Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(236,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.236");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 311.1 | ||
Character | \(\chi\) | \(=\) | 315.311 |
Dual form | 315.2.be.c.236.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27381 | − | 1.31279i | −1.60783 | − | 0.928280i | −0.989855 | − | 0.142079i | \(-0.954621\pi\) |
−0.617972 | − | 0.786200i | \(-0.712046\pi\) | |||||||
\(3\) | −0.933716 | − | 1.45883i | −0.539081 | − | 0.842254i | ||||
\(4\) | 2.44681 | + | 4.23800i | 1.22341 | + | 2.11900i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.207969 | + | 4.54286i | 0.0849028 | + | 1.85462i | ||||
\(7\) | −2.64220 | + | 0.136993i | −0.998659 | + | 0.0517786i | ||||
\(8\) | − | 7.59741i | − | 2.68609i | ||||||
\(9\) | −1.25635 | + | 2.72426i | −0.418783 | + | 0.908087i | ||||
\(10\) | 2.27381 | + | 1.31279i | 0.719042 | + | 0.415139i | ||||
\(11\) | − | 0.107931i | − | 0.0325425i | −0.999868 | − | 0.0162713i | \(-0.994820\pi\) | ||
0.999868 | − | 0.0162713i | \(-0.00517954\pi\) | |||||||
\(12\) | 3.89788 | − | 7.52656i | 1.12522 | − | 2.17273i | ||||
\(13\) | 5.35335 | + | 3.09076i | 1.48475 | + | 0.857223i | 0.999850 | − | 0.0173448i | \(-0.00552131\pi\) |
0.484904 | + | 0.874568i | \(0.338855\pi\) | |||||||
\(14\) | 6.18771 | + | 3.15715i | 1.65374 | + | 0.843783i | ||||
\(15\) | 0.933716 | + | 1.45883i | 0.241085 | + | 0.376667i | ||||
\(16\) | −5.08015 | + | 8.79908i | −1.27004 | + | 2.19977i | ||||
\(17\) | −0.643963 | + | 1.11538i | −0.156184 | + | 0.270519i | −0.933490 | − | 0.358605i | \(-0.883253\pi\) |
0.777306 | + | 0.629123i | \(0.216586\pi\) | |||||||
\(18\) | 6.43307 | − | 4.54514i | 1.51629 | − | 1.07130i | ||||
\(19\) | −2.22804 | + | 1.28636i | −0.511148 | + | 0.295111i | −0.733305 | − | 0.679899i | \(-0.762023\pi\) |
0.222158 | + | 0.975011i | \(0.428690\pi\) | |||||||
\(20\) | −2.44681 | − | 4.23800i | −0.547124 | − | 0.947646i | ||||
\(21\) | 2.66692 | + | 3.72660i | 0.581969 | + | 0.813211i | ||||
\(22\) | −0.141691 | + | 0.245416i | −0.0302086 | + | 0.0523228i | ||||
\(23\) | 0.764400i | 0.159388i | 0.996819 | + | 0.0796942i | \(0.0253944\pi\) | ||||
−0.996819 | + | 0.0796942i | \(0.974606\pi\) | |||||||
\(24\) | −11.0833 | + | 7.09383i | −2.26237 | + | 1.44802i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −8.11501 | − | 14.0556i | −1.59148 | − | 2.75653i | ||||
\(27\) | 5.14729 | − | 0.710892i | 0.990597 | − | 0.136811i | ||||
\(28\) | −7.04555 | − | 10.8625i | −1.33148 | − | 2.05281i | ||||
\(29\) | 8.71958 | − | 5.03425i | 1.61919 | − | 0.934838i | 0.632055 | − | 0.774923i | \(-0.282212\pi\) |
0.987131 | − | 0.159914i | \(-0.0511217\pi\) | |||||||
\(30\) | −0.207969 | − | 4.54286i | −0.0379697 | − | 0.829410i | ||||
\(31\) | 4.65132 | − | 2.68544i | 0.835402 | − | 0.482320i | −0.0202966 | − | 0.999794i | \(-0.506461\pi\) |
0.855699 | + | 0.517474i | \(0.173128\pi\) | |||||||
\(32\) | 9.94350 | − | 5.74088i | 1.75778 | − | 1.01485i | ||||
\(33\) | −0.157453 | + | 0.100777i | −0.0274091 | + | 0.0175431i | ||||
\(34\) | 2.92850 | − | 1.69077i | 0.502234 | − | 0.289965i | ||||
\(35\) | 2.64220 | − | 0.136993i | 0.446614 | − | 0.0231561i | ||||
\(36\) | −14.6195 | + | 1.34135i | −2.43658 | + | 0.223558i | ||||
\(37\) | −0.952679 | − | 1.65009i | −0.156619 | − | 0.271273i | 0.777028 | − | 0.629466i | \(-0.216726\pi\) |
−0.933648 | + | 0.358193i | \(0.883393\pi\) | |||||||
\(38\) | 6.75486 | 1.09578 | ||||||||
\(39\) | −0.489632 | − | 10.6955i | −0.0784038 | − | 1.71265i | ||||
\(40\) | 7.59741i | 1.20126i | ||||||||
\(41\) | −3.87282 | + | 6.70793i | −0.604834 | + | 1.04760i | 0.387244 | + | 0.921977i | \(0.373427\pi\) |
−0.992078 | + | 0.125625i | \(0.959906\pi\) | |||||||
\(42\) | −1.17184 | − | 11.9747i | −0.180818 | − | 1.84773i | ||||
\(43\) | −3.74174 | − | 6.48088i | −0.570610 | − | 0.988325i | −0.996503 | − | 0.0835517i | \(-0.973374\pi\) |
0.425894 | − | 0.904773i | \(-0.359960\pi\) | |||||||
\(44\) | 0.457414 | − | 0.264088i | 0.0689577 | − | 0.0398127i | ||||
\(45\) | 1.25635 | − | 2.72426i | 0.187285 | − | 0.406109i | ||||
\(46\) | 1.00349 | − | 1.73810i | 0.147957 | − | 0.256269i | ||||
\(47\) | −3.85718 | + | 6.68083i | −0.562627 | + | 0.974499i | 0.434639 | + | 0.900605i | \(0.356876\pi\) |
−0.997266 | + | 0.0738943i | \(0.976457\pi\) | |||||||
\(48\) | 17.5797 | − | 0.804786i | 2.53742 | − | 0.116161i | ||||
\(49\) | 6.96247 | − | 0.723928i | 0.994638 | − | 0.103418i | ||||
\(50\) | −2.27381 | − | 1.31279i | −0.321565 | − | 0.185656i | ||||
\(51\) | 2.22842 | − | 0.102015i | 0.312041 | − | 0.0142850i | ||||
\(52\) | 30.2500i | 4.19492i | ||||||||
\(53\) | 4.83694 | + | 2.79261i | 0.664405 | + | 0.383595i | 0.793953 | − | 0.607979i | \(-0.208019\pi\) |
−0.129548 | + | 0.991573i | \(0.541353\pi\) | |||||||
\(54\) | −12.6372 | − | 5.14086i | −1.71971 | − | 0.699582i | ||||
\(55\) | 0.107931i | 0.0145535i | ||||||||
\(56\) | 1.04080 | + | 20.0739i | 0.139082 | + | 2.68249i | ||||
\(57\) | 3.95694 | + | 2.04923i | 0.524109 | + | 0.271427i | ||||
\(58\) | −26.4356 | −3.47116 | ||||||||
\(59\) | 1.18518 | + | 2.05280i | 0.154298 | + | 0.267252i | 0.932803 | − | 0.360386i | \(-0.117355\pi\) |
−0.778505 | + | 0.627638i | \(0.784022\pi\) | |||||||
\(60\) | −3.89788 | + | 7.52656i | −0.503214 | + | 0.971675i | ||||
\(61\) | 7.25479 | + | 4.18855i | 0.928880 | + | 0.536289i | 0.886457 | − | 0.462811i | \(-0.153159\pi\) |
0.0424229 | + | 0.999100i | \(0.486492\pi\) | |||||||
\(62\) | −14.1016 | −1.79091 | ||||||||
\(63\) | 2.94632 | − | 7.37016i | 0.371201 | − | 0.928552i | ||||
\(64\) | −9.82559 | −1.22820 | ||||||||
\(65\) | −5.35335 | − | 3.09076i | −0.664002 | − | 0.383362i | ||||
\(66\) | 0.490318 | − | 0.0224463i | 0.0603539 | − | 0.00276295i | ||||
\(67\) | 4.21881 | + | 7.30720i | 0.515410 | + | 0.892717i | 0.999840 | + | 0.0178865i | \(0.00569374\pi\) |
−0.484430 | + | 0.874830i | \(0.660973\pi\) | |||||||
\(68\) | −6.30262 | −0.764305 | ||||||||
\(69\) | 1.11513 | − | 0.713733i | 0.134245 | − | 0.0859233i | ||||
\(70\) | −6.18771 | − | 3.15715i | −0.739573 | − | 0.377351i | ||||
\(71\) | 10.2356i | 1.21474i | 0.794420 | + | 0.607368i | \(0.207775\pi\) | ||||
−0.794420 | + | 0.607368i | \(0.792225\pi\) | |||||||
\(72\) | 20.6973 | + | 9.54499i | 2.43920 | + | 1.12489i | ||||
\(73\) | 9.71863 | + | 5.61106i | 1.13748 | + | 0.656724i | 0.945805 | − | 0.324734i | \(-0.105275\pi\) |
0.191675 | + | 0.981459i | \(0.438608\pi\) | |||||||
\(74\) | 5.00265i | 0.581547i | ||||||||
\(75\) | −0.933716 | − | 1.45883i | −0.107816 | − | 0.168451i | ||||
\(76\) | −10.9032 | − | 6.29496i | −1.25068 | − | 0.722082i | ||||
\(77\) | 0.0147859 | + | 0.285177i | 0.00168501 | + | 0.0324989i | ||||
\(78\) | −12.9276 | + | 24.9623i | −1.46376 | + | 2.82643i | ||||
\(79\) | 5.09156 | − | 8.81884i | 0.572845 | − | 0.992197i | −0.423427 | − | 0.905930i | \(-0.639173\pi\) |
0.996272 | − | 0.0862667i | \(-0.0274937\pi\) | |||||||
\(80\) | 5.08015 | − | 8.79908i | 0.567978 | − | 0.983767i | ||||
\(81\) | −5.84318 | − | 6.84524i | −0.649242 | − | 0.760582i | ||||
\(82\) | 17.6121 | − | 10.1684i | 1.94494 | − | 1.12291i | ||||
\(83\) | 7.13623 | + | 12.3603i | 0.783302 | + | 1.35672i | 0.930008 | + | 0.367539i | \(0.119800\pi\) |
−0.146705 | + | 0.989180i | \(0.546867\pi\) | |||||||
\(84\) | −9.26790 | + | 20.4207i | −1.01121 | + | 2.22808i | ||||
\(85\) | 0.643963 | − | 1.11538i | 0.0698476 | − | 0.120980i | ||||
\(86\) | 19.6484i | 2.11874i | ||||||||
\(87\) | −15.4857 | − | 8.01979i | −1.66024 | − | 0.859812i | ||||
\(88\) | −0.819999 | −0.0874122 | ||||||||
\(89\) | 0.334543 | + | 0.579445i | 0.0354615 | + | 0.0614211i | 0.883211 | − | 0.468975i | \(-0.155377\pi\) |
−0.847750 | + | 0.530396i | \(0.822043\pi\) | |||||||
\(90\) | −6.43307 | + | 4.54514i | −0.678105 | + | 0.479099i | ||||
\(91\) | −14.5681 | − | 7.43304i | −1.52715 | − | 0.779194i | ||||
\(92\) | −3.23953 | + | 1.87034i | −0.337744 | + | 0.194997i | ||||
\(93\) | −8.26061 | − | 4.27803i | −0.856585 | − | 0.443611i | ||||
\(94\) | 17.5410 | − | 10.1273i | 1.80922 | − | 1.04455i | ||||
\(95\) | 2.22804 | − | 1.28636i | 0.228592 | − | 0.131978i | ||||
\(96\) | −17.6594 | − | 9.14548i | −1.80235 | − | 0.933407i | ||||
\(97\) | −7.16437 | + | 4.13635i | −0.727431 | + | 0.419983i | −0.817482 | − | 0.575955i | \(-0.804630\pi\) |
0.0900505 | + | 0.995937i | \(0.471297\pi\) | |||||||
\(98\) | −16.7817 | − | 7.49415i | −1.69521 | − | 0.757023i | ||||
\(99\) | 0.294033 | + | 0.135599i | 0.0295514 | + | 0.0136283i | ||||
\(100\) | 2.44681 | + | 4.23800i | 0.244681 | + | 0.423800i | ||||
\(101\) | −11.1892 | −1.11337 | −0.556685 | − | 0.830724i | \(-0.687927\pi\) | ||||
−0.556685 | + | 0.830724i | \(0.687927\pi\) | |||||||
\(102\) | −5.20093 | − | 2.69347i | −0.514969 | − | 0.266694i | ||||
\(103\) | 2.55531i | 0.251782i | 0.992044 | + | 0.125891i | \(0.0401790\pi\) | ||||
−0.992044 | + | 0.125891i | \(0.959821\pi\) | |||||||
\(104\) | 23.4818 | − | 40.6716i | 2.30258 | − | 3.98818i | ||||
\(105\) | −2.66692 | − | 3.72660i | −0.260264 | − | 0.363679i | ||||
\(106\) | −7.33220 | − | 12.6997i | −0.712166 | − | 1.23351i | ||||
\(107\) | 6.29942 | − | 3.63697i | 0.608988 | − | 0.351599i | −0.163581 | − | 0.986530i | \(-0.552305\pi\) |
0.772569 | + | 0.634931i | \(0.218971\pi\) | |||||||
\(108\) | 15.6072 | + | 20.0748i | 1.50181 | + | 1.93170i | ||||
\(109\) | −5.61363 | + | 9.72309i | −0.537688 | + | 0.931303i | 0.461340 | + | 0.887223i | \(0.347369\pi\) |
−0.999028 | + | 0.0440795i | \(0.985965\pi\) | |||||||
\(110\) | 0.141691 | − | 0.245416i | 0.0135097 | − | 0.0233995i | ||||
\(111\) | −1.51766 | + | 2.93051i | −0.144050 | + | 0.278151i | ||||
\(112\) | 12.2174 | − | 23.9449i | 1.15443 | − | 2.26258i | ||||
\(113\) | 12.2520 | + | 7.07371i | 1.15257 | + | 0.665438i | 0.949513 | − | 0.313728i | \(-0.101578\pi\) |
0.203060 | + | 0.979166i | \(0.434911\pi\) | |||||||
\(114\) | −6.30712 | − | 9.85417i | −0.590716 | − | 0.922928i | ||||
\(115\) | − | 0.764400i | − | 0.0712807i | ||||||
