Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.f (of order \(5\), degree \(4\), 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: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + 7288 x^{12} + 5704 x^{11} + 24392 x^{10} + 10376 x^{9} + 48880 x^{8} + 21224 x^{7} + \cdots + 1936 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 229.4 | ||
Root | \(0.488718 + 1.50412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.229 |
Dual form | 418.2.f.h.115.4 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.951057i | −0.218508 | + | 0.672499i | ||||
\(3\) | 1.27948 | − | 0.929596i | 0.738708 | − | 0.536703i | −0.153598 | − | 0.988133i | \(-0.549086\pi\) |
0.892306 | + | 0.451431i | \(0.149086\pi\) | |||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 0.804188 | + | 2.47504i | 0.359644 | + | 1.10687i | 0.953268 | + | 0.302127i | \(0.0976967\pi\) |
−0.593624 | + | 0.804743i | \(0.702303\pi\) | |||||||
\(6\) | 0.488718 | + | 1.50412i | 0.199518 | + | 0.614054i | ||||
\(7\) | 1.25444 | + | 0.911401i | 0.474132 | + | 0.344477i | 0.799049 | − | 0.601265i | \(-0.205337\pi\) |
−0.324917 | + | 0.945742i | \(0.605337\pi\) | |||||||
\(8\) | 0.809017 | − | 0.587785i | 0.286031 | − | 0.207813i | ||||
\(9\) | −0.154132 | + | 0.474370i | −0.0513774 | + | 0.158123i | ||||
\(10\) | −2.60241 | −0.822953 | ||||||||
\(11\) | −1.72947 | + | 2.83001i | −0.521453 | + | 0.853280i | ||||
\(12\) | −1.58152 | −0.456547 | ||||||||
\(13\) | 0.710450 | − | 2.18654i | 0.197043 | − | 0.606437i | −0.802903 | − | 0.596109i | \(-0.796713\pi\) |
0.999947 | − | 0.0103276i | \(-0.00328744\pi\) | |||||||
\(14\) | −1.25444 | + | 0.911401i | −0.335262 | + | 0.243582i | ||||
\(15\) | 3.32973 | + | 2.41919i | 0.859732 | + | 0.624632i | ||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 0.0656020 | + | 0.201902i | 0.0159108 | + | 0.0489685i | 0.958697 | − | 0.284430i | \(-0.0918044\pi\) |
−0.942786 | + | 0.333399i | \(0.891804\pi\) | |||||||
\(18\) | −0.403523 | − | 0.293177i | −0.0951113 | − | 0.0691024i | ||||
\(19\) | 0.809017 | − | 0.587785i | 0.185601 | − | 0.134847i | ||||
\(20\) | 0.804188 | − | 2.47504i | 0.179822 | − | 0.553435i | ||||
\(21\) | 2.45226 | 0.535127 | ||||||||
\(22\) | −2.15706 | − | 2.51934i | −0.459888 | − | 0.537125i | ||||
\(23\) | −2.47068 | −0.515172 | −0.257586 | − | 0.966255i | \(-0.582927\pi\) | ||||
−0.257586 | + | 0.966255i | \(0.582927\pi\) | |||||||
\(24\) | 0.488718 | − | 1.50412i | 0.0997591 | − | 0.307027i | ||||
\(25\) | −1.43400 | + | 1.04186i | −0.286799 | + | 0.208372i | ||||
\(26\) | 1.85998 | + | 1.35136i | 0.364772 | + | 0.265023i | ||||
\(27\) | 1.70992 | + | 5.26258i | 0.329074 | + | 1.01278i | ||||
\(28\) | −0.479152 | − | 1.47468i | −0.0905511 | − | 0.278688i | ||||
\(29\) | 3.79183 | + | 2.75492i | 0.704125 | + | 0.511577i | 0.881273 | − | 0.472608i | \(-0.156687\pi\) |
−0.177148 | + | 0.984184i | \(0.556687\pi\) | |||||||
\(30\) | −3.32973 | + | 2.41919i | −0.607922 | + | 0.441681i | ||||
\(31\) | 1.22033 | − | 3.75578i | 0.219177 | − | 0.674558i | −0.779653 | − | 0.626211i | \(-0.784605\pi\) |
0.998831 | − | 0.0483468i | \(-0.0153953\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.417951 | + | 5.22864i | 0.0727559 | + | 0.910190i | ||||
\(34\) | −0.212293 | −0.0364079 | ||||||||
\(35\) | −1.24695 | + | 3.83771i | −0.210773 | + | 0.648691i | ||||
\(36\) | 0.403523 | − | 0.293177i | 0.0672539 | − | 0.0488628i | ||||
\(37\) | 2.14343 | + | 1.55729i | 0.352377 | + | 0.256017i | 0.749866 | − | 0.661590i | \(-0.230118\pi\) |
−0.397488 | + | 0.917607i | \(0.630118\pi\) | |||||||
\(38\) | 0.309017 | + | 0.951057i | 0.0501292 | + | 0.154282i | ||||
\(39\) | −1.12359 | − | 3.45806i | −0.179919 | − | 0.553733i | ||||
\(40\) | 2.10539 | + | 1.52966i | 0.332892 | + | 0.241860i | ||||
\(41\) | 6.10649 | − | 4.43662i | 0.953673 | − | 0.692884i | 0.00200054 | − | 0.999998i | \(-0.499363\pi\) |
0.951673 | + | 0.307114i | \(0.0993632\pi\) | |||||||
\(42\) | −0.757790 | + | 2.33224i | −0.116929 | + | 0.359872i | ||||
\(43\) | 5.85824 | 0.893374 | 0.446687 | − | 0.894690i | \(-0.352604\pi\) | ||||
0.446687 | + | 0.894690i | \(0.352604\pi\) | |||||||
\(44\) | 3.06260 | − | 1.27297i | 0.461705 | − | 0.191908i | ||||
\(45\) | −1.29803 | −0.193499 | ||||||||
\(46\) | 0.763482 | − | 2.34975i | 0.112569 | − | 0.346452i | ||||
\(47\) | −10.1002 | + | 7.33820i | −1.47326 | + | 1.07039i | −0.493608 | + | 0.869684i | \(0.664322\pi\) |
−0.979652 | + | 0.200702i | \(0.935678\pi\) | |||||||
\(48\) | 1.27948 | + | 0.929596i | 0.184677 | + | 0.134176i | ||||
\(49\) | −1.42016 | − | 4.37081i | −0.202880 | − | 0.624401i | ||||
\(50\) | −0.547738 | − | 1.68577i | −0.0774619 | − | 0.238403i | ||||
\(51\) | 0.271624 | + | 0.197346i | 0.0380350 | + | 0.0276340i | ||||
\(52\) | −1.85998 | + | 1.35136i | −0.257933 | + | 0.187399i | ||||
\(53\) | 2.31354 | − | 7.12033i | 0.317789 | − | 0.978053i | −0.656803 | − | 0.754062i | \(-0.728092\pi\) |
0.974591 | − | 0.223990i | \(-0.0719084\pi\) | |||||||
\(54\) | −5.53341 | −0.753001 | ||||||||
\(55\) | −8.39519 | − | 2.00463i | −1.13201 | − | 0.270304i | ||||
\(56\) | 1.55057 | 0.207203 | ||||||||
\(57\) | 0.488718 | − | 1.50412i | 0.0647323 | − | 0.199225i | ||||
\(58\) | −3.79183 | + | 2.75492i | −0.497891 | + | 0.361739i | ||||
\(59\) | −3.38431 | − | 2.45884i | −0.440599 | − | 0.320114i | 0.345274 | − | 0.938502i | \(-0.387786\pi\) |
−0.785873 | + | 0.618388i | \(0.787786\pi\) | |||||||
\(60\) | −1.27184 | − | 3.91433i | −0.164194 | − | 0.505338i | ||||
\(61\) | −4.02292 | − | 12.3813i | −0.515082 | − | 1.58526i | −0.783132 | − | 0.621856i | \(-0.786379\pi\) |
0.268050 | − | 0.963405i | \(-0.413621\pi\) | |||||||
\(62\) | 3.19486 | + | 2.32120i | 0.405747 | + | 0.294793i | ||||
\(63\) | −0.625690 | + | 0.454590i | −0.0788295 | + | 0.0572730i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 5.98310 | 0.742112 | ||||||||
\(66\) | −5.10189 | − | 1.21825i | −0.627999 | − | 0.149956i | ||||
\(67\) | −8.97065 | −1.09594 | −0.547970 | − | 0.836498i | \(-0.684599\pi\) | ||||
−0.547970 | + | 0.836498i | \(0.684599\pi\) | |||||||
\(68\) | 0.0656020 | − | 0.201902i | 0.00795541 | − | 0.0244842i | ||||
\(69\) | −3.16118 | + | 2.29673i | −0.380562 | + | 0.276494i | ||||
\(70\) | −3.26455 | − | 2.37183i | −0.390188 | − | 0.283488i | ||||
\(71\) | 2.10796 | + | 6.48762i | 0.250168 | + | 0.769939i | 0.994743 | + | 0.102400i | \(0.0326523\pi\) |
−0.744575 | + | 0.667539i | \(0.767348\pi\) | |||||||
\(72\) | 0.154132 | + | 0.474370i | 0.0181646 | + | 0.0559050i | ||||
\(73\) | 6.83808 | + | 4.96816i | 0.800337 | + | 0.581479i | 0.911013 | − | 0.412378i | \(-0.135302\pi\) |
−0.110676 | + | 0.993857i | \(0.535302\pi\) | |||||||
\(74\) | −2.14343 | + | 1.55729i | −0.249168 | + | 0.181031i | ||||
\(75\) | −0.866261 | + | 2.66608i | −0.100027 | + | 0.307852i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −4.74877 | + | 1.97383i | −0.541173 | + | 0.224939i | ||||
\(78\) | 3.63602 | 0.411699 | ||||||||
\(79\) | 2.77538 | − | 8.54173i | 0.312254 | − | 0.961020i | −0.664616 | − | 0.747185i | \(-0.731405\pi\) |
0.976870 | − | 0.213834i | \(-0.0685953\pi\) | |||||||
\(80\) | −2.10539 | + | 1.52966i | −0.235390 | + | 0.171021i | ||||
\(81\) | 5.86931 | + | 4.26431i | 0.652146 | + | 0.473812i | ||||
\(82\) | 2.33247 | + | 7.17861i | 0.257578 | + | 0.792745i | ||||
\(83\) | −5.03599 | − | 15.4992i | −0.552772 | − | 1.70126i | −0.701757 | − | 0.712417i | \(-0.747601\pi\) |
0.148985 | − | 0.988839i | \(-0.452399\pi\) | |||||||
\(84\) | −1.98392 | − | 1.44140i | −0.216463 | − | 0.157270i | ||||
\(85\) | −0.446959 | + | 0.324735i | −0.0484795 | + | 0.0352224i | ||||
\(86\) | −1.81030 | + | 5.57152i | −0.195209 | + | 0.600792i | ||||
\(87\) | 7.41253 | 0.794707 | ||||||||
\(88\) | 0.264271 | + | 3.30608i | 0.0281714 | + | 0.352429i | ||||
\(89\) | −3.58951 | −0.380487 | −0.190244 | − | 0.981737i | \(-0.560928\pi\) | ||||
−0.190244 | + | 0.981737i | \(0.560928\pi\) | |||||||
\(90\) | 0.401114 | − | 1.23450i | 0.0422812 | − | 0.130128i | ||||
\(91\) | 2.88403 | − | 2.09537i | 0.302328 | − | 0.219654i | ||||
\(92\) | 1.99882 | + | 1.45223i | 0.208391 | + | 0.151405i | ||||
\(93\) | −1.92998 | − | 5.93986i | −0.200129 | − | 0.615935i | ||||
\(94\) | −3.85792 | − | 11.8735i | −0.397914 | − | 1.22465i | ||||
\(95\) | 2.10539 | + | 1.52966i | 0.216009 | + | 0.156939i | ||||
\(96\) | −1.27948 | + | 0.929596i | −0.130586 | + | 0.0948765i | ||||
\(97\) | −0.460238 | + | 1.41647i | −0.0467301 | + | 0.143820i | −0.971699 | − | 0.236222i | \(-0.924091\pi\) |
0.924969 | + | 0.380043i | \(0.124091\pi\) | |||||||
\(98\) | 4.59574 | 0.464240 | ||||||||
\(99\) | −1.07590 | − | 1.25660i | −0.108133 | − | 0.126293i | ||||
\(100\) | 1.77252 | 0.177252 | ||||||||
\(101\) | −0.776576 | + | 2.39005i | −0.0772722 | + | 0.237819i | −0.982230 | − | 0.187683i | \(-0.939902\pi\) |
0.904958 | + | 0.425502i | \(0.139902\pi\) | |||||||
