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: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 236.6 | ||
Character | \(\chi\) | \(=\) | 315.236 |
Dual form | 315.2.be.b.311.6 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.804799 | + | 0.464651i | −0.569078 | + | 0.328558i | −0.756781 | − | 0.653668i | \(-0.773229\pi\) |
0.187703 | + | 0.982226i | \(0.439896\pi\) | |||||||
\(3\) | 1.68100 | + | 0.417423i | 0.970525 | + | 0.241000i | ||||
\(4\) | −0.568200 | + | 0.984151i | −0.284100 | + | 0.492075i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.54682 | + | 0.445136i | −0.631487 | + | 0.181726i | ||||
\(7\) | −2.32336 | + | 1.26570i | −0.878147 | + | 0.478390i | ||||
\(8\) | − | 2.91466i | − | 1.03049i | ||||||
\(9\) | 2.65152 | + | 1.40338i | 0.883838 | + | 0.467792i | ||||
\(10\) | −0.804799 | + | 0.464651i | −0.254500 | + | 0.146935i | ||||
\(11\) | 5.24269i | 1.58073i | 0.612636 | + | 0.790365i | \(0.290109\pi\) | ||||
−0.612636 | + | 0.790365i | \(0.709891\pi\) | |||||||
\(12\) | −1.36595 | + | 1.41718i | −0.394316 | + | 0.409104i | ||||
\(13\) | 0.516376 | − | 0.298130i | 0.143217 | − | 0.0826863i | −0.426679 | − | 0.904403i | \(-0.640317\pi\) |
0.569896 | + | 0.821717i | \(0.306983\pi\) | |||||||
\(14\) | 1.28173 | − | 2.09819i | 0.342556 | − | 0.560764i | ||||
\(15\) | 1.68100 | + | 0.417423i | 0.434032 | + | 0.107778i | ||||
\(16\) | 0.217899 | + | 0.377413i | 0.0544748 | + | 0.0943532i | ||||
\(17\) | 1.80401 | + | 3.12464i | 0.437536 | + | 0.757835i | 0.997499 | − | 0.0706826i | \(-0.0225178\pi\) |
−0.559962 | + | 0.828518i | \(0.689184\pi\) | |||||||
\(18\) | −2.78602 | + | 0.102593i | −0.656670 | + | 0.0241814i | ||||
\(19\) | −2.80984 | − | 1.62226i | −0.644622 | − | 0.372173i | 0.141771 | − | 0.989900i | \(-0.454720\pi\) |
−0.786393 | + | 0.617727i | \(0.788054\pi\) | |||||||
\(20\) | −0.568200 | + | 0.984151i | −0.127053 | + | 0.220063i | ||||
\(21\) | −4.43390 | + | 1.15782i | −0.967556 | + | 0.252657i | ||||
\(22\) | −2.43602 | − | 4.21931i | −0.519361 | − | 0.899560i | ||||
\(23\) | − | 2.75560i | − | 0.574582i | −0.957843 | − | 0.287291i | \(-0.907245\pi\) | ||
0.957843 | − | 0.287291i | \(-0.0927546\pi\) | |||||||
\(24\) | 1.21665 | − | 4.89954i | 0.248347 | − | 1.00011i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.277052 | + | 0.479869i | −0.0543344 | + | 0.0941100i | ||||
\(27\) | 3.87139 | + | 3.46588i | 0.745050 | + | 0.667009i | ||||
\(28\) | 0.0744906 | − | 3.00571i | 0.0140774 | − | 0.568025i | ||||
\(29\) | 3.53879 | + | 2.04312i | 0.657137 | + | 0.379398i | 0.791185 | − | 0.611576i | \(-0.209464\pi\) |
−0.134048 | + | 0.990975i | \(0.542798\pi\) | |||||||
\(30\) | −1.54682 | + | 0.445136i | −0.282410 | + | 0.0812703i | ||||
\(31\) | −5.53812 | − | 3.19744i | −0.994677 | − | 0.574277i | −0.0880076 | − | 0.996120i | \(-0.528050\pi\) |
−0.906669 | + | 0.421843i | \(0.861383\pi\) | |||||||
\(32\) | 4.69761 | + | 2.71217i | 0.830428 | + | 0.479448i | ||||
\(33\) | −2.18842 | + | 8.81296i | −0.380955 | + | 1.53414i | ||||
\(34\) | −2.90373 | − | 1.67647i | −0.497985 | − | 0.287512i | ||||
\(35\) | −2.32336 | + | 1.26570i | −0.392719 | + | 0.213943i | ||||
\(36\) | −2.88772 | + | 1.81209i | −0.481287 | + | 0.302015i | ||||
\(37\) | 0.988179 | − | 1.71158i | 0.162456 | − | 0.281381i | −0.773293 | − | 0.634049i | \(-0.781392\pi\) |
0.935749 | + | 0.352667i | \(0.114725\pi\) | |||||||
\(38\) | 3.01514 | 0.489121 | ||||||||
\(39\) | 0.992473 | − | 0.285608i | 0.158923 | − | 0.0457339i | ||||
\(40\) | − | 2.91466i | − | 0.460848i | ||||||
\(41\) | 4.89572 | + | 8.47964i | 0.764583 | + | 1.32430i | 0.940467 | + | 0.339886i | \(0.110388\pi\) |
−0.175884 | + | 0.984411i | \(0.556278\pi\) | |||||||
\(42\) | 3.03041 | − | 2.99202i | 0.467603 | − | 0.461679i | ||||
\(43\) | 0.604036 | − | 1.04622i | 0.0921146 | − | 0.159547i | −0.816286 | − | 0.577648i | \(-0.803971\pi\) |
0.908401 | + | 0.418101i | \(0.137304\pi\) | |||||||
\(44\) | −5.15960 | − | 2.97889i | −0.777838 | − | 0.449085i | ||||
\(45\) | 2.65152 | + | 1.40338i | 0.395265 | + | 0.209203i | ||||
\(46\) | 1.28039 | + | 2.21770i | 0.188783 | + | 0.326982i | ||||
\(47\) | −2.86588 | − | 4.96386i | −0.418032 | − | 0.724053i | 0.577709 | − | 0.816242i | \(-0.303947\pi\) |
−0.995741 | + | 0.0921898i | \(0.970613\pi\) | |||||||
\(48\) | 0.208748 | + | 0.725387i | 0.0301301 | + | 0.104701i | ||||
\(49\) | 3.79600 | − | 5.88136i | 0.542285 | − | 0.840194i | ||||
\(50\) | −0.804799 | + | 0.464651i | −0.113816 | + | 0.0657115i | ||||
\(51\) | 1.72824 | + | 6.00554i | 0.242002 | + | 0.840944i | ||||
\(52\) | 0.677589i | 0.0939646i | ||||||||
\(53\) | 8.79935 | − | 5.08031i | 1.20868 | − | 0.697834i | 0.246212 | − | 0.969216i | \(-0.420814\pi\) |
0.962472 | + | 0.271382i | \(0.0874806\pi\) | |||||||
\(54\) | −4.72611 | − | 0.990490i | −0.643143 | − | 0.134789i | ||||
\(55\) | 5.24269i | 0.706924i | ||||||||
\(56\) | 3.68909 | + | 6.77180i | 0.492975 | + | 0.904920i | ||||
\(57\) | −4.04617 | − | 3.89992i | −0.535928 | − | 0.516556i | ||||
\(58\) | −3.79735 | −0.498617 | ||||||||
\(59\) | 0.664164 | − | 1.15037i | 0.0864668 | − | 0.149765i | −0.819549 | − | 0.573010i | \(-0.805776\pi\) |
0.906015 | + | 0.423245i | \(0.139109\pi\) | |||||||
\(60\) | −1.36595 | + | 1.41718i | −0.176343 | + | 0.182957i | ||||
\(61\) | −8.71808 | + | 5.03339i | −1.11624 | + | 0.644459i | −0.940437 | − | 0.339967i | \(-0.889584\pi\) |
−0.175799 | + | 0.984426i | \(0.556251\pi\) | |||||||
\(62\) | 5.94277 | 0.754732 | ||||||||
\(63\) | −7.93668 | + | 0.0954797i | −0.999928 | + | 0.0120293i | ||||
\(64\) | −5.91244 | −0.739054 | ||||||||
\(65\) | 0.516376 | − | 0.298130i | 0.0640485 | − | 0.0369784i | ||||
\(66\) | −2.33371 | − | 8.10951i | −0.287260 | − | 0.998211i | ||||
\(67\) | 4.63278 | − | 8.02422i | 0.565985 | − | 0.980314i | −0.430973 | − | 0.902365i | \(-0.641829\pi\) |
0.996957 | − | 0.0779491i | \(-0.0248372\pi\) | |||||||
\(68\) | −4.10015 | −0.497216 | ||||||||
\(69\) | 1.15025 | − | 4.63215i | 0.138474 | − | 0.557646i | ||||
\(70\) | 1.28173 | − | 2.09819i | 0.153196 | − | 0.250781i | ||||
\(71\) | − | 11.6581i | − | 1.38357i | −0.722105 | − | 0.691784i | \(-0.756825\pi\) | ||
0.722105 | − | 0.691784i | \(-0.243175\pi\) | |||||||
\(72\) | 4.09037 | − | 7.72827i | 0.482054 | − | 0.910785i | ||||
\(73\) | 12.2136 | − | 7.05152i | 1.42949 | − | 0.825318i | 0.432413 | − | 0.901676i | \(-0.357662\pi\) |
0.997081 | + | 0.0763575i | \(0.0243290\pi\) | |||||||
\(74\) | 1.83663i | 0.213504i | ||||||||
\(75\) | 1.68100 | + | 0.417423i | 0.194105 | + | 0.0481999i | ||||
\(76\) | 3.19310 | − | 1.84354i | 0.366274 | − | 0.211468i | ||||
\(77\) | −6.63568 | − | 12.1807i | −0.756206 | − | 1.38811i | ||||
\(78\) | −0.666033 | + | 0.691011i | −0.0754134 | + | 0.0782415i | ||||
\(79\) | 6.48343 | + | 11.2296i | 0.729442 | + | 1.26343i | 0.957119 | + | 0.289695i | \(0.0935537\pi\) |
−0.227677 | + | 0.973737i | \(0.573113\pi\) | |||||||
\(80\) | 0.217899 | + | 0.377413i | 0.0243619 | + | 0.0421960i | ||||
\(81\) | 5.06107 | + | 7.44215i | 0.562341 | + | 0.826906i | ||||
\(82\) | −7.88014 | − | 4.54960i | −0.870215 | − | 0.502419i | ||||
\(83\) | 5.40645 | − | 9.36424i | 0.593435 | − | 1.02786i | −0.400331 | − | 0.916371i | \(-0.631105\pi\) |
0.993766 | − | 0.111489i | \(-0.0355619\pi\) | |||||||
\(84\) | 1.37987 | − | 5.02150i | 0.150556 | − | 0.547890i | ||||
\(85\) | 1.80401 | + | 3.12464i | 0.195672 | + | 0.338914i | ||||
\(86\) | 1.12266i | 0.121060i | ||||||||
\(87\) | 5.09586 | + | 4.91166i | 0.546333 | + | 0.526585i | ||||
\(88\) | 15.2807 | 1.62892 | ||||||||
\(89\) | 4.26740 | − | 7.39135i | 0.452343 | − | 0.783481i | −0.546188 | − | 0.837663i | \(-0.683922\pi\) |
0.998531 | + | 0.0541814i | \(0.0172549\pi\) | |||||||
\(90\) | −2.78602 | + | 0.102593i | −0.293672 | + | 0.0108142i | ||||
\(91\) | −0.822383 | + | 1.34624i | −0.0862092 | + | 0.141124i | ||||
\(92\) | 2.71192 | + | 1.56573i | 0.282737 | + | 0.163239i | ||||
\(93\) | −7.97490 | − | 7.68663i | −0.826958 | − | 0.797067i | ||||
\(94\) | 4.61292 | + | 2.66327i | 0.475786 | + | 0.274695i | ||||
\(95\) | −2.80984 | − | 1.62226i | −0.288284 | − | 0.166441i | ||||
\(96\) | 6.76455 | + | 6.52004i | 0.690404 | + | 0.665449i | ||||
\(97\) | −11.2557 | − | 6.49848i | −1.14284 | − | 0.659820i | −0.195709 | − | 0.980662i | \(-0.562701\pi\) |
−0.947133 | + | 0.320842i | \(0.896034\pi\) | |||||||
\(98\) | −0.322235 | + | 6.49712i | −0.0325507 | + | 0.656309i | ||||
\(99\) | −7.35747 | + | 13.9011i | −0.739453 | + | 1.39711i | ||||
\(100\) | −0.568200 | + | 0.984151i | −0.0568200 | + | 0.0984151i | ||||
\(101\) | 4.15057 | 0.412997 | 0.206498 | − | 0.978447i | \(-0.433793\pi\) | ||||
0.206498 | + | 0.978447i | \(0.433793\pi\) | |||||||
\(102\) | −4.18137 | − | 4.03022i | −0.414017 | − | 0.399052i | ||||
\(103\) | − | 11.5483i | − | 1.13789i | −0.822375 | − | 0.568946i | \(-0.807351\pi\) | ||
0.822375 | − | 0.568946i | \(-0.192649\pi\) | |||||||
\(104\) | −0.868946 | − | 1.50506i | −0.0852072 | − | 0.147583i | ||||
\(105\) | −4.43390 | + | 1.15782i | −0.432704 | + | 0.112992i | ||||
\(106\) | −4.72114 | + | 8.17725i | −0.458557 | + | 0.794245i | ||||
\(107\) | −0.875674 | − | 0.505571i | −0.0846546 | − | 0.0488753i | 0.457075 | − | 0.889428i | \(-0.348897\pi\) |
−0.541730 | + | 0.840553i | \(0.682230\pi\) | |||||||
\(108\) | −5.61067 | + | 1.84072i | −0.539887 | + | 0.177124i | ||||
\(109\) | 3.13405 | + | 5.42833i | 0.300187 | + | 0.519940i | 0.976178 | − | 0.216970i | \(-0.0696175\pi\) |
−0.675991 | + | 0.736910i | \(0.736284\pi\) | |||||||
\(110\) | −2.43602 | − | 4.21931i | −0.232265 | − | 0.402295i | ||||
\(111\) | 2.37558 | − | 2.46467i | 0.225480 | − | 0.233936i | ||||
\(112\) | −0.983951 | − | 0.601070i | −0.0929746 | − | 0.0567958i | ||||
\(113\) | −11.5944 | + | 6.69401i | −1.09071 | + | 0.629719i | −0.933764 | − | 0.357888i | \(-0.883497\pi\) |
−0.156942 | + | 0.987608i | \(0.550163\pi\) | |||||||
\(114\) | 5.06845 | + | 1.25859i | 0.474704 | + | 0.117878i | ||||
\(115\) | − | 2.75560i | − | 0.256961i | ||||||
