | ||||
\(219\) | 13.4274 | − | 7.75232i | 0.907341 | − | 0.523854i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.7110 | − | 14.0095i | 0.787767 | − | 0.942378i | ||||
\(222\) | − | 2.09941i | − | 0.140903i | ||||||
\(223\) | 5.12210 | + | 8.87174i | 0.343001 | + | 0.594095i | 0.984989 | − | 0.172620i | \(-0.0552232\pi\) |
−0.641987 | + | 0.766715i | \(0.721890\pi\) | |||||||
\(224\) | 0.423935 | + | 0.734278i | 0.0283254 | + | 0.0490610i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.02990i | 0.268065i | ||||||||
\(227\) | −3.52190 | + | 6.10012i | −0.233757 | + | 0.404879i | −0.958911 | − | 0.283708i | \(-0.908435\pi\) |
0.725154 | + | 0.688587i | \(0.241769\pi\) | |||||||
\(228\) | −3.54159 | + | 6.13421i | −0.234547 | + | 0.406248i | ||||
\(229\) | 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 | ||||
\(232\) | −1.26032 | − | 2.18294i | −0.0827440 | − | 0.143317i | ||||
\(233\) | 1.24746i | 0.0817238i | 0.999165 | + | 0.0408619i | \(0.0130104\pi\) | ||||
−0.999165 | + | 0.0408619i | \(0.986990\pi\) | |||||||
\(234\) | −0.0597962 | + | 0.342849i | −0.00390900 | + | 0.0224127i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.57606 | + | 2.64199i | −0.297876 | + | 0.171979i | ||||
\(237\) | 6.26180 | − | 3.61525i | 0.406748 | − | 0.234836i | ||||
\(238\) | −0.320121 | − | 0.184822i | −0.0207504 | − | 0.0119802i | ||||
\(239\) | 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 | −0.286944 | − | 0.957947i | \(-0.592640\pi\) |
−0.973079 | + | 0.230472i | \(0.925973\pi\) | |||||||
\(242\) | 3.92282 | 0.252168 | ||||||||
\(243\) | 3.92086 | + | 2.26371i | 0.251523 | + | 0.145217i | ||||
\(244\) | 13.7635 | + | 23.8391i | 0.881119 | + | 1.52614i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.31197 | −0.0836483 | ||||||||
\(247\) | 5.24455 | − | 6.27387i | 0.333702 | − | 0.399197i | ||||
\(248\) | 4.74363i | 0.301221i | ||||||||
\(249\) | −5.90869 | + | 3.41139i | −0.374448 | + | 0.216188i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.38418 | + | 5.86157i | −0.213608 | + | 0.369979i | −0.952841 | − | 0.303470i | \(-0.901855\pi\) |
0.739233 | + | 0.673449i | \(0.235188\pi\) | |||||||
\(252\) | −0.284915 | −0.0179480 | ||||||||
\(253\) | 7.62577 | − | 13.2082i | 0.479428 | − | 0.830394i | ||||
\(254\) | 0.616417 | + | 0.355888i | 0.0386774 | + | 0.0223304i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.13860 | + | 10.6324i | −0.383663 | + | 0.664523i | ||||
\(257\) | −8.88007 | + | 5.12691i | −0.553924 | + | 0.319808i | −0.750703 | − | 0.660640i | \(-0.770285\pi\) |
0.196779 | + | 0.980448i | \(0.436952\pi\) | |||||||
\(258\) | 0.890157 | + | 1.54180i | 0.0554187 | + | 0.0959881i | ||||
\(259\) | −1.98418 | −0.123291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.27571 | 0.0789645 | ||||||||
\(262\) | 0.0192955 | + | 0.0334208i | 0.00119208 | + | 0.00206474i | ||||
\(263\) | 16.1574 | − | 9.32850i | 0.996310 | − | 0.575220i | 0.0891555 | − | 0.996018i | \(-0.471583\pi\) |
0.907154 | + | 0.420798i | \(0.138250\pi\) | |||||||
\(264\) | −3.73127 | + | 6.46275i | −0.229644 | + | 0.397754i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.143360 | − | 0.0827690i | −0.00878998 | − | 0.00507489i | ||||
\(267\) | −2.58098 | + | 4.47040i | −0.157954 | + | 0.273584i | ||||
\(268\) | −20.1658 | −1.23182 | ||||||||
\(269\) | 8.97894 | − | 15.5520i | 0.547456 | − | 0.948221i | −0.450992 | − | 0.892528i | \(-0.648930\pi\) |
0.998448 | − | 0.0556934i | \(-0.0177369\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.7582 | + | 15.4488i | −1.62544 | + | 0.938450i | −0.640014 | + | 0.768363i | \(0.721071\pi\) |
−0.985429 | + | 0.170086i | \(0.945595\pi\) | |||||||
\(272\) | − | 18.8025i | − | 1.14007i | ||||||
\(273\) | −1.88842 | − | 0.329358i | −0.114292 | − | 0.0199337i | ||||
\(274\) | −3.95060 | −0.238665 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.43361 | + | 7.67923i | 0.266872 | + | 0.462235i | ||||
\(277\) | −22.9536 | − | 13.2522i | −1.37915 | − | 0.796250i | −0.387089 | − | 0.922042i | \(-0.626519\pi\) |
−0.992057 | + | 0.125792i | \(0.959853\pi\) | |||||||
\(278\) | 2.63320 | 0.157929 | ||||||||
\(279\) | −2.07914 | − | 1.20039i | −0.124475 | − | 0.0718656i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.97766i | − | 0.296942i | −0.988917 | − | 0.148471i | \(-0.952565\pi\) | ||
0.988917 | − | 0.148471i | \(-0.0474352\pi\) | |||||||
\(282\) | 2.53993 | + | 1.46643i | 0.151251 | + | 0.0873247i | ||||
\(283\) | 10.9001 | − | 6.29317i | 0.647943 | − | 0.374090i | −0.139725 | − | 0.990190i | \(-0.544622\pi\) |
0.787668 | + | 0.616100i | \(0.211288\pi\) | |||||||
\(284\) | −21.6307 | + | 12.4885i | −1.28355 | + | 0.741057i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.72898 | − | 3.26458i | 0.161368 | − | 0.193039i | ||||
\(287\) | 1.23996i | 0.0731926i | ||||||||
\(288\) | 0.560626 | + | 0.971033i | 0.0330352 | + | 0.0572187i | ||||
\(289\) | 4.32355 | + | 7.48861i | 0.254327 | + | 0.440507i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.01315i | 0.235255i | ||||||||
\(292\) | −9.45541 | + | 16.3772i | −0.553336 | + | 0.958406i | ||||
\(293\) | −8.45880 | + | 14.6511i | −0.494168 | + | 0.855925i | −0.999977 | − | 0.00672072i | \(-0.997861\pi\) |
0.505809 | + | 0.862645i | \(0.331194\pi\) | |||||||
\(294\) | − | 2.42199i | − | 0.141253i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.59229 | + | 4.48997i | 0.150674 | + | 0.260974i | ||||
\(297\) | −14.7824 | − | 25.6038i | −0.857759 | − | 1.48568i | ||||
\(298\) | − | 0.749222i | − | 0.0434012i | ||||||
\(299\) | −3.51908 | − | 9.61292i | −0.203514 | − | 0.555929i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.45717 | − | 0.841298i | 0.0839899 | − | 0.0484916i | ||||
\(302\) | 1.51469 | − | 0.874509i | 0.0871608 | − | 0.0503223i | ||||
\(303\) | −17.2488 | − | 9.95859i | −0.990917 | − | 0.572106i | ||||
\(304\) | − | 8.42034i | − | 0.482940i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.423339 | − | 0.244415i | −0.0242007 | − | 0.0139723i | ||||
\(307\) | 4.30426 | 0.245657 | 0.122828 | − | 0.992428i | \(-0.460803\pi\) | ||||
0.122828 | + | 0.992428i | \(0.460803\pi\) | |||||||
\(308\) | 3.01671 | + | 1.74170i | 0.171893 | + | 0.0992425i | ||||
\(309\) | −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 | \(0.479905\pi\) | |||||||
\(312\) | 1.72188 | + | 4.70357i | 0.0974820 | + | 0.266287i | ||||
\(313\) | 7.20887i | 0.407469i | 0.979026 | + | 0.203735i | \(0.0653080\pi\) | ||||
−0.979026 | + | 0.203735i | \(0.934692\pi\) | |||||||
\(314\) | −3.12642 | + | 1.80504i | −0.176434 | + | 0.101864i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.40948 | + | 7.63744i | −0.248052 | + | 0.429639i | ||||
\(317\) | −0.321644 | −0.0180653 | −0.00903266 | − | 0.999959i | \(-0.502875\pi\) | ||||
−0.00903266 | + | 0.999959i | \(0.502875\pi\) | |||||||
\(318\) | −0.274313 | + | 0.475124i | −0.0153827 | + | 0.0266436i | ||||
\(319\) | −13.5073 | − | 7.79847i | −0.756266 | − | 0.436630i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.4527 | + | 18.1046i | −0.583414 | + | 1.01050i | ||||
