Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [875,2,Mod(82,875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(875, base_ring=CyclotomicField(60))
chi = DirichletCharacter(H, H._module([27, 50]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("875.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 875 = 5^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 875.bb (of order \(60\), degree \(16\), 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: | \(6.98691017686\) |
Analytic rank: | \(0\) |
Dimension: | \(288\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{60})\) |
Twist minimal: | no (minimal twist has level 175) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{60}]$ |
Embedding invariants
Embedding label | 143.5 | ||
Character | \(\chi\) | \(=\) | 875.143 |
Dual form | 875.2.bb.a.257.5 |
$q$-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 \(\left(\mathbb{Z}/875\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(626\) |
\(\chi(n)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0848016 | − | 1.61811i | −0.0599638 | − | 1.14418i | −0.848502 | − | 0.529192i | \(-0.822495\pi\) |
0.788539 | − | 0.614985i | \(-0.210838\pi\) | |||||||
\(3\) | −2.12290 | − | 1.71909i | −1.22566 | − | 0.992519i | −0.999832 | − | 0.0183512i | \(-0.994158\pi\) |
−0.225827 | − | 0.974167i | \(-0.572508\pi\) | |||||||
\(4\) | −0.622046 | + | 0.0653797i | −0.311023 | + | 0.0326899i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.60166 | + | 3.58087i | −1.06212 | + | 1.46189i | ||||
\(7\) | 2.64114 | − | 0.156130i | 0.998257 | − | 0.0590114i | ||||
\(8\) | −0.348409 | − | 2.19977i | −0.123181 | − | 0.777736i | ||||
\(9\) | 0.927701 | + | 4.36449i | 0.309234 | + | 1.45483i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.84181 | − | 0.816603i | −1.15835 | − | 0.246215i | −0.411629 | − | 0.911352i | \(-0.635040\pi\) |
−0.746722 | + | 0.665137i | \(0.768373\pi\) | |||||||
\(12\) | 1.43294 | + | 0.930561i | 0.413653 | + | 0.268630i | ||||
\(13\) | 0.0441012 | + | 0.0865535i | 0.0122315 | + | 0.0240056i | 0.897041 | − | 0.441946i | \(-0.145712\pi\) |
−0.884810 | + | 0.465952i | \(0.845712\pi\) | |||||||
\(14\) | −0.476608 | − | 4.26042i | −0.127379 | − | 1.13864i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.75353 | + | 1.01039i | −1.18838 | + | 0.252599i | ||||
\(17\) | −3.12891 | − | 1.20108i | −0.758872 | − | 0.291304i | −0.0520016 | − | 0.998647i | \(-0.516560\pi\) |
−0.706870 | + | 0.707343i | \(0.749893\pi\) | |||||||
\(18\) | 6.98356 | − | 1.87124i | 1.64604 | − | 0.441055i | ||||
\(19\) | −0.637130 | + | 6.06189i | −0.146168 | + | 1.39069i | 0.637948 | + | 0.770079i | \(0.279783\pi\) |
−0.784116 | + | 0.620614i | \(0.786883\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.87529 | − | 4.20892i | −1.28209 | − | 0.918461i | ||||
\(22\) | −0.995562 | + | 6.28573i | −0.212254 | + | 1.34012i | ||||
\(23\) | −5.23739 | + | 0.274480i | −1.09207 | + | 0.0572331i | −0.589856 | − | 0.807509i | \(-0.700815\pi\) |
−0.502217 | + | 0.864742i | \(0.667482\pi\) | |||||||
\(24\) | −3.04197 | + | 5.26884i | −0.620939 | + | 1.07550i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.136313 | − | 0.0787005i | 0.0267332 | − | 0.0154344i | ||||
\(27\) | 1.81310 | − | 3.55840i | 0.348930 | − | 0.684814i | ||||
\(28\) | −1.63270 | + | 0.269797i | −0.308552 | + | 0.0509868i | ||||
\(29\) | −2.51245 | − | 3.45809i | −0.466550 | − | 0.642152i | 0.509301 | − | 0.860589i | \(-0.329904\pi\) |
−0.975851 | + | 0.218437i | \(0.929904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.287036 | − | 0.644694i | −0.0515533 | − | 0.115791i | 0.885932 | − | 0.463814i | \(-0.153520\pi\) |
−0.937486 | + | 0.348024i | \(0.886853\pi\) | |||||||
\(32\) | 0.885159 | + | 3.30346i | 0.156475 | + | 0.583975i | ||||
\(33\) | 6.75198 | + | 8.33800i | 1.17537 | + | 1.45146i | ||||
\(34\) | −1.67814 | + | 5.16477i | −0.287798 | + | 0.885751i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.862422 | − | 2.65426i | −0.143737 | − | 0.442377i | ||||
\(37\) | −4.20336 | + | 6.47261i | −0.691029 | + | 1.06409i | 0.302788 | + | 0.953058i | \(0.402083\pi\) |
−0.993817 | + | 0.111033i | \(0.964584\pi\) | |||||||
\(38\) | 9.86284 | + | 0.516889i | 1.59996 | + | 0.0838505i | ||||
\(39\) | 0.0551709 | − | 0.259559i | 0.00883442 | − | 0.0415627i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.124652 | + | 0.0405019i | 0.0194674 | + | 0.00632534i | 0.318735 | − | 0.947844i | \(-0.396742\pi\) |
−0.299267 | + | 0.954169i | \(0.596742\pi\) | |||||||
\(42\) | −6.31226 | + | 9.86378i | −0.974003 | + | 1.52202i | ||||
\(43\) | −8.25770 | − | 8.25770i | −1.25929 | − | 1.25929i | −0.951434 | − | 0.307854i | \(-0.900389\pi\) |
−0.307854 | − | 0.951434i | \(-0.599611\pi\) | |||||||
\(44\) | 2.44318 | + | 0.256788i | 0.368323 | + | 0.0387123i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.888279 | + | 8.45141i | 0.130970 | + | 1.24609i | ||||
\(47\) | 0.970816 | + | 2.52906i | 0.141608 | + | 0.368902i | 0.985982 | − | 0.166853i | \(-0.0533605\pi\) |
−0.844374 | + | 0.535755i | \(0.820027\pi\) | |||||||
\(48\) | 11.8282 | + | 6.02679i | 1.70726 | + | 0.869893i | ||||
\(49\) | 6.95125 | − | 0.824720i | 0.993035 | − | 0.117817i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.57761 | + | 7.92865i | 0.640993 | + | 1.11023i | ||||
\(52\) | −0.0330918 | − | 0.0509570i | −0.00458901 | − | 0.00706646i | ||||
\(53\) | 7.40118 | − | 9.13970i | 1.01663 | − | 1.25543i | 0.0501369 | − | 0.998742i | \(-0.484034\pi\) |
0.966493 | − | 0.256691i | \(-0.0826324\pi\) | |||||||
\(54\) | −5.91164 | − | 2.63203i | −0.804472 | − | 0.358174i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.26365 | − | 5.75550i | −0.168862 | − | 0.769111i | ||||
\(57\) | 11.7735 | − | 11.7735i | 1.55944 | − | 1.55944i | ||||
\(58\) | −5.38252 | + | 4.35867i | −0.706759 | + | 0.572322i | ||||
\(59\) | 3.45304 | + | 3.83499i | 0.449548 | + | 0.499273i | 0.924735 | − | 0.380611i | \(-0.124286\pi\) |
−0.475188 | + | 0.879885i | \(0.657620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.30099 | + | 4.77304i | 0.678723 | + | 0.611125i | 0.934649 | − | 0.355572i | \(-0.115714\pi\) |
−0.255926 | + | 0.966696i | \(0.582380\pi\) | |||||||
\(62\) | −1.01885 | + | 0.519128i | −0.129394 | + | 0.0659293i | ||||
\(63\) | 3.13162 | + | 11.3824i | 0.394546 | + | 1.43405i | ||||
\(64\) | −3.97346 | + | 1.29105i | −0.496682 | + | 0.161382i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.9192 | − | 11.6325i | 1.59025 | − | 1.43187i | ||||
\(67\) | 0.200027 | − | 0.521089i | 0.0244372 | − | 0.0636611i | −0.920819 | − | 0.389990i | \(-0.872478\pi\) |
0.945256 | + | 0.326329i | \(0.105812\pi\) | |||||||
\(68\) | 2.02485 | + | 0.542557i | 0.245549 | + | 0.0657947i | ||||
\(69\) | 11.5903 | + | 8.42087i | 1.39531 | + | 1.01375i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.818370 | − | 0.594581i | 0.0971227 | − | 0.0705637i | −0.538164 | − | 0.842840i | \(-0.680882\pi\) |
0.635287 | + | 0.772276i | \(0.280882\pi\) | |||||||
\(72\) | 9.27765 | − | 3.56136i | 1.09338 | − | 0.419710i | ||||
\(73\) | −1.78952 | + | 1.16213i | −0.209448 | + | 0.136017i | −0.645100 | − | 0.764098i | \(-0.723184\pi\) |
0.435652 | + | 0.900115i | \(0.356518\pi\) | |||||||
\(74\) | 10.8299 | + | 6.25262i | 1.25894 | + | 0.726852i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.81243i | − | 0.437316i | ||||||
\(77\) | −10.2743 | − | 1.55694i | −1.17086 | − | 0.177430i | ||||
\(78\) | −0.424673 | − | 0.0672616i | −0.0480848 | − | 0.00761588i | ||||
\(79\) | 6.28497 | − | 14.1163i | 0.707114 | − | 1.58820i | −0.0980696 | − | 0.995180i | \(-0.531267\pi\) |
0.805184 | − | 0.593025i | \(-0.202067\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.26247 | − | 1.00731i | 0.251385 | − | 0.111924i | ||||
\(82\) | 0.0549659 | − | 0.205136i | 0.00606997 | − | 0.0226534i | ||||
\(83\) | −10.6837 | + | 1.69214i | −1.17269 | + | 0.185736i | −0.712232 | − | 0.701944i | \(-0.752316\pi\) |
−0.460461 | + | 0.887680i | \(0.652316\pi\) | |||||||
\(84\) | 3.92988 | + | 2.23402i | 0.428785 | + | 0.243751i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.6616 | + | 14.0621i | −1.36534 | + | 1.51636i | ||||
\(87\) | −0.611092 | + | 11.6603i | −0.0655159 | + | 1.25012i | ||||
\(88\) | −0.457814 | + | 8.73562i | −0.0488032 | + | 0.931220i | ||||
\(89\) | 0.671570 | − | 0.745854i | 0.0711863 | − | 0.0790604i | −0.706500 | − | 0.707713i | \(-0.749727\pi\) |
0.777686 | + | 0.628653i | \(0.216393\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.129991 | + | 0.221714i | 0.0136268 | + | 0.0232420i | ||||
\(92\) | 3.23996 | − | 0.513159i | 0.337789 | − | 0.0535005i | ||||
\(93\) | −0.498939 | + | 1.86207i | −0.0517376 | + | 0.193087i | ||||
\(94\) | 4.00998 | − | 1.78536i | 0.413597 | − | 0.184145i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.79985 | − | 8.53459i | 0.387820 | − | 0.871058i | ||||
\(97\) | 11.1837 | + | 1.77133i | 1.13554 | + | 0.179851i | 0.695773 | − | 0.718262i | \(-0.255062\pi\) |
0.439764 | + | 0.898113i | \(0.355062\pi\) | |||||||
\(98\) | −1.92397 | − | 11.1779i | −0.194350 | − | 1.12914i | ||||
\(99\) | − | 17.5251i | − | 1.76134i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1623 | − | 5.86718i | −1.01118 | − | 0.583807i | −0.0996449 | − | 0.995023i | \(-0.531771\pi\) |
−0.911538 | + | 0.411216i | \(0.865104\pi\) | |||||||
\(102\) | 12.4412 | − | 8.07944i | 1.23187 | − | 0.799983i | ||||
\(103\) | −9.40258 | + | 3.60931i | −0.926464 | + | 0.355636i | −0.774372 | − | 0.632730i | \(-0.781934\pi\) |
−0.152092 | + | 0.988366i | \(0.548601\pi\) | |||||||
\(104\) | 0.175032 | − | 0.127168i | 0.0171633 | − | 0.0124699i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.4167 | − | 11.2009i | −1.49740 | − | 1.08792i | ||||
\(107\) | −1.09349 | − | 0.292999i | −0.105711 | − | 0.0283253i | 0.205576 | − | 0.978641i | \(-0.434093\pi\) |
−0.311287 | + | 0.950316i | \(0.600760\pi\) | |||||||
