Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(106,315)]
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([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.i (of order \(3\), 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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.3 | ||
Root | \(0.913545 - 0.406737i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.106 |
Dual form | 315.2.i.d.211.3 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.669131 | − | 1.15897i | 0.473147 | − | 0.819514i | −0.526381 | − | 0.850249i | \(-0.676451\pi\) |
0.999528 | + | 0.0307347i | \(0.00978469\pi\) | |||||||
\(3\) | 0.704489 | − | 1.58231i | 0.406737 | − | 0.913545i | ||||
\(4\) | 0.104528 | + | 0.181049i | 0.0522642 | + | 0.0905243i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | −1.36245 | − | 1.87525i | −0.556217 | − | 0.765568i | ||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 2.95630 | 1.04521 | ||||||||
\(9\) | −2.00739 | − | 2.22943i | −0.669131 | − | 0.743145i | ||||
\(10\) | 1.33826 | 0.423195 | ||||||||
\(11\) | −0.330869 | + | 0.573083i | −0.0997609 | + | 0.172791i | −0.911586 | − | 0.411110i | \(-0.865141\pi\) |
0.811825 | + | 0.583901i | \(0.198474\pi\) | |||||||
\(12\) | 0.360114 | − | 0.0378495i | 0.103956 | − | 0.0109262i | ||||
\(13\) | −0.891693 | − | 1.54446i | −0.247311 | − | 0.428355i | 0.715468 | − | 0.698646i | \(-0.246214\pi\) |
−0.962779 | + | 0.270290i | \(0.912880\pi\) | |||||||
\(14\) | −0.669131 | − | 1.15897i | −0.178833 | − | 0.309747i | ||||
\(15\) | 1.72256 | − | 0.181049i | 0.444764 | − | 0.0467465i | ||||
\(16\) | 1.76909 | − | 3.06415i | 0.442273 | − | 0.766039i | ||||
\(17\) | 1.33826 | 0.324576 | 0.162288 | − | 0.986743i | \(-0.448113\pi\) | ||||
0.162288 | + | 0.986743i | \(0.448113\pi\) | |||||||
\(18\) | −3.92705 | + | 0.834720i | −0.925615 | + | 0.196745i | ||||
\(19\) | −4.32157 | −0.991436 | −0.495718 | − | 0.868484i | \(-0.665095\pi\) | ||||
−0.495718 | + | 0.868484i | \(0.665095\pi\) | |||||||
\(20\) | −0.104528 | + | 0.181049i | −0.0233733 | + | 0.0404837i | ||||
\(21\) | −1.01807 | − | 1.40126i | −0.222162 | − | 0.305780i | ||||
\(22\) | 0.442790 | + | 0.766934i | 0.0944031 | + | 0.163511i | ||||
\(23\) | 2.60686 | + | 4.51522i | 0.543569 | + | 0.941489i | 0.998695 | + | 0.0510619i | \(0.0162606\pi\) |
−0.455127 | + | 0.890427i | \(0.650406\pi\) | |||||||
\(24\) | 2.08268 | − | 4.67777i | 0.425124 | − | 0.954845i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −2.38664 | −0.468058 | ||||||||
\(27\) | −4.94183 | + | 1.60570i | −0.951057 | + | 0.309017i | ||||
\(28\) | 0.209057 | 0.0395080 | ||||||||
\(29\) | −2.46086 | + | 4.26234i | −0.456971 | + | 0.791497i | −0.998799 | − | 0.0489924i | \(-0.984399\pi\) |
0.541828 | + | 0.840489i | \(0.317732\pi\) | |||||||
\(30\) | 0.942790 | − | 2.11754i | 0.172129 | − | 0.386608i | ||||
\(31\) | −0.344375 | − | 0.596475i | −0.0618516 | − | 0.107130i | 0.833441 | − | 0.552608i | \(-0.186367\pi\) |
−0.895293 | + | 0.445478i | \(0.853034\pi\) | |||||||
\(32\) | 0.588790 | + | 1.01981i | 0.104084 | + | 0.180279i | ||||
\(33\) | 0.673699 | + | 0.927267i | 0.117276 | + | 0.161416i | ||||
\(34\) | 0.895472 | − | 1.55100i | 0.153572 | − | 0.265995i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.193806 | − | 0.596475i | 0.0323011 | − | 0.0994125i | ||||
\(37\) | −6.53818 | −1.07487 | −0.537435 | − | 0.843305i | \(-0.680607\pi\) | ||||
−0.537435 | + | 0.843305i | \(0.680607\pi\) | |||||||
\(38\) | −2.89169 | + | 5.00856i | −0.469095 | + | 0.812496i | ||||
\(39\) | −3.07199 | + | 0.322880i | −0.491913 | + | 0.0517021i | ||||
\(40\) | 1.47815 | + | 2.56023i | 0.233716 | + | 0.404807i | ||||
\(41\) | 0.409767 | + | 0.709737i | 0.0639949 | + | 0.110842i | 0.896248 | − | 0.443554i | \(-0.146283\pi\) |
−0.832253 | + | 0.554396i | \(0.812949\pi\) | |||||||
\(42\) | −2.30524 | + | 0.242290i | −0.355706 | + | 0.0373862i | ||||
\(43\) | 0.819699 | − | 1.41976i | 0.125003 | − | 0.216511i | −0.796731 | − | 0.604334i | \(-0.793439\pi\) |
0.921734 | + | 0.387822i | \(0.126773\pi\) | |||||||
\(44\) | −0.138341 | −0.0208557 | ||||||||
\(45\) | 0.927051 | − | 2.85317i | 0.138197 | − | 0.425325i | ||||
\(46\) | 6.97733 | 1.02875 | ||||||||
\(47\) | −6.08406 | + | 10.5379i | −0.887451 | + | 1.53711i | −0.0445722 | + | 0.999006i | \(0.514192\pi\) |
−0.842879 | + | 0.538104i | \(0.819141\pi\) | |||||||
\(48\) | −3.60213 | − | 4.95791i | −0.519923 | − | 0.715612i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0.669131 | + | 1.15897i | 0.0946294 | + | 0.163903i | ||||
\(51\) | 0.942790 | − | 2.11754i | 0.132017 | − | 0.296515i | ||||
\(52\) | 0.186415 | − | 0.322880i | 0.0258511 | − | 0.0447753i | ||||
\(53\) | 13.8223 | 1.89864 | 0.949319 | − | 0.314314i | \(-0.101774\pi\) | ||||
0.949319 | + | 0.314314i | \(0.101774\pi\) | |||||||
\(54\) | −1.44578 | + | 6.80185i | −0.196745 | + | 0.925615i | ||||
\(55\) | −0.661739 | −0.0892288 | ||||||||
\(56\) | 1.47815 | − | 2.56023i | 0.197526 | − | 0.342125i | ||||
\(57\) | −3.04449 | + | 6.83805i | −0.403253 | + | 0.905721i | ||||
\(58\) | 3.29328 | + | 5.70413i | 0.432429 | + | 0.748988i | ||||
\(59\) | −2.74898 | − | 4.76138i | −0.357887 | − | 0.619879i | 0.629721 | − | 0.776822i | \(-0.283169\pi\) |
−0.987608 | + | 0.156943i | \(0.949836\pi\) | |||||||
\(60\) | 0.212835 | + | 0.292943i | 0.0274769 | + | 0.0378188i | ||||
\(61\) | 5.87218 | − | 10.1709i | 0.751855 | − | 1.30225i | −0.195068 | − | 0.980790i | \(-0.562493\pi\) |
0.946923 | − | 0.321461i | \(-0.104174\pi\) | |||||||
\(62\) | −0.921727 | −0.117059 | ||||||||
\(63\) | −2.93444 | + | 0.623735i | −0.369705 | + | 0.0785832i | ||||
\(64\) | 8.65227 | 1.08153 | ||||||||
\(65\) | 0.891693 | − | 1.54446i | 0.110601 | − | 0.191566i | ||||
\(66\) | 1.52547 | − | 0.160333i | 0.187772 | − | 0.0197356i | ||||
\(67\) | 3.30902 | + | 5.73139i | 0.404261 | + | 0.700200i | 0.994235 | − | 0.107222i | \(-0.0341955\pi\) |
−0.589974 | + | 0.807422i | \(0.700862\pi\) | |||||||
\(68\) | 0.139886 | + | 0.242290i | 0.0169637 | + | 0.0293820i | ||||
\(69\) | 8.98097 | − | 0.943938i | 1.08118 | − | 0.113637i | ||||
\(70\) | 0.669131 | − | 1.15897i | 0.0799764 | − | 0.138523i | ||||
\(71\) | 5.79659 | 0.687929 | 0.343964 | − | 0.938983i | \(-0.388230\pi\) | ||||
0.343964 | + | 0.938983i | \(0.388230\pi\) | |||||||
\(72\) | −5.93444 | − | 6.59087i | −0.699381 | − | 0.776741i | ||||
\(73\) | 0.0885901 | 0.0103687 | 0.00518434 | − | 0.999987i | \(-0.498350\pi\) | ||||
0.00518434 | + | 0.999987i | \(0.498350\pi\) | |||||||
\(74\) | −4.37490 | + | 7.57754i | −0.508571 | + | 0.880872i | ||||
\(75\) | 1.01807 | + | 1.40126i | 0.117557 | + | 0.161803i | ||||
\(76\) | −0.451727 | − | 0.782414i | −0.0518166 | − | 0.0897490i | ||||
\(77\) | 0.330869 | + | 0.573083i | 0.0377061 | + | 0.0653088i | ||||
\(78\) | −1.68136 | + | 3.77639i | −0.190376 | + | 0.427592i | ||||
\(79\) | −5.78477 | + | 10.0195i | −0.650837 | + | 1.12728i | 0.332083 | + | 0.943250i | \(0.392249\pi\) |
−0.982920 | + | 0.184033i | \(0.941085\pi\) | |||||||
\(80\) | 3.53818 | 0.395581 | ||||||||
\(81\) | −0.940756 | + | 8.95070i | −0.104528 | + | 0.994522i | ||||
\(82\) | 1.09675 | 0.121116 | ||||||||
\(83\) | −0.978938 | + | 1.69557i | −0.107452 | + | 0.186113i | −0.914737 | − | 0.404049i | \(-0.867603\pi\) |
0.807285 | + | 0.590162i | \(0.200936\pi\) | |||||||
\(84\) | 0.147278 | − | 0.330792i | 0.0160694 | − | 0.0360924i | ||||
\(85\) | 0.669131 | + | 1.15897i | 0.0725774 | + | 0.125708i | ||||
\(86\) | −1.09697 | − | 1.90001i | −0.118289 | − | 0.204883i | ||||
\(87\) | 5.01068 | + | 6.89661i | 0.537202 | + | 0.739394i | ||||
\(88\) | −0.978148 | + | 1.69420i | −0.104271 | + | 0.180602i | ||||
\(89\) | −13.1606 | −1.39502 | −0.697508 | − | 0.716577i | \(-0.745708\pi\) | ||||
−0.697508 | + | 0.716577i | \(0.745708\pi\) | |||||||
\(90\) | −2.68641 | − | 2.98357i | −0.283173 | − | 0.314495i | ||||
\(91\) | −1.78339 | −0.186950 | ||||||||
\(92\) | −0.544983 | + | 0.943938i | −0.0568184 | + | 0.0984123i | ||||
\(93\) | −1.18641 | + | 0.124697i | −0.123025 | + | 0.0129305i | ||||
\(94\) | 8.14206 | + | 14.1025i | 0.839789 | + | 1.45456i | ||||
\(95\) | −2.16078 | − | 3.74259i | −0.221692 | − | 0.383981i | ||||
\(96\) | 2.02845 | − | 0.213199i | 0.207028 | − | 0.0217595i | ||||
\(97\) | 8.33761 | − | 14.4412i | 0.846556 | − | 1.46628i | −0.0377074 | − | 0.999289i | \(-0.512005\pi\) |
0.884263 | − | 0.466989i | \(-0.154661\pi\) | |||||||
\(98\) | −1.33826 | −0.135185 | ||||||||
\(99\) | 1.94183 | − | 0.412750i | 0.195162 | − | 0.0414829i | ||||
\(100\) | −0.209057 | −0.0209057 | ||||||||
\(101\) | 0.651358 | − | 1.12819i | 0.0648126 | − | 0.112259i | −0.831798 | − | 0.555078i | \(-0.812688\pi\) |
0.896611 | + | 0.442819i | \(0.146022\pi\) | |||||||
\(102\) | −1.82331 | − | 2.50957i | −0.180535 | − | 0.248485i | ||||
\(103\) | −7.68704 | − | 13.3143i | −0.757426 | − | 1.31190i | −0.944159 | − | 0.329490i | \(-0.893123\pi\) |
0.186732 | − | 0.982411i | \(-0.440210\pi\) | |||||||
\(104\) | −2.63611 | − | 4.56587i | −0.258492 | − | 0.447721i | ||||
\(105\) | 0.704489 | − | 1.58231i | 0.0687510 | − | 0.154417i | ||||
\(106\) | 9.24892 | − | 16.0196i | 0.898335 | − | 1.55596i | ||||
\(107\) | −14.8776 | −1.43827 | −0.719137 | − | 0.694868i | \(-0.755463\pi\) | ||||
−0.719137 | + | 0.694868i | \(0.755463\pi\) | |||||||
\(108\) | −0.807272 | − | 0.726871i | −0.0776798 | − | 0.0699432i | ||||
\(109\) | −2.65727 | −0.254521 | −0.127260 | − | 0.991869i | \(-0.540618\pi\) | ||||
−0.127260 | + | 0.991869i | \(0.540618\pi\) | |||||||
\(110\) | −0.442790 | + | 0.766934i | −0.0422183 | + | 0.0731243i | ||||
\(111\) | −4.60607 | + | 10.3454i | −0.437189 | + | 0.981943i | ||||
\(112\) | −1.76909 | − | 3.06415i | −0.167163 | − | 0.289535i | ||||
\(113\) | 6.57969 | + | 11.3964i | 0.618965 | + | 1.07208i | 0.989675 | + | 0.143330i | \(0.0457810\pi\) |
−0.370710 | + | 0.928749i | \(0.620886\pi\) | |||||||