\(322\) | −0.179468 | + | 0.103616i | −0.0100014 | + | 0.00577430i | ||||
\(323\) | 5.74278 | + | 9.94679i | 0.319537 | + | 0.553454i | ||||
\(324\) | 14.6162 | 0.812013 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.91201 | −0.216666 | ||||||||
\(327\) | −8.98707 | − | 15.5661i | −0.496986 | − | 0.860805i | ||||
\(328\) | 2.80589 | − | 1.61998i | 0.154929 | − | 0.0894485i | ||||
\(329\) | 1.38594 | − | 2.40052i | 0.0764094 | − | 0.132345i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4037 | − | 8.31600i | −0.791701 | − | 0.457089i | 0.0488600 | − | 0.998806i | \(-0.484441\pi\) |
−0.840561 | + | 0.541717i | \(0.817775\pi\) | |||||||
\(332\) | 4.16082 | − | 7.20676i | 0.228355 | − | 0.395522i | ||||
\(333\) | −2.62395 | −0.143791 | ||||||||
\(334\) | 0.691317 | − | 1.19740i | 0.0378272 | − | 0.0655186i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.70947 | + | 0.986961i | −0.0932590 | + | 0.0538431i | ||||
\(337\) | 24.2186i | 1.31927i | 0.751586 | + | 0.659636i | \(0.229289\pi\) | ||||
−0.751586 | + | 0.659636i | \(0.770711\pi\) | |||||||
\(338\) | −0.506387 | − | 2.81068i | −0.0275438 | − | 0.152881i | ||||
\(339\) | −29.3537 | −1.59427 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.6761 | + | 25.4197i | 0.794754 | + | 1.37655i | ||||
\(342\) | −0.189584 | − | 0.109456i | −0.0102515 | − | 0.00591873i | ||||
\(343\) | −4.61478 | −0.249174 | ||||||||
\(344\) | −3.80752 | − | 2.19827i | −0.205288 | − | 0.118523i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.50952i | 0.188673i | ||||||||
\(347\) | −5.43309 | − | 3.13680i | −0.291664 | − | 0.168392i | 0.347028 | − | 0.937855i | \(-0.387191\pi\) |
−0.638692 | + | 0.769463i | \(0.720524\pi\) | |||||||
\(348\) | 7.85314 | − | 4.53401i | 0.420972 | − | 0.243049i | ||||
\(349\) | 6.12275 | − | 3.53497i | 0.327743 | − | 0.189223i | −0.327095 | − | 0.944991i | \(-0.606070\pi\) |
0.654839 | + | 0.755769i | \(0.272737\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.5487 | − | 3.40948i | −1.04343 | − | 0.181984i | ||||
\(352\) | − | 13.7085i | − | 0.730666i | ||||||
\(353\) | −10.8949 | − | 18.8705i | −0.579878 | − | 1.00438i | −0.995493 | − | 0.0948371i | \(-0.969767\pi\) |
0.415615 | − | 0.909541i | \(-0.363566\pi\) | |||||||
\(354\) | 0.475869 | + | 0.824229i | 0.0252921 | + | 0.0438073i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.29598i | − | 0.333687i | ||||||
\(357\) | 1.34624 | − | 2.33176i | 0.0712506 | − | 0.123410i | ||||
\(358\) | 2.59422 | − | 4.49332i | 0.137109 | − | 0.237479i | ||||
\(359\) | 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 | ||||
\(362\) | 0.288438 | + | 0.499589i | 0.0151600 | + | 0.0262578i | ||||
\(363\) | 28.5737i | 1.49973i | ||||||||
\(364\) | 2.19556 | − | 0.803745i | 0.115078 | − | 0.0421277i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.29384 | − | 2.47905i | 0.224443 | − | 0.129582i | ||||
\(367\) | −5.53505 | + | 3.19566i | −0.288927 | + | 0.166812i | −0.637458 | − | 0.770485i | \(-0.720014\pi\) |
0.348531 | + | 0.937297i | \(0.386681\pi\) | |||||||
\(368\) | −9.12892 | − | 5.27059i | −0.475878 | − | 0.274748i | ||||
\(369\) | 1.63977i | 0.0853628i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.449045 | + | 0.259256i | 0.0233133 | + | 0.0134599i | ||||
\(372\) | −17.0653 | −0.884793 | ||||||||
\(373\) | 17.3899 | + | 10.0401i | 0.900414 | + | 0.519855i | 0.877335 | − | 0.479879i | \(-0.159319\pi\) |
0.0230798 | + | 0.999734i | \(0.492653\pi\) | |||||||
\(374\) | 2.98823 | + | 5.17577i | 0.154518 | + | 0.267633i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.24280 | −0.373519 | ||||||||
\(377\) | −9.83062 | + | 3.59878i | −0.506302 | + | 0.185346i | ||||
\(378\) | 0.401714i | 0.0206619i | ||||||||
\(379\) | 4.73007 | − | 2.73091i | 0.242968 | − | 0.140277i | −0.373572 | − | 0.927601i | \(-0.621867\pi\) |
0.616540 | + | 0.787324i | \(0.288534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.59229 | + | 4.48997i | −0.132807 | + | 0.230028i | ||||
\(382\) | 0.442849 | 0.0226581 | ||||||||
\(383\) | −2.83388 | + | 4.90842i | −0.144804 | + | 0.250808i | −0.929300 | − | 0.369326i | \(-0.879589\pi\) |
0.784496 | + | 0.620134i | \(0.212922\pi\) | |||||||
\(384\) | 9.16297 | + | 5.29024i | 0.467596 | + | 0.269966i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.50675 | − | 4.34181i | 0.127590 | − | 0.220992i | ||||
\(387\) | 1.92701 | − | 1.11256i | 0.0979554 | − | 0.0565546i | ||||
\(388\) | −2.44739 | − | 4.23901i | −0.124247 | − | 0.215203i | ||||
\(389\) | 10.6174 | 0.538325 | 0.269162 | − | 0.963095i | \(-0.413253\pi\) | ||||
0.269162 | + | 0.963095i | \(0.413253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3784 | 0.727149 | ||||||||
\(392\) | 2.99059 | + | 5.17986i | 0.151048 | + | 0.261622i | ||||
\(393\) | −0.243436 | + | 0.140548i | −0.0122797 | + | 0.00708971i | ||||
\(394\) | −0.0706321 | + | 0.122338i | −0.00355840 | + | 0.00616332i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.98940 | + | 2.30328i | 0.200475 | + | 0.115744i | ||||
\(397\) | 14.0169 | − | 24.2780i | 0.703487 | − | 1.21848i | −0.263748 | − | 0.964592i | \(-0.584959\pi\) |
0.967235 | − | 0.253884i | \(-0.0817081\pi\) | |||||||
\(398\) | −0.673745 | −0.0337718 | ||||||||
\(399\) | 0.602888 | − | 1.04423i | 0.0301822 | − | 0.0522770i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.4979 | − | 11.2571i | 0.973680 | − | 0.562155i | 0.0733241 | − | 0.997308i | \(-0.476639\pi\) |
0.900356 | + | 0.435154i | \(0.143306\pi\) | |||||||
\(402\) | 3.63222i | 0.181159i | ||||||||
\(403\) | 19.4081 | + | 3.38496i | 0.966788 | + | 0.168617i | ||||
\(404\) | 24.2927 | 1.20861 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.105963 | + | 0.183533i | 0.00525884 | + | 0.00910857i | ||||
\(407\) | 27.7826 | + | 16.0403i | 1.37713 | + | 0.795087i | ||||
\(408\) | −7.03533 | −0.348301 | ||||||||
\(409\) | 3.71328 | + | 2.14386i | 0.183610 | + | 0.106007i | 0.588988 | − | 0.808142i | \(-0.299527\pi\) |
−0.405378 | + | 0.914149i | \(0.632860\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 28.7761i | − | 1.41942i | ||||||
\(412\) | 25.3956 | + | 14.6622i | 1.25115 | + | 0.722353i | ||||
\(413\) | 0.778989 | − | 0.449749i | 0.0383315 | − | 0.0221307i | ||||
\(414\) | −0.237335 | + | 0.137025i | −0.0116644 | + | 0.00673443i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.05946 | − | 5.90125i | −0.346119 | − | 0.289333i | ||||
\(417\) | 19.1802i | 0.939257i | ||||||||
\(418\) | 1.33822 | + | 2.31787i | 0.0654546 | + | 0.113371i | ||||
\(419\) | 8.85578 | + | 15.3387i | 0.432633 | + | 0.749343i | 0.997099 | − | 0.0761137i | \(-0.0242512\pi\) |
−0.564466 | + | 0.825456i | \(0.690918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.8787i | 0.627672i | 0.949477 | + | 0.313836i | \(0.101614\pi\) | ||||
−0.949477 | + | 0.313836i | \(0.898386\pi\) | |||||||
\(422\) | −0.900759 | + | 1.56016i | −0.0438483 | + | 0.0759474i | ||||