\(108\) | −0.895182 | + | 2.33203i | −0.0861389 | + | 0.224400i | ||||
\(109\) | 2.17553 | − | 1.95886i | 0.208378 | − | 0.187624i | −0.558333 | − | 0.829617i | \(-0.688559\pi\) |
0.766711 | + | 0.641993i | \(0.221892\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.0504 | − | 6.51476i | 1.90310 | − | 0.618353i | ||||
\(112\) | −12.3970 | + | 3.41076i | −1.17141 | + | 0.322287i | ||||
\(113\) | −4.16270 | + | 2.12100i | −0.391594 | + | 0.199527i | −0.638690 | − | 0.769464i | \(-0.720523\pi\) |
0.247097 | + | 0.968991i | \(0.420523\pi\) | |||||||
\(114\) | −20.0493 | − | 18.0524i | −1.87779 | − | 1.69077i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.78895 | + | 1.98683i | 0.166100 | + | 0.184473i | ||||
\(117\) | −0.336849 | + | 0.272775i | −0.0311417 | + | 0.0252181i | ||||
\(118\) | 5.91261 | − | 5.91261i | 0.544300 | − | 0.544300i | ||||
\(119\) | −8.45141 | − | 2.68369i | −0.774739 | − | 0.246014i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.04370 | + | 1.80037i | 0.367609 | + | 0.163670i | ||||
\(122\) | 7.27377 | − | 8.98236i | 0.658536 | − | 0.813224i | ||||
\(123\) | −0.194998 | − | 0.300270i | −0.0175824 | − | 0.0270745i | ||||
\(124\) | 0.220700 | + | 0.382263i | 0.0198194 | + | 0.0343283i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.1524 | − | 6.03254i | 1.61714 | − | 0.537422i | ||||
\(127\) | −14.7555 | − | 7.51832i | −1.30934 | − | 0.667143i | −0.346713 | − | 0.937971i | \(-0.612702\pi\) |
−0.962628 | + | 0.270829i | \(0.912702\pi\) | |||||||
\(128\) | 4.87725 | + | 12.7057i | 0.431092 | + | 1.12303i | ||||
\(129\) | 3.33454 | + | 31.7260i | 0.293590 | + | 2.79332i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.400325 | − | 0.0420758i | −0.0349765 | − | 0.00367618i | 0.0870240 | − | 0.996206i | \(-0.472264\pi\) |
−0.122001 | + | 0.992530i | \(0.538931\pi\) | |||||||
\(132\) | −4.74518 | − | 4.74518i | −0.413015 | − | 0.413015i | ||||
\(133\) | −0.736311 | + | 16.1098i | −0.0638462 | + | 1.39690i | ||||
\(134\) | −0.860142 | − | 0.279477i | −0.0743049 | − | 0.0241431i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.55195 | + | 7.30134i | −0.133078 | + | 0.626085i | ||||
\(137\) | 12.6497 | + | 0.662940i | 1.08073 | + | 0.0566388i | 0.584378 | − | 0.811481i | \(-0.301338\pi\) |
0.496354 | + | 0.868120i | \(0.334672\pi\) | |||||||
\(138\) | 12.6430 | − | 19.4685i | 1.07625 | − | 1.65727i | ||||
\(139\) | −4.44619 | − | 13.6840i | −0.377121 | − | 1.16066i | −0.942036 | − | 0.335511i | \(-0.891091\pi\) |
0.564915 | − | 0.825149i | \(-0.308909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.28674 | − | 7.03788i | 0.192579 | − | 0.592696i | ||||
\(142\) | −1.03150 | − | 1.27379i | −0.0865612 | − | 0.106894i | ||||
\(143\) | −0.0987488 | − | 0.368536i | −0.00825779 | − | 0.0308185i | ||||
\(144\) | −8.81972 | − | 19.8094i | −0.734976 | − | 1.65078i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.03221 | + | 2.79710i | 0.168187 | + | 0.231489i | ||||
\(147\) | −16.1746 | − | 10.1990i | −1.33406 | − | 0.841202i | ||||
\(148\) | 2.19151 | − | 4.30108i | 0.180141 | − | 0.353547i | ||||
\(149\) | −9.24670 | + | 5.33859i | −0.757519 | + | 0.437354i | −0.828404 | − | 0.560131i | \(-0.810751\pi\) |
0.0708851 | + | 0.997484i | \(0.477418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4396 | + | 18.0820i | −0.849565 | + | 1.47149i | 0.0320315 | + | 0.999487i | \(0.489802\pi\) |
−0.881597 | + | 0.472003i | \(0.843531\pi\) | |||||||
\(152\) | 13.5567 | − | 0.710479i | 1.09960 | − | 0.0576274i | ||||
\(153\) | 2.33939 | − | 14.7703i | 0.189128 | − | 1.19411i | ||||
\(154\) | −1.64803 | + | 16.7569i | −0.132802 | + | 1.35031i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0173490 | + | 0.165065i | −0.00138903 | + | 0.0132157i | ||||
\(157\) | −11.5468 | + | 3.09395i | −0.921533 | + | 0.246924i | −0.688241 | − | 0.725483i | \(-0.741617\pi\) |
−0.233293 | + | 0.972407i | \(0.574950\pi\) | |||||||
\(158\) | −23.3747 | − | 8.97269i | −1.85959 | − | 0.713829i | ||||
\(159\) | −31.4240 | + | 6.67937i | −2.49208 | + | 0.529709i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.7898 | + | 1.54265i | −1.08679 | + | 0.121578i | ||||
\(162\) | −1.82181 | − | 3.57550i | −0.143135 | − | 0.280918i | ||||
\(163\) | −12.1623 | − | 7.89827i | −0.952622 | − | 0.618640i | −0.0280333 | − | 0.999607i | \(-0.508924\pi\) |
−0.924589 | + | 0.380967i | \(0.875591\pi\) | |||||||
\(164\) | −0.0801874 | − | 0.0170444i | −0.00626159 | − | 0.00133094i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.64407 | + | 17.1440i | 0.282834 | + | 1.33063i | ||||
\(167\) | 0.261681 | + | 1.65219i | 0.0202495 | + | 0.127850i | 0.995742 | − | 0.0921813i | \(-0.0293839\pi\) |
−0.975493 | + | 0.220032i | \(0.929384\pi\) | |||||||
\(168\) | −7.21164 | + | 14.3907i | −0.556390 | + | 1.11027i | ||||
\(169\) | 7.63566 | − | 10.5096i | 0.587359 | − | 0.808430i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −27.0481 | + | 2.84287i | −2.06842 | + | 0.217400i | ||||
\(172\) | 5.67656 | + | 4.59679i | 0.432834 | + | 0.350502i | ||||
\(173\) | 0.0147195 | + | 0.280864i | 0.00111910 | + | 0.0213537i | 0.999132 | − | 0.0416561i | \(-0.0132634\pi\) |
−0.998013 | + | 0.0630098i | \(0.979930\pi\) | |||||||
\(174\) | 18.9195 | 1.43429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.0873 | 1.43876 | ||||||||
\(177\) | −0.737766 | − | 14.0774i | −0.0554539 | − | 1.05812i | ||||
\(178\) | −1.26383 | − | 1.02343i | −0.0947277 | − | 0.0767090i | ||||
\(179\) | −13.0417 | + | 1.37074i | −0.974782 | + | 0.102454i | −0.578506 | − | 0.815678i | \(-0.696364\pi\) |
−0.396275 | + | 0.918132i | \(0.629697\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5383 | − | 18.6338i | 1.00629 | − | 1.38504i | 0.0849076 | − | 0.996389i | \(-0.472940\pi\) |
0.921384 | − | 0.388653i | \(-0.127060\pi\) | |||||||
\(182\) | 0.347735 | − | 0.229142i | 0.0257758 | − | 0.0169851i | ||||
\(183\) | −3.04820 | − | 19.2456i | −0.225330 | − | 1.42268i | ||||
\(184\) | 2.42855 | + | 11.4254i | 0.179035 | + | 0.842294i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.05534 | + | 0.649432i | 0.224028 | + | 0.0476187i | ||||
\(187\) | 11.0399 | + | 7.16938i | 0.807316 | + | 0.524277i | ||||
\(188\) | −0.769242 | − | 1.50972i | −0.0561027 | − | 0.110108i | ||||
\(189\) | 4.23307 | − | 9.68131i | 0.307910 | − | 0.704212i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.95786 | + | 0.841270i | −0.286381 | + | 0.0608722i | −0.348862 | − | 0.937174i | \(-0.613432\pi\) |
0.0624813 | + | 0.998046i | \(0.480099\pi\) | |||||||
\(192\) | 10.6547 | + | 4.08996i | 0.768937 | + | 0.295167i | ||||
\(193\) | 2.96976 | − | 0.795745i | 0.213768 | − | 0.0572790i | −0.150346 | − | 0.988634i | \(-0.548039\pi\) |
0.364114 | + | 0.931355i | \(0.381372\pi\) | |||||||
\(194\) | 1.91781 | − | 18.2467i | 0.137691 | − | 1.31004i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.27008 | + | 0.967485i | −0.305006 | + | 0.0691061i | ||||
\(197\) | −1.97286 | + | 12.4561i | −0.140560 | + | 0.887464i | 0.812120 | + | 0.583490i | \(0.198313\pi\) |
−0.952681 | + | 0.303973i | \(0.901687\pi\) | |||||||
\(198\) | −28.3576 | + | 1.48616i | −2.01529 | + | 0.105617i | ||||
\(199\) | 2.17496 | − | 3.76715i | 0.154179 | − | 0.267046i | −0.778581 | − | 0.627545i | \(-0.784060\pi\) |
0.932760 | + | 0.360498i | \(0.117393\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.32044 | + | 0.762355i | −0.0931365 | + | 0.0537724i | ||||
\(202\) | −8.63198 | + | 16.9412i | −0.607344 | + | 1.19198i | ||||
\(203\) | −7.17565 | − | 8.74104i | −0.503632 | − | 0.613501i | ||||
\(204\) | −3.36586 | − | 4.63270i | −0.235657 | − | 0.324354i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.63762 | + | 14.9083i | 0.462465 | + | 1.03871i | ||||
\(207\) | −6.05670 | − | 22.6039i | −0.420970 | − | 1.57108i | ||||
\(208\) | −0.297090 | − | 0.366875i | −0.0205995 | − | 0.0254382i | ||||
\(209\) | 7.39789 | − | 22.7684i | 0.511723 | − | 1.57492i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.05986 | + | 6.33961i | 0.141807 | + | 0.436437i | 0.996587 | − | 0.0825543i | \(-0.0263078\pi\) |
−0.854780 | + | 0.518991i | \(0.826308\pi\) | |||||||
\(212\) | −4.00633 | + | 6.16920i | −0.275156 | + | 0.423703i | ||||
\(213\) | −2.75946 | − | 0.144617i | −0.189075 | − | 0.00990900i | ||||
\(214\) | −0.381375 | + | 1.79423i | −0.0260703 | + | 0.122651i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.45936 | − | 2.74861i | −0.575586 | − | 0.187019i | ||||
\(217\) | −0.858760 | − | 1.65791i | −0.0582964 | − | 0.112547i | ||||
\(218\) | −3.35413 | − | 3.35413i | −0.227171 | − | 0.227171i | ||||
\(219\) | 5.79680 | + | 0.609268i | 0.391711 | + | 0.0411705i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0340314 | − | 0.323787i | −0.00228920 | − | 0.0217803i | ||||
\(222\) | −12.2419 | − | 31.8912i | −0.821622 | − | 2.14040i | ||||
\(223\) | 13.7309 | + | 6.99626i | 0.919491 | + | 0.468504i | 0.848633 | − | 0.528982i | \(-0.177426\pi\) |
0.0708583 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(224\) | 2.85360 | + | 8.58670i | 0.190664 | + | 0.573723i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.78502 | + | 6.55584i | 0.251776 | + | 0.436088i | ||||
\(227\) | −7.21647 | − | 11.1124i | −0.478974 | − | 0.737556i | 0.513753 | − | 0.857938i | \(-0.328255\pi\) |
−0.992728 | + | 0.120382i | \(0.961588\pi\) | |||||||
\(228\) | −6.55393 | + | 8.09342i | −0.434044 | + | 0.536000i | ||||
\(229\) | 3.78909 | + | 1.68701i | 0.250390 | + | 0.111481i | 0.528094 | − | 0.849186i | \(-0.322907\pi\) |
−0.277704 | + | 0.960667i | \(0.589574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.1347 | + | 20.9677i | 1.25897 | + | 1.37957i | ||||
\(232\) | −6.73164 | + | 6.73164i | −0.441954 | + | 0.441954i | ||||
\(233\) | 20.0258 | − | 16.2166i | 1.31194 | − | 1.06238i | 0.318508 | − | 0.947920i | \(-0.396818\pi\) |
0.993427 | − | 0.114464i | \(-0.0365152\pi\) | |||||||