\(114\) | 5.88791 | + | 8.10402i | 0.551454 | + | 0.759011i | ||||
\(115\) | −2.60686 | + | 4.51522i | −0.243091 | + | 0.421046i | ||||
\(116\) | −1.02892 | −0.0955329 | ||||||||
\(117\) | −1.65329 | + | 5.08830i | −0.152847 | + | 0.470414i | ||||
\(118\) | −7.35772 | −0.677333 | ||||||||
\(119\) | 0.669131 | − | 1.15897i | 0.0613391 | − | 0.106242i | ||||
\(120\) | 5.09240 | − | 0.535233i | 0.464871 | − | 0.0488599i | ||||
\(121\) | 5.28105 | + | 9.14705i | 0.480096 | + | 0.831550i | ||||
\(122\) | −7.85851 | − | 13.6113i | −0.711476 | − | 1.23231i | ||||
\(123\) | 1.41170 | − | 0.148375i | 0.127289 | − | 0.0133786i | ||||
\(124\) | 0.0719940 | − | 0.124697i | 0.00646525 | − | 0.0111981i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.24064 | + | 3.81829i | −0.110525 | + | 0.340160i | ||||
\(127\) | −11.0026 | −0.976319 | −0.488159 | − | 0.872754i | \(-0.662332\pi\) | ||||
−0.488159 | + | 0.872754i | \(0.662332\pi\) | |||||||
\(128\) | 4.61192 | − | 7.98808i | 0.407640 | − | 0.706053i | ||||
\(129\) | −1.66903 | − | 2.29722i | −0.146950 | − | 0.202259i | ||||
\(130\) | −1.19332 | − | 2.06689i | −0.104661 | − | 0.181278i | ||||
\(131\) | −4.31651 | − | 7.47642i | −0.377135 | − | 0.653218i | 0.613509 | − | 0.789688i | \(-0.289757\pi\) |
−0.990644 | + | 0.136470i | \(0.956424\pi\) | |||||||
\(132\) | −0.0974597 | + | 0.218898i | −0.00848278 | + | 0.0190526i | ||||
\(133\) | −2.16078 | + | 3.74259i | −0.187364 | + | 0.324523i | ||||
\(134\) | 8.85666 | 0.765099 | ||||||||
\(135\) | −3.86149 | − | 3.47690i | −0.332344 | − | 0.299244i | ||||
\(136\) | 3.95630 | 0.339250 | ||||||||
\(137\) | 6.55248 | − | 11.3492i | 0.559816 | − | 0.969630i | −0.437695 | − | 0.899123i | \(-0.644205\pi\) |
0.997511 | − | 0.0705062i | \(-0.0224615\pi\) | |||||||
\(138\) | 4.91545 | − | 11.0403i | 0.418431 | − | 0.939811i | ||||
\(139\) | −2.84565 | − | 4.92882i | −0.241365 | − | 0.418057i | 0.719738 | − | 0.694246i | \(-0.244262\pi\) |
−0.961103 | + | 0.276189i | \(0.910928\pi\) | |||||||
\(140\) | 0.104528 | + | 0.181049i | 0.00883427 | + | 0.0153014i | ||||
\(141\) | 12.3880 | + | 17.0507i | 1.04326 | + | 1.43593i | ||||
\(142\) | 3.87868 | − | 6.71806i | 0.325491 | − | 0.563767i | ||||
\(143\) | 1.18014 | 0.0986879 | ||||||||
\(144\) | −10.3826 | + | 2.20689i | −0.865216 | + | 0.183907i | ||||
\(145\) | −4.92173 | −0.408727 | ||||||||
\(146\) | 0.0592784 | − | 0.102673i | 0.00490591 | − | 0.00849729i | ||||
\(147\) | −1.72256 | + | 0.181049i | −0.142075 | + | 0.0149326i | ||||
\(148\) | −0.683426 | − | 1.18373i | −0.0561773 | − | 0.0973019i | ||||
\(149\) | −4.81135 | − | 8.33351i | −0.394161 | − | 0.682707i | 0.598832 | − | 0.800874i | \(-0.295632\pi\) |
−0.992994 | + | 0.118167i | \(0.962298\pi\) | |||||||
\(150\) | 2.30524 | − | 0.242290i | 0.188222 | − | 0.0197829i | ||||
\(151\) | 3.62309 | − | 6.27538i | 0.294843 | − | 0.510683i | −0.680105 | − | 0.733114i | \(-0.738066\pi\) |
0.974948 | + | 0.222431i | \(0.0713993\pi\) | |||||||
\(152\) | −12.7758 | −1.03626 | ||||||||
\(153\) | −2.68641 | − | 2.98357i | −0.217184 | − | 0.241207i | ||||
\(154\) | 0.885579 | 0.0713620 | ||||||||
\(155\) | 0.344375 | − | 0.596475i | 0.0276609 | − | 0.0479100i | ||||
\(156\) | −0.379568 | − | 0.522430i | −0.0303897 | − | 0.0418279i | ||||
\(157\) | 9.54870 | + | 16.5388i | 0.762069 | + | 1.31994i | 0.941782 | + | 0.336223i | \(0.109150\pi\) |
−0.179713 | + | 0.983719i | \(0.557517\pi\) | |||||||
\(158\) | 7.74153 | + | 13.4087i | 0.615883 | + | 1.06674i | ||||
\(159\) | 9.73765 | − | 21.8711i | 0.772246 | − | 1.73449i | ||||
\(160\) | −0.588790 | + | 1.01981i | −0.0465479 | + | 0.0806234i | ||||
\(161\) | 5.21373 | 0.410899 | ||||||||
\(162\) | 9.74408 | + | 7.07949i | 0.765568 | + | 0.556217i | ||||
\(163\) | −17.7525 | −1.39048 | −0.695242 | − | 0.718776i | \(-0.744703\pi\) | ||||
−0.695242 | + | 0.718776i | \(0.744703\pi\) | |||||||
\(164\) | −0.0856646 | + | 0.148375i | −0.00668928 | + | 0.0115862i | ||||
\(165\) | −0.466187 | + | 1.04707i | −0.0362926 | + | 0.0815146i | ||||
\(166\) | 1.31007 | + | 2.26911i | 0.101681 | + | 0.176117i | ||||
\(167\) | 1.93822 | + | 3.35710i | 0.149984 | + | 0.259780i | 0.931221 | − | 0.364454i | \(-0.118744\pi\) |
−0.781237 | + | 0.624234i | \(0.785411\pi\) | |||||||
\(168\) | −3.00973 | − | 4.14253i | −0.232205 | − | 0.319603i | ||||
\(169\) | 4.90977 | − | 8.50397i | 0.377674 | − | 0.654151i | ||||
\(170\) | 1.79094 | 0.137359 | ||||||||
\(171\) | 8.67508 | + | 9.63465i | 0.663400 | + | 0.736780i | ||||
\(172\) | 0.342728 | 0.0261327 | ||||||||
\(173\) | 7.23560 | − | 12.5324i | 0.550113 | − | 0.952823i | −0.448153 | − | 0.893957i | \(-0.647918\pi\) |
0.998266 | − | 0.0588662i | \(-0.0187485\pi\) | |||||||
\(174\) | 11.3458 | − | 1.19249i | 0.860119 | − | 0.0904022i | ||||
\(175\) | 0.500000 | + | 0.866025i | 0.0377964 | + | 0.0654654i | ||||
\(176\) | 1.17068 | + | 2.02767i | 0.0882430 | + | 0.152841i | ||||
\(177\) | −9.47059 | + | 0.995399i | −0.711853 | + | 0.0748188i | ||||
\(178\) | −8.80613 | + | 15.2527i | −0.660047 | + | 1.14324i | ||||
\(179\) | 5.15248 | 0.385114 | 0.192557 | − | 0.981286i | \(-0.438322\pi\) | ||||
0.192557 | + | 0.981286i | \(0.438322\pi\) | |||||||
\(180\) | 0.613466 | − | 0.130396i | 0.0457250 | − | 0.00971915i | ||||
\(181\) | −20.8252 | −1.54792 | −0.773962 | − | 0.633232i | \(-0.781728\pi\) | ||||
−0.773962 | + | 0.633232i | \(0.781728\pi\) | |||||||
\(182\) | −1.19332 | + | 2.06689i | −0.0884546 | + | 0.153208i | ||||
\(183\) | −11.9566 | − | 16.4569i | −0.883859 | − | 1.21653i | ||||
\(184\) | 7.70666 | + | 13.3483i | 0.568142 | + | 0.984052i | ||||
\(185\) | −3.26909 | − | 5.66223i | −0.240348 | − | 0.416296i | ||||
\(186\) | −0.649346 | + | 1.45846i | −0.0476124 | + | 0.106939i | ||||
\(187\) | −0.442790 | + | 0.766934i | −0.0323800 | + | 0.0560838i | ||||
\(188\) | −2.54383 | −0.185528 | ||||||||
\(189\) | −1.08034 | + | 5.08260i | −0.0785832 | + | 0.369705i | ||||
\(190\) | −5.78339 | −0.419571 | ||||||||
\(191\) | 9.32177 | − | 16.1458i | 0.674499 | − | 1.16827i | −0.302116 | − | 0.953271i | \(-0.597693\pi\) |
0.976615 | − | 0.214996i | \(-0.0689738\pi\) | |||||||
\(192\) | 6.09543 | − | 13.6906i | 0.439899 | − | 0.988030i | ||||
\(193\) | −6.92735 | − | 11.9985i | −0.498642 | − | 0.863673i | 0.501357 | − | 0.865241i | \(-0.332834\pi\) |
−0.999999 | + | 0.00156765i | \(0.999501\pi\) | |||||||
\(194\) | −11.1579 | − | 19.3260i | −0.801090 | − | 1.38753i | ||||
\(195\) | −1.81562 | − | 2.49899i | −0.130019 | − | 0.178956i | ||||
\(196\) | 0.104528 | − | 0.181049i | 0.00746632 | − | 0.0129320i | ||||
\(197\) | 10.7261 | 0.764206 | 0.382103 | − | 0.924120i | \(-0.375200\pi\) | ||||
0.382103 | + | 0.924120i | \(0.375200\pi\) | |||||||
\(198\) | 0.820977 | − | 2.52671i | 0.0583443 | − | 0.179565i | ||||
\(199\) | 6.26970 | 0.444447 | 0.222224 | − | 0.974996i | \(-0.428668\pi\) | ||||
0.222224 | + | 0.974996i | \(0.428668\pi\) | |||||||
\(200\) | −1.47815 | + | 2.56023i | −0.104521 | + | 0.181035i | ||||
\(201\) | 11.4000 | − | 1.19819i | 0.804092 | − | 0.0845135i | ||||
\(202\) | −0.871688 | − | 1.50981i | −0.0613317 | − | 0.106230i | ||||
\(203\) | 2.46086 | + | 4.26234i | 0.172719 | + | 0.299158i | ||||
\(204\) | 0.481926 | − | 0.0506525i | 0.0337416 | − | 0.00354638i | ||||
\(205\) | −0.409767 | + | 0.709737i | −0.0286194 | + | 0.0495702i | ||||
\(206\) | −20.5745 | −1.43350 | ||||||||
\(207\) | 4.83339 | − | 14.8756i | 0.335944 | − | 1.03393i | ||||
\(208\) | −6.30994 | −0.437516 | ||||||||
\(209\) | 1.42987 | − | 2.47662i | 0.0989065 | − | 0.171311i | ||||
\(210\) | −1.36245 | − | 1.87525i | −0.0940179 | − | 0.129405i | ||||
\(211\) | −5.16168 | − | 8.94028i | −0.355344 | − | 0.615475i | 0.631832 | − | 0.775105i | \(-0.282303\pi\) |
−0.987177 | + | 0.159630i | \(0.948970\pi\) | |||||||
\(212\) | 1.44482 | + | 2.50251i | 0.0992309 | + | 0.171873i | ||||
\(213\) | 4.08363 | − | 9.17199i | 0.279806 | − | 0.628454i | ||||
\(214\) | −9.95507 | + | 17.2427i | −0.680515 | + | 1.17869i | ||||
\(215\) | 1.63940 | 0.111806 | ||||||||
\(216\) | −14.6095 | + | 4.74692i | −0.994052 | + | 0.322987i | ||||
\(217\) | −0.688750 | −0.0467554 | ||||||||
\(218\) | −1.77806 | + | 3.07969i | −0.120426 | + | 0.208583i | ||||
\(219\) | 0.0624107 | − | 0.140177i | 0.00421733 | − | 0.00947227i | ||||
\(220\) | −0.0691705 | − | 0.119807i | −0.00466348 | − | 0.00807738i | ||||
\(221\) | −1.19332 | − | 2.06689i | −0.0802713 | − | 0.139034i | ||||
\(222\) | 8.90794 | + | 12.2607i | 0.597862 | + | 0.822886i | ||||
\(223\) | −2.42626 | + | 4.20241i | −0.162474 | + | 0.281414i | −0.935756 | − | 0.352649i | \(-0.885281\pi\) |
0.773281 | + | 0.634063i | \(0.218614\pi\) | |||||||
\(224\) | 1.17758 | 0.0786803 | ||||||||
\(225\) | 2.93444 | − | 0.623735i | 0.195630 | − | 0.0415823i | ||||
\(226\) | 17.6107 | 1.17145 | ||||||||
\(227\) | 4.88588 | − | 8.46259i | 0.324287 | − | 0.561682i | −0.657081 | − | 0.753820i | \(-0.728209\pi\) |
0.981368 | + | 0.192138i | \(0.0615422\pi\) | |||||||
\(228\) | −1.55626 | + | 0.163569i | −0.103066 | + | 0.0108326i | ||||
\(229\) | −8.07427 | − | 13.9850i | −0.533563 | − | 0.924157i | −0.999231 | − | 0.0391984i | \(-0.987520\pi\) |
0.465669 | − | 0.884959i | \(-0.345814\pi\) | |||||||
\(230\) | 3.48866 | + | 6.04254i | 0.230036 | + | 0.398434i | ||||
\(231\) | 1.13989 | − | 0.119807i | 0.0749990 | − | 0.00788271i | ||||
\(232\) | −7.27504 | + | 12.6007i | −0.477630 | + | 0.827279i | ||||
\(233\) | 5.76414 | 0.377621 | 0.188811 | − | 0.982014i | \(-0.439537\pi\) | ||||
0.188811 | + | 0.982014i | \(0.439537\pi\) | |||||||
\(234\) | 4.79091 | + | 5.32085i | 0.313192 | + | 0.347835i | ||||
\(235\) | −12.1681 | −0.793760 | ||||||||
\(236\) | 0.574694 | − | 0.995399i | 0.0374094 | − | 0.0647950i | ||||
\(237\) | 11.7786 | + | 16.2119i | 0.765105 | + | 1.05308i | ||||
\(238\) | −0.895472 | − | 1.55100i | −0.0580448 | − | 0.100537i | ||||