\(423\) | 1.83281 | − | 3.17453i | 0.0891145 | − | 0.154351i | ||||
\(424\) | − | 1.35485i | − | 0.0657973i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.24940 | + | 3.89607i | 0.108984 | + | 0.188765i | ||||
\(427\) | −2.34298 | − | 4.05816i | −0.113385 | − | 0.196388i | ||||
\(428\) | − | 25.4981i | − | 1.23250i | ||||||
\(429\) | 23.7792 | + | 19.8778i | 1.14807 | + | 0.959710i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.22590 | − | 4.74923i | 0.396228 | − | 0.228762i | −0.288627 | − | 0.957442i | \(-0.593199\pi\) |
0.684855 | + | 0.728679i | \(0.259866\pi\) | |||||||
\(432\) | −17.6962 | + | 10.2169i | −0.851408 | + | 0.491560i | ||||
\(433\) | −1.20922 | − | 0.698141i | −0.0581112 | − | 0.0335505i | 0.470663 | − | 0.882313i | \(-0.344015\pi\) |
−0.528774 | + | 0.848763i | \(0.677348\pi\) | |||||||
\(434\) | − | 0.398826i | − | 0.0191443i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.9857 | + | 10.9614i | 0.909251 | + | 0.524956i | ||||
\(437\) | 6.43911 | 0.308024 | ||||||||
\(438\) | 2.94983 | + | 1.70308i | 0.140948 | + | 0.0813765i | ||||
\(439\) | −2.08090 | − | 3.60422i | −0.0993159 | − | 0.172020i | 0.812086 | − | 0.583538i | \(-0.198332\pi\) |
−0.911402 | + | 0.411518i | \(0.864999\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.02711 | −0.144148 | ||||||||
\(442\) | 3.95174 | + | 0.689221i | 0.187965 | + | 0.0327829i | ||||
\(443\) | 9.54563i | 0.453526i | 0.973950 | + | 0.226763i | \(0.0728144\pi\) | ||||
−0.973950 | + | 0.226763i | \(0.927186\pi\) | |||||||
\(444\) | −16.1527 | + | 9.32578i | −0.766574 | + | 0.442582i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.12526 | + | 1.94900i | −0.0532825 | + | 0.0922880i | ||||
\(447\) | 5.45732 | 0.258122 | ||||||||
\(448\) | 1.14042 | − | 1.97526i | 0.0538796 | − | 0.0933223i | ||||
\(449\) | −18.8075 | − | 10.8585i | −0.887582 | − | 0.512446i | −0.0144310 | − | 0.999896i | \(-0.504594\pi\) |
−0.873151 | + | 0.487450i | \(0.837927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0239 | − | 17.3620i | 0.472009 | − | 0.817544i | ||||
\(452\) | 31.0057 | − | 17.9012i | 1.45839 | − | 0.842000i | ||||
\(453\) | 6.36991 | + | 11.0330i | 0.299284 | + | 0.518376i | ||||
\(454\) | −1.54743 | −0.0726246 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.15064 | −0.147542 | ||||||||
\(457\) | −2.36130 | − | 4.08989i | −0.110457 | − | 0.191317i | 0.805498 | − | 0.592599i | \(-0.201898\pi\) |
−0.915955 | + | 0.401282i | \(0.868565\pi\) | |||||||
\(458\) | −0.252845 | + | 0.145980i | −0.0118147 | + | 0.00682122i | ||||
\(459\) | 13.9361 | − | 24.1381i | 0.650482 | − | 1.12667i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.54283 | + | 0.890753i | 0.0718568 | + | 0.0414865i | 0.535498 | − | 0.844537i | \(-0.320124\pi\) |
−0.463641 | + | 0.886023i | \(0.653457\pi\) | |||||||
\(462\) | 0.313710 | − | 0.543362i | 0.0145951 | − | 0.0252795i | ||||
\(463\) | 6.80200 | 0.316116 | 0.158058 | − | 0.987430i | \(-0.449477\pi\) | ||||
0.158058 | + | 0.987430i | \(0.449477\pi\) | |||||||
\(464\) | −5.38995 | + | 9.33566i | −0.250222 | + | 0.433397i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.237335 | + | 0.137025i | −0.0109943 | + | 0.00634758i | ||||
\(467\) | 18.2374i | 0.843927i | 0.906613 | + | 0.421963i | \(0.138659\pi\) | ||||
−0.906613 | + | 0.421963i | \(0.861341\pi\) | |||||||
\(468\) | 2.90348 | − | 1.06290i | 0.134213 | − | 0.0491325i | ||||
\(469\) | 3.43285 | 0.158514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.1479 | − | 22.7728i | −0.605823 | − | 1.04932i | ||||
\(472\) | −2.03546 | − | 1.17517i | −0.0936897 | − | 0.0540918i | ||||
\(473\) | −27.2045 | −1.25086 | ||||||||
\(474\) | 1.37564 | + | 0.794223i | 0.0631850 | + | 0.0364799i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.28398i | 0.150521i | ||||||||
\(477\) | 0.593832 | + | 0.342849i | 0.0271897 | + | 0.0156980i | ||||
\(478\) | −1.89152 | + | 1.09207i | −0.0865162 | + | 0.0499502i | ||||
\(479\) | −30.4674 | + | 17.5904i | −1.39209 | + | 0.803724i | −0.993547 | − | 0.113425i | \(-0.963818\pi\) |
−0.398544 | + | 0.917149i | \(0.630485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2201 | − | 7.40214i | 0.921957 | − | 0.337508i | ||||
\(482\) | − | 4.96204i | − | 0.226015i | ||||||
\(483\) | −0.754738 | − | 1.30724i | −0.0343418 | − | 0.0594817i | ||||
\(484\) | −17.4255 | − | 30.1819i | −0.792069 | − | 1.37190i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.994615i | 0.0451166i | ||||||||
\(487\) | 5.15200 | − | 8.92352i | 0.233459 | − | 0.404363i | −0.725364 | − | 0.688365i | \(-0.758329\pi\) |
0.958824 | + | 0.284002i | \(0.0916621\pi\) | |||||||
\(488\) | −6.12210 | + | 10.6038i | −0.277134 | + | 0.480011i | ||||
\(489\) | − | 28.4950i | − | 1.28859i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.66599 | + | 8.08174i | 0.210573 | + | 0.364724i | 0.951894 | − | 0.306427i | \(-0.0991336\pi\) |
−0.741321 | + | 0.671151i | \(0.765800\pi\) | |||||||
\(492\) | 5.82790 | + | 10.0942i | 0.262742 | + | 0.455083i | ||||
\(493\) | − | 14.7041i | − | 0.662238i | ||||||
\(494\) | 1.76971 | + | 0.308654i | 0.0796230 | + | 0.0138870i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.5689 | − | 10.1434i | 0.788869 | − | 0.455454i | ||||
\(497\) | 3.68222 | − | 2.12593i | 0.165170 | − | 0.0953611i | ||||
\(498\) | −1.29806 | − | 0.749437i | −0.0581676 | − | 0.0335831i | ||||
\(499\) | − | 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 | ||||
\(502\) | −1.48692 | −0.0663645 | ||||||||
\(503\) | −36.4980 | − | 21.0721i | −1.62737 | − | 0.939560i | −0.984875 | − | 0.173266i | \(-0.944568\pi\) |
−0.642490 | − | 0.766294i | \(-0.722099\pi\) | |||||||
\(504\) | −0.0633661 | − | 0.109753i | −0.00282255 | − | 0.00488880i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.35056 | 0.148951 | ||||||||
\(507\) | 20.4729 | − | 3.68852i | 0.909235 | − | 0.163813i | ||||
\(508\) | − | 6.32355i | − | 0.280562i | ||||||
\(509\) | 29.0640 | − | 16.7801i | 1.28824 | − | 0.743765i | 0.309899 | − | 0.950770i | \(-0.399705\pi\) |
0.978340 | + | 0.207005i | \(0.0663715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.60960 | − | 2.78792i | 0.0712047 | − | 0.123330i | ||||
\(512\) | −15.9211 | −0.703621 | ||||||||
\(513\) | 6.24102 | − | 10.8098i | 0.275548 | − | 0.477263i | ||||
\(514\) | −1.95084 | − | 1.12632i | −0.0860477 | − | 0.0496796i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.90831 | − | 13.6976i | 0.348144 | − | 0.603003i | ||||
\(517\) | −38.8120 | + | 22.4081i | −1.70695 | + | 0.985508i | ||||
\(518\) | −0.217949 | − | 0.377499i | −0.00957614 | − | 0.0165864i | ||||
\(519\) | −25.5633 | −1.12210 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4649 | 0.546098 | 0.273049 | − | 0.962000i | \(-0.411968\pi\) | ||||
0.273049 | + | 0.962000i | \(0.411968\pi\) | |||||||
\(522\) | 0.140128 | + | 0.242710i | 0.00613326 | + | 0.0106231i | ||||
\(523\) | −4.90132 | + | 2.82978i | −0.214320 | + | 0.123738i | −0.603317 | − | 0.797501i | \(-0.706155\pi\) |