\(234\) | 0.469946 | + | 0.521927i | 0.0307213 | + | 0.0341195i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.39868 | − | 2.15978i | −0.156141 | − | 0.140590i | ||||
\(237\) | −37.6096 | + | 19.1630i | −2.44300 | + | 1.24477i | ||||
\(238\) | −3.62582 | + | 13.9029i | −0.235027 | + | 0.901191i | ||||
\(239\) | 0.618920 | − | 0.201099i | 0.0400346 | − | 0.0130080i | −0.288931 | − | 0.957350i | \(-0.593300\pi\) |
0.328966 | + | 0.944342i | \(0.393300\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.853202 | + | 0.768226i | −0.0549596 | + | 0.0494858i | −0.696153 | − | 0.717894i | \(-0.745106\pi\) |
0.641193 | + | 0.767379i | \(0.278440\pi\) | |||||||
\(242\) | 2.57029 | − | 6.69582i | 0.165224 | − | 0.430424i | ||||
\(243\) | −18.1075 | − | 4.85188i | −1.16159 | − | 0.311248i | ||||
\(244\) | −3.60952 | − | 2.62247i | −0.231076 | − | 0.167887i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.469334 | + | 0.340991i | −0.0299237 | + | 0.0217408i | ||||
\(247\) | −0.552776 | + | 0.212191i | −0.0351723 | + | 0.0135014i | ||||
\(248\) | −1.31817 | + | 0.856031i | −0.0837040 | + | 0.0543580i | ||||
\(249\) | 25.5895 | + | 14.7741i | 1.62167 | + | 0.936270i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.8492i | − | 0.874153i | −0.899424 | − | 0.437076i | \(-0.856014\pi\) | ||
0.899424 | − | 0.437076i | \(-0.143986\pi\) | |||||||
\(252\) | −2.69219 | − | 6.87563i | −0.169592 | − | 0.433124i | ||||
\(253\) | 20.3452 | + | 3.22237i | 1.27909 | + | 0.202589i | ||||
\(254\) | −10.9142 | + | 24.5136i | −0.684816 | + | 1.53812i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.5121 | − | 5.57076i | 0.782008 | − | 0.348172i | ||||
\(257\) | 0.0943752 | − | 0.352213i | 0.00588696 | − | 0.0219704i | −0.962920 | − | 0.269788i | \(-0.913047\pi\) |
0.968807 | + | 0.247817i | \(0.0797132\pi\) | |||||||
\(258\) | 51.0535 | − | 8.08608i | 3.17845 | − | 0.503417i | ||||
\(259\) | −10.0911 | + | 17.7513i | −0.627031 | + | 1.10302i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.7620 | − | 14.1736i | 0.789948 | − | 0.877327i | ||||
\(262\) | −0.0341352 | + | 0.651338i | −0.00210888 | + | 0.0402398i | ||||
\(263\) | 1.55688 | − | 29.7070i | 0.0960011 | − | 1.83181i | −0.349967 | − | 0.936762i | \(-0.613807\pi\) |
0.445968 | − | 0.895049i | \(-0.352859\pi\) | |||||||
\(264\) | 15.9892 | − | 17.7578i | 0.984069 | − | 1.09292i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 26.1298 | − | 0.174703i | 1.60212 | − | 0.0107117i | ||||
\(267\) | −2.70787 | + | 0.428885i | −0.165719 | + | 0.0262473i | ||||
\(268\) | −0.0903576 | + | 0.337219i | −0.00551947 | + | 0.0205989i | ||||
\(269\) | −18.9335 | + | 8.42973i | −1.15439 | + | 0.513970i | −0.892465 | − | 0.451117i | \(-0.851026\pi\) |
−0.261930 | + | 0.965087i | \(0.584359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.28034 | + | 5.12174i | −0.138521 | + | 0.311123i | −0.969464 | − | 0.245235i | \(-0.921135\pi\) |
0.830943 | + | 0.556358i | \(0.187802\pi\) | |||||||
\(272\) | 16.0869 | + | 2.54792i | 0.975413 | + | 0.154490i | ||||
\(273\) | 0.105189 | − | 0.694145i | 0.00636635 | − | 0.0420116i | ||||
\(274\) | − | 20.5248i | − | 1.23995i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.76028 | − | 4.48040i | −0.467114 | − | 0.269688i | ||||
\(277\) | 4.95771 | − | 3.21957i | 0.297880 | − | 0.193445i | −0.387042 | − | 0.922062i | \(-0.626503\pi\) |
0.684922 | + | 0.728617i | \(0.259836\pi\) | |||||||
\(278\) | −21.7651 | + | 8.35486i | −1.30539 | + | 0.501091i | ||||
\(279\) | 2.54748 | − | 1.85085i | 0.152514 | − | 0.110808i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.92124 | − | 5.02858i | −0.412887 | − | 0.299980i | 0.361883 | − | 0.932224i | \(-0.382134\pi\) |
−0.774769 | + | 0.632244i | \(0.782134\pi\) | |||||||
\(282\) | −11.5820 | − | 3.10338i | −0.689697 | − | 0.184804i | ||||
\(283\) | 5.40796 | − | 14.0882i | 0.321470 | − | 0.837458i | −0.673674 | − | 0.739028i | \(-0.735285\pi\) |
0.995144 | − | 0.0984291i | \(-0.0313818\pi\) | |||||||
\(284\) | −0.470191 | + | 0.423361i | −0.0279007 | + | 0.0251219i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.587957 | + | 0.191039i | −0.0347666 | + | 0.0112964i | ||||
\(287\) | 0.335547 | + | 0.0875094i | 0.0198067 | + | 0.00516552i | ||||
\(288\) | −13.5968 | + | 6.92789i | −0.801196 | + | 0.408230i | ||||
\(289\) | −4.28598 | − | 3.85911i | −0.252116 | − | 0.227007i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.6969 | − | 22.9863i | −1.21327 | − | 1.34748i | ||||
\(292\) | 1.03719 | − | 0.839898i | 0.0606968 | − | 0.0491513i | ||||
\(293\) | −7.80680 | + | 7.80680i | −0.456078 | + | 0.456078i | −0.897366 | − | 0.441288i | \(-0.854522\pi\) |
0.441288 | + | 0.897366i | \(0.354522\pi\) | |||||||
\(294\) | −15.1315 | + | 27.0372i | −0.882489 | + | 1.57684i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.7027 | + | 6.99131i | 0.912703 | + | 0.406362i | ||||
\(297\) | −9.87137 | + | 12.1901i | −0.572795 | + | 0.707343i | ||||
\(298\) | 9.42256 | + | 14.5095i | 0.545834 | + | 0.840511i | ||||
\(299\) | −0.254733 | − | 0.441210i | −0.0147316 | − | 0.0255158i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.0990 | − | 20.5205i | −1.33141 | − | 1.18278i | ||||
\(302\) | 30.1439 | + | 15.3591i | 1.73459 | + | 0.883817i | ||||
\(303\) | 11.4873 | + | 29.9253i | 0.659926 | + | 1.71917i | ||||
\(304\) | −3.09628 | − | 29.4592i | −0.177584 | − | 1.68960i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −24.0984 | − | 2.53284i | −1.37761 | − | 0.144793i | ||||
\(307\) | −8.14095 | − | 8.14095i | −0.464628 | − | 0.464628i | 0.435541 | − | 0.900169i | \(-0.356557\pi\) |
−0.900169 | + | 0.435541i | \(0.856557\pi\) | |||||||
\(308\) | 6.49286 | + | 0.296762i | 0.369965 | + | 0.0169096i | ||||
\(309\) | 26.1655 | + | 8.50169i | 1.48850 | + | 0.483644i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.97488 | − | 28.1096i | 0.338804 | − | 1.59395i | −0.397700 | − | 0.917516i | \(-0.630192\pi\) |
0.736504 | − | 0.676433i | \(-0.236475\pi\) | |||||||
\(312\) | −0.590191 | − | 0.0309306i | −0.0334130 | − | 0.00175110i | ||||
\(313\) | −5.18386 | + | 7.98245i | −0.293009 | + | 0.451195i | −0.954263 | − | 0.298967i | \(-0.903358\pi\) |
0.661254 | + | 0.750162i | \(0.270025\pi\) | |||||||
\(314\) | 5.98554 | + | 18.4216i | 0.337783 | + | 1.03959i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.98662 | + | 9.19189i | −0.168011 | + | 0.517084i | ||||
\(317\) | −4.91231 | − | 6.06620i | −0.275903 | − | 0.340712i | 0.620293 | − | 0.784370i | \(-0.287014\pi\) |
−0.896196 | + | 0.443658i | \(0.853680\pi\) | |||||||
\(318\) | 13.4728 | + | 50.2810i | 0.755515 | + | 2.81962i | ||||
\(319\) | 6.82848 | + | 15.3370i | 0.382322 | + | 0.858708i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.81768 | + | 2.50182i | 0.101453 | + | 0.139638i | ||||
\(322\) | 3.66558 | + | 22.1827i | 0.204275 | + | 1.23619i | ||||
\(323\) | 9.27431 | − | 18.2019i | 0.516036 | − | 1.01278i | ||||
\(324\) | −1.34150 | + | 0.774516i | −0.0745278 | + | 0.0430287i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.7489 | + | 20.3497i | −0.650711 | + | 1.12706i | ||||
\(327\) | −7.98590 | + | 0.418523i | −0.441621 | + | 0.0231444i | ||||
\(328\) | 0.0456650 | − | 0.288317i | 0.00252143 | − | 0.0159197i | ||||
\(329\) | 2.95892 | + | 6.52804i | 0.163131 | + | 0.359902i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.108165 | + | 1.02912i | −0.00594527 | + | 0.0565654i | −0.997092 | − | 0.0762035i | \(-0.975720\pi\) |
0.991147 | + | 0.132769i | \(0.0423868\pi\) | |||||||
\(332\) | 6.53515 | − | 1.75109i | 0.358663 | − | 0.0961035i | ||||
\(333\) | −32.1491 | − | 12.3409i | −1.76176 | − | 0.676277i | ||||
\(334\) | 2.65124 | − | 0.563538i | 0.145069 | − | 0.0308354i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 32.1810 | + | 14.0709i | 1.75562 | + | 0.767629i | ||||
\(337\) | −0.849753 | − | 1.66773i | −0.0462890 | − | 0.0908472i | 0.866703 | − | 0.498824i | \(-0.166235\pi\) |
−0.912992 | + | 0.407977i | \(0.866235\pi\) | |||||||
\(338\) | −17.6532 | − | 11.4641i | −0.960207 | − | 0.623566i | ||||
\(339\) | 12.4832 | + | 2.65339i | 0.677994 | + | 0.144112i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.576281 | + | 2.71119i | 0.0312074 | + | 0.146819i | ||||
\(342\) | 6.89381 | + | 43.5258i | 0.372774 | + | 2.35361i | ||||
\(343\) | 18.2305 | − | 3.26350i | 0.984352 | − | 0.176212i | ||||
\(344\) | −15.2880 | + | 21.0421i | −0.824272 | + | 1.13451i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.453221 | − | 0.0476355i | 0.0243653 | − | 0.00256090i | ||||
\(347\) | 1.54512 | + | 1.25122i | 0.0829465 | + | 0.0671688i | 0.669897 | − | 0.742454i | \(-0.266338\pi\) |
−0.586950 | + | 0.809623i | \(0.699672\pi\) | |||||||
\(348\) | −0.382221 | − | 7.29322i | −0.0204892 | − | 0.390958i | ||||
\(349\) | 4.37015 | 0.233929 | 0.116964 | − | 0.993136i | \(-0.462684\pi\) | ||||
0.116964 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.387952 | 0.0207073 | ||||||||
\(352\) | −0.703003 | − | 13.4141i | −0.0374702 | − | 0.714974i | ||||
\(353\) | 14.5133 | + | 11.7526i | 0.772464 | + | 0.625529i | 0.932330 | − | 0.361610i | \(-0.117773\pi\) |
−0.159865 | + | 0.987139i | \(0.551106\pi\) | |||||||
\(354\) | −22.7162 | + | 2.38757i | −1.20735 | + | 0.126898i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.368984 | + | 0.507863i | −0.0195561 | + | 0.0269167i | ||||
\(357\) | 13.3280 | + | 20.2260i | 0.705393 | + | 1.07047i | ||||
\(358\) | 3.32396 | + | 20.9867i | 0.175677 | + | 1.10918i | ||||
\(359\) | 3.47497 | + | 16.3485i | 0.183402 | + | 0.862838i | 0.969568 | + | 0.244823i | \(0.0787298\pi\) |
−0.786166 | + | 0.618016i | \(0.787937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7558 | − | 3.77411i | −0.934515 | − | 0.198637i | ||||
\(362\) | −31.2997 | − | 20.3262i | −1.64507 | − | 1.06832i | ||||
\(363\) | −5.48937 | − | 10.7735i | −0.288117 | − | 0.565462i | ||||