\(102\) | −0.271624 | + | 0.197346i | −0.0268948 | + | 0.0195402i | ||||
\(103\) | −5.47964 | − | 3.98119i | −0.539925 | − | 0.392278i | 0.284132 | − | 0.958785i | \(-0.408294\pi\) |
−0.824057 | + | 0.566507i | \(0.808294\pi\) | |||||||
\(104\) | −0.710450 | − | 2.18654i | −0.0696653 | − | 0.214408i | ||||
\(105\) | 1.97208 | + | 6.06943i | 0.192455 | + | 0.592316i | ||||
\(106\) | 6.05692 | + | 4.40061i | 0.588300 | + | 0.427425i | ||||
\(107\) | 10.6272 | − | 7.72110i | 1.02737 | − | 0.746427i | 0.0595887 | − | 0.998223i | \(-0.481021\pi\) |
0.967780 | + | 0.251796i | \(0.0810211\pi\) | |||||||
\(108\) | 1.70992 | − | 5.26258i | 0.164537 | − | 0.506392i | ||||
\(109\) | −2.72603 | −0.261106 | −0.130553 | − | 0.991441i | \(-0.541675\pi\) | ||||
−0.130553 | + | 0.991441i | \(0.541675\pi\) | |||||||
\(110\) | 4.50077 | − | 7.36483i | 0.429132 | − | 0.702209i | ||||
\(111\) | 4.19012 | 0.397709 | ||||||||
\(112\) | −0.479152 | + | 1.47468i | −0.0452756 | + | 0.139344i | ||||
\(113\) | 7.16377 | − | 5.20479i | 0.673911 | − | 0.489625i | −0.197421 | − | 0.980319i | \(-0.563257\pi\) |
0.871332 | + | 0.490694i | \(0.163257\pi\) | |||||||
\(114\) | 1.27948 | + | 0.929596i | 0.119834 | + | 0.0870647i | ||||
\(115\) | −1.98689 | − | 6.11502i | −0.185278 | − | 0.570228i | ||||
\(116\) | −1.44835 | − | 4.45756i | −0.134476 | − | 0.413874i | ||||
\(117\) | 0.927725 | + | 0.674032i | 0.0857682 | + | 0.0623143i | ||||
\(118\) | 3.38431 | − | 2.45884i | 0.311551 | − | 0.226355i | ||||
\(119\) | −0.101720 | + | 0.313063i | −0.00932469 | + | 0.0286984i | ||||
\(120\) | 4.11577 | 0.375716 | ||||||||
\(121\) | −5.01790 | − | 9.78880i | −0.456173 | − | 0.889891i | ||||
\(122\) | 13.0184 | 1.17864 | ||||||||
\(123\) | 3.68886 | − | 11.3531i | 0.332613 | − | 1.02368i | ||||
\(124\) | −3.19486 | + | 2.32120i | −0.286907 | + | 0.208450i | ||||
\(125\) | 6.79511 | + | 4.93694i | 0.607773 | + | 0.441573i | ||||
\(126\) | −0.238992 | − | 0.735542i | −0.0212911 | − | 0.0655273i | ||||
\(127\) | −2.85928 | − | 8.79997i | −0.253720 | − | 0.780871i | −0.994079 | − | 0.108659i | \(-0.965344\pi\) |
0.740359 | − | 0.672212i | \(-0.234656\pi\) | |||||||
\(128\) | 0.809017 | + | 0.587785i | 0.0715077 | + | 0.0519534i | ||||
\(129\) | 7.49550 | − | 5.44580i | 0.659942 | − | 0.479476i | ||||
\(130\) | −1.84888 | + | 5.69026i | −0.162157 | + | 0.499069i | ||||
\(131\) | 12.1117 | 1.05821 | 0.529103 | − | 0.848558i | \(-0.322528\pi\) | ||||
0.529103 | + | 0.848558i | \(0.322528\pi\) | |||||||
\(132\) | 2.73519 | − | 4.47573i | 0.238068 | − | 0.389562i | ||||
\(133\) | 1.55057 | 0.134451 | ||||||||
\(134\) | 2.77208 | − | 8.53159i | 0.239471 | − | 0.737017i | ||||
\(135\) | −11.6500 | + | 8.46421i | −1.00267 | + | 0.728483i | ||||
\(136\) | 0.171748 | + | 0.124782i | 0.0147273 | + | 0.0107000i | ||||
\(137\) | −3.01282 | − | 9.27249i | −0.257402 | − | 0.792203i | −0.993347 | − | 0.115161i | \(-0.963262\pi\) |
0.735945 | − | 0.677042i | \(-0.236738\pi\) | |||||||
\(138\) | −1.20746 | − | 3.71619i | −0.102786 | − | 0.316343i | ||||
\(139\) | −10.2880 | − | 7.47470i | −0.872621 | − | 0.633996i | 0.0586683 | − | 0.998278i | \(-0.481315\pi\) |
−0.931289 | + | 0.364282i | \(0.881315\pi\) | |||||||
\(140\) | 3.26455 | − | 2.37183i | 0.275905 | − | 0.200457i | ||||
\(141\) | −6.10139 | + | 18.7782i | −0.513830 | + | 1.58141i | ||||
\(142\) | −6.82149 | −0.572447 | ||||||||
\(143\) | 4.95923 | + | 5.79212i | 0.414711 | + | 0.484361i | ||||
\(144\) | −0.498782 | −0.0415652 | ||||||||
\(145\) | −3.76919 | + | 11.6004i | −0.313014 | + | 0.963359i | ||||
\(146\) | −6.83808 | + | 4.96816i | −0.565924 | + | 0.411168i | ||||
\(147\) | −5.88016 | − | 4.27218i | −0.484987 | − | 0.352364i | ||||
\(148\) | −0.818716 | − | 2.51975i | −0.0672980 | − | 0.207122i | ||||
\(149\) | 4.19154 | + | 12.9002i | 0.343384 | + | 1.05683i | 0.962443 | + | 0.271483i | \(0.0875141\pi\) |
−0.619059 | + | 0.785344i | \(0.712486\pi\) | |||||||
\(150\) | −2.26790 | − | 1.64773i | −0.185173 | − | 0.134536i | ||||
\(151\) | −8.77937 | + | 6.37859i | −0.714455 | + | 0.519082i | −0.884608 | − | 0.466336i | \(-0.845574\pi\) |
0.170153 | + | 0.985418i | \(0.445574\pi\) | |||||||
\(152\) | 0.309017 | − | 0.951057i | 0.0250646 | − | 0.0771409i | ||||
\(153\) | −0.105888 | −0.00856051 | ||||||||
\(154\) | −0.409770 | − | 5.12630i | −0.0330202 | − | 0.413089i | ||||
\(155\) | 10.2771 | 0.825474 | ||||||||
\(156\) | −1.12359 | + | 3.45806i | −0.0899594 | + | 0.276867i | ||||
\(157\) | −4.18545 | + | 3.04091i | −0.334035 | + | 0.242691i | −0.742141 | − | 0.670244i | \(-0.766190\pi\) |
0.408106 | + | 0.912935i | \(0.366190\pi\) | |||||||
\(158\) | 7.26603 | + | 5.27908i | 0.578054 | + | 0.419981i | ||||
\(159\) | −3.65891 | − | 11.2610i | −0.290171 | − | 0.893054i | ||||
\(160\) | −0.804188 | − | 2.47504i | −0.0635766 | − | 0.195669i | ||||
\(161\) | −3.09931 | − | 2.25178i | −0.244260 | − | 0.177465i | ||||
\(162\) | −5.86931 | + | 4.26431i | −0.461137 | + | 0.335036i | ||||
\(163\) | −0.370823 | + | 1.14128i | −0.0290451 | + | 0.0893916i | −0.964528 | − | 0.263980i | \(-0.914965\pi\) |
0.935483 | + | 0.353371i | \(0.114965\pi\) | |||||||
\(164\) | −7.54804 | −0.589403 | ||||||||
\(165\) | −12.6050 | + | 5.23925i | −0.981295 | + | 0.407875i | ||||
\(166\) | 16.2968 | 1.26488 | ||||||||
\(167\) | −2.41844 | + | 7.44320i | −0.187145 | + | 0.575972i | −0.999979 | − | 0.00652332i | \(-0.997924\pi\) |
0.812834 | + | 0.582495i | \(0.197924\pi\) | |||||||
\(168\) | 1.98392 | − | 1.44140i | 0.153063 | − | 0.111207i | ||||
\(169\) | 6.24101 | + | 4.53436i | 0.480077 | + | 0.348797i | ||||
\(170\) | −0.170723 | − | 0.525432i | −0.0130939 | − | 0.0402988i | ||||
\(171\) | 0.154132 | + | 0.474370i | 0.0117868 | + | 0.0362760i | ||||
\(172\) | −4.73942 | − | 3.44339i | −0.361377 | − | 0.262556i | ||||
\(173\) | −3.97941 | + | 2.89121i | −0.302549 | + | 0.219815i | −0.728693 | − | 0.684841i | \(-0.759872\pi\) |
0.426144 | + | 0.904655i | \(0.359872\pi\) | |||||||
\(174\) | −2.29060 | + | 7.04974i | −0.173650 | + | 0.534439i | ||||
\(175\) | −2.74841 | −0.207760 | ||||||||
\(176\) | −3.22593 | − | 0.770298i | −0.243164 | − | 0.0580634i | ||||
\(177\) | −6.61589 | −0.497280 | ||||||||
\(178\) | 1.10922 | − | 3.41383i | 0.0831395 | − | 0.255877i | ||||
\(179\) | −7.71402 | + | 5.60457i | −0.576573 | + | 0.418905i | −0.837487 | − | 0.546457i | \(-0.815976\pi\) |
0.260914 | + | 0.965362i | \(0.415976\pi\) | |||||||
\(180\) | 1.05013 | + | 0.762965i | 0.0782722 | + | 0.0568680i | ||||
\(181\) | 5.97446 | + | 18.3875i | 0.444078 | + | 1.36673i | 0.883491 | + | 0.468447i | \(0.155186\pi\) |
−0.439413 | + | 0.898285i | \(0.644814\pi\) | |||||||
\(182\) | 1.10160 | + | 3.39038i | 0.0816560 | + | 0.251311i | ||||
\(183\) | −16.6568 | − | 12.1019i | −1.23131 | − | 0.894599i | ||||
\(184\) | −1.99882 | + | 1.45223i | −0.147355 | + | 0.107060i | ||||
\(185\) | −2.13063 | + | 6.55741i | −0.156647 | + | 0.482110i | ||||
\(186\) | 6.24554 | 0.457945 | ||||||||
\(187\) | −0.684841 | − | 0.163529i | −0.0500806 | − | 0.0119584i | ||||
\(188\) | 12.4845 | 0.910525 | ||||||||
\(189\) | −2.65134 | + | 8.15999i | −0.192857 | + | 0.593552i | ||||
\(190\) | −2.10539 | + | 1.52966i | −0.152741 | + | 0.110973i | ||||
\(191\) | 1.69016 | + | 1.22798i | 0.122296 | + | 0.0888533i | 0.647252 | − | 0.762276i | \(-0.275918\pi\) |
−0.524956 | + | 0.851129i | \(0.675918\pi\) | |||||||
\(192\) | −0.488718 | − | 1.50412i | −0.0352702 | − | 0.108550i | ||||
\(193\) | −2.33862 | − | 7.19752i | −0.168337 | − | 0.518089i | 0.830929 | − | 0.556378i | \(-0.187809\pi\) |
−0.999267 | + | 0.0382889i | \(0.987809\pi\) | |||||||
\(194\) | −1.20492 | − | 0.875424i | −0.0865081 | − | 0.0628518i | ||||
\(195\) | 7.65525 | − | 5.56186i | 0.548204 | − | 0.398293i | ||||
\(196\) | −1.42016 | + | 4.37081i | −0.101440 | + | 0.312201i | ||||
\(197\) | 1.65699 | 0.118055 | 0.0590277 | − | 0.998256i | \(-0.481200\pi\) | ||||
0.0590277 | + | 0.998256i | \(0.481200\pi\) | |||||||
\(198\) | 1.52757 | − | 0.634935i | 0.108560 | − | 0.0451229i | ||||
\(199\) | −3.68327 | −0.261100 | −0.130550 | − | 0.991442i | \(-0.541674\pi\) | ||||
−0.130550 | + | 0.991442i | \(0.541674\pi\) | |||||||
\(200\) | −0.547738 | + | 1.68577i | −0.0387309 | + | 0.119202i | ||||
\(201\) | −11.4778 | + | 8.33908i | −0.809579 | + | 0.588194i | ||||
\(202\) | −2.03310 | − | 1.47713i | −0.143049 | − | 0.103931i | ||||
\(203\) | 2.24576 | + | 6.91175i | 0.157622 | + | 0.485110i | ||||
\(204\) | −0.103751 | − | 0.319313i | −0.00726403 | − | 0.0223564i | ||||
\(205\) | 15.8916 | + | 11.5459i | 1.10992 | + | 0.806400i | ||||
\(206\) | 5.47964 | − | 3.98119i | 0.381784 | − | 0.277383i | ||||
\(207\) | 0.380811 | − | 1.17202i | 0.0264682 | − | 0.0814607i | ||||
\(208\) | 2.29906 | 0.159411 | ||||||||
\(209\) | 0.264271 | + | 3.30608i | 0.0182800 | + | 0.228686i | ||||
\(210\) | −6.38177 | −0.440384 | ||||||||