\(239\) | −0.0605219 | − | 0.104827i | −0.00391484 | − | 0.00678070i | 0.864061 | − | 0.503387i | \(-0.167913\pi\) |
−0.867976 | + | 0.496606i | \(0.834579\pi\) | |||||||
\(240\) | 2.49261 | − | 5.59849i | 0.160897 | − | 0.361381i | ||||
\(241\) | −10.4808 | + | 18.1533i | −0.675128 | + | 1.16936i | 0.301303 | + | 0.953528i | \(0.402578\pi\) |
−0.976431 | + | 0.215828i | \(0.930755\pi\) | |||||||
\(242\) | 14.1349 | 0.908623 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 2.45524 | 0.157181 | ||||||||
\(245\) | 0.500000 | − | 0.866025i | 0.0319438 | − | 0.0553283i | ||||
\(246\) | 0.772648 | − | 1.73540i | 0.0492622 | − | 0.110645i | ||||
\(247\) | 3.85351 | + | 6.67448i | 0.245193 | + | 0.424687i | ||||
\(248\) | −1.01807 | − | 1.76336i | −0.0646478 | − | 0.111973i | ||||
\(249\) | 1.99326 | + | 2.74349i | 0.126318 | + | 0.173862i | ||||
\(250\) | −0.669131 | + | 1.15897i | −0.0423195 | + | 0.0732996i | ||||
\(251\) | −15.1644 | −0.957170 | −0.478585 | − | 0.878041i | \(-0.658850\pi\) | ||||
−0.478585 | + | 0.878041i | \(0.658850\pi\) | |||||||
\(252\) | −0.419659 | − | 0.466079i | −0.0264360 | − | 0.0293602i | ||||
\(253\) | −3.45013 | −0.216908 | ||||||||
\(254\) | −7.36215 | + | 12.7516i | −0.461942 | + | 0.800107i | ||||
\(255\) | 2.30524 | − | 0.242290i | 0.144360 | − | 0.0151728i | ||||
\(256\) | 2.48032 | + | 4.29604i | 0.155020 | + | 0.268502i | ||||
\(257\) | 10.9827 | + | 19.0225i | 0.685080 | + | 1.18659i | 0.973412 | + | 0.229063i | \(0.0735663\pi\) |
−0.288331 | + | 0.957531i | \(0.593100\pi\) | |||||||
\(258\) | −3.77920 | + | 0.397210i | −0.235283 | + | 0.0247292i | ||||
\(259\) | −3.26909 | + | 5.66223i | −0.203131 | + | 0.351834i | ||||
\(260\) | 0.372829 | 0.0231219 | ||||||||
\(261\) | 14.4425 | − | 3.06985i | 0.893970 | − | 0.190019i | ||||
\(262\) | −11.5532 | −0.713761 | ||||||||
\(263\) | 16.0183 | − | 27.7446i | 0.987733 | − | 1.71080i | 0.358633 | − | 0.933478i | \(-0.383243\pi\) |
0.629099 | − | 0.777325i | \(-0.283424\pi\) | |||||||
\(264\) | 1.99165 | + | 2.74128i | 0.122578 | + | 0.168714i | ||||
\(265\) | 6.91115 | + | 11.9705i | 0.424548 | + | 0.735339i | ||||
\(266\) | 2.89169 | + | 5.00856i | 0.177301 | + | 0.307094i | ||||
\(267\) | −9.27146 | + | 20.8240i | −0.567404 | + | 1.27441i | ||||
\(268\) | −0.691773 | + | 1.19819i | −0.0422568 | + | 0.0731908i | ||||
\(269\) | 4.59293 | 0.280036 | 0.140018 | − | 0.990149i | \(-0.455284\pi\) | ||||
0.140018 | + | 0.990149i | \(0.455284\pi\) | |||||||
\(270\) | −6.61347 | + | 2.14885i | −0.402483 | + | 0.130775i | ||||
\(271\) | 16.2926 | 0.989708 | 0.494854 | − | 0.868976i | \(-0.335222\pi\) | ||||
0.494854 | + | 0.868976i | \(0.335222\pi\) | |||||||
\(272\) | 2.36751 | − | 4.10064i | 0.143551 | − | 0.248638i | ||||
\(273\) | −1.25638 | + | 2.82186i | −0.0760393 | + | 0.170787i | ||||
\(274\) | −8.76893 | − | 15.1882i | −0.529750 | − | 0.917554i | ||||
\(275\) | −0.330869 | − | 0.573083i | −0.0199522 | − | 0.0345582i | ||||
\(276\) | 1.10967 | + | 1.52732i | 0.0667940 | + | 0.0919341i | ||||
\(277\) | 15.5820 | − | 26.9889i | 0.936234 | − | 1.62161i | 0.163816 | − | 0.986491i | \(-0.447620\pi\) |
0.772418 | − | 0.635114i | \(-0.219047\pi\) | |||||||
\(278\) | −7.61645 | −0.456805 | ||||||||
\(279\) | −0.638506 | + | 1.96512i | −0.0382264 | + | 0.117649i | ||||
\(280\) | 2.95630 | 0.176672 | ||||||||
\(281\) | −9.74628 | + | 16.8811i | −0.581415 | + | 1.00704i | 0.413898 | + | 0.910323i | \(0.364167\pi\) |
−0.995312 | + | 0.0967160i | \(0.969166\pi\) | |||||||
\(282\) | 28.0504 | − | 2.94822i | 1.67038 | − | 0.175564i | ||||
\(283\) | 15.1440 | + | 26.2302i | 0.900219 | + | 1.55922i | 0.827209 | + | 0.561894i | \(0.189927\pi\) |
0.0730095 | + | 0.997331i | \(0.476740\pi\) | |||||||
\(284\) | 0.605909 | + | 1.04946i | 0.0359541 | + | 0.0622743i | ||||
\(285\) | −7.44417 | + | 0.782414i | −0.440955 | + | 0.0463462i | ||||
\(286\) | 0.789665 | − | 1.36774i | 0.0466939 | − | 0.0808762i | ||||
\(287\) | 0.819534 | 0.0483756 | ||||||||
\(288\) | 1.09168 | − | 3.35983i | 0.0643276 | − | 0.197980i | ||||
\(289\) | −15.2091 | −0.894650 | ||||||||
\(290\) | −3.29328 | + | 5.70413i | −0.193388 | + | 0.334958i | ||||
\(291\) | −16.9766 | − | 23.3663i | −0.995186 | − | 1.36976i | ||||
\(292\) | 0.00926019 | + | 0.0160391i | 0.000541912 | + | 0.000938618i | ||||
\(293\) | 12.3622 | + | 21.4119i | 0.722206 | + | 1.25090i | 0.960114 | + | 0.279610i | \(0.0902052\pi\) |
−0.237907 | + | 0.971288i | \(0.576461\pi\) | |||||||
\(294\) | −0.942790 | + | 2.11754i | −0.0549846 | + | 0.123497i | ||||
\(295\) | 2.74898 | − | 4.76138i | 0.160052 | − | 0.277218i | ||||
\(296\) | −19.3288 | −1.12346 | ||||||||
\(297\) | 0.714903 | − | 3.36336i | 0.0414829 | − | 0.195162i | ||||
\(298\) | −12.8777 | −0.745985 | ||||||||
\(299\) | 4.64904 | − | 8.05238i | 0.268861 | − | 0.465681i | ||||
\(300\) | −0.147278 | + | 0.330792i | −0.00850311 | + | 0.0190983i | ||||
\(301\) | −0.819699 | − | 1.41976i | −0.0472467 | − | 0.0818336i | ||||
\(302\) | −4.84864 | − | 8.39809i | −0.279008 | − | 0.483256i | ||||
\(303\) | −1.32626 | − | 1.82544i | −0.0761918 | − | 0.104869i | ||||
\(304\) | −7.64524 | + | 13.2420i | −0.438485 | + | 0.759478i | ||||
\(305\) | 11.7444 | 0.672480 | ||||||||
\(306\) | −5.25542 | + | 1.11707i | −0.300432 | + | 0.0638589i | ||||
\(307\) | 10.1284 | 0.578060 | 0.289030 | − | 0.957320i | \(-0.406667\pi\) | ||||
0.289030 | + | 0.957320i | \(0.406667\pi\) | |||||||
\(308\) | −0.0691705 | + | 0.119807i | −0.00394136 | + | 0.00682663i | ||||
\(309\) | −26.4828 | + | 2.78346i | −1.50655 | + | 0.158345i | ||||
\(310\) | −0.460864 | − | 0.798239i | −0.0261753 | − | 0.0453369i | ||||
\(311\) | −6.67150 | − | 11.5554i | −0.378306 | − | 0.655245i | 0.612510 | − | 0.790463i | \(-0.290160\pi\) |
−0.990816 | + | 0.135218i | \(0.956827\pi\) | |||||||
\(312\) | −9.08172 | + | 0.954527i | −0.514151 | + | 0.0540395i | ||||
\(313\) | −8.22745 | + | 14.2504i | −0.465043 | + | 0.805478i | −0.999203 | − | 0.0399048i | \(-0.987295\pi\) |
0.534160 | + | 0.845383i | \(0.320628\pi\) | |||||||
\(314\) | 25.5573 | 1.44228 | ||||||||
\(315\) | −2.00739 | − | 2.22943i | −0.113104 | − | 0.125614i | ||||
\(316\) | −2.41869 | −0.136062 | ||||||||
\(317\) | 8.81216 | − | 15.2631i | 0.494940 | − | 0.857262i | −0.505043 | − | 0.863094i | \(-0.668523\pi\) |
0.999983 | + | 0.00583249i | \(0.00185655\pi\) | |||||||
\(318\) | −18.8322 | − | 25.9203i | −1.05606 | − | 1.45354i | ||||
\(319\) | −1.62845 | − | 2.82056i | −0.0911756 | − | 0.157921i | ||||
\(320\) | 4.32614 | + | 7.49309i | 0.241838 | + | 0.418876i | ||||
\(321\) | −10.4811 | + | 23.5410i | −0.584999 | + | 1.31393i | ||||
\(322\) | 3.48866 | − | 6.04254i | 0.194416 | − | 0.336738i | ||||
\(323\) | −5.78339 | −0.321796 | ||||||||
\(324\) | −1.71885 | + | 0.765280i | −0.0954915 | + | 0.0425156i | ||||
\(325\) | 1.78339 | 0.0989245 | ||||||||
\(326\) | −11.8787 | + | 20.5746i | −0.657903 | + | 1.13952i | ||||
\(327\) | −1.87202 | + | 4.20462i | −0.103523 | + | 0.232516i | ||||
\(328\) | 1.21139 | + | 2.09819i | 0.0668879 | + | 0.115853i | ||||
\(329\) | 6.08406 | + | 10.5379i | 0.335425 | + | 0.580973i | ||||
\(330\) | 0.901585 | + | 1.24093i | 0.0496306 | + | 0.0683107i | ||||
\(331\) | −5.54082 | + | 9.59698i | −0.304551 | + | 0.527498i | −0.977161 | − | 0.212499i | \(-0.931840\pi\) |
0.672610 | + | 0.739997i | \(0.265173\pi\) | |||||||
\(332\) | −0.409307 | −0.0224637 | ||||||||
\(333\) | 13.1247 | + | 14.5764i | 0.719229 | + | 0.798784i | ||||
\(334\) | 5.18769 | 0.283858 | ||||||||
\(335\) | −3.30902 | + | 5.73139i | −0.180791 | + | 0.313139i | ||||
\(336\) | −6.09474 | + | 0.640583i | −0.332495 | + | 0.0349467i | ||||
\(337\) | 9.46448 | + | 16.3930i | 0.515563 | + | 0.892981i | 0.999837 | + | 0.0180647i | \(0.00575049\pi\) |
−0.484274 | + | 0.874916i | \(0.660916\pi\) | |||||||
\(338\) | −6.57055 | − | 11.3805i | −0.357391 | − | 0.619019i | ||||
\(339\) | 22.6678 | − | 2.38249i | 1.23115 | − | 0.129399i | ||||
\(340\) | −0.139886 | + | 0.242290i | −0.00758640 | + | 0.0131400i | ||||
\(341\) | 0.455772 | 0.0246815 | ||||||||
\(342\) | 16.9710 | − | 3.60730i | 0.917687 | − | 0.195060i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.42327 | − | 4.19723i | 0.130654 | − | 0.226300i | ||||
\(345\) | 5.30796 | + | 7.30578i | 0.285771 | + | 0.393330i | ||||
\(346\) | −9.68312 | − | 16.7717i | −0.520568 | − | 0.901650i | ||||
\(347\) | −9.71113 | − | 16.8202i | −0.521321 | − | 0.902954i | −0.999693 | − | 0.0247966i | \(-0.992106\pi\) |
0.478372 | − | 0.878157i | \(-0.341227\pi\) | |||||||
\(348\) | −0.724863 | + | 1.62807i | −0.0388567 | + | 0.0872737i | ||||
\(349\) | 11.2191 | − | 19.4320i | 0.600544 | − | 1.04017i | −0.392195 | − | 0.919882i | \(-0.628284\pi\) |
0.992739 | − | 0.120290i | \(-0.0383826\pi\) | |||||||
\(350\) | 1.33826 | 0.0715331 | ||||||||
\(351\) | 6.88653 | + | 6.20066i | 0.367576 | + | 0.330967i | ||||
\(352\) | −0.779250 | −0.0415342 | ||||||||
\(353\) | −6.72055 | + | 11.6403i | −0.357699 | + | 0.619552i | −0.987576 | − | 0.157142i | \(-0.949772\pi\) |
0.629877 | + | 0.776695i | \(0.283105\pi\) | |||||||
\(354\) | −5.18343 | + | 11.6422i | −0.275496 | + | 0.618774i | ||||
\(355\) | 2.89829 | + | 5.01999i | 0.153826 | + | 0.266434i | ||||
\(356\) | −1.37565 | − | 2.38270i | −0.0729094 | − | 0.126283i | ||||
\(357\) | −1.36245 | − | 1.87525i | −0.0721084 | − | 0.0992488i | ||||
\(358\) | 3.44768 | − | 5.97156i | 0.182216 | − | 0.315607i | ||||
\(359\) | −15.0019 | −0.791771 | −0.395885 | − | 0.918300i | \(-0.629562\pi\) | ||||
−0.395885 | + | 0.918300i | \(0.629562\pi\) | |||||||
\(360\) | 2.74064 | − | 8.43481i | 0.144444 | − | 0.444554i | ||||
\(361\) | −0.324055 | −0.0170555 | ||||||||
\(362\) | −13.9348 | + | 24.1357i | −0.732395 | + | 1.26855i | ||||
\(363\) | 18.1939 | − | 1.91225i | 0.954931 | − | 0.100367i | ||||
\(364\) | −0.186415 | − | 0.322880i | −0.00977078 | − | 0.0169235i | ||||
\(365\) | 0.0442951 | + | 0.0767213i | 0.00231851 | + | 0.00401578i | ||||
