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 | 49.2 | ||
Root | \(-1.27597 + 0.609843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.49 |
Dual form | 325.2.m.c.199.2 |
$q$-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 | 0.824574 | − | 0.565755i | \(-0.191415\pi\) |
−0.902245 | + | 0.431224i | \(0.858082\pi\) | |||||||
\(3\) | 1.38581 | − | 0.800098i | 0.800098 | − | 0.461937i | −0.0434075 | − | 0.999057i | \(-0.513821\pi\) |
0.843505 | + | 0.537121i | \(0.180488\pi\) | |||||||
\(4\) | 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 | −0.832922 | − | 0.553390i | \(-0.813334\pi\) |
0.895711 | + | 0.444637i | \(0.146667\pi\) | |||||||
\(8\) | −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 | −0.137258 | − | 0.990535i | \(-0.543829\pi\) |
−0.926458 | + | 0.376399i | \(0.877162\pi\) | |||||||
\(18\) | 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 | −0.733941 | − | 0.679213i | \(-0.762321\pi\) |
0.221246 | + | 0.975218i | \(0.428988\pi\) | |||||||
\(24\) | −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 | 0.509049 | − | 0.860738i | \(-0.329997\pi\) |
−0.999945 | + | 0.0104803i | \(0.996664\pi\) | |||||||
\(38\) | − | 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 | 0.795633 | − | 0.605779i | \(-0.207138\pi\) |
−0.126803 | + | 0.991928i | \(0.540472\pi\) | |||||||
\(44\) | − | 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 | \(-0.291786\pi\) | ||||
0.608465 | + | 0.793581i | \(0.291786\pi\) | |||||||
\(48\) | −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 | \(0.0341835\pi\) | ||||
−0.994239 | + | 0.107184i | \(0.965817\pi\) | |||||||
\(54\) | 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 | \(0.0507470\pi\) |
−0.356176 | + | 0.934419i | \(0.615920\pi\) | |||||||
\(68\) | −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 | \(-0.308097\pi\) | ||||
0.567019 | + | 0.823705i | \(0.308097\pi\) | |||||||
\(74\) | −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 | \(-0.575182\pi\) | ||||
−0.234001 | + | 0.972236i | \(0.575182\pi\) | |||||||
\(84\) | −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 | −0.922637 | − | 0.385669i | \(-0.873971\pi\) |
0.795318 | + | 0.606193i | \(0.207304\pi\) | |||||||
\(98\) | 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 | \(-0.734724\pi\) | ||
0.672370 | − | 0.740215i | \(-0.265276\pi\) | |||||||
\(104\) | 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 | −0.934577 | − | 0.355761i | \(-0.884222\pi\) |
−0.159190 | + | 0.987248i | \(0.550888\pi\) | |||||||
\(108\) | 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 | −0.494470 | − | 0.869195i | \(-0.664638\pi\) |
−0.999980 | + | 0.00637349i | \(0.997971\pi\) | |||||||
\(114\) | −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 | −0.619298 | − | 0.785156i | \(-0.712583\pi\) |
0.370316 | + | 0.928906i | \(0.379249\pi\) | |||||||
\(128\) | 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 | \(-0.554491\pi\) |
0.938543 | − | 0.345162i | \(-0.112176\pi\) | |||||||
\(138\) | 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 | \(-0.772356\pi\) | ||
0.754985 | − | 0.655742i | \(-0.227644\pi\) | |||||||
\(158\) | 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 | \(-0.587680\pi\) |
0.969370 | − | 0.245604i | \(-0.0789862\pi\) | |||||||
\(164\) | − | 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 | 0.961711 | − | 0.274064i | \(-0.0883682\pi\) |
−0.718202 | + | 0.695834i | \(0.755035\pi\) | |||||||
\(168\) | 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 | −0.128679 | − | 0.991686i | \(-0.541074\pi\) |
−0.923165 | + | 0.384404i | \(0.874407\pi\) | |||||||
\(174\) | 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 | \(0.140111\pi\) |
−0.0833298 | + | 0.996522i | \(0.526555\pi\) | |||||||
\(194\) | 0.550955 | 0.0395563 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4467 | 0.960480 | ||||||||
\(197\) | −0.321513 | − | 0.556877i | −0.0229068 | − | 0.0396758i | 0.854345 | − | 0.519707i | \(-0.173959\pi\) |
−0.877252 | + | 0.480031i | \(0.840625\pi\) | |||||||
