Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(41,315)]
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([5, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bl (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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.9 | ||
Character | \(\chi\) | \(=\) | 315.41 |
Dual form | 315.2.bl.i.146.9 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.58089 | − | 0.912729i | 1.11786 | − | 0.645397i | 0.177006 | − | 0.984210i | \(-0.443359\pi\) |
0.940854 | + | 0.338813i | \(0.110025\pi\) | |||||||
\(3\) | 0.791176 | − | 1.54079i | 0.456786 | − | 0.889577i | ||||
\(4\) | 0.666147 | − | 1.15380i | 0.333074 | − | 0.576901i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −0.155560 | − | 3.15796i | −0.0635072 | − | 1.28923i | ||||
\(7\) | 2.11583 | + | 1.58847i | 0.799710 | + | 0.600387i | ||||
\(8\) | 1.21887i | 0.430935i | ||||||||
\(9\) | −1.74808 | − | 2.43808i | −0.582693 | − | 0.812692i | ||||
\(10\) | − | 1.82546i | − | 0.577260i | ||||||
\(11\) | −0.549675 | + | 0.317355i | −0.165733 | + | 0.0956861i | −0.580572 | − | 0.814209i | \(-0.697171\pi\) |
0.414839 | + | 0.909895i | \(0.363838\pi\) | |||||||
\(12\) | −1.25073 | − | 1.93925i | −0.361054 | − | 0.559815i | ||||
\(13\) | −2.73324 | − | 1.57804i | −0.758064 | − | 0.437668i | 0.0705364 | − | 0.997509i | \(-0.477529\pi\) |
−0.828600 | + | 0.559841i | \(0.810862\pi\) | |||||||
\(14\) | 4.79475 | + | 0.580024i | 1.28145 | + | 0.155018i | ||||
\(15\) | −0.938777 | − | 1.45557i | −0.242391 | − | 0.375828i | ||||
\(16\) | 2.44479 | + | 4.23450i | 0.611198 | + | 1.05863i | ||||
\(17\) | −2.83015 | −0.686413 | −0.343207 | − | 0.939260i | \(-0.611513\pi\) | ||||
−0.343207 | + | 0.939260i | \(0.611513\pi\) | |||||||
\(18\) | −4.98883 | − | 2.25881i | −1.17588 | − | 0.532408i | ||||
\(19\) | 4.89715i | 1.12348i | 0.827313 | + | 0.561741i | \(0.189868\pi\) | ||||
−0.827313 | + | 0.561741i | \(0.810132\pi\) | |||||||
\(20\) | −0.666147 | − | 1.15380i | −0.148955 | − | 0.257998i | ||||
\(21\) | 4.12150 | − | 2.00330i | 0.899386 | − | 0.437155i | ||||
\(22\) | −0.579318 | + | 1.00341i | −0.123511 | + | 0.213927i | ||||
\(23\) | −3.83011 | − | 2.21132i | −0.798633 | − | 0.461091i | 0.0443596 | − | 0.999016i | \(-0.485875\pi\) |
−0.842993 | + | 0.537924i | \(0.819209\pi\) | |||||||
\(24\) | 1.87802 | + | 0.964339i | 0.383350 | + | 0.196845i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −5.76127 | −1.12988 | ||||||||
\(27\) | −5.13961 | + | 0.764479i | −0.989118 | + | 0.147124i | ||||
\(28\) | 3.24224 | − | 1.38309i | 0.612726 | − | 0.261380i | ||||
\(29\) | 0.0996181 | − | 0.0575146i | 0.0184986 | − | 0.0106802i | −0.490722 | − | 0.871316i | \(-0.663267\pi\) |
0.509221 | + | 0.860636i | \(0.329934\pi\) | |||||||
\(30\) | −2.81265 | − | 1.44426i | −0.513517 | − | 0.263684i | ||||
\(31\) | 0.272686 | + | 0.157435i | 0.0489759 | + | 0.0282762i | 0.524288 | − | 0.851541i | \(-0.324332\pi\) |
−0.475312 | + | 0.879817i | \(0.657665\pi\) | |||||||
\(32\) | 5.61876 | + | 3.24399i | 0.993266 | + | 0.573462i | ||||
\(33\) | 0.0540882 | + | 1.09802i | 0.00941554 | + | 0.191140i | ||||
\(34\) | −4.47417 | + | 2.58316i | −0.767314 | + | 0.443009i | ||||
\(35\) | 2.43358 | − | 1.03813i | 0.411349 | − | 0.175476i | ||||
\(36\) | −3.97753 | + | 0.392818i | −0.662922 | + | 0.0654697i | ||||
\(37\) | 10.7800 | 1.77223 | 0.886115 | − | 0.463466i | \(-0.153395\pi\) | ||||
0.886115 | + | 0.463466i | \(0.153395\pi\) | |||||||
\(38\) | 4.46977 | + | 7.74186i | 0.725092 | + | 1.25590i | ||||
\(39\) | −4.59390 | + | 2.96285i | −0.735612 | + | 0.474435i | ||||
\(40\) | 1.05557 | + | 0.609434i | 0.166900 | + | 0.0963599i | ||||
\(41\) | −1.11318 | + | 1.92808i | −0.173849 | + | 0.301115i | −0.939762 | − | 0.341828i | \(-0.888954\pi\) |
0.765913 | + | 0.642944i | \(0.222287\pi\) | |||||||
\(42\) | 4.68719 | − | 6.92881i | 0.723249 | − | 1.06914i | ||||
\(43\) | −0.870817 | − | 1.50830i | −0.132798 | − | 0.230013i | 0.791956 | − | 0.610578i | \(-0.209063\pi\) |
−0.924754 | + | 0.380565i | \(0.875730\pi\) | |||||||
\(44\) | 0.845620i | 0.127482i | ||||||||
\(45\) | −2.98548 | + | 0.294843i | −0.445048 | + | 0.0439527i | ||||
\(46\) | −8.07333 | −1.19035 | ||||||||
\(47\) | 3.95084 | + | 6.84306i | 0.576290 | + | 0.998163i | 0.995900 | + | 0.0904591i | \(0.0288334\pi\) |
−0.419610 | + | 0.907704i | \(0.637833\pi\) | |||||||
\(48\) | 8.45874 | − | 0.416676i | 1.22091 | − | 0.0601420i | ||||
\(49\) | 1.95350 | + | 6.72189i | 0.279072 | + | 0.960270i | ||||
\(50\) | −1.58089 | − | 0.912729i | −0.223572 | − | 0.129079i | ||||
\(51\) | −2.23915 | + | 4.36068i | −0.313544 | + | 0.610617i | ||||
\(52\) | −3.64148 | + | 2.10241i | −0.504982 | + | 0.291552i | ||||
\(53\) | − | 8.63571i | − | 1.18621i | −0.805127 | − | 0.593103i | \(-0.797903\pi\) | ||
0.805127 | − | 0.593103i | \(-0.202097\pi\) | |||||||
\(54\) | −7.42741 | + | 5.89963i | −1.01074 | + | 0.802838i | ||||
\(55\) | 0.634710i | 0.0855842i | ||||||||
\(56\) | −1.93614 | + | 2.57892i | −0.258727 | + | 0.344623i | ||||
\(57\) | 7.54548 | + | 3.87451i | 0.999424 | + | 0.513191i | ||||
\(58\) | 0.104990 | − | 0.181849i | 0.0137859 | − | 0.0238779i | ||||
\(59\) | 7.65048 | − | 13.2510i | 0.996008 | − | 1.72514i | 0.420699 | − | 0.907200i | \(-0.361785\pi\) |
0.575309 | − | 0.817936i | \(-0.304882\pi\) | |||||||
\(60\) | −2.30481 | + | 0.113534i | −0.297549 | + | 0.0146572i | ||||
\(61\) | −8.94576 | + | 5.16484i | −1.14539 | + | 0.661290i | −0.947759 | − | 0.318987i | \(-0.896657\pi\) |
−0.197628 | + | 0.980277i | \(0.563324\pi\) | |||||||
\(62\) | 0.574783 | 0.0729975 | ||||||||
\(63\) | 0.174174 | − | 7.93534i | 0.0219438 | − | 0.999759i | ||||
\(64\) | 2.06438 | 0.258048 | ||||||||
\(65\) | −2.73324 | + | 1.57804i | −0.339016 | + | 0.195731i | ||||
\(66\) | 1.08770 | + | 1.68648i | 0.133887 | + | 0.207591i | ||||
\(67\) | −2.40584 | + | 4.16704i | −0.293920 | + | 0.509084i | −0.974733 | − | 0.223373i | \(-0.928293\pi\) |
0.680813 | + | 0.732457i | \(0.261627\pi\) | |||||||
\(68\) | −1.88530 | + | 3.26543i | −0.228626 | + | 0.395992i | ||||
\(69\) | −6.43747 | + | 4.15186i | −0.774981 | + | 0.499826i | ||||
\(70\) | 2.89969 | − | 3.86236i | 0.346579 | − | 0.461641i | ||||
\(71\) | − | 12.9744i | − | 1.53978i | −0.638175 | − | 0.769892i | \(-0.720310\pi\) | ||
0.638175 | − | 0.769892i | \(-0.279690\pi\) | |||||||
\(72\) | 2.97169 | − | 2.13068i | 0.350217 | − | 0.251103i | ||||
\(73\) | − | 6.45973i | − | 0.756054i | −0.925794 | − | 0.378027i | \(-0.876603\pi\) | ||
0.925794 | − | 0.378027i | \(-0.123397\pi\) | |||||||
\(74\) | 17.0421 | − | 9.83926i | 1.98110 | − | 1.14379i | ||||
\(75\) | −1.72995 | + | 0.0852172i | −0.199758 | + | 0.00984003i | ||||
\(76\) | 5.65033 | + | 3.26222i | 0.648138 | + | 0.374202i | ||||
\(77\) | −1.66713 | − | 0.201674i | −0.189987 | − | 0.0229829i | ||||
\(78\) | −4.55818 | + | 8.87692i | −0.516113 | + | 1.00511i | ||||
\(79\) | 6.51973 | + | 11.2925i | 0.733527 | + | 1.27051i | 0.955366 | + | 0.295423i | \(0.0954606\pi\) |
−0.221839 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(80\) | 4.88958 | 0.546672 | ||||||||
\(81\) | −2.88843 | + | 8.52391i | −0.320937 | + | 0.947101i | ||||
\(82\) | 4.06412i | 0.448807i | ||||||||
\(83\) | 2.25090 | + | 3.89867i | 0.247068 | + | 0.427935i | 0.962711 | − | 0.270532i | \(-0.0871995\pi\) |
−0.715643 | + | 0.698466i | \(0.753866\pi\) | |||||||
\(84\) | 0.434124 | − | 6.08989i | 0.0473668 | − | 0.664461i | ||||
\(85\) | −1.41508 | + | 2.45099i | −0.153487 | + | 0.265847i | ||||
\(86\) | −2.75334 | − | 1.58964i | −0.296900 | − | 0.171415i | ||||
\(87\) | −0.00980246 | − | 0.198995i | −0.00105093 | − | 0.0213345i | ||||
\(88\) | −0.386814 | − | 0.669981i | −0.0412345 | − | 0.0714202i | ||||
\(89\) | −11.1029 | −1.17691 | −0.588454 | − | 0.808531i | \(-0.700263\pi\) | ||||
−0.588454 | + | 0.808531i | \(0.700263\pi\) | |||||||
\(90\) | −4.45060 | + | 3.19105i | −0.469135 | + | 0.336366i | ||||
\(91\) | −3.27641 | − | 7.68054i | −0.343461 | − | 0.805139i | ||||
\(92\) | −5.10284 | + | 2.94612i | −0.532008 | + | 0.307155i | ||||
\(93\) | 0.458318 | − | 0.295593i | 0.0475254 | − | 0.0306516i | ||||
\(94\) | 12.4917 | + | 7.21210i | 1.28842 | + | 0.743871i | ||||
\(95\) | 4.24105 | + | 2.44857i | 0.435123 | + | 0.251218i | ||||
\(96\) | 9.44375 | − | 6.09077i | 0.963848 | − | 0.621637i | ||||
\(97\) | 0.266943 | − | 0.154120i | 0.0271040 | − | 0.0156485i | −0.486387 | − | 0.873744i | \(-0.661685\pi\) |
0.513491 | + | 0.858095i | \(0.328352\pi\) | |||||||
\(98\) | 9.22354 | + | 8.84357i | 0.931718 | + | 0.893335i | ||||
\(99\) | 1.73461 | + | 0.785387i | 0.174335 | + | 0.0789344i | ||||
\(100\) | −1.33229 | −0.133229 | ||||||||
\(101\) | 0.986427 | + | 1.70854i | 0.0981531 | + | 0.170006i | 0.910920 | − | 0.412583i | \(-0.135373\pi\) |
−0.812767 | + | 0.582589i | \(0.802040\pi\) | |||||||
\(102\) | 0.440260 | + | 8.93750i | 0.0435922 | + | 0.884945i | ||||
\(103\) | −13.9294 | − | 8.04212i | −1.37250 | − | 0.792413i | −0.381258 | − | 0.924469i | \(-0.624509\pi\) |
−0.991242 | + | 0.132056i | \(0.957842\pi\) | |||||||
\(104\) | 1.92342 | − | 3.33145i | 0.188606 | − | 0.326676i | ||||
\(105\) | 0.325847 | − | 4.57098i | 0.0317994 | − | 0.446082i | ||||
\(106\) | −7.88206 | − | 13.6521i | −0.765573 | − | 1.32601i | ||||
\(107\) | − | 10.0764i | − | 0.974121i | −0.873368 | − | 0.487061i | \(-0.838069\pi\) | ||
0.873368 | − | 0.487061i | \(-0.161931\pi\) | |||||||
\(108\) | −2.54168 | + | 6.43934i | −0.244573 | + | 0.619626i | ||||
\(109\) | −14.2509 | −1.36499 | −0.682496 | − | 0.730889i | \(-0.739106\pi\) | ||||
−0.682496 | + | 0.730889i | \(0.739106\pi\) | |||||||
\(110\) | 0.579318 | + | 1.00341i | 0.0552358 | + | 0.0956712i | ||||
\(111\) | 8.52892 | − | 16.6098i | 0.809529 | − | 1.57653i | ||||
\(112\) | −1.55362 | + | 12.8430i | −0.146804 | + | 1.21355i | ||||
\(113\) | 0.175863 | + | 0.101534i | 0.0165438 | + | 0.00955155i | 0.508249 | − | 0.861210i | \(-0.330293\pi\) |
−0.491705 | + | 0.870762i | \(0.663626\pi\) | |||||||
\(114\) | 15.4650 | − | 0.761802i | 1.44843 | − | 0.0713493i | ||||