\(366\) | −27.0735 | + | 2.84554i | −1.41516 | + | 0.148739i | ||||
\(367\) | −1.22382 | + | 2.11972i | −0.0638828 | + | 0.110648i | −0.896198 | − | 0.443655i | \(-0.853682\pi\) |
0.832315 | + | 0.554303i | \(0.187015\pi\) | |||||||
\(368\) | 18.4471 | 0.961622 | ||||||||
\(369\) | 0.759750 | − | 2.33827i | 0.0395510 | − | 0.121725i | ||||
\(370\) | −8.74979 | −0.454880 | ||||||||
\(371\) | 6.91115 | − | 11.9705i | 0.358809 | − | 0.621475i | ||||
\(372\) | −0.146590 | − | 0.201764i | −0.00760036 | − | 0.0104610i | ||||
\(373\) | 9.56227 | + | 16.5623i | 0.495115 | + | 0.857565i | 0.999984 | − | 0.00563108i | \(-0.00179244\pi\) |
−0.504869 | + | 0.863196i | \(0.668459\pi\) | |||||||
\(374\) | 0.592568 | + | 1.02636i | 0.0306410 | + | 0.0530717i | ||||
\(375\) | −0.704489 | + | 1.58231i | −0.0363796 | + | 0.0817100i | ||||
\(376\) | −17.9863 | + | 31.1531i | −0.927571 | + | 1.60660i | ||||
\(377\) | 8.77734 | 0.452056 | ||||||||
\(378\) | 5.16769 | + | 4.65301i | 0.265797 | + | 0.239325i | ||||
\(379\) | −3.51235 | −0.180417 | −0.0902087 | − | 0.995923i | \(-0.528753\pi\) | ||||
−0.0902087 | + | 0.995923i | \(0.528753\pi\) | |||||||
\(380\) | 0.451727 | − | 0.782414i | 0.0231731 | − | 0.0401370i | ||||
\(381\) | −7.75117 | + | 17.4094i | −0.397105 | + | 0.891912i | ||||
\(382\) | −12.4750 | − | 21.6073i | −0.638274 | − | 1.10552i | ||||
\(383\) | 14.3290 | + | 24.8185i | 0.732176 | + | 1.26817i | 0.955951 | + | 0.293525i | \(0.0948283\pi\) |
−0.223776 | + | 0.974641i | \(0.571838\pi\) | |||||||
\(384\) | −9.39055 | − | 12.9250i | −0.479210 | − | 0.659575i | ||||
\(385\) | −0.330869 | + | 0.573083i | −0.0168627 | + | 0.0292070i | ||||
\(386\) | −18.5412 | −0.943723 | ||||||||
\(387\) | −4.81072 | + | 1.02255i | −0.244543 | + | 0.0519791i | ||||
\(388\) | 3.48607 | 0.176978 | ||||||||
\(389\) | −3.60861 | + | 6.25029i | −0.182964 | + | 0.316902i | −0.942888 | − | 0.333109i | \(-0.891902\pi\) |
0.759925 | + | 0.650011i | \(0.225236\pi\) | |||||||
\(390\) | −4.11113 | + | 0.432097i | −0.208175 | + | 0.0218801i | ||||
\(391\) | 3.48866 | + | 6.04254i | 0.176429 | + | 0.305585i | ||||
\(392\) | −1.47815 | − | 2.56023i | −0.0746577 | − | 0.129311i | ||||
\(393\) | −14.8709 | + | 1.56300i | −0.750139 | + | 0.0788427i | ||||
\(394\) | 7.17719 | − | 12.4313i | 0.361582 | − | 0.626278i | ||||
\(395\) | −11.5695 | −0.582126 | ||||||||
\(396\) | 0.277705 | + | 0.308422i | 0.0139552 | + | 0.0154988i | ||||
\(397\) | 19.8031 | 0.993890 | 0.496945 | − | 0.867782i | \(-0.334455\pi\) | ||||
0.496945 | + | 0.867782i | \(0.334455\pi\) | |||||||
\(398\) | 4.19525 | − | 7.26639i | 0.210289 | − | 0.364231i | ||||
\(399\) | 4.39968 | + | 6.05563i | 0.220259 | + | 0.303161i | ||||
\(400\) | 1.76909 | + | 3.06415i | 0.0884545 | + | 0.153208i | ||||
\(401\) | 4.53946 | + | 7.86257i | 0.226690 | + | 0.392638i | 0.956825 | − | 0.290664i | \(-0.0938763\pi\) |
−0.730135 | + | 0.683303i | \(0.760543\pi\) | |||||||
\(402\) | 6.23941 | − | 14.0140i | 0.311194 | − | 0.698952i | ||||
\(403\) | −0.614153 | + | 1.06374i | −0.0305932 | + | 0.0529889i | ||||
\(404\) | 0.272342 | 0.0135495 | ||||||||
\(405\) | −8.22191 | + | 3.66063i | −0.408550 | + | 0.181898i | ||||
\(406\) | 6.58656 | 0.326885 | ||||||||
\(407\) | 2.16328 | − | 3.74692i | 0.107230 | − | 0.185728i | ||||
\(408\) | 2.78716 | − | 6.26007i | 0.137985 | − | 0.309920i | ||||
\(409\) | −10.1702 | − | 17.6154i | −0.502886 | − | 0.871024i | −0.999994 | − | 0.00333589i | \(-0.998938\pi\) |
0.497108 | − | 0.867689i | \(-0.334395\pi\) | |||||||
\(410\) | 0.548375 | + | 0.949814i | 0.0270823 | + | 0.0469080i | ||||
\(411\) | −13.3418 | − | 18.3634i | −0.658103 | − | 0.905801i | ||||
\(412\) | 1.60703 | − | 2.78346i | 0.0791726 | − | 0.137131i | ||||
\(413\) | −5.49797 | −0.270537 | ||||||||
\(414\) | −14.0062 | − | 15.5555i | −0.688369 | − | 0.764511i | ||||
\(415\) | −1.95788 | −0.0961083 | ||||||||
\(416\) | 1.05004 | − | 1.81872i | 0.0514824 | − | 0.0891702i | ||||
\(417\) | −9.80363 | + | 1.03040i | −0.480086 | + | 0.0504591i | ||||
\(418\) | −1.91355 | − | 3.31436i | −0.0935946 | − | 0.162111i | ||||
\(419\) | −2.90773 | − | 5.03634i | −0.142052 | − | 0.246041i | 0.786217 | − | 0.617950i | \(-0.212037\pi\) |
−0.928269 | + | 0.371909i | \(0.878703\pi\) | |||||||
\(420\) | 0.360114 | − | 0.0378495i | 0.0175717 | − | 0.00184686i | ||||
\(421\) | 16.6573 | − | 28.8513i | 0.811827 | − | 1.40613i | −0.0997562 | − | 0.995012i | \(-0.531806\pi\) |
0.911584 | − | 0.411115i | \(-0.134860\pi\) | |||||||
\(422\) | −13.8153 | −0.672520 | ||||||||
\(423\) | 35.7066 | − | 7.58968i | 1.73612 | − | 0.369023i | ||||
\(424\) | 40.8628 | 1.98447 | ||||||||
\(425\) | −0.669131 | + | 1.15897i | −0.0324576 | + | 0.0562182i | ||||
\(426\) | −7.89756 | − | 10.8701i | −0.382638 | − | 0.526656i | ||||
\(427\) | −5.87218 | − | 10.1709i | −0.284175 | − | 0.492205i | ||||
\(428\) | −1.55514 | − | 2.69357i | −0.0751703 | − | 0.130199i | ||||
\(429\) | 0.831392 | − | 1.86734i | 0.0401400 | − | 0.0901559i | ||||
\(430\) | 1.09697 | − | 1.90001i | 0.0529007 | − | 0.0916266i | ||||
\(431\) | −33.1633 | −1.59742 | −0.798710 | − | 0.601716i | \(-0.794484\pi\) | ||||
−0.798710 | + | 0.601716i | \(0.794484\pi\) | |||||||
\(432\) | −3.82244 | + | 17.9832i | −0.183907 | + | 0.865216i | ||||
\(433\) | 33.2920 | 1.59991 | 0.799955 | − | 0.600060i | \(-0.204856\pi\) | ||||
0.799955 | + | 0.600060i | \(0.204856\pi\) | |||||||
\(434\) | −0.460864 | + | 0.798239i | −0.0221222 | + | 0.0383167i | ||||
\(435\) | −3.46730 | + | 7.78768i | −0.166244 | + | 0.373391i | ||||
\(436\) | −0.277761 | − | 0.481095i | −0.0133023 | − | 0.0230403i | ||||
\(437\) | −11.2657 | − | 19.5128i | −0.538913 | − | 0.933425i | ||||
\(438\) | −0.120699 | − | 0.166129i | −0.00576724 | − | 0.00793793i | ||||
\(439\) | 13.1127 | − | 22.7118i | 0.625834 | − | 1.08398i | −0.362546 | − | 0.931966i | \(-0.618092\pi\) |
0.988379 | − | 0.152009i | \(-0.0485744\pi\) | |||||||
\(440\) | −1.95630 | −0.0932627 | ||||||||
\(441\) | −0.927051 | + | 2.85317i | −0.0441453 | + | 0.135865i | ||||
\(442\) | −3.19394 | −0.151920 | ||||||||
\(443\) | −7.86257 | + | 13.6184i | −0.373562 | + | 0.647029i | −0.990111 | − | 0.140288i | \(-0.955197\pi\) |
0.616549 | + | 0.787317i | \(0.288530\pi\) | |||||||
\(444\) | −2.35449 | + | 0.247467i | −0.111739 | + | 0.0117442i | ||||
\(445\) | −6.58028 | − | 11.3974i | −0.311935 | − | 0.540287i | ||||
\(446\) | 3.24697 | + | 5.62392i | 0.153749 | + | 0.266300i | ||||
\(447\) | −16.5757 | + | 1.74218i | −0.784004 | + | 0.0824022i | ||||
\(448\) | 4.32614 | − | 7.49309i | 0.204391 | − | 0.354015i | ||||
\(449\) | 38.5915 | 1.82125 | 0.910624 | − | 0.413236i | \(-0.135602\pi\) | ||||
0.910624 | + | 0.413236i | \(0.135602\pi\) | |||||||
\(450\) | 1.24064 | − | 3.81829i | 0.0584842 | − | 0.179996i | ||||
\(451\) | −0.542317 | −0.0255367 | ||||||||
\(452\) | −1.37553 | + | 2.38249i | −0.0646995 | + | 0.112063i | ||||
\(453\) | −7.37715 | − | 10.1538i | −0.346609 | − | 0.477066i | ||||
\(454\) | −6.53859 | − | 11.3252i | −0.306871 | − | 0.531516i | ||||
\(455\) | −0.891693 | − | 1.54446i | −0.0418032 | − | 0.0724053i | ||||
\(456\) | −9.00043 | + | 20.2153i | −0.421484 | + | 0.946667i | ||||
\(457\) | 20.7219 | − | 35.8913i | 0.969328 | − | 1.67893i | 0.271821 | − | 0.962348i | \(-0.412374\pi\) |
0.697507 | − | 0.716578i | \(-0.254292\pi\) | |||||||
\(458\) | −21.6110 | −1.00981 | ||||||||
\(459\) | −6.61347 | + | 2.14885i | −0.308690 | + | 0.100300i | ||||
\(460\) | −1.08997 | −0.0508199 | ||||||||
\(461\) | 9.80816 | − | 16.9882i | 0.456812 | − | 0.791221i | −0.541979 | − | 0.840392i | \(-0.682325\pi\) |
0.998790 | + | 0.0491711i | \(0.0156580\pi\) | |||||||
\(462\) | 0.623880 | − | 1.40126i | 0.0290255 | − | 0.0651924i | ||||
\(463\) | −3.04373 | − | 5.27189i | −0.141454 | − | 0.245005i | 0.786590 | − | 0.617475i | \(-0.211844\pi\) |
−0.928044 | + | 0.372470i | \(0.878511\pi\) | |||||||
\(464\) | 8.70698 | + | 15.0809i | 0.404211 | + | 0.700115i | ||||
\(465\) | −0.701198 | − | 0.965117i | −0.0325173 | − | 0.0447562i | ||||
\(466\) | 3.85696 | − | 6.68045i | 0.178670 | − | 0.309466i | ||||
\(467\) | −20.9548 | −0.969672 | −0.484836 | − | 0.874605i | \(-0.661121\pi\) | ||||
−0.484836 | + | 0.874605i | \(0.661121\pi\) | |||||||
\(468\) | −1.09405 | + | 0.232547i | −0.0505723 | + | 0.0107495i | ||||
\(469\) | 6.61803 | 0.305592 | ||||||||
\(470\) | −8.14206 | + | 14.1025i | −0.375565 | + | 0.650498i | ||||
\(471\) | 32.8965 | − | 3.45756i | 1.51579 | − | 0.159316i | ||||
\(472\) | −8.12681 | − | 14.0760i | −0.374067 | − | 0.647902i | ||||
\(473\) | 0.542427 | + | 0.939511i | 0.0249408 | + | 0.0431987i | ||||
\(474\) | 26.6705 | − | 2.80319i | 1.22502 | − | 0.128755i | ||||
\(475\) | 2.16078 | − | 3.74259i | 0.0991436 | − | 0.171722i | ||||
\(476\) | 0.279773 | 0.0128234 | ||||||||
\(477\) | −27.7468 | − | 30.8159i | −1.27044 | − | 1.41096i | ||||
\(478\) | −0.161988 | −0.00740917 | ||||||||
\(479\) | −12.8915 | + | 22.3287i | −0.589026 | + | 1.02022i | 0.405334 | + | 0.914169i | \(0.367155\pi\) |
−0.994360 | + | 0.106055i | \(0.966178\pi\) | |||||||
\(480\) | 1.19886 | + | 1.65009i | 0.0547204 | + | 0.0753161i | ||||
\(481\) | 5.83005 | + | 10.0979i | 0.265827 | + | 0.460427i | ||||
\(482\) | 14.0261 | + | 24.2938i | 0.638869 | + | 1.10655i | ||||
\(483\) | 3.67301 | − | 8.24972i | 0.167128 | − | 0.375375i | ||||
\(484\) | −1.10404 | + | 1.91225i | −0.0501836 | + | 0.0869206i | ||||
\(485\) | 16.6752 | 0.757183 | ||||||||
\(486\) | 18.0665 | − | 10.4307i | 0.819514 | − | 0.473147i | ||||
\(487\) | 27.1083 | 1.22840 | 0.614198 | − | 0.789152i | \(-0.289480\pi\) | ||||
0.614198 | + | 0.789152i | \(0.289480\pi\) | |||||||
\(488\) | 17.3599 | − | 30.0682i | 0.785845 | − | 1.36112i | ||||
\(489\) | −12.5064 | + | 28.0899i | −0.565561 | + | 1.27027i | ||||
\(490\) | −0.669131 | − | 1.15897i | −0.0302282 | − | 0.0523568i | ||||