\(116\) | −4.02148 | + | 2.32180i | −0.373385 | + | 0.215574i | ||||
\(117\) | 1.78757 | − | 0.0658257i | 0.165261 | − | 0.00608559i | ||||
\(118\) | 1.23442i | 0.113637i | ||||||||
\(119\) | −8.14622 | − | 4.97631i | −0.746763 | − | 0.456178i | ||||
\(120\) | 1.21665 | − | 4.89954i | 0.111064 | − | 0.447265i | ||||
\(121\) | −16.4858 | −1.49871 | ||||||||
\(122\) | 4.67753 | − | 8.10172i | 0.423484 | − | 0.733496i | ||||
\(123\) | 4.69010 | + | 16.2978i | 0.422892 | + | 1.46953i | ||||
\(124\) | 6.29352 | − | 3.63357i | 0.565175 | − | 0.326304i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 6.34306 | − | 3.76463i | 0.565085 | − | 0.335379i | ||||
\(127\) | 12.6328 | 1.12098 | 0.560488 | − | 0.828162i | \(-0.310613\pi\) | ||||
0.560488 | + | 0.828162i | \(0.310613\pi\) | |||||||
\(128\) | −4.63690 | + | 2.67711i | −0.409848 | + | 0.236626i | ||||
\(129\) | 1.45210 | − | 1.50656i | 0.127850 | − | 0.132645i | ||||
\(130\) | −0.277052 | + | 0.479869i | −0.0242991 | + | 0.0420873i | ||||
\(131\) | 4.98386 | 0.435442 | 0.217721 | − | 0.976011i | \(-0.430138\pi\) | ||||
0.217721 | + | 0.976011i | \(0.430138\pi\) | |||||||
\(132\) | −7.42982 | − | 7.16125i | −0.646682 | − | 0.623307i | ||||
\(133\) | 8.58157 | + | 0.212678i | 0.744117 | + | 0.0184415i | ||||
\(134\) | 8.61050i | 0.743834i | ||||||||
\(135\) | 3.87139 | + | 3.46588i | 0.333196 | + | 0.298295i | ||||
\(136\) | 9.10725 | − | 5.25807i | 0.780940 | − | 0.450876i | ||||
\(137\) | 12.1794i | 1.04055i | 0.853998 | + | 0.520277i | \(0.174171\pi\) | ||||
−0.853998 | + | 0.520277i | \(0.825829\pi\) | |||||||
\(138\) | 1.22661 | + | 4.26242i | 0.104416 | + | 0.362841i | ||||
\(139\) | −14.5703 | + | 8.41218i | −1.23584 | + | 0.713512i | −0.968241 | − | 0.250019i | \(-0.919563\pi\) |
−0.267598 | + | 0.963531i | \(0.586230\pi\) | |||||||
\(140\) | 0.0744906 | − | 3.00571i | 0.00629560 | − | 0.254029i | ||||
\(141\) | −2.74552 | − | 9.54052i | −0.231214 | − | 0.803457i | ||||
\(142\) | 5.41697 | + | 9.38246i | 0.454582 | + | 0.787358i | ||||
\(143\) | 1.56300 | + | 2.70720i | 0.130705 | + | 0.226387i | ||||
\(144\) | 0.0481112 | + | 1.30651i | 0.00400927 | + | 0.108876i | ||||
\(145\) | 3.53879 | + | 2.04312i | 0.293881 | + | 0.169672i | ||||
\(146\) | −6.55299 | + | 11.3501i | −0.542329 | + | 0.939342i | ||||
\(147\) | 8.83609 | − | 8.30202i | 0.728788 | − | 0.684739i | ||||
\(148\) | 1.12297 | + | 1.94503i | 0.0923072 | + | 0.159881i | ||||
\(149\) | − | 4.74043i | − | 0.388351i | −0.980967 | − | 0.194175i | \(-0.937797\pi\) | ||
0.980967 | − | 0.194175i | \(-0.0622031\pi\) | |||||||
\(150\) | −1.54682 | + | 0.445136i | −0.126297 | + | 0.0363452i | ||||
\(151\) | −17.8242 | −1.45051 | −0.725257 | − | 0.688478i | \(-0.758279\pi\) | ||||
−0.725257 | + | 0.688478i | \(0.758279\pi\) | |||||||
\(152\) | −4.72834 | + | 8.18973i | −0.383519 | + | 0.664275i | ||||
\(153\) | 0.398317 | + | 10.8167i | 0.0322021 | + | 0.874480i | ||||
\(154\) | 11.0001 | + | 6.71970i | 0.886416 | + | 0.541489i | ||||
\(155\) | −5.53812 | − | 3.19744i | −0.444833 | − | 0.256824i | ||||
\(156\) | −0.282841 | + | 1.13903i | −0.0226454 | + | 0.0911950i | ||||
\(157\) | 5.13244 | + | 2.96322i | 0.409613 | + | 0.236490i | 0.690624 | − | 0.723214i | \(-0.257336\pi\) |
−0.281010 | + | 0.959705i | \(0.590670\pi\) | |||||||
\(158\) | −10.4357 | − | 6.02506i | −0.830220 | − | 0.479328i | ||||
\(159\) | 16.9123 | − | 4.86694i | 1.34124 | − | 0.385973i | ||||
\(160\) | 4.69761 | + | 2.71217i | 0.371379 | + | 0.214416i | ||||
\(161\) | 3.48776 | + | 6.40224i | 0.274874 | + | 0.504567i | ||||
\(162\) | −7.53114 | − | 3.63780i | −0.591702 | − | 0.285813i | ||||
\(163\) | −7.24254 | + | 12.5444i | −0.567279 | + | 0.982556i | 0.429554 | + | 0.903041i | \(0.358671\pi\) |
−0.996834 | + | 0.0795155i | \(0.974663\pi\) | |||||||
\(164\) | −11.1270 | −0.868871 | ||||||||
\(165\) | −2.18842 | + | 8.81296i | −0.170368 | + | 0.686088i | ||||
\(166\) | 10.0484i | 0.779910i | ||||||||
\(167\) | 6.15227 | + | 10.6560i | 0.476077 | + | 0.824589i | 0.999624 | − | 0.0274071i | \(-0.00872503\pi\) |
−0.523547 | + | 0.851997i | \(0.675392\pi\) | |||||||
\(168\) | 3.37465 | + | 12.9233i | 0.260360 | + | 0.997055i | ||||
\(169\) | −6.32224 | + | 10.9504i | −0.486326 | + | 0.842341i | ||||
\(170\) | −2.90373 | − | 1.67647i | −0.222706 | − | 0.128579i | ||||
\(171\) | −5.17369 | − | 8.24472i | −0.395642 | − | 0.630490i | ||||
\(172\) | 0.686426 | + | 1.18892i | 0.0523395 | + | 0.0906546i | ||||
\(173\) | −1.12513 | − | 1.94878i | −0.0855418 | − | 0.148163i | 0.820080 | − | 0.572249i | \(-0.193929\pi\) |
−0.905622 | + | 0.424086i | \(0.860595\pi\) | |||||||
\(174\) | −6.38335 | − | 1.58510i | −0.483920 | − | 0.120166i | ||||
\(175\) | −2.32336 | + | 1.26570i | −0.175629 | + | 0.0956781i | ||||
\(176\) | −1.97866 | + | 1.14238i | −0.149147 | + | 0.0861101i | ||||
\(177\) | 1.59665 | − | 1.65653i | 0.120011 | − | 0.124512i | ||||
\(178\) | 7.93139i | 0.594483i | ||||||||
\(179\) | −11.4279 | + | 6.59789i | −0.854159 | + | 0.493149i | −0.862052 | − | 0.506820i | \(-0.830821\pi\) |
0.00789264 | + | 0.999969i | \(0.497488\pi\) | |||||||
\(180\) | −2.88772 | + | 1.81209i | −0.215238 | + | 0.135065i | ||||
\(181\) | − | 6.74629i | − | 0.501448i | −0.968059 | − | 0.250724i | \(-0.919331\pi\) | ||
0.968059 | − | 0.250724i | \(-0.0806687\pi\) | |||||||
\(182\) | 0.0363214 | − | 1.46557i | 0.00269232 | − | 0.108635i | ||||
\(183\) | −16.7561 | + | 4.82199i | −1.23865 | + | 0.356452i | ||||
\(184\) | −8.03163 | −0.592099 | ||||||||
\(185\) | 0.988179 | − | 1.71158i | 0.0726523 | − | 0.125838i | ||||
\(186\) | 9.98978 | + | 2.48065i | 0.732486 | + | 0.181890i | ||||
\(187\) | −16.3815 | + | 9.45786i | −1.19793 | + | 0.691627i | ||||
\(188\) | 6.51357 | 0.475051 | ||||||||
\(189\) | −13.3814 | − | 3.15245i | −0.973354 | − | 0.229307i | ||||
\(190\) | 3.01514 | 0.218741 | ||||||||
\(191\) | 8.50532 | − | 4.91055i | 0.615424 | − | 0.355315i | −0.159662 | − | 0.987172i | \(-0.551040\pi\) |
0.775085 | + | 0.631857i | \(0.217707\pi\) | |||||||
\(192\) | −9.93880 | − | 2.46799i | −0.717271 | − | 0.178112i | ||||
\(193\) | −4.68248 | + | 8.11029i | −0.337052 | + | 0.583792i | −0.983877 | − | 0.178847i | \(-0.942763\pi\) |
0.646825 | + | 0.762639i | \(0.276097\pi\) | |||||||
\(194\) | 12.0781 | 0.867156 | ||||||||
\(195\) | 0.992473 | − | 0.285608i | 0.0710725 | − | 0.0204528i | ||||
\(196\) | 3.63126 | + | 7.07762i | 0.259376 | + | 0.505544i | ||||
\(197\) | 4.31693i | 0.307569i | 0.988104 | + | 0.153784i | \(0.0491461\pi\) | ||||
−0.988104 | + | 0.153784i | \(0.950854\pi\) | |||||||
\(198\) | −0.537863 | − | 14.6062i | −0.0382242 | − | 1.03802i | ||||
\(199\) | 14.8590 | − | 8.57887i | 1.05333 | − | 0.608140i | 0.129749 | − | 0.991547i | \(-0.458583\pi\) |
0.923579 | + | 0.383407i | \(0.125249\pi\) | |||||||
\(200\) | − | 2.91466i | − | 0.206098i | ||||||
\(201\) | 11.1372 | − | 11.5549i | 0.785558 | − | 0.815018i | ||||
\(202\) | −3.34037 | + | 1.92856i | −0.235028 | + | 0.135693i | ||||
\(203\) | −10.8079 | − | 0.267852i | −0.758564 | − | 0.0187995i | ||||
\(204\) | −6.89235 | − | 1.71150i | −0.482561 | − | 0.119829i | ||||
\(205\) | 4.89572 | + | 8.47964i | 0.341932 | + | 0.592243i | ||||
\(206\) | 5.36594 | + | 9.29408i | 0.373863 | + | 0.647549i | ||||
\(207\) | 3.86714 | − | 7.30651i | 0.268785 | − | 0.507837i | ||||
\(208\) | 0.225036 | + | 0.129925i | 0.0156034 | + | 0.00900864i | ||||
\(209\) | 8.50502 | − | 14.7311i | 0.588305 | − | 1.01897i | ||||
\(210\) | 3.03041 | − | 2.99202i | 0.209118 | − | 0.206469i | ||||
\(211\) | 10.0158 | + | 17.3479i | 0.689519 | + | 1.19428i | 0.971994 | + | 0.235007i | \(0.0755113\pi\) |
−0.282475 | + | 0.959275i | \(0.591155\pi\) | |||||||
\(212\) | 11.5465i | 0.793018i | ||||||||
\(213\) | 4.86638 | − | 19.5973i | 0.333439 | − | 1.34279i | ||||
\(214\) | 0.939655 | 0.0642335 | ||||||||
\(215\) | 0.604036 | − | 1.04622i | 0.0411949 | − | 0.0713517i | ||||
\(216\) | 10.1019 | − | 11.2838i | 0.687344 | − | 0.767765i | ||||
\(217\) | 16.9141 | + | 0.419182i | 1.14820 | + | 0.0284559i | ||||
\(218\) | −5.04455 | − | 2.91247i | −0.341660 | − | 0.197258i | ||||
\(219\) | 23.4745 | − | 6.75536i | 1.58626 | − | 0.456485i | ||||
\(220\) | −5.15960 | − | 2.97889i | −0.347860 | − | 0.200837i | ||||
\(221\) | 1.86309 | + | 1.07566i | 0.125325 | + | 0.0723565i | ||||
\(222\) | −0.766653 | + | 3.08738i | −0.0514544 | + | 0.207211i | ||||
\(223\) | −13.5808 | − | 7.84086i | −0.909435 | − | 0.525063i | −0.0291859 | − | 0.999574i | \(-0.509291\pi\) |
−0.880249 | + | 0.474511i | \(0.842625\pi\) | |||||||
\(224\) | −14.3470 | − | 0.355563i | −0.958601 | − | 0.0237571i | ||||
\(225\) | 2.65152 | + | 1.40338i | 0.176768 | + | 0.0935584i | ||||
\(226\) | 6.22075 | − | 10.7747i | 0.413798 | − | 0.716720i | ||||
\(227\) | −4.29396 | −0.285000 | −0.142500 | − | 0.989795i | \(-0.545514\pi\) | ||||
−0.142500 | + | 0.989795i | \(0.545514\pi\) | |||||||
\(228\) | 6.13714 | − | 1.76611i | 0.406442 | − | 0.116964i | ||||
\(229\) | − | 8.42278i | − | 0.556593i | −0.960495 | − | 0.278297i | \(-0.910230\pi\) | ||
0.960495 | − | 0.278297i | \(-0.0897698\pi\) | |||||||
\(230\) | 1.28039 | + | 2.21770i | 0.0844264 | + | 0.146231i | ||||
\(231\) | −6.07009 | − | 23.2456i | −0.399382 | − | 1.52945i | ||||
\(232\) | 5.95501 | − | 10.3144i | 0.390965 | − | 0.677172i | ||||
\(233\) | −13.0808 | − | 7.55221i | −0.856953 | − | 0.494762i | 0.00603784 | − | 0.999982i | \(-0.498078\pi\) |
−0.862991 | + | 0.505220i | \(0.831411\pi\) | |||||||
\(234\) | −1.40804 | + | 0.883570i | −0.0920468 | + | 0.0577608i | ||||
\(235\) | −2.86588 | − | 4.96386i | −0.186950 | − | 0.323806i | ||||
\(236\) | 0.754755 | + | 1.30727i | 0.0491304 | + | 0.0850963i | ||||
\(237\) | 6.21113 | + | 21.5833i | 0.403456 | + | 1.40199i | ||||
\(238\) | 8.86831 | + | 0.219784i | 0.574847 | + | 0.0142465i | ||||
\(239\) | −7.72892 | + | 4.46229i | −0.499942 | + | 0.288642i | −0.728690 | − | 0.684844i | \(-0.759870\pi\) |
0.228748 | + | 0.973486i | \(0.426537\pi\) | |||||||
\(240\) | 0.208748 | + | 0.725387i | 0.0134746 | + | 0.0468235i | ||||