\(116\) | 42.6704 | + | 24.6357i | 3.96184 | + | 2.28737i | ||||
\(117\) | −15.1457 | + | 10.7009i | −1.40022 | + | 0.989294i | ||||
\(118\) | − | 6.22357i | − | 0.572926i | ||||||
\(119\) | 1.54868 | − | 3.03527i | 0.141967 | − | 0.278243i | ||||
\(120\) | 11.0833 | − | 7.09383i | 1.01176 | − | 0.647575i | ||||
\(121\) | 10.9884 | 0.998941 | ||||||||
\(122\) | −10.9973 | − | 19.0480i | −0.995653 | − | 1.72452i | ||||
\(123\) | 13.4018 | − | 0.613524i | 1.20840 | − | 0.0553196i | ||||
\(124\) | 22.7618 | + | 13.1415i | 2.04407 | + | 1.18015i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −16.3748 | + | 12.8905i | −1.45878 | + | 1.14837i | ||||
\(127\) | −4.51354 | −0.400512 | −0.200256 | − | 0.979744i | \(-0.564177\pi\) | ||||
−0.200256 | + | 0.979744i | \(0.564177\pi\) | |||||||
\(128\) | 2.45453 | + | 1.41712i | 0.216952 | + | 0.125257i | ||||
\(129\) | −5.96076 | + | 11.5098i | −0.524815 | + | 1.01339i | ||||
\(130\) | 8.11501 | + | 14.0556i | 0.711734 | + | 1.23276i | ||||
\(131\) | 2.28491 | 0.199634 | 0.0998169 | − | 0.995006i | \(-0.468174\pi\) | ||||
0.0998169 | + | 0.995006i | \(0.468174\pi\) | |||||||
\(132\) | −0.812353 | − | 0.420704i | −0.0707062 | − | 0.0366176i | ||||
\(133\) | 5.71071 | − | 3.70405i | 0.495182 | − | 0.321182i | ||||
\(134\) | − | 22.1536i | − | 1.91378i | ||||||
\(135\) | −5.14729 | + | 0.710892i | −0.443009 | + | 0.0611839i | ||||
\(136\) | 8.47398 | + | 4.89245i | 0.726637 | + | 0.419524i | ||||
\(137\) | − | 13.6642i | − | 1.16741i | −0.811964 | − | 0.583707i | \(-0.801602\pi\) | ||
0.811964 | − | 0.583707i | \(-0.198398\pi\) | |||||||
\(138\) | −3.47257 | + | 0.158971i | −0.295604 | + | 0.0135325i | ||||
\(139\) | −14.1970 | − | 8.19662i | −1.20417 | − | 0.695229i | −0.242691 | − | 0.970104i | \(-0.578030\pi\) |
−0.961480 | + | 0.274875i | \(0.911363\pi\) | |||||||
\(140\) | 7.04555 | + | 10.8625i | 0.595458 | + | 0.918046i | ||||
\(141\) | 13.3477 | − | 0.611046i | 1.12408 | − | 0.0514593i | ||||
\(142\) | 13.4371 | − | 23.2737i | 1.12762 | − | 1.95309i | ||||
\(143\) | 0.333590 | − | 0.577795i | 0.0278962 | − | 0.0483177i | ||||
\(144\) | −17.5885 | − | 24.8944i | −1.46571 | − | 2.07453i | ||||
\(145\) | −8.71958 | + | 5.03425i | −0.724122 | + | 0.418072i | ||||
\(146\) | −14.7322 | − | 25.5170i | −1.21925 | − | 2.11180i | ||||
\(147\) | −7.55705 | − | 9.48108i | −0.623295 | − | 0.781987i | ||||
\(148\) | 4.66205 | − | 8.07491i | 0.383218 | − | 0.663754i | ||||
\(149\) | 5.36768i | 0.439738i | 0.975529 | + | 0.219869i | \(0.0705630\pi\) | ||||
−0.975529 | + | 0.219869i | \(0.929437\pi\) | |||||||
\(150\) | 0.207969 | + | 4.54286i | 0.0169806 | + | 0.370923i | ||||
\(151\) | −2.24506 | −0.182700 | −0.0913501 | − | 0.995819i | \(-0.529118\pi\) | ||||
−0.0913501 | + | 0.995819i | \(0.529118\pi\) | |||||||
\(152\) | 9.77301 | + | 16.9274i | 0.792696 | + | 1.37299i | ||||
\(153\) | −2.22953 | − | 3.15562i | −0.180247 | − | 0.255117i | ||||
\(154\) | 0.340755 | − | 0.667848i | 0.0274589 | − | 0.0538168i | ||||
\(155\) | −4.65132 | + | 2.68544i | −0.373603 | + | 0.215700i | ||||
\(156\) | 44.1295 | − | 28.2449i | 3.53319 | − | 2.26141i | ||||
\(157\) | −13.6999 | + | 7.90965i | −1.09337 | + | 0.631259i | −0.934472 | − | 0.356036i | \(-0.884128\pi\) |
−0.158900 | + | 0.987295i | \(0.550795\pi\) | |||||||
\(158\) | −23.1545 | + | 13.3683i | −1.84207 | + | 1.06352i | ||||
\(159\) | −0.442399 | − | 9.66377i | −0.0350846 | − | 0.766387i | ||||
\(160\) | −9.94350 | + | 5.74088i | −0.786103 | + | 0.453857i | ||||
\(161\) | −0.104718 | − | 2.01970i | −0.00825291 | − | 0.159175i | ||||
\(162\) | 4.29996 | + | 23.2356i | 0.337837 | + | 1.82556i | ||||
\(163\) | 4.56650 | + | 7.90941i | 0.357676 | + | 0.619513i | 0.987572 | − | 0.157167i | \(-0.0502360\pi\) |
−0.629896 | + | 0.776679i | \(0.716903\pi\) | |||||||
\(164\) | −37.9043 | −2.95983 | ||||||||
\(165\) | 0.157453 | − | 0.100777i | 0.0122577 | − | 0.00784550i | ||||
\(166\) | − | 37.4733i | − | 2.90849i | ||||||
\(167\) | 1.79055 | − | 3.10133i | 0.138557 | − | 0.239988i | −0.788394 | − | 0.615171i | \(-0.789087\pi\) |
0.926951 | + | 0.375183i | \(0.122420\pi\) | |||||||
\(168\) | 28.3125 | − | 20.2617i | 2.18436 | − | 1.56322i | ||||
\(169\) | 12.6056 | + | 21.8335i | 0.969662 | + | 1.67950i | ||||
\(170\) | −2.92850 | + | 1.69077i | −0.224606 | + | 0.129676i | ||||
\(171\) | −0.705185 | − | 7.68588i | −0.0539268 | − | 0.587754i | ||||
\(172\) | 18.3107 | − | 31.7150i | 1.39617 | − | 2.41824i | ||||
\(173\) | −0.0553457 | + | 0.0958615i | −0.00420785 | + | 0.00728821i | −0.868122 | − | 0.496351i | \(-0.834673\pi\) |
0.863914 | + | 0.503640i | \(0.168006\pi\) | |||||||
\(174\) | 24.6833 | + | 38.5649i | 1.87124 | + | 2.92360i | ||||
\(175\) | −2.64220 | + | 0.136993i | −0.199732 | + | 0.0103557i | ||||
\(176\) | 0.949697 | + | 0.548308i | 0.0715861 | + | 0.0413303i | ||||
\(177\) | 1.88805 | − | 3.64571i | 0.141915 | − | 0.274028i | ||||
\(178\) | − | 1.75673i | − | 0.131673i | ||||||
\(179\) | 0.238794 | + | 0.137868i | 0.0178483 | + | 0.0103047i | 0.508898 | − | 0.860827i | \(-0.330053\pi\) |
−0.491049 | + | 0.871132i | \(0.663387\pi\) | |||||||
\(180\) | 14.6195 | − | 1.34135i | 1.08967 | − | 0.0999780i | ||||
\(181\) | 9.56064i | 0.710637i | 0.934745 | + | 0.355319i | \(0.115628\pi\) | ||||
−0.934745 | + | 0.355319i | \(0.884372\pi\) | |||||||
\(182\) | 23.3670 | + | 36.0261i | 1.73208 | + | 2.67043i | ||||
\(183\) | −0.663541 | − | 14.4944i | −0.0490504 | − | 1.07146i | ||||
\(184\) | 5.80746 | 0.428132 | ||||||||
\(185\) | 0.952679 | + | 1.65009i | 0.0700424 | + | 0.121317i | ||||
\(186\) | 13.1669 | + | 20.5718i | 0.965446 | + | 1.50840i | ||||
\(187\) | 0.120384 | + | 0.0695038i | 0.00880336 | + | 0.00508262i | ||||
\(188\) | −37.7512 | −2.75329 | ||||||||
\(189\) | −13.5028 | + | 2.58347i | −0.982184 | + | 0.187920i | ||||
\(190\) | −6.75486 | −0.490049 | ||||||||
\(191\) | −11.5530 | − | 6.67014i | −0.835947 | − | 0.482634i | 0.0199377 | − | 0.999801i | \(-0.493653\pi\) |
−0.855884 | + | 0.517167i | \(0.826987\pi\) | |||||||
\(192\) | 9.17431 | + | 14.3338i | 0.662099 | + | 1.03445i | ||||
\(193\) | −7.69329 | − | 13.3252i | −0.553775 | − | 0.959167i | −0.997998 | − | 0.0632503i | \(-0.979853\pi\) |
0.444223 | − | 0.895916i | \(-0.353480\pi\) | |||||||
\(194\) | 21.7206 | 1.55944 | ||||||||
\(195\) | 0.489632 | + | 10.6955i | 0.0350632 | + | 0.765921i | ||||
\(196\) | 20.1039 | + | 27.7356i | 1.43599 | + | 1.98112i | ||||
\(197\) | 12.1119i | 0.862940i | 0.902127 | + | 0.431470i | \(0.142005\pi\) | ||||
−0.902127 | + | 0.431470i | \(0.857995\pi\) | |||||||
\(198\) | −0.490563 | − | 0.694330i | −0.0348628 | − | 0.0493439i | ||||
\(199\) | 0.805586 | + | 0.465105i | 0.0571065 | + | 0.0329704i | 0.528281 | − | 0.849069i | \(-0.322837\pi\) |
−0.471175 | + | 0.882040i | \(0.656170\pi\) | |||||||
\(200\) | − | 7.59741i | − | 0.537218i | ||||||
\(201\) | 6.72076 | − | 12.9774i | 0.474046 | − | 0.915353i | ||||
\(202\) | 25.4422 | + | 14.6891i | 1.79011 | + | 1.03352i | ||||
\(203\) | −22.3492 | + | 14.4960i | −1.56861 | + | 1.01742i | ||||
\(204\) | 5.88486 | + | 9.19443i | 0.412023 | + | 0.643739i | ||||
\(205\) | 3.87282 | − | 6.70793i | 0.270490 | − | 0.468502i | ||||
\(206\) | 3.35458 | − | 5.81030i | 0.233724 | − | 0.404823i | ||||
\(207\) | −2.08242 | − | 0.960352i | −0.144738 | − | 0.0667491i | ||||
\(208\) | −54.3917 | + | 31.4031i | −3.77138 | + | 2.17741i | ||||
\(209\) | 0.138839 | + | 0.240476i | 0.00960367 | + | 0.0166341i | ||||
\(210\) | 1.17184 | + | 11.9747i | 0.0808645 | + | 0.826331i | ||||
\(211\) | 4.55602 | − | 7.89127i | 0.313650 | − | 0.543257i | −0.665500 | − | 0.746398i | \(-0.731782\pi\) |
0.979150 | + | 0.203141i | \(0.0651149\pi\) | |||||||
\(212\) | 27.3320i | 1.87717i | ||||||||
\(213\) | 14.9319 | − | 9.55710i | 1.02312 | − | 0.654842i | ||||
\(214\) | −19.0983 | −1.30553 | ||||||||
\(215\) | 3.74174 | + | 6.48088i | 0.255184 | + | 0.441992i | ||||
\(216\) | −5.40094 | − | 39.1061i | −0.367488 | − | 2.66083i | ||||
\(217\) | −11.9218 | + | 7.73268i | −0.809308 | + | 0.524929i | ||||
\(218\) | 25.5287 | − | 14.7390i | 1.72902 | − | 0.998249i | ||||
\(219\) | −0.888891 | − | 19.4169i | −0.0600657 | − | 1.31207i | ||||
\(220\) | −0.457414 | + | 0.264088i | −0.0308388 | + | 0.0178048i | ||||
\(221\) | −6.89472 | + | 3.98067i | −0.463789 | + | 0.267769i | ||||
\(222\) | 7.29800 | − | 4.67106i | 0.489810 | − | 0.313501i | ||||
\(223\) | −5.56608 | + | 3.21358i | −0.372732 | + | 0.215197i | −0.674651 | − | 0.738137i | \(-0.735706\pi\) |
0.301919 | + | 0.953333i | \(0.402373\pi\) | |||||||
\(224\) | −25.4863 | + | 16.5308i | −1.70287 | + | 1.10451i | ||||
\(225\) | −1.25635 | + | 2.72426i | −0.0837565 | + | 0.181617i | ||||
\(226\) | −18.5725 | − | 32.1686i | −1.23543 | − | 2.13982i | ||||
\(227\) | 19.4261 | 1.28935 | 0.644677 | − | 0.764455i | \(-0.276992\pi\) | ||||
0.644677 | + | 0.764455i | \(0.276992\pi\) | |||||||
\(228\) | 0.997234 | + | 21.7836i | 0.0660435 | + | 1.44265i | ||||
\(229\) | 0.0783397i | 0.00517684i | 0.999997 | + | 0.00258842i | \(0.000823920\pi\) | ||||
−0.999997 | + | 0.00258842i | \(0.999176\pi\) | |||||||
\(230\) | −1.00349 | + | 1.73810i | −0.0661684 | + | 0.114607i | ||||
\(231\) | 0.402217 | − | 0.287844i | 0.0264640 | − | 0.0189388i | ||||
\(232\) | −38.2473 | − | 66.2463i | −2.51106 | − | 4.34928i | ||||
\(233\) | 13.4942 | − | 7.79085i | 0.884031 | − | 0.510396i | 0.0120459 | − | 0.999927i | \(-0.496166\pi\) |
0.871985 | + | 0.489532i | \(0.162832\pi\) | |||||||
\(234\) | 48.4864 | − | 4.44866i | 3.16966 | − | 0.290818i | ||||
\(235\) | 3.85718 | − | 6.68083i | 0.251615 | − | 0.435809i | ||||
\(236\) | −5.79985 | + | 10.0456i | −0.377538 | + | 0.653915i | ||||
\(237\) | −17.6192 | + | 0.806594i | −1.14449 | + | 0.0523939i | ||||
\(238\) | −7.50607 | + | 4.86854i | −0.486546 | + | 0.315581i | ||||
\(239\) | −9.50772 | − | 5.48929i | −0.615003 | − | 0.355072i | 0.159918 | − | 0.987130i | \(-0.448877\pi\) |
−0.774921 | + | 0.632058i | \(0.782210\pi\) | |||||||
\(240\) | −17.5797 | + | 0.804786i | −1.13477 | + | 0.0519487i | ||||