\(491\) | −11.2506 | − | 19.4866i | −0.507732 | − | 0.879417i | −0.999960 | − | 0.00895100i | \(-0.997151\pi\) |
0.492228 | − | 0.870466i | \(-0.336183\pi\) | |||||||
\(492\) | 0.174426 | + | 0.240077i | 0.00786372 | + | 0.0108235i | ||||
\(493\) | −3.29328 | + | 5.70413i | −0.148322 | + | 0.256901i | ||||
\(494\) | 10.3140 | 0.464049 | ||||||||
\(495\) | 1.32837 | + | 1.47530i | 0.0597057 | + | 0.0663100i | ||||
\(496\) | −2.43692 | −0.109421 | ||||||||
\(497\) | 2.89829 | − | 5.01999i | 0.130006 | − | 0.225178i | ||||
\(498\) | 4.51337 | − | 0.474374i | 0.202249 | − | 0.0212572i | ||||
\(499\) | −3.15174 | − | 5.45898i | −0.141091 | − | 0.244378i | 0.786816 | − | 0.617187i | \(-0.211728\pi\) |
−0.927908 | + | 0.372809i | \(0.878394\pi\) | |||||||
\(500\) | −0.104528 | − | 0.181049i | −0.00467465 | − | 0.00809674i | ||||
\(501\) | 6.67741 | − | 0.701825i | 0.298325 | − | 0.0313552i | ||||
\(502\) | −10.1470 | + | 17.5751i | −0.452882 | + | 0.784414i | ||||
\(503\) | −29.9283 | −1.33443 | −0.667217 | − | 0.744863i | \(-0.732515\pi\) | ||||
−0.667217 | + | 0.744863i | \(0.732515\pi\) | |||||||
\(504\) | −8.67508 | + | 1.84395i | −0.386419 | + | 0.0821358i | ||||
\(505\) | 1.30272 | 0.0579701 | ||||||||
\(506\) | −2.30858 | + | 3.99859i | −0.102629 | + | 0.177759i | ||||
\(507\) | −9.99701 | − | 13.7597i | −0.443983 | − | 0.611090i | ||||
\(508\) | −1.15008 | − | 1.99200i | −0.0510266 | − | 0.0883806i | ||||
\(509\) | 11.0491 | + | 19.1376i | 0.489743 | + | 0.848259i | 0.999930 | − | 0.0118037i | \(-0.00375733\pi\) |
−0.510187 | + | 0.860063i | \(0.670424\pi\) | |||||||
\(510\) | 1.26170 | − | 2.83382i | 0.0558690 | − | 0.125484i | ||||
\(511\) | 0.0442951 | − | 0.0767213i | 0.00195950 | − | 0.00339395i | ||||
\(512\) | 25.0863 | 1.10867 | ||||||||
\(513\) | 21.3565 | − | 6.93914i | 0.942911 | − | 0.306370i | ||||
\(514\) | 29.3954 | 1.29657 | ||||||||
\(515\) | 7.68704 | − | 13.3143i | 0.338731 | − | 0.586700i | ||||
\(516\) | 0.241448 | − | 0.542300i | 0.0106291 | − | 0.0238734i | ||||
\(517\) | −4.02606 | − | 6.97333i | −0.177066 | − | 0.306687i | ||||
\(518\) | 4.37490 | + | 7.57754i | 0.192222 | + | 0.332938i | ||||
\(519\) | −14.7328 | − | 20.2779i | −0.646696 | − | 0.890101i | ||||
\(520\) | 2.63611 | − | 4.56587i | 0.115601 | − | 0.200227i | ||||
\(521\) | −18.7772 | −0.822644 | −0.411322 | − | 0.911490i | \(-0.634933\pi\) | ||||
−0.411322 | + | 0.911490i | \(0.634933\pi\) | |||||||
\(522\) | 6.10607 | − | 18.7926i | 0.267256 | − | 0.822528i | ||||
\(523\) | 21.9797 | 0.961104 | 0.480552 | − | 0.876966i | \(-0.340436\pi\) | ||||
0.480552 | + | 0.876966i | \(0.340436\pi\) | |||||||
\(524\) | 0.902396 | − | 1.56300i | 0.0394214 | − | 0.0682798i | ||||
\(525\) | 1.72256 | − | 0.181049i | 0.0751788 | − | 0.00790161i | ||||
\(526\) | −21.4367 | − | 37.1295i | −0.934685 | − | 1.61892i | ||||
\(527\) | −0.460864 | − | 0.798239i | −0.0200755 | − | 0.0347718i | ||||
\(528\) | 4.03312 | − | 0.423898i | 0.175519 | − | 0.0184478i | ||||
\(529\) | −2.09148 | + | 3.62254i | −0.0909338 | + | 0.157502i | ||||
\(530\) | 18.4978 | 0.803495 | ||||||||
\(531\) | −5.09690 | + | 15.6866i | −0.221186 | + | 0.680742i | ||||
\(532\) | −0.903454 | −0.0391697 | ||||||||
\(533\) | 0.730773 | − | 1.26574i | 0.0316533 | − | 0.0548251i | ||||
\(534\) | 17.9306 | + | 24.6793i | 0.775932 | + | 1.06798i | ||||
\(535\) | −7.43881 | − | 12.8844i | −0.321608 | − | 0.557041i | ||||
\(536\) | 9.78243 | + | 16.9437i | 0.422537 | + | 0.731855i | ||||
\(537\) | 3.62986 | − | 8.15280i | 0.156640 | − | 0.351819i | ||||
\(538\) | 3.07327 | − | 5.32306i | 0.132498 | − | 0.229494i | ||||
\(539\) | 0.661739 | 0.0285031 | ||||||||
\(540\) | 0.225853 | − | 1.06255i | 0.00971915 | − | 0.0457250i | ||||
\(541\) | 1.77587 | 0.0763507 | 0.0381753 | − | 0.999271i | \(-0.487845\pi\) | ||||
0.0381753 | + | 0.999271i | \(0.487845\pi\) | |||||||
\(542\) | 10.9019 | − | 18.8827i | 0.468277 | − | 0.811080i | ||||
\(543\) | −14.6711 | + | 32.9518i | −0.629597 | + | 1.41410i | ||||
\(544\) | 0.787955 | + | 1.36478i | 0.0337833 | + | 0.0585143i | ||||
\(545\) | −1.32864 | − | 2.30127i | −0.0569125 | − | 0.0985754i | ||||
\(546\) | 2.42977 | + | 3.34429i | 0.103985 | + | 0.143123i | ||||
\(547\) | −8.58281 | + | 14.8659i | −0.366975 | + | 0.635619i | −0.989091 | − | 0.147306i | \(-0.952940\pi\) |
0.622116 | + | 0.782925i | \(0.286273\pi\) | |||||||
\(548\) | 2.73968 | 0.117033 | ||||||||
\(549\) | −34.4631 | + | 7.32536i | −1.47085 | + | 0.312639i | ||||
\(550\) | −0.885579 | −0.0377612 | ||||||||
\(551\) | 10.6348 | − | 18.4200i | 0.453057 | − | 0.784718i | ||||
\(552\) | 26.5504 | − | 2.79056i | 1.13006 | − | 0.118774i | ||||
\(553\) | 5.78477 | + | 10.0195i | 0.245993 | + | 0.426073i | ||||
\(554\) | −20.8528 | − | 36.1182i | −0.885952 | − | 1.53451i | ||||
\(555\) | −11.2624 | + | 1.18373i | −0.478063 | + | 0.0502465i | ||||
\(556\) | 0.594903 | − | 1.03040i | 0.0252295 | − | 0.0436988i | ||||
\(557\) | −24.2342 | −1.02684 | −0.513419 | − | 0.858138i | \(-0.671621\pi\) | ||||
−0.513419 | + | 0.858138i | \(0.671621\pi\) | |||||||
\(558\) | 1.85027 | + | 2.05493i | 0.0783281 | + | 0.0869921i | ||||
\(559\) | −2.92368 | −0.123658 | ||||||||
\(560\) | 1.76909 | − | 3.06415i | 0.0747577 | − | 0.129484i | ||||
\(561\) | 0.901585 | + | 1.24093i | 0.0380650 | + | 0.0523919i | ||||
\(562\) | 13.0431 | + | 22.5913i | 0.550189 | + | 0.952955i | ||||
\(563\) | −5.73052 | − | 9.92556i | −0.241513 | − | 0.418312i | 0.719633 | − | 0.694355i | \(-0.244310\pi\) |
−0.961145 | + | 0.276043i | \(0.910977\pi\) | |||||||
\(564\) | −1.79210 | + | 4.02512i | −0.0754609 | + | 0.169488i | ||||
\(565\) | −6.57969 | + | 11.3964i | −0.276810 | + | 0.479448i | ||||
\(566\) | 40.5333 | 1.70374 | ||||||||
\(567\) | 7.28115 | + | 5.29007i | 0.305780 | + | 0.222162i | ||||
\(568\) | 17.1364 | 0.719029 | ||||||||
\(569\) | −11.2104 | + | 19.4170i | −0.469966 | + | 0.814005i | −0.999410 | − | 0.0343398i | \(-0.989067\pi\) |
0.529444 | + | 0.848345i | \(0.322400\pi\) | |||||||
\(570\) | −4.07433 | + | 9.15109i | −0.170655 | + | 0.383297i | ||||
\(571\) | 5.44697 | + | 9.43443i | 0.227949 | + | 0.394819i | 0.957200 | − | 0.289427i | \(-0.0934648\pi\) |
−0.729251 | + | 0.684246i | \(0.760131\pi\) | |||||||
\(572\) | 0.123358 | + | 0.213662i | 0.00515785 | + | 0.00893365i | ||||
\(573\) | −18.9805 | − | 26.1244i | −0.792922 | − | 1.09136i | ||||
\(574\) | 0.548375 | − | 0.949814i | 0.0228887 | − | 0.0396445i | ||||
\(575\) | −5.21373 | −0.217427 | ||||||||
\(576\) | −17.3685 | − | 19.2897i | −0.723687 | − | 0.803736i | ||||
\(577\) | −2.67343 | −0.111296 | −0.0556482 | − | 0.998450i | \(-0.517723\pi\) | ||||
−0.0556482 | + | 0.998450i | \(0.517723\pi\) | |||||||
\(578\) | −10.1768 | + | 17.6268i | −0.423301 | + | 0.733179i | ||||
\(579\) | −23.8656 | + | 2.50838i | −0.991820 | + | 0.104245i | ||||
\(580\) | −0.514461 | − | 0.891072i | −0.0213618 | − | 0.0369997i | ||||
\(581\) | 0.978938 | + | 1.69557i | 0.0406132 | + | 0.0703441i | ||||
\(582\) | −38.4403 | + | 4.04024i | −1.59340 | + | 0.167473i | ||||
\(583\) | −4.57337 | + | 7.92132i | −0.189410 | + | 0.328067i | ||||
\(584\) | 0.261899 | 0.0108374 | ||||||||
\(585\) | −5.23324 | + | 1.11236i | −0.216368 | + | 0.0459904i | ||||
\(586\) | 33.0877 | 1.36684 | ||||||||
\(587\) | −7.58940 | + | 13.1452i | −0.313248 | + | 0.542562i | −0.979064 | − | 0.203555i | \(-0.934750\pi\) |
0.665815 | + | 0.746116i | \(0.268084\pi\) | |||||||
\(588\) | −0.212835 | − | 0.292943i | −0.00877718 | − | 0.0120808i | ||||
\(589\) | 1.48824 | + | 2.57771i | 0.0613218 | + | 0.106213i | ||||
\(590\) | −3.67886 | − | 6.37197i | −0.151456 | − | 0.262330i | ||||
\(591\) | 7.55645 | − | 16.9721i | 0.310831 | − | 0.698137i | ||||
\(592\) | −11.5666 | + | 20.0340i | −0.475386 | + | 0.823392i | ||||
\(593\) | −4.47015 | −0.183567 | −0.0917835 | − | 0.995779i | \(-0.529257\pi\) | ||||
−0.0917835 | + | 0.995779i | \(0.529257\pi\) | |||||||
\(594\) | −3.41966 | − | 3.07907i | −0.140310 | − | 0.126336i | ||||
\(595\) | 1.33826 | 0.0548634 | ||||||||
\(596\) | 1.00585 | − | 1.74218i | 0.0412011 | − | 0.0713624i | ||||
\(597\) | 4.41693 | − | 9.92059i | 0.180773 | − | 0.406023i | ||||
\(598\) | −6.22164 | − | 10.7762i | −0.254422 | − | 0.440671i | ||||
\(599\) | 13.7861 | + | 23.8783i | 0.563287 | + | 0.975641i | 0.997207 | + | 0.0746898i | \(0.0237967\pi\) |
−0.433920 | + | 0.900951i | \(0.642870\pi\) | |||||||
\(600\) | 3.00973 | + | 4.14253i | 0.122872 | + | 0.169118i | ||||
\(601\) | −6.64711 | + | 11.5131i | −0.271141 | + | 0.469631i | −0.969154 | − | 0.246454i | \(-0.920734\pi\) |
0.698013 | + | 0.716085i | \(0.254068\pi\) | |||||||
\(602\) | −2.19394 | −0.0894184 | ||||||||
\(603\) | 6.13525 | − | 18.8824i | 0.249847 | − | 0.768950i | ||||
\(604\) | 1.51486 | 0.0616390 | ||||||||
\(605\) | −5.28105 | + | 9.14705i | −0.214705 | + | 0.371880i | ||||
\(606\) | −3.00307 | + | 0.315636i | −0.121992 | + | 0.0128218i | ||||
\(607\) | 21.6602 | + | 37.5166i | 0.879161 | + | 1.52275i | 0.852263 | + | 0.523114i | \(0.175230\pi\) |
0.0268988 | + | 0.999638i | \(0.491437\pi\) | |||||||
\(608\) | −2.54449 | − | 4.40719i | −0.103193 | − | 0.178735i | ||||
\(609\) | 8.47798 | − | 0.891072i | 0.343545 | − | 0.0361081i | ||||
\(610\) | 7.85851 | − | 13.6113i | 0.318182 | − | 0.551107i | ||||
\(611\) | 21.7004 | 0.877906 | ||||||||
\(612\) | 0.259364 | − | 0.798239i | 0.0104842 | − | 0.0322669i | ||||
\(613\) | −34.4529 | −1.39154 | −0.695769 | − | 0.718265i | \(-0.744936\pi\) | ||||
−0.695769 | + | 0.718265i | \(0.744936\pi\) | |||||||
\(614\) | 6.77724 | − | 11.7385i | 0.273507 | − | 0.473729i | ||||
\(615\) | 0.834346 | + | 1.14838i | 0.0336441 | + | 0.0463071i | ||||
\(616\) | 0.978148 | + | 1.69420i | 0.0394107 | + | 0.0682613i | ||||
\(617\) | 5.22770 | + | 9.05464i | 0.210459 | + | 0.364526i | 0.951858 | − | 0.306538i | \(-0.0991707\pi\) |
−0.741399 | + | 0.671064i | \(0.765837\pi\) | |||||||
\(618\) | −14.4945 | + | 32.5552i | −0.583055 | + | 1.30956i | ||||