\(115\) | −3.83011 | + | 2.21132i | −0.357160 | + | 0.206206i | ||||
\(116\) | − | 0.153253i | − | 0.0142292i | ||||||
\(117\) | 0.930547 | + | 9.42237i | 0.0860291 | + | 0.871099i | ||||
\(118\) | − | 27.9313i | − | 2.57128i | ||||||
\(119\) | −5.98814 | − | 4.49562i | −0.548931 | − | 0.412113i | ||||
\(120\) | 1.77415 | − | 1.14424i | 0.161957 | − | 0.104455i | ||||
\(121\) | −5.29857 | + | 9.17740i | −0.481688 | + | 0.834309i | ||||
\(122\) | −9.42819 | + | 16.3301i | −0.853588 | + | 1.47846i | ||||
\(123\) | 2.09005 | + | 3.24063i | 0.188453 | + | 0.292197i | ||||
\(124\) | 0.363298 | − | 0.209750i | 0.0326251 | − | 0.0188361i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −6.96747 | − | 12.7039i | −0.620711 | − | 1.13175i | ||||
\(127\) | 4.60267 | 0.408421 | 0.204211 | − | 0.978927i | \(-0.434537\pi\) | ||||
0.204211 | + | 0.978927i | \(0.434537\pi\) | |||||||
\(128\) | −7.97396 | + | 4.60377i | −0.704805 | + | 0.406919i | ||||
\(129\) | −3.01295 | + | 0.148417i | −0.265275 | + | 0.0130674i | ||||
\(130\) | −2.88064 | + | 4.98941i | −0.252649 | + | 0.437600i | ||||
\(131\) | 0.755338 | − | 1.30828i | 0.0659942 | − | 0.114305i | −0.831140 | − | 0.556063i | \(-0.812311\pi\) |
0.897135 | + | 0.441757i | \(0.145645\pi\) | |||||||
\(132\) | 1.30293 | + | 0.669035i | 0.113405 | + | 0.0582320i | ||||
\(133\) | −7.77899 | + | 10.3615i | −0.674524 | + | 0.898460i | ||||
\(134\) | 8.78351i | 0.758780i | ||||||||
\(135\) | −1.90775 | + | 4.83327i | −0.164193 | + | 0.415982i | ||||
\(136\) | − | 3.44958i | − | 0.295799i | ||||||
\(137\) | 10.9225 | − | 6.30611i | 0.933172 | − | 0.538767i | 0.0453589 | − | 0.998971i | \(-0.485557\pi\) |
0.887814 | + | 0.460203i | \(0.152224\pi\) | |||||||
\(138\) | −6.38742 | + | 12.4393i | −0.543734 | + | 1.05890i | ||||
\(139\) | 4.86731 | + | 2.81014i | 0.412840 | + | 0.238353i | 0.692009 | − | 0.721889i | \(-0.256726\pi\) |
−0.279169 | + | 0.960242i | \(0.590059\pi\) | |||||||
\(140\) | 0.423326 | − | 3.49941i | 0.0357775 | − | 0.295754i | ||||
\(141\) | 13.6696 | − | 0.673360i | 1.15118 | − | 0.0567071i | ||||
\(142\) | −11.8421 | − | 20.5112i | −0.993771 | − | 1.72126i | ||||
\(143\) | 2.00319 | 0.167515 | ||||||||
\(144\) | 6.05035 | − | 13.3628i | 0.504196 | − | 1.11357i | ||||
\(145\) | − | 0.115029i | − | 0.00955265i | ||||||
\(146\) | −5.89598 | − | 10.2121i | −0.487955 | − | 0.845163i | ||||
\(147\) | 11.9026 | + | 2.30826i | 0.981710 | + | 0.190382i | ||||
\(148\) | 7.18110 | − | 12.4380i | 0.590283 | − | 1.02240i | ||||
\(149\) | −10.8483 | − | 6.26327i | −0.888727 | − | 0.513107i | −0.0152013 | − | 0.999884i | \(-0.504839\pi\) |
−0.873526 | + | 0.486778i | \(0.838172\pi\) | |||||||
\(150\) | −2.65709 | + | 1.71370i | −0.216950 | + | 0.139923i | ||||
\(151\) | −4.44709 | − | 7.70259i | −0.361899 | − | 0.626828i | 0.626374 | − | 0.779523i | \(-0.284538\pi\) |
−0.988273 | + | 0.152695i | \(0.951205\pi\) | |||||||
\(152\) | −5.96897 | −0.484148 | ||||||||
\(153\) | 4.94734 | + | 6.90013i | 0.399968 | + | 0.557843i | ||||
\(154\) | −2.81963 | + | 1.20281i | −0.227212 | + | 0.0969254i | ||||
\(155\) | 0.272686 | − | 0.157435i | 0.0219027 | − | 0.0126455i | ||||
\(156\) | 0.358323 | + | 7.27414i | 0.0286888 | + | 0.582397i | ||||
\(157\) | 1.47404 | + | 0.851038i | 0.117641 | + | 0.0679202i | 0.557666 | − | 0.830065i | \(-0.311697\pi\) |
−0.440025 | + | 0.897986i | \(0.645030\pi\) | |||||||
\(158\) | 20.6140 | + | 11.9015i | 1.63996 | + | 0.946832i | ||||
\(159\) | −13.3058 | − | 6.83237i | −1.05522 | − | 0.541842i | ||||
\(160\) | 5.61876 | − | 3.24399i | 0.444202 | − | 0.256460i | ||||
\(161\) | −4.59126 | − | 10.7628i | −0.361842 | − | 0.848228i | ||||
\(162\) | 3.21371 | + | 16.1117i | 0.252493 | + | 1.26586i | ||||
\(163\) | 18.8951 | 1.47998 | 0.739988 | − | 0.672620i | \(-0.234831\pi\) | ||||
0.739988 | + | 0.672620i | \(0.234831\pi\) | |||||||
\(164\) | 1.48308 | + | 2.56877i | 0.115809 | + | 0.200587i | ||||
\(165\) | 0.977956 | + | 0.502167i | 0.0761337 | + | 0.0390937i | ||||
\(166\) | 7.11686 | + | 4.10892i | 0.552375 | + | 0.318914i | ||||
\(167\) | 6.20475 | − | 10.7469i | 0.480138 | − | 0.831624i | −0.519602 | − | 0.854408i | \(-0.673920\pi\) |
0.999740 | + | 0.0227845i | \(0.00725316\pi\) | |||||||
\(168\) | 2.44175 | + | 5.02357i | 0.188385 | + | 0.387577i | ||||
\(169\) | −1.51961 | − | 2.63204i | −0.116893 | − | 0.202465i | ||||
\(170\) | 5.16633i | 0.396239i | ||||||||
\(171\) | 11.9396 | − | 8.56060i | 0.913045 | − | 0.654646i | ||||
\(172\) | −2.32037 | −0.176927 | ||||||||
\(173\) | 6.14289 | + | 10.6398i | 0.467035 | + | 0.808929i | 0.999291 | − | 0.0376549i | \(-0.0119888\pi\) |
−0.532255 | + | 0.846584i | \(0.678655\pi\) | |||||||
\(174\) | −0.197125 | − | 0.305643i | −0.0149440 | − | 0.0231707i | ||||
\(175\) | 0.317742 | − | 2.62660i | 0.0240190 | − | 0.198552i | ||||
\(176\) | −2.68768 | − | 1.55173i | −0.202591 | − | 0.116966i | ||||
\(177\) | −14.3642 | − | 22.2717i | −1.07968 | − | 1.67404i | ||||
\(178\) | −17.5525 | + | 10.1340i | −1.31562 | + | 0.759572i | ||||
\(179\) | 4.60808i | 0.344424i | 0.985060 | + | 0.172212i | \(0.0550914\pi\) | ||||
−0.985060 | + | 0.172212i | \(0.944909\pi\) | |||||||
\(180\) | −1.64858 | + | 3.64105i | −0.122878 | + | 0.271388i | ||||
\(181\) | 16.3361i | 1.21425i | 0.794605 | + | 0.607127i | \(0.207678\pi\) | ||||
−0.794605 | + | 0.607127i | \(0.792322\pi\) | |||||||
\(182\) | −12.1899 | − | 9.15163i | −0.903575 | − | 0.678364i | ||||
\(183\) | 0.880266 | + | 17.8699i | 0.0650711 | + | 1.32098i | ||||
\(184\) | 2.69530 | − | 4.66840i | 0.198700 | − | 0.344159i | ||||
\(185\) | 5.39002 | − | 9.33580i | 0.396282 | − | 0.686381i | ||||
\(186\) | 0.454755 | − | 0.885621i | 0.0333442 | − | 0.0649369i | ||||
\(187\) | 1.55566 | − | 0.898163i | 0.113761 | − | 0.0656802i | ||||
\(188\) | 10.5274 | 0.767788 | ||||||||
\(189\) | −12.0889 | − | 6.54662i | −0.879339 | − | 0.476197i | ||||
\(190\) | 8.93953 | 0.648542 | ||||||||
\(191\) | −21.0061 | + | 12.1279i | −1.51995 | + | 0.877543i | −0.520225 | + | 0.854029i | \(0.674152\pi\) |
−0.999724 | + | 0.0235140i | \(0.992515\pi\) | |||||||
\(192\) | 1.63329 | − | 3.18078i | 0.117872 | − | 0.229553i | ||||
\(193\) | 6.56678 | − | 11.3740i | 0.472687 | − | 0.818718i | −0.526825 | − | 0.849974i | \(-0.676618\pi\) |
0.999511 | + | 0.0312564i | \(0.00995083\pi\) | |||||||
\(194\) | 0.281339 | − | 0.487293i | 0.0201990 | − | 0.0349856i | ||||
\(195\) | 0.268951 | + | 5.45985i | 0.0192600 | + | 0.390988i | ||||
\(196\) | 9.05705 | + | 2.22382i | 0.646932 | + | 0.158844i | ||||
\(197\) | 3.76813i | 0.268468i | 0.990950 | + | 0.134234i | \(0.0428573\pi\) | ||||
−0.990950 | + | 0.134234i | \(0.957143\pi\) | |||||||
\(198\) | 3.45908 | − | 0.341616i | 0.245826 | − | 0.0242776i | ||||
\(199\) | − | 18.8678i | − | 1.33750i | −0.743487 | − | 0.668751i | \(-0.766829\pi\) | ||
0.743487 | − | 0.668751i | \(-0.233171\pi\) | |||||||
\(200\) | 1.05557 | − | 0.609434i | 0.0746401 | − | 0.0430935i | ||||
\(201\) | 4.51709 | + | 7.00376i | 0.318611 | + | 0.494007i | ||||
\(202\) | 3.11887 | + | 1.80068i | 0.219443 | + | 0.126695i | ||||
\(203\) | 0.302136 | + | 0.0365495i | 0.0212058 | + | 0.00256528i | ||||
\(204\) | 3.53975 | + | 5.48839i | 0.247832 | + | 0.384264i | ||||
\(205\) | 1.11318 | + | 1.92808i | 0.0777477 | + | 0.134663i | ||||
\(206\) | −29.3611 | −2.04568 | ||||||||
\(207\) | 1.30398 | + | 13.2037i | 0.0906332 | + | 0.917718i | ||||
\(208\) | − | 15.4319i | − | 1.07001i | ||||||
\(209\) | −1.55413 | − | 2.69184i | −0.107502 | − | 0.186198i | ||||
\(210\) | −3.65693 | − | 7.52363i | −0.252352 | − | 0.519180i | ||||
\(211\) | 12.9903 | − | 22.4999i | 0.894292 | − | 1.54896i | 0.0596142 | − | 0.998221i | \(-0.481013\pi\) |
0.834678 | − | 0.550738i | \(-0.185654\pi\) | |||||||
\(212\) | −9.96389 | − | 5.75265i | −0.684323 | − | 0.395094i | ||||
\(213\) | −19.9909 | − | 10.2651i | −1.36976 | − | 0.703351i | ||||
\(214\) | −9.19701 | − | 15.9297i | −0.628695 | − | 1.08893i | ||||
\(215\) | −1.74163 | −0.118778 | ||||||||
\(216\) | −0.931799 | − | 6.26450i | −0.0634009 | − | 0.426245i | ||||
\(217\) | 0.326876 | + | 0.766262i | 0.0221898 | + | 0.0520172i | ||||
\(218\) | −22.5292 | + | 13.0072i | −1.52587 | + | 0.880961i | ||||
\(219\) | −9.95310 | − | 5.11079i | −0.672568 | − | 0.345355i | ||||
\(220\) | 0.732329 | + | 0.422810i | 0.0493736 | + | 0.0285059i | ||||
\(221\) | 7.73548 | + | 4.46608i | 0.520345 | + | 0.300421i | ||||
\(222\) | −1.67695 | − | 34.0429i | −0.112549 | − | 2.28481i | ||||
\(223\) | 20.0761 | − | 11.5909i | 1.34440 | − | 0.776187i | 0.356946 | − | 0.934125i | \(-0.383818\pi\) |
0.987449 | + | 0.157938i | \(0.0504846\pi\) | |||||||
\(224\) | 6.73536 | + | 15.7890i | 0.450025 | + | 1.05495i | ||||
\(225\) | −1.23740 | + | 2.73292i | −0.0824931 | + | 0.182195i | ||||
\(226\) | 0.370693 | 0.0246582 | ||||||||
\(227\) | −9.75293 | − | 16.8926i | −0.647325 | − | 1.12120i | −0.983759 | − | 0.179493i | \(-0.942554\pi\) |
0.336434 | − | 0.941707i | \(-0.390779\pi\) | |||||||
\(228\) | 9.49681 | − | 6.12499i | 0.628942 | − | 0.405638i | ||||
\(229\) | 19.9441 | + | 11.5147i | 1.31794 | + | 0.760913i | 0.983397 | − | 0.181467i | \(-0.0580845\pi\) |
0.334544 | + | 0.942380i | \(0.391418\pi\) | |||||||
\(230\) | −4.03666 | + | 6.99171i | −0.266170 | + | 0.461019i | ||||
\(231\) | −1.62973 | + | 2.40914i | −0.107228 | + | 0.158510i | ||||
\(232\) | 0.0701026 | + | 0.121421i | 0.00460246 | + | 0.00797170i | ||||
\(233\) | 18.2501i | 1.19560i | 0.801644 | + | 0.597801i | \(0.203959\pi\) | ||||
−0.801644 | + | 0.597801i | \(0.796041\pi\) | |||||||
\(234\) | 10.0712 | + | 14.0464i | 0.658373 | + | 0.918243i | ||||
\(235\) | 7.90169 | 0.515449 | ||||||||
\(236\) | −10.1927 | − | 17.6543i | −0.663488 | − | 1.14920i | ||||
\(237\) | 22.5577 | − | 1.11119i | 1.46528 | − | 0.0721793i | ||||
\(238\) | −13.5699 | − | 1.64156i | −0.879605 | − | 0.106406i | ||||
\(239\) | −16.0585 | − | 9.27139i | −1.03874 | − | 0.599716i | −0.119263 | − | 0.992863i | \(-0.538053\pi\) |
−0.919476 | + | 0.393146i | \(0.871387\pi\) | |||||||