\(364\) | −0.0953561 | − | 0.129418i | −0.00499802 | − | 0.00678334i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −30.8830 | + | 6.56439i | −1.61428 | + | 0.343126i | ||||
\(367\) | 9.01861 | + | 3.46192i | 0.470768 | + | 0.180711i | 0.582174 | − | 0.813064i | \(-0.302202\pi\) |
−0.111406 | + | 0.993775i | \(0.535536\pi\) | |||||||
\(368\) | 24.6188 | − | 6.59659i | 1.28334 | − | 0.343871i | ||||
\(369\) | −0.0611304 | + | 0.581617i | −0.00318232 | + | 0.0302778i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.1206 | − | 25.2948i | 0.940774 | − | 1.31324i | ||||
\(372\) | 0.188622 | − | 1.19091i | 0.00977959 | − | 0.0617459i | ||||
\(373\) | −4.91126 | + | 0.257388i | −0.254295 | + | 0.0133271i | −0.179058 | − | 0.983839i | \(-0.557305\pi\) |
−0.0752376 | + | 0.997166i | \(0.523972\pi\) | |||||||
\(374\) | 10.6647 | − | 18.4717i | 0.551456 | − | 0.955150i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.22511 | − | 3.01672i | 0.269465 | − | 0.155575i | ||||
\(377\) | 0.188508 | − | 0.369967i | 0.00970865 | − | 0.0190543i | ||||
\(378\) | −16.0244 | − | 6.02858i | −0.824206 | − | 0.310077i | ||||
\(379\) | −7.39900 | − | 10.1839i | −0.380061 | − | 0.523109i | 0.575540 | − | 0.817774i | \(-0.304792\pi\) |
−0.955601 | + | 0.294665i | \(0.904792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.3999 | + | 41.3268i | 0.942654 | + | 2.11723i | ||||
\(382\) | 1.69690 | + | 6.33292i | 0.0868210 | + | 0.324020i | ||||
\(383\) | 11.2845 | + | 13.9353i | 0.576613 | + | 0.712058i | 0.979103 | − | 0.203366i | \(-0.0651883\pi\) |
−0.402489 | + | 0.915425i | \(0.631855\pi\) | |||||||
\(384\) | 11.4883 | − | 35.3574i | 0.586260 | − | 1.80432i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.53944 | − | 4.73792i | −0.0783556 | − | 0.241154i | ||||
\(387\) | 28.3800 | − | 43.7013i | 1.44264 | − | 2.22146i | ||||
\(388\) | −7.07262 | − | 0.370660i | −0.359058 | − | 0.0188174i | ||||
\(389\) | 2.47971 | − | 11.6661i | 0.125726 | − | 0.591495i | −0.869503 | − | 0.493928i | \(-0.835561\pi\) |
0.995229 | − | 0.0975672i | \(-0.0311061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7170 | + | 5.43168i | 0.845415 | + | 0.274692i | ||||
\(392\) | −4.23607 | − | 15.0038i | −0.213954 | − | 0.757806i | ||||
\(393\) | 0.777518 | + | 0.777518i | 0.0392206 | + | 0.0392206i | ||||
\(394\) | 20.3227 | + | 2.13600i | 1.02384 | + | 0.107610i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.14579 | + | 10.9014i | 0.0575780 | + | 0.547818i | ||||
\(397\) | 13.4462 | + | 35.0286i | 0.674846 | + | 1.75803i | 0.651909 | + | 0.758297i | \(0.273968\pi\) |
0.0229366 | + | 0.999737i | \(0.492698\pi\) | |||||||
\(398\) | −6.28010 | − | 3.19987i | −0.314793 | − | 0.160395i | ||||
\(399\) | 29.2573 | − | 32.9337i | 1.46470 | − | 1.64875i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.106730 | + | 0.184861i | 0.00532982 | + | 0.00923152i | 0.868678 | − | 0.495377i | \(-0.164970\pi\) |
−0.863348 | + | 0.504609i | \(0.831637\pi\) | |||||||
\(402\) | 1.34555 | + | 2.07197i | 0.0671099 | + | 0.103340i | ||||
\(403\) | 0.0431419 | − | 0.0532758i | 0.00214905 | − | 0.00265386i | ||||
\(404\) | 6.70499 | + | 2.98525i | 0.333586 | + | 0.148522i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.5355 | + | 12.3522i | −0.671754 | + | 0.613032i | ||||
\(407\) | 21.4341 | − | 21.4341i | 1.06245 | − | 1.06245i | ||||
\(408\) | 15.8463 | − | 12.8321i | 0.784509 | − | 0.635283i | ||||
\(409\) | −21.3736 | − | 23.7377i | −1.05685 | − | 1.17376i | −0.984320 | − | 0.176390i | \(-0.943558\pi\) |
−0.0725340 | − | 0.997366i | \(-0.523109\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.7143 | − | 23.1533i | −1.26839 | − | 1.14207i | ||||
\(412\) | 5.61287 | − | 2.85990i | 0.276526 | − | 0.140897i | ||||
\(413\) | 9.71872 | + | 9.58962i | 0.478227 | + | 0.471875i | ||||
\(414\) | −36.0620 | + | 11.7173i | −1.77235 | + | 0.575872i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.246889 | + | 0.222300i | −0.0121047 | + | 0.0108992i | ||||
\(417\) | −14.0852 | + | 36.6932i | −0.689755 | + | 1.79687i | ||||
\(418\) | −37.4691 | − | 10.0398i | −1.83267 | − | 0.491063i | ||||
\(419\) | −8.57555 | − | 6.23050i | −0.418943 | − | 0.304380i | 0.358269 | − | 0.933618i | \(-0.383367\pi\) |
−0.777212 | + | 0.629238i | \(0.783367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.12732 | − | 5.17830i | 0.347364 | − | 0.252375i | −0.400398 | − | 0.916341i | \(-0.631128\pi\) |
0.747762 | + | 0.663966i | \(0.231128\pi\) | |||||||
\(422\) | 10.0835 | − | 3.87070i | 0.490858 | − | 0.188423i | ||||
\(423\) | −10.1374 | + | 6.58333i | −0.492899 | + | 0.320093i | ||||
\(424\) | −22.6839 | − | 13.0965i | −1.10163 | − | 0.636024i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.47737i | 0.216929i | ||||||||
\(427\) | 14.7459 | + | 11.7786i | 0.713603 | + | 0.570007i | ||||
\(428\) | 0.699356 | + | 0.110767i | 0.0338047 | + | 0.00535413i | ||||
\(429\) | −0.423913 | + | 0.952124i | −0.0204667 | + | 0.0459690i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.59847 | − | 2.49260i | 0.269669 | − | 0.120064i | −0.267448 | − | 0.963572i | \(-0.586180\pi\) |
0.537116 | + | 0.843508i | \(0.319514\pi\) | |||||||
\(432\) | −5.02322 | + | 18.7469i | −0.241680 | + | 0.901961i | ||||
\(433\) | −35.2854 | + | 5.58866i | −1.69571 | + | 0.268574i | −0.928097 | − | 0.372339i | \(-0.878556\pi\) |
−0.767613 | + | 0.640913i | \(0.778556\pi\) | |||||||
\(434\) | −2.60986 | + | 1.53016i | −0.125277 | + | 0.0734501i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.22521 | + | 1.36074i | −0.0586770 | + | 0.0651674i | ||||
\(437\) | 1.67303 | − | 31.9234i | 0.0800321 | − | 1.52710i | ||||
\(438\) | 0.494285 | − | 9.43153i | 0.0236179 | − | 0.450656i | ||||
\(439\) | 17.4485 | − | 19.3785i | 0.832769 | − | 0.924884i | −0.165347 | − | 0.986235i | \(-0.552874\pi\) |
0.998116 | + | 0.0613516i | \(0.0195411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.0482 | + | 29.5736i | 0.478484 | + | 1.40826i | ||||
\(442\) | −0.521037 | + | 0.0825241i | −0.0247832 | + | 0.00392527i | ||||
\(443\) | 8.76626 | − | 32.7161i | 0.416498 | − | 1.55439i | −0.365319 | − | 0.930882i | \(-0.619040\pi\) |
0.781817 | − | 0.623508i | \(-0.214293\pi\) | |||||||
\(444\) | −12.0463 | + | 5.36337i | −0.571693 | + | 0.254534i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.1563 | − | 22.8115i | 0.480915 | − | 1.08015i | ||||
\(447\) | 28.8074 | + | 4.56264i | 1.36254 | + | 0.215805i | ||||
\(448\) | −10.2929 | + | 4.03023i | −0.486293 | + | 0.190410i | ||||
\(449\) | − | 17.8247i | − | 0.841199i | −0.907246 | − | 0.420600i | \(-0.861820\pi\) | ||
0.907246 | − | 0.420600i | \(-0.138180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.445816 | − | 0.257392i | −0.0209927 | − | 0.0121201i | ||||
\(452\) | 2.45072 | − | 1.59152i | 0.115272 | − | 0.0748586i | ||||
\(453\) | 53.2469 | − | 20.4396i | 2.50176 | − | 0.960335i | ||||
\(454\) | −17.3691 | + | 12.6194i | −0.815173 | + | 0.592258i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.0010 | − | 21.7970i | −1.40493 | − | 1.02074i | ||||
\(457\) | −8.24133 | − | 2.20826i | −0.385513 | − | 0.103298i | 0.0608568 | − | 0.998147i | \(-0.480617\pi\) |
−0.446370 | + | 0.894849i | \(0.647283\pi\) | |||||||
\(458\) | 2.40845 | − | 6.27422i | 0.112539 | − | 0.293175i | ||||
\(459\) | −9.94691 | + | 8.95624i | −0.464282 | + | 0.418042i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2246 | + | 8.19596i | −1.17483 | + | 0.381724i | −0.830442 | − | 0.557105i | \(-0.811912\pi\) |
−0.344384 | + | 0.938829i | \(0.611912\pi\) | |||||||
\(462\) | 32.3053 | − | 32.7402i | 1.50298 | − | 1.52321i | ||||
\(463\) | −20.3912 | + | 10.3899i | −0.947661 | + | 0.482857i | −0.858304 | − | 0.513142i | \(-0.828481\pi\) |
−0.0893575 | + | 0.996000i | \(0.528481\pi\) | |||||||
\(464\) | 15.4371 | + | 13.8996i | 0.716647 | + | 0.645272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.9385 | − | 31.0288i | −1.29422 | − | 1.43738i | ||||
\(467\) | 6.92961 | − | 5.61149i | 0.320664 | − | 0.259669i | −0.455450 | − | 0.890262i | \(-0.650521\pi\) |
0.776114 | + | 0.630593i | \(0.217188\pi\) | |||||||
\(468\) | 0.191702 | − | 0.191702i | 0.00886142 | − | 0.00886142i | ||||
\(469\) | 0.446943 | − | 1.40750i | 0.0206379 | − | 0.0649922i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.8315 | + | 13.2818i | 1.37456 | + | 0.611994i | ||||
\(472\) | 7.23302 | − | 8.93204i | 0.332927 | − | 0.411130i | ||||
\(473\) | 24.9813 | + | 38.4678i | 1.14864 | + | 1.76875i | ||||
\(474\) | 34.1972 | + | 59.2314i | 1.57073 | + | 2.72059i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.43263 | + | 1.11683i | 0.249004 | + | 0.0511899i | ||||
\(477\) | 46.7562 | + | 23.8235i | 2.14082 | + | 1.09080i | ||||
\(478\) | −0.377886 | − | 0.984427i | −0.0172841 | − | 0.0450266i | ||||
\(479\) | 0.250187 | + | 2.38037i | 0.0114314 | + | 0.108762i | 0.998750 | − | 0.0499911i | \(-0.0159193\pi\) |
−0.987318 | + | 0.158753i | \(0.949253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.745601 | − | 0.0783658i | −0.0339965 | − | 0.00357317i | ||||
\(482\) | 1.31543 | + | 1.31543i | 0.0599161 | + | 0.0599161i | ||||
\(483\) | 31.9265 | + | 20.4311i | 1.45270 | + | 0.929648i | ||||
\(484\) | −2.63308 | − | 0.855538i | −0.119685 | − | 0.0388881i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.31534 | + | 29.7113i | −0.286470 | + | 1.34773i | ||||
\(487\) | −4.83930 | − | 0.253617i | −0.219290 | − | 0.0114925i | −0.0576252 | − | 0.998338i | \(-0.518353\pi\) |
−0.161664 | + | 0.986846i | \(0.551686\pi\) | |||||||
\(488\) | 8.65266 | − | 13.3239i | 0.391688 | − | 0.603146i | ||||
\(489\) | 12.2414 | + | 37.6753i | 0.553577 | + | 1.70374i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.20020 | + | 28.3153i | −0.415199 | + | 1.27785i | 0.496874 | + | 0.867823i | \(0.334481\pi\) |
−0.912073 | + | 0.410029i | \(0.865519\pi\) | |||||||