\(619\) | −16.6377 | + | 28.8174i | −0.668726 | + | 1.15827i | 0.309535 | + | 0.950888i | \(0.399827\pi\) |
−0.978261 | + | 0.207379i | \(0.933507\pi\) | |||||||
\(620\) | 0.143988 | 0.00578269 | ||||||||
\(621\) | −20.1328 | − | 18.1276i | −0.807900 | − | 0.727437i | ||||
\(622\) | −17.8564 | −0.715977 | ||||||||
\(623\) | −6.58028 | + | 11.3974i | −0.263633 | + | 0.456626i | ||||
\(624\) | −4.44528 | + | 9.98427i | −0.177954 | + | 0.399691i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 11.0105 | + | 19.0707i | 0.440067 | + | 0.762219i | ||||
\(627\) | −2.91144 | − | 4.00725i | −0.116272 | − | 0.160034i | ||||
\(628\) | −1.99622 | + | 3.45756i | −0.0796579 | + | 0.137972i | ||||
\(629\) | −8.74979 | −0.348877 | ||||||||
\(630\) | −3.92705 | + | 0.834720i | −0.156457 | + | 0.0332561i | ||||
\(631\) | −31.7046 | −1.26214 | −0.631070 | − | 0.775726i | \(-0.717384\pi\) | ||||
−0.631070 | + | 0.775726i | \(0.717384\pi\) | |||||||
\(632\) | −17.1015 | + | 29.6206i | −0.680260 | + | 1.17825i | ||||
\(633\) | −17.7826 | + | 1.86903i | −0.706796 | + | 0.0742872i | ||||
\(634\) | −11.7930 | − | 20.4260i | −0.468359 | − | 0.811221i | ||||
\(635\) | −5.50128 | − | 9.52849i | −0.218312 | − | 0.378127i | ||||
\(636\) | 4.97760 | − | 0.523166i | 0.197375 | − | 0.0207449i | ||||
\(637\) | −0.891693 | + | 1.54446i | −0.0353302 | + | 0.0611936i | ||||
\(638\) | −4.35858 | −0.172558 | ||||||||
\(639\) | −11.6360 | − | 12.9231i | −0.460314 | − | 0.511231i | ||||
\(640\) | 9.22384 | 0.364604 | ||||||||
\(641\) | −21.9256 | + | 37.9763i | −0.866009 | + | 1.49997i | 3.25004e−5 | 1.00000i | \(0.499990\pi\) | |
−0.866042 | + | 0.499972i | \(0.833344\pi\) | |||||||
\(642\) | 20.2700 | + | 27.8993i | 0.799993 | + | 1.10110i | ||||
\(643\) | 5.20666 | + | 9.01820i | 0.205331 | + | 0.355643i | 0.950238 | − | 0.311525i | \(-0.100840\pi\) |
−0.744907 | + | 0.667168i | \(0.767506\pi\) | |||||||
\(644\) | 0.544983 | + | 0.943938i | 0.0214753 | + | 0.0371964i | ||||
\(645\) | 1.15494 | − | 2.59403i | 0.0454756 | − | 0.102140i | ||||
\(646\) | −3.86984 | + | 6.70276i | −0.152257 | + | 0.263717i | ||||
\(647\) | 4.14378 | 0.162909 | 0.0814545 | − | 0.996677i | \(-0.474043\pi\) | ||||
0.0814545 | + | 0.996677i | \(0.474043\pi\) | |||||||
\(648\) | −2.78115 | + | 26.4609i | −0.109254 | + | 1.03948i | ||||
\(649\) | 3.63822 | 0.142813 | ||||||||
\(650\) | 1.19332 | − | 2.06689i | 0.0468058 | − | 0.0810700i | ||||
\(651\) | −0.485216 | + | 1.08981i | −0.0190171 | + | 0.0427132i | ||||
\(652\) | −1.85564 | − | 3.21407i | −0.0726726 | − | 0.125873i | ||||
\(653\) | 2.13377 | + | 3.69580i | 0.0835010 | + | 0.144628i | 0.904751 | − | 0.425940i | \(-0.140056\pi\) |
−0.821250 | + | 0.570568i | \(0.806723\pi\) | |||||||
\(654\) | 3.62040 | + | 4.98305i | 0.141569 | + | 0.194853i | ||||
\(655\) | 4.31651 | − | 7.47642i | 0.168660 | − | 0.292128i | ||||
\(656\) | 2.89966 | 0.113213 | ||||||||
\(657\) | −0.177835 | − | 0.197506i | −0.00693801 | − | 0.00770544i | ||||
\(658\) | 16.2841 | 0.634821 | ||||||||
\(659\) | −8.97045 | + | 15.5373i | −0.349439 | + | 0.605247i | −0.986150 | − | 0.165856i | \(-0.946961\pi\) |
0.636711 | + | 0.771103i | \(0.280295\pi\) | |||||||
\(660\) | −0.238301 | + | 0.0250465i | −0.00927586 | + | 0.000974932i | ||||
\(661\) | −14.1837 | − | 24.5668i | −0.551681 | − | 0.955539i | −0.998154 | − | 0.0607417i | \(-0.980653\pi\) |
0.446473 | − | 0.894797i | \(-0.352680\pi\) | |||||||
\(662\) | 7.41506 | + | 12.8433i | 0.288195 | + | 0.499168i | ||||
\(663\) | −4.11113 | + | 0.432097i | −0.159663 | + | 0.0167813i | ||||
\(664\) | −2.89403 | + | 5.01260i | −0.112310 | + | 0.194527i | ||||
\(665\) | −4.32157 | −0.167583 | ||||||||
\(666\) | 25.6758 | − | 5.45755i | 0.994916 | − | 0.211476i | ||||
\(667\) | −25.6605 | −0.993580 | ||||||||
\(668\) | −0.405199 | + | 0.701825i | −0.0156776 | + | 0.0271544i | ||||
\(669\) | 4.94023 | + | 6.79964i | 0.191000 | + | 0.262889i | ||||
\(670\) | 4.42833 | + | 7.67009i | 0.171081 | + | 0.296321i | ||||
\(671\) | 3.88585 | + | 6.73048i | 0.150011 | + | 0.259827i | ||||
\(672\) | 0.829591 | − | 1.86329i | 0.0320022 | − | 0.0718781i | ||||
\(673\) | −9.33425 | + | 16.1674i | −0.359809 | + | 0.623208i | −0.987929 | − | 0.154909i | \(-0.950492\pi\) |
0.628120 | + | 0.778117i | \(0.283825\pi\) | |||||||
\(674\) | 25.3319 | 0.975748 | ||||||||
\(675\) | 1.08034 | − | 5.08260i | 0.0415823 | − | 0.195630i | ||||
\(676\) | 2.05284 | 0.0789554 | ||||||||
\(677\) | 2.08162 | − | 3.60547i | 0.0800031 | − | 0.138569i | −0.823248 | − | 0.567682i | \(-0.807840\pi\) |
0.903251 | + | 0.429113i | \(0.141174\pi\) | |||||||
\(678\) | 12.4065 | − | 27.8655i | 0.476470 | − | 1.07017i | ||||
\(679\) | −8.33761 | − | 14.4412i | −0.319968 | − | 0.554201i | ||||
\(680\) | 1.97815 | + | 3.42625i | 0.0758585 | + | 0.131391i | ||||
\(681\) | −9.94838 | − | 13.6928i | −0.381223 | − | 0.524708i | ||||
\(682\) | 0.304971 | − | 0.528226i | 0.0116780 | − | 0.0202268i | ||||
\(683\) | −28.2844 | −1.08227 | −0.541137 | − | 0.840934i | \(-0.682006\pi\) | ||||
−0.541137 | + | 0.840934i | \(0.682006\pi\) | |||||||
\(684\) | −0.837548 | + | 2.57771i | −0.0320244 | + | 0.0985611i | ||||
\(685\) | 13.1050 | 0.500715 | ||||||||
\(686\) | −0.669131 | + | 1.15897i | −0.0255475 | + | 0.0442496i | ||||
\(687\) | −27.8169 | + | 2.92367i | −1.06128 | + | 0.111545i | ||||
\(688\) | −2.90024 | − | 5.02337i | −0.110571 | − | 0.191514i | ||||
\(689\) | −12.3252 | − | 21.3479i | −0.469554 | − | 0.813292i | ||||
\(690\) | 12.0189 | − | 1.26324i | 0.457551 | − | 0.0480906i | ||||
\(691\) | −16.6210 | + | 28.7884i | −0.632292 | + | 1.09516i | 0.354790 | + | 0.934946i | \(0.384552\pi\) |
−0.987082 | + | 0.160215i | \(0.948781\pi\) | |||||||
\(692\) | 3.02531 | 0.115005 | ||||||||
\(693\) | 0.613466 | − | 1.88805i | 0.0233036 | − | 0.0717212i | ||||
\(694\) | −25.9921 | −0.986645 | ||||||||
\(695\) | 2.84565 | − | 4.92882i | 0.107942 | − | 0.186961i | ||||
\(696\) | 14.8131 | + | 20.3884i | 0.561487 | + | 0.772821i | ||||
\(697\) | 0.548375 | + | 0.949814i | 0.0207712 | + | 0.0359768i | ||||
\(698\) | −15.0141 | − | 26.0051i | −0.568291 | − | 0.984309i | ||||
\(699\) | 4.06077 | − | 9.12063i | 0.153592 | − | 0.344974i | ||||
\(700\) | −0.104528 | + | 0.181049i | −0.00395080 | + | 0.00684299i | ||||
\(701\) | 23.1546 | 0.874535 | 0.437268 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437268 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(702\) | 11.7944 | − | 3.83222i | 0.445150 | − | 0.144638i | ||||
\(703\) | 28.2552 | 1.06566 | ||||||||
\(704\) | −2.86277 | + | 4.95847i | −0.107895 | + | 0.186879i | ||||
\(705\) | −8.57230 | + | 19.2537i | −0.322851 | + | 0.725136i | ||||
\(706\) | 8.99385 | + | 15.5778i | 0.338488 | + | 0.586279i | ||||
\(707\) | −0.651358 | − | 1.12819i | −0.0244969 | − | 0.0424298i | ||||
\(708\) | −1.17016 | − | 1.61059i | −0.0439774 | − | 0.0605297i | ||||
\(709\) | −3.31151 | + | 5.73570i | −0.124366 | + | 0.215409i | −0.921485 | − | 0.388414i | \(-0.873023\pi\) |
0.797119 | + | 0.603823i | \(0.206356\pi\) | |||||||
\(710\) | 7.75735 | 0.291128 | ||||||||
\(711\) | 33.9501 | − | 7.21632i | 1.27323 | − | 0.270633i | ||||
\(712\) | −38.9065 | −1.45808 | ||||||||
\(713\) | 1.79548 | − | 3.10986i | 0.0672411 | − | 0.116465i | ||||
\(714\) | −3.08501 | + | 0.324248i | −0.115454 | + | 0.0121347i | ||||
\(715\) | 0.590068 | + | 1.02203i | 0.0220673 | + | 0.0382217i | ||||
\(716\) | 0.538581 | + | 0.932849i | 0.0201277 | + | 0.0348622i | ||||
\(717\) | −0.208506 | + | 0.0219148i | −0.00778679 | + | 0.000818424i | ||||
\(718\) | −10.0382 | + | 17.3867i | −0.374624 | + | 0.648867i | ||||
\(719\) | 38.0335 | 1.41841 | 0.709205 | − | 0.705002i | \(-0.249054\pi\) | ||||
0.709205 | + | 0.705002i | \(0.249054\pi\) | |||||||
\(720\) | −7.10252 | − | 7.88814i | −0.264695 | − | 0.293974i | ||||
\(721\) | −15.3741 | −0.572561 | ||||||||
\(722\) | −0.216835 | + | 0.375569i | −0.00806976 | + | 0.0139772i | ||||
\(723\) | 21.3405 | + | 29.3726i | 0.793661 | + | 1.09238i | ||||
\(724\) | −2.17682 | − | 3.77037i | −0.0809010 | − | 0.140125i | ||||
\(725\) | −2.46086 | − | 4.26234i | −0.0913942 | − | 0.158299i | ||||
\(726\) | 9.95784 | − | 22.3657i | 0.369570 | − | 0.830068i | ||||
\(727\) | −0.855278 | + | 1.48138i | −0.0317205 | + | 0.0549415i | −0.881450 | − | 0.472278i | \(-0.843432\pi\) |
0.849729 | + | 0.527219i | \(0.176765\pi\) | |||||||
\(728\) | −5.27222 | −0.195401 | ||||||||
\(729\) | 21.8435 | − | 15.8702i | 0.809017 | − | 0.587785i | ||||
\(730\) | 0.118557 | 0.00438798 | ||||||||
\(731\) | 1.09697 | − | 1.90001i | 0.0405730 | − | 0.0702744i | ||||
\(732\) | 1.72969 | − | 3.88494i | 0.0639311 | − | 0.143592i | ||||
\(733\) | −19.7037 | − | 34.1277i | −0.727771 | − | 1.26054i | −0.957823 | − | 0.287358i | \(-0.907223\pi\) |
0.230052 | − | 0.973178i | \(-0.426110\pi\) | |||||||
\(734\) | 1.63779 | + | 2.83674i | 0.0604519 | + | 0.104706i | ||||
\(735\) | −1.01807 | − | 1.40126i | −0.0375522 | − | 0.0516862i | ||||
\(736\) | −3.06979 | + | 5.31703i | −0.113154 | + | 0.195988i | ||||
\(737\) | −4.37941 | −0.161318 | ||||||||
\(738\) | −2.20161 | − | 2.44513i | −0.0810423 | − | 0.0900066i | ||||
\(739\) | 2.91159 | 0.107104 | 0.0535522 | − | 0.998565i | \(-0.482946\pi\) | ||||
0.0535522 | + | 0.998565i | \(0.482946\pi\) | |||||||
\(740\) | 0.683426 | − | 1.18373i | 0.0251232 | − | 0.0435147i | ||||
\(741\) | 13.2758 | − | 1.39535i | 0.487700 | − | 0.0512593i | ||||
\(742\) | −9.24892 | − | 16.0196i | −0.339539 | − | 0.588098i | ||||
\(743\) | −5.63117 | − | 9.75347i | −0.206588 | − | 0.357820i | 0.744050 | − | 0.668124i | \(-0.232903\pi\) |
−0.950637 | + | 0.310304i | \(0.899569\pi\) | |||||||
\(744\) | −3.50739 | + | 0.368642i | −0.128587 | + | 0.0135151i | ||||
\(745\) | 4.81135 | − | 8.33351i | 0.176274 | − | 0.305316i | ||||
\(746\) | 25.5936 | 0.937049 | ||||||||
\(747\) | 5.74527 | − | 1.22120i | 0.210209 | − | 0.0446812i | ||||