\(240\) | 3.86852 | − | 7.53383i | 0.249712 | − | 0.486306i | ||||
\(241\) | −6.19724 | + | 3.57798i | −0.399200 | + | 0.230478i | −0.686139 | − | 0.727471i | \(-0.740696\pi\) |
0.286939 | + | 0.957949i | \(0.407362\pi\) | |||||||
\(242\) | 19.3446i | 1.24352i | ||||||||
\(243\) | 10.8483 | + | 11.1944i | 0.695919 | + | 0.718120i | ||||
\(244\) | 13.7622i | 0.881033i | ||||||||
\(245\) | 6.79808 | + | 1.66916i | 0.434313 | + | 0.106639i | ||||
\(246\) | 6.26196 | + | 3.21543i | 0.399248 | + | 0.205008i | ||||
\(247\) | 7.72787 | − | 13.3851i | 0.491713 | − | 0.851671i | ||||
\(248\) | −0.191893 | + | 0.332368i | −0.0121852 | + | 0.0211054i | ||||
\(249\) | 7.78790 | − | 0.383631i | 0.493538 | − | 0.0243116i | ||||
\(250\) | −1.58089 | + | 0.912729i | −0.0999844 | + | 0.0577260i | ||||
\(251\) | 29.5574 | 1.86564 | 0.932822 | − | 0.360338i | \(-0.117339\pi\) | ||||
0.932822 | + | 0.360338i | \(0.117339\pi\) | |||||||
\(252\) | −9.03978 | − | 5.48707i | −0.569453 | − | 0.345653i | ||||
\(253\) | 2.80709 | 0.176480 | ||||||||
\(254\) | 7.27633 | − | 4.20099i | 0.456558 | − | 0.263594i | ||||
\(255\) | 2.65688 | + | 4.11950i | 0.166380 | + | 0.257973i | ||||
\(256\) | −10.4684 | + | 18.1317i | −0.654272 | + | 1.13323i | ||||
\(257\) | 4.33852 | − | 7.51453i | 0.270629 | − | 0.468744i | −0.698394 | − | 0.715714i | \(-0.746102\pi\) |
0.969023 | + | 0.246970i | \(0.0794349\pi\) | |||||||
\(258\) | −4.62768 | + | 2.98463i | −0.288107 | + | 0.185815i | ||||
\(259\) | 22.8088 | + | 17.1238i | 1.41727 | + | 1.06402i | ||||
\(260\) | 4.20482i | 0.260772i | ||||||||
\(261\) | −0.314365 | − | 0.142337i | −0.0194587 | − | 0.00881041i | ||||
\(262\) | − | 2.75768i | − | 0.170370i | ||||||
\(263\) | −5.81261 | + | 3.35591i | −0.358421 | + | 0.206934i | −0.668388 | − | 0.743813i | \(-0.733015\pi\) |
0.309967 | + | 0.950747i | \(0.399682\pi\) | |||||||
\(264\) | −1.33834 | + | 0.0659263i | −0.0823691 | + | 0.00405749i | ||||
\(265\) | −7.47874 | − | 4.31785i | −0.459415 | − | 0.265244i | ||||
\(266\) | −2.84046 | + | 23.4806i | −0.174160 | + | 1.43969i | ||||
\(267\) | −8.78437 | + | 17.1073i | −0.537595 | + | 1.04695i | ||||
\(268\) | 3.20529 | + | 5.55172i | 0.195794 | + | 0.339125i | ||||
\(269\) | −7.10403 | −0.433140 | −0.216570 | − | 0.976267i | \(-0.569487\pi\) | ||||
−0.216570 | + | 0.976267i | \(0.569487\pi\) | |||||||
\(270\) | 1.39552 | + | 9.38214i | 0.0849289 | + | 0.570979i | ||||
\(271\) | 24.9418i | 1.51511i | 0.652773 | + | 0.757554i | \(0.273606\pi\) | ||||
−0.652773 | + | 0.757554i | \(0.726394\pi\) | |||||||
\(272\) | −6.91913 | − | 11.9843i | −0.419534 | − | 0.726654i | ||||
\(273\) | −14.4263 | − | 1.02839i | −0.873121 | − | 0.0622413i | ||||
\(274\) | 11.5115 | − | 19.9386i | 0.695437 | − | 1.20453i | ||||
\(275\) | 0.549675 | + | 0.317355i | 0.0331466 | + | 0.0191372i | ||||
\(276\) | 0.502121 | + | 10.1933i | 0.0302241 | + | 0.613565i | ||||
\(277\) | −3.69399 | − | 6.39818i | −0.221950 | − | 0.384429i | 0.733450 | − | 0.679744i | \(-0.237909\pi\) |
−0.955400 | + | 0.295314i | \(0.904576\pi\) | |||||||
\(278\) | 10.2596 | 0.615330 | ||||||||
\(279\) | −0.0928376 | − | 0.940039i | −0.00555804 | − | 0.0562787i | ||||
\(280\) | 1.26534 | + | 2.96621i | 0.0756186 | + | 0.177265i | ||||
\(281\) | −4.56414 | + | 2.63511i | −0.272274 | + | 0.157197i | −0.629921 | − | 0.776660i | \(-0.716913\pi\) |
0.357647 | + | 0.933857i | \(0.383579\pi\) | |||||||
\(282\) | 20.9955 | − | 13.5411i | 1.25026 | − | 0.806361i | ||||
\(283\) | 19.8282 | + | 11.4478i | 1.17867 | + | 0.680503i | 0.955706 | − | 0.294325i | \(-0.0950947\pi\) |
0.222960 | + | 0.974828i | \(0.428428\pi\) | |||||||
\(284\) | −14.9699 | − | 8.64289i | −0.888302 | − | 0.512861i | ||||
\(285\) | 7.12816 | − | 4.59733i | 0.422236 | − | 0.272322i | ||||
\(286\) | 3.16683 | − | 1.82837i | 0.187258 | − | 0.108114i | ||||
\(287\) | −5.41800 | + | 2.31124i | −0.319815 | + | 0.136428i | ||||
\(288\) | −1.91294 | − | 19.3697i | −0.112721 | − | 1.14137i | ||||
\(289\) | −8.99023 | −0.528837 | ||||||||
\(290\) | −0.104990 | − | 0.181849i | −0.00616525 | − | 0.0106785i | ||||
\(291\) | −0.0262673 | − | 0.533240i | −0.00153982 | − | 0.0312591i | ||||
\(292\) | −7.45325 | − | 4.30313i | −0.436168 | − | 0.251822i | ||||
\(293\) | −12.2600 | + | 21.2349i | −0.716236 | + | 1.24056i | 0.246244 | + | 0.969208i | \(0.420803\pi\) |
−0.962481 | + | 0.271350i | \(0.912530\pi\) | |||||||
\(294\) | 20.9235 | − | 7.21474i | 1.22029 | − | 0.420772i | ||||
\(295\) | −7.65048 | − | 13.2510i | −0.445428 | − | 0.771504i | ||||
\(296\) | 13.1395i | 0.763715i | ||||||||
\(297\) | 2.58250 | − | 2.05129i | 0.149852 | − | 0.119028i | ||||
\(298\) | −22.8667 | −1.32463 | ||||||||
\(299\) | 6.97907 | + | 12.0881i | 0.403610 | + | 0.699073i | ||||
\(300\) | −1.05408 | + | 2.05279i | −0.0608573 | + | 0.118518i | ||||
\(301\) | 0.553390 | − | 4.57458i | 0.0318969 | − | 0.263674i | ||||
\(302\) | −14.0607 | − | 8.11798i | −0.809105 | − | 0.467137i | ||||
\(303\) | 3.41294 | − | 0.168121i | 0.196069 | − | 0.00965830i | ||||
\(304\) | −20.7370 | + | 11.9725i | −1.18935 | + | 0.686670i | ||||
\(305\) | 10.3297i | 0.591475i | ||||||||
\(306\) | 14.1192 | + | 6.39279i | 0.807138 | + | 0.365452i | ||||
\(307\) | 23.9095i | 1.36459i | 0.731078 | + | 0.682294i | \(0.239017\pi\) | ||||
−0.731078 | + | 0.682294i | \(0.760983\pi\) | |||||||
\(308\) | −1.34325 | + | 1.78919i | −0.0765385 | + | 0.101949i | ||||
\(309\) | −23.4118 | + | 15.0995i | −1.33185 | + | 0.858981i | ||||
\(310\) | 0.287392 | − | 0.497777i | 0.0163227 | − | 0.0282718i | ||||
\(311\) | −11.9796 | + | 20.7493i | −0.679303 | + | 1.17659i | 0.295889 | + | 0.955222i | \(0.404384\pi\) |
−0.975191 | + | 0.221364i | \(0.928949\pi\) | |||||||
\(312\) | −3.61132 | − | 5.59935i | −0.204451 | − | 0.317001i | ||||
\(313\) | 20.2952 | − | 11.7174i | 1.14715 | − | 0.662307i | 0.198959 | − | 0.980008i | \(-0.436244\pi\) |
0.948191 | + | 0.317701i | \(0.102911\pi\) | |||||||
\(314\) | 3.10707 | 0.175342 | ||||||||
\(315\) | −6.78512 | − | 4.11851i | −0.382298 | − | 0.232052i | ||||
\(316\) | 17.3724 | 0.977274 | ||||||||
\(317\) | 0.0621219 | − | 0.0358661i | 0.00348911 | − | 0.00201444i | −0.498254 | − | 0.867031i | \(-0.666025\pi\) |
0.501744 | + | 0.865016i | \(0.332692\pi\) | |||||||
\(318\) | −27.2712 | + | 1.34337i | −1.52929 | + | 0.0753326i | ||||
\(319\) | −0.0365051 | + | 0.0632286i | −0.00204389 | + | 0.00354012i | ||||
\(320\) | 1.03219 | − | 1.78781i | 0.0577012 | − | 0.0999414i | ||||
\(321\) | −15.5256 | − | 7.97220i | −0.866556 | − | 0.444965i | ||||
\(322\) | −17.0818 | − | 12.8243i | −0.951932 | − | 0.714668i | ||||
\(323\) | − | 13.8597i | − | 0.771173i | ||||||
\(324\) | 7.91077 | + | 9.01085i | 0.439487 | + | 0.500603i | ||||
\(325\) | 3.15607i | 0.175067i | ||||||||
\(326\) | 29.8711 | − | 17.2461i | 1.65441 | − | 0.955171i | ||||
\(327\) | −11.2750 | + | 21.9577i | −0.623509 | + | 1.21426i | ||||
\(328\) | −2.35007 | − | 1.35682i | −0.129761 | − | 0.0749176i | ||||
\(329\) | −2.51070 | + | 20.7546i | −0.138419 | + | 1.14424i | ||||
\(330\) | 2.00439 | − | 0.0987357i | 0.110338 | − | 0.00543522i | ||||
\(331\) | 5.30278 | + | 9.18468i | 0.291467 | + | 0.504836i | 0.974157 | − | 0.225873i | \(-0.0725233\pi\) |
−0.682690 | + | 0.730708i | \(0.739190\pi\) | |||||||
\(332\) | 5.99772 | 0.329168 | ||||||||
\(333\) | −18.8444 | − | 26.2826i | −1.03267 | − | 1.44028i | ||||
\(334\) | − | 22.6530i | − | 1.23952i | ||||||
\(335\) | 2.40584 | + | 4.16704i | 0.131445 | + | 0.227669i | ||||
\(336\) | 18.5592 | + | 12.5549i | 1.01249 | + | 0.684925i | ||||
\(337\) | −7.49923 | + | 12.9890i | −0.408509 | + | 0.707558i | −0.994723 | − | 0.102598i | \(-0.967284\pi\) |
0.586214 | + | 0.810156i | \(0.300618\pi\) | |||||||
\(338\) | −4.80468 | − | 2.77398i | −0.261340 | − | 0.150885i | ||||
\(339\) | 0.295582 | − | 0.190636i | 0.0160538 | − | 0.0103539i | ||||
\(340\) | 1.88530 | + | 3.26543i | 0.102245 | + | 0.177093i | ||||
\(341\) | −0.199852 | −0.0108226 | ||||||||
\(342\) | 11.0617 | − | 24.4310i | 0.598150 | − | 1.32108i | ||||
\(343\) | −6.54426 | + | 17.3255i | −0.353357 | + | 0.935489i | ||||
\(344\) | 1.83842 | − | 1.06141i | 0.0991208 | − | 0.0572274i | ||||
\(345\) | 0.376884 | + | 7.65095i | 0.0202908 | + | 0.411913i | ||||
\(346\) | 19.4225 | + | 11.2136i | 1.04416 | + | 0.602846i | ||||
\(347\) | 8.94211 | + | 5.16273i | 0.480037 | + | 0.277150i | 0.720432 | − | 0.693525i | \(-0.243944\pi\) |
−0.240395 | + | 0.970675i | \(0.577277\pi\) | |||||||
\(348\) | −0.236131 | − | 0.121250i | −0.0126579 | − | 0.00649968i | ||||
\(349\) | −11.0162 | + | 6.36020i | −0.589683 | + | 0.340454i | −0.764972 | − | 0.644063i | \(-0.777247\pi\) |
0.175289 | + | 0.984517i | \(0.443914\pi\) | |||||||
\(350\) | −1.89506 | − | 4.44239i | −0.101295 | − | 0.237456i | ||||
\(351\) | 15.2541 | + | 6.02098i | 0.814206 | + | 0.321376i | ||||
\(352\) | −4.11799 | −0.219489 | ||||||||
\(353\) | 2.64706 | + | 4.58484i | 0.140889 | + | 0.244027i | 0.927832 | − | 0.372999i | \(-0.121671\pi\) |
−0.786943 | + | 0.617026i | \(0.788337\pi\) | |||||||
\(354\) | −43.0363 | − | 22.0986i | −2.28735 | − | 1.17452i | ||||
\(355\) | −11.2362 | − | 6.48722i | −0.596356 | − | 0.344306i | ||||
\(356\) | −7.39618 | + | 12.8106i | −0.391997 | + | 0.678959i | ||||
\(357\) | −11.6645 | + | 5.66964i | −0.617350 | + | 0.300069i | ||||
\(358\) | 4.20592 | + | 7.28488i | 0.222290 | + | 0.385018i | ||||
\(359\) | 28.3441i | 1.49594i | 0.663730 | + | 0.747972i | \(0.268972\pi\) | ||||
−0.663730 | + | 0.747972i | \(0.731028\pi\) | |||||||
\(360\) | −0.359375 | − | 3.63890i | −0.0189407 | − | 0.191787i | ||||
\(361\) | −4.98204 | −0.262212 | ||||||||
\(362\) | 14.9104 | + | 25.8256i | 0.783675 | + | 1.35736i | ||||
\(363\) | 9.94835 | + | 15.4249i | 0.522153 | + | 0.809599i | ||||
\(364\) | −11.0444 | − | 1.33605i | −0.578883 | − | 0.0700278i | ||||
\(365\) | −5.59429 | − | 3.22987i | −0.292819 | − | 0.169059i | ||||
\(366\) | 17.7019 | + | 27.4469i | 0.925295 | + | 1.43467i | ||||
\(367\) | 16.6696 | − | 9.62420i | 0.870146 | − | 0.502379i | 0.00274922 | − | 0.999996i | \(-0.499125\pi\) |