\(211\) | −0.645508 | + | 1.98667i | −0.0444386 | + | 0.136768i | −0.970814 | − | 0.239833i | \(-0.922907\pi\) |
0.926376 | + | 0.376601i | \(0.122907\pi\) | |||||||
\(212\) | −6.05692 | + | 4.40061i | −0.415991 | + | 0.302235i | ||||
\(213\) | 8.72796 | + | 6.34123i | 0.598030 | + | 0.434494i | ||||
\(214\) | 4.05923 | + | 12.4930i | 0.277483 | + | 0.854005i | ||||
\(215\) | 4.71113 | + | 14.4994i | 0.321296 | + | 0.988848i | ||||
\(216\) | 4.47662 | + | 3.25246i | 0.304595 | + | 0.221302i | ||||
\(217\) | 4.95384 | − | 3.59918i | 0.336289 | − | 0.244328i | ||||
\(218\) | 0.842389 | − | 2.59261i | 0.0570538 | − | 0.175593i | ||||
\(219\) | 13.3676 | 0.903297 | ||||||||
\(220\) | 5.61356 | + | 6.55635i | 0.378466 | + | 0.442029i | ||||
\(221\) | 0.488074 | 0.0328314 | ||||||||
\(222\) | −1.29482 | + | 3.98504i | −0.0869026 | + | 0.267459i | ||||
\(223\) | −18.7493 | + | 13.6222i | −1.25555 | + | 0.912209i | −0.998530 | − | 0.0541981i | \(-0.982740\pi\) |
−0.257017 | + | 0.966407i | \(0.582740\pi\) | |||||||
\(224\) | −1.25444 | − | 0.911401i | −0.0838155 | − | 0.0608955i | ||||
\(225\) | −0.273202 | − | 0.840829i | −0.0182135 | − | 0.0560553i | ||||
\(226\) | 2.73632 | + | 8.42152i | 0.182017 | + | 0.560191i | ||||
\(227\) | −7.45948 | − | 5.41963i | −0.495103 | − | 0.359714i | 0.312040 | − | 0.950069i | \(-0.398988\pi\) |
−0.807143 | + | 0.590355i | \(0.798988\pi\) | |||||||
\(228\) | −1.27948 | + | 0.929596i | −0.0847356 | + | 0.0615640i | ||||
\(229\) | −5.03217 | + | 15.4874i | −0.332535 | + | 1.02344i | 0.635388 | + | 0.772193i | \(0.280840\pi\) |
−0.967923 | + | 0.251245i | \(0.919160\pi\) | |||||||
\(230\) | 6.42971 | 0.423962 | ||||||||
\(231\) | −4.24110 | + | 6.93992i | −0.279044 | + | 0.456613i | ||||
\(232\) | 4.68696 | 0.307714 | ||||||||
\(233\) | −4.84624 | + | 14.9152i | −0.317488 | + | 0.977128i | 0.657230 | + | 0.753690i | \(0.271728\pi\) |
−0.974718 | + | 0.223438i | \(0.928272\pi\) | |||||||
\(234\) | −0.927725 | + | 0.674032i | −0.0606473 | + | 0.0440628i | ||||
\(235\) | −26.2847 | − | 19.0970i | −1.71463 | − | 1.24575i | ||||
\(236\) | 1.29269 | + | 3.97849i | 0.0841470 | + | 0.258978i | ||||
\(237\) | −4.38932 | − | 13.5089i | −0.285117 | − | 0.877501i | ||||
\(238\) | −0.266307 | − | 0.193484i | −0.0172621 | − | 0.0125417i | ||||
\(239\) | 19.3770 | − | 14.0782i | 1.25339 | − | 0.910644i | 0.254981 | − | 0.966946i | \(-0.417931\pi\) |
0.998414 | + | 0.0563017i | \(0.0179309\pi\) | |||||||
\(240\) | −1.27184 | + | 3.91433i | −0.0820971 | + | 0.252669i | ||||
\(241\) | −3.80838 | −0.245320 | −0.122660 | − | 0.992449i | \(-0.539142\pi\) | ||||
−0.122660 | + | 0.992449i | \(0.539142\pi\) | |||||||
\(242\) | 10.8603 | − | 1.74740i | 0.698128 | − | 0.112327i | ||||
\(243\) | −5.12647 | −0.328863 | ||||||||
\(244\) | −4.02292 | + | 12.3813i | −0.257541 | + | 0.792630i | ||||
\(245\) | 9.67583 | − | 7.02990i | 0.618166 | − | 0.449124i | ||||
\(246\) | 9.65756 | + | 7.01663i | 0.615743 | + | 0.447364i | ||||
\(247\) | −0.710450 | − | 2.18654i | −0.0452048 | − | 0.139126i | ||||
\(248\) | −1.22033 | − | 3.75578i | −0.0774909 | − | 0.238492i | ||||
\(249\) | −20.8514 | − | 15.1494i | −1.32141 | − | 0.960057i | ||||
\(250\) | −6.79511 | + | 4.93694i | −0.429761 | + | 0.312239i | ||||
\(251\) | 1.43218 | − | 4.40778i | 0.0903981 | − | 0.278217i | −0.895629 | − | 0.444802i | \(-0.853274\pi\) |
0.986027 | + | 0.166585i | \(0.0532741\pi\) | |||||||
\(252\) | 0.773395 | 0.0487193 | ||||||||
\(253\) | 4.27295 | − | 6.99204i | 0.268638 | − | 0.439586i | ||||
\(254\) | 9.25283 | 0.580574 | ||||||||
\(255\) | −0.270003 | + | 0.830983i | −0.0169082 | + | 0.0520381i | ||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 20.7952 | + | 15.1086i | 1.29717 | + | 0.942449i | 0.999924 | − | 0.0123525i | \(-0.00393203\pi\) |
0.297245 | + | 0.954801i | \(0.403932\pi\) | |||||||
\(258\) | 2.86303 | + | 8.81149i | 0.178244 | + | 0.548580i | ||||
\(259\) | 1.26947 | + | 3.90704i | 0.0788813 | + | 0.242772i | ||||
\(260\) | −4.84043 | − | 3.51678i | −0.300190 | − | 0.218101i | ||||
\(261\) | −1.89130 | + | 1.37411i | −0.117068 | + | 0.0850551i | ||||
\(262\) | −3.74273 | + | 11.5189i | −0.231227 | + | 0.711642i | ||||
\(263\) | −21.8725 | −1.34872 | −0.674358 | − | 0.738405i | \(-0.735579\pi\) | ||||
−0.674358 | + | 0.738405i | \(0.735579\pi\) | |||||||
\(264\) | 3.41145 | + | 3.98440i | 0.209960 | + | 0.245223i | ||||
\(265\) | 19.4836 | 1.19687 | ||||||||
\(266\) | −0.479152 | + | 1.47468i | −0.0293787 | + | 0.0904183i | ||||
\(267\) | −4.59270 | + | 3.33680i | −0.281069 | + | 0.204209i | ||||
\(268\) | 7.25741 | + | 5.27281i | 0.443317 | + | 0.322088i | ||||
\(269\) | −6.36520 | − | 19.5901i | −0.388093 | − | 1.19443i | −0.934211 | − | 0.356720i | \(-0.883895\pi\) |
0.546118 | − | 0.837708i | \(-0.316105\pi\) | |||||||
\(270\) | −4.44990 | − | 13.6954i | −0.270812 | − | 0.833474i | ||||
\(271\) | 17.9197 | + | 13.0194i | 1.08854 | + | 0.790872i | 0.979152 | − | 0.203127i | \(-0.0651103\pi\) |
0.109390 | + | 0.993999i | \(0.465110\pi\) | |||||||
\(272\) | −0.171748 | + | 0.124782i | −0.0104138 | + | 0.00756605i | ||||
\(273\) | 1.74221 | − | 5.36196i | 0.105443 | − | 0.324521i | ||||
\(274\) | 9.74968 | 0.588999 | ||||||||
\(275\) | −0.468425 | − | 5.86009i | −0.0282471 | − | 0.353376i | ||||
\(276\) | 3.90744 | 0.235200 | ||||||||
\(277\) | −2.71751 | + | 8.36362i | −0.163279 | + | 0.502521i | −0.998905 | − | 0.0467770i | \(-0.985105\pi\) |
0.835626 | + | 0.549298i | \(0.185105\pi\) | |||||||
\(278\) | 10.2880 | − | 7.47470i | 0.617036 | − | 0.448303i | ||||
\(279\) | 1.59354 | + | 1.15777i | 0.0954026 | + | 0.0693141i | ||||
\(280\) | 1.24695 | + | 3.83771i | 0.0745193 | + | 0.229347i | ||||
\(281\) | 5.28386 | + | 16.2621i | 0.315209 | + | 0.970113i | 0.975668 | + | 0.219252i | \(0.0703615\pi\) |
−0.660459 | + | 0.750862i | \(0.729638\pi\) | |||||||
\(282\) | −15.9737 | − | 11.6055i | −0.951217 | − | 0.691100i | ||||
\(283\) | 19.4980 | − | 14.1661i | 1.15904 | − | 0.842090i | 0.169381 | − | 0.985551i | \(-0.445823\pi\) |
0.989656 | + | 0.143461i | \(0.0458231\pi\) | |||||||
\(284\) | 2.10796 | − | 6.48762i | 0.125084 | − | 0.384970i | ||||
\(285\) | 4.11577 | 0.243797 | ||||||||
\(286\) | −7.04112 | + | 2.92664i | −0.416350 | + | 0.173056i | ||||
\(287\) | 11.7037 | 0.690850 | ||||||||
\(288\) | 0.154132 | − | 0.474370i | 0.00908232 | − | 0.0279525i | ||||
\(289\) | 13.7168 | − | 9.96586i | 0.806872 | − | 0.586227i | ||||
\(290\) | −9.86788 | − | 7.16943i | −0.579462 | − | 0.421003i | ||||
\(291\) | 0.727877 | + | 2.24018i | 0.0426689 | + | 0.131321i | ||||
\(292\) | −2.61192 | − | 8.03865i | −0.152851 | − | 0.470426i | ||||
\(293\) | 2.06559 | + | 1.50074i | 0.120673 | + | 0.0876740i | 0.646485 | − | 0.762927i | \(-0.276238\pi\) |
−0.525812 | + | 0.850601i | \(0.676238\pi\) | |||||||
\(294\) | 5.88016 | − | 4.27218i | 0.342938 | − | 0.249159i | ||||
\(295\) | 3.36411 | − | 10.3537i | 0.195866 | − | 0.602813i | ||||
\(296\) | 2.64942 | 0.153994 | ||||||||
\(297\) | −17.8504 | − | 4.26237i | −1.03579 | − | 0.247328i | ||||
\(298\) | −13.5641 | −0.785747 | ||||||||
\(299\) | −1.75529 | + | 5.40223i | −0.101511 | + | 0.312419i | ||||
\(300\) | 2.26790 | − | 1.64773i | 0.130937 | − | 0.0951315i | ||||
\(301\) | 7.34879 | + | 5.33921i | 0.423577 | + | 0.307747i | ||||
\(302\) | −3.35342 | − | 10.3208i | −0.192968 | − | 0.593894i | ||||
\(303\) | 1.22817 | + | 3.77993i | 0.0705567 | + | 0.217151i | ||||
\(304\) | 0.809017 | + | 0.587785i | 0.0464003 | + | 0.0337118i | ||||
\(305\) | 27.4089 | − | 19.9137i | 1.56943 | − | 1.14026i | ||||
\(306\) | 0.0327211 | − | 0.100705i | 0.00187054 | − | 0.00575693i | ||||
\(307\) | −18.9304 | −1.08041 | −0.540207 | − | 0.841532i | \(-0.681654\pi\) | ||||
−0.540207 | + | 0.841532i | \(0.681654\pi\) | |||||||
\(308\) | 5.00203 | + | 1.19440i | 0.285017 | + | 0.0680572i | ||||
\(309\) | −10.7120 | −0.609383 | ||||||||
\(310\) | −3.17579 | + | 9.77407i | −0.180373 | + | 0.555130i | ||||
\(311\) | −13.6085 | + | 9.88713i | −0.771666 | + | 0.560648i | −0.902466 | − | 0.430761i | \(-0.858245\pi\) |
0.130801 | + | 0.991409i | \(0.458245\pi\) | |||||||
\(312\) | −2.94160 | − | 2.13720i | −0.166536 | − | 0.120995i | ||||
\(313\) | −7.62692 | − | 23.4733i | −0.431099 | − | 1.32679i | −0.897032 | − | 0.441966i | \(-0.854281\pi\) |
0.465932 | − | 0.884820i | \(-0.345719\pi\) | |||||||
\(314\) | −1.59870 | − | 4.92029i | −0.0902199 | − | 0.277668i | ||||
\(315\) | −1.62830 | − | 1.18303i | −0.0917443 | − | 0.0666561i | ||||
\(316\) | −7.26603 | + | 5.27908i | −0.408746 | + | 0.296971i | ||||
\(317\) | 7.24916 | − | 22.3106i | 0.407154 | − | 1.25309i | −0.511930 | − | 0.859027i | \(-0.671069\pi\) |
0.919084 | − | 0.394063i | \(-0.128931\pi\) | |||||||
\(318\) | 11.8405 | 0.663982 | ||||||||
\(319\) | −14.3543 | + | 5.96636i | −0.803686 | + | 0.334052i | ||||
\(320\) | 2.60241 | 0.145479 | ||||||||