\(748\) | −0.185136 | −0.00676926 | ||||||||
\(749\) | −7.43881 | + | 12.8844i | −0.271808 | + | 0.470786i | ||||
\(750\) | 1.36245 | + | 1.87525i | 0.0497496 | + | 0.0684744i | ||||
\(751\) | 23.4586 | + | 40.6315i | 0.856016 | + | 1.48266i | 0.875699 | + | 0.482857i | \(0.160401\pi\) |
−0.0196831 | + | 0.999806i | \(0.506266\pi\) | |||||||
\(752\) | 21.5265 | + | 37.2850i | 0.784990 | + | 1.35964i | ||||
\(753\) | −10.6832 | + | 23.9948i | −0.389316 | + | 0.874418i | ||||
\(754\) | 5.87319 | − | 10.1727i | 0.213889 | − | 0.370466i | ||||
\(755\) | 7.24618 | 0.263716 | ||||||||
\(756\) | −1.03312 | + | 0.335683i | −0.0375744 | + | 0.0122087i | ||||
\(757\) | 28.9715 | 1.05299 | 0.526494 | − | 0.850179i | \(-0.323506\pi\) | ||||
0.526494 | + | 0.850179i | \(0.323506\pi\) | |||||||
\(758\) | −2.35022 | + | 4.07070i | −0.0853639 | + | 0.147855i | ||||
\(759\) | −2.43057 | + | 5.45916i | −0.0882242 | + | 0.198155i | ||||
\(760\) | −6.38791 | − | 11.0642i | −0.231714 | − | 0.401340i | ||||
\(761\) | 10.3462 | + | 17.9202i | 0.375050 | + | 0.649606i | 0.990335 | − | 0.138699i | \(-0.0442921\pi\) |
−0.615284 | + | 0.788305i | \(0.710959\pi\) | |||||||
\(762\) | 14.9904 | + | 20.6325i | 0.543046 | + | 0.747438i | ||||
\(763\) | −1.32864 | + | 2.30127i | −0.0480999 | + | 0.0833114i | ||||
\(764\) | 3.89756 | 0.141009 | ||||||||
\(765\) | 1.24064 | − | 3.81829i | 0.0448553 | − | 0.138050i | ||||
\(766\) | 38.3518 | 1.38571 | ||||||||
\(767\) | −4.90250 | + | 8.49138i | −0.177019 | + | 0.306606i | ||||
\(768\) | 8.54500 | − | 0.898116i | 0.308341 | − | 0.0324080i | ||||
\(769\) | 7.93589 | + | 13.7454i | 0.286175 | + | 0.495670i | 0.972894 | − | 0.231253i | \(-0.0742827\pi\) |
−0.686718 | + | 0.726924i | \(0.740949\pi\) | |||||||
\(770\) | 0.442790 | + | 0.766934i | 0.0159570 | + | 0.0276384i | ||||
\(771\) | 37.8367 | − | 3.97680i | 1.36265 | − | 0.143221i | ||||
\(772\) | 1.44821 | − | 2.50838i | 0.0521223 | − | 0.0902784i | ||||
\(773\) | 2.13874 | 0.0769251 | 0.0384626 | − | 0.999260i | \(-0.487754\pi\) | ||||
0.0384626 | + | 0.999260i | \(0.487754\pi\) | |||||||
\(774\) | −2.03390 | + | 6.25969i | −0.0731069 | + | 0.225000i | ||||
\(775\) | 0.688750 | 0.0247406 | ||||||||
\(776\) | 24.6484 | − | 42.6923i | 0.884827 | − | 1.53257i | ||||
\(777\) | 6.65635 | + | 9.16168i | 0.238795 | + | 0.328674i | ||||
\(778\) | 4.82926 | + | 8.36453i | 0.173137 | + | 0.299883i | ||||
\(779\) | −1.77084 | − | 3.06718i | −0.0634468 | − | 0.109893i | ||||
\(780\) | 0.262654 | − | 0.589930i | 0.00940452 | − | 0.0211229i | ||||
\(781\) | −1.91791 | + | 3.32192i | −0.0686284 | + | 0.118868i | ||||
\(782\) | 9.33749 | 0.333908 | ||||||||
\(783\) | 5.31714 | − | 25.0152i | 0.190019 | − | 0.893970i | ||||
\(784\) | −3.53818 | −0.126364 | ||||||||
\(785\) | −9.54870 | + | 16.5388i | −0.340808 | + | 0.590296i | ||||
\(786\) | −8.13912 | + | 18.2808i | −0.290313 | + | 0.652054i | ||||
\(787\) | 11.1445 | + | 19.3029i | 0.397259 | + | 0.688073i | 0.993387 | − | 0.114817i | \(-0.0366281\pi\) |
−0.596128 | + | 0.802890i | \(0.703295\pi\) | |||||||
\(788\) | 1.12119 | + | 1.94195i | 0.0399407 | + | 0.0691792i | ||||
\(789\) | −32.6157 | − | 44.8917i | −1.16115 | − | 1.59819i | ||||
\(790\) | −7.74153 | + | 13.4087i | −0.275431 | + | 0.477061i | ||||
\(791\) | 13.1594 | 0.467894 | ||||||||
\(792\) | 5.74064 | − | 1.22021i | 0.203985 | − | 0.0433583i | ||||
\(793\) | −20.9447 | −0.743769 | ||||||||
\(794\) | 13.2509 | − | 22.9512i | 0.470256 | − | 0.814507i | ||||
\(795\) | 23.8098 | − | 2.50251i | 0.844445 | − | 0.0887548i | ||||
\(796\) | 0.655362 | + | 1.13512i | 0.0232287 | + | 0.0402333i | ||||
\(797\) | −10.3177 | − | 17.8707i | −0.365470 | − | 0.633013i | 0.623381 | − | 0.781918i | \(-0.285758\pi\) |
−0.988851 | + | 0.148905i | \(0.952425\pi\) | |||||||
\(798\) | 9.96224 | − | 1.04707i | 0.352660 | − | 0.0370660i | ||||
\(799\) | −8.14206 | + | 14.1025i | −0.288045 | + | 0.498909i | ||||
\(800\) | −1.17758 | −0.0416337 | ||||||||
\(801\) | 26.4184 | + | 29.3406i | 0.933448 | + | 1.03670i | ||||
\(802\) | 12.1500 | 0.429030 | ||||||||
\(803\) | −0.0293118 | + | 0.0507695i | −0.00103439 | + | 0.00179161i | ||||
\(804\) | 1.40855 | + | 1.93871i | 0.0496758 | + | 0.0683729i | ||||
\(805\) | 2.60686 | + | 4.51522i | 0.0918799 | + | 0.159141i | ||||
\(806\) | 0.821898 | + | 1.42357i | 0.0289501 | + | 0.0501431i | ||||
\(807\) | 3.23567 | − | 7.26743i | 0.113901 | − | 0.255826i | ||||
\(808\) | 1.92561 | − | 3.33525i | 0.0677426 | − | 0.117334i | ||||
\(809\) | 15.4866 | 0.544479 | 0.272240 | − | 0.962229i | \(-0.412236\pi\) | ||||
0.272240 | + | 0.962229i | \(0.412236\pi\) | |||||||
\(810\) | −1.25898 | + | 11.9784i | −0.0442360 | + | 0.420877i | ||||
\(811\) | −2.30279 | −0.0808617 | −0.0404309 | − | 0.999182i | \(-0.512873\pi\) | ||||
−0.0404309 | + | 0.999182i | \(0.512873\pi\) | |||||||
\(812\) | −0.514461 | + | 0.891072i | −0.0180540 | + | 0.0312705i | ||||
\(813\) | 11.4780 | − | 25.7800i | 0.402550 | − | 0.904143i | ||||
\(814\) | −2.89504 | − | 5.01435i | −0.101471 | − | 0.175753i | ||||
\(815\) | −8.87626 | − | 15.3741i | −0.310922 | − | 0.538532i | ||||
\(816\) | −4.82059 | − | 6.63497i | −0.168754 | − | 0.232271i | ||||
\(817\) | −3.54238 | + | 6.13559i | −0.123932 | + | 0.214657i | ||||
\(818\) | −27.2209 | −0.951756 | ||||||||
\(819\) | 3.57995 | + | 3.97594i | 0.125094 | + | 0.138931i | ||||
\(820\) | −0.171329 | −0.00598308 | ||||||||
\(821\) | −0.147155 | + | 0.254880i | −0.00513574 | + | 0.00889536i | −0.868582 | − | 0.495546i | \(-0.834968\pi\) |
0.863446 | + | 0.504441i | \(0.168301\pi\) | |||||||
\(822\) | −30.2100 | + | 3.17520i | −1.05370 | + | 0.110748i | ||||
\(823\) | −24.5553 | − | 42.5310i | −0.855943 | − | 1.48254i | −0.875767 | − | 0.482733i | \(-0.839644\pi\) |
0.0198242 | − | 0.999803i | \(-0.493689\pi\) | |||||||
\(824\) | −22.7252 | − | 39.3611i | −0.791668 | − | 1.37121i | ||||
\(825\) | −1.13989 | + | 0.119807i | −0.0396858 | + | 0.00417114i | ||||
\(826\) | −3.67886 | + | 6.37197i | −0.128004 | + | 0.221709i | ||||
\(827\) | 51.5805 | 1.79363 | 0.896815 | − | 0.442405i | \(-0.145875\pi\) | ||||
0.896815 | + | 0.442405i | \(0.145875\pi\) | |||||||
\(828\) | 3.19844 | − | 0.679850i | 0.111154 | − | 0.0236264i | ||||
\(829\) | −39.4858 | −1.37140 | −0.685699 | − | 0.727885i | \(-0.740503\pi\) | ||||
−0.685699 | + | 0.727885i | \(0.740503\pi\) | |||||||
\(830\) | −1.31007 | + | 2.26911i | −0.0454733 | + | 0.0787621i | ||||
\(831\) | −31.7273 | − | 43.6689i | −1.10061 | − | 1.51486i | ||||
\(832\) | −7.71517 | − | 13.3631i | −0.267475 | − | 0.463281i | ||||
\(833\) | −0.669131 | − | 1.15897i | −0.0231840 | − | 0.0401559i | ||||
\(834\) | −5.36570 | + | 12.0516i | −0.185799 | + | 0.417312i | ||||
\(835\) | −1.93822 | + | 3.35710i | −0.0670749 | + | 0.116177i | ||||
\(836\) | 0.597850 | 0.0206771 | ||||||||
\(837\) | 2.65960 | + | 2.39472i | 0.0919293 | + | 0.0827735i | ||||
\(838\) | −7.78261 | −0.268846 | ||||||||
\(839\) | −23.7956 | + | 41.2152i | −0.821516 | + | 1.42291i | 0.0830379 | + | 0.996546i | \(0.473538\pi\) |
−0.904553 | + | 0.426360i | \(0.859796\pi\) | |||||||
\(840\) | 2.08268 | − | 4.67777i | 0.0718592 | − | 0.161398i | ||||
\(841\) | 2.38830 | + | 4.13666i | 0.0823552 | + | 0.142643i | ||||
\(842\) | −22.2918 | − | 38.6106i | −0.768227 | − | 1.33061i | ||||
\(843\) | 19.8449 | + | 27.3141i | 0.683494 | + | 0.940748i | ||||
\(844\) | 1.07908 | − | 1.86903i | 0.0371436 | − | 0.0643346i | ||||
\(845\) | 9.81953 | 0.337802 | ||||||||
\(846\) | 15.0962 | − | 46.4613i | 0.519018 | − | 1.59737i | ||||
\(847\) | 10.5621 | 0.362918 | ||||||||
\(848\) | 24.4529 | − | 42.3537i | 0.839716 | − | 1.45443i | ||||
\(849\) | 52.1731 | − | 5.48361i | 1.79057 | − | 0.188197i | ||||
\(850\) | 0.895472 | + | 1.55100i | 0.0307144 | + | 0.0531989i | ||||
\(851\) | −17.0441 | − | 29.5213i | −0.584266 | − | 1.01198i | ||||
\(852\) | 2.08743 | − | 0.219398i | 0.0715142 | − | 0.00751645i | ||||
\(853\) | 11.5193 | − | 19.9520i | 0.394414 | − | 0.683145i | −0.598612 | − | 0.801039i | \(-0.704281\pi\) |
0.993026 | + | 0.117894i | \(0.0376144\pi\) | |||||||
\(854\) | −15.7170 | −0.537825 | ||||||||
\(855\) | −4.00631 | + | 12.3302i | −0.137013 | + | 0.421683i | ||||
\(856\) | −43.9826 | −1.50330 | ||||||||
\(857\) | 5.61860 | − | 9.73171i | 0.191928 | − | 0.332429i | −0.753961 | − | 0.656919i | \(-0.771859\pi\) |
0.945889 | + | 0.324490i | \(0.105193\pi\) | |||||||
\(858\) | −1.60787 | − | 2.21305i | −0.0548919 | − | 0.0755523i | ||||
\(859\) | −1.46731 | − | 2.54145i | −0.0500639 | − | 0.0867132i | 0.839907 | − | 0.542730i | \(-0.182609\pi\) |
−0.889971 | + | 0.456016i | \(0.849276\pi\) | |||||||
\(860\) | 0.171364 | + | 0.296811i | 0.00584346 | + | 0.0101212i | ||||
\(861\) | 0.577352 | − | 1.29675i | 0.0196761 | − | 0.0441933i | ||||
\(862\) | −22.1906 | + | 38.4352i | −0.755814 | + | 1.30911i | ||||
\(863\) | −36.2827 | −1.23508 | −0.617539 | − | 0.786540i | \(-0.711870\pi\) | ||||
−0.617539 | + | 0.786540i | \(0.711870\pi\) | |||||||
\(864\) | −4.54722 | − | 4.09433i | −0.154699 | − | 0.139292i | ||||
\(865\) | 14.4712 | 0.492036 | ||||||||
\(866\) | 22.2767 | − | 38.5844i | 0.756993 | − | 1.31115i | ||||
\(867\) | −10.7146 | + | 24.0654i | −0.363887 | + | 0.817304i | ||||
\(868\) | −0.0719940 | − | 0.124697i | −0.00244363 | − | 0.00423250i | ||||
\(869\) | −3.82800 | − | 6.63030i | −0.129856 | − | 0.224917i | ||||
\(870\) | 6.70560 | + | 9.22947i | 0.227341 | + | 0.312908i | ||||
\(871\) | 5.90125 | − | 10.2213i | 0.199956 | − | 0.346335i | ||||
\(872\) | −7.85568 | −0.266027 | ||||||||
\(873\) | −48.9325 | + | 10.4009i | −1.65611 | + | 0.352018i | ||||
\(874\) | −30.1530 | −1.01994 | ||||||||
\(875\) | −0.500000 | + | 0.866025i | −0.0169031 | + | 0.0292770i | ||||
\(876\) | 0.0319025 | − | 0.00335309i | 0.00107789 | − | 0.000113290i | ||||
\(877\) | −18.1302 | − | 31.4024i | −0.612213 | − | 1.06038i | −0.990867 | − | 0.134846i | \(-0.956946\pi\) |