\(241\) | − | 30.4936i | − | 1.96426i | −0.188194 | − | 0.982132i | \(-0.560263\pi\) | ||
0.188194 | − | 0.982132i | \(-0.439737\pi\) | |||||||
\(242\) | 13.2677 | − | 7.66014i | 0.852883 | − | 0.492412i | ||||
\(243\) | 5.40112 | + | 14.6229i | 0.346482 | + | 0.938057i | ||||
\(244\) | − | 11.4399i | − | 0.732363i | ||||||
\(245\) | 3.79600 | − | 5.88136i | 0.242517 | − | 0.375746i | ||||
\(246\) | −11.3474 | − | 10.9372i | −0.723483 | − | 0.697332i | ||||
\(247\) | −1.93458 | −0.123094 | ||||||||
\(248\) | −9.31944 | + | 16.1417i | −0.591785 | + | 1.02500i | ||||
\(249\) | 12.9971 | − | 13.4845i | 0.823657 | − | 0.854546i | ||||
\(250\) | −0.804799 | + | 0.464651i | −0.0508999 | + | 0.0293871i | ||||
\(251\) | −9.76019 | −0.616058 | −0.308029 | − | 0.951377i | \(-0.599669\pi\) | ||||
−0.308029 | + | 0.951377i | \(0.599669\pi\) | |||||||
\(252\) | 4.41565 | − | 7.86514i | 0.278160 | − | 0.495457i | ||||
\(253\) | 14.4467 | 0.908259 | ||||||||
\(254\) | −10.1668 | + | 5.86982i | −0.637924 | + | 0.368305i | ||||
\(255\) | 1.72824 | + | 6.00554i | 0.108227 | + | 0.376082i | ||||
\(256\) | 8.40028 | − | 14.5497i | 0.525018 | − | 0.909357i | ||||
\(257\) | −10.4201 | −0.649987 | −0.324993 | − | 0.945716i | \(-0.605362\pi\) | ||||
−0.324993 | + | 0.945716i | \(0.605362\pi\) | |||||||
\(258\) | −0.468626 | + | 1.88719i | −0.0291754 | + | 0.117492i | ||||
\(259\) | −0.129550 | + | 5.22735i | −0.00804982 | + | 0.324811i | ||||
\(260\) | 0.677589i | 0.0420223i | ||||||||
\(261\) | 6.51589 | + | 10.3836i | 0.403324 | + | 0.642731i | ||||
\(262\) | −4.01100 | + | 2.31575i | −0.247801 | + | 0.143068i | ||||
\(263\) | − | 23.1446i | − | 1.42716i | −0.700575 | − | 0.713579i | \(-0.747073\pi\) | ||
0.700575 | − | 0.713579i | \(-0.252927\pi\) | |||||||
\(264\) | 25.6868 | + | 6.37850i | 1.58091 | + | 0.392570i | ||||
\(265\) | 8.79935 | − | 5.08031i | 0.540540 | − | 0.312081i | ||||
\(266\) | −7.00526 | + | 3.81627i | −0.429520 | + | 0.233991i | ||||
\(267\) | 10.2588 | − | 10.6435i | 0.627829 | − | 0.651374i | ||||
\(268\) | 5.26469 | + | 9.11871i | 0.321592 | + | 0.557014i | ||||
\(269\) | 15.6437 | + | 27.0957i | 0.953815 | + | 1.65206i | 0.737056 | + | 0.675831i | \(0.236215\pi\) |
0.216759 | + | 0.976225i | \(0.430451\pi\) | |||||||
\(270\) | −4.72611 | − | 0.990490i | −0.287622 | − | 0.0602793i | ||||
\(271\) | −16.0145 | − | 9.24600i | −0.972814 | − | 0.561654i | −0.0727211 | − | 0.997352i | \(-0.523168\pi\) |
−0.900093 | + | 0.435698i | \(0.856502\pi\) | |||||||
\(272\) | −0.786185 | + | 1.36171i | −0.0476695 | + | 0.0825659i | ||||
\(273\) | −1.94438 | + | 1.91975i | −0.117679 | + | 0.116188i | ||||
\(274\) | −5.65915 | − | 9.80193i | −0.341882 | − | 0.592156i | ||||
\(275\) | 5.24269i | 0.316146i | ||||||||
\(276\) | 3.90517 | + | 3.76401i | 0.235063 | + | 0.226567i | ||||
\(277\) | −17.4674 | −1.04952 | −0.524758 | − | 0.851252i | \(-0.675844\pi\) | ||||
−0.524758 | + | 0.851252i | \(0.675844\pi\) | |||||||
\(278\) | 7.81745 | − | 13.5402i | 0.468859 | − | 0.812088i | ||||
\(279\) | −10.1972 | − | 16.2501i | −0.610491 | − | 0.972870i | ||||
\(280\) | 3.68909 | + | 6.77180i | 0.220465 | + | 0.404693i | ||||
\(281\) | 17.7776 | + | 10.2639i | 1.06052 | + | 0.612292i | 0.925576 | − | 0.378561i | \(-0.123581\pi\) |
0.134945 | + | 0.990853i | \(0.456914\pi\) | |||||||
\(282\) | 6.64260 | + | 6.40249i | 0.395561 | + | 0.381263i | ||||
\(283\) | −19.8142 | − | 11.4397i | −1.17783 | − | 0.680021i | −0.222319 | − | 0.974974i | \(-0.571363\pi\) |
−0.955512 | + | 0.294953i | \(0.904696\pi\) | |||||||
\(284\) | 11.4734 | + | 6.62415i | 0.680819 | + | 0.393071i | ||||
\(285\) | −4.04617 | − | 3.89992i | −0.239674 | − | 0.231011i | ||||
\(286\) | −2.51580 | − | 1.45250i | −0.148763 | − | 0.0858881i | ||||
\(287\) | −22.1072 | − | 13.5047i | −1.30495 | − | 0.797158i | ||||
\(288\) | 8.64959 | + | 13.7839i | 0.509682 | + | 0.812222i | ||||
\(289\) | 1.99110 | − | 3.44869i | 0.117124 | − | 0.202864i | ||||
\(290\) | −3.79735 | −0.222988 | ||||||||
\(291\) | −16.2082 | − | 15.6223i | −0.950141 | − | 0.915797i | ||||
\(292\) | 16.0267i | 0.937891i | ||||||||
\(293\) | −6.87701 | − | 11.9113i | −0.401759 | − | 0.695868i | 0.592179 | − | 0.805806i | \(-0.298268\pi\) |
−0.993938 | + | 0.109939i | \(0.964934\pi\) | |||||||
\(294\) | −3.25373 | + | 10.7871i | −0.189761 | + | 0.629119i | ||||
\(295\) | 0.664164 | − | 1.15037i | 0.0386691 | − | 0.0669769i | ||||
\(296\) | −4.98866 | − | 2.88020i | −0.289960 | − | 0.167409i | ||||
\(297\) | −18.1705 | + | 20.2965i | −1.05436 | + | 1.17772i | ||||
\(298\) | 2.20264 | + | 3.81509i | 0.127596 | + | 0.221002i | ||||
\(299\) | −0.821525 | − | 1.42292i | −0.0475100 | − | 0.0822898i | ||||
\(300\) | −1.36595 | + | 1.41718i | −0.0788632 | + | 0.0818207i | ||||
\(301\) | −0.0791887 | + | 3.19528i | −0.00456436 | + | 0.184173i | ||||
\(302\) | 14.3449 | − | 8.28203i | 0.825457 | − | 0.476578i | ||||
\(303\) | 6.97710 | + | 1.73254i | 0.400824 | + | 0.0995320i | ||||
\(304\) | − | 1.41396i | − | 0.0810962i | ||||||
\(305\) | −8.71808 | + | 5.03339i | −0.499196 | + | 0.288211i | ||||
\(306\) | −5.34656 | − | 8.52020i | −0.305643 | − | 0.487068i | ||||
\(307\) | 21.7512i | 1.24141i | 0.784046 | + | 0.620703i | \(0.213153\pi\) | ||||
−0.784046 | + | 0.620703i | \(0.786847\pi\) | |||||||
\(308\) | 15.7580 | + | 0.390531i | 0.897895 | + | 0.0222526i | ||||
\(309\) | 4.82055 | − | 19.4127i | 0.274231 | − | 1.10435i | ||||
\(310\) | 5.94277 | 0.337526 | ||||||||
\(311\) | −5.74473 | + | 9.95016i | −0.325754 | + | 0.564222i | −0.981665 | − | 0.190616i | \(-0.938951\pi\) |
0.655911 | + | 0.754838i | \(0.272285\pi\) | |||||||
\(312\) | −0.832451 | − | 2.89272i | −0.0471283 | − | 0.163768i | ||||
\(313\) | 24.5684 | − | 14.1846i | 1.38869 | − | 0.801758i | 0.395519 | − | 0.918458i | \(-0.370565\pi\) |
0.993167 | + | 0.116699i | \(0.0372314\pi\) | |||||||
\(314\) | −5.50744 | −0.310803 | ||||||||
\(315\) | −7.93668 | + | 0.0954797i | −0.447181 | + | 0.00537967i | ||||
\(316\) | −14.7355 | −0.828938 | ||||||||
\(317\) | −11.7960 | + | 6.81041i | −0.662528 | + | 0.382511i | −0.793240 | − | 0.608909i | \(-0.791607\pi\) |
0.130711 | + | 0.991420i | \(0.458274\pi\) | |||||||
\(318\) | −11.3496 | + | 11.7752i | −0.636454 | + | 0.660322i | ||||
\(319\) | −10.7115 | + | 18.5528i | −0.599727 | + | 1.03876i | ||||
\(320\) | −5.91244 | −0.330515 | ||||||||
\(321\) | −1.26097 | − | 1.21539i | −0.0703805 | − | 0.0678365i | ||||
\(322\) | −5.78175 | − | 3.53192i | −0.322204 | − | 0.196826i | ||||
\(323\) | − | 11.7063i | − | 0.651356i | ||||||
\(324\) | −10.1999 | + | 0.752226i | −0.566661 | + | 0.0417903i | ||||
\(325\) | 0.516376 | − | 0.298130i | 0.0286434 | − | 0.0165373i | ||||
\(326\) | − | 13.4610i | − | 0.745536i | ||||||
\(327\) | 3.00242 | + | 10.4332i | 0.166034 | + | 0.576959i | ||||
\(328\) | 24.7153 | − | 14.2694i | 1.36467 | − | 0.787893i | ||||
\(329\) | 12.9412 | + | 7.90547i | 0.713473 | + | 0.435842i | ||||
\(330\) | −2.33371 | − | 8.10951i | −0.128466 | − | 0.446414i | ||||
\(331\) | 11.5126 | + | 19.9404i | 0.632789 | + | 1.09602i | 0.986979 | + | 0.160849i | \(0.0514232\pi\) |
−0.354190 | + | 0.935173i | \(0.615244\pi\) | |||||||
\(332\) | 6.14388 | + | 10.6415i | 0.337189 | + | 0.584029i | ||||
\(333\) | 5.02216 | − | 3.15148i | 0.275212 | − | 0.172700i | ||||
\(334\) | −9.90268 | − | 5.71731i | −0.541850 | − | 0.312837i | ||||
\(335\) | 4.63278 | − | 8.02422i | 0.253116 | − | 0.438410i | ||||
\(336\) | −1.40312 | − | 1.42112i | −0.0765464 | − | 0.0775286i | ||||
\(337\) | 5.15757 | + | 8.93317i | 0.280951 | + | 0.486621i | 0.971619 | − | 0.236551i | \(-0.0760169\pi\) |
−0.690668 | + | 0.723172i | \(0.742684\pi\) | |||||||
\(338\) | − | 11.7505i | − | 0.639144i | ||||||
\(339\) | −22.2844 | + | 6.41286i | −1.21032 | + | 0.348299i | ||||
\(340\) | −4.10015 | −0.222362 | ||||||||
\(341\) | 16.7632 | − | 29.0347i | 0.907777 | − | 1.57232i | ||||
\(342\) | 7.99469 | + | 4.23138i | 0.432304 | + | 0.228807i | ||||
\(343\) | −1.37542 | + | 18.4691i | −0.0742655 | + | 0.997239i | ||||
\(344\) | −3.04938 | − | 1.76056i | −0.164411 | − | 0.0949230i | ||||
\(345\) | 1.15025 | − | 4.63215i | 0.0619274 | − | 0.249387i | ||||
\(346\) | 1.81100 | + | 1.04558i | 0.0973600 | + | 0.0562108i | ||||
\(347\) | 21.6894 | + | 12.5224i | 1.16435 | + | 0.672237i | 0.952343 | − | 0.305031i | \(-0.0986667\pi\) |
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(348\) | −7.72928 | + | 2.22429i | −0.414333 | + | 0.119234i | ||||
\(349\) | −2.42311 | − | 1.39898i | −0.129706 | − | 0.0748859i | 0.433743 | − | 0.901037i | \(-0.357193\pi\) |
−0.563449 | + | 0.826151i | \(0.690526\pi\) | |||||||
\(350\) | 1.28173 | − | 2.09819i | 0.0685112 | − | 0.112153i | ||||
\(351\) | 3.03237 | + | 0.635519i | 0.161856 | + | 0.0339215i | ||||
\(352\) | −14.2190 | + | 24.6281i | −0.757878 | + | 1.31268i | ||||
\(353\) | −0.787634 | −0.0419215 | −0.0209608 | − | 0.999780i | \(-0.506673\pi\) | ||||
−0.0209608 | + | 0.999780i | \(0.506673\pi\) | |||||||
\(354\) | −0.515274 | + | 2.07505i | −0.0273865 | + | 0.110288i | ||||
\(355\) | − | 11.6581i | − | 0.618750i | ||||||
\(356\) | 4.84946 | + | 8.39952i | 0.257021 | + | 0.445174i | ||||
\(357\) | −11.6166 | − | 11.7656i | −0.614813 | − | 0.622702i | ||||
\(358\) | 6.13142 | − | 10.6199i | 0.324056 | − | 0.561281i | ||||
\(359\) | 3.14705 | + | 1.81695i | 0.166095 | + | 0.0958950i | 0.580743 | − | 0.814087i | \(-0.302762\pi\) |
−0.414648 | + | 0.909982i | \(0.636095\pi\) | |||||||
\(360\) | 4.09037 | − | 7.72827i | 0.215581 | − | 0.407315i | ||||
\(361\) | −4.23653 | − | 7.33788i | −0.222975 | − | 0.386204i | ||||
\(362\) | 3.13467 | + | 5.42941i | 0.164755 | + | 0.285363i | ||||
\(363\) | −27.7126 | − | 6.88156i | −1.45454 | − | 0.361188i | ||||
\(364\) | −0.857625 | − | 1.57428i | −0.0449518 | − | 0.0825148i | ||||
\(365\) | 12.2136 | − | 7.05152i | 0.639289 | − | 0.369094i | ||||
\(366\) | 11.2448 | − | 11.6665i | 0.587774 | − | 0.609817i | ||||
\(367\) | 12.4626i | 0.650545i | 0.945620 | + | 0.325272i | \(0.105456\pi\) | ||||