\(241\) | − | 23.6574i | − | 1.52391i | −0.647632 | − | 0.761954i | \(-0.724240\pi\) | ||
0.647632 | − | 0.761954i | \(-0.275760\pi\) | |||||||
\(242\) | −24.9854 | − | 14.4253i | −1.60612 | − | 0.927296i | ||||
\(243\) | −4.53014 | + | 14.9157i | −0.290608 | + | 0.956842i | ||||
\(244\) | 40.9944i | 2.62440i | ||||||||
\(245\) | −6.96247 | + | 0.723928i | −0.444816 | + | 0.0462501i | ||||
\(246\) | −31.2786 | − | 16.1987i | −1.99425 | − | 1.03279i | ||||
\(247\) | −15.9033 | −1.01190 | ||||||||
\(248\) | −20.4024 | − | 35.3380i | −1.29555 | − | 2.24397i | ||||
\(249\) | 11.3683 | − | 21.9515i | 0.720438 | − | 1.39112i | ||||
\(250\) | 2.27381 | + | 1.31279i | 0.143808 | + | 0.0830278i | ||||
\(251\) | 10.0851 | 0.636567 | 0.318283 | − | 0.947996i | \(-0.396894\pi\) | ||||
0.318283 | + | 0.947996i | \(0.396894\pi\) | |||||||
\(252\) | 38.4438 | − | 5.54687i | 2.42173 | − | 0.349420i | ||||
\(253\) | 0.0825028 | 0.00518690 | ||||||||
\(254\) | 10.2629 | + | 5.92531i | 0.643954 | + | 0.371787i | ||||
\(255\) | −2.22842 | + | 0.102015i | −0.139549 | + | 0.00638844i | ||||
\(256\) | 6.10483 | + | 10.5739i | 0.381552 | + | 0.660867i | ||||
\(257\) | 1.88604 | 0.117648 | 0.0588240 | − | 0.998268i | \(-0.481265\pi\) | ||||
0.0588240 | + | 0.998268i | \(0.481265\pi\) | |||||||
\(258\) | 28.6636 | − | 18.3460i | 1.78452 | − | 1.14217i | ||||
\(259\) | 2.74322 | + | 4.22936i | 0.170456 | + | 0.262799i | ||||
\(260\) | − | 30.2500i | − | 1.87603i | ||||||
\(261\) | 2.75978 | + | 30.0792i | 0.170826 | + | 1.86185i | ||||
\(262\) | −5.19546 | − | 2.99960i | −0.320977 | − | 0.185316i | ||||
\(263\) | − | 28.6816i | − | 1.76858i | −0.466937 | − | 0.884291i | \(-0.654642\pi\) | ||
0.466937 | − | 0.884291i | \(-0.345358\pi\) | |||||||
\(264\) | 0.765647 | + | 1.19624i | 0.0471223 | + | 0.0736233i | ||||
\(265\) | −4.83694 | − | 2.79261i | −0.297131 | − | 0.171549i | ||||
\(266\) | −17.8477 | + | 0.925371i | −1.09431 | + | 0.0567381i | ||||
\(267\) | 0.532942 | − | 1.02908i | 0.0326155 | − | 0.0629785i | ||||
\(268\) | −20.6453 | + | 35.7587i | −1.26111 | + | 2.18431i | ||||
\(269\) | −15.5910 | + | 27.0044i | −0.950601 | + | 1.64649i | −0.206472 | + | 0.978452i | \(0.566198\pi\) |
−0.744129 | + | 0.668036i | \(0.767135\pi\) | |||||||
\(270\) | 12.6372 | + | 5.14086i | 0.769077 | + | 0.312863i | ||||
\(271\) | 9.11994 | − | 5.26540i | 0.553997 | − | 0.319850i | −0.196736 | − | 0.980457i | \(-0.563034\pi\) |
0.750733 | + | 0.660606i | \(0.229701\pi\) | |||||||
\(272\) | −6.54286 | − | 11.3326i | −0.396719 | − | 0.687137i | ||||
\(273\) | 2.75892 | + | 28.1926i | 0.166977 | + | 1.70629i | ||||
\(274\) | −17.9382 | + | 31.0699i | −1.08369 | + | 1.87700i | ||||
\(275\) | − | 0.107931i | − | 0.00650851i | ||||||
\(276\) | 5.75331 | + | 2.97954i | 0.346308 | + | 0.179347i | ||||
\(277\) | −21.4605 | −1.28944 | −0.644718 | − | 0.764420i | \(-0.723025\pi\) | ||||
−0.644718 | + | 0.764420i | \(0.723025\pi\) | |||||||
\(278\) | 21.5208 | + | 37.2751i | 1.29073 | + | 2.23561i | ||||
\(279\) | 1.47216 | + | 16.0453i | 0.0881361 | + | 0.960604i | ||||
\(280\) | −1.04080 | − | 20.0739i | −0.0621994 | − | 1.19965i | ||||
\(281\) | 7.44154 | − | 4.29637i | 0.443925 | − | 0.256300i | −0.261336 | − | 0.965248i | \(-0.584163\pi\) |
0.705261 | + | 0.708948i | \(0.250830\pi\) | |||||||
\(282\) | −31.1523 | − | 16.1332i | −1.85509 | − | 0.960720i | ||||
\(283\) | 3.96638 | − | 2.28999i | 0.235777 | − | 0.136126i | −0.377457 | − | 0.926027i | \(-0.623202\pi\) |
0.613234 | + | 0.789901i | \(0.289868\pi\) | |||||||
\(284\) | −43.3783 | + | 25.0445i | −2.57403 | + | 1.48612i | ||||
\(285\) | −3.95694 | − | 2.04923i | −0.234389 | − | 0.121386i | ||||
\(286\) | −1.51704 | + | 0.875865i | −0.0897046 | + | 0.0517910i | ||||
\(287\) | 9.31384 | − | 18.2543i | 0.549779 | − | 1.07751i | ||||
\(288\) | 3.14716 | + | 34.3012i | 0.185448 | + | 2.02122i | ||||
\(289\) | 7.67062 | + | 13.2859i | 0.451213 | + | 0.781524i | ||||
\(290\) | 26.4356 | 1.55235 | ||||||||
\(291\) | 12.7237 | + | 6.58939i | 0.745876 | + | 0.386277i | ||||
\(292\) | 54.9168i | 3.21376i | ||||||||
\(293\) | 3.19302 | − | 5.53047i | 0.186538 | − | 0.323094i | −0.757556 | − | 0.652771i | \(-0.773607\pi\) |
0.944094 | + | 0.329677i | \(0.106940\pi\) | |||||||
\(294\) | 4.73668 | + | 31.4790i | 0.276249 | + | 1.83589i | ||||
\(295\) | −1.18518 | − | 2.05280i | −0.0690041 | − | 0.119519i | ||||
\(296\) | −12.5364 | + | 7.23790i | −0.728664 | + | 0.420694i | ||||
\(297\) | −0.0767276 | − | 0.555555i | −0.00445219 | − | 0.0322366i | ||||
\(298\) | 7.04662 | − | 12.2051i | 0.408200 | − | 0.707023i | ||||
\(299\) | −2.36258 | + | 4.09210i | −0.136631 | + | 0.236652i | ||||
\(300\) | 3.89788 | − | 7.52656i | 0.225044 | − | 0.434546i | ||||
\(301\) | 10.7743 | + | 16.6112i | 0.621018 | + | 0.957454i | ||||
\(302\) | 5.10484 | + | 2.94728i | 0.293750 | + | 0.169597i | ||||
\(303\) | 10.4476 | + | 16.3231i | 0.600197 | + | 0.937740i | ||||
\(304\) | − | 26.1396i | − | 1.49921i | ||||||
\(305\) | −7.25479 | − | 4.18855i | −0.415408 | − | 0.239836i | ||||
\(306\) | 0.926883 | + | 10.1022i | 0.0529863 | + | 0.577504i | ||||
\(307\) | − | 8.86419i | − | 0.505906i | −0.967479 | − | 0.252953i | \(-0.918598\pi\) | ||
0.967479 | − | 0.252953i | \(-0.0814018\pi\) | |||||||
\(308\) | −1.17240 | + | 0.760436i | −0.0668037 | + | 0.0433299i | ||||
\(309\) | 3.72776 | − | 2.38594i | 0.212065 | − | 0.135731i | ||||
\(310\) | 14.1016 | 0.800919 | ||||||||
\(311\) | −3.40803 | − | 5.90288i | −0.193252 | − | 0.334721i | 0.753074 | − | 0.657935i | \(-0.228570\pi\) |
−0.946326 | + | 0.323214i | \(0.895237\pi\) | |||||||
\(312\) | −81.2582 | + | 3.71993i | −4.60034 | + | 0.210600i | ||||
\(313\) | 10.4831 | + | 6.05239i | 0.592537 | + | 0.342101i | 0.766100 | − | 0.642721i | \(-0.222195\pi\) |
−0.173563 | + | 0.984823i | \(0.555528\pi\) | |||||||
\(314\) | 41.5347 | 2.34394 | ||||||||
\(315\) | −2.94632 | + | 7.37016i | −0.166006 | + | 0.415261i | ||||
\(316\) | 49.8323 | 2.80329 | ||||||||
\(317\) | 9.38015 | + | 5.41563i | 0.526842 | + | 0.304172i | 0.739729 | − | 0.672904i | \(-0.234953\pi\) |
−0.212888 | + | 0.977077i | \(0.568287\pi\) | |||||||
\(318\) | −11.6805 | + | 22.5544i | −0.655011 | + | 1.26479i | ||||
\(319\) | −0.543354 | − | 0.941117i | −0.0304220 | − | 0.0526924i | ||||
\(320\) | 9.82559 | 0.549267 | ||||||||
\(321\) | −11.1876 | − | 5.79386i | −0.624430 | − | 0.323382i | ||||
\(322\) | −2.41332 | + | 4.72989i | −0.134489 | + | 0.263586i | ||||
\(323\) | − | 3.31347i | − | 0.184367i | ||||||
\(324\) | 14.7130 | − | 41.5124i | 0.817387 | − | 2.30624i | ||||
\(325\) | 5.35335 | + | 3.09076i | 0.296951 | + | 0.171445i | ||||
\(326\) | − | 23.9793i | − | 1.32809i | ||||||
\(327\) | 19.4258 | − | 0.889299i | 1.07425 | − | 0.0491783i | ||||
\(328\) | 50.9629 | + | 29.4234i | 2.81396 | + | 1.62464i | ||||
\(329\) | 9.27622 | − | 18.1805i | 0.511414 | − | 1.00232i | ||||
\(330\) | −0.490318 | + | 0.0224463i | −0.0269911 | + | 0.00123563i | ||||
\(331\) | −8.07381 | + | 13.9842i | −0.443777 | + | 0.768644i | −0.997966 | − | 0.0637468i | \(-0.979695\pi\) |
0.554189 | + | 0.832391i | \(0.313028\pi\) | |||||||
\(332\) | −34.9220 | + | 60.4867i | −1.91659 | + | 3.31964i | ||||
\(333\) | 5.69217 | − | 0.522260i | 0.311929 | − | 0.0286197i | ||||
\(334\) | −8.14275 | + | 4.70122i | −0.445552 | + | 0.257239i | ||||
\(335\) | −4.21881 | − | 7.30720i | −0.230498 | − | 0.399235i | ||||
\(336\) | −46.3390 | + | 4.53472i | −2.52800 | + | 0.247389i | ||||
\(337\) | 11.4187 | − | 19.7777i | 0.622015 | − | 1.07736i | −0.367096 | − | 0.930183i | \(-0.619648\pi\) |
0.989110 | − | 0.147178i | \(-0.0470189\pi\) | |||||||
\(338\) | − | 66.1938i | − | 3.60047i | ||||||
\(339\) | −1.12060 | − | 24.4784i | −0.0608627 | − | 1.32948i | ||||
\(340\) | 6.30262 | 0.341808 | ||||||||
\(341\) | −0.289844 | − | 0.502024i | −0.0156959 | − | 0.0271861i | ||||
\(342\) | −8.48646 | + | 18.4020i | −0.458895 | + | 0.995066i | ||||
\(343\) | −18.2971 | + | 2.86658i | −0.987949 | + | 0.154781i | ||||
\(344\) | −49.2379 | + | 28.4275i | −2.65473 | + | 1.53271i | ||||
\(345\) | −1.11513 | + | 0.713733i | −0.0600364 | + | 0.0384261i | ||||
\(346\) | 0.251691 | − | 0.145314i | 0.0135310 | − | 0.00781213i | ||||
\(347\) | −0.0935690 | + | 0.0540221i | −0.00502305 | + | 0.00290006i | −0.502509 | − | 0.864572i | \(-0.667590\pi\) |
0.497486 | + | 0.867472i | \(0.334256\pi\) | |||||||
\(348\) | −3.90274 | − | 85.2514i | −0.209209 | − | 4.56996i | ||||
\(349\) | −19.0311 | + | 10.9876i | −1.01871 | + | 0.588153i | −0.913730 | − | 0.406321i | \(-0.866811\pi\) |
−0.104981 | + | 0.994474i | \(0.533478\pi\) | |||||||
\(350\) | 6.18771 | + | 3.15715i | 0.330747 | + | 0.168757i | ||||
\(351\) | 29.7525 | + | 12.1034i | 1.58807 | + | 0.646031i | ||||
\(352\) | −0.619622 | − | 1.07322i | −0.0330259 | − | 0.0572026i | ||||
\(353\) | −17.1796 | −0.914376 | −0.457188 | − | 0.889370i | \(-0.651143\pi\) | ||||
−0.457188 | + | 0.889370i | \(0.651143\pi\) | |||||||
\(354\) | −9.07911 | + | 5.81105i | −0.482549 | + | 0.308854i | ||||
\(355\) | − | 10.2356i | − | 0.543247i | ||||||
\(356\) | −1.63713 | + | 2.83559i | −0.0867675 | + | 0.150286i | ||||
\(357\) | −5.87396 | + | 0.574823i | −0.310883 | + | 0.0304229i | ||||
\(358\) | −0.361982 | − | 0.626970i | −0.0191313 | − | 0.0331364i | ||||
\(359\) | 14.1707 | − | 8.18146i | 0.747901 | − | 0.431801i | −0.0770340 | − | 0.997028i | \(-0.524545\pi\) |
0.824935 | + | 0.565228i | \(0.191212\pi\) | |||||||
\(360\) | −20.6973 | − | 9.54499i | −1.09084 | − | 0.503065i | ||||
\(361\) | −6.19055 | + | 10.7224i | −0.325819 | + | 0.564334i | ||||
\(362\) | 12.5511 | − | 21.7391i | 0.659670 | − | 1.14258i | ||||
\(363\) | −10.2600 | − | 16.0301i | −0.538510 | − | 0.841362i | ||||
\(364\) | −4.14405 | − | 79.9267i | −0.217207 | − | 4.18930i | ||||
\(365\) | −9.71863 | − | 5.61106i | −0.508697 | − | 0.293696i | ||||
\(366\) | −17.5193 | + | 33.8286i | −0.915746 | + | 1.76825i | ||||
\(367\) | 14.8575i | 0.775556i | 0.921753 | + | 0.387778i | \(0.126757\pi\) | ||||