\(492\) | 0.140929 | + | 0.174033i | 0.00635358 | + | 0.00784602i | ||||
\(493\) | 3.70780 | + | 13.8377i | 0.166991 | + | 0.623218i | ||||
\(494\) | 0.390225 | + | 0.876459i | 0.0175570 | + | 0.0394337i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.01583 | + | 2.77456i | 0.0905136 | + | 0.124581i | ||||
\(497\) | 2.06860 | − | 1.69814i | 0.0927893 | − | 0.0761721i | ||||
\(498\) | 21.7361 | − | 42.6595i | 0.974018 | − | 1.91162i | ||||
\(499\) | −33.6862 | + | 19.4488i | −1.50800 | + | 0.870646i | −0.508046 | + | 0.861330i | \(0.669632\pi\) |
−0.999957 | + | 0.00931623i | \(0.997035\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.28474 | − | 3.95729i | 0.102075 | − | 0.176799i | ||||
\(502\) | −22.4095 | + | 1.17443i | −1.00019 | + | 0.0524175i | ||||
\(503\) | −5.93752 | + | 37.4880i | −0.264741 | + | 1.67151i | 0.393979 | + | 0.919120i | \(0.371098\pi\) |
−0.658719 | + | 0.752389i | \(0.728902\pi\) | |||||||
\(504\) | 23.9475 | − | 10.8546i | 1.06671 | − | 0.483501i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.48884 | − | 33.1941i | 0.155098 | − | 1.47566i | ||||
\(507\) | −34.2767 | + | 9.18442i | −1.52228 | + | 0.407894i | ||||
\(508\) | 9.67017 | + | 3.71203i | 0.429044 | + | 0.164695i | ||||
\(509\) | 10.1538 | − | 2.15825i | 0.450057 | − | 0.0956626i | 0.0226937 | − | 0.999742i | \(-0.492776\pi\) |
0.427364 | + | 0.904080i | \(0.359442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.54494 | + | 3.34875i | −0.201056 | + | 0.148140i | ||||
\(512\) | 2.28214 | + | 4.47894i | 0.100857 | + | 0.197943i | ||||
\(513\) | 20.4155 | + | 13.2579i | 0.901364 | + | 0.585353i | ||||
\(514\) | −0.577923 | − | 0.122841i | −0.0254911 | − | 0.00541830i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.14848 | − | 19.5171i | −0.182627 | − | 0.859191i | ||||
\(517\) | −1.66446 | − | 10.5090i | −0.0732027 | − | 0.462184i | ||||
\(518\) | 29.5794 | + | 14.8232i | 1.29964 | + | 0.651293i | ||||
\(519\) | 0.451584 | − | 0.621552i | 0.0198223 | − | 0.0272831i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9577 | + | 1.25680i | −0.523874 | + | 0.0550614i | −0.362775 | − | 0.931877i | \(-0.618171\pi\) |
−0.161099 | + | 0.986938i | \(0.551504\pi\) | |||||||
\(522\) | −24.0168 | − | 19.4484i | −1.05119 | − | 0.851233i | ||||
\(523\) | 1.25486 | + | 23.9442i | 0.0548713 | + | 1.04701i | 0.877850 | + | 0.478935i | \(0.158977\pi\) |
−0.822979 | + | 0.568071i | \(0.807690\pi\) | |||||||
\(524\) | 0.251771 | 0.0109987 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −48.2012 | −2.10167 | ||||||||
\(527\) | 0.123784 | + | 2.36194i | 0.00539212 | + | 0.102888i | ||||
\(528\) | −40.5204 | − | 32.8128i | −1.76343 | − | 1.42799i | ||||
\(529\) | 4.48096 | − | 0.470968i | 0.194824 | − | 0.0204769i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.5344 | + | 18.6285i | −0.587342 | + | 0.808407i | ||||
\(532\) | −0.595233 | − | 10.0692i | −0.0258066 | − | 0.436554i | ||||
\(533\) | 0.00199173 | + | 0.0125753i | 8.62712e−5 | + | 0.000544695i | ||||
\(534\) | 0.923615 | + | 4.34527i | 0.0399687 | + | 0.188038i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.21597 | − | 0.258462i | −0.0525217 | − | 0.0111638i | ||||
\(537\) | 30.0427 | + | 19.5099i | 1.29644 | + | 0.841916i | ||||
\(538\) | 15.2458 | + | 29.9216i | 0.657294 | + | 1.29001i | ||||
\(539\) | −27.3789 | − | 2.50799i | −1.17929 | − | 0.108027i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7246 | − | 3.98003i | 0.805031 | − | 0.171115i | 0.213024 | − | 0.977047i | \(-0.431669\pi\) |
0.592008 | + | 0.805932i | \(0.298336\pi\) | |||||||
\(542\) | 8.48091 | + | 3.25552i | 0.364286 | + | 0.139836i | ||||
\(543\) | −60.7737 | + | 16.2843i | −2.60805 | + | 0.698825i | ||||
\(544\) | 1.19812 | − | 11.3994i | 0.0513690 | − | 0.488744i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.13212 | − | 0.111343i | −0.0484504 | − | 0.00476506i | ||||
\(547\) | 1.95187 | − | 12.3236i | 0.0834558 | − | 0.526919i | −0.910174 | − | 0.414226i | \(-0.864052\pi\) |
0.993630 | − | 0.112693i | \(-0.0359477\pi\) | |||||||
\(548\) | −7.91201 | + | 0.414651i | −0.337984 | + | 0.0177130i | ||||
\(549\) | −15.9141 | + | 27.5641i | −0.679199 | + | 1.17641i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.5633 | − | 13.0269i | 0.961230 | − | 0.554967i | ||||
\(552\) | 14.4858 | − | 28.4300i | 0.616556 | − | 1.21006i | ||||
\(553\) | 14.3955 | − | 38.2643i | 0.612160 | − | 1.62716i | ||||
\(554\) | −5.63005 | − | 7.74910i | −0.239198 | − | 0.329228i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.66039 | + | 8.22138i | 0.155235 | + | 0.348664i | ||||
\(557\) | 5.89390 | + | 21.9963i | 0.249732 | + | 0.932014i | 0.970946 | + | 0.239301i | \(0.0769182\pi\) |
−0.721213 | + | 0.692713i | \(0.756415\pi\) | |||||||
\(558\) | −3.21091 | − | 3.96515i | −0.135929 | − | 0.167858i | ||||
\(559\) | 0.350558 | − | 1.07891i | 0.0148270 | − | 0.0456329i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.1118 | − | 34.1985i | −0.469139 | − | 1.44386i | ||||
\(562\) | −7.54986 | + | 11.6258i | −0.318472 | + | 0.490403i | ||||
\(563\) | −29.1436 | − | 1.52735i | −1.22826 | − | 0.0643701i | −0.572858 | − | 0.819654i | \(-0.694165\pi\) |
−0.655397 | + | 0.755284i | \(0.727499\pi\) | |||||||
\(564\) | −0.962327 | + | 4.52739i | −0.0405213 | + | 0.190638i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.2549 | − | 7.55597i | −0.977476 | − | 0.317601i | ||||
\(567\) | 5.81822 | − | 3.01370i | 0.244342 | − | 0.126563i | ||||
\(568\) | −1.59307 | − | 1.59307i | −0.0668436 | − | 0.0668436i | ||||
\(569\) | 1.57943 | + | 0.166005i | 0.0662130 | + | 0.00695927i | 0.137577 | − | 0.990491i | \(-0.456069\pi\) |
−0.0713640 | + | 0.997450i | \(0.522735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.375690 | − | 3.57445i | −0.0157221 | − | 0.149586i | 0.983844 | − | 0.179025i | \(-0.0572945\pi\) |
−0.999567 | + | 0.0294394i | \(0.990628\pi\) | |||||||
\(572\) | 0.0855211 | + | 0.222790i | 0.00357582 | + | 0.00931532i | ||||
\(573\) | 9.84838 | + | 5.01800i | 0.411422 | + | 0.209630i | ||||
\(574\) | 0.113145 | − | 0.550374i | 0.00472258 | − | 0.0229722i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.32098 | − | 16.1444i | −0.388374 | − | 0.672683i | ||||
\(577\) | 12.1657 | + | 18.7335i | 0.506465 | + | 0.779887i | 0.995736 | − | 0.0922444i | \(-0.0294041\pi\) |
−0.489272 | + | 0.872131i | \(0.662737\pi\) | |||||||
\(578\) | −5.88101 | + | 7.26245i | −0.244618 | + | 0.302078i | ||||
\(579\) | −7.67247 | − | 3.41601i | −0.318857 | − | 0.141964i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.9531 | + | 6.13722i | −1.15969 | + | 0.254615i | ||||
\(582\) | −35.4392 | + | 35.4392i | −1.46900 | + | 1.46900i | ||||
\(583\) | −35.8975 | + | 29.0692i | −1.48672 | + | 1.20392i | ||||
\(584\) | 3.17991 | + | 3.53164i | 0.131585 | + | 0.146140i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.2943 | + | 11.9702i | 0.549182 | + | 0.494486i | ||||
\(587\) | −38.6684 | + | 19.7026i | −1.59602 | + | 0.813211i | −0.596070 | + | 0.802933i | \(0.703272\pi\) |
−0.999947 | + | 0.0102788i | \(0.996728\pi\) | |||||||
\(588\) | 10.7282 | + | 5.28678i | 0.442422 | + | 0.218023i | ||||
\(589\) | 4.09095 | − | 1.32923i | 0.168565 | − | 0.0547699i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.6015 | − | 23.0517i | 1.05310 | − | 0.948218i | ||||
\(592\) | 13.4409 | − | 35.0148i | 0.552419 | − | 1.43910i | ||||
\(593\) | 12.4912 | + | 3.34701i | 0.512953 | + | 0.137445i | 0.506005 | − | 0.862531i | \(-0.331122\pi\) |
0.00694789 | + | 0.999976i | \(0.497788\pi\) | |||||||
\(594\) | 20.5621 | + | 14.9392i | 0.843673 | + | 0.612964i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.40284 | − | 3.92539i | 0.221309 | − | 0.160790i | ||||
\(597\) | −11.0933 | + | 4.25833i | −0.454019 | + | 0.174282i | ||||
\(598\) | −0.692325 | + | 0.449601i | −0.0283113 | + | 0.0183855i | ||||
\(599\) | 19.9444 | + | 11.5149i | 0.814905 | + | 0.470485i | 0.848656 | − | 0.528945i | \(-0.177412\pi\) |
−0.0337516 | + | 0.999430i | \(0.510745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0409i | 0.572740i | 0.958119 | + | 0.286370i | \(0.0924486\pi\) | ||||
−0.958119 | + | 0.286370i | \(0.907551\pi\) | |||||||
\(602\) | −31.2456 | + | 39.1169i | −1.27347 | + | 1.59429i | ||||
\(603\) | 2.45985 | + | 0.389602i | 0.100173 | + | 0.0158658i | ||||
\(604\) | 5.31174 | − | 11.9304i | 0.216132 | − | 0.485440i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 47.4483 | − | 21.1254i | 1.92746 | − | 0.858159i | ||||
\(607\) | −10.2468 | + | 38.2415i | −0.415904 | + | 1.55218i | 0.367113 | + | 0.930176i | \(0.380346\pi\) |
−0.783017 | + | 0.622000i | \(0.786320\pi\) | |||||||
\(608\) | −20.5892 | + | 3.26100i | −0.835001 | + | 0.132251i | ||||
\(609\) | 0.206542 | + | 30.8920i | 0.00836952 | + | 1.25181i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.176085 | + | 0.195562i | −0.00712364 | + | 0.00791160i | ||||
\(612\) | −0.489529 | + | 9.34078i | −0.0197881 | + | 0.377579i | ||||
\(613\) | −0.203103 | + | 3.87544i | −0.00820325 | + | 0.156527i | 0.991456 | + | 0.130439i | \(0.0416386\pi\) |
−0.999660 | + | 0.0260887i | \(0.991695\pi\) | |||||||
\(614\) | −12.4826 | + | 13.8633i | −0.503756 | + | 0.559478i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.154736 | + | 23.1435i | 0.00623450 | + | 0.932477i | ||||
\(617\) | 27.5463 | − | 4.36290i | 1.10897 | − | 0.175644i | 0.425029 | − | 0.905180i | \(-0.360264\pi\) |
0.683943 | + | 0.729536i | \(0.260264\pi\) | |||||||
\(618\) | 11.5378 | − | 43.0597i | 0.464118 | − | 1.73211i | ||||
\(619\) | 24.6623 | − | 10.9803i | 0.991260 | − | 0.441337i | 0.153958 | − | 0.988077i | \(-0.450798\pi\) |
0.837302 | + | 0.546740i | \(0.184131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.51918 | + | 19.1344i | −0.341863 | + | 0.767837i | ||||
\(622\) | −45.9911 | − | 7.28427i | −1.84408 | − | 0.292073i | ||||
\(623\) | 1.65726 | − | 2.07476i | 0.0663968 | − | 0.0831234i | ||||