−0.945620 | + | 0.325272i | \(0.894544\pi\) | |||||||
\(368\) | 1.04000 | − | 0.600443i | 0.0542136 | − | 0.0313002i | ||||
\(369\) | 1.08095 | + | 29.3544i | 0.0562722 | + | 1.52813i | ||||
\(370\) | 1.83663i | 0.0954819i | ||||||||
\(371\) | −14.0139 | + | 22.9407i | −0.727565 | + | 1.19102i | ||||
\(372\) | 12.0961 | − | 3.48096i | 0.627155 | − | 0.180479i | ||||
\(373\) | 10.2662 | 0.531562 | 0.265781 | − | 0.964033i | \(-0.414370\pi\) | ||||
0.265781 | + | 0.964033i | \(0.414370\pi\) | |||||||
\(374\) | 8.78920 | − | 15.2233i | 0.454479 | − | 0.787180i | ||||
\(375\) | 1.68100 | + | 0.417423i | 0.0868064 | + | 0.0215557i | ||||
\(376\) | −14.4679 | + | 8.35307i | −0.746127 | + | 0.430777i | ||||
\(377\) | 2.43646 | 0.125484 | ||||||||
\(378\) | 12.2341 | − | 3.68059i | 0.629256 | − | 0.189309i | ||||
\(379\) | −21.1937 | −1.08864 | −0.544322 | − | 0.838876i | \(-0.683213\pi\) | ||||
−0.544322 | + | 0.838876i | \(0.683213\pi\) | |||||||
\(380\) | 3.19310 | − | 1.84354i | 0.163803 | − | 0.0945715i | ||||
\(381\) | 21.2357 | + | 5.27321i | 1.08794 | + | 0.270155i | ||||
\(382\) | −4.56338 | + | 7.90401i | −0.233483 | + | 0.404404i | ||||
\(383\) | −6.97284 | −0.356296 | −0.178148 | − | 0.984004i | \(-0.557011\pi\) | ||||
−0.178148 | + | 0.984004i | \(0.557011\pi\) | |||||||
\(384\) | −8.91211 | + | 2.56468i | −0.454794 | + | 0.130878i | ||||
\(385\) | −6.63568 | − | 12.1807i | −0.338186 | − | 0.620784i | ||||
\(386\) | − | 8.70287i | − | 0.442964i | ||||||
\(387\) | 3.06985 | − | 1.92638i | 0.156049 | − | 0.0979234i | ||||
\(388\) | 12.7910 | − | 7.38486i | 0.649362 | − | 0.374910i | ||||
\(389\) | − | 18.9856i | − | 0.962610i | −0.876553 | − | 0.481305i | \(-0.840163\pi\) | ||
0.876553 | − | 0.481305i | \(-0.159837\pi\) | |||||||
\(390\) | −0.666033 | + | 0.691011i | −0.0337259 | + | 0.0349907i | ||||
\(391\) | 8.61023 | − | 4.97112i | 0.435438 | − | 0.251400i | ||||
\(392\) | −17.1422 | − | 11.0640i | −0.865810 | − | 0.558818i | ||||
\(393\) | 8.37787 | + | 2.08038i | 0.422607 | + | 0.104941i | ||||
\(394\) | −2.00587 | − | 3.47426i | −0.101054 | − | 0.175031i | ||||
\(395\) | 6.48343 | + | 11.2296i | 0.326217 | + | 0.565024i | ||||
\(396\) | −9.50024 | − | 15.1394i | −0.477405 | − | 0.760786i | ||||
\(397\) | −20.5199 | − | 11.8472i | −1.02987 | − | 0.594593i | −0.112919 | − | 0.993604i | \(-0.536020\pi\) |
−0.916946 | + | 0.399011i | \(0.869353\pi\) | |||||||
\(398\) | −7.97235 | + | 13.8085i | −0.399618 | + | 0.692158i | ||||
\(399\) | 14.3368 | + | 3.93966i | 0.717740 | + | 0.197230i | ||||
\(400\) | 0.217899 | + | 0.377413i | 0.0108950 | + | 0.0188706i | ||||
\(401\) | − | 27.1825i | − | 1.35743i | −0.734403 | − | 0.678714i | \(-0.762538\pi\) | ||
0.734403 | − | 0.678714i | \(-0.237462\pi\) | |||||||
\(402\) | −3.59423 | + | 14.4742i | −0.179264 | + | 0.721910i | ||||
\(403\) | −3.81300 | −0.189939 | ||||||||
\(404\) | −2.35835 | + | 4.08478i | −0.117332 | + | 0.203226i | ||||
\(405\) | 5.06107 | + | 7.44215i | 0.251486 | + | 0.369803i | ||||
\(406\) | 8.82262 | − | 4.80632i | 0.437859 | − | 0.238533i | ||||
\(407\) | 8.97326 | + | 5.18072i | 0.444788 | + | 0.256799i | ||||
\(408\) | 17.5041 | − | 5.03724i | 0.866583 | − | 0.249380i | ||||
\(409\) | 3.00100 | + | 1.73263i | 0.148390 | + | 0.0856729i | 0.572357 | − | 0.820005i | \(-0.306029\pi\) |
−0.423967 | + | 0.905678i | \(0.639363\pi\) | |||||||
\(410\) | −7.88014 | − | 4.54960i | −0.389172 | − | 0.224689i | ||||
\(411\) | −5.08395 | + | 20.4735i | −0.250773 | + | 1.00988i | ||||
\(412\) | 11.3653 | + | 6.56176i | 0.559928 | + | 0.323275i | ||||
\(413\) | −0.0870715 | + | 3.51335i | −0.00428451 | + | 0.172880i | ||||
\(414\) | 0.282705 | + | 7.67713i | 0.0138942 | + | 0.377311i | ||||
\(415\) | 5.40645 | − | 9.36424i | 0.265392 | − | 0.459673i | ||||
\(416\) | 3.23431 | 0.158575 | ||||||||
\(417\) | −28.0041 | + | 8.05887i | −1.37137 | + | 0.394645i | ||||
\(418\) | 15.8075i | 0.773168i | ||||||||
\(419\) | −0.596980 | − | 1.03400i | −0.0291644 | − | 0.0505142i | 0.851075 | − | 0.525044i | \(-0.175951\pi\) |
−0.880239 | + | 0.474530i | \(0.842618\pi\) | |||||||
\(420\) | 1.37987 | − | 5.02150i | 0.0673308 | − | 0.245024i | ||||
\(421\) | 15.3249 | − | 26.5435i | 0.746889 | − | 1.29365i | −0.202417 | − | 0.979299i | \(-0.564880\pi\) |
0.949307 | − | 0.314351i | \(-0.101787\pi\) | |||||||
\(422\) | −16.1215 | − | 9.30773i | −0.784781 | − | 0.453093i | ||||
\(423\) | −0.632775 | − | 17.1837i | −0.0307666 | − | 0.835498i | ||||
\(424\) | −14.8074 | − | 25.6471i | −0.719109 | − | 1.24553i | ||||
\(425\) | 1.80401 | + | 3.12464i | 0.0875073 | + | 0.151567i | ||||
\(426\) | 5.18946 | + | 18.0331i | 0.251430 | + | 0.873705i | ||||
\(427\) | 13.8845 | − | 22.7289i | 0.671917 | − | 1.09993i | ||||
\(428\) | 0.995115 | − | 0.574530i | 0.0481007 | − | 0.0277710i | ||||
\(429\) | 1.49736 | + | 5.20323i | 0.0722930 | + | 0.251214i | ||||
\(430\) | 1.12266i | 0.0541396i | ||||||||
\(431\) | −21.2265 | + | 12.2551i | −1.02244 | + | 0.590307i | −0.914811 | − | 0.403883i | \(-0.867660\pi\) |
−0.107632 | + | 0.994191i | \(0.534327\pi\) | |||||||
\(432\) | −0.464493 | + | 2.21633i | −0.0223479 | + | 0.106633i | ||||
\(433\) | 21.7966i | 1.04748i | 0.851879 | + | 0.523739i | \(0.175463\pi\) | ||||
−0.851879 | + | 0.523739i | \(0.824537\pi\) | |||||||
\(434\) | −13.8072 | + | 7.52177i | −0.662766 | + | 0.361057i | ||||
\(435\) | 5.09586 | + | 4.91166i | 0.244328 | + | 0.235496i | ||||
\(436\) | −7.12306 | −0.341133 | ||||||||
\(437\) | −4.47030 | + | 7.74279i | −0.213844 | + | 0.370388i | ||||
\(438\) | −15.7534 | + | 16.3442i | −0.752725 | + | 0.780954i | ||||
\(439\) | 0.662694 | − | 0.382607i | 0.0316287 | − | 0.0182608i | −0.484102 | − | 0.875011i | \(-0.660854\pi\) |
0.515731 | + | 0.856751i | \(0.327520\pi\) | |||||||
\(440\) | 15.2807 | 0.728477 | ||||||||
\(441\) | 18.3189 | − | 10.2673i | 0.872329 | − | 0.488919i | ||||
\(442\) | −1.99922 | −0.0950932 | ||||||||
\(443\) | 0.478086 | − | 0.276023i | 0.0227145 | − | 0.0131142i | −0.488600 | − | 0.872508i | \(-0.662492\pi\) |
0.511314 | + | 0.859394i | \(0.329159\pi\) | |||||||
\(444\) | 1.07580 | + | 3.73835i | 0.0510553 | + | 0.177414i | ||||
\(445\) | 4.26740 | − | 7.39135i | 0.202294 | − | 0.350383i | ||||
\(446\) | 14.5730 | 0.690053 | ||||||||
\(447\) | 1.97876 | − | 7.96865i | 0.0935924 | − | 0.376904i | ||||
\(448\) | 13.7367 | − | 7.48338i | 0.648999 | − | 0.353557i | ||||
\(449\) | 38.0738i | 1.79681i | 0.439164 | + | 0.898407i | \(0.355275\pi\) | ||||
−0.439164 | + | 0.898407i | \(0.644725\pi\) | |||||||
\(450\) | −2.78602 | + | 0.102593i | −0.131334 | + | 0.00483627i | ||||
\(451\) | −44.4561 | + | 25.6667i | −2.09336 | + | 1.20860i | ||||
\(452\) | − | 15.2141i | − | 0.715613i | ||||||
\(453\) | −29.9625 | − | 7.44025i | −1.40776 | − | 0.349573i | ||||
\(454\) | 3.45577 | − | 1.99519i | 0.162187 | − | 0.0936389i | ||||
\(455\) | −0.822383 | + | 1.34624i | −0.0385539 | + | 0.0631127i | ||||
\(456\) | −11.3669 | + | 11.7932i | −0.532305 | + | 0.552268i | ||||
\(457\) | −15.2716 | − | 26.4512i | −0.714375 | − | 1.23733i | −0.963200 | − | 0.268786i | \(-0.913378\pi\) |
0.248825 | − | 0.968549i | \(-0.419956\pi\) | |||||||
\(458\) | 3.91365 | + | 6.77864i | 0.182873 | + | 0.316745i | ||||
\(459\) | −3.84558 | + | 18.3492i | −0.179496 | + | 0.856466i | ||||
\(460\) | 2.71192 | + | 1.56573i | 0.126444 | + | 0.0730025i | ||||
\(461\) | 16.1726 | − | 28.0117i | 0.753232 | − | 1.30464i | −0.193016 | − | 0.981196i | \(-0.561827\pi\) |
0.946248 | − | 0.323441i | \(-0.104840\pi\) | |||||||
\(462\) | 15.6863 | + | 15.8875i | 0.729791 | + | 0.739154i | ||||
\(463\) | −0.0238247 | − | 0.0412655i | −0.00110723 | − | 0.00191777i | 0.865471 | − | 0.500959i | \(-0.167019\pi\) |
−0.866578 | + | 0.499041i | \(0.833686\pi\) | |||||||
\(464\) | 1.78078i | 0.0826707i | ||||||||
\(465\) | −7.97490 | − | 7.68663i | −0.369827 | − | 0.356459i | ||||
\(466\) | 14.0366 | 0.650231 | ||||||||
\(467\) | 8.92449 | − | 15.4577i | 0.412976 | − | 0.715296i | −0.582237 | − | 0.813019i | \(-0.697823\pi\) |
0.995214 | + | 0.0977230i | \(0.0311559\pi\) | |||||||
\(468\) | −0.950912 | + | 1.79664i | −0.0439559 | + | 0.0830495i | ||||
\(469\) | −0.607355 | + | 24.5069i | −0.0280450 | + | 1.13162i | ||||
\(470\) | 4.61292 | + | 2.66327i | 0.212778 | + | 0.122847i | ||||
\(471\) | 7.39071 | + | 7.12356i | 0.340546 | + | 0.328236i | ||||
\(472\) | −3.35292 | − | 1.93581i | −0.154331 | − | 0.0891030i | ||||
\(473\) | 5.48501 | + | 3.16677i | 0.252201 | + | 0.145608i | ||||
\(474\) | −15.0274 | − | 14.4842i | −0.690232 | − | 0.665282i | ||||
\(475\) | −2.80984 | − | 1.62226i | −0.128924 | − | 0.0744345i | ||||
\(476\) | 9.52612 | − | 5.18957i | 0.436629 | − | 0.237863i | ||||
\(477\) | 30.4612 | − | 1.12171i | 1.39472 | − | 0.0513596i | ||||
\(478\) | 4.14681 | − | 7.18249i | 0.189671 | − | 0.328520i | ||||
\(479\) | −0.813442 | −0.0371671 | −0.0185835 | − | 0.999827i | \(-0.505916\pi\) | ||||
−0.0185835 | + | 0.999827i | \(0.505916\pi\) | |||||||
\(480\) | 6.76455 | + | 6.52004i | 0.308758 | + | 0.297598i | ||||
\(481\) | − | 1.17842i | − | 0.0537314i | ||||||
\(482\) | 14.1689 | + | 24.5412i | 0.645374 | + | 1.11782i | ||||
\(483\) | 3.19048 | + | 12.2180i | 0.145172 | + | 0.555940i | ||||
\(484\) | 9.36722 | − | 16.2245i | 0.425783 | − | 0.737478i | ||||
\(485\) | −11.2557 | − | 6.49848i | −0.511095 | − | 0.295081i | ||||
\(486\) | −11.1413 | − | 9.25882i | −0.505381 | − | 0.419988i | ||||
\(487\) | −1.30232 | − | 2.25568i | −0.0590137 | − | 0.102215i | 0.835009 | − | 0.550236i | \(-0.185462\pi\) |
−0.894023 | + | 0.448021i | \(0.852129\pi\) | |||||||
\(488\) | 14.6706 | + | 25.4102i | 0.664107 | + | 1.15027i | ||||
\(489\) | −17.4110 | + | 18.0640i | −0.787354 | + | 0.816882i | ||||
\(490\) | −0.322235 | + | 6.49712i | −0.0145571 | + | 0.293510i | ||||
\(491\) | 14.8669 | − | 8.58341i | 0.670934 | − | 0.387364i | −0.125496 | − | 0.992094i | \(-0.540052\pi\) |
0.796430 | + | 0.604730i | \(0.206719\pi\) | |||||||
\(492\) | −18.7044 | − | 4.64466i | −0.843262 | − | 0.209398i | ||||