0.867397 | + | 0.497617i | \(0.165792\pi\) | |||||||
\(368\) | − | 21.6248i | − | 1.12727i | ||||||
\(369\) | 6.64673 | − | 0.656426i | 0.346015 | − | 0.0341722i | ||||
\(370\) | − | 19.6785i | − | 1.02304i | ||||||
\(371\) | 13.7176 | − | 18.2717i | 0.712182 | − | 0.948620i | ||||
\(372\) | −0.0357487 | − | 0.725716i | −0.00185348 | − | 0.0376266i | ||||
\(373\) | −0.291671 | + | 0.505190i | −0.0151022 | + | 0.0261577i | −0.873478 | − | 0.486864i | \(-0.838141\pi\) |
0.858376 | + | 0.513022i | \(0.171474\pi\) | |||||||
\(374\) | 1.63956 | − | 2.83980i | 0.0847796 | − | 0.146843i | ||||
\(375\) | −0.791176 | + | 1.54079i | −0.0408562 | + | 0.0795662i | ||||
\(376\) | −8.34079 | + | 4.81556i | −0.430143 | + | 0.248343i | ||||
\(377\) | −0.363040 | −0.0186975 | ||||||||
\(378\) | −25.0866 | + | 0.684392i | −1.29031 | + | 0.0352013i | ||||
\(379\) | −13.7533 | −0.706458 | −0.353229 | − | 0.935537i | \(-0.614916\pi\) | ||||
−0.353229 | + | 0.935537i | \(0.614916\pi\) | |||||||
\(380\) | 5.65033 | − | 3.26222i | 0.289856 | − | 0.167348i | ||||
\(381\) | 3.64153 | − | 7.09176i | 0.186561 | − | 0.363322i | ||||
\(382\) | −22.1389 | + | 38.3458i | −1.13273 | + | 1.96194i | ||||
\(383\) | 17.9867 | − | 31.1539i | 0.919078 | − | 1.59189i | 0.118260 | − | 0.992983i | \(-0.462268\pi\) |
0.800818 | − | 0.598907i | \(-0.204398\pi\) | |||||||
\(384\) | 0.784640 | + | 15.9286i | 0.0400410 | + | 0.812853i | ||||
\(385\) | −1.00822 | + | 1.34294i | −0.0513836 | + | 0.0684426i | ||||
\(386\) | − | 23.9747i | − | 1.22028i | ||||||
\(387\) | −2.15509 | + | 4.75975i | −0.109549 | + | 0.241952i | ||||
\(388\) | − | 0.410666i | − | 0.0208484i | ||||||
\(389\) | 1.51792 | − | 0.876372i | 0.0769616 | − | 0.0444338i | −0.461025 | − | 0.887387i | \(-0.652518\pi\) |
0.537987 | + | 0.842953i | \(0.319185\pi\) | |||||||
\(390\) | 5.40855 | + | 8.38596i | 0.273873 | + | 0.424640i | ||||
\(391\) | 10.8398 | + | 6.25836i | 0.548193 | + | 0.316499i | ||||
\(392\) | −8.19310 | + | 2.38106i | −0.413814 | + | 0.120262i | ||||
\(393\) | −1.41819 | − | 2.19890i | −0.0715381 | − | 0.110920i | ||||
\(394\) | 3.43928 | + | 5.95700i | 0.173268 | + | 0.300109i | ||||
\(395\) | 13.0395 | 0.656087 | ||||||||
\(396\) | 2.06169 | − | 1.47821i | 0.103604 | − | 0.0742830i | ||||
\(397\) | 5.19511i | 0.260735i | 0.991466 | + | 0.130367i | \(0.0416157\pi\) | ||||
−0.991466 | + | 0.130367i | \(0.958384\pi\) | |||||||
\(398\) | −17.2212 | − | 29.8279i | −0.863219 | − | 1.49514i | ||||
\(399\) | 9.81044 | + | 20.1836i | 0.491136 | + | 1.01044i | ||||
\(400\) | 2.44479 | − | 4.23450i | 0.122240 | − | 0.211725i | ||||
\(401\) | 24.3757 | + | 14.0733i | 1.21726 | + | 0.702788i | 0.964332 | − | 0.264696i | \(-0.0852717\pi\) |
0.252932 | + | 0.967484i | \(0.418605\pi\) | |||||||
\(402\) | 13.5336 | + | 6.94931i | 0.674993 | + | 0.346600i | ||||
\(403\) | −0.496877 | − | 0.860617i | −0.0247512 | − | 0.0428704i | ||||
\(404\) | 2.62842 | 0.130769 | ||||||||
\(405\) | 5.93770 | + | 6.76341i | 0.295047 | + | 0.336076i | ||||
\(406\) | 0.511004 | − | 0.217987i | 0.0253607 | − | 0.0108185i | ||||
\(407\) | −5.92552 | + | 3.42110i | −0.293717 | + | 0.169578i | ||||
\(408\) | −5.31509 | − | 2.72923i | −0.263136 | − | 0.135117i | ||||
\(409\) | −30.3765 | − | 17.5379i | −1.50202 | − | 0.867193i | −0.999997 | − | 0.00234081i | \(-0.999255\pi\) |
−0.502026 | − | 0.864853i | \(-0.667412\pi\) | |||||||
\(410\) | 3.51963 | + | 2.03206i | 0.173822 | + | 0.100356i | ||||
\(411\) | −1.07478 | − | 21.8186i | −0.0530149 | − | 1.07623i | ||||
\(412\) | −18.5580 | + | 10.7145i | −0.914287 | + | 0.527864i | ||||
\(413\) | 37.2360 | − | 15.8844i | 1.83227 | − | 0.781619i | ||||
\(414\) | 14.1128 | + | 19.6834i | 0.693607 | + | 0.967386i | ||||
\(415\) | 4.50180 | 0.220985 | ||||||||
\(416\) | −10.2383 | − | 17.7332i | −0.501972 | − | 0.869442i | ||||
\(417\) | 8.18075 | − | 5.27620i | 0.400613 | − | 0.258376i | ||||
\(418\) | −4.91383 | − | 2.83700i | −0.240344 | − | 0.138762i | ||||
\(419\) | −5.42356 | + | 9.39389i | −0.264958 | + | 0.458921i | −0.967553 | − | 0.252669i | \(-0.918692\pi\) |
0.702594 | + | 0.711591i | \(0.252025\pi\) | |||||||
\(420\) | −5.05694 | − | 3.42091i | −0.246753 | − | 0.166923i | ||||
\(421\) | 10.3703 | + | 17.9619i | 0.505417 | + | 0.875408i | 0.999980 | + | 0.00626646i | \(0.00199469\pi\) |
−0.494563 | + | 0.869142i | \(0.664672\pi\) | |||||||
\(422\) | − | 47.4266i | − | 2.30869i | ||||||
\(423\) | 9.77752 | − | 21.5947i | 0.475399 | − | 1.04997i | ||||
\(424\) | 10.5258 | 0.511177 | ||||||||
\(425\) | 1.41508 | + | 2.45099i | 0.0686413 | + | 0.118890i | ||||
\(426\) | −40.9727 | + | 2.01831i | −1.98514 | + | 0.0977874i | ||||
\(427\) | −27.1319 | − | 3.28217i | −1.31301 | − | 0.158835i | ||||
\(428\) | −11.6261 | − | 6.71236i | −0.561971 | − | 0.324454i | ||||
\(429\) | 1.58488 | − | 3.08650i | 0.0765185 | − | 0.149017i | ||||
\(430\) | −2.75334 | + | 1.58964i | −0.132778 | + | 0.0766592i | ||||
\(431\) | 10.0323i | 0.483240i | 0.970371 | + | 0.241620i | \(0.0776787\pi\) | ||||
−0.970371 | + | 0.241620i | \(0.922321\pi\) | |||||||
\(432\) | −15.8025 | − | 19.8947i | −0.760296 | − | 0.957183i | ||||
\(433\) | − | 11.9241i | − | 0.573034i | −0.958075 | − | 0.286517i | \(-0.907503\pi\) | ||
0.958075 | − | 0.286517i | \(-0.0924975\pi\) | |||||||
\(434\) | 1.21615 | + | 0.913028i | 0.0583769 | + | 0.0438267i | ||||
\(435\) | −0.177236 | − | 0.0910083i | −0.00849781 | − | 0.00436352i | ||||
\(436\) | −9.49322 | + | 16.4427i | −0.454643 | + | 0.787465i | ||||
\(437\) | 10.8291 | − | 18.7566i | 0.518028 | − | 0.897251i | ||||
\(438\) | −20.3995 | + | 1.00488i | −0.974728 | + | 0.0480149i | ||||
\(439\) | 21.8143 | − | 12.5945i | 1.04114 | − | 0.601103i | 0.120985 | − | 0.992654i | \(-0.461395\pi\) |
0.920156 | + | 0.391552i | \(0.128062\pi\) | |||||||
\(440\) | −0.773627 | −0.0368812 | ||||||||
\(441\) | 12.9736 | − | 16.5132i | 0.617791 | − | 0.786343i | ||||
\(442\) | 16.3053 | 0.775564 | ||||||||
\(443\) | 19.2098 | − | 11.0908i | 0.912687 | − | 0.526940i | 0.0313921 | − | 0.999507i | \(-0.490006\pi\) |
0.881295 | + | 0.472567i | \(0.156673\pi\) | |||||||
\(444\) | −13.4829 | − | 20.9053i | −0.639870 | − | 0.992120i | ||||
\(445\) | −5.55146 | + | 9.61541i | −0.263165 | + | 0.455814i | ||||
\(446\) | 21.1588 | − | 36.6481i | 1.00190 | − | 1.73534i | ||||
\(447\) | −18.2333 | + | 11.7596i | −0.862406 | + | 0.556211i | ||||
\(448\) | 4.36788 | + | 3.27921i | 0.206363 | + | 0.154928i | ||||
\(449\) | − | 24.3237i | − | 1.14791i | −0.818888 | − | 0.573954i | \(-0.805409\pi\) | ||
0.818888 | − | 0.573954i | \(-0.194591\pi\) | |||||||
\(450\) | 0.538224 | + | 5.44986i | 0.0253721 | + | 0.256909i | ||||
\(451\) | − | 1.41309i | − | 0.0665398i | ||||||
\(452\) | 0.234301 | − | 0.135274i | 0.0110206 | − | 0.00636274i | ||||
\(453\) | −15.3865 | + | 0.757937i | −0.722922 | + | 0.0356110i | ||||
\(454\) | −30.8367 | − | 17.8036i | −1.44724 | − | 0.835563i | ||||
\(455\) | −8.28974 | − | 1.00282i | −0.388629 | − | 0.0470127i | ||||
\(456\) | −4.72251 | + | 9.19694i | −0.221152 | + | 0.430686i | ||||
\(457\) | −6.84087 | − | 11.8487i | −0.320002 | − | 0.554261i | 0.660486 | − | 0.750839i | \(-0.270350\pi\) |
−0.980488 | + | 0.196578i | \(0.937017\pi\) | |||||||
\(458\) | 42.0392 | 1.96436 | ||||||||
\(459\) | 14.5459 | − | 2.16359i | 0.678944 | − | 0.100988i | ||||
\(460\) | 5.89225i | 0.274728i | ||||||||
\(461\) | 13.9624 | + | 24.1836i | 0.650293 | + | 1.12634i | 0.983052 | + | 0.183329i | \(0.0586872\pi\) |
−0.332759 | + | 0.943012i | \(0.607979\pi\) | |||||||
\(462\) | −0.377537 | + | 5.29610i | −0.0175646 | + | 0.246397i | ||||
\(463\) | 5.19491 | − | 8.99785i | 0.241428 | − | 0.418165i | −0.719693 | − | 0.694292i | \(-0.755718\pi\) |
0.961121 | + | 0.276127i | \(0.0890509\pi\) | |||||||
\(464\) | 0.487091 | + | 0.281222i | 0.0226126 | + | 0.0130554i | ||||
\(465\) | −0.0268324 | − | 0.544712i | −0.00124432 | − | 0.0252604i | ||||
\(466\) | 16.6574 | + | 28.8514i | 0.771638 | + | 1.33652i | ||||
\(467\) | −13.3976 | −0.619968 | −0.309984 | − | 0.950742i | \(-0.600324\pi\) | ||||
−0.309984 | + | 0.950742i | \(0.600324\pi\) | |||||||
\(468\) | 11.4914 | + | 5.20302i | 0.531191 | + | 0.240510i | ||||
\(469\) | −11.7096 | + | 4.99514i | −0.540698 | + | 0.230654i | ||||
\(470\) | 12.4917 | − | 7.21210i | 0.576200 | − | 0.332669i | ||||
\(471\) | 2.47750 | − | 1.59787i | 0.114157 | − | 0.0736259i | ||||
\(472\) | 16.1512 | + | 9.32493i | 0.743421 | + | 0.429214i | ||||
\(473\) | 0.957332 | + | 0.552716i | 0.0440182 | + | 0.0254139i | ||||
\(474\) | 34.6470 | − | 22.3457i | 1.59139 | − | 1.02637i | ||||
\(475\) | 4.24105 | − | 2.44857i | 0.194593 | − | 0.112348i | ||||
\(476\) | −9.17604 | + | 3.91437i | −0.420583 | + | 0.179415i | ||||
\(477\) | −21.0545 | + | 15.0959i | −0.964020 | + | 0.691194i | ||||
\(478\) | −33.8491 | −1.54822 | ||||||||
\(479\) | 3.08962 | + | 5.35139i | 0.141169 | + | 0.244511i | 0.927937 | − | 0.372737i | \(-0.121581\pi\) |
−0.786768 | + | 0.617248i | \(0.788247\pi\) | |||||||
\(480\) | −0.552888 | − | 11.2239i | −0.0252358 | − | 0.512299i | ||||
\(481\) | −29.4644 | − | 17.0113i | −1.34346 | − | 0.775648i | ||||
\(482\) | −6.53145 | + | 11.3128i | −0.297499 | + | 0.515284i | ||||
\(483\) | −20.2157 | − | 1.44110i | −0.919848 | − | 0.0655723i | ||||
\(484\) | 7.05926 | + | 12.2270i | 0.320875 | + | 0.555773i | ||||
\(485\) | − | 0.308239i | − | 0.0139964i | ||||||
\(486\) | 27.3674 | + | 7.79556i | 1.24141 | + | 0.353614i | ||||
\(487\) | 11.0928 | 0.502665 | 0.251332 | − | 0.967901i | \(-0.419131\pi\) | ||||
0.251332 | + | 0.967901i | \(0.419131\pi\) | |||||||
\(488\) | −6.29525 | − | 10.9037i | −0.284973 | − | 0.493587i | ||||
\(489\) | 14.9493 | − | 29.1134i | 0.676032 | − | 1.31655i | ||||
\(490\) | 12.2705 | − | 3.56604i | 0.554326 | − | 0.161097i | ||||
\(491\) | −0.777992 | − | 0.449174i | −0.0351103 | − | 0.0202709i | 0.482342 | − | 0.875983i | \(-0.339786\pi\) |
−0.517452 | + | 0.855712i | \(0.673120\pi\) | |||||||
\(492\) | 5.13132 | − | 0.252768i | 0.231338 | − | 0.0113957i | ||||