−0.921753 | + | 0.387778i | \(0.873243\pi\) | |||||||
\(368\) | −6.72602 | − | 3.88327i | −0.350618 | − | 0.202429i | ||||
\(369\) | −13.4085 | − | 18.9781i | −0.698020 | − | 0.987959i | ||||
\(370\) | − | 5.00265i | − | 0.260076i | ||||||
\(371\) | −13.1628 | − | 6.71601i | −0.683376 | − | 0.348678i | ||||
\(372\) | −2.08185 | − | 45.4760i | −0.107939 | − | 2.35782i | ||||
\(373\) | −2.53984 | −0.131508 | −0.0657541 | − | 0.997836i | \(-0.520945\pi\) | ||||
−0.0657541 | + | 0.997836i | \(0.520945\pi\) | |||||||
\(374\) | −0.182487 | − | 0.316077i | −0.00943619 | − | 0.0163440i | ||||
\(375\) | 0.933716 | + | 1.45883i | 0.0482169 | + | 0.0753335i | ||||
\(376\) | 50.7570 | + | 29.3046i | 2.61759 | + | 1.51127i | ||||
\(377\) | 62.2387 | 3.20546 | ||||||||
\(378\) | 34.0944 | + | 11.8520i | 1.75362 | + | 0.609600i | ||||
\(379\) | −9.92334 | −0.509728 | −0.254864 | − | 0.966977i | \(-0.582031\pi\) | ||||
−0.254864 | + | 0.966977i | \(0.582031\pi\) | |||||||
\(380\) | 10.9032 | + | 6.29496i | 0.559322 | + | 0.322925i | ||||
\(381\) | 4.21437 | + | 6.58447i | 0.215909 | + | 0.337333i | ||||
\(382\) | 17.5129 | + | 30.3333i | 0.896039 | + | 1.55198i | ||||
\(383\) | 15.9699 | 0.816024 | 0.408012 | − | 0.912976i | \(-0.366222\pi\) | ||||
0.408012 | + | 0.912976i | \(0.366222\pi\) | |||||||
\(384\) | −0.224498 | − | 4.90393i | −0.0114564 | − | 0.250252i | ||||
\(385\) | −0.0147859 | − | 0.285177i | −0.000753559 | − | 0.0145339i | ||||
\(386\) | 40.3986i | 2.05623i | ||||||||
\(387\) | 22.3565 | − | 2.05123i | 1.13645 | − | 0.104270i | ||||
\(388\) | −35.0597 | − | 20.2417i | −1.77989 | − | 1.02762i | ||||
\(389\) | − | 21.2886i | − | 1.07938i | −0.841865 | − | 0.539688i | \(-0.818542\pi\) | ||
0.841865 | − | 0.539688i | \(-0.181458\pi\) | |||||||
\(390\) | 12.9276 | − | 24.9623i | 0.654613 | − | 1.26402i | ||||
\(391\) | −0.852594 | − | 0.492245i | −0.0431175 | − | 0.0248939i | ||||
\(392\) | −5.49998 | − | 52.8967i | −0.277791 | − | 2.67169i | ||||
\(393\) | −2.13346 | − | 3.33329i | −0.107619 | − | 0.168142i | ||||
\(394\) | 15.9004 | − | 27.5403i | 0.801049 | − | 1.38746i | ||||
\(395\) | −5.09156 | + | 8.81884i | −0.256184 | + | 0.443724i | ||||
\(396\) | 0.144773 | + | 1.57790i | 0.00727513 | + | 0.0792924i | ||||
\(397\) | 7.42803 | − | 4.28857i | 0.372802 | − | 0.215237i | −0.301880 | − | 0.953346i | \(-0.597614\pi\) |
0.674682 | + | 0.738109i | \(0.264281\pi\) | |||||||
\(398\) | −1.22117 | − | 2.11512i | −0.0612115 | − | 0.106022i | ||||
\(399\) | −10.7358 | − | 4.87241i | −0.537460 | − | 0.243925i | ||||
\(400\) | −5.08015 | + | 8.79908i | −0.254008 | + | 0.439954i | ||||
\(401\) | − | 21.2268i | − | 1.06001i | −0.847993 | − | 0.530007i | \(-0.822189\pi\) | ||
0.847993 | − | 0.530007i | \(-0.177811\pi\) | |||||||
\(402\) | −32.3182 | + | 20.6852i | −1.61189 | + | 1.03168i | ||||
\(403\) | 33.2002 | 1.65382 | ||||||||
\(404\) | −27.3779 | − | 47.4200i | −1.36210 | − | 2.35923i | ||||
\(405\) | 5.84318 | + | 6.84524i | 0.290350 | + | 0.340142i | ||||
\(406\) | 69.8482 | − | 3.62150i | 3.46651 | − | 0.179732i | ||||
\(407\) | −0.178096 | + | 0.102824i | −0.00882791 | + | 0.00509680i | ||||
\(408\) | −0.775052 | − | 16.9302i | −0.0383708 | − | 0.838171i | ||||
\(409\) | 3.04788 | − | 1.75969i | 0.150708 | − | 0.0870112i | −0.422750 | − | 0.906246i | \(-0.638935\pi\) |
0.573458 | + | 0.819235i | \(0.305602\pi\) | |||||||
\(410\) | −17.6121 | + | 10.1684i | −0.869802 | + | 0.502180i | ||||
\(411\) | −19.9337 | + | 12.7585i | −0.983259 | + | 0.629331i | ||||
\(412\) | −10.8294 | + | 6.25237i | −0.533527 | + | 0.308032i | ||||
\(413\) | −3.41272 | − | 5.26155i | −0.167929 | − | 0.258904i | ||||
\(414\) | 3.47430 | + | 4.91744i | 0.170753 | + | 0.241679i | ||||
\(415\) | −7.13623 | − | 12.3603i | −0.350304 | − | 0.606743i | ||||
\(416\) | 70.9748 | 3.47982 | ||||||||
\(417\) | 1.29849 | + | 28.3642i | 0.0635874 | + | 1.38900i | ||||
\(418\) | − | 0.729062i | − | 0.0356596i | ||||||
\(419\) | −10.2456 | + | 17.7459i | −0.500529 | + | 0.866942i | 0.499471 | + | 0.866331i | \(0.333528\pi\) |
−1.00000 | 0.000610964i | \(0.999806\pi\) | ||||||||
\(420\) | 9.26790 | − | 20.4207i | 0.452227 | − | 0.996428i | ||||
\(421\) | −13.7370 | − | 23.7931i | −0.669499 | − | 1.15961i | −0.978044 | − | 0.208396i | \(-0.933176\pi\) |
0.308546 | − | 0.951210i | \(-0.400158\pi\) | |||||||
\(422\) | −20.7191 | + | 11.9622i | −1.00859 | + | 0.582309i | ||||
\(423\) | −13.3544 | − | 18.9014i | −0.649311 | − | 0.919018i | ||||
\(424\) | 21.2166 | − | 36.7483i | 1.03037 | − | 1.78465i | ||||
\(425\) | −0.643963 | + | 1.11538i | −0.0312368 | + | 0.0541037i | ||||
\(426\) | −46.4987 | + | 2.12867i | −2.25287 | + | 0.103135i | ||||
\(427\) | −19.7424 | − | 10.0731i | −0.955402 | − | 0.487474i | ||||
\(428\) | 30.8270 | + | 17.7980i | 1.49008 | + | 0.860297i | ||||
\(429\) | −1.15438 | + | 0.0528466i | −0.0557340 | + | 0.00255146i | ||||
\(430\) | − | 19.6484i | − | 0.947530i | ||||||
\(431\) | −1.34674 | − | 0.777543i | −0.0648704 | − | 0.0374529i | 0.467214 | − | 0.884144i | \(-0.345258\pi\) |
−0.532084 | + | 0.846691i | \(0.678591\pi\) | |||||||
\(432\) | −19.8938 | + | 48.9029i | −0.957142 | + | 2.35284i | ||||
\(433\) | 8.27463i | 0.397653i | 0.980035 | + | 0.198827i | \(0.0637131\pi\) | ||||
−0.980035 | + | 0.198827i | \(0.936287\pi\) | |||||||
\(434\) | 37.2594 | − | 1.93183i | 1.78851 | − | 0.0927308i | ||||
\(435\) | 15.4857 | + | 8.01979i | 0.742483 | + | 0.384520i | ||||
\(436\) | −54.9420 | −2.63124 | ||||||||
\(437\) | −0.983294 | − | 1.70312i | −0.0470373 | − | 0.0814710i | ||||
\(438\) | −23.4691 | + | 45.3174i | −1.12140 | + | 2.16535i | ||||
\(439\) | −3.09254 | − | 1.78548i | −0.147599 | − | 0.0852164i | 0.424382 | − | 0.905483i | \(-0.360491\pi\) |
−0.571981 | + | 0.820267i | \(0.693825\pi\) | |||||||
\(440\) | 0.819999 | 0.0390919 | ||||||||
\(441\) | −6.77511 | + | 19.8771i | −0.322624 | + | 0.946527i | ||||
\(442\) | 20.9031 | 0.994257 | ||||||||
\(443\) | 29.0928 | + | 16.7967i | 1.38224 | + | 0.798037i | 0.992425 | − | 0.122855i | \(-0.0392051\pi\) |
0.389817 | + | 0.920893i | \(0.372538\pi\) | |||||||
\(444\) | −16.1329 | + | 0.738552i | −0.765635 | + | 0.0350501i | ||||
\(445\) | −0.334543 | − | 0.579445i | −0.0158589 | − | 0.0274683i | ||||
\(446\) | 16.8749 | 0.799052 | ||||||||
\(447\) | 7.83052 | − | 5.01189i | 0.370371 | − | 0.237054i | ||||
\(448\) | 25.9612 | − | 1.34604i | 1.22655 | − | 0.0635944i | ||||
\(449\) | − | 7.96280i | − | 0.375788i | −0.982189 | − | 0.187894i | \(-0.939834\pi\) | ||
0.982189 | − | 0.187894i | \(-0.0601661\pi\) | |||||||
\(450\) | 6.43307 | − | 4.54514i | 0.303258 | − | 0.214260i | ||||
\(451\) | 0.723996 | + | 0.417999i | 0.0340917 | + | 0.0196828i | ||||
\(452\) | 69.2321i | 3.25640i | ||||||||
\(453\) | 2.09625 | + | 3.27515i | 0.0984902 | + | 0.153880i | ||||
\(454\) | −44.1712 | − | 25.5023i | −2.07306 | − | 1.19688i | ||||
\(455\) | 14.5681 | + | 7.43304i | 0.682961 | + | 0.348466i | ||||
\(456\) | 15.5688 | − | 30.0625i | 0.729078 | − | 1.40780i | ||||
\(457\) | −18.3495 | + | 31.7823i | −0.858356 | + | 1.48672i | 0.0151411 | + | 0.999885i | \(0.495180\pi\) |
−0.873497 | + | 0.486830i | \(0.838153\pi\) | |||||||
\(458\) | 0.102843 | − | 0.178130i | 0.00480555 | − | 0.00832346i | ||||
\(459\) | −2.52175 | + | 6.19896i | −0.117705 | + | 0.289343i | ||||
\(460\) | 3.23953 | − | 1.87034i | 0.151044 | − | 0.0872052i | ||||
\(461\) | 3.34188 | + | 5.78830i | 0.155647 | + | 0.269588i | 0.933294 | − | 0.359112i | \(-0.116921\pi\) |
−0.777648 | + | 0.628700i | \(0.783587\pi\) | |||||||
\(462\) | −1.29244 | + | 0.126478i | −0.0601299 | + | 0.00588429i | ||||
\(463\) | 3.45184 | − | 5.97877i | 0.160421 | − | 0.277857i | −0.774599 | − | 0.632453i | \(-0.782048\pi\) |
0.935020 | + | 0.354596i | \(0.115382\pi\) | |||||||
\(464\) | 102.299i | 4.74912i | ||||||||
\(465\) | 8.26061 | + | 4.27803i | 0.383077 | + | 0.198389i | ||||
\(466\) | −40.9109 | −1.89516 | ||||||||
\(467\) | −3.63751 | − | 6.30035i | −0.168324 | − | 0.291545i | 0.769507 | − | 0.638639i | \(-0.220502\pi\) |
−0.937831 | + | 0.347093i | \(0.887169\pi\) | |||||||
\(468\) | −82.4089 | − | 38.0046i | −3.80935 | − | 1.75676i | ||||
\(469\) | −12.1480 | − | 18.7292i | −0.560942 | − | 0.864832i | ||||
\(470\) | −17.5410 | + | 10.1273i | −0.809106 | + | 0.467137i | ||||
\(471\) | 24.3306 | + | 12.6004i | 1.12110 | + | 0.580597i | ||||
\(472\) | 15.5960 | − | 9.00434i | 0.717863 | − | 0.414458i | ||||
\(473\) | −0.699491 | + | 0.403851i | −0.0321626 | + | 0.0185691i | ||||
\(474\) | 41.1217 | + | 21.2962i | 1.88878 | + | 0.978168i | ||||
\(475\) | −2.22804 | + | 1.28636i | −0.102230 | + | 0.0590223i | ||||
\(476\) | 16.6528 | − | 0.863418i | 0.763280 | − | 0.0395747i | ||||
\(477\) | −13.6847 | + | 9.66860i | −0.626578 | + | 0.442695i | ||||
\(478\) | 14.4125 | + | 24.9632i | 0.659213 | + | 1.14179i | ||||
\(479\) | 15.7473 | 0.719511 | 0.359755 | − | 0.933047i | \(-0.382860\pi\) | ||||
0.359755 | + | 0.933047i | \(0.382860\pi\) | |||||||
\(480\) | 17.6594 | + | 9.14548i | 0.806036 | + | 0.417432i | ||||
\(481\) | − | 11.7780i | − | 0.537031i | ||||||
\(482\) | −31.0571 | + | 53.7925i | −1.41461 | + | 2.45018i | ||||
\(483\) | −2.84861 | + | 2.03859i | −0.129616 | + | 0.0927591i | ||||
\(484\) | 26.8864 | + | 46.5687i | 1.22211 | + | 2.11676i | ||||
\(485\) | 7.16437 | − | 4.13635i | 0.325317 | − | 0.187822i | ||||
\(486\) | 29.8818 | − | 27.9684i | 1.35546 | − | 1.26867i | ||||
\(487\) | 7.41905 | − | 12.8502i | 0.336189 | − | 0.582297i | −0.647523 | − | 0.762046i | \(-0.724195\pi\) |
0.983713 | + | 0.179749i | \(0.0575285\pi\) | |||||||
\(488\) | 31.8222 | − | 55.1176i | 1.44052 | − | 2.49506i | ||||
\(489\) | 7.27464 | − | 14.0469i | 0.328970 | − | 0.635221i | ||||
\(490\) | 16.7817 | + | 7.49415i | 0.758120 | + | 0.338551i | ||||
\(491\) | 28.9366 | + | 16.7066i | 1.30589 | + | 0.753956i | 0.981408 | − | 0.191935i | \(-0.0614763\pi\) |
0.324483 | + | 0.945891i | \(0.394810\pi\) | |||||||
\(492\) | 35.3919 | + | 55.2958i | 1.59559 | + | 2.49293i | ||||