\(624\) | 1.28957i | 0.0516239i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.3561 | + | 7.71114i | 0.533816 | + | 0.308199i | ||||
\(627\) | −54.8460 | + | 35.6174i | −2.19034 | + | 1.42242i | ||||
\(628\) | 6.98035 | − | 2.67950i | 0.278546 | − | 0.106924i | ||||
\(629\) | 20.9260 | − | 15.2037i | 0.834376 | − | 0.606209i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.70119 | + | 6.32178i | 0.346389 | + | 0.251666i | 0.747353 | − | 0.664428i | \(-0.231325\pi\) |
−0.400964 | + | 0.916094i | \(0.631325\pi\) | |||||||
\(632\) | −33.2423 | − | 8.90724i | −1.32231 | − | 0.354311i | ||||
\(633\) | 6.52549 | − | 16.9995i | 0.259365 | − | 0.675668i | ||||
\(634\) | −9.39921 | + | 8.46309i | −0.373290 | + | 0.336112i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 19.1105 | − | 6.20937i | 0.757780 | − | 0.246217i | ||||
\(637\) | 0.377941 | + | 0.565284i | 0.0149746 | + | 0.0223974i | ||||
\(638\) | 24.2379 | − | 12.3498i | 0.959589 | − | 0.488935i | ||||
\(639\) | 3.35424 | + | 3.02018i | 0.132692 | + | 0.119476i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.1580 | + | 22.3877i | 0.796191 | + | 0.884260i | 0.995411 | − | 0.0956947i | \(-0.0305073\pi\) |
−0.199219 | + | 0.979955i | \(0.563841\pi\) | |||||||
\(642\) | 3.89407 | − | 3.15336i | 0.153687 | − | 0.124453i | ||||
\(643\) | 20.4056 | − | 20.4056i | 0.804720 | − | 0.804720i | −0.179110 | − | 0.983829i | \(-0.557322\pi\) |
0.983829 | + | 0.179110i | \(0.0573217\pi\) | |||||||
\(644\) | 8.47706 | − | 1.86118i | 0.334043 | − | 0.0733407i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.2391 | − | 13.4633i | −1.18974 | − | 0.529707i | ||||
\(647\) | 12.0473 | − | 14.8771i | 0.473627 | − | 0.584880i | −0.483211 | − | 0.875504i | \(-0.660529\pi\) |
0.956837 | + | 0.290624i | \(0.0938628\pi\) | |||||||
\(648\) | −3.00412 | − | 4.62594i | −0.118013 | − | 0.181724i | ||||
\(649\) | −10.1343 | − | 17.5531i | −0.397805 | − | 0.689019i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.02704 | + | 4.99588i | −0.0402531 | + | 0.195804i | ||||
\(652\) | 8.08188 | + | 4.11792i | 0.316511 | + | 0.161270i | ||||
\(653\) | 4.32563 | + | 11.2686i | 0.169275 | + | 0.440976i | 0.991807 | − | 0.127742i | \(-0.0407729\pi\) |
−0.822533 | + | 0.568718i | \(0.807440\pi\) | |||||||
\(654\) | 1.35443 | + | 12.8866i | 0.0529625 | + | 0.503905i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.633461 | − | 0.0665794i | −0.0247325 | − | 0.00259949i | ||||
\(657\) | −6.73225 | − | 6.73225i | −0.262650 | − | 0.262650i | ||||
\(658\) | 10.3122 | − | 5.34145i | 0.402010 | − | 0.208232i | ||||
\(659\) | −15.5052 | − | 5.03793i | −0.603995 | − | 0.196250i | −0.00897383 | − | 0.999960i | \(-0.502856\pi\) |
−0.595022 | + | 0.803710i | \(0.702856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.91594 | + | 13.7184i | −0.113417 | + | 0.533585i | 0.884352 | + | 0.466821i | \(0.154601\pi\) |
−0.997769 | + | 0.0667642i | \(0.978732\pi\) | |||||||
\(662\) | 1.67440 | + | 0.0877515i | 0.0650774 | + | 0.00341056i | ||||
\(663\) | −0.484374 | + | 0.745871i | −0.0188115 | + | 0.0289672i | ||||
\(664\) | 7.44463 | + | 22.9122i | 0.288908 | + | 0.889166i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −17.2426 | + | 53.0674i | −0.668138 | + | 2.05632i | ||||
\(667\) | 14.1079 | + | 17.4218i | 0.546259 | + | 0.674574i | ||||
\(668\) | −0.270798 | − | 1.01063i | −0.0104775 | − | 0.0391025i | ||||
\(669\) | −17.1222 | − | 38.4571i | −0.661983 | − | 1.48684i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.4678 | − | 22.6659i | −0.635731 | − | 0.875008i | ||||
\(672\) | 8.70342 | − | 23.1343i | 0.335742 | − | 0.892426i | ||||
\(673\) | −0.128682 | + | 0.252552i | −0.00496031 | + | 0.00973515i | −0.893473 | − | 0.449116i | \(-0.851739\pi\) |
0.888513 | + | 0.458851i | \(0.151739\pi\) | |||||||
\(674\) | −2.62652 | + | 1.51642i | −0.101170 | + | 0.0584103i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.06262 | + | 7.03667i | −0.156255 | + | 0.270641i | ||||
\(677\) | −33.4491 | + | 1.75299i | −1.28555 | + | 0.0673729i | −0.682829 | − | 0.730578i | \(-0.739251\pi\) |
−0.602723 | + | 0.797951i | \(0.705917\pi\) | |||||||
\(678\) | 3.23488 | − | 20.4242i | 0.124235 | − | 0.784387i | ||||
\(679\) | 29.8144 | + | 2.93222i | 1.14417 | + | 0.112528i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.78337 | + | 35.9963i | −0.144979 | + | 1.37938i | ||||
\(682\) | 4.33814 | − | 1.16240i | 0.166116 | − | 0.0445106i | ||||
\(683\) | 21.1225 | + | 8.10815i | 0.808228 | + | 0.310250i | 0.727168 | − | 0.686460i | \(-0.240836\pi\) |
0.0810601 | + | 0.996709i | \(0.474169\pi\) | |||||||
\(684\) | 16.6393 | − | 3.53680i | 0.636221 | − | 0.135233i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.82667 | − | 29.2221i | −0.260644 | − | 1.11571i | ||||
\(687\) | −5.14374 | − | 10.0951i | −0.196246 | − | 0.385154i | ||||
\(688\) | 47.5968 | + | 30.9097i | 1.81461 | + | 1.17842i | ||||
\(689\) | 1.11747 | + | 0.237526i | 0.0425724 | + | 0.00904903i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.91700 | − | 27.8373i | −0.225093 | − | 1.05898i | −0.934990 | − | 0.354674i | \(-0.884592\pi\) |
0.709897 | − | 0.704306i | \(-0.248742\pi\) | |||||||
\(692\) | −0.0275190 | − | 0.173748i | −0.00104612 | − | 0.00660492i | ||||
\(693\) | −2.73619 | − | 46.2863i | −0.103939 | − | 1.75827i | ||||
\(694\) | 1.89358 | − | 2.60628i | 0.0718792 | − | 0.0989332i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 25.8629 | − | 2.71830i | 0.980332 | − | 0.103037i | ||||
\(697\) | −0.341379 | − | 0.276443i | −0.0129307 | − | 0.0104710i | ||||
\(698\) | −0.370596 | − | 7.07139i | −0.0140273 | − | 0.267656i | ||||
\(699\) | −70.3907 | −2.66242 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.7376 | 1.12317 | 0.561587 | − | 0.827418i | \(-0.310191\pi\) | ||||
0.561587 | + | 0.827418i | \(0.310191\pi\) | |||||||
\(702\) | −0.0328989 | − | 0.627749i | −0.00124169 | − | 0.0236928i | ||||
\(703\) | −36.5582 | − | 29.6042i | −1.37882 | − | 1.11654i | ||||
\(704\) | 16.3196 | − | 1.71525i | 0.615067 | − | 0.0646461i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.7863 | − | 24.4807i | 0.669396 | − | 0.921345i | ||||
\(707\) | −27.7560 | − | 13.9094i | −1.04387 | − | 0.523118i | ||||
\(708\) | 1.37930 | + | 8.70856i | 0.0518373 | + | 0.327288i | ||||
\(709\) | 1.79995 | + | 8.46811i | 0.0675986 | + | 0.318026i | 0.998935 | − | 0.0461328i | \(-0.0146897\pi\) |
−0.931337 | + | 0.364159i | \(0.881356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 67.4409 | + | 14.3350i | 2.52923 | + | 0.537605i | ||||
\(712\) | −1.87469 | − | 1.21744i | −0.0702569 | − | 0.0456254i | ||||
\(713\) | 1.68028 | + | 3.29773i | 0.0629269 | + | 0.123501i | ||||
\(714\) | 31.5976 | − | 23.2814i | 1.18251 | − | 0.871283i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.02292 | − | 1.70532i | 0.299830 | − | 0.0637309i | ||||
\(717\) | −1.65961 | − | 0.637066i | −0.0619794 | − | 0.0237917i | ||||
\(718\) | 26.1589 | − | 7.00926i | 0.976242 | − | 0.261583i | ||||
\(719\) | 2.82649 | − | 26.8922i | 0.105410 | − | 1.00291i | −0.806141 | − | 0.591724i | \(-0.798448\pi\) |
0.911551 | − | 0.411187i | \(-0.134886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.2700 | + | 11.0007i | −0.903863 | + | 0.409689i | ||||
\(722\) | −4.60121 | + | 29.0509i | −0.171239 | + | 1.08116i | ||||
\(723\) | 3.13192 | − | 0.164137i | 0.116477 | − | 0.00610431i | ||||
\(724\) | −7.20316 | + | 12.4762i | −0.267703 | + | 0.463676i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −16.9672 | + | 9.79602i | −0.629712 | + | 0.363565i | ||||
\(727\) | 7.90873 | − | 15.5218i | 0.293318 | − | 0.575670i | −0.696575 | − | 0.717484i | \(-0.745294\pi\) |
0.989893 | + | 0.141814i | \(0.0452936\pi\) | |||||||
\(728\) | 0.442430 | − | 0.363198i | 0.0163976 | − | 0.0134610i | ||||
\(729\) | 25.7325 | + | 35.4177i | 0.953055 | + | 1.31177i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.9195 | + | 35.7557i | 0.588803 | + | 1.32247i | ||||
\(732\) | 3.15439 | + | 11.7724i | 0.116590 | + | 0.435119i | ||||
\(733\) | −28.8928 | − | 35.6797i | −1.06718 | − | 1.31786i | −0.945619 | − | 0.325275i | \(-0.894543\pi\) |
−0.121562 | − | 0.992584i | \(-0.538790\pi\) | |||||||
\(734\) | 4.83698 | − | 14.8867i | 0.178536 | − | 0.549477i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.54266 | − | 17.0586i | −0.204305 | − | 0.628787i | ||||
\(737\) | −1.19399 | + | 1.83858i | −0.0439812 | + | 0.0677251i | ||||
\(738\) | 0.946304 | + | 0.0495937i | 0.0348339 | + | 0.00182557i | ||||
\(739\) | 5.11747 | − | 24.0758i | 0.188249 | − | 0.885642i | −0.778046 | − | 0.628207i | \(-0.783789\pi\) |
0.966296 | − | 0.257435i | \(-0.0828774\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.53827 | + | 0.499813i | 0.0565096 | + | 0.0183611i | ||||
\(742\) | −42.4664 | − | 27.1761i | −1.55899 | − | 0.997665i | ||||
\(743\) | 10.2323 | + | 10.2323i | 0.375388 | + | 0.375388i | 0.869435 | − | 0.494047i | \(-0.164483\pi\) |
−0.494047 | + | 0.869435i | \(0.664483\pi\) | |||||||
\(744\) | 4.26995 | + | 0.448790i | 0.156544 | + | 0.0164534i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.832965 | + | 7.92513i | 0.0304970 | + | 0.290160i | ||||
\(747\) | −17.2966 | − | 45.0593i | −0.632851 | − | 1.64863i | ||||
\(748\) | −7.33605 | − | 3.73790i | −0.268233 | − | 0.136671i | ||||
\(749\) | −2.93380 | − | 0.603126i | −0.107199 | − | 0.0220377i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.60583 | + | 9.70959i | 0.204560 | + | 0.354308i | 0.949992 | − | 0.312273i | \(-0.101090\pi\) |
−0.745433 | + | 0.666581i | \(0.767757\pi\) | |||||||
\(752\) | −7.17016 | − | 11.0411i | −0.261469 | − | 0.402627i | ||||
\(753\) | −23.8080 | + | 29.4005i | −0.867613 | + | 1.07141i | ||||
\(754\) | −0.614634 | − | 0.273653i | −0.0223836 | − | 0.00996584i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00020 | + | 6.29898i | −0.0727467 | + | 0.229092i | ||||