\(321\) | 6.41976 | − | 19.7580i | 0.358316 | − | 1.10278i | ||||
\(322\) | 3.09931 | − | 2.25178i | 0.172718 | − | 0.125487i | ||||
\(323\) | 0.171748 | + | 0.124782i | 0.00955633 | + | 0.00694308i | ||||
\(324\) | −2.24188 | − | 6.89979i | −0.124549 | − | 0.383322i | ||||
\(325\) | 1.25928 | + | 3.87568i | 0.0698525 | + | 0.214984i | ||||
\(326\) | −0.970827 | − | 0.705347i | −0.0537691 | − | 0.0390655i | ||||
\(327\) | −3.48790 | + | 2.53411i | −0.192881 | + | 0.140136i | ||||
\(328\) | 2.33247 | − | 7.17861i | 0.128789 | − | 0.396372i | ||||
\(329\) | −19.3580 | −1.06724 | ||||||||
\(330\) | −1.08768 | − | 13.6071i | −0.0598747 | − | 0.749044i | ||||
\(331\) | 16.6549 | 0.915436 | 0.457718 | − | 0.889097i | \(-0.348667\pi\) | ||||
0.457718 | + | 0.889097i | \(0.348667\pi\) | |||||||
\(332\) | −5.03599 | + | 15.4992i | −0.276386 | + | 0.850628i | ||||
\(333\) | −1.06910 | + | 0.776748i | −0.0585865 | + | 0.0425656i | ||||
\(334\) | −6.33156 | − | 4.60015i | −0.346448 | − | 0.251709i | ||||
\(335\) | −7.21409 | − | 22.2027i | −0.394148 | − | 1.21306i | ||||
\(336\) | 0.757790 | + | 2.33224i | 0.0413408 | + | 0.127234i | ||||
\(337\) | 18.1247 | + | 13.1684i | 0.987317 | + | 0.717328i | 0.959332 | − | 0.282281i | \(-0.0910909\pi\) |
0.0279850 | + | 0.999608i | \(0.491091\pi\) | |||||||
\(338\) | −6.24101 | + | 4.53436i | −0.339466 | + | 0.246637i | ||||
\(339\) | 4.32755 | − | 13.3188i | 0.235040 | − | 0.723380i | ||||
\(340\) | 0.552471 | 0.0299620 | ||||||||
\(341\) | 8.51838 | + | 9.94903i | 0.461296 | + | 0.538770i | ||||
\(342\) | −0.498782 | −0.0269710 | ||||||||
\(343\) | 5.55612 | − | 17.1000i | 0.300002 | − | 0.923312i | ||||
\(344\) | 4.73942 | − | 3.44339i | 0.255532 | − | 0.185655i | ||||
\(345\) | −8.22668 | − | 5.97703i | −0.442910 | − | 0.321793i | ||||
\(346\) | −1.52000 | − | 4.67808i | −0.0817157 | − | 0.251495i | ||||
\(347\) | −3.11524 | − | 9.58771i | −0.167235 | − | 0.514695i | 0.831959 | − | 0.554837i | \(-0.187219\pi\) |
−0.999194 | + | 0.0401412i | \(0.987219\pi\) | |||||||
\(348\) | −5.99687 | − | 4.35698i | −0.321466 | − | 0.233559i | ||||
\(349\) | −20.7205 | + | 15.0543i | −1.10914 | + | 0.805839i | −0.982528 | − | 0.186113i | \(-0.940411\pi\) |
−0.126614 | + | 0.991952i | \(0.540411\pi\) | |||||||
\(350\) | 0.849305 | − | 2.61389i | 0.0453973 | − | 0.139718i | ||||
\(351\) | 12.7217 | 0.679032 | ||||||||
\(352\) | 1.72947 | − | 2.83001i | 0.0921808 | − | 0.150840i | ||||
\(353\) | −6.10891 | −0.325144 | −0.162572 | − | 0.986697i | \(-0.551979\pi\) | ||||
−0.162572 | + | 0.986697i | \(0.551979\pi\) | |||||||
\(354\) | 2.04442 | − | 6.29208i | 0.108660 | − | 0.334420i | ||||
\(355\) | −14.3619 | + | 10.4345i | −0.762251 | + | 0.553808i | ||||
\(356\) | 2.90397 | + | 2.10986i | 0.153910 | + | 0.111822i | ||||
\(357\) | 0.160873 | + | 0.495117i | 0.00851431 | + | 0.0262043i | ||||
\(358\) | −2.94650 | − | 9.06838i | −0.155727 | − | 0.479279i | ||||
\(359\) | 20.8917 | + | 15.1787i | 1.10262 | + | 0.801102i | 0.981486 | − | 0.191534i | \(-0.0613463\pi\) |
0.121136 | + | 0.992636i | \(0.461346\pi\) | |||||||
\(360\) | −1.05013 | + | 0.762965i | −0.0553468 | + | 0.0402118i | ||||
\(361\) | 0.309017 | − | 0.951057i | 0.0162641 | − | 0.0500556i | ||||
\(362\) | −19.3338 | −1.01616 | ||||||||
\(363\) | −15.5199 | − | 7.85995i | −0.814586 | − | 0.412541i | ||||
\(364\) | −3.56485 | −0.186849 | ||||||||
\(365\) | −6.79727 | + | 20.9198i | −0.355785 | + | 1.09499i | ||||
\(366\) | 16.6568 | − | 12.1019i | 0.870667 | − | 0.632577i | ||||
\(367\) | 19.7237 | + | 14.3301i | 1.02957 | + | 0.748026i | 0.968223 | − | 0.250090i | \(-0.0804602\pi\) |
0.0613474 | + | 0.998116i | \(0.480460\pi\) | |||||||
\(368\) | −0.763482 | − | 2.34975i | −0.0397992 | − | 0.122489i | ||||
\(369\) | 1.16339 | + | 3.58056i | 0.0605639 | + | 0.186397i | ||||
\(370\) | −5.57807 | − | 4.05270i | −0.289990 | − | 0.210690i | ||||
\(371\) | 9.39166 | − | 6.82344i | 0.487591 | − | 0.354255i | ||||
\(372\) | −1.92998 | + | 5.93986i | −0.100065 | + | 0.307967i | ||||
\(373\) | 4.33069 | 0.224234 | 0.112117 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112117 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(374\) | 0.367153 | − | 0.600790i | 0.0189850 | − | 0.0310661i | ||||
\(375\) | 13.2836 | 0.685960 | ||||||||
\(376\) | −3.85792 | + | 11.8735i | −0.198957 | + | 0.612327i | ||||
\(377\) | 8.71765 | − | 6.33374i | 0.448982 | − | 0.326204i | ||||
\(378\) | −6.94130 | − | 5.04315i | −0.357022 | − | 0.259392i | ||||
\(379\) | −0.762790 | − | 2.34763i | −0.0391819 | − | 0.120589i | 0.929552 | − | 0.368690i | \(-0.120194\pi\) |
−0.968734 | + | 0.248101i | \(0.920194\pi\) | |||||||
\(380\) | −0.804188 | − | 2.47504i | −0.0412540 | − | 0.126967i | ||||
\(381\) | −11.8388 | − | 8.60140i | −0.606521 | − | 0.440663i | ||||
\(382\) | −1.69016 | + | 1.22798i | −0.0864764 | + | 0.0628287i | ||||
\(383\) | −6.62480 | + | 20.3890i | −0.338512 | + | 1.04183i | 0.626455 | + | 0.779458i | \(0.284505\pi\) |
−0.964966 | + | 0.262374i | \(0.915495\pi\) | |||||||
\(384\) | 1.58152 | 0.0807068 | ||||||||
\(385\) | −8.70420 | − | 10.1661i | −0.443607 | − | 0.518110i | ||||
\(386\) | 7.56792 | 0.385197 | ||||||||
\(387\) | −0.902943 | + | 2.77897i | −0.0458992 | + | 0.141263i | ||||
\(388\) | 1.20492 | − | 0.875424i | 0.0611705 | − | 0.0444429i | ||||
\(389\) | 4.77449 | + | 3.46887i | 0.242076 | + | 0.175879i | 0.702208 | − | 0.711972i | \(-0.252198\pi\) |
−0.460132 | + | 0.887851i | \(0.652198\pi\) | |||||||
\(390\) | 2.92405 | + | 8.99929i | 0.148065 | + | 0.455697i | ||||
\(391\) | −0.162081 | − | 0.498835i | −0.00819681 | − | 0.0252272i | ||||
\(392\) | −3.71803 | − | 2.70131i | −0.187789 | − | 0.136437i | ||||
\(393\) | 15.4967 | − | 11.2590i | 0.781705 | − | 0.567942i | ||||
\(394\) | −0.512037 | + | 1.57589i | −0.0257961 | + | 0.0793921i | ||||
\(395\) | 23.3730 | 1.17602 | ||||||||
\(396\) | 0.131814 | + | 1.64901i | 0.00662388 | + | 0.0828660i | ||||
\(397\) | 11.4881 | 0.576571 | 0.288286 | − | 0.957544i | \(-0.406915\pi\) | ||||
0.288286 | + | 0.957544i | \(0.406915\pi\) | |||||||
\(398\) | 1.13819 | − | 3.50300i | 0.0570525 | − | 0.175589i | ||||
\(399\) | 1.98392 | − | 1.44140i | 0.0993202 | − | 0.0721603i | ||||
\(400\) | −1.43400 | − | 1.04186i | −0.0716999 | − | 0.0520930i | ||||
\(401\) | 8.68180 | + | 26.7198i | 0.433549 | + | 1.33433i | 0.894567 | + | 0.446935i | \(0.147484\pi\) |
−0.461018 | + | 0.887391i | \(0.652516\pi\) | |||||||
\(402\) | −4.38412 | − | 13.4929i | −0.218660 | − | 0.672966i | ||||
\(403\) | −7.34518 | − | 5.33659i | −0.365889 | − | 0.265834i | ||||
\(404\) | 2.03310 | − | 1.47713i | 0.101151 | − | 0.0734902i | ||||
\(405\) | −5.83428 | + | 17.9561i | −0.289908 | + | 0.892244i | ||||
\(406\) | −7.26744 | −0.360677 | ||||||||
\(407\) | −8.11413 | + | 3.37264i | −0.402202 | + | 0.167175i | ||||
\(408\) | 0.335746 | 0.0166219 | ||||||||
\(409\) | 9.44920 | − | 29.0816i | 0.467233 | − | 1.43799i | −0.388920 | − | 0.921272i | \(-0.627152\pi\) |
0.856153 | − | 0.516723i | \(-0.172848\pi\) | |||||||
\(410\) | −15.8916 | + | 11.5459i | −0.784828 | + | 0.570211i | ||||
\(411\) | −12.4745 | − | 9.06326i | −0.615322 | − | 0.447058i | ||||
\(412\) | 2.09303 | + | 6.44170i | 0.103116 | + | 0.317360i | ||||
\(413\) | −2.00440 | − | 6.16892i | −0.0986303 | − | 0.303553i | ||||
\(414\) | 0.996976 | + | 0.724345i | 0.0489987 | + | 0.0355996i | ||||
\(415\) | 34.3111 | − | 24.9285i | 1.68427 | − | 1.22369i | ||||
\(416\) | −0.710450 | + | 2.18654i | −0.0348327 | + | 0.107204i | ||||
\(417\) | −20.1118 | −0.984879 | ||||||||
\(418\) | −3.22593 | − | 0.770298i | −0.157786 | − | 0.0376765i | ||||
\(419\) | −29.3802 | −1.43532 | −0.717658 | − | 0.696395i | \(-0.754786\pi\) | ||||
−0.717658 | + | 0.696395i | \(0.754786\pi\) | |||||||
\(420\) | 1.97208 | − | 6.06943i | 0.0962275 | − | 0.296158i | ||||
\(421\) | 10.6786 | − | 7.75846i | 0.520444 | − | 0.378124i | −0.296327 | − | 0.955086i | \(-0.595762\pi\) |
0.816771 | + | 0.576962i | \(0.195762\pi\) | |||||||
\(422\) | −1.68996 | − | 1.22783i | −0.0822660 | − | 0.0597698i | ||||
\(423\) | −1.92426 | − | 5.92227i | −0.0935608 | − | 0.287950i | ||||
\(424\) | −2.31354 | − | 7.12033i | −0.112355 | − | 0.345794i | ||||
\(425\) | −0.304427 | − | 0.221179i | −0.0147669 | − | 0.0107288i | ||||
\(426\) | −8.72796 | + | 6.34123i | −0.422871 | + | 0.307234i | ||||
\(427\) | 6.23781 | − | 19.1980i | 0.301869 | − | 0.929057i | ||||
\(428\) | −13.1359 | −0.634949 | ||||||||
\(429\) | 11.7296 | + | 2.80082i | 0.566309 | + | 0.135225i | ||||
\(430\) | −15.2455 | −0.735205 | ||||||||
\(431\) | −10.4157 | + | 32.0562i | −0.501706 | + | 1.54409i | 0.304532 | + | 0.952502i | \(0.401500\pi\) |
−0.806238 | + | 0.591591i | \(0.798500\pi\) | |||||||
\(432\) | −4.47662 | + | 3.25246i | −0.215382 | + | 0.156484i | ||||
\(433\) | 29.3735 | + | 21.3411i | 1.41160 | + | 1.02559i | 0.993088 | + | 0.117374i | \(0.0374477\pi\) |