0.378654 | − | 0.925538i | \(-0.376387\pi\) | |||||||
\(878\) | −17.5482 | − | 30.3943i | −0.592222 | − | 1.02576i | ||||
\(879\) | 42.5893 | − | 4.47631i | 1.43650 | − | 0.150982i | ||||
\(880\) | −1.17068 | + | 2.02767i | −0.0394635 | + | 0.0683527i | ||||
\(881\) | 50.7854 | 1.71101 | 0.855503 | − | 0.517799i | \(-0.173248\pi\) | ||||
0.855503 | + | 0.517799i | \(0.173248\pi\) | |||||||
\(882\) | 2.68641 | + | 2.98357i | 0.0904563 | + | 0.100462i | ||||
\(883\) | 14.4337 | 0.485734 | 0.242867 | − | 0.970060i | \(-0.421912\pi\) | ||||
0.242867 | + | 0.970060i | \(0.421912\pi\) | |||||||
\(884\) | 0.249471 | − | 0.432097i | 0.00839063 | − | 0.0145330i | ||||
\(885\) | −5.59734 | − | 7.70407i | −0.188152 | − | 0.258970i | ||||
\(886\) | 10.5222 | + | 18.2249i | 0.353499 | + | 0.612279i | ||||
\(887\) | 8.66324 | + | 15.0052i | 0.290883 | + | 0.503824i | 0.974019 | − | 0.226467i | \(-0.0727176\pi\) |
−0.683136 | + | 0.730292i | \(0.739384\pi\) | |||||||
\(888\) | −13.6169 | + | 30.5841i | −0.456954 | + | 1.02633i | ||||
\(889\) | −5.50128 | + | 9.52849i | −0.184507 | + | 0.319575i | ||||
\(890\) | −17.6123 | −0.590364 | ||||||||
\(891\) | −4.81822 | − | 3.50064i | −0.161416 | − | 0.117276i | ||||
\(892\) | −1.01445 | −0.0339664 | ||||||||
\(893\) | 26.2927 | − | 45.5402i | 0.879850 | − | 1.52395i | ||||
\(894\) | −9.07219 | + | 20.3765i | −0.303419 | + | 0.681491i | ||||
\(895\) | 2.57624 | + | 4.46218i | 0.0861142 | + | 0.149154i | ||||
\(896\) | −4.61192 | − | 7.98808i | −0.154073 | − | 0.266863i | ||||
\(897\) | −9.46614 | − | 13.0290i | −0.316065 | − | 0.435027i | ||||
\(898\) | 25.8228 | − | 44.7264i | 0.861717 | − | 1.49254i | ||||
\(899\) | 3.38984 | 0.113057 | ||||||||
\(900\) | 0.419659 | + | 0.466079i | 0.0139886 | + | 0.0155360i | ||||
\(901\) | 18.4978 | 0.616252 | ||||||||
\(902\) | −0.362881 | + | 0.628529i | −0.0120826 | + | 0.0209277i | ||||
\(903\) | −2.82397 | + | 0.296811i | −0.0939757 | + | 0.00987724i | ||||
\(904\) | 19.4515 | + | 33.6910i | 0.646947 | + | 1.12055i | ||||
\(905\) | −10.4126 | − | 18.0351i | −0.346126 | − | 0.599508i | ||||
\(906\) | −16.7042 | + | 1.75568i | −0.554959 | + | 0.0583285i | ||||
\(907\) | −22.3839 | + | 38.7700i | −0.743245 | + | 1.28734i | 0.207766 | + | 0.978179i | \(0.433381\pi\) |
−0.951010 | + | 0.309159i | \(0.899952\pi\) | |||||||
\(908\) | 2.04285 | 0.0677945 | ||||||||
\(909\) | −3.82275 | + | 0.812550i | −0.126793 | + | 0.0269506i | ||||
\(910\) | −2.38664 | −0.0791162 | ||||||||
\(911\) | −21.8640 | + | 37.8695i | −0.724385 | + | 1.25467i | 0.234841 | + | 0.972034i | \(0.424543\pi\) |
−0.959226 | + | 0.282639i | \(0.908790\pi\) | |||||||
\(912\) | 15.5668 | + | 21.4259i | 0.515470 | + | 0.709483i | ||||
\(913\) | −0.647801 | − | 1.12202i | −0.0214391 | − | 0.0371336i | ||||
\(914\) | −27.7313 | − | 48.0320i | −0.917269 | − | 1.58876i | ||||
\(915\) | 8.27376 | − | 18.5832i | 0.273522 | − | 0.614341i | ||||
\(916\) | 1.68798 | − | 2.92367i | 0.0557725 | − | 0.0966008i | ||||
\(917\) | −8.63302 | −0.285087 | ||||||||
\(918\) | −1.93483 | + | 9.10265i | −0.0638589 | + | 0.300432i | ||||
\(919\) | 23.3354 | 0.769764 | 0.384882 | − | 0.922966i | \(-0.374242\pi\) | ||||
0.384882 | + | 0.922966i | \(0.374242\pi\) | |||||||
\(920\) | −7.70666 | + | 13.3483i | −0.254081 | + | 0.440081i | ||||
\(921\) | 7.13536 | − | 16.0263i | 0.235118 | − | 0.528084i | ||||
\(922\) | −13.1259 | − | 22.7347i | −0.432278 | − | 0.748727i | ||||
\(923\) | −5.16878 | − | 8.95259i | −0.170132 | − | 0.294678i | ||||
\(924\) | 0.140841 | + | 0.193852i | 0.00463334 | + | 0.00637725i | ||||
\(925\) | 3.26909 | − | 5.66223i | 0.107487 | − | 0.186173i | ||||
\(926\) | −8.14660 | −0.267714 | ||||||||
\(927\) | −14.2526 | + | 43.8649i | −0.468115 | + | 1.44071i | ||||
\(928\) | −5.79573 | −0.190254 | ||||||||
\(929\) | −17.8371 | + | 30.8947i | −0.585215 | + | 1.01362i | 0.409634 | + | 0.912250i | \(0.365656\pi\) |
−0.994849 | + | 0.101372i | \(0.967677\pi\) | |||||||
\(930\) | −1.58773 | + | 0.166877i | −0.0520638 | + | 0.00547213i | ||||
\(931\) | 2.16078 | + | 3.74259i | 0.0708168 | + | 0.122658i | ||||
\(932\) | 0.602516 | + | 1.04359i | 0.0197361 | + | 0.0341839i | ||||
\(933\) | −22.9842 | + | 2.41573i | −0.752467 | + | 0.0790875i | ||||
\(934\) | −14.0215 | + | 24.2859i | −0.458797 | + | 0.794660i | ||||
\(935\) | −0.885579 | −0.0289615 | ||||||||
\(936\) | −4.88761 | + | 15.0425i | −0.159757 | + | 0.491680i | ||||
\(937\) | −53.4359 | −1.74567 | −0.872837 | − | 0.488011i | \(-0.837723\pi\) | ||||
−0.872837 | + | 0.488011i | \(0.837723\pi\) | |||||||
\(938\) | 4.42833 | − | 7.67009i | 0.144590 | − | 0.250437i | ||||
\(939\) | 16.7523 | + | 23.0576i | 0.546691 | + | 0.752456i | ||||
\(940\) | −1.27191 | − | 2.20302i | −0.0414853 | − | 0.0718546i | ||||
\(941\) | 10.0914 | + | 17.4789i | 0.328971 | + | 0.569795i | 0.982308 | − | 0.187273i | \(-0.0599648\pi\) |
−0.653337 | + | 0.757067i | \(0.726631\pi\) | |||||||
\(942\) | 18.0048 | − | 40.4395i | 0.586629 | − | 1.31759i | ||||
\(943\) | −2.13641 | + | 3.70038i | −0.0695712 | + | 0.120501i | ||||
\(944\) | −19.4528 | −0.633135 | ||||||||
\(945\) | −4.94183 | + | 1.60570i | −0.160758 | + | 0.0522334i | ||||
\(946\) | 1.45182 | 0.0472026 | ||||||||
\(947\) | 16.6730 | − | 28.8786i | 0.541801 | − | 0.938427i | −0.457000 | − | 0.889467i | \(-0.651076\pi\) |
0.998801 | − | 0.0489603i | \(-0.0155908\pi\) | |||||||
\(948\) | −1.70394 | + | 3.82711i | −0.0553414 | + | 0.124299i | ||||
\(949\) | −0.0789952 | − | 0.136824i | −0.00256429 | − | 0.00444148i | ||||
\(950\) | −2.89169 | − | 5.00856i | −0.0938189 | − | 0.162499i | ||||
\(951\) | −17.9429 | − | 24.6962i | −0.581837 | − | 0.800830i | ||||
\(952\) | 1.97815 | − | 3.42625i | 0.0641121 | − | 0.111045i | ||||
\(953\) | −29.0960 | −0.942513 | −0.471257 | − | 0.881996i | \(-0.656199\pi\) | ||||
−0.471257 | + | 0.881996i | \(0.656199\pi\) | |||||||
\(954\) | −54.2809 | + | 11.5378i | −1.75741 | + | 0.373549i | ||||
\(955\) | 18.6435 | 0.603291 | ||||||||
\(956\) | 0.0126525 | − | 0.0219148i | 0.000409212 | − | 0.000708776i | ||||
\(957\) | −5.61021 | + | 0.589657i | −0.181352 | + | 0.0190609i | ||||
\(958\) | 17.2521 | + | 29.8816i | 0.557392 | + | 0.965431i | ||||
\(959\) | −6.55248 | − | 11.3492i | −0.211591 | − | 0.366486i | ||||
\(960\) | 14.9041 | − | 1.56648i | 0.481027 | − | 0.0505580i | ||||
\(961\) | 15.2628 | − | 26.4360i | 0.492349 | − | 0.852773i | ||||
\(962\) | 15.6043 | 0.503102 | ||||||||
\(963\) | 29.8652 | + | 33.1687i | 0.962393 | + | 1.06885i | ||||
\(964\) | −4.38217 | −0.141140 | ||||||||
\(965\) | 6.92735 | − | 11.9985i | 0.222999 | − | 0.386246i | ||||
\(966\) | −7.10344 | − | 9.77704i | −0.228549 | − | 0.314571i | ||||
\(967\) | 18.0186 | + | 31.2091i | 0.579439 | + | 1.00362i | 0.995544 | + | 0.0943013i | \(0.0300617\pi\) |
−0.416105 | + | 0.909317i | \(0.636605\pi\) | |||||||
\(968\) | 15.6123 | + | 27.0414i | 0.501800 | + | 0.869143i | ||||
\(969\) | −4.07433 | + | 9.15109i | −0.130886 | + | 0.293975i | ||||
\(970\) | 11.1579 | − | 19.3260i | 0.358258 | − | 0.620522i | ||||
\(971\) | 4.97188 | 0.159555 | 0.0797776 | − | 0.996813i | \(-0.474579\pi\) | ||||
0.0797776 | + | 0.996813i | \(0.474579\pi\) | |||||||
\(972\) | 3.25887i | 0.104528i | ||||||||
\(973\) | −5.69131 | −0.182455 | ||||||||
\(974\) | 18.1390 | − | 31.4177i | 0.581211 | − | 1.00669i | ||||
\(975\) | 1.25638 | − | 2.82186i | 0.0402362 | − | 0.0903720i | ||||
\(976\) | −20.7768 | − | 35.9865i | −0.665050 | − | 1.15190i | ||||
\(977\) | −3.27500 | − | 5.67247i | −0.104777 | − | 0.181479i | 0.808870 | − | 0.587987i | \(-0.200079\pi\) |
−0.913647 | + | 0.406509i | \(0.866746\pi\) | |||||||
\(978\) | 24.1869 | + | 33.2904i | 0.773411 | + | 1.06451i | ||||
\(979\) | 4.35443 | − | 7.54209i | 0.139168 | − | 0.241046i | ||||
\(980\) | 0.209057 | 0.00667808 | ||||||||
\(981\) | 5.33419 | + | 5.92421i | 0.170307 | + | 0.189146i | ||||
\(982\) | −30.1124 | −0.960927 | ||||||||
\(983\) | −28.5941 | + | 49.5264i | −0.912010 | + | 1.57965i | −0.100788 | + | 0.994908i | \(0.532136\pi\) |
−0.811221 | + | 0.584739i | \(0.801197\pi\) | |||||||
\(984\) | 4.17340 | − | 0.438642i | 0.133043 | − | 0.0139834i | ||||
\(985\) | 5.36307 | + | 9.28912i | 0.170882 | + | 0.295976i | ||||
\(986\) | 4.40727 | + | 7.63361i | 0.140356 | + | 0.243104i | ||||
\(987\) | 20.9603 | − | 2.20302i | 0.667175 | − | 0.0701229i | ||||
\(988\) | −0.805603 | + | 1.39535i | −0.0256297 | + | 0.0443919i | ||||
\(989\) | 8.54738 | 0.271791 | ||||||||
\(990\) | 2.59868 | − | 0.552367i | 0.0825915 | − | 0.0175554i | ||||
\(991\) | 24.1639 | 0.767591 | 0.383796 | − | 0.923418i | \(-0.374617\pi\) | ||||
0.383796 | + | 0.923418i | \(0.374617\pi\) | |||||||
\(992\) | 0.405529 | − | 0.702397i | 0.0128756 | − | 0.0223011i | ||||
\(993\) | 11.2819 | + | 15.5282i | 0.358021 | + | 0.492774i | ||||
\(994\) | −3.87868 | − | 6.71806i | −0.123024 | − | 0.213084i | ||||
\(995\) | 3.13485 | + | 5.42972i | 0.0993815 | + | 0.172134i | ||||
\(996\) | −0.288352 | + | 0.647650i | −0.00913679 | + | 0.0205216i | ||||
\(997\) | 3.04761 | − | 5.27861i | 0.0965187 | − | 0.167175i | −0.813723 | − | 0.581253i | \(-0.802563\pi\) |
0.910241 | + | 0.414078i | \(0.135896\pi\) | |||||||
\(998\) | −8.43571 | −0.267028 | ||||||||
\(999\) | 32.3106 | − | 10.4984i | 1.02226 | − | 0.332153i |
(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.i.d.106.3 | ✓ | 8 | |
3.2 | odd | 2 | 945.2.i.c.316.2 | 8 | |||
9.2 | odd | 6 | 2835.2.a.q.1.3 | 4 | |||
9.4 | even | 3 | inner | 315.2.i.d.211.3 | yes | 8 | |
9.5 | odd | 6 | 945.2.i.c.631.2 | 8 | |||
9.7 | even | 3 | 2835.2.a.l.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.i.d.106.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
315.2.i.d.211.3 | yes | 8 | 9.4 | even | 3 | inner | |
945.2.i.c.316.2 | 8 | 3.2 | odd | 2 | |||
945.2.i.c.631.2 | 8 | 9.5 | odd | 6 | |||
2835.2.a.l.1.2 | 4 | 9.7 | even | 3 | |||
2835.2.a.q.1.3 | 4 | 9.2 | odd | 6 |