\(493\) | 12.9675i | 0.584026i | ||||||||
\(494\) | 36.1612 | + | 20.8777i | 1.62697 | + | 0.939330i | ||||
\(495\) | −0.294033 | − | 0.135599i | −0.0132158 | − | 0.00609474i | ||||
\(496\) | 54.5698i | 2.45026i | ||||||||
\(497\) | −1.40220 | − | 27.0444i | −0.0628974 | − | 1.21311i | ||||
\(498\) | −54.6671 | + | 34.9895i | −2.44969 | + | 1.56792i | ||||
\(499\) | −10.6896 | −0.478534 | −0.239267 | − | 0.970954i | \(-0.576907\pi\) | ||||
−0.239267 | + | 0.970954i | \(0.576907\pi\) | |||||||
\(500\) | −2.44681 | − | 4.23800i | −0.109425 | − | 0.189529i | ||||
\(501\) | −6.19616 | + | 0.283655i | −0.276824 | + | 0.0126728i | ||||
\(502\) | −22.9316 | − | 13.2396i | −1.02349 | − | 0.590912i | ||||
\(503\) | 2.28280 | 0.101785 | 0.0508925 | − | 0.998704i | \(-0.483793\pi\) | ||||
0.0508925 | + | 0.998704i | \(0.483793\pi\) | |||||||
\(504\) | −55.9941 | − | 22.3844i | −2.49418 | − | 0.997081i | ||||
\(505\) | 11.1892 | 0.497914 | ||||||||
\(506\) | −0.187596 | − | 0.108308i | −0.00833965 | − | 0.00481490i | ||||
\(507\) | 20.0813 | − | 38.7757i | 0.891841 | − | 1.72209i | ||||
\(508\) | −11.0438 | − | 19.1284i | −0.489989 | − | 0.848685i | ||||
\(509\) | −23.1092 | −1.02430 | −0.512149 | − | 0.858897i | \(-0.671150\pi\) | ||||
−0.512149 | + | 0.858897i | \(0.671150\pi\) | |||||||
\(510\) | 5.20093 | + | 2.69347i | 0.230301 | + | 0.119269i | ||||
\(511\) | −26.4473 | − | 13.4942i | −1.16996 | − | 0.596946i | ||||
\(512\) | − | 37.7258i | − | 1.66726i | ||||||
\(513\) | −10.5539 | + | 8.20517i | −0.465967 | + | 0.362267i | ||||
\(514\) | −4.28850 | − | 2.47597i | −0.189158 | − | 0.109210i | ||||
\(515\) | − | 2.55531i | − | 0.112601i | ||||||
\(516\) | −63.3636 | + | 2.90073i | −2.78943 | + | 0.127698i | ||||
\(517\) | 0.721071 | + | 0.416311i | 0.0317127 | + | 0.0183093i | ||||
\(518\) | −0.685330 | − | 13.2180i | −0.0301117 | − | 0.580766i | ||||
\(519\) | 0.191522 | − | 0.00876774i | 0.00840690 | − | 0.000384861i | ||||
\(520\) | −23.4818 | + | 40.6716i | −1.02974 | + | 1.78357i | ||||
\(521\) | −7.37414 | + | 12.7724i | −0.323067 | + | 0.559569i | −0.981119 | − | 0.193404i | \(-0.938047\pi\) |
0.658052 | + | 0.752972i | \(0.271381\pi\) | |||||||
\(522\) | 33.2123 | − | 72.0174i | 1.45366 | − | 3.15212i | ||||
\(523\) | −22.9326 | + | 13.2401i | −1.00277 | + | 0.578950i | −0.909067 | − | 0.416650i | \(-0.863204\pi\) |
−0.0937044 | + | 0.995600i | \(0.529871\pi\) | |||||||
\(524\) | 5.59075 | + | 9.68346i | 0.244233 | + | 0.423024i | ||||
\(525\) | 2.66692 | + | 3.72660i | 0.116394 | + | 0.162642i | ||||
\(526\) | −37.6528 | + | 65.2165i | −1.64174 | + | 2.84357i | ||||
\(527\) | 6.91730i | 0.301322i | ||||||||
\(528\) | −0.0868617 | − | 1.89741i | −0.00378017 | − | 0.0825740i | ||||
\(529\) | 22.4157 | 0.974595 | ||||||||
\(530\) | 7.33220 | + | 12.6997i | 0.318490 | + | 0.551641i | ||||
\(531\) | −7.08136 | + | 0.649720i | −0.307305 | + | 0.0281954i | ||||
\(532\) | 29.6708 | + | 15.1389i | 1.28639 | + | 0.656355i | ||||
\(533\) | −41.4652 | + | 23.9399i | −1.79606 | + | 1.03695i | ||||
\(534\) | −2.56277 | + | 1.64029i | −0.110902 | + | 0.0709823i | ||||
\(535\) | −6.29942 | + | 3.63697i | −0.272348 | + | 0.157240i | ||||
\(536\) | 55.5158 | − | 32.0521i | 2.39792 | − | 1.38444i | ||||
\(537\) | −0.0218407 | − | 0.477088i | −0.000942496 | − | 0.0205879i | ||||
\(538\) | 70.9020 | − | 40.9353i | 3.05680 | − | 1.76485i | ||||
\(539\) | −0.0781346 | − | 0.751469i | −0.00336550 | − | 0.0323681i | ||||
\(540\) | −15.6072 | − | 20.0748i | −0.671628 | − | 0.863883i | ||||
\(541\) | −18.8183 | − | 32.5943i | −0.809062 | − | 1.40134i | −0.913514 | − | 0.406807i | \(-0.866642\pi\) |
0.104452 | − | 0.994530i | \(-0.466691\pi\) | |||||||
\(542\) | −27.6494 | −1.18764 | ||||||||
\(543\) | 13.9473 | − | 8.92693i | 0.598537 | − | 0.383091i | ||||
\(544\) | 14.7877i | 0.634016i | ||||||||
\(545\) | 5.61363 | − | 9.72309i | 0.240461 | − | 0.416491i | ||||
\(546\) | 30.7376 | − | 67.7266i | 1.31545 | − | 2.89843i | ||||
\(547\) | 15.4329 | + | 26.7305i | 0.659862 | + | 1.14292i | 0.980651 | + | 0.195764i | \(0.0627188\pi\) |
−0.320788 | + | 0.947151i | \(0.603948\pi\) | |||||||
\(548\) | 57.9091 | − | 33.4338i | 2.47375 | − | 1.42822i | ||||
\(549\) | −20.5252 | + | 14.5016i | −0.875996 | + | 0.618915i | ||||
\(550\) | −0.141691 | + | 0.245416i | −0.00604172 | + | 0.0104646i | ||||
\(551\) | −12.9517 | + | 22.4331i | −0.551762 | + | 0.955680i | ||||
\(552\) | −5.42252 | − | 8.47208i | −0.230798 | − | 0.360596i | ||||
\(553\) | −12.2448 | + | 23.9987i | −0.520702 | + | 1.02053i | ||||
\(554\) | 48.7971 | + | 28.1730i | 2.07319 | + | 1.19696i | ||||
\(555\) | 1.51766 | − | 2.93051i | 0.0644211 | − | 0.124393i | ||||
\(556\) | − | 80.2224i | − | 3.40219i | ||||||
\(557\) | −0.431897 | − | 0.249356i | −0.0183001 | − | 0.0105655i | 0.490822 | − | 0.871260i | \(-0.336697\pi\) |
−0.509122 | + | 0.860694i | \(0.670030\pi\) | |||||||
\(558\) | 17.7166 | − | 38.4165i | 0.750002 | − | 1.62630i | ||||
\(559\) | − | 46.2593i | − | 1.95656i | ||||||
\(560\) | −12.2174 | + | 23.9449i | −0.516278 | + | 1.01186i | ||||
\(561\) | −0.0110106 | − | 0.240516i | −0.000464870 | − | 0.0101546i | ||||
\(562\) | −22.5609 | −0.951673 | ||||||||
\(563\) | −2.41559 | − | 4.18392i | −0.101805 | − | 0.176331i | 0.810623 | − | 0.585568i | \(-0.199128\pi\) |
−0.912428 | + | 0.409237i | \(0.865795\pi\) | |||||||
\(564\) | 35.2489 | + | 55.0724i | 1.48425 | + | 2.31897i | ||||
\(565\) | −12.2520 | − | 7.07371i | −0.515446 | − | 0.297593i | ||||
\(566\) | −12.0251 | −0.505451 | ||||||||
\(567\) | 16.3766 | + | 17.2860i | 0.687753 | + | 0.725945i | ||||
\(568\) | 77.7637 | 3.26289 | ||||||||
\(569\) | 3.18125 | + | 1.83670i | 0.133365 | + | 0.0769983i | 0.565198 | − | 0.824955i | \(-0.308800\pi\) |
−0.431833 | + | 0.901954i | \(0.642133\pi\) | |||||||
\(570\) | 6.30712 | + | 9.85417i | 0.264176 | + | 0.412746i | ||||
\(571\) | 12.1396 | + | 21.0264i | 0.508025 | + | 0.879926i | 0.999957 | + | 0.00929175i | \(0.00295770\pi\) |
−0.491932 | + | 0.870634i | \(0.663709\pi\) | |||||||
\(572\) | 3.26493 | 0.136514 | ||||||||
\(573\) | 1.05667 | + | 23.0819i | 0.0441430 | + | 0.964258i | ||||
\(574\) | −45.1418 | + | 29.2797i | −1.88418 | + | 1.22211i | ||||
\(575\) | 0.764400i | 0.0318777i | ||||||||
\(576\) | 12.3444 | − | 26.7675i | 0.514348 | − | 1.11531i | ||||
\(577\) | 25.8066 | + | 14.8995i | 1.07434 | + | 0.620273i | 0.929365 | − | 0.369162i | \(-0.120355\pi\) |
0.144979 | + | 0.989435i | \(0.453689\pi\) | |||||||
\(578\) | − | 40.2795i | − | 1.67541i | ||||||
\(579\) | −12.2558 | + | 23.6651i | −0.509332 | + | 0.983488i | ||||
\(580\) | −42.6704 | − | 24.6357i | −1.77179 | − | 1.02294i | ||||
\(581\) | −20.5486 | − | 31.6808i | −0.852501 | − | 1.31434i | ||||
\(582\) | −20.2808 | − | 31.6865i | −0.840668 | − | 1.31345i | ||||
\(583\) | 0.301410 | − | 0.522058i | 0.0124831 | − | 0.0216214i | ||||
\(584\) | 42.6295 | − | 73.8365i | 1.76402 | − | 3.05537i | ||||
\(585\) | 15.1457 | − | 10.7009i | 0.626198 | − | 0.442426i | ||||
\(586\) | −14.5206 | + | 8.38350i | −0.599842 | + | 0.346319i | ||||
\(587\) | −10.5048 | − | 18.1948i | −0.433579 | − | 0.750981i | 0.563599 | − | 0.826048i | \(-0.309416\pi\) |
−0.997178 | + | 0.0750669i | \(0.976083\pi\) | |||||||
\(588\) | 21.6902 | − | 55.2252i | 0.894487 | − | 2.27745i | ||||
\(589\) | −6.90889 | + | 11.9666i | −0.284676 | + | 0.493073i | ||||
\(590\) | 6.22357i | 0.256220i | ||||||||
\(591\) | 17.6692 | − | 11.3091i | 0.726814 | − | 0.465195i | ||||
\(592\) | 19.3590 | 0.795650 | ||||||||
\(593\) | −0.141047 | − | 0.244300i | −0.00579210 | − | 0.0100322i | 0.863115 | − | 0.505008i | \(-0.168510\pi\) |
−0.868907 | + | 0.494976i | \(0.835177\pi\) | |||||||
\(594\) | −0.554860 | + | 1.36395i | −0.0227662 | + | 0.0559637i | ||||
\(595\) | −1.54868 | + | 3.03527i | −0.0634897 | + | 0.124434i | ||||
\(596\) | −22.7483 | + | 13.1337i | −0.931805 | + | 0.537978i | ||||
\(597\) | −0.0736809 | − | 1.60949i | −0.00301556 | − | 0.0658719i | ||||
\(598\) | 10.7441 | − | 6.20311i | 0.439359 | − | 0.253664i | ||||
\(599\) | −39.9757 | + | 23.0800i | −1.63336 | + | 0.943022i | −0.650317 | + | 0.759663i | \(0.725364\pi\) |
−0.983046 | + | 0.183359i | \(0.941303\pi\) | |||||||
\(600\) | −11.0833 | + | 7.09383i | −0.452474 | + | 0.289604i | ||||
\(601\) | 33.5229 | − | 19.3544i | 1.36743 | − | 0.789484i | 0.376827 | − | 0.926284i | \(-0.377015\pi\) |
0.990599 | + | 0.136800i | \(0.0436818\pi\) | |||||||
\(602\) | −2.69170 | − | 51.9150i | −0.109705 | − | 2.11590i | ||||
\(603\) | −25.2070 | + | 2.31276i | −1.02651 | + | 0.0941828i | ||||
\(604\) | −5.49323 | − | 9.51456i | −0.223516 | − | 0.387142i | ||||
\(605\) | −10.9884 | −0.446740 | ||||||||
\(606\) | −2.32701 | − | 50.8312i | −0.0945283 | − | 2.06487i | ||||
\(607\) | − | 2.88257i | − | 0.117000i | −0.998287 | − | 0.0585000i | \(-0.981368\pi\) | ||
0.998287 | − | 0.0585000i | \(-0.0186318\pi\) | |||||||
\(608\) | −14.7697 | + | 25.5819i | −0.598990 | + | 1.03748i | ||||
\(609\) | 42.0151 | + | 19.0685i | 1.70254 | + | 0.772694i | ||||
\(610\) | 10.9973 | + | 19.0480i | 0.445269 | + | 0.771229i | ||||
\(611\) | −41.2977 | + | 23.8432i | −1.67073 | + | 0.964594i | ||||
\(612\) | 7.91829 | − | 17.1700i | 0.320078 | − | 0.694055i | ||||
\(613\) | −4.23686 | + | 7.33845i | −0.171125 | + | 0.296397i | −0.938813 | − | 0.344426i | \(-0.888074\pi\) |
0.767688 | + | 0.640823i | \(0.221407\pi\) | |||||||
\(614\) | −11.6368 | + | 20.1555i | −0.469622 | + | 0.813409i | ||||
\(615\) | −13.4018 | + | 0.613524i | −0.540414 | + | 0.0247397i | ||||
\(616\) | 2.16660 | − | 0.112334i | 0.0872950 | − | 0.00452609i | ||||
\(617\) | −13.3572 | − | 7.71176i | −0.537739 | − | 0.310464i | 0.206423 | − | 0.978463i | \(-0.433818\pi\) |
−0.744162 | + | 0.667999i | \(0.767151\pi\) | |||||||
\(618\) | −11.6084 | + | 0.531425i | −0.466960 | + | 0.0213770i | ||||
\(619\) | 28.3024i | 1.13757i | 0.822487 | + | 0.568784i | \(0.192586\pi\) | ||||
−0.822487 | + | 0.568784i | \(0.807414\pi\) | |||||||