0.388998 | + | 0.921239i | \(0.372821\pi\) | |||||||
\(524\) | 0.171425 | − | 0.296916i | 0.00748872 | − | 0.0129708i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.54958 | + | 2.04935i | 0.154769 | + | 0.0893558i | ||||
\(527\) | −13.8359 | + | 23.9645i | −0.602702 | + | 1.04391i | ||||
\(528\) | 31.9147 | 1.38891 | ||||||||
\(529\) | −7.46953 | + | 12.9376i | −0.324762 | + | 0.562505i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.03016 | − | 0.594763i | 0.0447051 | − | 0.0258105i | ||||
\(532\) | 1.47067i | 0.0637616i | ||||||||
\(533\) | −4.62577 | − | 12.6360i | −0.200364 | − | 0.547327i | ||||
\(534\) | −1.13402 | −0.0490737 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.48494 | − | 7.76815i | −0.193720 | − | 0.335533i | ||||
\(537\) | 32.7293 | + | 18.8963i | 1.41237 | + | 0.815433i | ||||
\(538\) | 3.94511 | 0.170086 | ||||||||
\(539\) | 32.0514 | + | 18.5049i | 1.38055 | + | 0.797061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.4750i | 0.665321i | 0.943047 | + | 0.332660i | \(0.107946\pi\) | ||||
−0.943047 | + | 0.332660i | \(0.892054\pi\) | |||||||
\(542\) | −5.87842 | − | 3.39391i | −0.252500 | − | 0.145781i | ||||
\(543\) | −3.63900 | + | 2.10098i | −0.156165 | + | 0.0901616i | ||||
\(544\) | 11.1923 | − | 6.46187i | 0.479866 | − | 0.277051i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.144769 | − | 0.395458i | −0.00619552 | − | 0.0169240i | ||||
\(547\) | − | 25.1765i | − | 1.07647i | −0.842795 | − | 0.538234i | \(-0.819092\pi\) | ||
0.842795 | − | 0.538234i | \(-0.180908\pi\) | |||||||
\(548\) | 17.5489 | + | 30.3956i | 0.749653 | + | 1.29844i | ||||
\(549\) | −3.09843 | − | 5.36665i | −0.132238 | − | 0.229043i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.58493i | − | 0.280528i | ||||||
\(552\) | −1.97210 | + | 3.41577i | −0.0839380 | + | 0.145385i | ||||
\(553\) | 0.750630 | − | 1.30013i | 0.0319200 | − | 0.0552871i | ||||
\(554\) | − | 5.82269i | − | 0.247382i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.6969 | − | 20.2596i | −0.496059 | − | 0.859199i | ||||
\(557\) | 21.1744 | + | 36.6752i | 0.897190 | + | 1.55398i | 0.831071 | + | 0.556167i | \(0.187728\pi\) |
0.0661194 | + | 0.997812i | \(0.478938\pi\) | |||||||
\(558\) | − | 0.527420i | − | 0.0223275i | ||||||
\(559\) | −11.7110 | + | 14.0095i | −0.495322 | + | 0.592537i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.7002 | + | 21.7662i | −1.59171 | + | 0.918971i | ||||
\(562\) | 0.947022 | − | 0.546763i | 0.0399477 | − | 0.0230638i | ||||
\(563\) | 20.6032 | + | 11.8953i | 0.868322 | + | 0.501326i | 0.866790 | − | 0.498673i | \(-0.166179\pi\) |
0.00153173 | + | 0.999999i | \(0.499512\pi\) | |||||||
\(564\) | − | 26.0561i | − | 1.09716i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.39461 | + | 1.38253i | 0.100653 | + | 0.0581119i | ||||
\(567\) | −2.48814 | −0.104492 | ||||||||
\(568\) | −9.62148 | − | 5.55497i | −0.403709 | − | 0.233081i | ||||
\(569\) | 13.3710 | + | 23.1593i | 0.560543 | + | 0.970889i | 0.997449 | + | 0.0713817i | \(0.0227408\pi\) |
−0.436906 | + | 0.899507i | \(0.643926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.7159 | 0.699539 | 0.349769 | − | 0.936836i | \(-0.386260\pi\) | ||||
0.349769 | + | 0.936836i | \(0.386260\pi\) | |||||||
\(572\) | −37.2398 | − | 6.49498i | −1.55707 | − | 0.271569i | ||||
\(573\) | 3.22571i | 0.134756i | ||||||||
\(574\) | −0.235908 | + | 0.136202i | −0.00984661 | + | 0.00568494i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50812 | − | 2.61215i | 0.0628385 | − | 0.108840i | ||||
\(577\) | −20.6768 | −0.860786 | −0.430393 | − | 0.902642i | \(-0.641625\pi\) | ||||
−0.430393 | + | 0.902642i | \(0.641625\pi\) | |||||||
\(578\) | −0.949828 | + | 1.64515i | −0.0395076 | + | 0.0684292i | ||||
\(579\) | 31.6257 | + | 18.2591i | 1.31432 | + | 0.758822i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.708301 | + | 1.22681i | −0.0293853 | + | 0.0508968i | ||||
\(582\) | −0.763519 | + | 0.440818i | −0.0316489 | + | 0.0182725i | ||||
\(583\) | −4.19170 | − | 7.26023i | −0.173602 | − | 0.300688i | ||||
\(584\) | −8.41165 | −0.348076 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.71657 | −0.153530 | ||||||||
\(587\) | −10.3986 | − | 18.0109i | −0.429196 | − | 0.743388i | 0.567606 | − | 0.823300i | \(-0.307870\pi\) |
−0.996802 | + | 0.0799116i | \(0.974536\pi\) | |||||||
\(588\) | −18.6346 | + | 10.7587i | −0.768478 | + | 0.443681i | ||||
\(589\) | −6.19615 | + | 10.7321i | −0.255308 | + | 0.442206i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.891111 | − | 0.514483i | −0.0366554 | − | 0.0211630i | ||||
\(592\) | 11.0863 | − | 19.2021i | 0.455644 | − | 0.789199i | ||||
\(593\) | −21.8475 | −0.897169 | −0.448585 | − | 0.893740i | \(-0.648072\pi\) | ||||
−0.448585 | + | 0.893740i | \(0.648072\pi\) | |||||||
\(594\) | 3.24749 | − | 5.62482i | 0.133246 | − | 0.230789i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.76446 | + | 3.32811i | −0.236121 | + | 0.136325i | ||||
\(597\) | − | 4.90755i | − | 0.200853i | ||||||
\(598\) | 1.44235 | − | 1.72544i | 0.0589822 | − | 0.0705583i | ||||
\(599\) | 3.58040 | 0.146291 | 0.0731456 | − | 0.997321i | \(-0.476696\pi\) | ||||
0.0731456 | + | 0.997321i | \(0.476696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6743 | − | 18.4885i | −0.435414 | − | 0.754160i | 0.561915 | − | 0.827195i | \(-0.310065\pi\) |
−0.997329 | + | 0.0730352i | \(0.976731\pi\) | |||||||
\(602\) | 0.320121 | + | 0.184822i | 0.0130472 | + | 0.00753278i | ||||
\(603\) | 4.53972 | 0.184872 | ||||||||
\(604\) | −13.4568 | − | 7.76929i | −0.547550 | − | 0.316128i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 4.37554i | − | 0.177744i | ||||||
\(607\) | −2.85767 | − | 1.64988i | −0.115989 | − | 0.0669665i | 0.440883 | − | 0.897565i | \(-0.354665\pi\) |
−0.556872 | + | 0.830598i | \(0.687999\pi\) | |||||||
\(608\) | 5.01226 | − | 2.89383i | 0.203274 | − | 0.117360i | ||||
\(609\) | −1.33685 | + | 0.771830i | −0.0541718 | + | 0.0312761i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.16832 | + | 29.6332i | −0.209088 | + | 1.19883i | ||||
\(612\) | 4.34285i | 0.175549i | ||||||||
\(613\) | 4.94318 | + | 8.56183i | 0.199653 | + | 0.345809i | 0.948416 | − | 0.317029i | \(-0.102685\pi\) |
−0.748763 | + | 0.662838i | \(0.769352\pi\) | |||||||
\(614\) | 0.472795 | + | 0.818904i | 0.0190804 | + | 0.0330483i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.54944i | 0.0624286i | ||||||||
\(617\) | 22.8584 | − | 39.5920i | 0.920246 | − | 1.59391i | 0.121213 | − | 0.992626i | \(-0.461321\pi\) |
0.799033 | − | 0.601287i | \(-0.205345\pi\) | |||||||
\(618\) | 2.64091 | − | 4.57419i | 0.106233 | − | 0.184001i | ||||
\(619\) | 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 | ||||
\(622\) | 0.244415 | + | 0.423339i | 0.00980014 | + | 0.0169743i | ||||
\(623\) | 1.07177i | 0.0429397i | ||||||||
\(624\) | 13.7386 | − | 16.4351i | 0.549986 | − | 0.657930i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.37152 | + | 0.791847i | −0.0548169 | + | 0.0316486i | ||||