\(493\) | −0.281935 | + | 0.162775i | −0.0126977 | + | 0.00733102i | ||||
\(494\) | − | 28.2138i | − | 1.26940i | ||||||
\(495\) | 1.54747 | − | 1.10952i | 0.0695536 | − | 0.0498694i | ||||
\(496\) | 1.53959i | 0.0691294i | ||||||||
\(497\) | 20.6096 | − | 27.4518i | 0.924465 | − | 1.23138i | ||||
\(498\) | 11.9617 | − | 7.71472i | 0.536016 | − | 0.345705i | ||||
\(499\) | 17.0653 | − | 29.5579i | 0.763946 | − | 1.32319i | −0.176857 | − | 0.984237i | \(-0.556593\pi\) |
0.940802 | − | 0.338956i | \(-0.110074\pi\) | |||||||
\(500\) | −0.666147 | + | 1.15380i | −0.0297910 | + | 0.0515996i | ||||
\(501\) | −11.6498 | − | 18.0630i | −0.520473 | − | 0.806994i | ||||
\(502\) | 46.7270 | − | 26.9778i | 2.08553 | − | 1.20408i | ||||
\(503\) | −39.5756 | −1.76459 | −0.882294 | − | 0.470698i | \(-0.844002\pi\) | ||||
−0.882294 | + | 0.470698i | \(0.844002\pi\) | |||||||
\(504\) | 9.67213 | + | 0.212294i | 0.430831 | + | 0.00945635i | ||||
\(505\) | 1.97285 | 0.0877908 | ||||||||
\(506\) | 4.43770 | − | 2.56211i | 0.197280 | − | 0.113900i | ||||
\(507\) | −5.25770 | + | 0.258994i | −0.233503 | + | 0.0115023i | ||||
\(508\) | 3.06606 | − | 5.31057i | 0.136034 | − | 0.235618i | ||||
\(509\) | −4.36091 | + | 7.55332i | −0.193294 | + | 0.334795i | −0.946340 | − | 0.323173i | \(-0.895250\pi\) |
0.753046 | + | 0.657968i | \(0.228584\pi\) | |||||||
\(510\) | 7.96023 | + | 4.08747i | 0.352485 | + | 0.180996i | ||||
\(511\) | 10.2611 | − | 13.6677i | 0.453925 | − | 0.604624i | ||||
\(512\) | 19.8040i | 0.875222i | ||||||||
\(513\) | −3.74377 | − | 25.1694i | −0.165291 | − | 1.11126i | ||||
\(514\) | − | 15.8396i | − | 0.698653i | ||||||
\(515\) | −13.9294 | + | 8.04212i | −0.613801 | + | 0.354378i | ||||
\(516\) | −1.83582 | + | 3.57521i | −0.0808175 | + | 0.157390i | ||||
\(517\) | −4.34336 | − | 2.50764i | −0.191021 | − | 0.110286i | ||||
\(518\) | 51.6876 | + | 6.25269i | 2.27102 | + | 0.274727i | ||||
\(519\) | 21.2538 | − | 1.04696i | 0.932939 | − | 0.0459564i | ||||
\(520\) | −1.92342 | − | 3.33145i | −0.0843474 | − | 0.146094i | ||||
\(521\) | −17.4216 | −0.763256 | −0.381628 | − | 0.924316i | \(-0.624636\pi\) | ||||
−0.381628 | + | 0.924316i | \(0.624636\pi\) | |||||||
\(522\) | −0.626893 | + | 0.0619115i | −0.0274383 | + | 0.00270979i | ||||
\(523\) | 13.2690i | 0.580215i | 0.956994 | + | 0.290107i | \(0.0936910\pi\) | ||||
−0.956994 | + | 0.290107i | \(0.906309\pi\) | |||||||
\(524\) | −1.00633 | − | 1.74302i | −0.0439619 | − | 0.0761442i | ||||
\(525\) | −3.79566 | − | 2.56768i | −0.165656 | − | 0.112063i | ||||
\(526\) | −6.12607 | + | 10.6107i | −0.267109 | + | 0.462647i | ||||
\(527\) | −0.771744 | − | 0.445566i | −0.0336177 | − | 0.0194092i | ||||
\(528\) | −4.51732 | + | 2.91346i | −0.196591 | + | 0.126792i | ||||
\(529\) | −1.72016 | − | 2.97941i | −0.0747897 | − | 0.129540i | ||||
\(530\) | −15.7641 | −0.684749 | ||||||||
\(531\) | −45.6807 | + | 4.51139i | −1.98237 | + | 0.195778i | ||||
\(532\) | 6.77321 | + | 15.8777i | 0.293656 | + | 0.688386i | ||||
\(533\) | 6.08516 | − | 3.51327i | 0.263577 | − | 0.152176i | ||||
\(534\) | 1.72717 | + | 35.0625i | 0.0747422 | + | 1.51730i | ||||
\(535\) | −8.72641 | − | 5.03820i | −0.377276 | − | 0.217820i | ||||
\(536\) | −5.07906 | − | 2.93240i | −0.219382 | − | 0.126660i | ||||
\(537\) | 7.10009 | + | 3.64580i | 0.306391 | + | 0.157328i | ||||
\(538\) | −11.2307 | + | 6.48405i | −0.484190 | + | 0.279547i | ||||
\(539\) | −3.20702 | − | 3.07490i | −0.138136 | − | 0.132445i | ||||
\(540\) | 4.30579 | + | 5.42083i | 0.185292 | + | 0.233275i | ||||
\(541\) | −2.60119 | −0.111834 | −0.0559170 | − | 0.998435i | \(-0.517808\pi\) | ||||
−0.0559170 | + | 0.998435i | \(0.517808\pi\) | |||||||
\(542\) | 22.7651 | + | 39.4303i | 0.977845 | + | 1.69368i | ||||
\(543\) | 25.1705 | + | 12.9247i | 1.08017 | + | 0.554654i | ||||
\(544\) | −15.9020 | − | 9.18100i | −0.681791 | − | 0.393632i | ||||
\(545\) | −7.12547 | + | 12.3417i | −0.305221 | + | 0.528659i | ||||
\(546\) | −23.7451 | + | 11.5415i | −1.01620 | + | 0.493932i | ||||
\(547\) | −0.836471 | − | 1.44881i | −0.0357649 | − | 0.0619467i | 0.847589 | − | 0.530653i | \(-0.178053\pi\) |
−0.883354 | + | 0.468707i | \(0.844720\pi\) | |||||||
\(548\) | − | 16.8032i | − | 0.717797i | ||||||
\(549\) | 28.2302 | + | 12.7819i | 1.20483 | + | 0.545518i | ||||
\(550\) | 1.15864 | 0.0494044 | ||||||||
\(551\) | 0.281657 | + | 0.487845i | 0.0119990 | + | 0.0207829i | ||||
\(552\) | −5.06057 | − | 7.84643i | −0.215392 | − | 0.333966i | ||||
\(553\) | −4.14318 | + | 34.2495i | −0.176186 | + | 1.45644i | ||||
\(554\) | −11.6796 | − | 6.74322i | −0.496219 | − | 0.286492i | ||||
\(555\) | −10.1201 | − | 15.6912i | −0.429573 | − | 0.666053i | ||||
\(556\) | 6.48470 | − | 3.74394i | 0.275012 | − | 0.158778i | ||||
\(557\) | 14.5888i | 0.618147i | 0.951038 | + | 0.309073i | \(0.100019\pi\) | ||||
−0.951038 | + | 0.309073i | \(0.899981\pi\) | |||||||
\(558\) | −1.00477 | − | 1.40137i | −0.0425352 | − | 0.0593245i | ||||
\(559\) | 5.49672i | 0.232486i | ||||||||
\(560\) | 10.3455 | + | 7.76697i | 0.437179 | + | 0.328214i | ||||
\(561\) | −0.153078 | − | 3.10756i | −0.00646295 | − | 0.131201i | ||||
\(562\) | −4.81028 | + | 8.33165i | −0.202909 | + | 0.351450i | ||||
\(563\) | 6.16179 | − | 10.6725i | 0.259688 | − | 0.449793i | −0.706470 | − | 0.707743i | \(-0.749713\pi\) |
0.966158 | + | 0.257950i | \(0.0830468\pi\) | |||||||
\(564\) | 8.32901 | − | 16.2205i | 0.350715 | − | 0.683006i | ||||
\(565\) | 0.175863 | − | 0.101534i | 0.00739860 | − | 0.00427158i | ||||
\(566\) | 41.7951 | 1.75678 | ||||||||
\(567\) | −19.6514 | + | 13.4470i | −0.825283 | + | 0.564719i | ||||
\(568\) | 15.8141 | 0.663546 | ||||||||
\(569\) | 21.4923 | − | 12.4086i | 0.901004 | − | 0.520195i | 0.0234780 | − | 0.999724i | \(-0.492526\pi\) |
0.877526 | + | 0.479530i | \(0.159193\pi\) | |||||||
\(570\) | 7.07275 | − | 13.7740i | 0.296245 | − | 0.576928i | ||||
\(571\) | 14.8775 | − | 25.7686i | 0.622605 | − | 1.07838i | −0.366393 | − | 0.930460i | \(-0.619407\pi\) |
0.988999 | − | 0.147924i | \(-0.0472592\pi\) | |||||||
\(572\) | 1.33442 | − | 2.31128i | 0.0557949 | − | 0.0966395i | ||||
\(573\) | 2.06701 | + | 41.9613i | 0.0863505 | + | 1.75296i | ||||
\(574\) | −6.45574 | + | 8.59899i | −0.269457 | + | 0.358915i | ||||
\(575\) | 4.42263i | 0.184436i | ||||||||
\(576\) | −3.60870 | − | 5.03312i | −0.150363 | − | 0.209713i | ||||
\(577\) | − | 37.2085i | − | 1.54901i | −0.632568 | − | 0.774505i | \(-0.717999\pi\) | ||
0.632568 | − | 0.774505i | \(-0.282001\pi\) | |||||||
\(578\) | −14.2126 | + | 8.20564i | −0.591166 | + | 0.341310i | ||||
\(579\) | −12.3295 | − | 19.1169i | −0.512395 | − | 0.794470i | ||||
\(580\) | −0.132721 | − | 0.0766264i | −0.00551093 | − | 0.00318174i | ||||
\(581\) | −1.43041 | + | 11.8244i | −0.0593434 | + | 0.490560i | ||||
\(582\) | −0.528229 | − | 0.819020i | −0.0218958 | − | 0.0339495i | ||||
\(583\) | 2.74058 | + | 4.74683i | 0.113503 | + | 0.196594i | ||||
\(584\) | 7.87356 | 0.325810 | ||||||||
\(585\) | 8.62529 | + | 3.90531i | 0.356612 | + | 0.161465i | ||||
\(586\) | 44.7602i | 1.84903i | ||||||||
\(587\) | −8.94805 | − | 15.4985i | −0.369326 | − | 0.639691i | 0.620135 | − | 0.784495i | \(-0.287078\pi\) |
−0.989460 | + | 0.144805i | \(0.953745\pi\) | |||||||
\(588\) | 10.5922 | − | 12.1956i | 0.436813 | − | 0.502938i | ||||
\(589\) | −0.770984 | + | 1.33538i | −0.0317678 | + | 0.0550235i | ||||
\(590\) | −24.1892 | − | 13.9656i | −0.995853 | − | 0.574956i | ||||
\(591\) | 5.80590 | + | 2.98125i | 0.238823 | + | 0.122632i | ||||
\(592\) | 26.3550 | + | 45.6481i | 1.08318 | + | 1.87613i | ||||
\(593\) | −19.2039 | −0.788610 | −0.394305 | − | 0.918980i | \(-0.629015\pi\) | ||||
−0.394305 | + | 0.918980i | \(0.629015\pi\) | |||||||
\(594\) | 2.21038 | − | 5.60000i | 0.0906931 | − | 0.229771i | ||||
\(595\) | −6.88739 | + | 2.93806i | −0.282356 | + | 0.120449i | ||||
\(596\) | −14.4531 | + | 8.34452i | −0.592023 | + | 0.341805i | ||||
\(597\) | −29.0713 | − | 14.9277i | −1.18981 | − | 0.610952i | ||||
\(598\) | 22.0663 | + | 12.7400i | 0.902359 | + | 0.520977i | ||||
\(599\) | −11.0142 | − | 6.35908i | −0.450030 | − | 0.259825i | 0.257813 | − | 0.966195i | \(-0.416998\pi\) |
−0.707843 | + | 0.706370i | \(0.750331\pi\) | |||||||
\(600\) | −0.103868 | − | 2.10858i | −0.00424041 | − | 0.0860826i | ||||
\(601\) | −26.1187 | + | 15.0797i | −1.06541 | + | 0.615112i | −0.926922 | − | 0.375253i | \(-0.877556\pi\) |
−0.138483 | + | 0.990365i | \(0.544223\pi\) | |||||||
\(602\) | −3.30050 | − | 7.73701i | −0.134518 | − | 0.315337i | ||||
\(603\) | 14.3651 | − | 1.41869i | 0.584994 | − | 0.0577736i | ||||
\(604\) | −11.8497 | −0.482156 | ||||||||
\(605\) | 5.29857 | + | 9.17740i | 0.215418 | + | 0.373114i | ||||
\(606\) | 5.24205 | − | 3.38087i | 0.212944 | − | 0.137339i | ||||
\(607\) | −12.2648 | − | 7.08106i | −0.497811 | − | 0.287411i | 0.229998 | − | 0.973191i | \(-0.426128\pi\) |
−0.727809 | + | 0.685780i | \(0.759461\pi\) | |||||||
\(608\) | −15.8863 | + | 27.5159i | −0.644275 | + | 1.11592i | ||||
\(609\) | 0.295358 | − | 0.436611i | 0.0119685 | − | 0.0176924i | ||||
\(610\) | 9.42819 | + | 16.3301i | 0.381736 | + | 0.661187i | ||||
\(611\) | − | 24.9383i | − | 1.00890i | ||||||
\(612\) | 11.2570 | − | 1.11174i | 0.455039 | − | 0.0449393i | ||||
\(613\) | −15.2883 | −0.617488 | −0.308744 | − | 0.951145i | \(-0.599909\pi\) | ||||
−0.308744 | + | 0.951145i | \(0.599909\pi\) | |||||||
\(614\) | 21.8229 | + | 37.7983i | 0.880700 | + | 1.52542i | ||||
\(615\) | 3.85149 | − | 0.189724i | 0.155307 | − | 0.00765040i | ||||
\(616\) | 0.245814 | − | 2.03201i | 0.00990411 | − | 0.0818721i | ||||
\(617\) | 8.33983 | + | 4.81500i | 0.335749 | + | 0.193845i | 0.658391 | − | 0.752677i | \(-0.271238\pi\) |
−0.322642 | + | 0.946521i | \(0.604571\pi\) | |||||||
\(618\) | −23.2298 | + | 45.2393i | −0.934439 | + | 1.81979i | ||||
\(619\) | 0.588045 | − | 0.339508i | 0.0236355 | − | 0.0136460i | −0.488136 | − | 0.872768i | \(-0.662323\pi\) |
0.511771 | + | 0.859122i | \(0.328990\pi\) | |||||||