\(493\) | 14.7432i | 0.664002i | ||||||||
\(494\) | 1.55695 | − | 0.898903i | 0.0700503 | − | 0.0404436i | ||||
\(495\) | −7.35747 | + | 13.9011i | −0.330694 | + | 0.624807i | ||||
\(496\) | − | 2.78688i | − | 0.125135i | ||||||
\(497\) | 14.7557 | + | 27.0861i | 0.661885 | + | 1.21498i | ||||
\(498\) | −4.19445 | + | 16.8914i | −0.187958 | + | 0.756923i | ||||
\(499\) | −3.58235 | −0.160368 | −0.0801840 | − | 0.996780i | \(-0.525551\pi\) | ||||
−0.0801840 | + | 0.996780i | \(0.525551\pi\) | |||||||
\(500\) | −0.568200 | + | 0.984151i | −0.0254107 | + | 0.0440125i | ||||
\(501\) | 5.89388 | + | 20.4809i | 0.263319 | + | 0.915019i | ||||
\(502\) | 7.85498 | − | 4.53508i | 0.350585 | − | 0.202410i | ||||
\(503\) | −9.90167 | −0.441494 | −0.220747 | − | 0.975331i | \(-0.570849\pi\) | ||||
−0.220747 | + | 0.975331i | \(0.570849\pi\) | |||||||
\(504\) | 0.278291 | + | 23.1327i | 0.0123961 | + | 1.03041i | ||||
\(505\) | 4.15057 | 0.184698 | ||||||||
\(506\) | −11.6267 | + | 6.71269i | −0.516870 | + | 0.298415i | ||||
\(507\) | −15.1986 | + | 15.7686i | −0.674995 | + | 0.700309i | ||||
\(508\) | −7.17793 | + | 12.4325i | −0.318469 | + | 0.551605i | ||||
\(509\) | 33.4933 | 1.48457 | 0.742283 | − | 0.670086i | \(-0.233743\pi\) | ||||
0.742283 | + | 0.670086i | \(0.233743\pi\) | |||||||
\(510\) | −4.18137 | − | 4.03022i | −0.185154 | − | 0.178461i | ||||
\(511\) | −19.4514 | + | 31.8420i | −0.860481 | + | 1.40861i | ||||
\(512\) | 4.90433i | 0.216743i | ||||||||
\(513\) | −5.25543 | − | 16.0190i | −0.232033 | − | 0.707256i | ||||
\(514\) | 8.38606 | − | 4.84170i | 0.369893 | − | 0.213558i | ||||
\(515\) | − | 11.5483i | − | 0.508880i | ||||||
\(516\) | 0.657596 | + | 2.28511i | 0.0289491 | + | 0.100596i | ||||
\(517\) | 26.0240 | − | 15.0249i | 1.14453 | − | 0.660796i | ||||
\(518\) | −2.32463 | − | 4.26716i | −0.102138 | − | 0.187488i | ||||
\(519\) | −1.07787 | − | 3.74554i | −0.0473133 | − | 0.164411i | ||||
\(520\) | −0.868946 | − | 1.50506i | −0.0381058 | − | 0.0660012i | ||||
\(521\) | 1.46842 | + | 2.54339i | 0.0643329 | + | 0.111428i | 0.896398 | − | 0.443250i | \(-0.146175\pi\) |
−0.832065 | + | 0.554678i | \(0.812841\pi\) | |||||||
\(522\) | −10.0687 | − | 5.32912i | −0.440697 | − | 0.233249i | ||||
\(523\) | −6.60049 | − | 3.81080i | −0.288619 | − | 0.166634i | 0.348700 | − | 0.937234i | \(-0.386623\pi\) |
−0.637319 | + | 0.770600i | \(0.719957\pi\) | |||||||
\(524\) | −2.83183 | + | 4.90487i | −0.123709 | + | 0.214270i | ||||
\(525\) | −4.43390 | + | 1.15782i | −0.193511 | + | 0.0505314i | ||||
\(526\) | 10.7542 | + | 18.6268i | 0.468904 | + | 0.812165i | ||||
\(527\) | − | 23.0728i | − | 1.00507i | ||||||
\(528\) | −3.80298 | + | 1.09440i | −0.165503 | + | 0.0476276i | ||||
\(529\) | 15.4067 | 0.669856 | ||||||||
\(530\) | −4.72114 | + | 8.17725i | −0.205073 | + | 0.355197i | ||||
\(531\) | 3.37544 | − | 2.11814i | 0.146481 | − | 0.0919195i | ||||
\(532\) | −5.08535 | + | 8.32472i | −0.220478 | + | 0.360922i | ||||
\(533\) | 5.05606 | + | 2.91912i | 0.219002 | + | 0.126441i | ||||
\(534\) | −3.31075 | + | 13.3327i | −0.143270 | + | 0.576961i | ||||
\(535\) | −0.875674 | − | 0.505571i | −0.0378587 | − | 0.0218577i | ||||
\(536\) | −23.3879 | − | 13.5030i | −1.01020 | − | 0.583240i | ||||
\(537\) | −21.9644 | + | 6.32078i | −0.947832 | + | 0.272762i | ||||
\(538\) | −25.1801 | − | 14.5377i | −1.08559 | − | 0.626767i | ||||
\(539\) | 30.8342 | + | 19.9012i | 1.32812 | + | 0.857207i | ||||
\(540\) | −5.61067 | + | 1.84072i | −0.241445 | + | 0.0792121i | ||||
\(541\) | 2.00276 | − | 3.46888i | 0.0861053 | − | 0.149139i | −0.819756 | − | 0.572712i | \(-0.805891\pi\) |
0.905862 | + | 0.423574i | \(0.139225\pi\) | |||||||
\(542\) | 17.1846 | 0.738143 | ||||||||
\(543\) | 2.81606 | − | 11.3405i | 0.120849 | − | 0.486668i | ||||
\(544\) | 19.5711i | 0.839103i | ||||||||
\(545\) | 3.13405 | + | 5.42833i | 0.134248 | + | 0.232524i | ||||
\(546\) | 0.672821 | − | 2.44846i | 0.0287941 | − | 0.104785i | ||||
\(547\) | 19.4542 | − | 33.6956i | 0.831800 | − | 1.44072i | −0.0648089 | − | 0.997898i | \(-0.520644\pi\) |
0.896609 | − | 0.442823i | \(-0.146023\pi\) | |||||||
\(548\) | −11.9863 | − | 6.92031i | −0.512030 | − | 0.295621i | ||||
\(549\) | −30.1799 | + | 1.11135i | −1.28805 | + | 0.0474313i | ||||
\(550\) | −2.43602 | − | 4.21931i | −0.103872 | − | 0.179912i | ||||
\(551\) | −6.62896 | − | 11.4817i | −0.282403 | − | 0.489137i | ||||
\(552\) | −13.5012 | − | 3.35259i | −0.574647 | − | 0.142696i | ||||
\(553\) | −29.2767 | − | 17.8844i | −1.24497 | − | 0.760521i | ||||
\(554\) | 14.0578 | − | 8.11625i | 0.597257 | − | 0.344826i | ||||
\(555\) | 2.37558 | − | 2.46467i | 0.100838 | − | 0.104619i | ||||
\(556\) | − | 19.1192i | − | 0.810834i | ||||||
\(557\) | −6.65261 | + | 3.84089i | −0.281880 | + | 0.162744i | −0.634274 | − | 0.773108i | \(-0.718701\pi\) |
0.352394 | + | 0.935852i | \(0.385368\pi\) | |||||||
\(558\) | 15.7573 | + | 8.33994i | 0.667061 | + | 0.353058i | ||||
\(559\) | − | 0.720324i | − | 0.0304665i | ||||||
\(560\) | −0.983951 | − | 0.601070i | −0.0415795 | − | 0.0253998i | ||||
\(561\) | −31.4852 | + | 9.06064i | −1.32931 | + | 0.382540i | ||||
\(562\) | −19.0765 | −0.804693 | ||||||||
\(563\) | 17.3061 | − | 29.9751i | 0.729367 | − | 1.26330i | −0.227784 | − | 0.973712i | \(-0.573148\pi\) |
0.957151 | − | 0.289589i | \(-0.0935187\pi\) | |||||||
\(564\) | 10.9493 | + | 2.71892i | 0.461049 | + | 0.114487i | ||||
\(565\) | −11.5944 | + | 6.69401i | −0.487779 | + | 0.281619i | ||||
\(566\) | 21.2619 | 0.893704 | ||||||||
\(567\) | −21.1782 | − | 10.8850i | −0.889402 | − | 0.457126i | ||||
\(568\) | −33.9795 | −1.42575 | ||||||||
\(569\) | 9.90288 | − | 5.71743i | 0.415150 | − | 0.239687i | −0.277850 | − | 0.960625i | \(-0.589622\pi\) |
0.693000 | + | 0.720937i | \(0.256288\pi\) | |||||||
\(570\) | 5.06845 | + | 1.25859i | 0.212294 | + | 0.0527166i | ||||
\(571\) | 16.7798 | − | 29.0635i | 0.702215 | − | 1.21627i | −0.265473 | − | 0.964118i | \(-0.585528\pi\) |
0.967687 | − | 0.252153i | \(-0.0811387\pi\) | |||||||
\(572\) | −3.55239 | −0.148533 | ||||||||
\(573\) | 16.3472 | − | 4.70431i | 0.682915 | − | 0.196525i | ||||
\(574\) | 24.0668 | + | 0.596449i | 1.00453 | + | 0.0248953i | ||||
\(575\) | − | 2.75560i | − | 0.114916i | ||||||
\(576\) | −15.6769 | − | 8.29737i | −0.653205 | − | 0.345724i | ||||
\(577\) | 11.4056 | − | 6.58501i | 0.474820 | − | 0.274137i | −0.243435 | − | 0.969917i | \(-0.578274\pi\) |
0.718255 | + | 0.695780i | \(0.244941\pi\) | |||||||
\(578\) | 3.70067i | 0.153927i | ||||||||
\(579\) | −11.2567 | + | 11.6788i | −0.467811 | + | 0.485355i | ||||
\(580\) | −4.02148 | + | 2.32180i | −0.166983 | + | 0.0964076i | ||||
\(581\) | −0.708782 | + | 28.5995i | −0.0294052 | + | 1.18651i | ||||
\(582\) | 20.3032 | + | 5.04168i | 0.841597 | + | 0.208984i | ||||
\(583\) | 26.6345 | + | 46.1323i | 1.10309 | + | 1.91060i | ||||
\(584\) | −20.5528 | − | 35.5985i | −0.850480 | − | 1.47308i | ||||
\(585\) | 1.78757 | − | 0.0658257i | 0.0739068 | − | 0.00272156i | ||||
\(586\) | 11.0692 | + | 6.39082i | 0.457265 | + | 0.264002i | ||||
\(587\) | −14.3135 | + | 24.7917i | −0.590781 | + | 1.02326i | 0.403346 | + | 0.915047i | \(0.367847\pi\) |
−0.994127 | + | 0.108215i | \(0.965486\pi\) | |||||||
\(588\) | 3.14978 | + | 13.4132i | 0.129895 | + | 0.553153i | ||||
\(589\) | 10.3742 | + | 17.9686i | 0.427460 | + | 0.740383i | ||||
\(590\) | 1.23442i | 0.0508201i | ||||||||
\(591\) | −1.80199 | + | 7.25676i | −0.0741239 | + | 0.298503i | ||||
\(592\) | 0.861294 | 0.0353990 | ||||||||
\(593\) | 10.6177 | − | 18.3904i | 0.436016 | − | 0.755202i | −0.561362 | − | 0.827571i | \(-0.689722\pi\) |
0.997378 | + | 0.0723683i | \(0.0230557\pi\) | |||||||
\(594\) | 5.19283 | − | 24.7776i | 0.213064 | − | 1.01664i | ||||
\(595\) | −8.14622 | − | 4.97631i | −0.333962 | − | 0.204009i | ||||
\(596\) | 4.66529 | + | 2.69351i | 0.191098 | + | 0.110330i | ||||
\(597\) | 28.5590 | − | 8.21856i | 1.16884 | − | 0.336363i | ||||
\(598\) | 1.32232 | + | 0.763444i | 0.0540739 | + | 0.0312196i | ||||
\(599\) | 41.7758 | + | 24.1193i | 1.70691 | + | 0.985486i | 0.938334 | + | 0.345729i | \(0.112368\pi\) |
0.768577 | + | 0.639757i | \(0.220965\pi\) | |||||||
\(600\) | 1.21665 | − | 4.89954i | 0.0496694 | − | 0.200023i | ||||
\(601\) | −14.1137 | − | 8.14853i | −0.575708 | − | 0.332385i | 0.183718 | − | 0.982979i | \(-0.441187\pi\) |
−0.759426 | + | 0.650594i | \(0.774520\pi\) | |||||||
\(602\) | −1.42096 | − | 2.60835i | −0.0579138 | − | 0.106308i | ||||
\(603\) | 23.5449 | − | 14.7748i | 0.958822 | − | 0.601676i | ||||
\(604\) | 10.1277 | − | 17.5417i | 0.412091 | − | 0.713762i | ||||
\(605\) | −16.4858 | −0.670243 | ||||||||
\(606\) | −6.42019 | + | 1.84756i | −0.260802 | + | 0.0750522i | ||||
\(607\) | − | 8.09904i | − | 0.328730i | −0.986400 | − | 0.164365i | \(-0.947443\pi\) | ||
0.986400 | − | 0.164365i | \(-0.0525574\pi\) | |||||||
\(608\) | −8.79969 | − | 15.2415i | −0.356875 | − | 0.618125i | ||||
\(609\) | −18.0562 | − | 4.96172i | −0.731675 | − | 0.201059i | ||||
\(610\) | 4.67753 | − | 8.10172i | 0.189388 | − | 0.328029i | ||||
\(611\) | −2.95974 | − | 1.70881i | −0.119738 | − | 0.0691310i | ||||
\(612\) | −10.8716 | − | 5.75405i | −0.439459 | − | 0.232594i | ||||
\(613\) | −18.0545 | − | 31.2713i | −0.729215 | − | 1.26304i | −0.957215 | − | 0.289376i | \(-0.906552\pi\) |
0.228001 | − | 0.973661i | \(-0.426781\pi\) | |||||||
\(614\) | −10.1067 | − | 17.5053i | −0.407873 | − | 0.706457i | ||||
\(615\) | 4.69010 | + | 16.2978i | 0.189123 | + | 0.657193i | ||||
\(616\) | −35.5025 | + | 19.3408i | −1.43043 | + | 0.779261i | ||||
\(617\) | −34.0805 | + | 19.6764i | −1.37203 | + | 0.792141i | −0.991183 | − | 0.132499i | \(-0.957700\pi\) |
−0.380844 | + | 0.924639i | \(0.624367\pi\) | |||||||
\(618\) | 5.14057 | + | 17.8632i | 0.206784 | + | 0.718564i | ||||
\(619\) | − | 6.16025i | − | 0.247601i | −0.992307 | − | 0.123801i | \(-0.960492\pi\) | ||
0.992307 | − | 0.123801i | \(-0.0395084\pi\) | |||||||
\(620\) | 6.29352 | − | 3.63357i | 0.252754 | − | 0.145927i | ||||