\(198\) | 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 | 0.641987 | − | 0.766715i | \(-0.278110\pi\) |
−0.984989 | + | 0.172620i | \(0.944777\pi\) | |||||||
\(224\) | 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 | −0.725154 | − | 0.688587i | \(-0.758231\pi\) |
0.958911 | + | 0.283708i | \(0.0915646\pi\) | |||||||
\(228\) | 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 | \(-0.986990\pi\) | ||
0.999165 | − | 0.0408619i | \(-0.0130104\pi\) | |||||||
\(234\) | −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 | −0.196779 | − | 0.980448i | \(-0.563048\pi\) |
0.750703 | + | 0.660640i | \(0.229715\pi\) | |||||||
\(258\) | −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 | −0.907154 | − | 0.420798i | \(-0.861750\pi\) |
−0.0891555 | + | 0.996018i | \(0.528417\pi\) | |||||||
\(264\) | −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 | 0.992057 | − | 0.125792i | \(-0.0401472\pi\) |
0.387089 | + | 0.922042i | \(0.373481\pi\) | |||||||
\(278\) | −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 | −0.787668 | − | 0.616100i | \(-0.788712\pi\) |
0.139725 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(284\) | −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 | −0.505809 | − | 0.862645i | \(-0.668806\pi\) |
0.999977 | + | 0.00672072i | \(0.00213929\pi\) | |||||||
\(294\) | − | 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 | \(-0.539197\pi\) | ||||
−0.122828 | + | 0.992428i | \(0.539197\pi\) | |||||||
\(308\) | −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 | \(-0.934692\pi\) | ||
0.979026 | − | 0.203735i | \(-0.0653080\pi\) | |||||||
\(314\) | −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 | \(-0.497125\pi\) | ||||
0.00903266 | + | 0.999959i | \(0.497125\pi\) | |||||||
\(318\) | 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 | \(-0.770711\pi\) | ||
0.751586 | − | 0.659636i | \(-0.229289\pi\) | |||||||
\(338\) | 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 | 0.638692 | − | 0.769463i | \(-0.279476\pi\) |
−0.347028 | + | 0.937855i | \(0.612809\pi\) | |||||||
\(348\) | −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 | \(0.0302330\pi\) |
−0.415615 | + | 0.909541i | \(0.636434\pi\) | |||||||
\(354\) | 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 | −0.348531 | − | 0.937297i | \(-0.613319\pi\) |
0.637458 | + | 0.770485i | \(0.279986\pi\) | |||||||
\(368\) | 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 | −0.0230798 | − | 0.999734i | \(-0.507347\pi\) |
−0.877335 | + | 0.479879i | \(0.840681\pi\) | |||||||
\(374\) | 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 | −0.784496 | − | 0.620134i | \(-0.787078\pi\) |
0.929300 | + | 0.369326i | \(0.120411\pi\) | |||||||
\(384\) | 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 | \(0.415041\pi\) |
−0.967235 | + | 0.253884i | \(0.918292\pi\) | |||||||
\(398\) | 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 | 0.528774 | − | 0.848763i | \(-0.322652\pi\) |
−0.470663 | + | 0.882313i | \(0.655985\pi\) | |||||||
\(434\) | − | 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 | \(-0.927186\pi\) | ||
0.973950 | − | 0.226763i | \(-0.0728144\pi\) | |||||||
\(444\) | −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 | 0.915955 | − | 0.401282i | \(-0.131435\pi\) |
−0.805498 | + | 0.592599i | \(0.798102\pi\) | |||||||
\(458\) | 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 | \(-0.550523\pi\) | ||||
−0.158058 | + | 0.987430i | \(0.550523\pi\) | |||||||
\(464\) | −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 | \(-0.861341\pi\) | ||
0.906613 | − | 0.421963i | \(-0.138659\pi\) | |||||||
\(468\) | −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 | −0.958824 | − | 0.284002i | \(-0.908338\pi\) |
0.725364 | + | 0.688365i | \(0.241671\pi\) | |||||||
\(488\) | 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 | \(0.0554320\pi\) |
0.642490 | + | 0.766294i | \(0.277901\pi\) | |||||||
\(504\) | −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 | −0.388998 | − | 0.921239i | \(-0.627179\pi\) |
0.603317 | + | 0.797501i | \(0.293845\pi\) | |||||||
\(524\) | 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 | \(0.180908\pi\) | ||||