\(620\) | −22.7618 | − | 13.1415i | −0.914137 | − | 0.527777i | ||||
\(621\) | 0.543406 | + | 3.93459i | 0.0218061 | + | 0.157890i | ||||
\(622\) | 17.8960i | 0.717566i | ||||||||
\(623\) | −0.963310 | − | 1.48518i | −0.0385942 | − | 0.0595025i | ||||
\(624\) | 96.5980 | + | 50.0265i | 3.86701 | + | 2.00266i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.8910 | − | 27.5240i | −0.635131 | − | 1.10008i | ||||
\(627\) | 0.221176 | − | 0.427078i | 0.00883293 | − | 0.0170558i | ||||
\(628\) | −67.0422 | − | 38.7069i | −2.67528 | − | 1.54457i | ||||
\(629\) | 2.45396 | 0.0978458 | ||||||||
\(630\) | 16.3748 | − | 12.8905i | 0.652388 | − | 0.513568i | ||||
\(631\) | −10.3968 | −0.413890 | −0.206945 | − | 0.978353i | \(-0.566352\pi\) | ||||
−0.206945 | + | 0.978353i | \(0.566352\pi\) | |||||||
\(632\) | −67.0004 | − | 38.6827i | −2.66513 | − | 1.53871i | ||||
\(633\) | −15.7660 | + | 0.721755i | −0.626643 | + | 0.0286872i | ||||
\(634\) | −14.2191 | − | 24.6283i | −0.564714 | − | 0.978113i | ||||
\(635\) | 4.51354 | 0.179114 | ||||||||
\(636\) | 39.8726 | − | 25.5203i | 1.58105 | − | 1.01195i | ||||
\(637\) | 39.5100 | + | 17.6439i | 1.56544 | + | 0.699076i | ||||
\(638\) | 2.85323i | 0.112960i | ||||||||
\(639\) | −27.8843 | − | 12.8594i | −1.10309 | − | 0.508711i | ||||
\(640\) | −2.45453 | − | 1.41712i | −0.0970238 | − | 0.0560167i | ||||
\(641\) | − | 15.2686i | − | 0.603075i | −0.953454 | − | 0.301538i | \(-0.902500\pi\) | ||
0.953454 | − | 0.301538i | \(-0.0974999\pi\) | |||||||
\(642\) | 17.8324 | + | 27.8610i | 0.703787 | + | 1.09959i | ||||
\(643\) | −26.0206 | − | 15.0230i | −1.02615 | − | 0.592450i | −0.110273 | − | 0.993901i | \(-0.535172\pi\) |
−0.915880 | + | 0.401452i | \(0.868506\pi\) | |||||||
\(644\) | 8.30327 | − | 5.38562i | 0.327194 | − | 0.212223i | ||||
\(645\) | 5.96076 | − | 11.5098i | 0.234705 | − | 0.453200i | ||||
\(646\) | −4.34988 | + | 7.53421i | −0.171144 | + | 0.296430i | ||||
\(647\) | −1.09203 | + | 1.89146i | −0.0429323 | + | 0.0743608i | −0.886693 | − | 0.462359i | \(-0.847003\pi\) |
0.843761 | + | 0.536719i | \(0.180337\pi\) | |||||||
\(648\) | −52.0061 | + | 44.3931i | −2.04299 | + | 1.74392i | ||||
\(649\) | 0.221562 | − | 0.127919i | 0.00869705 | − | 0.00502125i | ||||
\(650\) | −8.11501 | − | 14.0556i | −0.318297 | − | 0.551306i | ||||
\(651\) | 22.4123 | + | 10.1718i | 0.878406 | + | 0.398663i | ||||
\(652\) | −22.3467 | + | 38.7057i | −0.875165 | + | 1.51583i | ||||
\(653\) | 3.01533i | 0.117999i | 0.998258 | + | 0.0589995i | \(0.0187910\pi\) | ||||
−0.998258 | + | 0.0589995i | \(0.981209\pi\) | |||||||
\(654\) | −45.3381 | − | 23.4799i | −1.77286 | − | 0.918135i | ||||
\(655\) | −2.28491 | −0.0892789 | ||||||||
\(656\) | −39.3491 | − | 68.1546i | −1.53632 | − | 2.66099i | ||||
\(657\) | −27.4960 | + | 19.4266i | −1.07272 | + | 0.757906i | ||||
\(658\) | −44.9595 | + | 29.1614i | −1.75270 | + | 1.13683i | ||||
\(659\) | −17.4300 | + | 10.0632i | −0.678978 | + | 0.392008i | −0.799470 | − | 0.600706i | \(-0.794886\pi\) |
0.120492 | + | 0.992714i | \(0.461553\pi\) | |||||||
\(660\) | 0.812353 | + | 0.420704i | 0.0316208 | + | 0.0163759i | ||||
\(661\) | 23.8655 | − | 13.7788i | 0.928261 | − | 0.535932i | 0.0420000 | − | 0.999118i | \(-0.486627\pi\) |
0.886261 | + | 0.463186i | \(0.153294\pi\) | |||||||
\(662\) | 36.7166 | − | 21.1984i | 1.42703 | − | 0.823898i | ||||
\(663\) | 12.2448 | + | 6.34139i | 0.475549 | + | 0.246279i | ||||
\(664\) | 93.9063 | − | 54.2168i | 3.64427 | − | 2.10402i | ||||
\(665\) | −5.71071 | + | 3.70405i | −0.221452 | + | 0.143637i | ||||
\(666\) | −13.6285 | − | 6.28507i | −0.528095 | − | 0.243542i | ||||
\(667\) | 3.84818 | + | 6.66525i | 0.149002 | + | 0.258080i | ||||
\(668\) | 17.5246 | 0.678046 | ||||||||
\(669\) | 9.88518 | + | 5.11937i | 0.382183 | + | 0.197926i | ||||
\(670\) | 22.1536i | 0.855868i | ||||||||
\(671\) | 0.452076 | − | 0.783019i | 0.0174522 | − | 0.0302281i | ||||
\(672\) | 47.9125 | + | 21.7450i | 1.84826 | + | 0.838832i | ||||
\(673\) | −4.21453 | − | 7.29978i | −0.162458 | − | 0.281386i | 0.773292 | − | 0.634051i | \(-0.218609\pi\) |
−0.935750 | + | 0.352665i | \(0.885276\pi\) | |||||||
\(674\) | −51.9278 | + | 29.9805i | −2.00018 | + | 1.15481i | ||||
\(675\) | 5.14729 | − | 0.710892i | 0.198119 | − | 0.0273623i | ||||
\(676\) | −61.6871 | + | 106.845i | −2.37258 | + | 4.10943i | ||||
\(677\) | 2.84727 | − | 4.93161i | 0.109429 | − | 0.189537i | −0.806110 | − | 0.591766i | \(-0.798431\pi\) |
0.915539 | + | 0.402229i | \(0.131764\pi\) | |||||||
\(678\) | −29.5869 | + | 57.1304i | −1.13628 | + | 2.19408i | ||||
\(679\) | 18.3631 | − | 11.9105i | 0.704709 | − | 0.457085i | ||||
\(680\) | −8.47398 | − | 4.89245i | −0.324962 | − | 0.187617i | ||||
\(681\) | −18.1384 | − | 28.3393i | −0.695066 | − | 1.08596i | ||||
\(682\) | 1.52201i | 0.0582808i | ||||||||
\(683\) | 3.57383 | + | 2.06335i | 0.136749 | + | 0.0789519i | 0.566814 | − | 0.823846i | \(-0.308176\pi\) |
−0.430065 | + | 0.902798i | \(0.641509\pi\) | |||||||
\(684\) | 30.8473 | − | 21.7945i | 1.17948 | − | 0.833333i | ||||
\(685\) | 13.6642i | 0.522084i | ||||||||
\(686\) | 45.3673 | + | 17.5021i | 1.73213 | + | 0.668232i | ||||
\(687\) | 0.114284 | − | 0.0731471i | 0.00436021 | − | 0.00279074i | ||||
\(688\) | 76.0344 | 2.89878 | ||||||||
\(689\) | 17.2626 | + | 29.8997i | 0.657652 | + | 1.13909i | ||||
\(690\) | 3.47257 | − | 0.158971i | 0.132198 | − | 0.00605193i | ||||
\(691\) | 28.4622 | + | 16.4327i | 1.08275 | + | 0.625128i | 0.931638 | − | 0.363389i | \(-0.118380\pi\) |
0.151115 | + | 0.988516i | \(0.451714\pi\) | |||||||
\(692\) | −0.541682 | −0.0205916 | ||||||||
\(693\) | −0.795471 | − | 0.318000i | −0.0302175 | − | 0.0120798i | ||||
\(694\) | 0.283678 | 0.0107683 | ||||||||
\(695\) | 14.1970 | + | 8.19662i | 0.538522 | + | 0.310916i | ||||
\(696\) | −60.9297 | + | 117.651i | −2.30953 | + | 4.45956i | ||||
\(697\) | −4.98791 | − | 8.63932i | −0.188931 | − | 0.327237i | ||||
\(698\) | 57.6975 | 2.18388 | ||||||||
\(699\) | −23.9652 | − | 12.4112i | −0.906448 | − | 0.469434i | ||||
\(700\) | −7.04555 | − | 10.8625i | −0.266297 | − | 0.410562i | ||||
\(701\) | − | 14.8571i | − | 0.561143i | −0.959833 | − | 0.280572i | \(-0.909476\pi\) | ||
0.959833 | − | 0.280572i | \(-0.0905240\pi\) | |||||||
\(702\) | −51.7624 | − | 66.5795i | −1.95364 | − | 2.51288i | ||||
\(703\) | 4.24522 | + | 2.45098i | 0.160111 | + | 0.0924404i | ||||
\(704\) | 1.06049i | 0.0399687i | ||||||||
\(705\) | −13.3477 | + | 0.611046i | −0.502703 | + | 0.0230133i | ||||
\(706\) | 39.0631 | + | 22.5531i | 1.47016 | + | 0.848796i | ||||
\(707\) | 29.5642 | − | 1.53285i | 1.11188 | − | 0.0576488i | ||||
\(708\) | 20.0702 | − | 0.918799i | 0.754286 | − | 0.0345306i | ||||
\(709\) | 23.3828 | − | 40.5002i | 0.878161 | − | 1.52102i | 0.0248031 | − | 0.999692i | \(-0.492104\pi\) |
0.853357 | − | 0.521326i | \(-0.174563\pi\) | |||||||
\(710\) | −13.4371 | + | 23.2737i | −0.504285 | + | 0.873447i | ||||
\(711\) | 17.6280 | + | 24.9503i | 0.661103 | + | 0.935708i | ||||
\(712\) | 4.40228 | − | 2.54166i | 0.164983 | − | 0.0952527i | ||||
\(713\) | 2.05275 | + | 3.55547i | 0.0768762 | + | 0.133153i | ||||
\(714\) | 14.1109 | + | 6.40421i | 0.528087 | + | 0.239671i | ||||
\(715\) | −0.333590 | + | 0.577795i | −0.0124756 | + | 0.0216083i | ||||
\(716\) | 1.34935i | 0.0504274i | ||||||||
\(717\) | 0.869601 | + | 18.9956i | 0.0324758 | + | 0.709402i | ||||
\(718\) | −42.9620 | −1.60333 | ||||||||
\(719\) | −10.5490 | − | 18.2715i | −0.393413 | − | 0.681410i | 0.599485 | − | 0.800386i | \(-0.295372\pi\) |
−0.992897 | + | 0.118976i | \(0.962039\pi\) | |||||||
\(720\) | 17.5885 | + | 24.8944i | 0.655486 | + | 0.927758i | ||||
\(721\) | −0.350061 | − | 6.75165i | −0.0130369 | − | 0.251445i | ||||
\(722\) | 28.1523 | − | 16.2537i | 1.04772 | − | 0.604901i | ||||
\(723\) | −34.5120 | + | 22.0893i | −1.28352 | + | 0.821510i | ||||
\(724\) | −40.5180 | + | 23.3931i | −1.50584 | + | 0.869397i | ||||
\(725\) | 8.71958 | − | 5.03425i | 0.323837 | − | 0.186968i | ||||
\(726\) | 2.28523 | + | 49.9186i | 0.0848129 | + | 1.85265i | ||||
\(727\) | −19.2054 | + | 11.0883i | −0.712290 | + | 0.411241i | −0.811908 | − | 0.583785i | \(-0.801571\pi\) |
0.0996181 | + | 0.995026i | \(0.468238\pi\) | |||||||
\(728\) | −56.4719 | + | 110.680i | −2.09299 | + | 4.10206i | ||||
\(729\) | 25.9893 | − | 7.31834i | 0.962565 | − | 0.271050i | ||||
\(730\) | 14.7322 | + | 25.5170i | 0.545264 | + | 0.944425i | ||||
\(731\) | 9.63816 | 0.356480 | ||||||||
\(732\) | 59.8037 | − | 38.2771i | 2.21041 | − | 1.41476i | ||||
\(733\) | − | 17.2139i | − | 0.635810i | −0.948123 | − | 0.317905i | \(-0.897021\pi\) | ||
0.948123 | − | 0.317905i | \(-0.102979\pi\) | |||||||
\(734\) | 19.5047 | − | 33.7832i | 0.719933 | − | 1.24696i | ||||
\(735\) | 7.55705 | + | 9.48108i | 0.278746 | + | 0.349715i | ||||
\(736\) | 4.38833 | + | 7.60081i | 0.161756 | + | 0.280170i | ||||
\(737\) | 0.788676 | − | 0.455343i | 0.0290513 | − | 0.0167728i | ||||
\(738\) | 5.57432 | + | 60.7551i | 0.205193 | + | 2.23642i | ||||
\(739\) | −23.2171 | + | 40.2133i | −0.854057 | + | 1.47927i | 0.0234608 | + | 0.999725i | \(0.492532\pi\) |
−0.877517 | + | 0.479545i | \(0.840802\pi\) | |||||||
\(740\) | −4.66205 | + | 8.07491i | −0.171380 | + | 0.296840i | ||||
\(741\) | 14.8492 | + | 23.2002i | 0.545499 | + | 0.852280i | ||||
\(742\) | 21.1129 | + | 32.5508i | 0.775080 | + | 1.19498i | ||||
\(743\) | −13.0366 | − | 7.52670i | −0.478267 | − | 0.276128i | 0.241427 | − | 0.970419i | \(-0.422385\pi\) |
−0.719694 | + | 0.694291i | \(0.755718\pi\) | |||||||
\(744\) | −32.5020 | + | 62.7593i | −1.19158 | + | 2.30087i | ||||
\(745\) | − | 5.36768i | − | 0.196657i | ||||||
\(746\) | 5.77513 | + | 3.33427i | 0.211442 | + | 0.122076i | ||||
\(747\) | −42.6383 | + | 3.91209i | −1.56005 | + | 0.143136i | ||||
\(748\) | 0.680251i | 0.0248724i | ||||||||
\(749\) | −16.1461 | + | 10.4726i | −0.589966 | + | 0.382660i | ||||
\(750\) | −0.207969 | − | 4.54286i | −0.00759394 | − | 0.165882i | ||||
\(751\) | 26.5121 | 0.967440 | 0.483720 | − | 0.875223i | \(-0.339285\pi\) | ||||