\(621\) | 9.55057 | − | 10.6680i | 0.383251 | − | 0.428092i | ||||
\(622\) | − | 10.6772i | − | 0.428115i | ||||||
\(623\) | −0.559453 | + | 22.5740i | −0.0224140 | + | 0.904408i | ||||
\(624\) | 0.324052 | + | 0.312338i | 0.0129724 | + | 0.0125035i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −13.1817 | + | 22.8314i | −0.526848 | + | 0.912527i | ||||
\(627\) | 20.4460 | − | 21.2128i | 0.816537 | − | 0.847158i | ||||
\(628\) | −5.83250 | + | 3.36740i | −0.232742 | + | 0.134374i | ||||
\(629\) | 7.13073 | 0.284321 | ||||||||
\(630\) | 6.34306 | − | 3.76463i | 0.252714 | − | 0.149986i | ||||
\(631\) | 22.3970 | 0.891610 | 0.445805 | − | 0.895130i | \(-0.352917\pi\) | ||||
0.445805 | + | 0.895130i | \(0.352917\pi\) | |||||||
\(632\) | 32.7305 | − | 18.8970i | 1.30195 | − | 0.751682i | ||||
\(633\) | 9.59518 | + | 33.3427i | 0.381374 | + | 1.32525i | ||||
\(634\) | 6.32893 | − | 10.9620i | 0.251354 | − | 0.435358i | ||||
\(635\) | 12.6328 | 0.501316 | ||||||||
\(636\) | −4.81979 | + | 19.4097i | −0.191117 | + | 0.769644i | ||||
\(637\) | 0.206753 | − | 4.16869i | 0.00819184 | − | 0.165170i | ||||
\(638\) | − | 19.9083i | − | 0.788179i | ||||||
\(639\) | 16.3608 | − | 30.9118i | 0.647222 | − | 1.22285i | ||||
\(640\) | −4.63690 | + | 2.67711i | −0.183289 | + | 0.105822i | ||||
\(641\) | 44.4010i | 1.75374i | 0.480732 | + | 0.876868i | \(0.340371\pi\) | ||||
−0.480732 | + | 0.876868i | \(0.659629\pi\) | |||||||
\(642\) | 1.57956 | + | 0.392234i | 0.0623402 | + | 0.0154802i | ||||
\(643\) | 3.06913 | − | 1.77196i | 0.121035 | − | 0.0698794i | −0.438260 | − | 0.898848i | \(-0.644405\pi\) |
0.559295 | + | 0.828969i | \(0.311072\pi\) | |||||||
\(644\) | −8.28251 | − | 0.205266i | −0.326377 | − | 0.00808861i | ||||
\(645\) | 1.45210 | − | 1.50656i | 0.0571764 | − | 0.0593206i | ||||
\(646\) | 5.43934 | + | 9.42122i | 0.214008 | + | 0.370673i | ||||
\(647\) | −10.3018 | − | 17.8432i | −0.405005 | − | 0.701489i | 0.589317 | − | 0.807902i | \(-0.299397\pi\) |
−0.994322 | + | 0.106413i | \(0.966063\pi\) | |||||||
\(648\) | 21.6913 | − | 14.7513i | 0.852116 | − | 0.579485i | ||||
\(649\) | 6.03101 | + | 3.48201i | 0.236738 | + | 0.136681i | ||||
\(650\) | −0.277052 | + | 0.479869i | −0.0108669 | + | 0.0188220i | ||||
\(651\) | 28.2575 | + | 7.76497i | 1.10750 | + | 0.304333i | ||||
\(652\) | −8.23041 | − | 14.2555i | −0.322328 | − | 0.558288i | ||||
\(653\) | 42.7103i | 1.67138i | 0.549200 | + | 0.835691i | \(0.314933\pi\) | ||||
−0.549200 | + | 0.835691i | \(0.685067\pi\) | |||||||
\(654\) | −7.26415 | − | 7.00158i | −0.284051 | − | 0.273783i | ||||
\(655\) | 4.98386 | 0.194736 | ||||||||
\(656\) | −2.13355 | + | 3.69541i | −0.0833011 | + | 0.144282i | ||||
\(657\) | 42.2805 | − | 1.55695i | 1.64952 | − | 0.0607422i | ||||
\(658\) | −14.0884 | − | 0.349153i | −0.549222 | − | 0.0136114i | ||||
\(659\) | −25.4695 | − | 14.7048i | −0.992152 | − | 0.572819i | −0.0862351 | − | 0.996275i | \(-0.527484\pi\) |
−0.905917 | + | 0.423456i | \(0.860817\pi\) | |||||||
\(660\) | −7.42982 | − | 7.16125i | −0.289205 | − | 0.278751i | ||||
\(661\) | −6.66816 | − | 3.84986i | −0.259361 | − | 0.149742i | 0.364682 | − | 0.931132i | \(-0.381178\pi\) |
−0.624043 | + | 0.781390i | \(0.714511\pi\) | |||||||
\(662\) | −18.5306 | − | 10.6987i | −0.720213 | − | 0.415815i | ||||
\(663\) | 2.68285 | + | 2.58588i | 0.104193 | + | 0.100427i | ||||
\(664\) | −27.2936 | − | 15.7580i | −1.05920 | − | 0.611527i | ||||
\(665\) | 8.58157 | + | 0.212678i | 0.332779 | + | 0.00824728i | ||||
\(666\) | −2.57749 | + | 4.86986i | −0.0998756 | + | 0.188703i | ||||
\(667\) | 5.63002 | − | 9.75148i | 0.217995 | − | 0.377579i | ||||
\(668\) | −13.9829 | −0.541013 | ||||||||
\(669\) | −19.5563 | − | 18.8494i | −0.756090 | − | 0.728760i | ||||
\(670\) | 8.61050i | 0.332653i | ||||||||
\(671\) | −26.3885 | − | 45.7062i | −1.01872 | − | 1.76447i | ||||
\(672\) | −23.9689 | − | 6.58649i | −0.924621 | − | 0.254079i | ||||
\(673\) | −15.3084 | + | 26.5148i | −0.590094 | + | 1.02207i | 0.404126 | + | 0.914703i | \(0.367576\pi\) |
−0.994219 | + | 0.107369i | \(0.965757\pi\) | |||||||
\(674\) | −8.30161 | − | 4.79294i | −0.319766 | − | 0.184617i | ||||
\(675\) | 3.87139 | + | 3.46588i | 0.149010 | + | 0.133402i | ||||
\(676\) | −7.18459 | − | 12.4441i | −0.276330 | − | 0.478618i | ||||
\(677\) | −14.3069 | − | 24.7802i | −0.549857 | − | 0.952381i | −0.998284 | − | 0.0585609i | \(-0.981349\pi\) |
0.448427 | − | 0.893820i | \(-0.351985\pi\) | |||||||
\(678\) | 14.9547 | − | 15.5155i | 0.574331 | − | 0.595869i | ||||
\(679\) | 34.3761 | + | 0.851946i | 1.31924 | + | 0.0326947i | ||||
\(680\) | 9.10725 | − | 5.25807i | 0.349247 | − | 0.201638i | ||||
\(681\) | −7.21814 | − | 1.79240i | −0.276600 | − | 0.0686849i | ||||
\(682\) | 31.1561i | 1.19303i | ||||||||
\(683\) | 12.4676 | − | 7.19817i | 0.477059 | − | 0.275430i | −0.242131 | − | 0.970244i | \(-0.577846\pi\) |
0.719190 | + | 0.694813i | \(0.244513\pi\) | |||||||
\(684\) | 11.0537 | − | 0.407045i | 0.422650 | − | 0.0155638i | ||||
\(685\) | 12.1794i | 0.465349i | ||||||||
\(686\) | −7.47475 | − | 15.5030i | −0.285387 | − | 0.591907i | ||||
\(687\) | 3.51587 | − | 14.1587i | 0.134139 | − | 0.540188i | ||||
\(688\) | 0.526476 | 0.0200717 | ||||||||
\(689\) | 3.02918 | − | 5.24670i | 0.115403 | − | 0.199883i | ||||
\(690\) | 1.22661 | + | 4.26242i | 0.0466964 | + | 0.162267i | ||||
\(691\) | 8.95724 | − | 5.17146i | 0.340749 | − | 0.196732i | −0.319854 | − | 0.947467i | \(-0.603634\pi\) |
0.660603 | + | 0.750735i | \(0.270301\pi\) | |||||||
\(692\) | 2.55718 | 0.0972096 | ||||||||
\(693\) | −0.500571 | − | 41.6096i | −0.0190151 | − | 1.58062i | ||||
\(694\) | −23.2742 | −0.883475 | ||||||||
\(695\) | −14.5703 | + | 8.41218i | −0.552684 | + | 0.319092i | ||||
\(696\) | 14.3158 | − | 14.8527i | 0.542640 | − | 0.562990i | ||||
\(697\) | −17.6638 | + | 30.5947i | −0.669066 | + | 1.15886i | ||||
\(698\) | 2.60016 | 0.0984173 | ||||||||
\(699\) | −18.8364 | − | 18.1555i | −0.712457 | − | 0.686704i | ||||
\(700\) | 0.0744906 | − | 3.00571i | 0.00281548 | − | 0.113605i | ||||
\(701\) | 13.7649i | 0.519894i | 0.965623 | + | 0.259947i | \(0.0837052\pi\) | ||||
−0.965623 | + | 0.259947i | \(0.916295\pi\) | |||||||
\(702\) | −2.73574 | + | 0.897530i | −0.103254 | + | 0.0338751i | ||||
\(703\) | −5.55325 | + | 3.20617i | −0.209445 | + | 0.120923i | ||||
\(704\) | − | 30.9971i | − | 1.16825i | ||||||
\(705\) | −2.74552 | − | 9.54052i | −0.103402 | − | 0.359317i | ||||
\(706\) | 0.633886 | − | 0.365974i | 0.0238566 | − | 0.0137736i | ||||
\(707\) | −9.64326 | + | 5.25338i | −0.362672 | + | 0.197574i | ||||
\(708\) | 0.723056 | + | 2.51258i | 0.0271741 | + | 0.0944285i | ||||
\(709\) | −17.6097 | − | 30.5008i | −0.661345 | − | 1.14548i | −0.980262 | − | 0.197701i | \(-0.936653\pi\) |
0.318917 | − | 0.947783i | \(-0.396681\pi\) | |||||||
\(710\) | 5.41697 | + | 9.38246i | 0.203295 | + | 0.352117i | ||||
\(711\) | 1.43151 | + | 38.8742i | 0.0536859 | + | 1.45790i | ||||
\(712\) | −21.5433 | − | 12.4380i | −0.807368 | − | 0.466134i | ||||
\(713\) | −8.81085 | + | 15.2608i | −0.329969 | + | 0.571523i | ||||
\(714\) | 14.8159 | + | 4.07130i | 0.554470 | + | 0.152364i | ||||
\(715\) | 1.56300 | + | 2.70720i | 0.0584529 | + | 0.101243i | ||||
\(716\) | − | 14.9957i | − | 0.560414i | ||||||
\(717\) | −14.8550 | + | 4.27488i | −0.554769 | + | 0.159648i | ||||
\(718\) | −3.37699 | −0.126028 | ||||||||
\(719\) | −4.86513 | + | 8.42665i | −0.181439 | + | 0.314261i | −0.942371 | − | 0.334571i | \(-0.891409\pi\) |
0.760932 | + | 0.648832i | \(0.224742\pi\) | |||||||
\(720\) | 0.0481112 | + | 1.30651i | 0.00179300 | + | 0.0486908i | ||||
\(721\) | 14.6168 | + | 26.8309i | 0.544356 | + | 0.999236i | ||||
\(722\) | 6.81910 | + | 3.93701i | 0.253781 | + | 0.146520i | ||||
\(723\) | 12.7287 | − | 51.2597i | 0.473387 | − | 1.90637i | ||||
\(724\) | 6.63937 | + | 3.83324i | 0.246750 | + | 0.142461i | ||||
\(725\) | 3.53879 | + | 2.04312i | 0.131427 | + | 0.0758797i | ||||
\(726\) | 25.5006 | − | 7.33842i | 0.946416 | − | 0.272354i | ||||
\(727\) | 25.3316 | + | 14.6252i | 0.939495 | + | 0.542418i | 0.889802 | − | 0.456347i | \(-0.150842\pi\) |
0.0496933 | + | 0.998765i | \(0.484176\pi\) | |||||||
\(728\) | 3.92383 | + | 2.39697i | 0.145427 | + | 0.0888375i | ||||
\(729\) | 2.97536 | + | 26.8356i | 0.110199 | + | 0.993910i | ||||
\(730\) | −6.55299 | + | 11.3501i | −0.242537 | + | 0.420086i | ||||
\(731\) | 4.35874 | 0.161214 | ||||||||
\(732\) | 4.77527 | − | 19.2304i | 0.176499 | − | 0.710777i | ||||
\(733\) | − | 7.11527i | − | 0.262809i | −0.991329 | − | 0.131404i | \(-0.958051\pi\) | ||
0.991329 | − | 0.131404i | \(-0.0419486\pi\) | |||||||
\(734\) | −5.79078 | − | 10.0299i | −0.213741 | − | 0.370211i | ||||
\(735\) | 8.83609 | − | 8.30202i | 0.325924 | − | 0.306225i | ||||
\(736\) | 7.47363 | − | 12.9447i | 0.275482 | − | 0.477148i | ||||
\(737\) | 42.0685 | + | 24.2882i | 1.54961 | + | 0.894669i | ||||
\(738\) | −14.5095 | − | 23.1221i | −0.534102 | − | 0.851137i | ||||
\(739\) | 5.44572 | + | 9.43227i | 0.200324 | + | 0.346972i | 0.948633 | − | 0.316379i | \(-0.102467\pi\) |
−0.748309 | + | 0.663351i | \(0.769134\pi\) | |||||||
\(740\) | 1.12297 | + | 1.94503i | 0.0412810 | + | 0.0715008i | ||||
\(741\) | −3.25202 | − | 0.807538i | −0.119466 | − | 0.0296657i | ||||
\(742\) | 0.618938 | − | 24.9742i | 0.0227219 | − | 0.916833i | ||||
\(743\) | −43.0548 | + | 24.8577i | −1.57953 | + | 0.911941i | −0.584604 | + | 0.811319i | \(0.698750\pi\) |
−0.994925 | + | 0.100623i | \(0.967917\pi\) | |||||||
\(744\) | −22.4039 | + | 23.2441i | −0.821367 | + | 0.852170i | ||||
\(745\) | − | 4.74043i | − | 0.173676i | ||||||
\(746\) | −8.26219 | + | 4.77018i | −0.302500 | + | 0.174649i | ||||
\(747\) | 27.4768 | − | 17.2422i | 1.00533 | − | 0.630857i | ||||
\(748\) | − | 21.4958i | − | 0.785965i | ||||||
\(749\) | 2.67441 | + | 0.0662800i | 0.0977207 | + | 0.00242182i | ||||
\(750\) | −1.54682 | + | 0.445136i | −0.0564819 | + | 0.0162541i | ||||
\(751\) | 12.2123 | 0.445634 | 0.222817 | − | 0.974860i | \(-0.428475\pi\) | ||||