0.418510 | + | 0.908212i | \(0.362552\pi\) | |||||||
\(434\) | 1.89220 | + | 5.82359i | 0.0908285 | + | 0.279541i | ||||
\(435\) | 5.96107 | + | 18.3463i | 0.285811 | + | 0.879637i | ||||
\(436\) | 2.20540 | + | 1.60232i | 0.105620 | + | 0.0767371i | ||||
\(437\) | −1.99882 | + | 1.45223i | −0.0956166 | + | 0.0694695i | ||||
\(438\) | −4.13081 | + | 12.7133i | −0.197378 | + | 0.607466i | ||||
\(439\) | −15.5926 | −0.744196 | −0.372098 | − | 0.928194i | \(-0.621361\pi\) | ||||
−0.372098 | + | 0.928194i | \(0.621361\pi\) | |||||||
\(440\) | −7.97014 | + | 3.31279i | −0.379962 | + | 0.157931i | ||||
\(441\) | 2.29227 | 0.109156 | ||||||||
\(442\) | −0.150823 | + | 0.464186i | −0.00717392 | + | 0.0220791i | ||||
\(443\) | 5.79119 | − | 4.20755i | 0.275148 | − | 0.199907i | −0.441650 | − | 0.897187i | \(-0.645607\pi\) |
0.716798 | + | 0.697281i | \(0.245607\pi\) | |||||||
\(444\) | −3.38988 | − | 2.46289i | −0.160877 | − | 0.116884i | ||||
\(445\) | −2.88664 | − | 8.88416i | −0.136840 | − | 0.421150i | ||||
\(446\) | −7.16160 | − | 22.0412i | −0.339112 | − | 1.04368i | ||||
\(447\) | 17.3550 | + | 12.6091i | 0.820863 | + | 0.596392i | ||||
\(448\) | 1.25444 | − | 0.911401i | 0.0592665 | − | 0.0430596i | ||||
\(449\) | 4.49288 | − | 13.8277i | 0.212032 | − | 0.652567i | −0.787319 | − | 0.616546i | \(-0.788532\pi\) |
0.999351 | − | 0.0360215i | \(-0.0114685\pi\) | |||||||
\(450\) | 0.884100 | 0.0416769 | ||||||||
\(451\) | 1.99473 | + | 24.9544i | 0.0939280 | + | 1.17506i | ||||
\(452\) | −8.85491 | −0.416500 | ||||||||
\(453\) | −5.30352 | + | 16.3225i | −0.249181 | + | 0.766900i | ||||
\(454\) | 7.45948 | − | 5.41963i | 0.350091 | − | 0.254356i | ||||
\(455\) | 7.50541 | + | 5.45300i | 0.351859 | + | 0.255640i | ||||
\(456\) | −0.488718 | − | 1.50412i | −0.0228863 | − | 0.0704368i | ||||
\(457\) | −0.893475 | − | 2.74983i | −0.0417950 | − | 0.128632i | 0.927982 | − | 0.372626i | \(-0.121542\pi\) |
−0.969777 | + | 0.243994i | \(0.921542\pi\) | |||||||
\(458\) | −13.1744 | − | 9.57176i | −0.615599 | − | 0.447259i | ||||
\(459\) | −0.950353 | + | 0.690472i | −0.0443587 | + | 0.0322285i | ||||
\(460\) | −1.98689 | + | 6.11502i | −0.0926392 | + | 0.285114i | ||||
\(461\) | −22.8907 | −1.06612 | −0.533062 | − | 0.846076i | \(-0.678959\pi\) | ||||
−0.533062 | + | 0.846076i | \(0.678959\pi\) | |||||||
\(462\) | −5.28968 | − | 6.17807i | −0.246098 | − | 0.287430i | ||||
\(463\) | −39.1694 | −1.82036 | −0.910178 | − | 0.414218i | \(-0.864055\pi\) | ||||
−0.910178 | + | 0.414218i | \(0.864055\pi\) | |||||||
\(464\) | −1.44835 | + | 4.45756i | −0.0672379 | + | 0.206937i | ||||
\(465\) | 13.1493 | − | 9.55352i | 0.609784 | − | 0.443034i | ||||
\(466\) | −12.6876 | − | 9.21810i | −0.587743 | − | 0.427020i | ||||
\(467\) | −8.56679 | − | 26.3659i | −0.396424 | − | 1.22007i | −0.927847 | − | 0.372960i | \(-0.878343\pi\) |
0.531424 | − | 0.847106i | \(-0.321657\pi\) | |||||||
\(468\) | −0.354359 | − | 1.09061i | −0.0163803 | − | 0.0504133i | ||||
\(469\) | −11.2531 | − | 8.17585i | −0.519620 | − | 0.377526i | ||||
\(470\) | 26.2847 | − | 19.0970i | 1.21242 | − | 0.880878i | ||||
\(471\) | −2.52838 | + | 7.78156i | −0.116502 | + | 0.358555i | ||||
\(472\) | −4.18323 | −0.192549 | ||||||||
\(473\) | −10.1316 | + | 16.5789i | −0.465853 | + | 0.762298i | ||||
\(474\) | 14.2041 | 0.652418 | ||||||||
\(475\) | −0.547738 | + | 1.68577i | −0.0251320 | + | 0.0773482i | ||||
\(476\) | 0.266307 | − | 0.193484i | 0.0122062 | − | 0.00886830i | ||||
\(477\) | 3.02108 | + | 2.19494i | 0.138326 | + | 0.100500i | ||||
\(478\) | 7.40136 | + | 22.7790i | 0.338530 | + | 1.04189i | ||||
\(479\) | 5.20943 | + | 16.0330i | 0.238025 | + | 0.732565i | 0.996706 | + | 0.0811029i | \(0.0258442\pi\) |
−0.758681 | + | 0.651463i | \(0.774156\pi\) | |||||||
\(480\) | −3.32973 | − | 2.41919i | −0.151981 | − | 0.110420i | ||||
\(481\) | 4.92787 | − | 3.58031i | 0.224692 | − | 0.163248i | ||||
\(482\) | 1.17686 | − | 3.62199i | 0.0536043 | − | 0.164977i | ||||
\(483\) | −6.05874 | −0.275682 | ||||||||
\(484\) | −1.69415 | + | 10.8688i | −0.0770067 | + | 0.494034i | ||||
\(485\) | −3.87592 | −0.175997 | ||||||||
\(486\) | 1.58417 | − | 4.87556i | 0.0718593 | − | 0.221160i | ||||
\(487\) | 22.2862 | − | 16.1918i | 1.00988 | − | 0.733723i | 0.0456980 | − | 0.998955i | \(-0.485449\pi\) |
0.964184 | + | 0.265233i | \(0.0854488\pi\) | |||||||
\(488\) | −10.5321 | − | 7.65205i | −0.476768 | − | 0.346392i | ||||
\(489\) | 0.586465 | + | 1.80495i | 0.0265209 | + | 0.0816228i | ||||
\(490\) | 3.69584 | + | 11.3746i | 0.166961 | + | 0.513853i | ||||
\(491\) | −16.2475 | − | 11.8045i | −0.733239 | − | 0.532729i | 0.157347 | − | 0.987543i | \(-0.449706\pi\) |
−0.890587 | + | 0.454814i | \(0.849706\pi\) | |||||||
\(492\) | −9.65756 | + | 7.01663i | −0.435396 | + | 0.316334i | ||||
\(493\) | −0.307474 | + | 0.946307i | −0.0138479 | + | 0.0426195i | ||||
\(494\) | 2.29906 | 0.103440 | ||||||||
\(495\) | 2.24490 | − | 3.67345i | 0.100901 | − | 0.165109i | ||||
\(496\) | 3.94906 | 0.177318 | ||||||||
\(497\) | −3.26853 | + | 10.0595i | −0.146614 | + | 0.451230i | ||||
\(498\) | 20.8514 | − | 15.1494i | 0.934375 | − | 0.678863i | ||||
\(499\) | 13.4352 | + | 9.76122i | 0.601441 | + | 0.436972i | 0.846390 | − | 0.532564i | \(-0.178771\pi\) |
−0.244949 | + | 0.969536i | \(0.578771\pi\) | |||||||
\(500\) | −2.59550 | − | 7.98813i | −0.116074 | − | 0.357240i | ||||
\(501\) | 3.82482 | + | 11.7716i | 0.170881 | + | 0.525916i | ||||
\(502\) | 3.74948 | + | 2.72416i | 0.167348 | + | 0.121585i | ||||
\(503\) | −18.5466 | + | 13.4749i | −0.826954 | + | 0.600817i | −0.918696 | − | 0.394966i | \(-0.870757\pi\) |
0.0917419 | + | 0.995783i | \(0.470757\pi\) | |||||||
\(504\) | −0.238992 | + | 0.735542i | −0.0106456 | + | 0.0327637i | ||||
\(505\) | −6.53998 | −0.291025 | ||||||||
\(506\) | 5.32941 | + | 6.22448i | 0.236921 | + | 0.276712i | ||||
\(507\) | 12.2004 | 0.541837 | ||||||||
\(508\) | −2.85928 | + | 8.79997i | −0.126860 | + | 0.390435i | ||||
\(509\) | 28.8493 | − | 20.9603i | 1.27872 | − | 0.929048i | 0.279211 | − | 0.960230i | \(-0.409927\pi\) |
0.999514 | + | 0.0311824i | \(0.00992727\pi\) | |||||||
\(510\) | −0.706876 | − | 0.513575i | −0.0313010 | − | 0.0227415i | ||||
\(511\) | 4.04995 | + | 12.4645i | 0.179159 | + | 0.551396i | ||||
\(512\) | −0.309017 | − | 0.951057i | −0.0136568 | − | 0.0420312i | ||||
\(513\) | 4.47662 | + | 3.25246i | 0.197648 | + | 0.143599i | ||||
\(514\) | −20.7952 | + | 15.1086i | −0.917237 | + | 0.666412i | ||||
\(515\) | 5.44693 | − | 16.7639i | 0.240020 | − | 0.738706i | ||||
\(516\) | −9.26495 | −0.407867 | ||||||||
\(517\) | −3.29929 | − | 41.2747i | −0.145102 | − | 1.81526i | ||||
\(518\) | −4.10810 | −0.180500 | ||||||||
\(519\) | −2.40392 | + | 7.39849i | −0.105520 | + | 0.324758i | ||||
\(520\) | 4.84043 | − | 3.51678i | 0.212267 | − | 0.154221i | ||||
\(521\) | −13.2413 | − | 9.62034i | −0.580110 | − | 0.421475i | 0.258653 | − | 0.965970i | \(-0.416721\pi\) |
−0.838764 | + | 0.544495i | \(0.816721\pi\) | |||||||
\(522\) | −0.722411 | − | 2.22335i | −0.0316191 | − | 0.0973134i | ||||
\(523\) | −10.9362 | − | 33.6580i | −0.478205 | − | 1.47176i | −0.841586 | − | 0.540123i | \(-0.818378\pi\) |
0.363381 | − | 0.931640i | \(-0.381622\pi\) | |||||||
\(524\) | −9.79859 | − | 7.11909i | −0.428053 | − | 0.310999i | ||||
\(525\) | −3.51653 | + | 2.55491i | −0.153474 | + | 0.111505i | ||||
\(526\) | 6.75897 | − | 20.8020i | 0.294705 | − | 0.907009i | ||||
\(527\) | 0.838356 | 0.0365194 | ||||||||
\(528\) | −4.84358 | + | 2.01323i | −0.210790 | + | 0.0876148i | ||||
\(529\) | −16.8957 | −0.734598 | ||||||||
\(530\) | −6.02076 | + | 18.5300i | −0.261525 | + | 0.804892i | ||||
\(531\) | 1.68803 | − | 1.22643i | 0.0732543 | − | 0.0532224i | ||||
\(532\) | −1.25444 | − | 0.911401i | −0.0543867 | − | 0.0395142i | ||||
\(533\) | −5.36250 | − | 16.5041i | −0.232276 | − | 0.714871i | ||||
\(534\) | −1.75426 | − | 5.39905i | −0.0759141 | − | 0.233640i | ||||
\(535\) | 27.6563 | + | 20.0935i | 1.19568 | + | 0.868716i | ||||
\(536\) | −7.25741 | + | 5.27281i | −0.313472 | + | 0.227751i | ||||
\(537\) | −4.65995 | + | 14.3419i | −0.201092 | + | 0.618897i | ||||
\(538\) | 20.5982 | 0.888053 | ||||||||
\(539\) | 14.8256 | + | 3.54009i | 0.638582 | + | 0.152483i | ||||
\(540\) | 14.4002 | 0.619685 | ||||||||
\(541\) | 11.3076 | − | 34.8012i | 0.486151 | − | 1.49622i | −0.344156 | − | 0.938913i | \(-0.611835\pi\) |
0.830307 | − | 0.557307i | \(-0.188165\pi\) | |||||||
\(542\) | −17.9197 | + | 13.0194i | −0.769716 | + | 0.559231i | ||||
\(543\) | 24.7372 | + | 17.9726i | 1.06157 | + | 0.771278i | ||||
\(544\) | −0.0656020 | − | 0.201902i | −0.00281266 | − | 0.00865649i | ||||
\(545\) | −2.19224 | − | 6.74701i | −0.0939051 | − | 0.289010i | ||||
\(546\) | 4.56116 | + | 3.31387i | 0.195199 | + | 0.141821i | ||||
\(547\) | −11.5303 | + | 8.37727i | −0.493001 | + | 0.358186i | −0.806337 | − | 0.591456i | \(-0.798553\pi\) |