0.483720 | + | 0.875223i | \(0.339285\pi\) | |||||||
\(752\) | −39.1901 | − | 67.8792i | −1.42912 | − | 2.47530i | ||||
\(753\) | −9.41663 | − | 14.7124i | −0.343161 | − | 0.536151i | ||||
\(754\) | −141.519 | − | 81.7061i | −5.15382 | − | 2.97556i | ||||
\(755\) | 2.24506 | 0.0817060 | ||||||||
\(756\) | −43.9876 | − | 50.9037i | −1.59981 | − | 1.85135i | ||||
\(757\) | 0.366541 | 0.0133222 | 0.00666108 | − | 0.999978i | \(-0.497880\pi\) | ||||
0.00666108 | + | 0.999978i | \(0.497880\pi\) | |||||||
\(758\) | 22.5638 | + | 13.0272i | 0.819554 | + | 0.473170i | ||||
\(759\) | −0.0770342 | − | 0.120357i | −0.00279616 | − | 0.00436869i | ||||
\(760\) | −9.77301 | − | 16.9274i | −0.354504 | − | 0.614020i | ||||
\(761\) | 14.3679 | 0.520835 | 0.260418 | − | 0.965496i | \(-0.416140\pi\) | ||||
0.260418 | + | 0.965496i | \(0.416140\pi\) | |||||||
\(762\) | −0.938675 | − | 20.5044i | −0.0340046 | − | 0.742796i | ||||
\(763\) | 13.5003 | − | 26.4594i | 0.488745 | − | 0.957894i | ||||
\(764\) | − | 65.2823i | − | 2.36183i | ||||||
\(765\) | 2.22953 | + | 3.15562i | 0.0806090 | + | 0.114092i | ||||
\(766\) | −36.3126 | − | 20.9651i | −1.31203 | − | 0.757499i | ||||
\(767\) | 14.6525i | 0.529071i | ||||||||
\(768\) | 9.72526 | − | 18.7789i | 0.350930 | − | 0.677624i | ||||
\(769\) | −16.6324 | − | 9.60274i | −0.599781 | − | 0.346284i | 0.169174 | − | 0.985586i | \(-0.445890\pi\) |
−0.768955 | + | 0.639302i | \(0.779223\pi\) | |||||||
\(770\) | −0.340755 | + | 0.667848i | −0.0122800 | + | 0.0240676i | ||||
\(771\) | −1.76103 | − | 2.75140i | −0.0634218 | − | 0.0990894i | ||||
\(772\) | 37.6481 | − | 65.2084i | 1.35498 | − | 2.34690i | ||||
\(773\) | 8.19251 | − | 14.1898i | 0.294664 | − | 0.510373i | −0.680243 | − | 0.732987i | \(-0.738126\pi\) |
0.974907 | + | 0.222614i | \(0.0714589\pi\) | |||||||
\(774\) | −53.5273 | − | 24.6852i | −1.92400 | − | 0.887292i | ||||
\(775\) | 4.65132 | − | 2.68544i | 0.167080 | − | 0.0964639i | ||||
\(776\) | 31.4255 | + | 54.4306i | 1.12811 | + | 1.95395i | ||||
\(777\) | 3.60851 | − | 7.95090i | 0.129454 | − | 0.285237i | ||||
\(778\) | −27.9474 | + | 48.4063i | −1.00196 | + | 1.73545i | ||||
\(779\) | − | 19.9274i | − | 0.713973i | ||||||
\(780\) | −44.1295 | + | 28.2449i | −1.58009 | + | 1.01133i | ||||
\(781\) | 1.10474 | 0.0395306 | ||||||||
\(782\) | 1.29242 | + | 2.23855i | 0.0462170 | + | 0.0800502i | ||||
\(783\) | 41.3034 | − | 32.1115i | 1.47606 | − | 1.14757i | ||||
\(784\) | −29.0005 | + | 64.9409i | −1.03573 | + | 2.31932i | ||||
\(785\) | 13.6999 | − | 7.90965i | 0.488971 | − | 0.282308i | ||||
\(786\) | 0.475190 | + | 10.3800i | 0.0169495 | + | 0.370244i | ||||
\(787\) | 20.3684 | − | 11.7597i | 0.726055 | − | 0.419188i | −0.0909221 | − | 0.995858i | \(-0.528981\pi\) |
0.816977 | + | 0.576670i | \(0.195648\pi\) | |||||||
\(788\) | −51.3304 | + | 29.6356i | −1.82857 | + | 1.05573i | ||||
\(789\) | −41.8414 | + | 26.7805i | −1.48959 | + | 0.953409i | ||||
\(790\) | 23.1545 | − | 13.3683i | 0.823800 | − | 0.475621i | ||||
\(791\) | −33.3414 | − | 17.0117i | −1.18548 | − | 0.604867i | ||||
\(792\) | 1.03020 | − | 2.23389i | 0.0366067 | − | 0.0793779i | ||||
\(793\) | 25.8916 | + | 44.8456i | 0.919439 | + | 1.59251i | ||||
\(794\) | −22.5199 | −0.799202 | ||||||||
\(795\) | 0.442399 | + | 9.66377i | 0.0156903 | + | 0.342738i | ||||
\(796\) | 4.55210i | 0.161345i | ||||||||
\(797\) | 7.30322 | − | 12.6495i | 0.258693 | − | 0.448070i | −0.707199 | − | 0.707015i | \(-0.750041\pi\) |
0.965892 | + | 0.258945i | \(0.0833748\pi\) | |||||||
\(798\) | 18.0147 | + | 25.1727i | 0.637712 | + | 0.891103i | ||||
\(799\) | −4.96776 | − | 8.60441i | −0.175747 | − | 0.304402i | ||||
\(800\) | 9.94350 | − | 5.74088i | 0.351556 | − | 0.202971i | ||||
\(801\) | −1.99886 | + | 0.183397i | −0.0706263 | + | 0.00648001i | ||||
\(802\) | −27.8662 | + | 48.2657i | −0.983990 | + | 1.70432i | ||||
\(803\) | 0.605609 | − | 1.04895i | 0.0213715 | − | 0.0370165i | ||||
\(804\) | 71.4425 | − | 3.27058i | 2.51958 | − | 0.115345i | ||||
\(805\) | 0.104718 | + | 2.01970i | 0.00369081 | + | 0.0711851i | ||||
\(806\) | −75.4911 | − | 43.5848i | −2.65906 | − | 1.53521i | ||||
\(807\) | 53.9523 | − | 2.46989i | 1.89921 | − | 0.0869444i | ||||
\(808\) | 85.0092i | 2.99061i | ||||||||
\(809\) | −29.0893 | − | 16.7947i | −1.02272 | − | 0.590471i | −0.107833 | − | 0.994169i | \(-0.534391\pi\) |
−0.914892 | + | 0.403699i | \(0.867724\pi\) | |||||||
\(810\) | −4.29996 | − | 23.2356i | −0.151085 | − | 0.816416i | ||||
\(811\) | − | 39.1986i | − | 1.37645i | −0.725499 | − | 0.688224i | \(-0.758391\pi\) | ||
0.725499 | − | 0.688224i | \(-0.241609\pi\) | |||||||
\(812\) | −116.119 | − | 59.2471i | −4.07497 | − | 2.07916i | ||||
\(813\) | −16.1967 | − | 8.38802i | −0.568045 | − | 0.294181i | ||||
\(814\) | 0.539943 | 0.0189250 | ||||||||
\(815\) | −4.56650 | − | 7.90941i | −0.159957 | − | 0.277054i | ||||
\(816\) | −10.4231 | + | 20.1263i | −0.364880 | + | 0.704561i | ||||
\(817\) | 16.6735 | + | 9.62645i | 0.583332 | + | 0.336787i | ||||
\(818\) | −9.24039 | −0.323083 | ||||||||
\(819\) | 38.5521 | − | 30.3487i | 1.34712 | − | 1.06047i | ||||
\(820\) | 37.9043 | 1.32368 | ||||||||
\(821\) | 17.6061 | + | 10.1649i | 0.614458 | + | 0.354758i | 0.774708 | − | 0.632319i | \(-0.217897\pi\) |
−0.160250 | + | 0.987076i | \(0.551230\pi\) | |||||||
\(822\) | 62.0748 | − | 2.84173i | 2.16511 | − | 0.0991168i | ||||
\(823\) | 12.6928 | + | 21.9846i | 0.442443 | + | 0.766334i | 0.997870 | − | 0.0652312i | \(-0.0207785\pi\) |
−0.555427 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(824\) | 19.4138 | 0.676311 | ||||||||
\(825\) | −0.157453 | + | 0.100777i | −0.00548182 | + | 0.00350862i | ||||
\(826\) | 0.852588 | + | 16.4439i | 0.0296653 | + | 0.572158i | ||||
\(827\) | 2.03073i | 0.0706153i | 0.999376 | + | 0.0353076i | \(0.0112411\pi\) | ||||
−0.999376 | + | 0.0353076i | \(0.988759\pi\) | |||||||
\(828\) | −1.02532 | − | 11.1751i | −0.0356325 | − | 0.388362i | ||||
\(829\) | 31.5729 | + | 18.2286i | 1.09657 | + | 0.633107i | 0.935319 | − | 0.353806i | \(-0.115113\pi\) |
0.161255 | + | 0.986913i | \(0.448446\pi\) | |||||||
\(830\) | 37.4733i | 1.30072i | ||||||||
\(831\) | 20.0380 | + | 31.3071i | 0.695111 | + | 1.08603i | ||||
\(832\) | −52.5998 | − | 30.3685i | −1.82357 | − | 1.05284i | ||||
\(833\) | −3.67612 | + | 8.23195i | −0.127370 | + | 0.285220i | ||||
\(834\) | 34.2836 | − | 66.1995i | 1.18714 | − | 2.29230i | ||||
\(835\) | −1.79055 | + | 3.10133i | −0.0619646 | + | 0.107326i | ||||
\(836\) | −0.679424 | + | 1.17680i | −0.0234984 | + | 0.0407004i | ||||
\(837\) | 22.0327 | − | 17.1293i | 0.761560 | − | 0.592077i | ||||
\(838\) | 46.5930 | − | 26.9005i | 1.60953 | − | 0.929262i | ||||
\(839\) | 25.1634 | + | 43.5842i | 0.868735 | + | 1.50469i | 0.863290 | + | 0.504709i | \(0.168400\pi\) |
0.00544570 | + | 0.999985i | \(0.498267\pi\) | |||||||
\(840\) | −28.3125 | + | 20.2617i | −0.976875 | + | 0.699094i | ||||
\(841\) | 36.1874 | − | 62.6785i | 1.24784 | − | 2.16133i | ||||
\(842\) | 72.1348i | 2.48593i | ||||||||
\(843\) | −13.2160 | − | 6.84432i | −0.455182 | − | 0.235731i | ||||
\(844\) | 44.5909 | 1.53488 | ||||||||
\(845\) | −12.6056 | − | 21.8335i | −0.433646 | − | 0.751097i | ||||
\(846\) | 5.55180 | + | 60.5096i | 0.190875 | + | 2.08036i | ||||
\(847\) | −29.0334 | + | 1.50533i | −0.997601 | + | 0.0517238i | ||||
\(848\) | −49.1448 | + | 28.3738i | −1.68764 | + | 0.974359i | ||||
\(849\) | −7.04417 | − | 3.64806i | −0.241755 | − | 0.125201i | ||||
\(850\) | 2.92850 | − | 1.69077i | 0.100447 | − | 0.0579929i | ||||
\(851\) | 1.26133 | − | 0.728228i | 0.0432378 | − | 0.0249633i | ||||
\(852\) | 77.0386 | + | 39.8970i | 2.63930 | + | 1.36685i | ||||
\(853\) | 31.9795 | − | 18.4634i | 1.09496 | − | 0.632175i | 0.160066 | − | 0.987106i | \(-0.448829\pi\) |
0.934892 | + | 0.354932i | \(0.115496\pi\) | |||||||
\(854\) | 31.6666 | + | 48.8220i | 1.08361 | + | 1.67065i | ||||
\(855\) | 0.705185 | + | 7.68588i | 0.0241168 | + | 0.262852i | ||||
\(856\) | −27.6316 | − | 47.8593i | −0.944428 | − | 1.63580i | ||||
\(857\) | 39.7259 | 1.35701 | 0.678505 | − | 0.734596i | \(-0.262628\pi\) | ||||
0.678505 | + | 0.734596i | \(0.262628\pi\) | |||||||
\(858\) | 2.69422 | + | 1.39529i | 0.0919792 | + | 0.0476345i | ||||
\(859\) | 40.2393i | 1.37295i | 0.727155 | + | 0.686474i | \(0.240842\pi\) | ||||
−0.727155 | + | 0.686474i | \(0.759158\pi\) | |||||||
\(860\) | −18.3107 | + | 31.7150i | −0.624388 | + | 1.08147i | ||||
\(861\) | −35.3263 | + | 3.45702i | −1.20392 | + | 0.117815i | ||||
\(862\) | 2.04150 | + | 3.53597i | 0.0695336 | + | 0.120436i | ||||
\(863\) | −38.0305 | + | 21.9569i | −1.29457 | + | 0.747422i | −0.979461 | − | 0.201632i | \(-0.935376\pi\) |
−0.315112 | + | 0.949054i | \(0.602042\pi\) | |||||||
\(864\) | 47.1010 | − | 36.6188i | 1.60241 | − | 1.24580i | ||||
\(865\) | 0.0553457 | − | 0.0958615i | 0.00188181 | − | 0.00325939i | ||||
\(866\) | 10.8628 | − | 18.8149i | 0.369133 | − | 0.639358i | ||||
\(867\) | 12.2196 | − | 23.5954i | 0.415001 | − | 0.801341i | ||||
\(868\) | −61.9416 | − | 31.6044i | −2.10244 | − | 1.07272i | ||||
\(869\) | −0.951830 | − | 0.549539i | −0.0322886 | − | 0.0186418i | ||||
\(870\) | −24.6833 | − | 38.5649i | −0.836843 | − | 1.30747i | ||||
\(871\) | 52.1574i | 1.76729i | ||||||||
\(872\) | 73.8703 | + | 42.6490i | 2.50156 | + | 1.44428i | ||||
\(873\) | −2.26755 | − | 24.7143i | −0.0767450 | − | 0.836452i | ||||
\(874\) | 5.16342i | 0.174655i | ||||||||
\(875\) | 2.64220 | − | 0.136993i | 0.0893227 | − | 0.00463122i | ||||
\(876\) | 80.1140 | − | 51.2767i | 2.70680 | − | 1.73248i | ||||
\(877\) | −12.5212 | −0.422811 | −0.211406 | − | 0.977398i | \(-0.567804\pi\) | ||||
−0.211406 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(878\) | 4.68791 | + | 8.11969i | 0.158209 | + | 0.274026i | ||||
\(879\) | −11.0494 | + | 0.505831i | −0.372686 | + | 0.0170613i | ||||
\(880\) | −0.949697 | − | 0.548308i | −0.0320143 | − | 0.0184835i | ||||
\(881\) | 5.13011 | 0.172838 | 0.0864189 | − | 0.996259i | \(-0.472458\pi\) | ||||