\(757\) | 34.2009 | − | 34.2009i | 1.24305 | − | 1.24305i | 0.284326 | − | 0.958728i | \(-0.408230\pi\) |
0.958728 | − | 0.284326i | \(-0.0917697\pi\) | |||||||
\(758\) | −15.8511 | + | 12.8360i | −0.575740 | + | 0.466225i | ||||
\(759\) | −37.6514 | − | 41.8161i | −1.36666 | − | 1.51783i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7666 | + | 11.4951i | 0.462789 | + | 0.416697i | 0.867261 | − | 0.497853i | \(-0.165878\pi\) |
−0.404472 | + | 0.914550i | \(0.632545\pi\) | |||||||
\(762\) | 65.3109 | − | 33.2776i | 2.36597 | − | 1.20552i | ||||
\(763\) | 5.44005 | − | 5.51328i | 0.196943 | − | 0.199594i | ||||
\(764\) | 2.40697 | − | 0.782073i | 0.0870812 | − | 0.0282944i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.5918 | − | 19.4414i | 0.780145 | − | 0.702445i | ||||
\(767\) | −0.179649 | + | 0.468000i | −0.00648673 | + | 0.0168985i | ||||
\(768\) | −36.1387 | − | 9.68333i | −1.30404 | − | 0.349417i | ||||
\(769\) | 15.2142 | + | 11.0538i | 0.548638 | + | 0.398609i | 0.827283 | − | 0.561785i | \(-0.189885\pi\) |
−0.278645 | + | 0.960394i | \(0.589885\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.805836 | + | 0.585474i | −0.0290215 | + | 0.0210853i | ||||
\(772\) | −1.79530 | + | 0.689152i | −0.0646144 | + | 0.0248031i | ||||
\(773\) | 27.1011 | − | 17.5997i | 0.974759 | − | 0.633016i | 0.0441474 | − | 0.999025i | \(-0.485943\pi\) |
0.930611 | + | 0.366009i | \(0.119276\pi\) | |||||||
\(774\) | −73.1203 | − | 42.2160i | −2.62825 | − | 1.51742i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 25.2188i | − | 0.905302i | ||||||
\(777\) | 51.9387 | − | 20.3368i | 1.86329 | − | 0.729580i | ||||
\(778\) | −19.0873 | − | 3.02314i | −0.684314 | − | 0.108385i | ||||
\(779\) | −0.324938 | + | 0.729823i | −0.0116421 | + | 0.0261486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.62956 | + | 1.61599i | −0.129876 | + | 0.0578245i | ||||
\(782\) | 7.37143 | − | 27.5106i | 0.263602 | − | 0.983776i | ||||
\(783\) | −16.8606 | + | 2.67045i | −0.602548 | + | 0.0954343i | ||||
\(784\) | −32.2097 | + | 10.9438i | −1.15035 | + | 0.390851i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.19218 | − | 1.32405i | 0.0425235 | − | 0.0472271i | ||||
\(787\) | 0.695360 | − | 13.2683i | 0.0247869 | − | 0.472962i | −0.957832 | − | 0.287328i | \(-0.907233\pi\) |
0.982619 | − | 0.185634i | \(-0.0594338\pi\) | |||||||
\(788\) | 0.412831 | − | 7.87728i | 0.0147065 | − | 0.280617i | ||||
\(789\) | −54.3742 | + | 60.3886i | −1.93577 | + | 2.14989i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6631 | + | 6.25178i | −0.379137 | + | 0.222288i | ||||
\(792\) | −38.5512 | + | 6.10592i | −1.36986 | + | 0.216964i | ||||
\(793\) | −0.179343 | + | 0.669316i | −0.00636865 | + | 0.0237681i | ||||
\(794\) | 55.5398 | − | 24.7279i | 1.97104 | − | 0.877561i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.10663 | + | 2.48554i | −0.0392236 | + | 0.0880976i | ||||
\(797\) | −37.9724 | − | 6.01424i | −1.34505 | − | 0.213035i | −0.557959 | − | 0.829869i | \(-0.688415\pi\) |
−0.787094 | + | 0.616833i | \(0.788415\pi\) | |||||||
\(798\) | −55.7715 | − | 44.5488i | −1.97429 | − | 1.57701i | ||||
\(799\) | − | 9.07923i | − | 0.321200i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.87829 | + | 2.23913i | 0.137033 | + | 0.0791159i | ||||
\(802\) | 0.290075 | − | 0.188377i | 0.0102429 | − | 0.00665182i | ||||
\(803\) | 7.82402 | − | 3.00336i | 0.276104 | − | 0.105986i | ||||
\(804\) | 0.771531 | − | 0.560550i | 0.0272098 | − | 0.0197691i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.0898647 | − | 0.0652905i | −0.00316535 | − | 0.00229976i | ||||
\(807\) | 54.6854 | + | 14.6529i | 1.92502 | + | 0.515807i | ||||
\(808\) | −9.36582 | + | 24.3988i | −0.329488 | + | 0.858347i | ||||
\(809\) | 0.858767 | − | 0.773238i | 0.0301927 | − | 0.0271856i | −0.653896 | − | 0.756584i | \(-0.726867\pi\) |
0.684089 | + | 0.729399i | \(0.260200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.7589 | + | 3.82070i | −0.412911 | + | 0.134163i | −0.508104 | − | 0.861296i | \(-0.669653\pi\) |
0.0951926 | + | 0.995459i | \(0.469653\pi\) | |||||||
\(812\) | 5.03507 | + | 4.96819i | 0.176696 | + | 0.174349i | ||||
\(813\) | 13.6457 | − | 6.95282i | 0.478575 | − | 0.243846i | ||||
\(814\) | −36.5004 | − | 32.8651i | −1.27934 | − | 1.15192i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −29.7709 | − | 33.0639i | −1.04219 | − | 1.15747i | ||||
\(817\) | 55.3185 | − | 44.7960i | 1.93535 | − | 1.56722i | ||||
\(818\) | −36.5978 | + | 36.5978i | −1.27961 | + | 1.27961i | ||||
\(819\) | −0.847078 | + | 0.773030i | −0.0295993 | + | 0.0270118i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.8881 | − | 15.0880i | −1.18270 | − | 0.526574i | −0.281328 | − | 0.959612i | \(-0.590775\pi\) |
−0.901376 | + | 0.433038i | \(0.857442\pi\) | |||||||
\(822\) | −35.2840 | + | 43.5721i | −1.23067 | + | 1.51975i | ||||
\(823\) | −27.3912 | − | 42.1788i | −0.954799 | − | 1.47026i | −0.881072 | − | 0.472983i | \(-0.843177\pi\) |
−0.0737269 | − | 0.997278i | \(-0.523489\pi\) | |||||||
\(824\) | 11.2156 | + | 19.4260i | 0.390714 | + | 0.676737i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.6929 | − | 16.5392i | 0.511232 | − | 0.575472i | ||||
\(827\) | −17.5564 | − | 8.94542i | −0.610495 | − | 0.311063i | 0.121270 | − | 0.992620i | \(-0.461303\pi\) |
−0.731765 | + | 0.681557i | \(0.761303\pi\) | |||||||
\(828\) | 5.24539 | + | 13.6647i | 0.182290 | + | 0.474881i | ||||
\(829\) | −2.37030 | − | 22.5519i | −0.0823239 | − | 0.783260i | −0.955328 | − | 0.295547i | \(-0.904498\pi\) |
0.873004 | − | 0.487713i | \(-0.162169\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0595 | − | 1.68792i | −0.557097 | − | 0.0585533i | ||||
\(832\) | −0.286979 | − | 0.286979i | −0.00994922 | − | 0.00994922i | ||||
\(833\) | −22.7404 | − | 5.76850i | −0.787907 | − | 0.199867i | ||||
\(834\) | 60.5681 | + | 19.6798i | 2.09730 | + | 0.681454i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.11324 | + | 14.6467i | −0.107674 | + | 0.506565i | ||||
\(837\) | −2.81450 | − | 0.147502i | −0.0972835 | − | 0.00509841i | ||||
\(838\) | −9.35442 | + | 14.4045i | −0.323143 | + | 0.497597i | ||||
\(839\) | −5.77620 | − | 17.7773i | −0.199417 | − | 0.613742i | −0.999897 | − | 0.0143819i | \(-0.995422\pi\) |
0.800480 | − | 0.599360i | \(-0.204578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31550 | − | 10.2041i | 0.114328 | − | 0.351864i | ||||
\(842\) | −8.98347 | − | 11.0937i | −0.309591 | − | 0.382313i | ||||
\(843\) | 6.04853 | + | 22.5734i | 0.208323 | + | 0.777470i | ||||
\(844\) | −1.69581 | − | 3.80886i | −0.0583723 | − | 0.131106i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.5122 | + | 15.8452i | 0.395799 | + | 0.544770i | ||||
\(847\) | 10.9611 | + | 4.12369i | 0.376627 | + | 0.141692i | ||||
\(848\) | −25.9471 | + | 50.9240i | −0.891025 | + | 1.74874i | ||||
\(849\) | −35.6995 | + | 20.6111i | −1.22520 | + | 0.707372i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.2381 | − | 35.0534i | 0.693752 | − | 1.20161i | ||||
\(852\) | 1.72597 | − | 0.0904541i | 0.0591306 | − | 0.00309891i | ||||
\(853\) | 5.30806 | − | 33.5138i | 0.181744 | − | 1.14749i | −0.713084 | − | 0.701079i | \(-0.752702\pi\) |
0.894828 | − | 0.446410i | \(-0.147298\pi\) | |||||||
\(854\) | 17.8086 | − | 24.8593i | 0.609399 | − | 0.850668i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.263549 | + | 2.50750i | −0.00900793 | + | 0.0857047i | ||||
\(857\) | 8.64649 | − | 2.31682i | 0.295358 | − | 0.0791410i | −0.108097 | − | 0.994140i | \(-0.534476\pi\) |
0.403455 | + | 0.914999i | \(0.367809\pi\) | |||||||
\(858\) | 1.57659 | + | 0.605196i | 0.0538239 | + | 0.0206611i | ||||
\(859\) | 22.5915 | − | 4.80196i | 0.770810 | − | 0.163841i | 0.194313 | − | 0.980940i | \(-0.437752\pi\) |
0.576498 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.561898 | − | 0.762611i | −0.0191494 | − | 0.0259897i | ||||
\(862\) | −4.50806 | − | 8.84757i | −0.153545 | − | 0.301349i | ||||
\(863\) | 3.09204 | + | 2.00799i | 0.105254 | + | 0.0683529i | 0.596193 | − | 0.802841i | \(-0.296679\pi\) |
−0.490939 | + | 0.871194i | \(0.663346\pi\) | |||||||
\(864\) | 13.3599 | + | 2.83974i | 0.454513 | + | 0.0966098i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.0353 | + | 56.6218i | 0.408977 | + | 1.92409i | ||||
\(867\) | 2.46454 | + | 15.5605i | 0.0837003 | + | 0.528463i | ||||
\(868\) | 0.642582 | + | 0.975154i | 0.0218107 | + | 0.0330989i | ||||
\(869\) | −35.6731 | + | 49.0998i | −1.21013 | + | 1.66560i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0539235 | − | 0.00566759i | 0.00182713 | − | 0.000192039i | ||||
\(872\) | −5.06701 | − | 4.10318i | −0.171590 | − | 0.138951i | ||||
\(873\) | 2.64421 | + | 50.4546i | 0.0894931 | + | 1.70763i | ||||
\(874\) | −51.7975 | −1.75208 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.64571 | −0.123177 | ||||||||
\(877\) | 1.57330 | + | 30.0203i | 0.0531265 | + | 1.01371i | 0.887003 | + | 0.461763i | \(0.152783\pi\) |
−0.833877 | + | 0.551951i | \(0.813884\pi\) | |||||||
\(878\) | −32.8362 | − | 26.5902i | −1.10817 | − | 0.897376i | ||||
\(879\) | 29.9937 | − | 3.15246i | 1.01166 | − | 0.106330i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.3597 | − | 36.2810i | 0.888079 | − | 1.22234i | −0.0860376 | − | 0.996292i | \(-0.527421\pi\) |
0.974117 | − | 0.226045i | \(-0.0725795\pi\) | |||||||
\(882\) | 47.0012 | − | 18.7669i | 1.58261 | − | 0.631915i | ||||
\(883\) | 4.53057 | + | 28.6049i | 0.152466 | + | 0.962631i | 0.938708 | + | 0.344713i | \(0.112024\pi\) |
−0.786242 | + | 0.617918i | \(0.787976\pi\) | |||||||
\(884\) | 0.0423382 | + | 0.199185i | 0.00142399 | + | 0.00669933i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −53.6817 | − | 11.4104i | −1.80347 | − | 0.383340i | ||||
\(887\) | 20.2001 | + | 13.1181i | 0.678253 | + | 0.440463i | 0.837253 | − | 0.546816i | \(-0.184160\pi\) |