\(620\) | − | 0.419501i | − | 0.0168476i | ||||||
\(621\) | 21.3758 | + | 8.43726i | 0.857780 | + | 0.338575i | ||||
\(622\) | 43.7366i | 1.75368i | ||||||||
\(623\) | −23.4919 | − | 17.6367i | −0.941185 | − | 0.706599i | ||||
\(624\) | −23.7773 | − | 12.2093i | −0.951853 | − | 0.488764i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 21.3896 | − | 37.0479i | 0.854902 | − | 1.48073i | ||||
\(627\) | −5.37716 | + | 0.264878i | −0.214743 | + | 0.0105782i | ||||
\(628\) | 1.96386 | − | 1.13383i | 0.0783664 | − | 0.0452449i | ||||
\(629\) | −30.5092 | −1.21648 | ||||||||
\(630\) | −14.4856 | − | 0.317946i | −0.577121 | − | 0.0126673i | ||||
\(631\) | −18.5432 | −0.738192 | −0.369096 | − | 0.929391i | \(-0.620333\pi\) | ||||
−0.369096 | + | 0.929391i | \(0.620333\pi\) | |||||||
\(632\) | −13.7641 | + | 7.94669i | −0.547505 | + | 0.316102i | ||||
\(633\) | −24.3901 | − | 37.8168i | −0.969418 | − | 1.50308i | ||||
\(634\) | 0.0654720 | − | 0.113401i | 0.00260023 | − | 0.00450372i | ||||
\(635\) | 2.30134 | − | 3.98603i | 0.0913258 | − | 0.158181i | ||||
\(636\) | −16.7468 | + | 10.8009i | −0.664055 | + | 0.428284i | ||||
\(637\) | 5.26799 | − | 21.4552i | 0.208725 | − | 0.850087i | ||||
\(638\) | 0.133277i | 0.00527648i | ||||||||
\(639\) | −31.6327 | + | 22.6804i | −1.25137 | + | 0.897221i | ||||
\(640\) | 9.20753i | 0.363960i | ||||||||
\(641\) | −25.0099 | + | 14.4395i | −0.987831 | + | 0.570325i | −0.904625 | − | 0.426208i | \(-0.859849\pi\) |
−0.0832059 | + | 0.996532i | \(0.526516\pi\) | |||||||
\(642\) | −31.8208 | + | 1.56749i | −1.25587 | + | 0.0618638i | ||||
\(643\) | −3.83286 | − | 2.21290i | −0.151153 | − | 0.0872683i | 0.422516 | − | 0.906356i | \(-0.361147\pi\) |
−0.573669 | + | 0.819087i | \(0.694480\pi\) | |||||||
\(644\) | −15.4766 | − | 1.87221i | −0.609863 | − | 0.0737755i | ||||
\(645\) | −1.37794 | + | 2.68350i | −0.0542563 | + | 0.105663i | ||||
\(646\) | −12.6501 | − | 21.9107i | −0.497713 | − | 0.862063i | ||||
\(647\) | 7.06316 | 0.277681 | 0.138841 | − | 0.990315i | \(-0.455662\pi\) | ||||
0.138841 | + | 0.990315i | \(0.455662\pi\) | |||||||
\(648\) | −10.3895 | − | 3.52062i | −0.408139 | − | 0.138303i | ||||
\(649\) | 9.71167i | 0.381216i | ||||||||
\(650\) | 2.88064 | + | 4.98941i | 0.112988 | + | 0.195701i | ||||
\(651\) | 1.43927 | + | 0.102600i | 0.0564093 | + | 0.00402119i | ||||
\(652\) | 12.5869 | − | 21.8011i | 0.492941 | − | 0.853799i | ||||
\(653\) | 40.1784 | + | 23.1970i | 1.57230 | + | 0.907768i | 0.995886 | + | 0.0906102i | \(0.0288817\pi\) |
0.576414 | + | 0.817158i | \(0.304452\pi\) | |||||||
\(654\) | 2.21688 | + | 45.0038i | 0.0866869 | + | 1.75979i | ||||
\(655\) | −0.755338 | − | 1.30828i | −0.0295135 | − | 0.0511189i | ||||
\(656\) | −10.8859 | −0.425025 | ||||||||
\(657\) | −15.7493 | + | 11.2921i | −0.614439 | + | 0.440548i | ||||
\(658\) | 14.9742 | + | 35.1024i | 0.583754 | + | 1.36843i | ||||
\(659\) | −17.1849 | + | 9.92173i | −0.669431 | + | 0.386496i | −0.795861 | − | 0.605480i | \(-0.792981\pi\) |
0.126430 | + | 0.991975i | \(0.459648\pi\) | |||||||
\(660\) | 1.23086 | − | 0.793849i | 0.0479113 | − | 0.0309005i | ||||
\(661\) | 3.50683 | + | 2.02467i | 0.136400 | + | 0.0787505i | 0.566647 | − | 0.823961i | \(-0.308240\pi\) |
−0.430247 | + | 0.902711i | \(0.641574\pi\) | |||||||
\(662\) | 16.7662 | + | 9.67999i | 0.651638 | + | 0.376224i | ||||
\(663\) | 13.0014 | − | 8.38531i | 0.504934 | − | 0.325658i | ||||
\(664\) | −4.75196 | + | 2.74355i | −0.184412 | + | 0.106470i | ||||
\(665\) | 5.08387 | + | 11.9176i | 0.197144 | + | 0.462144i | ||||
\(666\) | −53.7798 | − | 24.3501i | −2.08393 | − | 0.943548i | ||||
\(667\) | −0.508732 | −0.0196982 | ||||||||
\(668\) | −8.26656 | − | 14.3181i | −0.319843 | − | 0.553984i | ||||
\(669\) | −1.97550 | − | 40.1036i | −0.0763771 | − | 1.55049i | ||||
\(670\) | 7.60674 | + | 4.39176i | 0.293874 | + | 0.169668i | ||||
\(671\) | 3.27817 | − | 5.67796i | 0.126552 | − | 0.219195i | ||||
\(672\) | 29.6564 | + | 2.11409i | 1.14402 | + | 0.0815527i | ||||
\(673\) | 2.08333 | + | 3.60844i | 0.0803066 | + | 0.139095i | 0.903382 | − | 0.428838i | \(-0.141077\pi\) |
−0.823075 | + | 0.567933i | \(0.807743\pi\) | |||||||
\(674\) | 27.3790i | 1.05460i | ||||||||
\(675\) | 3.23186 | + | 4.06879i | 0.124394 | + | 0.156608i | ||||
\(676\) | −4.04913 | −0.155736 | ||||||||
\(677\) | 10.5329 | + | 18.2435i | 0.404812 | + | 0.701155i | 0.994300 | − | 0.106622i | \(-0.0340035\pi\) |
−0.589487 | + | 0.807778i | \(0.700670\pi\) | |||||||
\(678\) | 0.293284 | − | 0.571161i | 0.0112635 | − | 0.0219353i | ||||
\(679\) | 0.809622 | + | 0.0979405i | 0.0310705 | + | 0.00375861i | ||||
\(680\) | −2.98743 | − | 1.72479i | −0.114563 | − | 0.0661427i | ||||
\(681\) | −33.7442 | + | 1.66224i | −1.29308 | + | 0.0636970i | ||||
\(682\) | −0.315944 | + | 0.182410i | −0.0120981 | + | 0.00698485i | ||||
\(683\) | 14.6226i | 0.559518i | 0.960070 | + | 0.279759i | \(0.0902546\pi\) | ||||
−0.960070 | + | 0.279759i | \(0.909745\pi\) | |||||||
\(684\) | −1.92369 | − | 19.4786i | −0.0735541 | − | 0.744781i | ||||
\(685\) | − | 12.6122i | − | 0.481888i | ||||||
\(686\) | 5.46770 | + | 33.3629i | 0.208758 | + | 1.27380i | ||||
\(687\) | 33.5210 | − | 21.6195i | 1.27891 | − | 0.824835i | ||||
\(688\) | 4.25793 | − | 7.37495i | 0.162332 | − | 0.281167i | ||||
\(689\) | −13.6274 | + | 23.6034i | −0.519164 | + | 0.899219i | ||||
\(690\) | 7.57905 | + | 11.7513i | 0.288530 | + | 0.447365i | ||||
\(691\) | 9.11482 | − | 5.26245i | 0.346744 | − | 0.200193i | −0.316506 | − | 0.948590i | \(-0.602510\pi\) |
0.663250 | + | 0.748398i | \(0.269176\pi\) | |||||||
\(692\) | 16.3683 | 0.622229 | ||||||||
\(693\) | 2.42258 | + | 4.41713i | 0.0920262 | + | 0.167793i | ||||
\(694\) | 18.8487 | 0.715486 | ||||||||
\(695\) | 4.86731 | − | 2.81014i | 0.184628 | − | 0.106595i | ||||
\(696\) | 0.242549 | − | 0.0119479i | 0.00919378 | − | 0.000452884i | ||||
\(697\) | 3.15046 | − | 5.45676i | 0.119332 | − | 0.206690i | ||||
\(698\) | −11.6103 | + | 20.1096i | −0.439455 | + | 0.761159i | ||||
\(699\) | 28.1196 | + | 14.4390i | 1.06358 | + | 0.546134i | ||||
\(700\) | −2.81891 | − | 2.11631i | −0.106545 | − | 0.0799892i | ||||
\(701\) | 22.2426i | 0.840090i | 0.907503 | + | 0.420045i | \(0.137986\pi\) | ||||
−0.907503 | + | 0.420045i | \(0.862014\pi\) | |||||||
\(702\) | 29.6107 | − | 4.40437i | 1.11758 | − | 0.166232i | ||||
\(703\) | 52.7915i | 1.99107i | ||||||||
\(704\) | −1.13474 | + | 0.655141i | −0.0427670 | + | 0.0246916i | ||||
\(705\) | 6.25163 | − | 12.1749i | 0.235450 | − | 0.458532i | ||||
\(706\) | 8.36944 | + | 4.83210i | 0.314988 | + | 0.181858i | ||||
\(707\) | −0.626858 | + | 5.18190i | −0.0235754 | + | 0.194885i | ||||
\(708\) | −35.2658 | + | 1.73719i | −1.32537 | + | 0.0652874i | ||||
\(709\) | 12.3741 | + | 21.4326i | 0.464721 | + | 0.804920i | 0.999189 | − | 0.0402687i | \(-0.0128214\pi\) |
−0.534468 | + | 0.845189i | \(0.679488\pi\) | |||||||
\(710\) | −23.6843 | −0.888856 | ||||||||
\(711\) | 16.1350 | − | 35.6358i | 0.605109 | − | 1.33645i | ||||
\(712\) | − | 13.5330i | − | 0.507170i | ||||||
\(713\) | −0.696279 | − | 1.20599i | −0.0260758 | − | 0.0451647i | ||||
\(714\) | −13.2655 | + | 19.6096i | −0.496448 | + | 0.733871i | ||||
\(715\) | 1.00159 | − | 1.73481i | 0.0374575 | − | 0.0648783i | ||||
\(716\) | 5.31680 | + | 3.06966i | 0.198698 | + | 0.114719i | ||||
\(717\) | −26.9904 | + | 17.4075i | −1.00798 | + | 0.650096i | ||||
\(718\) | 25.8705 | + | 44.8090i | 0.965477 | + | 1.67226i | ||||
\(719\) | −26.6502 | −0.993885 | −0.496942 | − | 0.867784i | \(-0.665544\pi\) | ||||
−0.496942 | + | 0.867784i | \(0.665544\pi\) | |||||||
\(720\) | −8.54738 | − | 11.9212i | −0.318542 | − | 0.444276i | ||||
\(721\) | −16.6975 | − | 39.1422i | −0.621848 | − | 1.45773i | ||||
\(722\) | −7.87606 | + | 4.54725i | −0.293117 | + | 0.169231i | ||||
\(723\) | 0.609811 | + | 12.3795i | 0.0226791 | + | 0.460398i | ||||
\(724\) | 18.8486 | + | 10.8823i | 0.700503 | + | 0.404436i | ||||
\(725\) | −0.0996181 | − | 0.0575146i | −0.00369973 | − | 0.00213604i | ||||
\(726\) | 29.8061 | + | 15.3050i | 1.10621 | + | 0.568022i | ||||
\(727\) | −17.4130 | + | 10.0534i | −0.645811 | + | 0.372859i | −0.786850 | − | 0.617145i | \(-0.788289\pi\) |
0.141038 | + | 0.990004i | \(0.454956\pi\) | |||||||
\(728\) | 9.36156 | − | 3.99351i | 0.346962 | − | 0.148009i | ||||
\(729\) | 25.8311 | − | 7.85825i | 0.956709 | − | 0.291046i | ||||
\(730\) | −11.7920 | −0.436440 | ||||||||
\(731\) | 2.46455 | + | 4.26872i | 0.0911545 | + | 0.157884i | ||||
\(732\) | 21.2046 | + | 10.8883i | 0.783746 | + | 0.402443i | ||||
\(733\) | 2.85584 | + | 1.64882i | 0.105483 | + | 0.0609005i | 0.551813 | − | 0.833968i | \(-0.313936\pi\) |
−0.446331 | + | 0.894868i | \(0.647269\pi\) | |||||||
\(734\) | 17.5686 | − | 30.4296i | 0.648467 | − | 1.12318i | ||||
\(735\) | 7.95031 | − | 9.15383i | 0.293252 | − | 0.337644i | ||||
\(736\) | −14.3470 | − | 24.8497i | −0.528837 | − | 0.915972i | ||||
\(737\) | − | 3.05402i | − | 0.112496i | ||||||
\(738\) | 9.90862 | − | 7.10440i | 0.364742 | − | 0.261517i | ||||
\(739\) | 44.1618 | 1.62452 | 0.812259 | − | 0.583296i | \(-0.198237\pi\) | ||||
0.812259 | + | 0.583296i | \(0.198237\pi\) | |||||||
\(740\) | −7.18110 | − | 12.4380i | −0.263983 | − | 0.457231i | ||||
\(741\) | −14.5095 | − | 22.4970i | −0.533019 | − | 0.826447i | ||||
\(742\) | 5.00892 | − | 41.4061i | 0.183883 | − | 1.52006i | ||||
\(743\) | 15.6185 | + | 9.01733i | 0.572986 | + | 0.330814i | 0.758341 | − | 0.651858i | \(-0.226010\pi\) |
−0.185355 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(744\) | 0.360289 | + | 0.558629i | 0.0132088 | + | 0.0204803i | ||||
\(745\) | −10.8483 | + | 6.26327i | −0.397451 | + | 0.229468i | ||||
\(746\) | 1.06487i | 0.0389876i | ||||||||
\(747\) | 5.57051 | − | 12.3031i | 0.203814 | − | 0.450145i | ||||
\(748\) | − | 2.39324i | − | 0.0875054i | ||||||
\(749\) | 16.0061 | − | 21.3200i | 0.584849 | − | 0.779015i | ||||
\(750\) | 0.155560 | + | 3.15796i | 0.00568026 | + | 0.115312i | ||||
\(751\) | 13.9337 | − | 24.1338i | 0.508447 | − | 0.880655i | −0.491505 | − | 0.870874i | \(-0.663553\pi\) |