0.0864189 | + | 0.996259i | \(0.472458\pi\) | |||||||
\(882\) | 41.4996 | − | 36.3024i | 1.39737 | − | 1.22237i | ||||
\(883\) | 10.5436 | 0.354820 | 0.177410 | − | 0.984137i | \(-0.443228\pi\) | ||||
0.177410 | + | 0.984137i | \(0.443228\pi\) | |||||||
\(884\) | −33.7402 | − | 19.4799i | −1.13480 | − | 0.655180i | ||||
\(885\) | −1.88805 | + | 3.64571i | −0.0634662 | + | 0.122549i | ||||
\(886\) | −44.1010 | − | 76.3852i | −1.48160 | − | 2.56621i | ||||
\(887\) | 13.3651 | 0.448757 | 0.224379 | − | 0.974502i | \(-0.427965\pi\) | ||||
0.224379 | + | 0.974502i | \(0.427965\pi\) | |||||||
\(888\) | 22.2643 | + | 11.5303i | 0.747140 | + | 0.386931i | ||||
\(889\) | 11.9257 | − | 0.618325i | 0.399975 | − | 0.0207380i | ||||
\(890\) | 1.75673i | 0.0588858i | ||||||||
\(891\) | −0.738816 | + | 0.630663i | −0.0247513 | + | 0.0211280i | ||||
\(892\) | −27.2383 | − | 15.7260i | −0.912005 | − | 0.526546i | ||||
\(893\) | − | 19.8469i | − | 0.664151i | ||||||
\(894\) | −24.3847 | + | 1.11631i | −0.815545 | + | 0.0373350i | ||||
\(895\) | −0.238794 | − | 0.137868i | −0.00798200 | − | 0.00460841i | ||||
\(896\) | −6.67950 | − | 3.40807i | −0.223147 | − | 0.113856i | ||||
\(897\) | 8.17565 | − | 0.374274i | 0.272977 | − | 0.0124967i | ||||
\(898\) | −10.4535 | + | 18.1059i | −0.348836 | + | 0.604202i | ||||
\(899\) | 27.0384 | − | 46.8319i | 0.901781 | − | 1.56193i | ||||
\(900\) | −14.6195 | + | 1.34135i | −0.487315 | + | 0.0447115i | ||||
\(901\) | −6.22963 | + | 3.59668i | −0.207539 | + | 0.119823i | ||||
\(902\) | −1.09749 | − | 1.90090i | −0.0365423 | − | 0.0632932i | ||||
\(903\) | 14.1728 | − | 31.2279i | 0.471640 | − | 1.03920i | ||||
\(904\) | 53.7419 | − | 93.0837i | 1.78743 | − | 3.09592i | ||||
\(905\) | − | 9.56064i | − | 0.317807i | ||||||
\(906\) | −0.466901 | − | 10.1990i | −0.0155118 | − | 0.338839i | ||||
\(907\) | −58.5432 | −1.94389 | −0.971947 | − | 0.235201i | \(-0.924425\pi\) | ||||
−0.971947 | + | 0.235201i | \(0.924425\pi\) | |||||||
\(908\) | 47.5319 | + | 82.3277i | 1.57740 | + | 2.73214i | ||||
\(909\) | 14.0576 | − | 30.4824i | 0.466260 | − | 1.01104i | ||||
\(910\) | −23.3670 | − | 36.0261i | −0.774609 | − | 1.19425i | ||||
\(911\) | −42.7733 | + | 24.6952i | −1.41714 | + | 0.818188i | −0.996047 | − | 0.0888275i | \(-0.971688\pi\) |
−0.421097 | + | 0.907016i | \(0.638355\pi\) | |||||||
\(912\) | −38.1332 | + | 24.4070i | −1.26272 | + | 0.808196i | ||||
\(913\) | 1.33407 | − | 0.770223i | 0.0441511 | − | 0.0254907i | ||||
\(914\) | 83.4468 | − | 48.1780i | 2.76018 | − | 1.59359i | ||||
\(915\) | 0.663541 | + | 14.4944i | 0.0219360 | + | 0.479170i | ||||
\(916\) | −0.332004 | + | 0.191683i | −0.0109697 | + | 0.00633337i | ||||
\(917\) | −6.03720 | + | 0.313018i | −0.199366 | + | 0.0103368i | ||||
\(918\) | 13.8719 | − | 10.7847i | 0.457841 | − | 0.355949i | ||||
\(919\) | −14.0820 | − | 24.3908i | −0.464523 | − | 0.804577i | 0.534657 | − | 0.845069i | \(-0.320441\pi\) |
−0.999180 | + | 0.0404918i | \(0.987108\pi\) | |||||||
\(920\) | −5.80746 | −0.191466 | ||||||||
\(921\) | −12.9313 | + | 8.27663i | −0.426101 | + | 0.272724i | ||||
\(922\) | − | 17.5487i | − | 0.577935i | ||||||
\(923\) | −31.6356 | + | 54.7945i | −1.04130 | + | 1.80358i | ||||
\(924\) | 2.20403 | + | 1.00030i | 0.0725074 | + | 0.0329074i | ||||
\(925\) | −0.952679 | − | 1.65009i | −0.0313239 | − | 0.0542546i | ||||
\(926\) | −15.6977 | + | 9.06306i | −0.515858 | + | 0.297831i | ||||
\(927\) | −6.96134 | − | 3.21036i | −0.228640 | − | 0.105442i | ||||
\(928\) | 57.8021 | − | 100.116i | 1.89745 | − | 3.28648i | ||||
\(929\) | −12.1384 | + | 21.0243i | −0.398248 | + | 0.689785i | −0.993510 | − | 0.113746i | \(-0.963715\pi\) |
0.595262 | + | 0.803532i | \(0.297048\pi\) | |||||||
\(930\) | −13.1669 | − | 20.5718i | −0.431761 | − | 0.674577i | ||||
\(931\) | −14.5814 | + | 10.5692i | −0.477887 | + | 0.346391i | ||||
\(932\) | 66.0353 | + | 38.1255i | 2.16306 | + | 1.24884i | ||||
\(933\) | −5.42914 | + | 10.4833i | −0.177742 | + | 0.343209i | ||||
\(934\) | 19.1011i | 0.625006i | ||||||||
\(935\) | −0.120384 | − | 0.0695038i | −0.00393698 | − | 0.00227302i | ||||
\(936\) | 81.2988 | + | 115.068i | 2.65734 | + | 3.76112i | ||||
\(937\) | − | 40.1097i | − | 1.31033i | −0.755487 | − | 0.655163i | \(-0.772600\pi\) | ||
0.755487 | − | 0.655163i | \(-0.227400\pi\) | |||||||
\(938\) | 3.03489 | + | 58.5343i | 0.0990928 | + | 1.91121i | ||||
\(939\) | −0.958807 | − | 20.9442i | −0.0312895 | − | 0.683487i | ||||
\(940\) | 37.7512 | 1.23131 | ||||||||
\(941\) | 7.28495 | + | 12.6179i | 0.237482 | + | 0.411332i | 0.959991 | − | 0.280030i | \(-0.0903444\pi\) |
−0.722509 | + | 0.691362i | \(0.757011\pi\) | |||||||
\(942\) | −38.7816 | − | 60.5919i | −1.26357 | − | 1.97419i | ||||
\(943\) | −5.12754 | − | 2.96039i | −0.166976 | − | 0.0964035i | ||||
\(944\) | −24.0837 | −0.783856 | ||||||||
\(945\) | 13.5028 | − | 2.58347i | 0.439246 | − | 0.0840402i | ||||
\(946\) | 2.12068 | 0.0689492 | ||||||||
\(947\) | 44.2920 | + | 25.5720i | 1.43930 | + | 0.830978i | 0.997801 | − | 0.0662863i | \(-0.0211151\pi\) |
0.441495 | + | 0.897264i | \(0.354448\pi\) | |||||||
\(948\) | −46.5293 | − | 72.6967i | −1.51120 | − | 2.36108i | ||||
\(949\) | 34.6849 | + | 60.0759i | 1.12592 | + | 1.95015i | ||||
\(950\) | 6.75486 | 0.219157 | ||||||||
\(951\) | −0.857933 | − | 18.7407i | −0.0278204 | − | 0.607708i | ||||
\(952\) | −23.0602 | − | 11.7660i | −0.747385 | − | 0.381337i | ||||
\(953\) | − | 11.2676i | − | 0.364992i | −0.983207 | − | 0.182496i | \(-0.941582\pi\) | ||
0.983207 | − | 0.182496i | \(-0.0584177\pi\) | |||||||
\(954\) | 43.8092 | − | 4.01952i | 1.41837 | − | 0.130137i | ||||
\(955\) | 11.5530 | + | 6.67014i | 0.373847 | + | 0.215841i | ||||
\(956\) | − | 53.7250i | − | 1.73759i | ||||||
\(957\) | −0.865588 | + | 1.67140i | −0.0279805 | + | 0.0540285i | ||||
\(958\) | −35.8063 | − | 20.6728i | −1.15685 | − | 0.667907i | ||||
\(959\) | 1.87191 | + | 36.1037i | 0.0604471 | + | 1.16585i | ||||
\(960\) | −9.17431 | − | 14.3338i | −0.296100 | − | 0.462622i | ||||
\(961\) | −1.07680 | + | 1.86508i | −0.0347355 | + | 0.0601637i | ||||
\(962\) | −15.4620 | + | 26.7810i | −0.498515 | + | 0.863453i | ||||
\(963\) | 1.99379 | + | 21.7306i | 0.0642491 | + | 0.700257i | ||||
\(964\) | 100.260 | − | 57.8852i | 3.22916 | − | 1.86436i | ||||
\(965\) | 7.69329 | + | 13.3252i | 0.247656 | + | 0.428952i | ||||
\(966\) | 9.15344 | − | 0.895753i | 0.294507 | − | 0.0288204i | ||||
\(967\) | 18.2443 | − | 31.6001i | 0.586697 | − | 1.01619i | −0.407964 | − | 0.912998i | \(-0.633761\pi\) |
0.994661 | − | 0.103192i | \(-0.0329055\pi\) | |||||||
\(968\) | − | 83.4830i | − | 2.68325i | ||||||
\(969\) | −4.83378 | + | 3.09384i | −0.155283 | + | 0.0993886i | ||||
\(970\) | −21.7206 | −0.697405 | ||||||||
\(971\) | −15.7734 | − | 27.3203i | −0.506193 | − | 0.876752i | −0.999974 | − | 0.00716569i | \(-0.997719\pi\) |
0.493781 | − | 0.869586i | \(-0.335614\pi\) | |||||||
\(972\) | −74.2971 | + | 17.2972i | −2.38308 | + | 0.554807i | ||||
\(973\) | 38.6341 | + | 19.7122i | 1.23855 | + | 0.631946i | ||||
\(974\) | −33.7390 | + | 19.4792i | −1.08107 | + | 0.624155i | ||||
\(975\) | −0.489632 | − | 10.6955i | −0.0156808 | − | 0.342530i | ||||
\(976\) | −73.7108 | + | 42.5570i | −2.35943 | + | 1.36221i | ||||
\(977\) | −25.9666 | + | 14.9918i | −0.830744 | + | 0.479630i | −0.854107 | − | 0.520097i | \(-0.825896\pi\) |
0.0233634 | + | 0.999727i | \(0.492563\pi\) | |||||||
\(978\) | −34.9817 | + | 22.3899i | −1.11859 | + | 0.715950i | ||||
\(979\) | 0.0625403 | − | 0.0361077i | 0.00199880 | − | 0.00115401i | ||||
\(980\) | −20.1039 | − | 27.7356i | −0.642194 | − | 0.885982i | ||||
\(981\) | −19.4355 | − | 27.5086i | −0.620529 | − | 0.878281i | ||||
\(982\) | −43.8643 | − | 75.9751i | −1.39976 | − | 2.42446i | ||||
\(983\) | 1.24727 | 0.0397819 | 0.0198909 | − | 0.999802i | \(-0.493668\pi\) | ||||
0.0198909 | + | 0.999802i | \(0.493668\pi\) | |||||||
\(984\) | −4.66120 | − | 101.819i | −0.148594 | − | 3.24588i | ||||
\(985\) | − | 12.1119i | − | 0.385918i | ||||||
\(986\) | 17.0235 | − | 29.4856i | 0.542140 | − | 0.939014i | ||||
\(987\) | −35.1836 | + | 3.44305i | −1.11991 | + | 0.109594i | ||||
\(988\) | −38.9124 | − | 67.3983i | −1.23797 | − | 2.14423i | ||||
\(989\) | 4.95398 | − | 2.86018i | 0.157528 | − | 0.0909486i | ||||
\(990\) | 0.490563 | + | 0.694330i | 0.0155911 | + | 0.0220673i | ||||
\(991\) | 3.10232 | − | 5.37338i | 0.0985485 | − | 0.170691i | −0.812536 | − | 0.582912i | \(-0.801913\pi\) |
0.911084 | + | 0.412221i | \(0.135247\pi\) | |||||||
\(992\) | 30.8336 | − | 53.4054i | 0.978968 | − | 1.69562i | ||||
\(993\) | 27.9392 | − | 1.27904i | 0.886625 | − | 0.0405890i | ||||
\(994\) | −32.3152 | + | 63.3347i | −1.02497 | + | 2.00885i | ||||
\(995\) | −0.805586 | − | 0.465105i | −0.0255388 | − | 0.0147448i | ||||
\(996\) | 120.847 | − | 5.53227i | 3.82918 | − | 0.175297i | ||||
\(997\) | − | 53.3709i | − | 1.69027i | −0.534551 | − | 0.845137i | \(-0.679519\pi\) | ||
0.534551 | − | 0.845137i | \(-0.320481\pi\) | |||||||
\(998\) | 24.3062 | + | 14.0332i | 0.769400 | + | 0.444213i | ||||
\(999\) | −6.07675 | − | 7.81624i | −0.192260 | − | 0.247295i |
(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 | 315.2.be.c.311.1 | yes | 32 | |
3.2 | odd | 2 | 945.2.be.c.206.16 | 32 | |||
7.5 | odd | 6 | 315.2.t.c.131.16 | yes | 32 | ||
9.2 | odd | 6 | 315.2.t.c.101.1 | ✓ | 32 | ||
9.7 | even | 3 | 945.2.t.c.521.16 | 32 | |||
21.5 | even | 6 | 945.2.t.c.341.1 | 32 | |||
63.47 | even | 6 | inner | 315.2.be.c.236.1 | yes | 32 | |
63.61 | odd | 6 | 945.2.be.c.656.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.t.c.101.1 | ✓ | 32 | 9.2 | odd | 6 | ||
315.2.t.c.131.16 | yes | 32 | 7.5 | odd | 6 | ||
315.2.be.c.236.1 | yes | 32 | 63.47 | even | 6 | inner | |
315.2.be.c.311.1 | yes | 32 | 1.1 | even | 1 | trivial | |
945.2.t.c.341.1 | 32 | 21.5 | even | 6 | |||
945.2.t.c.521.16 | 32 | 9.7 | even | 3 | |||
945.2.be.c.206.16 | 32 | 3.2 | odd | 2 | |||
945.2.be.c.656.16 | 32 | 63.61 | odd | 6 |