\(627\) | −16.8833 | + | 9.74760i | −0.674255 | + | 0.389282i | ||||
\(628\) | 27.7757 | + | 16.0363i | 1.10837 | + | 0.639918i | ||||
\(629\) | 30.2440i | 1.20591i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6403 | + | 7.29790i | 0.503204 | + | 0.290525i | 0.730036 | − | 0.683409i | \(-0.239503\pi\) |
−0.226832 | + | 0.973934i | \(0.572837\pi\) | |||||||
\(632\) | −3.92272 | −0.156038 | ||||||||
\(633\) | −11.3642 | − | 6.56112i | −0.451686 | − | 0.260781i | ||||
\(634\) | −0.0353305 | − | 0.0611942i | −0.00140315 | − | 0.00243033i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.87409 | 0.193270 | ||||||||
\(637\) | 23.3269 | − | 8.53948i | 0.924246 | − | 0.338346i | ||||
\(638\) | − | 3.42644i | − | 0.135654i | ||||||
\(639\) | 4.86950 | − | 2.81140i | 0.192634 | − | 0.111217i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.08183 | + | 12.2661i | −0.279716 | + | 0.484482i | −0.971314 | − | 0.237801i | \(-0.923573\pi\) |
0.691598 | + | 0.722282i | \(0.256907\pi\) | |||||||
\(642\) | −4.59265 | −0.181257 | ||||||||
\(643\) | 8.38581 | − | 14.5246i | 0.330704 | − | 0.572796i | −0.651946 | − | 0.758265i | \(-0.726047\pi\) |
0.982650 | + | 0.185469i | \(0.0593805\pi\) | |||||||
\(644\) | 1.59443 | + | 0.920544i | 0.0628293 | + | 0.0362745i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.26161 | + | 2.18518i | −0.0496376 | + | 0.0859748i | ||||
\(647\) | −2.59087 | + | 1.49584i | −0.101858 | + | 0.0588075i | −0.550063 | − | 0.835123i | \(-0.685396\pi\) |
0.448206 | + | 0.893930i | \(0.352063\pi\) | |||||||
\(648\) | 3.25069 | + | 5.63037i | 0.127699 | + | 0.221182i | ||||
\(649\) | −14.5432 | −0.570872 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.90504 | 0.113858 | ||||||||
\(652\) | 17.3775 | + | 30.0987i | 0.680556 | + | 1.17876i | ||||
\(653\) | −10.1016 | + | 5.83217i | −0.395307 | + | 0.228230i | −0.684457 | − | 0.729053i | \(-0.739961\pi\) |
0.289150 | + | 0.957284i | \(0.406627\pi\) | |||||||
\(654\) | 1.97434 | − | 3.41966i | 0.0772028 | − | 0.133719i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.9998 | − | 6.92810i | −0.468514 | − | 0.270497i | ||||
\(657\) | 2.12859 | − | 3.68683i | 0.0830444 | − | 0.143837i | ||||
\(658\) | 0.608946 | 0.0237392 | ||||||||
\(659\) | −0.905237 | + | 1.56792i | −0.0352630 | + | 0.0610773i | −0.883118 | − | 0.469150i | \(-0.844560\pi\) |
0.847855 | + | 0.530228i | \(0.177894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6872 | − | 6.17028i | 0.415686 | − | 0.239996i | −0.277544 | − | 0.960713i | \(-0.589520\pi\) |
0.693230 | + | 0.720717i | \(0.256187\pi\) | |||||||
\(662\) | − | 3.65383i | − | 0.142010i | ||||||
\(663\) | −5.02027 | + | 28.7844i | −0.194971 | + | 1.11789i | ||||
\(664\) | 3.70152 | 0.143647 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.288223 | − | 0.499217i | −0.0111684 | − | 0.0193443i | ||||
\(667\) | −7.13907 | − | 4.12174i | −0.276426 | − | 0.159594i | ||||
\(668\) | −12.2836 | −0.475265 | ||||||||
\(669\) | −14.1965 | − | 8.19636i | −0.548869 | − | 0.316890i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 75.7634i | 2.92481i | ||||||||
\(672\) | −1.17499 | − | 0.678380i | −0.0453262 | − | 0.0261691i | ||||
\(673\) | −8.02481 | + | 4.63313i | −0.309334 | + | 0.178594i | −0.646628 | − | 0.762805i | \(-0.723822\pi\) |
0.337295 | + | 0.941399i | \(0.390488\pi\) | |||||||
\(674\) | −4.60770 | + | 2.66025i | −0.177482 | + | 0.102469i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.3757 | + | 16.3814i | −0.745220 | + | 0.630053i | ||||
\(677\) | − | 13.8984i | − | 0.534158i | −0.963675 | − | 0.267079i | \(-0.913941\pi\) | ||
0.963675 | − | 0.267079i | \(-0.0860585\pi\) | |||||||
\(678\) | −3.22431 | − | 5.58467i | −0.123829 | − | 0.214478i | ||||
\(679\) | 0.416622 | + | 0.721611i | 0.0159885 | + | 0.0276929i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 11.2715i | − | 0.431924i | ||||||
\(682\) | −3.22414 | + | 5.58438i | −0.123459 | + | 0.213837i | ||||
\(683\) | 18.8756 | − | 32.6935i | 0.722255 | − | 1.25098i | −0.237838 | − | 0.971305i | \(-0.576439\pi\) |
0.960094 | − | 0.279678i | \(-0.0902278\pi\) | |||||||
\(684\) | 1.94486i | 0.0743637i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.506903 | − | 0.877981i | −0.0193536 | − | 0.0335215i | ||||
\(687\) | −1.06332 | − | 1.84172i | −0.0405681 | − | 0.0702661i | ||||
\(688\) | 18.8025i | 0.716838i | ||||||||
\(689\) | −5.54324 | − | 0.966794i | −0.211181 | − | 0.0368319i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.43146 | + | 0.826456i | −0.0544554 | + | 0.0314399i | −0.526981 | − | 0.849877i | \(-0.676676\pi\) |
0.472525 | + | 0.881317i | \(0.343343\pi\) | |||||||
\(692\) | 27.0020 | − | 15.5896i | 1.02646 | − | 0.592628i | ||||
\(693\) | −0.679120 | − | 0.392090i | −0.0257976 | − | 0.0148943i | ||||
\(694\) | − | 1.37823i | − | 0.0523168i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.49312 | + | 2.01676i | 0.132407 | + | 0.0764450i | ||||
\(697\) | 18.9002 | 0.715897 | ||||||||
\(698\) | 1.34509 | + | 0.776587i | 0.0509123 | + | 0.0293943i | ||||
\(699\) | −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 | \(0.626418\pi\) | |||||||
\(702\) | −1.49863 | − | 4.09373i | −0.0565620 | − | 0.154508i | ||||
\(703\) | 13.5442i | 0.510830i | ||||||||
\(704\) | −31.9363 | + | 18.4384i | −1.20365 | + | 0.694925i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.39347 | − | 4.14561i | 0.0900794 | − | 0.156022i | ||||
\(707\) | −4.13538 | −0.155527 | ||||||||
\(708\) | 4.22770 | − | 7.32260i | 0.158887 | − | 0.275200i | ||||
\(709\) | −19.0021 | − | 10.9709i | −0.713639 | − | 0.412020i | 0.0987679 | − | 0.995110i | \(-0.468510\pi\) |
−0.812407 | + | 0.583091i | \(0.801843\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.992658 | − | 1.71933i | 0.0372276 | − | 0.0644801i | ||||
\(712\) | 2.42530 | − | 1.40025i | 0.0908919 | − | 0.0524764i | ||||
\(713\) | 7.75678 | + | 13.4351i | 0.290494 | + | 0.503150i | ||||
\(714\) | 0.591503 | 0.0221364 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −46.0950 | −1.72265 | ||||||||
\(717\) | −7.95463 | − | 13.7778i | −0.297071 | − | 0.514542i | ||||
\(718\) | −4.56110 | + | 2.63335i | −0.170219 | + | 0.0982759i | ||||
\(719\) | −19.4237 | + | 33.6429i | −0.724384 | + | 1.25467i | 0.234844 | + | 0.972033i | \(0.424542\pi\) |
−0.959227 | + | 0.282636i | \(0.908791\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.32312 | − | 2.49596i | −0.161002 | − | 0.0929543i | ||||
\(722\) | 1.52204 | − | 2.63624i | 0.0566443 | − | 0.0981108i | ||||
\(723\) | 36.1434 | 1.34419 | ||||||||
\(724\) | 2.56254 | − | 4.43844i | 0.0952359 | − | 0.164953i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.43628 | + | 3.13864i | −0.201759 | + | 0.116486i | ||||
\(727\) | − | 30.6598i | − | 1.13711i | −0.822645 | − | 0.568555i | \(-0.807503\pi\) | ||
0.822645 | − | 0.568555i | \(-0.192497\pi\) | |||||||
\(728\) | 0.797912 | + | 0.667002i | 0.0295726 | + | 0.0247207i | ||||