0.999952 | − | 0.00978101i | \(-0.00311344\pi\) | |||||||
\(752\) | −19.3180 | + | 33.4597i | −0.704454 | + | 1.22015i | ||||
\(753\) | 23.3851 | − | 45.5417i | 0.852200 | − | 1.65963i | ||||
\(754\) | −0.573927 | + | 0.331357i | −0.0209012 | + | 0.0120673i | ||||
\(755\) | −8.89418 | −0.323692 | ||||||||
\(756\) | −15.6065 | + | 9.58718i | −0.567603 | + | 0.348683i | ||||
\(757\) | −15.4396 | −0.561162 | −0.280581 | − | 0.959830i | \(-0.590527\pi\) | ||||
−0.280581 | + | 0.959830i | \(0.590527\pi\) | |||||||
\(758\) | −21.7424 | + | 12.5530i | −0.789721 | + | 0.455946i | ||||
\(759\) | 2.22090 | − | 4.32514i | 0.0806136 | − | 0.156993i | ||||
\(760\) | −2.98449 | + | 5.16928i | −0.108259 | + | 0.187510i | ||||
\(761\) | 25.1763 | − | 43.6066i | 0.912639 | − | 1.58074i | 0.102318 | − | 0.994752i | \(-0.467374\pi\) |
0.810321 | − | 0.585986i | \(-0.199293\pi\) | |||||||
\(762\) | −0.715994 | − | 14.5350i | −0.0259377 | − | 0.526549i | ||||
\(763\) | −30.1526 | − | 22.6372i | −1.09160 | − | 0.819523i | ||||
\(764\) | 32.3158i | 1.16915i | ||||||||
\(765\) | 8.44936 | − | 0.834453i | 0.305487 | − | 0.0301697i | ||||
\(766\) | − | 65.6680i | − | 2.37268i | ||||||
\(767\) | −41.8212 | + | 24.1455i | −1.51007 | + | 0.871842i | ||||
\(768\) | 19.6549 | + | 30.4750i | 0.709235 | + | 1.09967i | ||||
\(769\) | 28.8897 | + | 16.6795i | 1.04179 | + | 0.601478i | 0.920340 | − | 0.391120i | \(-0.127912\pi\) |
0.121450 | + | 0.992598i | \(0.461245\pi\) | |||||||
\(770\) | −0.368147 | + | 3.04328i | −0.0132671 | + | 0.109672i | ||||
\(771\) | −8.14580 | − | 12.6301i | −0.293364 | − | 0.454861i | ||||
\(772\) | −8.74888 | − | 15.1535i | −0.314879 | − | 0.545387i | ||||
\(773\) | −5.27400 | −0.189693 | −0.0948463 | − | 0.995492i | \(-0.530236\pi\) | ||||
−0.0948463 | + | 0.995492i | \(0.530236\pi\) | |||||||
\(774\) | 0.937390 | + | 9.49166i | 0.0336938 | + | 0.341171i | ||||
\(775\) | − | 0.314871i | − | 0.0113105i | ||||||
\(776\) | 0.187852 | + | 0.325368i | 0.00674348 | + | 0.0116800i | ||||
\(777\) | 44.4300 | − | 21.5956i | 1.59392 | − | 0.774739i | ||||
\(778\) | 1.59978 | − | 2.77090i | 0.0573549 | − | 0.0993415i | ||||
\(779\) | −9.44209 | − | 5.45139i | −0.338298 | − | 0.195316i | ||||
\(780\) | 6.47875 | + | 3.32675i | 0.231976 | + | 0.119117i | ||||
\(781\) | 4.11750 | + | 7.13173i | 0.147336 | + | 0.255193i | ||||
\(782\) | 22.8488 | 0.817070 | ||||||||
\(783\) | −0.468030 | + | 0.371758i | −0.0167260 | + | 0.0132856i | ||||
\(784\) | −23.6879 | + | 24.7057i | −0.845998 | + | 0.882347i | ||||
\(785\) | 1.47404 | − | 0.851038i | 0.0526108 | − | 0.0303748i | ||||
\(786\) | −4.24900 | − | 2.18181i | −0.151557 | − | 0.0778225i | ||||
\(787\) | −9.49824 | − | 5.48381i | −0.338576 | − | 0.195477i | 0.321066 | − | 0.947057i | \(-0.395959\pi\) |
−0.659642 | + | 0.751580i | \(0.729292\pi\) | |||||||
\(788\) | 4.34767 | + | 2.51013i | 0.154879 | + | 0.0894196i | ||||
\(789\) | 0.571962 | + | 11.6111i | 0.0203624 | + | 0.413367i | ||||
\(790\) | 20.6140 | − | 11.9015i | 0.733413 | − | 0.423436i | ||||
\(791\) | 0.210812 | + | 0.494183i | 0.00749559 | + | 0.0175711i | ||||
\(792\) | −0.957283 | + | 2.11426i | −0.0340156 | + | 0.0751270i | ||||
\(793\) | 32.6012 | 1.15770 | ||||||||
\(794\) | 4.74172 | + | 8.21290i | 0.168277 | + | 0.291465i | ||||
\(795\) | −12.5699 | + | 8.10700i | −0.445809 | + | 0.287526i | ||||
\(796\) | −21.7697 | − | 12.5687i | −0.771606 | − | 0.445487i | ||||
\(797\) | 25.1385 | − | 43.5412i | 0.890452 | − | 1.54231i | 0.0511176 | − | 0.998693i | \(-0.483722\pi\) |
0.839334 | − | 0.543615i | \(-0.182945\pi\) | |||||||
\(798\) | 33.9314 | + | 22.9539i | 1.20116 | + | 0.812558i | ||||
\(799\) | −11.1815 | − | 19.3669i | −0.395573 | − | 0.685153i | ||||
\(800\) | − | 6.48799i | − | 0.229385i | ||||||
\(801\) | 19.4088 | + | 27.0698i | 0.685776 | + | 0.956463i | ||||
\(802\) | 51.3805 | 1.81431 | ||||||||
\(803\) | 2.05003 | + | 3.55075i | 0.0723439 | + | 0.125303i | ||||
\(804\) | 11.0900 | − | 0.546291i | 0.391114 | − | 0.0192662i | ||||
\(805\) | −11.6165 | − | 1.40525i | −0.409428 | − | 0.0495287i | ||||
\(806\) | −1.57102 | − | 0.907028i | −0.0553368 | − | 0.0319487i | ||||
\(807\) | −5.62054 | + | 10.9458i | −0.197852 | + | 0.385312i | ||||
\(808\) | −2.08249 | + | 1.20232i | −0.0732616 | + | 0.0422976i | ||||
\(809\) | 35.3803i | 1.24391i | 0.783055 | + | 0.621953i | \(0.213661\pi\) | ||||
−0.783055 | + | 0.621953i | \(0.786339\pi\) | |||||||
\(810\) | 15.5600 | + | 5.27271i | 0.546724 | + | 0.185264i | ||||
\(811\) | − | 3.52553i | − | 0.123798i | −0.998082 | − | 0.0618991i | \(-0.980284\pi\) | ||
0.998082 | − | 0.0618991i | \(-0.0197157\pi\) | |||||||
\(812\) | 0.243438 | − | 0.324257i | 0.00854299 | − | 0.0113792i | ||||
\(813\) | 38.4301 | + | 19.7334i | 1.34780 | + | 0.692079i | ||||
\(814\) | −6.24507 | + | 10.8168i | −0.218890 | + | 0.379128i | ||||
\(815\) | 9.44753 | − | 16.3636i | 0.330933 | − | 0.573192i | ||||
\(816\) | −23.9396 | + | 1.17926i | −0.838052 | + | 0.0412823i | ||||
\(817\) | 7.38636 | − | 4.26452i | 0.258416 | − | 0.149197i | ||||
\(818\) | −64.0294 | −2.23873 | ||||||||
\(819\) | −12.9983 | + | 21.4143i | −0.454198 | + | 0.748277i | ||||
\(820\) | 2.96616 | 0.103583 | ||||||||
\(821\) | −6.40672 | + | 3.69892i | −0.223596 | + | 0.129093i | −0.607614 | − | 0.794232i | \(-0.707873\pi\) |
0.384018 | + | 0.923326i | \(0.374540\pi\) | |||||||
\(822\) | −21.6135 | − | 33.5118i | −0.753858 | − | 1.16886i | ||||
\(823\) | −0.413321 | + | 0.715893i | −0.0144075 | + | 0.0249545i | −0.873139 | − | 0.487471i | \(-0.837920\pi\) |
0.858732 | + | 0.512425i | \(0.171253\pi\) | |||||||
\(824\) | 9.80227 | − | 16.9780i | 0.341478 | − | 0.591458i | ||||
\(825\) | 0.923868 | − | 0.595851i | 0.0321649 | − | 0.0207449i | ||||
\(826\) | 44.3681 | − | 59.0979i | 1.54376 | − | 2.05628i | ||||
\(827\) | 4.54802i | 0.158150i | 0.996869 | + | 0.0790750i | \(0.0251967\pi\) | ||||
−0.996869 | + | 0.0790750i | \(0.974803\pi\) | |||||||
\(828\) | 16.1030 | + | 7.29105i | 0.559619 | + | 0.253381i | ||||
\(829\) | 5.00576i | 0.173857i | 0.996215 | + | 0.0869286i | \(0.0277052\pi\) | ||||
−0.996215 | + | 0.0869286i | \(0.972295\pi\) | |||||||
\(830\) | 7.11686 | − | 4.10892i | 0.247030 | − | 0.142623i | ||||
\(831\) | −12.7809 | + | 0.629583i | −0.443363 | + | 0.0218400i | ||||
\(832\) | −5.64244 | − | 3.25766i | −0.195616 | − | 0.112939i | ||||
\(833\) | −5.52872 | − | 19.0240i | −0.191559 | − | 0.659142i | ||||
\(834\) | 8.11715 | − | 15.8079i | 0.281074 | − | 0.547383i | ||||
\(835\) | −6.20475 | − | 10.7469i | −0.214724 | − | 0.371913i | ||||
\(836\) | −4.14113 | −0.143224 | ||||||||
\(837\) | −1.52186 | − | 0.600693i | −0.0526030 | − | 0.0207630i | ||||
\(838\) | 19.8010i | 0.684013i | ||||||||
\(839\) | 7.84346 | + | 13.5853i | 0.270786 | + | 0.469016i | 0.969063 | − | 0.246812i | \(-0.0793829\pi\) |
−0.698277 | + | 0.715828i | \(0.746050\pi\) | |||||||
\(840\) | 5.57141 | + | 0.397164i | 0.192232 | + | 0.0137035i | ||||
\(841\) | −14.4934 | + | 25.1033i | −0.499772 | + | 0.865630i | ||||
\(842\) | 32.7886 | + | 18.9305i | 1.12997 | + | 0.652389i | ||||
\(843\) | 0.449113 | + | 9.11723i | 0.0154683 | + | 0.314014i | ||||
\(844\) | −17.3070 | − | 29.9765i | −0.595730 | − | 1.03184i | ||||
\(845\) | −3.03922 | −0.104552 | ||||||||
\(846\) | −4.25288 | − | 43.0631i | −0.146217 | − | 1.48054i | ||||
\(847\) | −25.7889 | + | 11.0012i | −0.886119 | + | 0.378006i | ||||
\(848\) | 36.5679 | − | 21.1125i | 1.25575 | − | 0.725006i | ||||
\(849\) | 33.3264 | − | 21.4939i | 1.14376 | − | 0.737669i | ||||
\(850\) | 4.47417 | + | 2.58316i | 0.153463 | + | 0.0886018i | ||||
\(851\) | −41.2888 | − | 23.8381i | −1.41536 | − | 0.817159i | ||||
\(852\) | −25.1608 | + | 16.2275i | −0.861993 | + | 0.555945i | ||||
\(853\) | 20.9096 | − | 12.0722i | 0.715931 | − | 0.413343i | −0.0973224 | − | 0.995253i | \(-0.531028\pi\) |
0.813253 | + | 0.581910i | \(0.197694\pi\) | |||||||
\(854\) | −45.8884 | + | 19.5754i | −1.57027 | + | 0.669855i | ||||
\(855\) | −1.44389 | − | 14.6203i | −0.0493801 | − | 0.500004i | ||||
\(856\) | 12.2818 | 0.419783 | ||||||||
\(857\) | −16.3837 | − | 28.3774i | −0.559657 | − | 0.969354i | −0.997525 | − | 0.0703148i | \(-0.977600\pi\) |
0.437868 | − | 0.899039i | \(-0.355734\pi\) | |||||||
\(858\) | −0.311617 | − | 6.32598i | −0.0106384 | − | 0.215965i | ||||
\(859\) | −17.9251 | − | 10.3490i | −0.611595 | − | 0.353105i | 0.161994 | − | 0.986792i | \(-0.448207\pi\) |
−0.773589 | + | 0.633687i | \(0.781541\pi\) | |||||||
\(860\) | −1.16018 | + | 2.00950i | −0.0395620 | + | 0.0685234i | ||||
\(861\) | −0.725450 | + | 10.1766i | −0.0247233 | + | 0.346818i | ||||
\(862\) | 9.15679 | + | 15.8600i | 0.311881 | + | 0.540194i | ||||
\(863\) | − | 21.0272i | − | 0.715774i | −0.933765 | − | 0.357887i | \(-0.883497\pi\) | ||
0.933765 | − | 0.357887i | \(-0.116503\pi\) | |||||||
\(864\) | −31.3582 | − | 12.3774i | −1.06683 | − | 0.421089i | ||||
\(865\) | 12.2858 | 0.417729 | ||||||||
\(866\) | −10.8834 | − | 18.8507i | −0.369834 | − | 0.640572i | ||||
\(867\) | −7.11286 | + | 13.8521i | −0.241565 | + | 0.470441i | ||||
\(868\) | 1.10186 | + | 0.133293i | 0.0373996 | + | 0.00452425i | ||||
\(869\) | −7.16747 | − | 4.13814i | −0.243140 | − | 0.140377i | ||||
\(870\) | −0.363257 | + | 0.0178940i | −0.0123156 | + | 0.000606662i | ||||
\(871\) | 13.1515 | − | 7.59300i | 0.445620 | − | 0.257279i | ||||
\(872\) | − | 17.3700i | − | 0.588222i | ||||||
\(873\) | −0.842394 | − | 0.381414i | −0.0285107 | − | 0.0129089i | ||||
\(874\) | − | 39.5363i | − | 1.33733i | ||||||
\(875\) | −2.11583 | − | 1.58847i | −0.0715282 | − | 0.0537002i | ||||
\(876\) | −12.5271 | + | 8.07936i | −0.423250 | + | 0.272976i | ||||
\(877\) | −1.25552 | + | 2.17463i | −0.0423960 | + | 0.0734320i | −0.886445 | − | 0.462834i | \(-0.846832\pi\) |
0.844049 | + | 0.536266i | \(0.180166\pi\) | |||||||
\(878\) | 22.9907 | − | 39.8211i | 0.775900 | − | 1.34390i | ||||
\(879\) | 23.0188 | + | 35.6907i | 0.776405 | + | 1.20382i | ||||
\(880\) | −2.68768 | + | 1.55173i | −0.0906016 | + | 0.0523089i | ||||