0.222817 | + | 0.974860i | \(0.428475\pi\) | |||||||
\(752\) | 1.24895 | − | 2.16324i | 0.0455445 | − | 0.0788853i | ||||
\(753\) | −16.4069 | − | 4.07413i | −0.597899 | − | 0.148470i | ||||
\(754\) | −1.96086 | + | 1.13210i | −0.0714103 | + | 0.0412288i | ||||
\(755\) | −17.8242 | −0.648690 | ||||||||
\(756\) | 10.7058 | − | 11.3781i | 0.389366 | − | 0.413817i | ||||
\(757\) | −27.4472 | −0.997587 | −0.498794 | − | 0.866721i | \(-0.666223\pi\) | ||||
−0.498794 | + | 0.866721i | \(0.666223\pi\) | |||||||
\(758\) | 17.0566 | − | 9.84764i | 0.619524 | − | 0.357683i | ||||
\(759\) | 24.2850 | + | 6.03041i | 0.881488 | + | 0.218890i | ||||
\(760\) | −4.72834 | + | 8.18973i | −0.171515 | + | 0.297073i | ||||
\(761\) | 6.07967 | 0.220388 | 0.110194 | − | 0.993910i | \(-0.464853\pi\) | ||||
0.110194 | + | 0.993910i | \(0.464853\pi\) | |||||||
\(762\) | −19.5406 | + | 5.62329i | −0.707882 | + | 0.203710i | ||||
\(763\) | −14.1522 | − | 8.64519i | −0.512343 | − | 0.312977i | ||||
\(764\) | 11.1607i | 0.403780i | ||||||||
\(765\) | 0.398317 | + | 10.8167i | 0.0144012 | + | 0.391079i | ||||
\(766\) | 5.61173 | − | 3.23994i | 0.202760 | − | 0.117064i | ||||
\(767\) | − | 0.792028i | − | 0.0285985i | ||||||
\(768\) | 20.1943 | − | 20.9516i | 0.728697 | − | 0.756025i | ||||
\(769\) | 14.1929 | − | 8.19430i | 0.511811 | − | 0.295494i | −0.221767 | − | 0.975100i | \(-0.571182\pi\) |
0.733578 | + | 0.679606i | \(0.237849\pi\) | |||||||
\(770\) | 11.0001 | + | 6.71970i | 0.396417 | + | 0.242161i | ||||
\(771\) | −17.5161 | − | 4.34958i | −0.630828 | − | 0.156646i | ||||
\(772\) | −5.32117 | − | 9.21653i | −0.191513 | − | 0.331710i | ||||
\(773\) | −8.90571 | − | 15.4251i | −0.320316 | − | 0.554804i | 0.660237 | − | 0.751057i | \(-0.270456\pi\) |
−0.980553 | + | 0.196253i | \(0.937123\pi\) | |||||||
\(774\) | −1.57552 | + | 2.97676i | −0.0566308 | + | 0.106997i | ||||
\(775\) | −5.53812 | − | 3.19744i | −0.198935 | − | 0.114855i | ||||
\(776\) | −18.9408 | + | 32.8065i | −0.679937 | + | 1.17769i | ||||
\(777\) | −2.39979 | + | 8.73309i | −0.0860920 | + | 0.313298i | ||||
\(778\) | 8.82169 | + | 15.2796i | 0.316273 | + | 0.547801i | ||||
\(779\) | − | 31.7686i | − | 1.13823i | ||||||
\(780\) | −0.282841 | + | 1.13903i | −0.0101273 | + | 0.0407837i | ||||
\(781\) | 61.1201 | 2.18705 | ||||||||
\(782\) | −4.61967 | + | 8.00150i | −0.165199 | + | 0.286133i | ||||
\(783\) | 6.61884 | + | 20.1748i | 0.236538 | + | 0.720987i | ||||
\(784\) | 3.04685 | + | 0.151113i | 0.108816 | + | 0.00539690i | ||||
\(785\) | 5.13244 | + | 2.96322i | 0.183185 | + | 0.105762i | ||||
\(786\) | −7.70915 | + | 2.21849i | −0.274976 | + | 0.0791311i | ||||
\(787\) | 41.1137 | + | 23.7370i | 1.46555 | + | 0.846133i | 0.999259 | − | 0.0385008i | \(-0.0122582\pi\) |
0.466287 | + | 0.884634i | \(0.345592\pi\) | |||||||
\(788\) | −4.24851 | − | 2.45288i | −0.151347 | − | 0.0873802i | ||||
\(789\) | 9.66110 | − | 38.9061i | 0.343944 | − | 1.38509i | ||||
\(790\) | −10.4357 | − | 6.02506i | −0.371286 | − | 0.214362i | ||||
\(791\) | 18.4653 | − | 30.2276i | 0.656549 | − | 1.07477i | ||||
\(792\) | 40.5169 | + | 21.4445i | 1.43971 | + | 0.761998i | ||||
\(793\) | −3.00120 | + | 5.19824i | −0.106576 | + | 0.184595i | ||||
\(794\) | 22.0192 | 0.781432 | ||||||||
\(795\) | 16.9123 | − | 4.86694i | 0.599819 | − | 0.172612i | ||||
\(796\) | 19.4980i | 0.691089i | ||||||||
\(797\) | −8.92350 | − | 15.4560i | −0.316087 | − | 0.547478i | 0.663581 | − | 0.748104i | \(-0.269036\pi\) |
−0.979668 | + | 0.200626i | \(0.935702\pi\) | |||||||
\(798\) | −13.3688 | + | 3.49099i | −0.473251 | + | 0.123580i | ||||
\(799\) | 10.3402 | − | 17.9097i | 0.365809 | − | 0.633599i | ||||
\(800\) | 4.69761 | + | 2.71217i | 0.166086 | + | 0.0958895i | ||||
\(801\) | 21.6879 | − | 13.6095i | 0.766305 | − | 0.480868i | ||||
\(802\) | 12.6304 | + | 21.8764i | 0.445993 | + | 0.772483i | ||||
\(803\) | 36.9689 | + | 64.0321i | 1.30461 | + | 2.25964i | ||||
\(804\) | 5.04358 | + | 17.5262i | 0.177873 | + | 0.618100i | ||||
\(805\) | 3.48776 | + | 6.40224i | 0.122928 | + | 0.225649i | ||||
\(806\) | 3.06870 | − | 1.77171i | 0.108090 | − | 0.0624060i | ||||
\(807\) | 14.9867 | + | 52.0780i | 0.527557 | + | 1.83323i | ||||
\(808\) | − | 12.0975i | − | 0.425588i | ||||||
\(809\) | 4.88185 | − | 2.81854i | 0.171637 | − | 0.0990944i | −0.411721 | − | 0.911310i | \(-0.635072\pi\) |
0.583357 | + | 0.812216i | \(0.301739\pi\) | |||||||
\(810\) | −7.53114 | − | 3.63780i | −0.264617 | − | 0.127819i | ||||
\(811\) | 20.3541i | 0.714729i | 0.933965 | + | 0.357364i | \(0.116325\pi\) | ||||
−0.933965 | + | 0.357364i | \(0.883675\pi\) | |||||||
\(812\) | 6.40463 | − | 10.4844i | 0.224759 | − | 0.367930i | ||||
\(813\) | −23.0609 | − | 22.2274i | −0.808782 | − | 0.779548i | ||||
\(814\) | −9.62889 | −0.337492 | ||||||||
\(815\) | −7.24254 | + | 12.5444i | −0.253695 | + | 0.439413i | ||||
\(816\) | −1.88999 | + | 1.96086i | −0.0661628 | + | 0.0686440i | ||||
\(817\) | −3.39449 | + | 1.95981i | −0.118758 | + | 0.0685650i | ||||
\(818\) | −3.22027 | −0.112594 | ||||||||
\(819\) | −4.06984 | + | 2.41546i | −0.142212 | + | 0.0844031i | ||||
\(820\) | −11.1270 | −0.388571 | ||||||||
\(821\) | 5.05686 | − | 2.91958i | 0.176486 | − | 0.101894i | −0.409155 | − | 0.912465i | \(-0.634176\pi\) |
0.585640 | + | 0.810571i | \(0.300843\pi\) | |||||||
\(822\) | −5.42147 | − | 18.8393i | −0.189095 | − | 0.657096i | ||||
\(823\) | −23.5677 | + | 40.8205i | −0.821518 | + | 1.42291i | 0.0830328 | + | 0.996547i | \(0.473539\pi\) |
−0.904551 | + | 0.426365i | \(0.859794\pi\) | |||||||
\(824\) | −33.6595 | −1.17258 | ||||||||
\(825\) | −2.18842 | + | 8.81296i | −0.0761911 | + | 0.306828i | ||||
\(826\) | −1.56240 | − | 2.86799i | −0.0543630 | − | 0.0997903i | ||||
\(827\) | − | 35.6635i | − | 1.24014i | −0.784546 | − | 0.620070i | \(-0.787104\pi\) | ||
0.784546 | − | 0.620070i | \(-0.212896\pi\) | |||||||
\(828\) | 4.99339 | + | 7.95740i | 0.173532 | + | 0.276539i | ||||
\(829\) | 0.0501046 | − | 0.0289279i | 0.00174020 | − | 0.00100471i | −0.499130 | − | 0.866527i | \(-0.666347\pi\) |
0.500870 | + | 0.865523i | \(0.333014\pi\) | |||||||
\(830\) | 10.0484i | 0.348786i | ||||||||
\(831\) | −29.3627 | − | 7.29131i | −1.01858 | − | 0.252933i | ||||
\(832\) | −3.05304 | + | 1.76267i | −0.105845 | + | 0.0611097i | ||||
\(833\) | 25.2251 | + | 1.25108i | 0.873999 | + | 0.0433473i | ||||
\(834\) | 18.7931 | − | 19.4979i | 0.650753 | − | 0.675157i | ||||
\(835\) | 6.15227 | + | 10.6560i | 0.212908 | + | 0.368768i | ||||
\(836\) | 9.66510 | + | 16.7404i | 0.334274 | + | 0.578980i | ||||
\(837\) | −10.3583 | − | 31.5730i | −0.358036 | − | 1.09132i | ||||
\(838\) | 0.960897 | + | 0.554774i | 0.0331936 | + | 0.0191644i | ||||
\(839\) | 5.35115 | − | 9.26846i | 0.184742 | − | 0.319983i | −0.758747 | − | 0.651385i | \(-0.774188\pi\) |
0.943490 | + | 0.331402i | \(0.107522\pi\) | |||||||
\(840\) | 3.37465 | + | 12.9233i | 0.116436 | + | 0.445896i | ||||
\(841\) | −6.15130 | − | 10.6544i | −0.212114 | − | 0.367392i | ||||
\(842\) | 28.4829i | 0.981585i | ||||||||
\(843\) | 25.5997 | + | 24.6744i | 0.881701 | + | 0.849830i | ||||
\(844\) | −22.7640 | −0.783569 | ||||||||
\(845\) | −6.32224 | + | 10.9504i | −0.217492 | + | 0.376706i | ||||
\(846\) | 8.49365 | + | 13.5354i | 0.292018 | + | 0.465355i | ||||
\(847\) | 38.3024 | − | 20.8661i | 1.31609 | − | 0.716968i | ||||
\(848\) | 3.83475 | + | 2.21399i | 0.131686 | + | 0.0760288i | ||||
\(849\) | −28.5324 | − | 27.5011i | −0.979229 | − | 0.943834i | ||||
\(850\) | −2.90373 | − | 1.67647i | −0.0995970 | − | 0.0575024i | ||||
\(851\) | −4.71641 | − | 2.72302i | −0.161677 | − | 0.0933440i | ||||
\(852\) | 16.5216 | + | 15.9244i | 0.566022 | + | 0.545563i | ||||
\(853\) | −26.8003 | − | 15.4732i | −0.917625 | − | 0.529791i | −0.0347485 | − | 0.999396i | \(-0.511063\pi\) |
−0.882877 | + | 0.469605i | \(0.844396\pi\) | |||||||
\(854\) | −0.613221 | + | 24.7436i | −0.0209840 | + | 0.846708i | ||||
\(855\) | −5.17369 | − | 8.24472i | −0.176937 | − | 0.281963i | ||||
\(856\) | −1.47357 | + | 2.55229i | −0.0503654 | + | 0.0872355i | ||||
\(857\) | −35.7192 | −1.22014 | −0.610072 | − | 0.792346i | \(-0.708859\pi\) | ||||
−0.610072 | + | 0.792346i | \(0.708859\pi\) | |||||||
\(858\) | −3.62275 | − | 3.49180i | −0.123679 | − | 0.119208i | ||||
\(859\) | 0.664661i | 0.0226779i | 0.999936 | + | 0.0113390i | \(0.00360938\pi\) | ||||
−0.999936 | + | 0.0113390i | \(0.996391\pi\) | |||||||
\(860\) | 0.686426 | + | 1.18892i | 0.0234069 | + | 0.0405420i | ||||
\(861\) | −31.5250 | − | 31.9295i | −1.07437 | − | 1.08815i | ||||
\(862\) | 11.3887 | − | 19.7258i | 0.387900 | − | 0.671863i | ||||
\(863\) | −1.34228 | − | 0.774964i | −0.0456916 | − | 0.0263801i | 0.476980 | − | 0.878914i | \(-0.341731\pi\) |
−0.522672 | + | 0.852534i | \(0.675065\pi\) | |||||||
\(864\) | 8.78625 | + | 26.7812i | 0.298914 | + | 0.911115i | ||||
\(865\) | −1.12513 | − | 1.94878i | −0.0382554 | − | 0.0662604i | ||||
\(866\) | −10.1278 | − | 17.5419i | −0.344157 | − | 0.596097i | ||||
\(867\) | 4.78660 | − | 4.96611i | 0.162562 | − | 0.168658i | ||||
\(868\) | −10.0231 | + | 16.4078i | −0.340206 | + | 0.556917i | ||||
\(869\) | −58.8734 | + | 33.9906i | −1.99714 | + | 1.15305i | ||||
\(870\) | −6.38335 | − | 1.58510i | −0.216416 | − | 0.0537401i | ||||
\(871\) | − | 5.52468i | − | 0.187197i | ||||||
\(872\) | 15.8217 | − | 9.13468i | 0.535791 | − | 0.309339i | ||||
\(873\) | −20.7248 | − | 33.0268i | −0.701429 | − | 1.11779i | ||||
\(874\) | − | 8.30851i | − | 0.281040i | ||||||
\(875\) | −2.32336 | + | 1.26570i | −0.0785439 | + | 0.0427885i | ||||
\(876\) | −6.68991 | + | 26.9408i | −0.226031 | + | 0.910247i | ||||
\(877\) | 7.17466 | 0.242271 | 0.121136 | − | 0.992636i | \(-0.461346\pi\) | ||||
0.121136 | + | 0.992636i | \(0.461346\pi\) | |||||||
\(878\) | −0.355557 | + | 0.615842i | −0.0119995 | + | 0.0207837i | ||||
\(879\) | −6.58818 | − | 22.8936i | −0.222214 | − | 0.772181i | ||||
\(880\) | −1.97866 | + | 1.14238i | −0.0667006 | + | 0.0385096i | ||||