\(729\) | −29.7112 | −1.10042 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.8236 | − | 22.2110i | −0.474296 | − | 0.821505i | ||||
\(732\) | −38.1473 | − | 22.0243i | −1.40996 | − | 0.814043i | ||||
\(733\) | −24.3858 | −0.900709 | −0.450355 | − | 0.892850i | \(-0.648702\pi\) | ||||
−0.450355 | + | 0.892850i | \(0.648702\pi\) | |||||||
\(734\) | −1.21598 | − | 0.702045i | −0.0448826 | − | 0.0259130i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.24539i | − | 0.267069i | ||||||
\(737\) | −48.0669 | − | 27.7515i | −1.77057 | − | 1.02224i | ||||
\(738\) | −0.311973 | + | 0.180117i | −0.0114839 | + | 0.00663021i | ||||
\(739\) | 33.1504 | − | 19.1394i | 1.21946 | − | 0.704054i | 0.254656 | − | 0.967032i | \(-0.418038\pi\) |
0.964802 | + | 0.262977i | \(0.0847044\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.24823 | + | 12.8905i | −0.0825909 | + | 0.473546i | ||||
\(742\) | 0.113910i | 0.00418178i | ||||||||
\(743\) | −20.0040 | − | 34.6479i | −0.733874 | − | 1.27111i | −0.955216 | − | 0.295910i | \(-0.904377\pi\) |
0.221342 | − | 0.975196i | \(-0.428956\pi\) | |||||||
\(744\) | −3.79537 | − | 6.57377i | −0.139145 | − | 0.241006i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.41134i | 0.161511i | ||||||||
\(747\) | −0.936681 | + | 1.62238i | −0.0342714 | + | 0.0593598i | ||||
\(748\) | 26.5480 | − | 45.9825i | 0.970691 | − | 1.68129i | ||||
\(749\) | 4.34057i | 0.158601i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8010 | + | 22.1720i | 0.467115 | + | 0.809067i | 0.999294 | − | 0.0375648i | \(-0.0119601\pi\) |
−0.532179 | + | 0.846632i | \(0.678627\pi\) | |||||||
\(752\) | 15.4875 | + | 26.8251i | 0.564770 | + | 0.978211i | ||||
\(753\) | − | 10.8307i | − | 0.394693i | ||||||
\(754\) | −1.76451 | − | 1.47502i | −0.0642597 | − | 0.0537169i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.09076 | − | 1.78445i | 0.112410 | − | 0.0648998i | ||||
\(757\) | 1.60083 | − | 0.924239i | 0.0581831 | − | 0.0335920i | −0.470626 | − | 0.882333i | \(-0.655972\pi\) |
0.528809 | + | 0.848741i | \(0.322639\pi\) | |||||||
\(758\) | 1.03914 | + | 0.599945i | 0.0377431 | + | 0.0217910i | ||||
\(759\) | 24.4055i | 0.885862i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.7006 | + | 13.1062i | 0.822896 | + | 0.475099i | 0.851414 | − | 0.524494i | \(-0.175745\pi\) |
−0.0285179 | + | 0.999593i | \(0.509079\pi\) | |||||||
\(762\) | −1.13898 | −0.0412610 | ||||||||
\(763\) | −3.23196 | − | 1.86597i | −0.117005 | − | 0.0675528i | ||||
\(764\) | −1.96718 | − | 3.40725i | −0.0711699 | − | 0.123270i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.24513 | −0.0449884 | ||||||||
\(767\) | −6.26058 | + | 7.48932i | −0.226056 | + | 0.270424i | ||||
\(768\) | − | 19.6459i | − | 0.708911i | ||||||
\(769\) | 38.4078 | − | 22.1747i | 1.38502 | − | 0.799641i | 0.392271 | − | 0.919850i | \(-0.371690\pi\) |
0.992749 | + | 0.120208i | \(0.0383562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.20406 | − | 14.2099i | 0.295462 | − | 0.511755i | ||||
\(772\) | −44.5408 | −1.60306 | ||||||||
\(773\) | −11.6319 | + | 20.1471i | −0.418371 | + | 0.724640i | −0.995776 | − | 0.0918181i | \(-0.970732\pi\) |
0.577405 | + | 0.816458i | \(0.304065\pi\) | |||||||
\(774\) | 0.423339 | + | 0.244415i | 0.0152166 | + | 0.00878531i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.08861 | − | 1.88554i | 0.0390790 | − | 0.0676868i | ||||
\(777\) | 2.74970 | − | 1.58754i | 0.0986448 | − | 0.0569526i | ||||
\(778\) | 1.16625 | + | 2.02001i | 0.0418122 | + | 0.0724209i | ||||
\(779\) | 8.46410 | 0.303258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −68.7449 | −2.45989 | ||||||||
\(782\) | 1.57938 | + | 2.73556i | 0.0564784 | + | 0.0978235i | ||||
\(783\) | −13.8389 | + | 7.98989i | −0.494562 | + | 0.285535i | ||||
\(784\) | 12.7897 | − | 22.1524i | 0.456776 | − | 0.791159i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.0534798 | − | 0.0308766i | −0.00190756 | − | 0.00110133i | ||||
\(787\) | −23.9567 | + | 41.4942i | −0.853963 | + | 1.47911i | 0.0236408 | + | 0.999721i | \(0.492474\pi\) |
−0.877604 | + | 0.479387i | \(0.840859\pi\) | |||||||
\(788\) | 1.25502 | 0.0447081 | ||||||||
\(789\) | −14.9274 | + | 25.8551i | −0.531430 | + | 0.920464i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.27814 | + | 3.04734i | −0.187669 | + | 0.108351i | ||||
\(792\) | 2.04903i | 0.0728090i | ||||||||
\(793\) | 39.0158 | + | 32.6147i | 1.38549 | + | 1.15818i | ||||
\(794\) | 6.15865 | 0.218562 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.99284 | + | 5.18374i | 0.106078 | + | 0.183733i | ||||
\(797\) | 17.9225 | + | 10.3476i | 0.634849 | + | 0.366530i | 0.782627 | − | 0.622490i | \(-0.213879\pi\) |
−0.147779 | + | 0.989020i | \(0.547212\pi\) | |||||||
\(798\) | 0.264893 | 0.00937712 | ||||||||
\(799\) | −36.5902 | − | 21.1253i | −1.29447 | − | 0.747361i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.41735i | 0.0500795i | ||||||||
\(802\) | 4.28344 | + | 2.47305i | 0.151254 | + | 0.0873263i | ||||
\(803\) | −45.0755 | + | 26.0244i | −1.59068 | + | 0.918380i | ||||
\(804\) | 27.9460 | − | 16.1346i | 0.985580 | − | 0.569025i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.48785 | + | 4.06430i | 0.0524073 | + | 0.143159i | ||||
\(807\) | 28.7361i | 1.01156i | ||||||||
\(808\) | 5.40278 | + | 9.35788i | 0.190069 | + | 0.329209i | ||||
\(809\) | 7.94574 | + | 13.7624i | 0.279357 | + | 0.483861i | 0.971225 | − | 0.238163i | \(-0.0765453\pi\) |
−0.691868 | + | 0.722024i | \(0.743212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.8796i | − | 0.838525i | −0.907865 | − | 0.419263i | \(-0.862289\pi\) | ||
0.907865 | − | 0.419263i | \(-0.137711\pi\) | |||||||
\(812\) | 0.941391 | − | 1.63054i | 0.0330363 | − | 0.0572206i | ||||
\(813\) | 24.7212 | − | 42.8183i | 0.867009 | − | 1.50170i | ||||
\(814\) | 7.04768i | 0.247021i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15.0438 | + | 26.0567i | 0.526640 | + | 0.912167i | ||||
\(817\) | −5.74278 | − | 9.94679i | −0.200915 | − | 0.347994i | ||||
\(818\) | 0.941956i | 0.0329347i | ||||||||
\(819\) | −0.494262 | + | 0.180939i | −0.0172709 | + | 0.00632250i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7782 | − | 7.95484i | 0.480862 | − | 0.277626i | −0.239914 | − | 0.970794i | \(-0.577119\pi\) |
0.720776 | + | 0.693169i | \(0.243786\pi\) | |||||||
\(822\) | 5.47478 | − | 3.16087i | 0.190955 | − | 0.110248i | ||||
\(823\) | −12.8271 | − | 7.40573i | −0.447124 | − | 0.258147i | 0.259491 | − | 0.965746i | \(-0.416445\pi\) |
−0.706615 | + | 0.707598i | \(0.749779\pi\) | |||||||
\(824\) | 13.0436i | 0.454397i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.171134 | + | 0.0988040i | 0.00595450 | + | 0.00343783i | ||||
\(827\) | −33.9498 | −1.18055 | −0.590275 | − | 0.807202i | \(-0.700981\pi\) | ||||
−0.590275 | + | 0.807202i | \(0.700981\pi\) | |||||||
\(828\) | 2.10853 | + | 1.21736i | 0.0732763 | + | 0.0423061i | ||||
\(829\) | −11.6573 | − | 20.1910i | −0.404875 | − | 0.701264i | 0.589432 | − | 0.807818i | \(-0.299352\pi\) |