0.313336 | + | 0.949642i | \(0.398553\pi\) | |||||||
\(548\) | −3.01282 | + | 9.27249i | −0.128701 | + | 0.396101i | ||||
\(549\) | 6.49337 | 0.277130 | ||||||||
\(550\) | 5.71802 | + | 1.36537i | 0.243817 | + | 0.0582195i | ||||
\(551\) | 4.68696 | 0.199671 | ||||||||
\(552\) | −1.20746 | + | 3.71619i | −0.0513931 | + | 0.158172i | ||||
\(553\) | 11.2665 | − | 8.18557i | 0.479099 | − | 0.348086i | ||||
\(554\) | −7.11452 | − | 5.16900i | −0.302267 | − | 0.219610i | ||||
\(555\) | 3.36964 | + | 10.3707i | 0.143033 | + | 0.440212i | ||||
\(556\) | 3.92968 | + | 12.0943i | 0.166656 | + | 0.512913i | ||||
\(557\) | −26.5043 | − | 19.2565i | −1.12302 | − | 0.815924i | −0.138359 | − | 0.990382i | \(-0.544183\pi\) |
−0.984665 | + | 0.174458i | \(0.944183\pi\) | |||||||
\(558\) | −1.59354 | + | 1.15777i | −0.0674598 | + | 0.0490124i | ||||
\(559\) | 4.16199 | − | 12.8093i | 0.176033 | − | 0.541775i | ||||
\(560\) | −4.03521 | −0.170519 | ||||||||
\(561\) | −1.02826 | + | 0.427395i | −0.0434130 | + | 0.0180446i | ||||
\(562\) | −17.0989 | −0.721275 | ||||||||
\(563\) | 3.11500 | − | 9.58698i | 0.131282 | − | 0.404043i | −0.863712 | − | 0.503986i | \(-0.831866\pi\) |
0.994993 | + | 0.0999433i | \(0.0318661\pi\) | |||||||
\(564\) | 15.9737 | − | 11.6055i | 0.672612 | − | 0.488681i | ||||
\(565\) | 18.6430 | + | 13.5450i | 0.784319 | + | 0.569841i | ||||
\(566\) | 7.44758 | + | 22.9213i | 0.313045 | + | 0.963454i | ||||
\(567\) | 3.47618 | + | 10.6986i | 0.145986 | + | 0.449299i | ||||
\(568\) | 5.51870 | + | 4.00957i | 0.231560 | + | 0.168238i | ||||
\(569\) | −33.0609 | + | 24.0201i | −1.38598 | + | 1.00698i | −0.389692 | + | 0.920945i | \(0.627418\pi\) |
−0.996292 | + | 0.0860311i | \(0.972582\pi\) | |||||||
\(570\) | −1.27184 | + | 3.91433i | −0.0532716 | + | 0.163953i | ||||
\(571\) | −28.0002 | −1.17177 | −0.585886 | − | 0.810393i | \(-0.699253\pi\) | ||||
−0.585886 | + | 0.810393i | \(0.699253\pi\) | |||||||
\(572\) | −0.607575 | − | 7.60088i | −0.0254040 | − | 0.317809i | ||||
\(573\) | 3.30405 | 0.138029 | ||||||||
\(574\) | −3.61665 | + | 11.1309i | −0.150956 | + | 0.464595i | ||||
\(575\) | 3.54295 | − | 2.57410i | 0.147751 | − | 0.107347i | ||||
\(576\) | 0.403523 | + | 0.293177i | 0.0168135 | + | 0.0122157i | ||||
\(577\) | −8.73832 | − | 26.8938i | −0.363781 | − | 1.11960i | −0.950741 | − | 0.309987i | \(-0.899675\pi\) |
0.586960 | − | 0.809616i | \(-0.300325\pi\) | |||||||
\(578\) | 5.23936 | + | 16.1251i | 0.217929 | + | 0.670716i | ||||
\(579\) | −9.68300 | − | 7.03511i | −0.402412 | − | 0.292369i | ||||
\(580\) | 9.86788 | − | 7.16943i | 0.409741 | − | 0.297694i | ||||
\(581\) | 7.80864 | − | 24.0325i | 0.323957 | − | 0.997037i | ||||
\(582\) | −2.35546 | −0.0976370 | ||||||||
\(583\) | 16.1494 | + | 18.8617i | 0.668841 | + | 0.781172i | ||||
\(584\) | 8.45234 | 0.349760 | ||||||||
\(585\) | −0.922187 | + | 2.83820i | −0.0381278 | + | 0.117345i | ||||
\(586\) | −2.06559 | + | 1.50074i | −0.0853286 | + | 0.0619949i | ||||
\(587\) | 10.3272 | + | 7.50317i | 0.426250 | + | 0.309689i | 0.780148 | − | 0.625595i | \(-0.215144\pi\) |
−0.353897 | + | 0.935284i | \(0.615144\pi\) | |||||||
\(588\) | 2.24602 | + | 6.91254i | 0.0926243 | + | 0.285068i | ||||
\(589\) | −1.22033 | − | 3.75578i | −0.0502827 | − | 0.154754i | ||||
\(590\) | 8.80734 | + | 6.39891i | 0.362593 | + | 0.263439i | ||||
\(591\) | 2.12008 | − | 1.54033i | 0.0872085 | − | 0.0633607i | ||||
\(592\) | −0.818716 | + | 2.51975i | −0.0336490 | + | 0.103561i | ||||
\(593\) | −25.1426 | −1.03248 | −0.516242 | − | 0.856443i | \(-0.672669\pi\) | ||||
−0.516242 | + | 0.856443i | \(0.672669\pi\) | |||||||
\(594\) | 9.56984 | − | 15.6596i | 0.392655 | − | 0.642521i | ||||
\(595\) | −0.856644 | −0.0351190 | ||||||||
\(596\) | 4.19154 | − | 12.9002i | 0.171692 | − | 0.528414i | ||||
\(597\) | −4.71267 | + | 3.42395i | −0.192877 | + | 0.140133i | ||||
\(598\) | −4.59541 | − | 3.33876i | −0.187920 | − | 0.136532i | ||||
\(599\) | 14.6543 | + | 45.1012i | 0.598757 | + | 1.84278i | 0.535060 | + | 0.844814i | \(0.320289\pi\) |
0.0636963 | + | 0.997969i | \(0.479711\pi\) | |||||||
\(600\) | 0.866261 | + | 2.66608i | 0.0353650 | + | 0.108842i | ||||
\(601\) | 19.2860 | + | 14.0121i | 0.786692 | + | 0.571565i | 0.906980 | − | 0.421174i | \(-0.138382\pi\) |
−0.120288 | + | 0.992739i | \(0.538382\pi\) | |||||||
\(602\) | −7.34879 | + | 5.33921i | −0.299514 | + | 0.217610i | ||||
\(603\) | 1.38267 | − | 4.25541i | 0.0563065 | − | 0.173294i | ||||
\(604\) | 10.8519 | 0.441557 | ||||||||
\(605\) | 20.1923 | − | 20.2915i | 0.820934 | − | 0.824968i | ||||
\(606\) | −3.97445 | −0.161451 | ||||||||
\(607\) | −0.906405 | + | 2.78963i | −0.0367899 | + | 0.113228i | −0.967765 | − | 0.251855i | \(-0.918959\pi\) |
0.930975 | + | 0.365083i | \(0.118959\pi\) | |||||||
\(608\) | −0.809017 | + | 0.587785i | −0.0328100 | + | 0.0238378i | ||||
\(609\) | 9.29854 | + | 6.75579i | 0.376796 | + | 0.273758i | ||||
\(610\) | 10.4693 | + | 32.2211i | 0.423889 | + | 1.30460i | ||||
\(611\) | 8.86960 | + | 27.2978i | 0.358826 | + | 1.10435i | ||||
\(612\) | 0.0856650 | + | 0.0622392i | 0.00346280 | + | 0.00251587i | ||||
\(613\) | −4.94153 | + | 3.59023i | −0.199587 | + | 0.145008i | −0.683090 | − | 0.730335i | \(-0.739364\pi\) |
0.483503 | + | 0.875343i | \(0.339364\pi\) | |||||||
\(614\) | 5.84982 | − | 18.0039i | 0.236079 | − | 0.726577i | ||||
\(615\) | 31.0660 | 1.25270 | ||||||||
\(616\) | −2.68165 | + | 4.38812i | −0.108047 | + | 0.176802i | ||||
\(617\) | −21.6728 | −0.872513 | −0.436257 | − | 0.899822i | \(-0.643696\pi\) | ||||
−0.436257 | + | 0.899822i | \(0.643696\pi\) | |||||||
\(618\) | 3.31018 | − | 10.1877i | 0.133155 | − | 0.409809i | ||||
\(619\) | −6.57355 | + | 4.77596i | −0.264213 | + | 0.191962i | −0.712002 | − | 0.702177i | \(-0.752212\pi\) |
0.447789 | + | 0.894139i | \(0.352212\pi\) | |||||||
\(620\) | −8.31432 | − | 6.04071i | −0.333911 | − | 0.242601i | ||||
\(621\) | −4.22465 | − | 13.0022i | −0.169530 | − | 0.521758i | ||||
\(622\) | −5.19797 | − | 15.9977i | −0.208420 | − | 0.641450i | ||||
\(623\) | −4.50281 | − | 3.27148i | −0.180401 | − | 0.131069i | ||||
\(624\) | 2.94160 | − | 2.13720i | 0.117758 | − | 0.0855565i | ||||
\(625\) | −9.49324 | + | 29.2172i | −0.379730 | + | 1.16869i | ||||
\(626\) | 24.6812 | 0.986461 | ||||||||
\(627\) | 3.41145 | + | 3.98440i | 0.136240 | + | 0.159121i | ||||
\(628\) | 5.17350 | 0.206445 | ||||||||
\(629\) | −0.173807 | + | 0.534924i | −0.00693015 | + | 0.0213288i | ||||
\(630\) | 1.62830 | − | 1.18303i | 0.0648730 | − | 0.0471330i | ||||
\(631\) | 35.0530 | + | 25.4675i | 1.39544 | + | 1.01384i | 0.995244 | + | 0.0974129i | \(0.0310567\pi\) |
0.400192 | + | 0.916431i | \(0.368943\pi\) | |||||||
\(632\) | −2.77538 | − | 8.54173i | −0.110399 | − | 0.339772i | ||||
\(633\) | 1.02089 | + | 3.14196i | 0.0405766 | + | 0.124882i | ||||
\(634\) | 18.9786 | + | 13.7887i | 0.753735 | + | 0.547620i | ||||
\(635\) | 19.4808 | − | 14.1536i | 0.773073 | − | 0.561670i | ||||
\(636\) | −3.65891 | + | 11.2610i | −0.145085 | + | 0.446527i | ||||
\(637\) | −10.5659 | −0.418636 | ||||||||
\(638\) | −1.23863 | − | 15.4954i | −0.0490377 | − | 0.613471i | ||||
\(639\) | −3.40244 | −0.134598 | ||||||||
\(640\) | −0.804188 | + | 2.47504i | −0.0317883 | + | 0.0978344i | ||||
\(641\) | −29.8500 | + | 21.6873i | −1.17900 | + | 0.856597i | −0.992059 | − | 0.125774i | \(-0.959859\pi\) |
−0.186945 | + | 0.982370i | \(0.559859\pi\) | |||||||
\(642\) | 16.8072 | + | 12.2111i | 0.663325 | + | 0.481934i | ||||
\(643\) | 8.23856 | + | 25.3557i | 0.324897 | + | 0.999930i | 0.971487 | + | 0.237092i | \(0.0761944\pi\) |
−0.646590 | + | 0.762838i | \(0.723806\pi\) | |||||||
\(644\) | 1.18383 | + | 3.64345i | 0.0466494 | + | 0.143572i | ||||
\(645\) | 19.5063 | + | 14.1722i | 0.768062 | + | 0.558029i | ||||
\(646\) | −0.171748 | + | 0.124782i | −0.00675735 | + | 0.00490950i | ||||
\(647\) | 4.54738 | − | 13.9954i | 0.178776 | − | 0.550216i | −0.821010 | − | 0.570914i | \(-0.806589\pi\) |
0.999786 | + | 0.0206984i | \(0.00658898\pi\) | |||||||
\(648\) | 7.25487 | 0.284998 | ||||||||
\(649\) | 12.8116 | − | 5.32514i | 0.502899 | − | 0.209030i | ||||
\(650\) | −4.07513 | −0.159840 | ||||||||
\(651\) | 2.99256 | − | 9.21015i | 0.117288 | − | 0.360974i | ||||
\(652\) | 0.970827 | − | 0.705347i | 0.0380205 | − | 0.0276235i | ||||
\(653\) | −29.4101 | − | 21.3677i | −1.15091 | − | 0.836183i | −0.162305 | − | 0.986741i | \(-0.551893\pi\) |
−0.988601 | + | 0.150558i | \(0.951893\pi\) | |||||||
\(654\) | −1.33226 | − | 4.10027i | −0.0520954 | − | 0.160333i | ||||
\(655\) | 9.74010 | + | 29.9769i | 0.380577 | + | 1.17130i | ||||
\(656\) | 6.10649 | + | 4.43662i | 0.238418 | + | 0.173221i | ||||
\(657\) | −3.41071 | + | 2.47803i | −0.133065 | + | 0.0966771i | ||||
\(658\) | 5.98196 | − | 18.4106i | 0.233201 | − | 0.717720i | ||||