−0.842795 | + | 0.538234i | \(0.819092\pi\) | |||||||
\(548\) | −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 | \(-0.812272\pi\) |
−0.0661194 | − | 0.997812i | \(-0.521062\pi\) | |||||||
\(558\) | 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 | −0.00153173 | − | 0.999999i | \(-0.500488\pi\) |
−0.866790 | + | 0.498673i | \(0.833821\pi\) | |||||||
\(564\) | − | 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 | \(-0.358375\pi\) | ||||
0.430393 | + | 0.902642i | \(0.358375\pi\) | |||||||
\(578\) | 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 | 0.996802 | − | 0.0799116i | \(-0.0254638\pi\) |
−0.567606 | + | 0.823300i | \(0.692130\pi\) | |||||||
\(588\) | 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 | \(-0.351928\pi\) | ||||
0.448585 | + | 0.893740i | \(0.351928\pi\) | |||||||
\(594\) | 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 | 0.556872 | − | 0.830598i | \(-0.312001\pi\) |
−0.440883 | + | 0.897565i | \(0.645335\pi\) | |||||||
\(608\) | −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 | 0.748763 | − | 0.662838i | \(-0.230648\pi\) |
−0.948416 | + | 0.317029i | \(0.897315\pi\) | |||||||
\(614\) | 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 | \(0.538679\pi\) |
−0.799033 | + | 0.601287i | \(0.794655\pi\) | |||||||
\(618\) | −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 | −0.982650 | − | 0.185469i | \(-0.940620\pi\) |
0.651946 | + | 0.758265i | \(0.273953\pi\) | |||||||
\(644\) | 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 | −0.448206 | − | 0.893930i | \(-0.647937\pi\) |
0.550063 | + | 0.835123i | \(0.314604\pi\) | |||||||
\(648\) | −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 | −0.289150 | − | 0.957284i | \(-0.593373\pi\) |
0.684457 | + | 0.729053i | \(0.260039\pi\) | |||||||
\(654\) | 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 | −0.337295 | − | 0.941399i | \(-0.609512\pi\) |
0.646628 | + | 0.762805i | \(0.276178\pi\) | |||||||
\(674\) | −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 | \(0.0860585\pi\) | ||||
−0.963675 | + | 0.267079i | \(0.913941\pi\) | |||||||
\(678\) | 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 | \(0.423561\pi\) |
−0.960094 | + | 0.279678i | \(0.909772\pi\) | |||||||
\(684\) | 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 | \(0.192497\pi\) | ||||
−0.822645 | + | 0.568555i | \(0.807503\pi\) | |||||||
\(728\) | −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 | \(-0.351298\pi\) | ||||
0.450355 | + | 0.892850i | \(0.351298\pi\) | |||||||
\(734\) | −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 | \(0.0956230\pi\) |
−0.221342 | + | 0.975196i | \(0.571044\pi\) | |||||||
\(744\) | −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 | −0.528809 | − | 0.848741i | \(-0.677361\pi\) |
0.470626 | + | 0.882333i | \(0.344028\pi\) | |||||||
\(758\) | −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 | −0.577405 | − | 0.816458i | \(-0.695935\pi\) |
0.995776 | + | 0.0918181i | \(0.0292678\pi\) | |||||||
\(774\) | 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 | \(-0.507526\pi\) |
0.877604 | − | 0.479387i | \(-0.159141\pi\) | |||||||
\(788\) | −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 | 0.147779 | − | 0.989020i | \(-0.452788\pi\) |
−0.782627 | + | 0.622490i | \(0.786121\pi\) | |||||||
\(798\) | −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 | 0.706615 | − | 0.707598i | \(-0.250221\pi\) |
−0.259491 | + | 0.965746i | \(0.583555\pi\) | |||||||
\(824\) | 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 | \(-0.299019\pi\) | ||||
0.590275 | + | 0.807202i | \(0.299019\pi\) | |||||||
\(828\) | −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 | \(-0.409724\pi\) | ||||
0.279825 | + | 0.960051i | \(0.409724\pi\) | |||||||
\(854\) | 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 | \(0.198173\pi\) | ||||
−0.812378 | + | 0.583132i | \(0.801827\pi\) | |||||||
\(858\) | 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 | \(-0.474235\pi\) | ||||
0.0808559 | + | 0.996726i | \(0.474235\pi\) | |||||||