\(881\) | 24.5031 | 0.825531 | 0.412766 | − | 0.910837i | \(-0.364563\pi\) | ||||
0.412766 | + | 0.910837i | \(0.364563\pi\) | |||||||
\(882\) | 5.43781 | − | 37.9470i | 0.183100 | − | 1.27774i | ||||
\(883\) | −40.4938 | −1.36273 | −0.681363 | − | 0.731945i | \(-0.738613\pi\) | ||||
−0.681363 | + | 0.731945i | \(0.738613\pi\) | |||||||
\(884\) | 10.3059 | − | 5.95014i | 0.346626 | − | 0.200125i | ||||
\(885\) | −26.4700 | + | 1.30391i | −0.889778 | + | 0.0438303i | ||||
\(886\) | 20.2458 | − | 35.0667i | 0.680171 | − | 1.17809i | ||||
\(887\) | −12.4282 | + | 21.5262i | −0.417297 | + | 0.722779i | −0.995667 | − | 0.0929957i | \(-0.970356\pi\) |
0.578370 | + | 0.815775i | \(0.303689\pi\) | |||||||
\(888\) | 20.2452 | + | 10.3956i | 0.679383 | + | 0.348854i | ||||
\(889\) | 9.73849 | + | 7.31123i | 0.326619 | + | 0.245211i | ||||
\(890\) | 20.2679i | 0.679382i | ||||||||
\(891\) | −1.11740 | − | 5.60203i | −0.0374345 | − | 0.187675i | ||||
\(892\) | − | 30.8851i | − | 1.03411i | ||||||
\(893\) | −33.5115 | + | 19.3479i | −1.12142 | + | 0.647452i | ||||
\(894\) | −18.0916 | + | 35.2328i | −0.605072 | + | 1.17836i | ||||
\(895\) | 3.99071 | + | 2.30404i | 0.133395 | + | 0.0770155i | ||||
\(896\) | −24.1845 | − | 2.92562i | −0.807948 | − | 0.0977380i | ||||
\(897\) | 24.1469 | − | 1.18947i | 0.806242 | − | 0.0397154i | ||||
\(898\) | −22.2010 | − | 38.4532i | −0.740856 | − | 1.28320i | ||||
\(899\) | 0.0362193 | 0.00120798 | ||||||||
\(900\) | 2.32896 | + | 3.24824i | 0.0776319 | + | 0.108275i | ||||
\(901\) | 24.4404i | 0.814227i | ||||||||
\(902\) | −1.28977 | − | 2.23394i | −0.0429445 | − | 0.0743821i | ||||
\(903\) | −6.61065 | − | 4.47196i | −0.219989 | − | 0.148817i | ||||
\(904\) | −0.123757 | + | 0.214353i | −0.00411610 | + | 0.00712929i | ||||
\(905\) | 14.1475 | + | 8.16805i | 0.470278 | + | 0.271515i | ||||
\(906\) | −23.6326 | + | 15.2419i | −0.785142 | + | 0.506379i | ||||
\(907\) | 7.71147 | + | 13.3567i | 0.256055 | + | 0.443500i | 0.965182 | − | 0.261581i | \(-0.0842438\pi\) |
−0.709127 | + | 0.705081i | \(0.750911\pi\) | |||||||
\(908\) | −25.9876 | −0.862428 | ||||||||
\(909\) | 2.44120 | − | 5.39165i | 0.0809695 | − | 0.178830i | ||||
\(910\) | −14.0205 | + | 5.98094i | −0.464775 | + | 0.198266i | ||||
\(911\) | −22.9764 | + | 13.2654i | −0.761243 | + | 0.439504i | −0.829742 | − | 0.558148i | \(-0.811512\pi\) |
0.0684992 | + | 0.997651i | \(0.478179\pi\) | |||||||
\(912\) | 2.04052 | + | 41.4237i | 0.0675685 | + | 1.37168i | ||||
\(913\) | −2.47453 | − | 1.42867i | −0.0818948 | − | 0.0472820i | ||||
\(914\) | −21.6294 | − | 12.4877i | −0.715436 | − | 0.413057i | ||||
\(915\) | 15.9159 | + | 8.17259i | 0.526163 | + | 0.270178i | ||||
\(916\) | 26.5714 | − | 15.3410i | 0.877943 | − | 0.506881i | ||||
\(917\) | 3.67634 | − | 1.56828i | 0.121404 | − | 0.0517891i | ||||
\(918\) | 21.0207 | − | 16.6969i | 0.693787 | − | 0.551078i | ||||
\(919\) | −14.6707 | −0.483943 | −0.241972 | − | 0.970283i | \(-0.577794\pi\) | ||||
−0.241972 | + | 0.970283i | \(0.577794\pi\) | |||||||
\(920\) | −2.69530 | − | 4.66840i | −0.0888615 | − | 0.153913i | ||||
\(921\) | 36.8396 | + | 18.9166i | 1.21390 | + | 0.623324i | ||||
\(922\) | 44.1461 | + | 25.4877i | 1.45387 | + | 0.839394i | ||||
\(923\) | −20.4741 | + | 35.4622i | −0.673914 | + | 1.16725i | ||||
\(924\) | 1.69403 | + | 3.48523i | 0.0557295 | + | 0.114656i | ||||
\(925\) | −5.39002 | − | 9.33580i | −0.177223 | − | 0.306959i | ||||
\(926\) | − | 18.9662i | − | 0.623267i | ||||||
\(927\) | 4.74233 | + | 48.0191i | 0.155759 | + | 1.57715i | ||||
\(928\) | 0.746307 | 0.0244987 | ||||||||
\(929\) | 5.60554 | + | 9.70909i | 0.183912 | + | 0.318545i | 0.943209 | − | 0.332199i | \(-0.107791\pi\) |
−0.759297 | + | 0.650744i | \(0.774457\pi\) | |||||||
\(930\) | −0.539593 | − | 0.836640i | −0.0176940 | − | 0.0274345i | ||||
\(931\) | −32.9181 | + | 9.56659i | −1.07885 | + | 0.313532i | ||||
\(932\) | 21.0570 | + | 12.1572i | 0.689744 | + | 0.398224i | ||||
\(933\) | 22.4924 | + | 34.8745i | 0.736368 | + | 1.14174i | ||||
\(934\) | −21.1802 | + | 12.2284i | −0.693037 | + | 0.400125i | ||||
\(935\) | − | 1.79633i | − | 0.0587462i | ||||||
\(936\) | −11.4846 | + | 1.13421i | −0.375387 | + | 0.0370729i | ||||
\(937\) | − | 9.04669i | − | 0.295543i | −0.989022 | − | 0.147771i | \(-0.952790\pi\) | ||
0.989022 | − | 0.147771i | \(-0.0472099\pi\) | |||||||
\(938\) | −13.9524 | + | 18.5845i | −0.455561 | + | 0.606804i | ||||
\(939\) | −1.99705 | − | 40.5411i | −0.0651713 | − | 1.32301i | ||||
\(940\) | 5.26369 | − | 9.11698i | 0.171683 | − | 0.297363i | ||||
\(941\) | −25.3643 | + | 43.9322i | −0.826851 | + | 1.43215i | 0.0736454 | + | 0.997284i | \(0.476537\pi\) |
−0.900496 | + | 0.434863i | \(0.856797\pi\) | |||||||
\(942\) | 2.45824 | − | 4.78734i | 0.0800937 | − | 0.155980i | ||||
\(943\) | 8.52719 | − | 4.92317i | 0.277683 | − | 0.160321i | ||||
\(944\) | 74.8153 | 2.43503 | ||||||||
\(945\) | −11.7140 | + | 7.19599i | −0.381056 | + | 0.234086i | ||||
\(946\) | 2.01792 | 0.0656082 | ||||||||
\(947\) | −7.30505 | + | 4.21757i | −0.237382 | + | 0.137053i | −0.613973 | − | 0.789327i | \(-0.710430\pi\) |
0.376591 | + | 0.926380i | \(0.377096\pi\) | |||||||
\(948\) | 13.7446 | − | 26.7673i | 0.446405 | − | 0.869361i | ||||
\(949\) | −10.1937 | + | 17.6560i | −0.330901 | + | 0.573137i | ||||
\(950\) | 4.46977 | − | 7.74186i | 0.145018 | − | 0.251179i | ||||
\(951\) | −0.00611281 | − | 0.124093i | −0.000198222 | − | 0.00402400i | ||||
\(952\) | 5.47957 | − | 7.29874i | 0.177594 | − | 0.236554i | ||||
\(953\) | 7.58700i | 0.245767i | 0.992421 | + | 0.122884i | \(0.0392142\pi\) | ||||
−0.992421 | + | 0.122884i | \(0.960786\pi\) | |||||||
\(954\) | −19.5065 | + | 43.0821i | −0.631545 | + | 1.39483i | ||||
\(955\) | 24.2558i | 0.784898i | ||||||||
\(956\) | −21.3947 | + | 12.3522i | −0.691953 | + | 0.399500i | ||||
\(957\) | 0.0685402 | + | 0.106272i | 0.00221559 | + | 0.00343528i | ||||
\(958\) | 9.76873 | + | 5.63998i | 0.315613 | + | 0.182219i | ||||
\(959\) | 33.1273 | + | 4.00743i | 1.06974 | + | 0.129407i | ||||
\(960\) | −1.93799 | − | 3.00486i | −0.0625484 | − | 0.0969814i | ||||
\(961\) | −15.4504 | − | 26.7609i | −0.498401 | − | 0.863256i | ||||
\(962\) | −62.1068 | −2.00240 | ||||||||
\(963\) | −24.5670 | + | 17.6143i | −0.791661 | + | 0.567614i | ||||
\(964\) | 9.53385i | 0.307065i | ||||||||
\(965\) | −6.56678 | − | 11.3740i | −0.211392 | − | 0.366142i | ||||
\(966\) | −33.2743 | + | 16.1733i | −1.07058 | + | 0.520366i | ||||
\(967\) | 10.2508 | − | 17.7549i | 0.329643 | − | 0.570958i | −0.652798 | − | 0.757532i | \(-0.726405\pi\) |
0.982441 | + | 0.186574i | \(0.0597383\pi\) | |||||||
\(968\) | −11.1860 | − | 6.45826i | −0.359533 | − | 0.207576i | ||||
\(969\) | −21.3549 | − | 10.9654i | −0.686018 | − | 0.352261i | ||||
\(970\) | −0.281339 | − | 0.487293i | −0.00903325 | − | 0.0156460i | ||||
\(971\) | 14.4194 | 0.462741 | 0.231370 | − | 0.972866i | \(-0.425679\pi\) | ||||
0.231370 | + | 0.972866i | \(0.425679\pi\) | |||||||
\(972\) | 20.1427 | − | 5.05968i | 0.646076 | − | 0.162289i | ||||
\(973\) | 5.83458 | + | 13.6774i | 0.187048 | + | 0.438477i | ||||
\(974\) | 17.5366 | − | 10.1248i | 0.561909 | − | 0.324418i | ||||
\(975\) | 4.86285 | + | 2.49701i | 0.155736 | + | 0.0799683i | ||||
\(976\) | −43.7410 | − | 25.2539i | −1.40012 | − | 0.808357i | ||||
\(977\) | −7.27578 | − | 4.20067i | −0.232773 | − | 0.134391i | 0.379078 | − | 0.925365i | \(-0.376241\pi\) |
−0.611851 | + | 0.790973i | \(0.709575\pi\) | |||||||
\(978\) | −2.93932 | − | 59.6698i | −0.0939892 | − | 1.90803i | ||||
\(979\) | 6.10300 | − | 3.52357i | 0.195053 | − | 0.112614i | ||||
\(980\) | 6.45440 | − | 6.73172i | 0.206178 | − | 0.215037i | ||||
\(981\) | 24.9118 | + | 34.7449i | 0.795372 | + | 1.10932i | ||||
\(982\) | −1.63990 | −0.0523312 | ||||||||
\(983\) | −1.36690 | − | 2.36754i | −0.0435973 | − | 0.0755127i | 0.843403 | − | 0.537281i | \(-0.180549\pi\) |
−0.887001 | + | 0.461768i | \(0.847215\pi\) | |||||||
\(984\) | −3.94989 | + | 2.54749i | −0.125918 | + | 0.0812112i | ||||
\(985\) | 3.26329 | + | 1.88406i | 0.103977 | + | 0.0600312i | ||||
\(986\) | −0.297139 | + | 0.514660i | −0.00946283 | + | 0.0163901i | ||||
\(987\) | 29.9921 | + | 20.2890i | 0.954660 | + | 0.645806i | ||||
\(988\) | −10.2958 | − | 17.8328i | −0.327553 | − | 0.567338i | ||||
\(989\) | 7.70261i | 0.244929i | ||||||||
\(990\) | 1.43369 | − | 3.16646i | 0.0455657 | − | 0.100637i | ||||
\(991\) | −42.1641 | −1.33939 | −0.669693 | − | 0.742638i | \(-0.733574\pi\) | ||||
−0.669693 | + | 0.742638i | \(0.733574\pi\) | |||||||
\(992\) | 1.02144 | + | 1.76918i | 0.0324307 | + | 0.0561716i | ||||
\(993\) | 18.3471 | − | 0.903775i | 0.582228 | − | 0.0286804i | ||||
\(994\) | 7.52549 | − | 62.2092i | 0.238694 | − | 1.97316i | ||||
\(995\) | −16.3400 | − | 9.43389i | −0.518012 | − | 0.299075i | ||||
\(996\) | 4.74526 | − | 9.24124i | 0.150359 | − | 0.292820i | ||||
\(997\) | −27.5027 | + | 15.8787i | −0.871019 | + | 0.502883i | −0.867687 | − | 0.497111i | \(-0.834394\pi\) |
−0.00333236 | + | 0.999994i | \(0.501061\pi\) | |||||||
\(998\) | − | 62.3038i | − | 1.97219i | ||||||
\(999\) | −55.4052 | + | 8.24112i | −1.75294 | + | 0.260738i |
(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.bl.i.41.9 | ✓ | 24 | |
3.2 | odd | 2 | 945.2.bl.i.881.4 | 24 | |||
7.6 | odd | 2 | 315.2.bl.j.41.9 | yes | 24 | ||
9.2 | odd | 6 | 315.2.bl.j.146.9 | yes | 24 | ||
9.7 | even | 3 | 945.2.bl.j.251.4 | 24 | |||
21.20 | even | 2 | 945.2.bl.j.881.4 | 24 | |||
63.20 | even | 6 | inner | 315.2.bl.i.146.9 | yes | 24 | |
63.34 | odd | 6 | 945.2.bl.i.251.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bl.i.41.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
315.2.bl.i.146.9 | yes | 24 | 63.20 | even | 6 | inner | |
315.2.bl.j.41.9 | yes | 24 | 7.6 | odd | 2 | ||
315.2.bl.j.146.9 | yes | 24 | 9.2 | odd | 6 | ||
945.2.bl.i.251.4 | 24 | 63.34 | odd | 6 | |||
945.2.bl.i.881.4 | 24 | 3.2 | odd | 2 | |||
945.2.bl.j.251.4 | 24 | 9.7 | even | 3 | |||
945.2.bl.j.881.4 | 24 | 21.20 | even | 2 |