\(881\) | −28.8710 | −0.972690 | −0.486345 | − | 0.873767i | \(-0.661670\pi\) | ||||
−0.486345 | + | 0.873767i | \(0.661670\pi\) | |||||||
\(882\) | −9.97232 | + | 16.7750i | −0.335786 | + | 0.564844i | ||||
\(883\) | 19.1653 | 0.644964 | 0.322482 | − | 0.946576i | \(-0.395483\pi\) | ||||
0.322482 | + | 0.946576i | \(0.395483\pi\) | |||||||
\(884\) | −2.11722 | + | 1.22238i | −0.0712097 | + | 0.0411130i | ||||
\(885\) | 1.59665 | − | 1.65653i | 0.0536708 | − | 0.0556835i | ||||
\(886\) | −0.256508 | + | 0.444286i | −0.00861757 | + | 0.0149261i | ||||
\(887\) | −27.8814 | −0.936165 | −0.468083 | − | 0.883685i | \(-0.655055\pi\) | ||||
−0.468083 | + | 0.883685i | \(0.655055\pi\) | |||||||
\(888\) | −7.18367 | − | 6.92401i | −0.241068 | − | 0.232354i | ||||
\(889\) | −29.3505 | + | 15.9893i | −0.984383 | + | 0.536264i | ||||
\(890\) | 7.93139i | 0.265861i | ||||||||
\(891\) | −39.0169 | + | 26.5336i | −1.30711 | + | 0.888909i | ||||
\(892\) | 15.4332 | − | 8.91035i | 0.516741 | − | 0.298340i | ||||
\(893\) | 18.5969i | 0.622320i | ||||||||
\(894\) | 2.11013 | + | 7.33259i | 0.0705734 | + | 0.245239i | ||||
\(895\) | −11.4279 | + | 6.59789i | −0.381992 | + | 0.220543i | ||||
\(896\) | 7.38475 | − | 12.0888i | 0.246707 | − | 0.403859i | ||||
\(897\) | −0.787021 | − | 2.73486i | −0.0262779 | − | 0.0913142i | ||||
\(898\) | −17.6910 | − | 30.6417i | −0.590357 | − | 1.02253i | ||||
\(899\) | −13.0655 | − | 22.6301i | −0.435759 | − | 0.754757i | ||||
\(900\) | −2.88772 | + | 1.81209i | −0.0962575 | + | 0.0604031i | ||||
\(901\) | 31.7482 | + | 18.3298i | 1.05769 | + | 0.610656i | ||||
\(902\) | 23.8521 | − | 41.3131i | 0.794189 | − | 1.37558i | ||||
\(903\) | −1.46690 | + | 5.33820i | −0.0488153 | + | 0.177644i | ||||
\(904\) | 19.5108 | + | 33.7936i | 0.648918 | + | 1.12396i | ||||
\(905\) | − | 6.74629i | − | 0.224254i | ||||||
\(906\) | 27.5709 | − | 7.93419i | 0.915981 | − | 0.263596i | ||||
\(907\) | −11.8171 | −0.392380 | −0.196190 | − | 0.980566i | \(-0.562857\pi\) | ||||
−0.196190 | + | 0.980566i | \(0.562857\pi\) | |||||||
\(908\) | 2.43982 | − | 4.22590i | 0.0809684 | − | 0.140241i | ||||
\(909\) | 11.0053 | + | 5.82481i | 0.365023 | + | 0.193197i | ||||
\(910\) | 0.0363214 | − | 1.46557i | 0.00120404 | − | 0.0485833i | ||||
\(911\) | −8.86875 | − | 5.12037i | −0.293835 | − | 0.169646i | 0.345835 | − | 0.938295i | \(-0.387596\pi\) |
−0.639670 | + | 0.768650i | \(0.720929\pi\) | |||||||
\(912\) | 0.590220 | − | 2.37687i | 0.0195441 | − | 0.0787059i | ||||
\(913\) | 49.0938 | + | 28.3443i | 1.62477 | + | 0.938061i | ||||
\(914\) | 24.5811 | + | 14.1919i | 0.813071 | + | 0.469427i | ||||
\(915\) | −16.7561 | + | 4.82199i | −0.553941 | + | 0.159410i | ||||
\(916\) | 8.28929 | + | 4.78582i | 0.273886 | + | 0.158128i | ||||
\(917\) | −11.5793 | + | 6.30808i | −0.382382 | + | 0.208311i | ||||
\(918\) | −5.43103 | − | 16.5542i | −0.179251 | − | 0.546371i | ||||
\(919\) | −7.52608 | + | 13.0355i | −0.248262 | + | 0.430003i | −0.963044 | − | 0.269345i | \(-0.913193\pi\) |
0.714781 | + | 0.699348i | \(0.246526\pi\) | |||||||
\(920\) | −8.03163 | −0.264795 | ||||||||
\(921\) | −9.07945 | + | 36.5637i | −0.299178 | + | 1.20482i | ||||
\(922\) | 30.0584i | 0.989921i | ||||||||
\(923\) | −3.47564 | − | 6.01998i | −0.114402 | − | 0.198150i | ||||
\(924\) | 26.3261 | + | 7.23424i | 0.866067 | + | 0.237989i | ||||
\(925\) | 0.988179 | − | 1.71158i | 0.0324911 | − | 0.0562763i | ||||
\(926\) | 0.0383481 | + | 0.0221403i | 0.00126020 | + | 0.000727575i | ||||
\(927\) | 16.2067 | − | 30.6206i | 0.532297 | − | 1.00571i | ||||
\(928\) | 11.0826 | + | 19.1956i | 0.363803 | + | 0.630126i | ||||
\(929\) | −1.58065 | − | 2.73777i | −0.0518596 | − | 0.0898235i | 0.838930 | − | 0.544239i | \(-0.183181\pi\) |
−0.890790 | + | 0.454415i | \(0.849848\pi\) | |||||||
\(930\) | 9.98978 | + | 2.48065i | 0.327578 | + | 0.0813437i | ||||
\(931\) | −20.2073 | + | 10.3676i | −0.662266 | + | 0.339784i | ||||
\(932\) | 14.8650 | − | 8.58233i | 0.486920 | − | 0.281124i | ||||
\(933\) | −13.8103 | + | 14.3282i | −0.452129 | + | 0.469085i | ||||
\(934\) | 16.5871i | 0.542746i | ||||||||
\(935\) | −16.3815 | + | 9.45786i | −0.535732 | + | 0.309305i | ||||
\(936\) | −0.191860 | − | 5.21015i | −0.00627113 | − | 0.170299i | ||||
\(937\) | 25.7818i | 0.842255i | 0.907001 | + | 0.421128i | \(0.138366\pi\) | ||||
−0.907001 | + | 0.421128i | \(0.861634\pi\) | |||||||
\(938\) | −10.8983 | − | 20.0053i | −0.355843 | − | 0.653196i | ||||
\(939\) | 47.2204 | − | 13.5888i | 1.54098 | − | 0.443454i | ||||
\(940\) | 6.51357 | 0.212449 | ||||||||
\(941\) | −26.9751 | + | 46.7222i | −0.879362 | + | 1.52310i | −0.0273203 | + | 0.999627i | \(0.508697\pi\) |
−0.852042 | + | 0.523473i | \(0.824636\pi\) | |||||||
\(942\) | −9.25800 | − | 2.29893i | −0.301642 | − | 0.0749033i | ||||
\(943\) | 23.3665 | − | 13.4906i | 0.760916 | − | 0.439315i | ||||
\(944\) | 0.578884 | 0.0188411 | ||||||||
\(945\) | −13.3814 | − | 3.15245i | −0.435297 | − | 0.102549i | ||||
\(946\) | −5.88577 | −0.191363 | ||||||||
\(947\) | 5.26239 | − | 3.03824i | 0.171005 | − | 0.0987296i | −0.412055 | − | 0.911159i | \(-0.635189\pi\) |
0.583059 | + | 0.812429i | \(0.301855\pi\) | |||||||
\(948\) | −24.7704 | − | 6.15095i | −0.804505 | − | 0.199774i | ||||
\(949\) | 4.20454 | − | 7.28247i | 0.136485 | − | 0.236399i | ||||
\(950\) | 3.01514 | 0.0978241 | ||||||||
\(951\) | −22.6719 | + | 6.52438i | −0.735186 | + | 0.211568i | ||||
\(952\) | −14.5043 | + | 23.7435i | −0.470086 | + | 0.769530i | ||||
\(953\) | 32.7280i | 1.06016i | 0.847947 | + | 0.530082i | \(0.177839\pi\) | ||||
−0.847947 | + | 0.530082i | \(0.822161\pi\) | |||||||
\(954\) | −23.9939 | + | 15.0566i | −0.776832 | + | 0.487474i | ||||
\(955\) | 8.50532 | − | 4.91055i | 0.275226 | − | 0.158902i | ||||
\(956\) | − | 10.1419i | − | 0.328012i | ||||||
\(957\) | −25.7503 | + | 26.7160i | −0.832390 | + | 0.863606i | ||||
\(958\) | 0.654657 | − | 0.377966i | 0.0211510 | − | 0.0122115i | ||||
\(959\) | −15.4154 | − | 28.2970i | −0.497791 | − | 0.913759i | ||||
\(960\) | −9.93880 | − | 2.46799i | −0.320773 | − | 0.0796540i | ||||
\(961\) | 4.94722 | + | 8.56883i | 0.159588 | + | 0.276414i | ||||
\(962\) | 0.547554 | + | 0.948392i | 0.0176539 | + | 0.0305774i | ||||
\(963\) | −1.61236 | − | 2.56943i | −0.0519575 | − | 0.0827987i | ||||
\(964\) | 30.0103 | + | 17.3264i | 0.966566 | + | 0.558047i | ||||
\(965\) | −4.68248 | + | 8.11029i | −0.150734 | + | 0.261080i | ||||
\(966\) | −8.24481 | − | 8.35060i | −0.265273 | − | 0.268676i | ||||
\(967\) | −10.6606 | − | 18.4646i | −0.342821 | − | 0.593783i | 0.642135 | − | 0.766592i | \(-0.278049\pi\) |
−0.984955 | + | 0.172809i | \(0.944716\pi\) | |||||||
\(968\) | 48.0505i | 1.54440i | ||||||||
\(969\) | 4.88649 | − | 19.6783i | 0.156977 | − | 0.632158i | ||||
\(970\) | 12.0781 | 0.387804 | ||||||||
\(971\) | 0.486914 | − | 0.843360i | 0.0156258 | − | 0.0270647i | −0.858107 | − | 0.513471i | \(-0.828359\pi\) |
0.873733 | + | 0.486407i | \(0.161693\pi\) | |||||||
\(972\) | −17.4600 | − | 2.99318i | −0.560030 | − | 0.0960064i | ||||
\(973\) | 23.2048 | − | 37.9862i | 0.743911 | − | 1.21778i | ||||
\(974\) | 2.09621 | + | 1.21025i | 0.0671669 | + | 0.0387788i | ||||
\(975\) | 0.992473 | − | 0.285608i | 0.0317846 | − | 0.00914679i | ||||
\(976\) | −3.79933 | − | 2.19354i | −0.121614 | − | 0.0702136i | ||||
\(977\) | −18.6445 | − | 10.7644i | −0.596490 | − | 0.344383i | 0.171170 | − | 0.985242i | \(-0.445245\pi\) |
−0.767659 | + | 0.640858i | \(0.778579\pi\) | |||||||
\(978\) | 5.61894 | − | 22.6279i | 0.179674 | − | 0.723561i | ||||
\(979\) | 38.7505 | + | 22.3726i | 1.23847 | + | 0.715033i | ||||
\(980\) | 3.63126 | + | 7.07762i | 0.115996 | + | 0.226086i | ||||
\(981\) | 0.691984 | + | 18.7915i | 0.0220933 | + | 0.599968i | ||||
\(982\) | −7.97658 | + | 13.8158i | −0.254543 | + | 0.440881i | ||||
\(983\) | 8.07739 | 0.257629 | 0.128814 | − | 0.991669i | \(-0.458883\pi\) | ||||
0.128814 | + | 0.991669i | \(0.458883\pi\) | |||||||
\(984\) | 47.5027 | − | 13.6701i | 1.51433 | − | 0.435785i | ||||
\(985\) | 4.31693i | 0.137549i | ||||||||
\(986\) | −6.85046 | − | 11.8653i | −0.218163 | − | 0.377870i | ||||
\(987\) | 18.4543 | + | 18.6911i | 0.587406 | + | 0.594943i | ||||
\(988\) | 1.09923 | − | 1.90392i | 0.0349711 | − | 0.0605716i | ||||
\(989\) | −2.88296 | − | 1.66448i | −0.0916729 | − | 0.0529273i | ||||
\(990\) | −0.537863 | − | 14.6062i | −0.0170944 | − | 0.464216i | ||||
\(991\) | 19.8268 | + | 34.3411i | 0.629820 | + | 1.09088i | 0.987587 | + | 0.157070i | \(0.0502049\pi\) |
−0.357767 | + | 0.933811i | \(0.616462\pi\) | |||||||
\(992\) | −17.3440 | − | 30.0406i | −0.550671 | − | 0.953791i | ||||
\(993\) | 11.0291 | + | 38.3254i | 0.349997 | + | 1.21622i | ||||
\(994\) | −24.4610 | − | 14.9426i | −0.775854 | − | 0.473949i | ||||
\(995\) | 14.8590 | − | 8.57887i | 0.471063 | − | 0.271968i | ||||
\(996\) | 5.88584 | + | 20.4530i | 0.186500 | + | 0.648078i | ||||
\(997\) | − | 21.9609i | − | 0.695509i | −0.937586 | − | 0.347755i | \(-0.886944\pi\) | ||
0.937586 | − | 0.347755i | \(-0.113056\pi\) | |||||||
\(998\) | 2.88307 | − | 1.66454i | 0.0912619 | − | 0.0526901i | ||||
\(999\) | 9.75774 | − | 3.20127i | 0.308721 | − | 0.101284i |
(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.b.236.6 | yes | 30 | |
3.2 | odd | 2 | 945.2.be.b.656.10 | 30 | |||
7.3 | odd | 6 | 315.2.t.b.101.6 | ✓ | 30 | ||
9.4 | even | 3 | 945.2.t.b.341.6 | 30 | |||
9.5 | odd | 6 | 315.2.t.b.131.10 | yes | 30 | ||
21.17 | even | 6 | 945.2.t.b.521.10 | 30 | |||
63.31 | odd | 6 | 945.2.be.b.206.10 | 30 | |||
63.59 | even | 6 | inner | 315.2.be.b.311.6 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.t.b.101.6 | ✓ | 30 | 7.3 | odd | 6 | ||
315.2.t.b.131.10 | yes | 30 | 9.5 | odd | 6 | ||
315.2.be.b.236.6 | yes | 30 | 1.1 | even | 1 | trivial | |
315.2.be.b.311.6 | yes | 30 | 63.59 | even | 6 | inner | |
945.2.t.b.341.6 | 30 | 9.4 | even | 3 | |||
945.2.t.b.521.10 | 30 | 21.17 | even | 6 | |||
945.2.be.b.206.10 | 30 | 63.31 | odd | 6 | |||
945.2.be.b.656.10 | 30 | 3.2 | odd | 2 |