−0.994307 | + | 0.106554i | \(0.966018\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.4124 | 1.47127 | ||||||||
\(832\) | −4.25274 | + | 24.3836i | −0.147437 | + | 0.845350i | ||||
\(833\) | 34.8910i | 1.20890i | ||||||||
\(834\) | −3.64911 | + | 2.10682i | −0.126358 | + | 0.0729530i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.8890 | − | 20.5924i | 0.411190 | − | 0.712202i | ||||
\(837\) | 30.0726 | 1.03946 | ||||||||
\(838\) | −1.94550 | + | 3.36970i | −0.0672061 | + | 0.116404i | ||||
\(839\) | 12.8111 | + | 7.39649i | 0.442288 | + | 0.255355i | 0.704568 | − | 0.709637i | \(-0.251141\pi\) |
−0.262280 | + | 0.964992i | \(0.584474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.2849 | − | 17.8140i | 0.354652 | − | 0.614276i | ||||
\(842\) | −2.45024 | + | 1.41465i | −0.0844408 | + | 0.0487519i | ||||
\(843\) | 3.98261 | + | 6.89809i | 0.137169 | + | 0.237583i | ||||
\(844\) | 16.0050 | 0.550915 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.805291 | 0.0276865 | ||||||||
\(847\) | 2.96636 | + | 5.13789i | 0.101925 | + | 0.176540i | ||||
\(848\) | −5.01794 | + | 2.89711i | −0.172317 | + | 0.0994872i | ||||
\(849\) | −10.0703 | + | 17.4423i | −0.345612 | + | 0.598617i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6840 | + | 8.47780i | 0.503360 | + | 0.290615i | ||||
\(852\) | 19.9841 | − | 34.6134i | 0.684643 | − | 1.18584i | ||||
\(853\) | −16.3452 | −0.559650 | −0.279825 | − | 0.960051i | \(-0.590276\pi\) | ||||
−0.279825 | + | 0.960051i | \(0.590276\pi\) | |||||||
\(854\) | 0.514722 | − | 0.891525i | 0.0176134 | − | 0.0305073i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.82220 | − | 5.67085i | 0.335716 | − | 0.193826i | ||||
\(857\) | − | 34.1418i | − | 1.16626i | −0.812378 | − | 0.583132i | \(-0.801827\pi\) | ||
0.812378 | − | 0.583132i | \(-0.198173\pi\) | |||||||
\(858\) | −1.16986 | + | 6.70754i | −0.0399383 | + | 0.228992i | ||||
\(859\) | 45.1996 | 1.54219 | 0.771096 | − | 0.636719i | \(-0.219709\pi\) | ||||
0.771096 | + | 0.636719i | \(0.219709\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.992090 | − | 1.71835i | −0.0338103 | − | 0.0585612i | ||||
\(862\) | 1.80712 | + | 1.04334i | 0.0615508 | + | 0.0355364i | ||||
\(863\) | −4.75058 | −0.161712 | −0.0808559 | − | 0.996726i | \(-0.525765\pi\) | ||||
−0.0808559 | + | 0.996726i | \(0.525765\pi\) | |||||||
\(864\) | −12.1633 | − | 7.02250i | −0.413805 | − | 0.238910i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 0.306745i | − | 0.0104236i | ||||||
\(867\) | −11.9832 | − | 6.91853i | −0.406972 | − | 0.234966i | ||||
\(868\) | −3.06854 | + | 1.77162i | −0.104153 | + | 0.0601327i | ||||
\(869\) | −21.0207 | + | 12.1363i | −0.713079 | + | 0.411696i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.9830 | + | 12.8065i | −1.18535 | + | 0.433933i | ||||
\(872\) | 9.75140i | 0.330224i | ||||||||
\(873\) | 0.550955 | + | 0.954282i | 0.0186470 | + | 0.0322975i | ||||
\(874\) | 0.707294 | + | 1.22507i | 0.0239246 | + | 0.0414386i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 30.2610i | − | 1.02242i | ||||||
\(877\) | −1.12753 | + | 1.95294i | −0.0380741 | + | 0.0659462i | −0.884434 | − | 0.466664i | \(-0.845456\pi\) |
0.846360 | + | 0.532611i | \(0.178789\pi\) | |||||||
\(878\) | 0.457146 | − | 0.791801i | 0.0154279 | − | 0.0267220i | ||||
\(879\) | − | 27.0715i | − | 0.913098i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.49152 | − | 2.58339i | −0.0502507 | − | 0.0870367i | 0.839806 | − | 0.542887i | \(-0.182669\pi\) |
−0.890057 | + | 0.455850i | \(0.849335\pi\) | |||||||
\(882\) | −0.332509 | − | 0.575922i | −0.0111961 | − | 0.0193923i | ||||
\(883\) | − | 28.2874i | − | 0.951947i | −0.879460 | − | 0.475973i | \(-0.842096\pi\) | ||
0.879460 | − | 0.475973i | \(-0.157904\pi\) | |||||||
\(884\) | −12.2512 | − | 33.4660i | −0.412051 | − | 1.12558i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.81610 | + | 1.04852i | −0.0610130 | + | 0.0352259i | ||||
\(887\) | 24.2328 | − | 13.9908i | 0.813658 | − | 0.469766i | −0.0345665 | − | 0.999402i | \(-0.511005\pi\) |
0.848225 | + | 0.529637i | \(0.177672\pi\) | |||||||
\(888\) | −7.18483 | − | 4.14816i | −0.241107 | − | 0.139203i | ||||
\(889\) | 1.07647i | 0.0361035i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34.8390 | + | 20.1143i | 1.16715 | + | 0.673855i | ||||
\(892\) | 19.9940 | 0.669448 | ||||||||
\(893\) | −16.3862 | − | 9.46058i | −0.548343 | − | 0.316586i | ||||
\(894\) | 0.599451 | + | 1.03828i | 0.0200486 | + | 0.0347252i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.19681 | 0.0733903 | ||||||||
\(897\) | 12.5681 | + | 10.5061i | 0.419635 | + | 0.350787i | ||||
\(898\) | − | 4.77095i | − | 0.159209i | ||||||
\(899\) | 13.7394 | − | 7.93244i | 0.458234 | − | 0.264562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.95174 | − | 6.84461i | 0.131651 | − | 0.228027i | ||||
\(902\) | 4.40426 | 0.146646 | ||||||||
\(903\) | −1.34624 | + | 2.33176i | −0.0448001 | + | 0.0775960i | ||||
\(904\) | 13.7915 | + | 7.96255i | 0.458700 | + | 0.264830i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.39938 | + | 2.42381i | −0.0464914 | + | 0.0805255i | ||||
\(907\) | 14.3344 | − | 8.27600i | 0.475967 | − | 0.274800i | −0.242767 | − | 0.970085i | \(-0.578055\pi\) |
0.718734 | + | 0.695285i | \(0.244722\pi\) | |||||||
\(908\) | 6.87383 | + | 11.9058i | 0.228116 | + | 0.395109i | ||||
\(909\) | −5.46876 | −0.181387 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.04863 | 0.233532 | 0.116766 | − | 0.993159i | \(-0.462747\pi\) | ||||
0.116766 | + | 0.993159i | \(0.462747\pi\) | |||||||
\(912\) | 6.73710 | + | 11.6690i | 0.223088 | + | 0.386399i | ||||
\(913\) | 19.8353 | − | 11.4519i | 0.656454 | − | 0.379004i | ||||
\(914\) | 0.518746 | − | 0.898494i | 0.0171586 | − | 0.0297196i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.24632 | + | 1.29692i | 0.0742206 | + | 0.0428513i | ||||
\(917\) | −0.0291818 | + | 0.0505443i | −0.000963668 | + | 0.00166912i | ||||
\(918\) | 6.12316 | 0.202094 | ||||||||
\(919\) | 8.27188 | − | 14.3273i | 0.272864 | − | 0.472615i | −0.696730 | − | 0.717334i | \(-0.745362\pi\) |
0.969594 | + | 0.244719i | \(0.0786957\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.96488 | + | 3.44383i | −0.196550 | + | 0.113478i | ||||
\(922\) | 0.391374i | 0.0128892i | ||||||||
\(923\) | −29.5933 | + | 35.4015i | −0.974076 | + | 1.16525i | ||||
\(924\) | −5.57412 | −0.183375 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.747155 | + | 1.29411i | 0.0245530 | + | 0.0425271i | ||||
\(927\) | −5.71704 | − | 3.30074i | −0.187772 | − | 0.108410i | ||||
\(928\) | −7.40948 | −0.243228 | ||||||||
\(929\) | 29.3035 | + | 16.9184i | 0.961416 | + | 0.555074i | 0.896609 | − | 0.442824i | \(-0.146023\pi\) |
0.0648073 | + | 0.997898i | \(0.479357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.6253i | 0.512098i | ||||||||
\(932\) | 2.10853 | + | 1.21736i | 0.0690670 | + | 0.0398759i | ||||
\(933\) | −3.08359 | + | 1.78031i | −0.100952 | + | 0.0582848i | ||||