\(864\) | −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 | −0.846360 | − | 0.532611i | \(-0.821211\pi\) |
0.884434 | + | 0.466664i | \(0.154544\pi\) | |||||||
\(878\) | −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 | \(0.157904\pi\) | ||||
−0.879460 | + | 0.475973i | \(0.842096\pi\) | |||||||
\(884\) | −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 | −0.848225 | − | 0.529637i | \(-0.822328\pi\) |
0.0345665 | + | 0.999402i | \(0.488995\pi\) | |||||||
\(888\) | 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 | −0.718734 | − | 0.695285i | \(-0.755278\pi\) |
0.242767 | + | 0.970085i | \(0.421945\pi\) | |||||||
\(908\) | −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 | \(-0.834232\pi\) | ||
0.867434 | − | 0.497552i | \(-0.165768\pi\) | |||||||
\(938\) | −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 | \(-0.841953\pi\) |
0.0270773 | − | 0.999633i | \(-0.491380\pi\) | |||||||
\(948\) | 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 | −0.174969 | − | 0.984574i | \(-0.555982\pi\) |
−0.940150 | + | 0.340760i | \(0.889316\pi\) | |||||||
\(954\) | 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 | \(-0.636081\pi\) | ||||
−0.414607 | + | 0.910001i | \(0.636081\pi\) | |||||||
\(968\) | −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 | \(-0.942226\pi\) |
0.335461 | − | 0.942054i | \(-0.391108\pi\) | |||||||
\(978\) | −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 | \(-0.687308\pi\) | ||||
−0.555068 | + | 0.831805i | \(0.687308\pi\) | |||||||
\(984\) | −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 | 0.573413 | − | 0.819267i | \(-0.305619\pi\) |
−0.422799 | + | 0.906223i | \(0.638952\pi\) | |||||||
\(998\) | −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.c.49.2 | 8 | ||
5.2 | odd | 4 | 325.2.n.d.101.3 | 8 | |||
5.3 | odd | 4 | 65.2.m.a.36.2 | ✓ | 8 | ||
5.4 | even | 2 | 325.2.m.b.49.3 | 8 | |||
13.4 | even | 6 | 325.2.m.b.199.3 | 8 | |||
15.8 | even | 4 | 585.2.bu.c.361.3 | 8 | |||
20.3 | even | 4 | 1040.2.da.b.881.2 | 8 | |||
65.2 | even | 12 | 4225.2.a.bi.1.3 | 4 | |||
65.3 | odd | 12 | 845.2.c.g.506.4 | 8 | |||
65.4 | even | 6 | inner | 325.2.m.c.199.2 | 8 | ||
65.8 | even | 4 | 845.2.e.n.146.2 | 8 | |||
65.17 | odd | 12 | 325.2.n.d.251.3 | 8 | |||
65.18 | even | 4 | 845.2.e.m.146.3 | 8 | |||
65.23 | odd | 12 | 845.2.c.g.506.5 | 8 | |||
65.28 | even | 12 | 845.2.a.m.1.2 | 4 | |||
65.33 | even | 12 | 845.2.e.n.191.2 | 8 | |||
65.37 | even | 12 | 4225.2.a.bl.1.2 | 4 | |||
65.38 | odd | 4 | 845.2.m.g.361.3 | 8 | |||
65.43 | odd | 12 | 65.2.m.a.56.2 | yes | 8 | ||
65.48 | odd | 12 | 845.2.m.g.316.3 | 8 | |||
65.58 | even | 12 | 845.2.e.m.191.3 | 8 | |||
65.63 | even | 12 | 845.2.a.l.1.3 | 4 | |||
195.128 | odd | 12 | 7605.2.a.cj.1.2 | 4 | |||
195.158 | odd | 12 | 7605.2.a.cf.1.3 | 4 | |||
195.173 | even | 12 | 585.2.bu.c.316.3 | 8 | |||
260.43 | 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 | 5.3 | odd | 4 | ||
65.2.m.a.56.2 | yes | 8 | 65.43 | odd | 12 | ||
325.2.m.b.49.3 | 8 | 5.4 | even | 2 | |||
325.2.m.b.199.3 | 8 | 13.4 | even | 6 | |||
325.2.m.c.49.2 | 8 | 1.1 | even | 1 | trivial | ||
325.2.m.c.199.2 | 8 | 65.4 | even | 6 | inner | ||
325.2.n.d.101.3 | 8 | 5.2 | odd | 4 | |||
325.2.n.d.251.3 | 8 | 65.17 | odd | 12 | |||
585.2.bu.c.316.3 | 8 | 195.173 | even | 12 | |||
585.2.bu.c.361.3 | 8 | 15.8 | even | 4 | |||
845.2.a.l.1.3 | 4 | 65.63 | even | 12 | |||
845.2.a.m.1.2 | 4 | 65.28 | even | 12 | |||
845.2.c.g.506.4 | 8 | 65.3 | odd | 12 | |||
845.2.c.g.506.5 | 8 | 65.23 | odd | 12 | |||
845.2.e.m.146.3 | 8 | 65.18 | even | 4 | |||
845.2.e.m.191.3 | 8 | 65.58 | even | 12 | |||
845.2.e.n.146.2 | 8 | 65.8 | even | 4 | |||
845.2.e.n.191.2 | 8 | 65.33 | even | 12 | |||
845.2.m.g.316.3 | 8 | 65.48 | odd | 12 | |||
845.2.m.g.361.3 | 8 | 65.38 | odd | 4 | |||
1040.2.da.b.641.2 | 8 | 260.43 | even | 12 | |||
1040.2.da.b.881.2 | 8 | 20.3 | even | 4 | |||
4225.2.a.bi.1.3 | 4 | 65.2 | even | 12 | |||
4225.2.a.bl.1.2 | 4 | 65.37 | even | 12 | |||
7605.2.a.cf.1.3 | 4 | 195.158 | odd | 12 | |||
7605.2.a.cj.1.2 | 4 | 195.128 | odd | 12 |