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(888\) | −21.3167 | − | 41.8363i | −0.715341 | − | 1.40394i | ||||
\(889\) | −40.1452 | − | 17.5532i | −1.34643 | − | 0.588714i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.51455 | + | 2.02238i | −0.318749 | + | 0.0677523i | ||||
\(892\) | −8.99869 | − | 3.45427i | −0.301298 | − | 0.115658i | ||||
\(893\) | −15.9494 | + | 4.27364i | −0.533728 | + | 0.143012i | ||||
\(894\) | 4.93994 | − | 47.0004i | 0.165216 | − | 1.57193i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 14.8652 | + | 32.7960i | 0.496613 | + | 1.09564i | ||||
\(897\) | −0.217708 | + | 1.37455i | −0.00726906 | + | 0.0458950i | ||||
\(898\) | −28.8423 | + | 1.51156i | −0.962481 | + | 0.0504415i | ||||
\(899\) | −1.50825 | + | 2.61236i | −0.0503029 | + | 0.0871271i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.1351 | + | 19.7079i | −1.13720 | + | 0.656565i | ||||
\(902\) | −0.378683 | + | 0.743207i | −0.0126088 | + | 0.0247461i | ||||
\(903\) | 13.7604 | + | 83.2723i | 0.457916 | + | 2.77113i | ||||
\(904\) | 6.11603 | + | 8.41800i | 0.203416 | + | 0.279978i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −37.5889 | − | 84.4261i | −1.24881 | − | 2.80487i | ||||
\(907\) | −0.937438 | − | 3.49857i | −0.0311271 | − | 0.116168i | 0.948614 | − | 0.316435i | \(-0.102486\pi\) |
−0.979741 | + | 0.200267i | \(0.935819\pi\) | |||||||
\(908\) | 5.21551 | + | 6.44061i | 0.173083 | + | 0.213739i | ||||
\(909\) | 16.1797 | − | 49.7961i | 0.536648 | − | 1.65163i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.97054 | + | 9.14238i | 0.0984183 | + | 0.302900i | 0.988129 | − | 0.153623i | \(-0.0490943\pi\) |
−0.889711 | + | 0.456524i | \(0.849094\pi\) | |||||||
\(912\) | −44.0699 | + | 67.8617i | −1.45930 | + | 2.24713i | ||||
\(913\) | 42.4268 | + | 2.22349i | 1.40412 | + | 0.0735869i | ||||
\(914\) | −2.87433 | + | 13.5226i | −0.0950743 | + | 0.447289i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.46728 | − | 0.801669i | −0.0815213 | − | 0.0264879i | ||||
\(917\) | −1.06388 | − | 0.0486256i | −0.0351325 | − | 0.00160576i | ||||
\(918\) | 15.3357 | + | 15.3357i | 0.506154 | + | 0.506154i | ||||
\(919\) | 7.32146 | + | 0.769517i | 0.241513 | + | 0.0253840i | 0.224511 | − | 0.974471i | \(-0.427921\pi\) |
0.0170013 | + | 0.999855i | \(0.494588\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.28740 | + | 31.2775i | 0.108323 | + | 1.03063i | ||||
\(922\) | 15.4011 | + | 40.1211i | 0.507207 | + | 1.32132i | ||||
\(923\) | 0.0875541 | + | 0.0446111i | 0.00288188 | + | 0.00146839i | ||||
\(924\) | −13.2736 | − | 11.7918i | −0.436668 | − | 0.387923i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.5411 | + | 32.1142i | 0.609300 | + | 1.05534i | ||||
\(927\) | −24.4756 | − | 37.6891i | −0.803884 | − | 1.23787i | ||||
\(928\) | 9.19975 | − | 11.3607i | 0.301996 | − | 0.372935i | ||||
\(929\) | −53.5074 | − | 23.8230i | −1.75552 | − | 0.781608i | −0.990485 | − | 0.137618i | \(-0.956055\pi\) |
−0.765034 | − | 0.643989i | \(-0.777278\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.570514 | + | 42.6632i | 0.0186978 | + | 1.39823i | ||||
\(932\) | −11.3968 | + | 11.3968i | −0.373313 | + | 0.373313i | ||||
\(933\) | −61.0071 | + | 49.4026i | −1.99728 | + | 1.61737i | ||||
\(934\) | −9.66765 | − | 10.7370i | −0.316335 | − | 0.351326i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.717404 | + | 0.645953i | 0.0234491 | + | 0.0211136i | ||||
\(937\) | 4.14402 | − | 2.11148i | 0.135379 | − | 0.0689791i | −0.384989 | − | 0.922921i | \(-0.625795\pi\) |
0.520368 | + | 0.853942i | \(0.325795\pi\) | |||||||
\(938\) | −2.31539 | − | 0.603844i | −0.0756002 | − | 0.0197162i | ||||
\(939\) | 24.7274 | − | 8.03442i | 0.806948 | − | 0.262193i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.7072 | − | 19.5452i | 0.707634 | − | 0.637157i | −0.234608 | − | 0.972090i | \(-0.575381\pi\) |
0.942242 | + | 0.334933i | \(0.108714\pi\) | |||||||
\(942\) | 18.9617 | − | 49.3969i | 0.617806 | − | 1.60944i | ||||
\(943\) | −0.663969 | − | 0.177910i | −0.0216218 | − | 0.00579355i | ||||
\(944\) | −20.2890 | − | 14.7408i | −0.660350 | − | 0.479773i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 60.1267 | − | 43.6846i | 1.95489 | − | 1.42031i | ||||
\(947\) | −5.68779 | + | 2.18334i | −0.184828 | + | 0.0709490i | −0.449022 | − | 0.893521i | \(-0.648228\pi\) |
0.264194 | + | 0.964470i | \(0.414894\pi\) | |||||||
\(948\) | 22.1420 | − | 14.3792i | 0.719139 | − | 0.467015i | ||||
\(949\) | −0.179507 | − | 0.103638i | −0.00582703 | − | 0.00336424i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.3227i | 0.691435i | ||||||||
\(952\) | −2.95896 | + | 19.5262i | −0.0959003 | + | 0.632847i | ||||
\(953\) | 5.50713 | + | 0.872243i | 0.178393 | + | 0.0282547i | 0.244992 | − | 0.969525i | \(-0.421215\pi\) |
−0.0665986 | + | 0.997780i | \(0.521215\pi\) | |||||||
\(954\) | 34.5840 | − | 77.6770i | 1.11970 | − | 2.51488i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.371849 | + | 0.165558i | −0.0120265 | + | 0.00535452i | ||||
\(957\) | 11.8696 | − | 44.2978i | 0.383688 | − | 1.43194i | ||||
\(958\) | 3.83049 | − | 0.606690i | 0.123758 | − | 0.0196013i | ||||
\(959\) | 33.5130 | − | 0.224067i | 1.08219 | − | 0.00723549i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.4098 | − | 22.6674i | 0.658381 | − | 0.731206i | ||||
\(962\) | −0.0635764 | + | 1.21311i | −0.00204979 | + | 0.0391122i | ||||
\(963\) | 0.264362 | − | 5.04433i | 0.00851895 | − | 0.162551i | ||||
\(964\) | 0.480505 | − | 0.533655i | 0.0154760 | − | 0.0171879i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 30.3524 | − | 53.3931i | 0.976572 | − | 1.71790i | ||||
\(967\) | −58.4215 | + | 9.25305i | −1.87871 | + | 0.297558i | −0.987692 | − | 0.156414i | \(-0.950007\pi\) |
−0.891016 | + | 0.453972i | \(0.850007\pi\) | |||||||
\(968\) | 2.55154 | − | 9.52247i | 0.0820095 | − | 0.306064i | ||||
\(969\) | −50.9791 | + | 22.6974i | −1.63769 | + | 0.729145i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.4670 | + | 48.2157i | −0.688909 | + | 1.54731i | 0.141364 | + | 0.989958i | \(0.454851\pi\) |
−0.830273 | + | 0.557357i | \(0.811815\pi\) | |||||||
\(972\) | 11.5809 | + | 1.83423i | 0.371458 | + | 0.0588331i | ||||
\(973\) | −13.8795 | − | 35.4471i | −0.444956 | − | 1.13638i | ||||
\(974\) | 7.85203i | 0.251595i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.0211 | − | 17.3327i | −0.960952 | − | 0.554806i | ||||
\(977\) | 11.0553 | − | 7.17937i | 0.353689 | − | 0.229688i | −0.355549 | − | 0.934658i | \(-0.615706\pi\) |
0.709238 | + | 0.704969i | \(0.249039\pi\) | |||||||
\(978\) | 59.9247 | − | 23.0029i | 1.91618 | − | 0.735553i | ||||
\(979\) | −3.18912 | + | 2.31703i | −0.101925 | + | 0.0740525i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5677 | + | 7.67785i | 0.337399 | + | 0.245135i | ||||
\(982\) | 46.5975 | + | 12.4858i | 1.48699 | + | 0.398436i | ||||
\(983\) | 19.2414 | − | 50.1256i | 0.613706 | − | 1.59876i | −0.175398 | − | 0.984498i | \(-0.556121\pi\) |
0.789103 | − | 0.614260i | \(-0.210546\pi\) | |||||||
\(984\) | −0.592586 | + | 0.533567i | −0.0188910 | + | 0.0170095i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22.0765 | − | 7.17309i | 0.703059 | − | 0.228438i | ||||
\(987\) | 4.94079 | − | 18.9451i | 0.157267 | − | 0.603028i | ||||
\(988\) | 0.329979 | − | 0.168133i | 0.0104980 | − | 0.00534902i | ||||
\(989\) | 45.5154 | + | 40.9823i | 1.44731 | + | 1.30316i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.06342 | + | 7.84472i | 0.224377 | + | 0.249196i | 0.844814 | − | 0.535061i | \(-0.179711\pi\) |
−0.620437 | + | 0.784257i | \(0.713045\pi\) | |||||||
\(992\) | 1.87565 | − | 1.51887i | 0.0595519 | − | 0.0482242i | ||||
\(993\) | 1.99877 | − | 1.99877i | 0.0634291 | − | 0.0634291i | ||||
\(994\) | −2.92320 | − | 3.20322i | −0.0927184 | − | 0.101600i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −16.8838 | − | 7.51714i | −0.534983 | − | 0.238190i | ||||
\(997\) | 37.6753 | − | 46.5252i | 1.19319 | − | 1.47347i | 0.349249 | − | 0.937030i | \(-0.386437\pi\) |
0.843940 | − | 0.536437i | \(-0.180230\pi\) | |||||||
\(998\) | 34.3269 | + | 52.8588i | 1.08660 | + | 1.67321i | ||||
\(999\) | 15.4110 | + | 26.6927i | 0.487584 | + | 0.844520i |
(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 | 875.2.bb.a.143.5 | 288 | ||
5.2 | odd | 4 | 875.2.bb.c.857.14 | 288 | |||
5.3 | odd | 4 | 175.2.x.a.17.5 | yes | 288 | ||
5.4 | even | 2 | 875.2.bb.b.143.14 | 288 | |||
7.5 | odd | 6 | inner | 875.2.bb.a.768.5 | 288 | ||
25.3 | odd | 20 | 875.2.bb.b.507.14 | 288 | |||
25.4 | even | 10 | 175.2.x.a.3.14 | ✓ | 288 | ||
25.21 | even | 5 | 875.2.bb.c.493.5 | 288 | |||
25.22 | odd | 20 | inner | 875.2.bb.a.507.5 | 288 | ||
35.12 | even | 12 | 875.2.bb.c.607.5 | 288 | |||
35.19 | odd | 6 | 875.2.bb.b.768.14 | 288 | |||
35.33 | even | 12 | 175.2.x.a.117.14 | yes | 288 | ||
175.47 | even | 60 | inner | 875.2.bb.a.257.5 | 288 | ||
175.54 | odd | 30 | 175.2.x.a.103.5 | yes | 288 | ||
175.96 | odd | 30 | 875.2.bb.c.243.14 | 288 | |||
175.103 | even | 60 | 875.2.bb.b.257.14 | 288 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.x.a.3.14 | ✓ | 288 | 25.4 | even | 10 | ||
175.2.x.a.17.5 | yes | 288 | 5.3 | odd | 4 | ||
175.2.x.a.103.5 | yes | 288 | 175.54 | odd | 30 | ||
175.2.x.a.117.14 | yes | 288 | 35.33 | even | 12 | ||
875.2.bb.a.143.5 | 288 | 1.1 | even | 1 | trivial | ||
875.2.bb.a.257.5 | 288 | 175.47 | even | 60 | inner | ||
875.2.bb.a.507.5 | 288 | 25.22 | odd | 20 | inner | ||
875.2.bb.a.768.5 | 288 | 7.5 | odd | 6 | inner | ||
875.2.bb.b.143.14 | 288 | 5.4 | even | 2 | |||
875.2.bb.b.257.14 | 288 | 175.103 | even | 60 | |||
875.2.bb.b.507.14 | 288 | 25.3 | odd | 20 | |||
875.2.bb.b.768.14 | 288 | 35.19 | odd | 6 | |||
875.2.bb.c.243.14 | 288 | 175.96 | odd | 30 | |||
875.2.bb.c.493.5 | 288 | 25.21 | even | 5 | |||
875.2.bb.c.607.5 | 288 | 35.12 | even | 12 | |||
875.2.bb.c.857.14 | 288 | 5.2 | odd | 4 |