\(659\) | 12.1432 | 0.473030 | 0.236515 | − | 0.971628i | \(-0.423995\pi\) | ||||
0.236515 | + | 0.971628i | \(0.423995\pi\) | |||||||
\(660\) | 13.2772 | + | 3.17037i | 0.516814 | + | 0.123406i | ||||
\(661\) | −6.74774 | −0.262457 | −0.131228 | − | 0.991352i | \(-0.541892\pi\) | ||||
−0.131228 | + | 0.991352i | \(0.541892\pi\) | |||||||
\(662\) | −5.14665 | + | 15.8397i | −0.200030 | + | 0.615629i | ||||
\(663\) | 0.624481 | − | 0.453712i | 0.0242528 | − | 0.0176207i | ||||
\(664\) | −13.1844 | − | 9.57902i | −0.511654 | − | 0.371738i | ||||
\(665\) | 1.24695 | + | 3.83771i | 0.0483545 | + | 0.148820i | ||||
\(666\) | −0.408361 | − | 1.25681i | −0.0158237 | − | 0.0487002i | ||||
\(667\) | −9.36839 | − | 6.80653i | −0.362745 | − | 0.263550i | ||||
\(668\) | 6.33156 | − | 4.60015i | 0.244976 | − | 0.177985i | ||||
\(669\) | −11.3262 | + | 34.8586i | −0.437898 | + | 1.34771i | ||||
\(670\) | 23.3453 | 0.901907 | ||||||||
\(671\) | 41.9966 | + | 10.0281i | 1.62126 | + | 0.387130i | ||||
\(672\) | −2.45226 | −0.0945980 | ||||||||
\(673\) | −2.72016 | + | 8.37178i | −0.104854 | + | 0.322709i | −0.989696 | − | 0.143183i | \(-0.954266\pi\) |
0.884842 | + | 0.465891i | \(0.154266\pi\) | |||||||
\(674\) | −18.1247 | + | 13.1684i | −0.698138 | + | 0.507227i | ||||
\(675\) | −7.93489 | − | 5.76504i | −0.305414 | − | 0.221896i | ||||
\(676\) | −2.38385 | − | 7.33674i | −0.0916866 | − | 0.282182i | ||||
\(677\) | −1.97991 | − | 6.09352i | −0.0760939 | − | 0.234193i | 0.905773 | − | 0.423762i | \(-0.139291\pi\) |
−0.981867 | + | 0.189569i | \(0.939291\pi\) | |||||||
\(678\) | 11.3297 | + | 8.23149i | 0.435114 | + | 0.316129i | ||||
\(679\) | −1.86831 | + | 1.35740i | −0.0716990 | + | 0.0520924i | ||||
\(680\) | −0.170723 | + | 0.525432i | −0.00654693 | + | 0.0201494i | ||||
\(681\) | −14.5823 | −0.558796 | ||||||||
\(682\) | −12.0944 | + | 5.02704i | −0.463119 | + | 0.192495i | ||||
\(683\) | −33.6400 | −1.28720 | −0.643600 | − | 0.765362i | \(-0.722560\pi\) | ||||
−0.643600 | + | 0.765362i | \(0.722560\pi\) | |||||||
\(684\) | 0.154132 | − | 0.474370i | 0.00589339 | − | 0.0181380i | ||||
\(685\) | 20.5269 | − | 14.9137i | 0.784292 | − | 0.569821i | ||||
\(686\) | 14.5461 | + | 10.5684i | 0.555373 | + | 0.403502i | ||||
\(687\) | 7.95850 | + | 24.4937i | 0.303636 | + | 0.934494i | ||||
\(688\) | 1.81030 | + | 5.57152i | 0.0690169 | + | 0.212412i | ||||
\(689\) | −13.9252 | − | 10.1173i | −0.530509 | − | 0.385437i | ||||
\(690\) | 8.22668 | − | 5.97703i | 0.313184 | − | 0.227542i | ||||
\(691\) | −7.28286 | + | 22.4143i | −0.277053 | + | 0.852682i | 0.711616 | + | 0.702569i | \(0.247964\pi\) |
−0.988669 | + | 0.150113i | \(0.952036\pi\) | |||||||
\(692\) | 4.91882 | 0.186986 | ||||||||
\(693\) | −0.204386 | − | 2.55691i | −0.00776397 | − | 0.0971288i | ||||
\(694\) | 10.0811 | 0.382674 | ||||||||
\(695\) | 10.2266 | − | 31.4743i | 0.387918 | − | 1.19389i | ||||
\(696\) | 5.99687 | − | 4.35698i | 0.227311 | − | 0.165151i | ||||
\(697\) | 1.29636 | + | 0.941862i | 0.0491032 | + | 0.0356756i | ||||
\(698\) | −7.91453 | − | 24.3584i | −0.299569 | − | 0.921979i | ||||
\(699\) | 7.66445 | + | 23.5888i | 0.289896 | + | 0.892209i | ||||
\(700\) | 2.22351 | + | 1.61547i | 0.0840408 | + | 0.0610592i | ||||
\(701\) | −39.5136 | + | 28.7083i | −1.49241 | + | 1.08430i | −0.519120 | + | 0.854701i | \(0.673740\pi\) |
−0.973286 | + | 0.229596i | \(0.926260\pi\) | |||||||
\(702\) | −3.93121 | + | 12.0990i | −0.148374 | + | 0.456648i | ||||
\(703\) | 2.64942 | 0.0999248 | ||||||||
\(704\) | 2.15706 | + | 2.51934i | 0.0812974 | + | 0.0949512i | ||||
\(705\) | −51.3833 | −1.93521 | ||||||||
\(706\) | 1.88776 | − | 5.80992i | 0.0710467 | − | 0.218659i | ||||
\(707\) | −3.15246 | + | 2.29040i | −0.118560 | + | 0.0861392i | ||||
\(708\) | 5.35236 | + | 3.88872i | 0.201154 | + | 0.146147i | ||||
\(709\) | 1.40048 | + | 4.31022i | 0.0525960 | + | 0.161874i | 0.973904 | − | 0.226959i | \(-0.0728783\pi\) |
−0.921308 | + | 0.388833i | \(0.872878\pi\) | |||||||
\(710\) | −5.48576 | − | 16.8834i | −0.205877 | − | 0.633624i | ||||
\(711\) | 3.62416 | + | 2.63311i | 0.135917 | + | 0.0987493i | ||||
\(712\) | −2.90397 | + | 2.10986i | −0.108831 | + | 0.0790704i | ||||
\(713\) | −3.01504 | + | 9.27933i | −0.112914 | + | 0.347513i | ||||
\(714\) | −0.520596 | −0.0194828 | ||||||||
\(715\) | −10.3476 | + | 16.9322i | −0.386977 | + | 0.633229i | ||||
\(716\) | 9.53506 | 0.356342 | ||||||||
\(717\) | 11.7054 | − | 36.0256i | 0.437147 | − | 1.34540i | ||||
\(718\) | −20.8917 | + | 15.1787i | −0.779671 | + | 0.566464i | ||||
\(719\) | −33.9454 | − | 24.6628i | −1.26595 | − | 0.919766i | −0.266916 | − | 0.963720i | \(-0.586005\pi\) |
−0.999034 | + | 0.0439532i | \(0.986005\pi\) | |||||||
\(720\) | −0.401114 | − | 1.23450i | −0.0149487 | − | 0.0460072i | ||||
\(721\) | −3.24539 | − | 9.98829i | −0.120865 | − | 0.371983i | ||||
\(722\) | 0.809017 | + | 0.587785i | 0.0301085 | + | 0.0218751i | ||||
\(723\) | −4.87275 | + | 3.54026i | −0.181220 | + | 0.131664i | ||||
\(724\) | 5.97446 | − | 18.3875i | 0.222039 | − | 0.683366i | ||||
\(725\) | −8.30772 | −0.308541 | ||||||||
\(726\) | 12.2712 | − | 12.3315i | 0.455426 | − | 0.457664i | ||||
\(727\) | −25.2797 | −0.937572 | −0.468786 | − | 0.883312i | \(-0.655308\pi\) | ||||
−0.468786 | + | 0.883312i | \(0.655308\pi\) | |||||||
\(728\) | 1.10160 | − | 3.39038i | 0.0408280 | − | 0.125656i | ||||
\(729\) | −24.1672 | + | 17.5585i | −0.895080 | + | 0.650314i | ||||
\(730\) | −17.7955 | − | 12.9292i | −0.658640 | − | 0.478530i | ||||
\(731\) | 0.384312 | + | 1.18279i | 0.0142143 | + | 0.0437471i | ||||
\(732\) | 6.36235 | + | 19.5813i | 0.235159 | + | 0.723745i | ||||
\(733\) | 25.0916 | + | 18.2301i | 0.926779 | + | 0.673344i | 0.945202 | − | 0.326486i | \(-0.105865\pi\) |
−0.0184232 | + | 0.999830i | \(0.505865\pi\) | |||||||
\(734\) | −19.7237 | + | 14.3301i | −0.728016 | + | 0.528935i | ||||
\(735\) | 5.84506 | − | 17.9892i | 0.215598 | − | 0.663543i | ||||
\(736\) | 2.47068 | 0.0910704 | ||||||||
\(737\) | 15.5144 | − | 25.3870i | 0.571481 | − | 0.935143i | ||||
\(738\) | −3.76482 | −0.138585 | ||||||||
\(739\) | −10.7093 | + | 32.9597i | −0.393947 | + | 1.21244i | 0.535832 | + | 0.844325i | \(0.319998\pi\) |
−0.929779 | + | 0.368119i | \(0.880002\pi\) | |||||||
\(740\) | 5.57807 | − | 4.05270i | 0.205054 | − | 0.148980i | ||||
\(741\) | −2.94160 | − | 2.13720i | −0.108063 | − | 0.0785120i | ||||
\(742\) | 3.58729 | + | 11.0406i | 0.131694 | + | 0.405311i | ||||
\(743\) | 2.76915 | + | 8.52258i | 0.101590 | + | 0.312663i | 0.988915 | − | 0.148482i | \(-0.0474387\pi\) |
−0.887325 | + | 0.461145i | \(0.847439\pi\) | |||||||
\(744\) | −5.05274 | − | 3.67103i | −0.185243 | − | 0.134587i | ||||
\(745\) | −28.5577 | + | 20.7484i | −1.04627 | + | 0.760163i | ||||
\(746\) | −1.33826 | + | 4.11873i | −0.0489970 | + | 0.150797i | ||||
\(747\) | 8.12855 | 0.297408 | ||||||||
\(748\) | 0.457929 | + | 0.534837i | 0.0167435 | + | 0.0195556i | ||||
\(749\) | 20.3681 | 0.744236 | ||||||||
\(750\) | −4.10485 | + | 12.6334i | −0.149888 | + | 0.461307i | ||||
\(751\) | −7.40654 | + | 5.38117i | −0.270269 | + | 0.196362i | −0.714662 | − | 0.699470i | \(-0.753419\pi\) |
0.444393 | + | 0.895832i | \(0.353419\pi\) | |||||||
\(752\) | −10.1002 | − | 7.33820i | −0.368315 | − | 0.267597i | ||||
\(753\) | −2.26502 | − | 6.97102i | −0.0825419 | − | 0.254038i | ||||
\(754\) | 3.32985 | + | 10.2482i | 0.121266 | + | 0.373218i | ||||
\(755\) | −22.8475 | − | 16.5997i | −0.831505 | − | 0.604124i | ||||
\(756\) | 6.94130 | − | 5.04315i | 0.252453 | − | 0.183418i | ||||
\(757\) | 7.09476 | − | 21.8354i | 0.257863 | − | 0.793622i | −0.735389 | − | 0.677646i | \(-0.763000\pi\) |
0.993252 | − | 0.115976i | \(-0.0369997\pi\) | |||||||
\(758\) | 2.46844 | 0.0896578 | ||||||||
\(759\) | −1.03262 | − | 12.9183i | −0.0374818 | − | 0.468904i | ||||
\(760\) | 2.60241 | 0.0943992 | ||||||||
\(761\) | 10.3237 | − | 31.7730i | 0.374233 | − | 1.15177i | −0.569762 | − | 0.821809i | \(-0.692965\pi\) |
0.943995 | − | 0.329960i | \(-0.107035\pi\) | |||||||
\(762\) | 11.8388 | − | 8.60140i | 0.428875 | − | 0.311596i | ||||
\(763\) | −3.41962 | − | 2.48450i | −0.123799 | − | 0.0899450i | ||||
\(764\) | −0.645585 | − | 1.98691i | −0.0233565 | − | 0.0718838i | ||||
\(765\) | −0.0851536 | − | 0.262076i | −0.00307873 | − | 0.00947537i | ||||
\(766\) | −17.3440 | − | 12.6011i | −0.626663 | − | 0.455297i | ||||
\(767\) | −7.78074 | + | 5.65304i | −0.280946 | + | 0.204119i | ||||
\(768\) | −0.488718 | + | 1.50412i | −0.0176351 | + | 0.0542752i | ||||
\(769\) | 16.2969 | 0.587681 | 0.293841 | − | 0.955854i | \(-0.405066\pi\) | ||||
0.293841 | + | 0.955854i | \(0.405066\pi\) | |||||||
\(770\) | 12.3582 | − | 5.13670i | 0.445360 | − | 0.185114i | ||||
\(771\) | 40.6519 | 1.46404 | ||||||||
\(772\) | −2.33862 | + | 7.19752i | −0.0841687 | + | 0.259045i | ||||
\(773\) | −32.2035 | + | 23.3972i | −1.15828 | + | 0.841539i | −0.989559 | − | 0.144125i | \(-0.953963\pi\) |