\(934\) | −3.46975 | + | 2.00326i | −0.113534 | + | 0.0655487i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.05518 | + | 0.882066i | 0.0344898 | + | 0.0288312i | ||||
\(937\) | 30.4606i | 0.995104i | 0.867434 | + | 0.497552i | \(0.165768\pi\) | ||||
−0.867434 | + | 0.497552i | \(0.834232\pi\) | |||||||
\(938\) | 0.377076 | + | 0.653115i | 0.0123120 | + | 0.0213250i | ||||
\(939\) | −5.76780 | − | 9.99012i | −0.188225 | − | 0.326015i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 38.2101i | − | 1.24561i | −0.782375 | − | 0.622807i | \(-0.785992\pi\) | ||
0.782375 | − | 0.622807i | \(-0.214008\pi\) | |||||||
\(942\) | 2.88842 | − | 5.00289i | 0.0941098 | − | 0.163003i | ||||
\(943\) | 5.29798 | − | 9.17637i | 0.172526 | − | 0.298824i | ||||
\(944\) | 10.0516i | 0.327153i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.98823 | − | 5.17577i | −0.0971558 | − | 0.168279i | ||||
\(947\) | 26.2241 | + | 45.4215i | 0.852169 | + | 1.47600i | 0.879247 | + | 0.476367i | \(0.158047\pi\) |
−0.0270773 | + | 0.999633i | \(0.508620\pi\) | |||||||
\(948\) | − | 14.1120i | − | 0.458338i | ||||||
\(949\) | −6.00239 | + | 34.4155i | −0.194846 | + | 1.11717i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.445737 | − | 0.257347i | 0.0144540 | − | 0.00834504i | ||||
\(952\) | −1.26503 | + | 0.730368i | −0.0410000 | + | 0.0236714i | ||||
\(953\) | 34.4245 | + | 19.8750i | 1.11512 | + | 0.643814i | 0.940150 | − | 0.340760i | \(-0.110684\pi\) |
0.174969 | + | 0.984574i | \(0.444018\pi\) | |||||||
\(954\) | 0.150639i | 0.00487711i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.8046 | + | 9.70215i | 0.543500 | + | 0.313790i | ||||
\(957\) | 24.9581 | 0.806782 | ||||||||
\(958\) | −6.69329 | − | 3.86437i | −0.216250 | − | 0.124852i | ||||
\(959\) | −2.98737 | − | 5.17428i | −0.0964673 | − | 0.167086i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.14359 | 0.0368901 | ||||||||
\(962\) | 3.62933 | + | 3.03389i | 0.117014 | + | 0.0978164i | ||||
\(963\) | 5.74011i | 0.184972i | ||||||||
\(964\) | −38.1776 | + | 22.0418i | −1.22962 | + | 0.709920i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.165806 | − | 0.287184i | 0.00533472 | − | 0.00924001i | ||||
\(967\) | 25.7857 | 0.829214 | 0.414607 | − | 0.910001i | \(-0.363919\pi\) | ||||
0.414607 | + | 0.910001i | \(0.363919\pi\) | |||||||
\(968\) | 7.75097 | − | 13.4251i | 0.249126 | − | 0.431498i | ||||
\(969\) | −15.9168 | − | 9.18958i | −0.511322 | − | 0.295212i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.7626 | − | 48.0863i | 0.890945 | − | 1.54316i | 0.0522005 | − | 0.998637i | \(-0.483377\pi\) |
0.838744 | − | 0.544525i | \(-0.183290\pi\) | |||||||
\(972\) | 7.65249 | − | 4.41817i | 0.245454 | − | 0.141713i | ||||
\(973\) | 1.99118 | + | 3.44882i | 0.0638342 | + | 0.110564i | ||||
\(974\) | 2.26365 | 0.0725321 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.3642 | 1.67614 | ||||||||
\(977\) | 20.2580 | + | 35.0879i | 0.648112 | + | 1.12256i | 0.983573 | + | 0.180509i | \(0.0577745\pi\) |
−0.335461 | + | 0.942054i | \(0.608892\pi\) | |||||||
\(978\) | 5.42130 | − | 3.12999i | 0.173354 | − | 0.100086i | ||||
\(979\) | 8.66430 | − | 15.0070i | 0.276912 | − | 0.479626i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.27405 | − | 2.46762i | −0.136460 | − | 0.0787852i | ||||
\(982\) | −1.02506 | + | 1.77545i | −0.0327109 | + | 0.0566569i | ||||
\(983\) | 34.8059 | 1.11014 | 0.555068 | − | 0.831805i | \(-0.312692\pi\) | ||||
0.555068 | + | 0.831805i | \(0.312692\pi\) | |||||||
\(984\) | −2.59229 | + | 4.48997i | −0.0826390 | + | 0.143135i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.79751 | − | 1.61514i | 0.0890910 | − | 0.0514367i | ||||
\(987\) | 4.43555i | 0.141185i | ||||||||
\(988\) | −5.48645 | − | 14.9871i | −0.174547 | − | 0.476803i | ||||
\(989\) | −14.3784 | −0.457208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.9427 | − | 38.0059i | −0.697034 | − | 1.20730i | −0.969490 | − | 0.245130i | \(-0.921169\pi\) |
0.272456 | − | 0.962168i | \(-0.412164\pi\) | |||||||
\(992\) | 12.0759 | + | 6.97201i | 0.383410 | + | 0.221362i | ||||
\(993\) | 26.6145 | 0.844584 | ||||||||
\(994\) | 0.808936 | + | 0.467040i | 0.0256579 | + | 0.0148136i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.3163i | 0.421942i | ||||||||
\(997\) | −4.75567 | − | 2.74569i | −0.150614 | − | 0.0869568i | 0.422799 | − | 0.906223i | \(-0.361048\pi\) |
−0.573413 | + | 0.819267i | \(0.694381\pi\) | |||||||
\(998\) | 4.55508 | − | 2.62988i | 0.144189 | − | 0.0832474i | ||||
\(999\) | 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.m.b.49.3 | 8 | ||
5.2 | odd | 4 | 65.2.m.a.36.2 | ✓ | 8 | ||
5.3 | odd | 4 | 325.2.n.d.101.3 | 8 | |||
5.4 | even | 2 | 325.2.m.c.49.2 | 8 | |||
13.4 | even | 6 | 325.2.m.c.199.2 | 8 | |||
15.2 | even | 4 | 585.2.bu.c.361.3 | 8 | |||
20.7 | even | 4 | 1040.2.da.b.881.2 | 8 | |||
65.2 | even | 12 | 845.2.a.m.1.2 | 4 | |||
65.4 | even | 6 | inner | 325.2.m.b.199.3 | 8 | ||
65.7 | even | 12 | 845.2.e.n.191.2 | 8 | |||
65.12 | odd | 4 | 845.2.m.g.361.3 | 8 | |||
65.17 | odd | 12 | 65.2.m.a.56.2 | yes | 8 | ||
65.22 | odd | 12 | 845.2.m.g.316.3 | 8 | |||
65.28 | even | 12 | 4225.2.a.bi.1.3 | 4 | |||
65.32 | even | 12 | 845.2.e.m.191.3 | 8 | |||
65.37 | even | 12 | 845.2.a.l.1.3 | 4 | |||
65.42 | odd | 12 | 845.2.c.g.506.4 | 8 | |||
65.43 | odd | 12 | 325.2.n.d.251.3 | 8 | |||
65.47 | even | 4 | 845.2.e.n.146.2 | 8 | |||
65.57 | even | 4 | 845.2.e.m.146.3 | 8 | |||
65.62 | odd | 12 | 845.2.c.g.506.5 | 8 | |||
65.63 | even | 12 | 4225.2.a.bl.1.2 | 4 | |||
195.2 | odd | 12 | 7605.2.a.cf.1.3 | 4 | |||
195.17 | even | 12 | 585.2.bu.c.316.3 | 8 | |||
195.167 | odd | 12 | 7605.2.a.cj.1.2 | 4 | |||
260.147 | even | 12 | 1040.2.da.b.641.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.2 | ✓ | 8 | 5.2 | odd | 4 | ||
65.2.m.a.56.2 | yes | 8 | 65.17 | odd | 12 | ||
325.2.m.b.49.3 | 8 | 1.1 | even | 1 | trivial | ||
325.2.m.b.199.3 | 8 | 65.4 | even | 6 | inner | ||
325.2.m.c.49.2 | 8 | 5.4 | even | 2 | |||
325.2.m.c.199.2 | 8 | 13.4 | even | 6 | |||
325.2.n.d.101.3 | 8 | 5.3 | odd | 4 | |||
325.2.n.d.251.3 | 8 | 65.43 | odd | 12 | |||
585.2.bu.c.316.3 | 8 | 195.17 | even | 12 | |||
585.2.bu.c.361.3 | 8 | 15.2 | even | 4 | |||
845.2.a.l.1.3 | 4 | 65.37 | even | 12 | |||
845.2.a.m.1.2 | 4 | 65.2 | even | 12 | |||
845.2.c.g.506.4 | 8 | 65.42 | odd | 12 | |||
845.2.c.g.506.5 | 8 | 65.62 | odd | 12 | |||
845.2.e.m.146.3 | 8 | 65.57 | even | 4 | |||
845.2.e.m.191.3 | 8 | 65.32 | even | 12 | |||
845.2.e.n.146.2 | 8 | 65.47 | even | 4 | |||
845.2.e.n.191.2 | 8 | 65.7 | even | 12 | |||
845.2.m.g.316.3 | 8 | 65.22 | odd | 12 | |||
845.2.m.g.361.3 | 8 | 65.12 | odd | 4 | |||
1040.2.da.b.641.2 | 8 | 260.147 | even | 12 | |||
1040.2.da.b.881.2 | 8 | 20.7 | even | 4 | |||
4225.2.a.bi.1.3 | 4 | 65.28 | even | 12 | |||
4225.2.a.bl.1.2 | 4 | 65.63 | even | 12 | |||
7605.2.a.cf.1.3 | 4 | 195.2 | odd | 12 | |||
7605.2.a.cj.1.2 | 4 | 195.167 | odd | 12 |