−0.168720 | + | 0.985664i | \(0.553963\pi\) | |||||||
\(774\) | −2.36394 | − | 1.71750i | −0.0849699 | − | 0.0617343i | ||||
\(775\) | 2.16305 | + | 6.65719i | 0.0776991 | + | 0.239133i | ||||
\(776\) | 0.460238 | + | 1.41647i | 0.0165216 | + | 0.0508482i | ||||
\(777\) | 5.25624 | + | 3.81888i | 0.188566 | + | 0.137002i | ||||
\(778\) | −4.77449 | + | 3.46887i | −0.171174 | + | 0.124365i | ||||
\(779\) | 2.33247 | − | 7.17861i | 0.0835695 | − | 0.257200i | ||||
\(780\) | −9.46241 | −0.338809 | ||||||||
\(781\) | −22.0057 | − | 5.25458i | −0.787425 | − | 0.188024i | ||||
\(782\) | 0.524507 | 0.0187563 | ||||||||
\(783\) | −8.01431 | + | 24.6655i | −0.286408 | + | 0.881473i | ||||
\(784\) | 3.71803 | − | 2.70131i | 0.132787 | − | 0.0964753i | ||||
\(785\) | −10.8922 | − | 7.91368i | −0.388761 | − | 0.282451i | ||||
\(786\) | 5.91921 | + | 18.2175i | 0.211131 | + | 0.649796i | ||||
\(787\) | −11.4162 | − | 35.1355i | −0.406945 | − | 1.25245i | −0.919261 | − | 0.393650i | \(-0.871212\pi\) |
0.512316 | − | 0.858797i | \(-0.328788\pi\) | |||||||
\(788\) | −1.34053 | − | 0.973952i | −0.0477544 | − | 0.0346956i | ||||
\(789\) | −27.9854 | + | 20.3326i | −0.996307 | + | 0.723860i | ||||
\(790\) | −7.22266 | + | 22.2290i | −0.256971 | + | 0.790874i | ||||
\(791\) | 13.7301 | 0.488187 | ||||||||
\(792\) | −1.60904 | − | 0.384211i | −0.0571746 | − | 0.0136523i | ||||
\(793\) | −29.9302 | −1.06285 | ||||||||
\(794\) | −3.55002 | + | 10.9258i | −0.125985 | + | 0.387743i | ||||
\(795\) | 24.9289 | − | 18.1119i | 0.884136 | − | 0.642362i | ||||
\(796\) | 2.97983 | + | 2.16497i | 0.105617 | + | 0.0767354i | ||||
\(797\) | −15.8721 | − | 48.8493i | −0.562218 | − | 1.73033i | −0.676075 | − | 0.736833i | \(-0.736320\pi\) |
0.113856 | − | 0.993497i | \(-0.463680\pi\) | |||||||
\(798\) | 0.757790 | + | 2.33224i | 0.0268255 | + | 0.0825603i | ||||
\(799\) | −2.14419 | − | 1.55784i | −0.0758560 | − | 0.0551126i | ||||
\(800\) | 1.43400 | − | 1.04186i | 0.0506995 | − | 0.0368353i | ||||
\(801\) | 0.553259 | − | 1.70276i | 0.0195484 | − | 0.0601639i | ||||
\(802\) | −28.0949 | −0.992066 | ||||||||
\(803\) | −25.8862 | + | 10.7596i | −0.913503 | + | 0.379697i | ||||
\(804\) | 14.1873 | 0.500347 | ||||||||
\(805\) | 3.08081 | − | 9.48174i | 0.108584 | − | 0.334188i | ||||
\(806\) | 7.34518 | − | 5.33659i | 0.258723 | − | 0.187973i | ||||
\(807\) | −26.3550 | − | 19.1480i | −0.927741 | − | 0.674043i | ||||
\(808\) | 0.776576 | + | 2.39005i | 0.0273198 | + | 0.0840818i | ||||
\(809\) | 2.71886 | + | 8.36778i | 0.0955899 | + | 0.294195i | 0.987407 | − | 0.158201i | \(-0.0505693\pi\) |
−0.891817 | + | 0.452396i | \(0.850569\pi\) | |||||||
\(810\) | −15.2743 | − | 11.0975i | −0.536686 | − | 0.389925i | ||||
\(811\) | 27.7158 | − | 20.1367i | 0.973233 | − | 0.707095i | 0.0170466 | − | 0.999855i | \(-0.494574\pi\) |
0.956186 | + | 0.292760i | \(0.0945736\pi\) | |||||||
\(812\) | 2.24576 | − | 6.91175i | 0.0788108 | − | 0.242555i | ||||
\(813\) | 35.0306 | 1.22858 | ||||||||
\(814\) | −0.700165 | − | 8.75919i | −0.0245408 | − | 0.307010i | ||||
\(815\) | −3.12291 | −0.109391 | ||||||||
\(816\) | −0.103751 | + | 0.319313i | −0.00363202 | + | 0.0111782i | ||||
\(817\) | 4.73942 | − | 3.44339i | 0.165811 | − | 0.120469i | ||||
\(818\) | 24.7383 | + | 17.9734i | 0.864955 | + | 0.628427i | ||||
\(819\) | 0.549458 | + | 1.69106i | 0.0191996 | + | 0.0590904i | ||||
\(820\) | −6.07004 | − | 18.6817i | −0.211975 | − | 0.652392i | ||||
\(821\) | −22.6766 | − | 16.4755i | −0.791419 | − | 0.574999i | 0.116965 | − | 0.993136i | \(-0.462683\pi\) |
−0.908384 | + | 0.418137i | \(0.862683\pi\) | |||||||
\(822\) | 12.4745 | − | 9.06326i | 0.435099 | − | 0.316118i | ||||
\(823\) | 8.51814 | − | 26.2161i | 0.296924 | − | 0.913837i | −0.685645 | − | 0.727936i | \(-0.740480\pi\) |
0.982568 | − | 0.185901i | \(-0.0595204\pi\) | |||||||
\(824\) | −6.77320 | −0.235956 | ||||||||
\(825\) | −6.04686 | − | 7.06242i | −0.210524 | − | 0.245882i | ||||
\(826\) | 6.48639 | 0.225690 | ||||||||
\(827\) | 12.6598 | − | 38.9628i | 0.440223 | − | 1.35487i | −0.447415 | − | 0.894327i | \(-0.647655\pi\) |
0.887638 | − | 0.460542i | \(-0.152345\pi\) | |||||||
\(828\) | −0.996976 | + | 0.724345i | −0.0346473 | + | 0.0251727i | ||||
\(829\) | 10.3317 | + | 7.50638i | 0.358833 | + | 0.260707i | 0.752565 | − | 0.658518i | \(-0.228816\pi\) |
−0.393732 | + | 0.919225i | \(0.628816\pi\) | |||||||
\(830\) | 13.1057 | + | 40.3352i | 0.454905 | + | 1.40005i | ||||
\(831\) | 4.29780 | + | 13.2273i | 0.149089 | + | 0.458849i | ||||
\(832\) | −1.85998 | − | 1.35136i | −0.0644832 | − | 0.0468498i | ||||
\(833\) | 0.789311 | − | 0.573468i | 0.0273480 | − | 0.0198695i | ||||
\(834\) | 6.21489 | − | 19.1275i | 0.215204 | − | 0.662330i | ||||
\(835\) | −20.3671 | −0.704831 | ||||||||
\(836\) | 1.72947 | − | 2.83001i | 0.0598148 | − | 0.0978779i | ||||
\(837\) | 21.8518 | 0.755308 | ||||||||
\(838\) | 9.07898 | − | 27.9422i | 0.313628 | − | 0.965248i | ||||
\(839\) | −4.26472 | + | 3.09850i | −0.147235 | + | 0.106972i | −0.658964 | − | 0.752174i | \(-0.729005\pi\) |
0.511729 | + | 0.859147i | \(0.329005\pi\) | |||||||
\(840\) | 5.16296 | + | 3.75111i | 0.178139 | + | 0.129426i | ||||
\(841\) | −2.17314 | − | 6.68825i | −0.0749360 | − | 0.230629i | ||||
\(842\) | 4.07887 | + | 12.5535i | 0.140567 | + | 0.432621i | ||||
\(843\) | 21.8778 | + | 15.8951i | 0.753510 | + | 0.547457i | ||||
\(844\) | 1.68996 | − | 1.22783i | 0.0581709 | − | 0.0422636i | ||||
\(845\) | −6.20375 | + | 19.0932i | −0.213416 | + | 0.656826i | ||||
\(846\) | 6.22704 | 0.214090 | ||||||||
\(847\) | 2.62689 | − | 16.8527i | 0.0902610 | − | 0.579067i | ||||
\(848\) | 7.48676 | 0.257096 | ||||||||
\(849\) | 11.7785 | − | 36.2506i | 0.404238 | − | 1.24412i | ||||
\(850\) | 0.304427 | − | 0.221179i | 0.0104418 | − | 0.00758638i | ||||
\(851\) | −5.29572 | − | 3.84756i | −0.181535 | − | 0.131893i | ||||
\(852\) | −3.33378 | − | 10.2603i | −0.114214 | − | 0.351513i | ||||
\(853\) | −0.840042 | − | 2.58538i | −0.0287625 | − | 0.0885219i | 0.935645 | − | 0.352943i | \(-0.114819\pi\) |
−0.964407 | + | 0.264421i | \(0.914819\pi\) | |||||||
\(854\) | 16.3308 | + | 11.8650i | 0.558829 | + | 0.406013i | ||||
\(855\) | −1.05013 | + | 0.762965i | −0.0359137 | + | 0.0260929i | ||||
\(856\) | 4.05923 | − | 12.4930i | 0.138741 | − | 0.427002i | ||||
\(857\) | 51.9734 | 1.77538 | 0.887689 | − | 0.460443i | \(-0.152309\pi\) | ||||
0.887689 | + | 0.460443i | \(0.152309\pi\) | |||||||
\(858\) | −6.28838 | + | 10.2900i | −0.214682 | + | 0.351294i | ||||
\(859\) | −44.7212 | −1.52587 | −0.762933 | − | 0.646477i | \(-0.776242\pi\) | ||||
−0.762933 | + | 0.646477i | \(0.776242\pi\) | |||||||
\(860\) | 4.71113 | − | 14.4994i | 0.160648 | − | 0.494424i | ||||
\(861\) | 14.9747 | − | 10.8798i | 0.510336 | − | 0.370781i | ||||
\(862\) | −27.2686 | − | 19.8118i | −0.928774 | − | 0.674793i | ||||
\(863\) | 12.3271 | + | 37.9389i | 0.419619 | + | 1.29146i | 0.908053 | + | 0.418854i | \(0.137568\pi\) |
−0.488434 | + | 0.872601i | \(0.662432\pi\) | |||||||
\(864\) | −1.70992 | − | 5.26258i | −0.0581726 | − | 0.179037i | ||||
\(865\) | −10.3560 | − | 7.52411i | −0.352116 | − | 0.255827i | ||||
\(866\) | −29.3735 | + | 21.3411i | −0.998151 | + | 0.725199i | ||||
\(867\) | 8.28618 | − | 25.5022i | 0.281413 | − | 0.866101i | ||||
\(868\) | −6.12329 | −0.207838 | ||||||||
\(869\) | 19.3733 | + | 22.6270i | 0.657193 | + | 0.767567i | ||||
\(870\) | −19.2904 | −0.654007 | ||||||||
\(871\) | −6.37319 | + | 19.6147i | −0.215947 | + | 0.664618i | ||||
\(872\) | −2.20540 | + | 1.60232i | −0.0746843 | + | 0.0542614i | ||||
\(873\) | −0.600992 | − | 0.436646i | −0.0203405 | − | 0.0147782i | ||||
\(874\) | −0.763482 | − | 2.34975i | −0.0258251 | − | 0.0794816i | ||||
\(875\) | 4.02450 | + | 12.3861i | 0.136053 | + | 0.418728i | ||||
\(876\) | −10.8146 | − | 7.85726i | −0.365391 | − | 0.265472i | ||||
\(877\) | −2.42391 | + | 1.76108i | −0.0818497 | + | 0.0594673i | −0.627958 | − | 0.778248i | \(-0.716109\pi\) |
0.546108 | + | 0.837715i | \(0.316109\pi\) | |||||||
\(878\) | 4.81839 | − | 14.8295i | 0.162613 | − | 0.500470i | ||||
\(879\) | 4.03796 | 0.136197 | ||||||||
\(880\) | −0.687740 | − | 8.60376i | −0.0231837 | − | 0.290033i | ||||
\(881\) | 20.5582 | 0.692625 | 0.346312 | − | 0.938119i | \(-0.387434\pi\) | ||||
0.346312 | + | 0.938119i | \(0.387434\pi\) | |||||||
\(882\) | −0.708351 | + | 2.18008i | −0.0238514 | + | 0.0734072i | ||||
\(883\) | 16.6620 | − | 12.1056i | 0.560720 | − | 0.407387i | −0.271002 | − | 0.962579i | \(-0.587355\pi\) |
0.831723 | + | 0.555192i | \(0.187355\pi\) | |||||||
\(884\) | −0.394860 | − | 0.286883i | −0.0132806 | − | 0.00964891i | ||||
\(885\) | −5.32041 | − | 16.3746i | −0.178844 | − | 0.550425i | ||||
\(886\) | 2.21204 | + | 6.80795i | 0.0743149 | + | 0.228718i | ||||
\(887\) | −34.5512 | − | 25.1029i | −1.16011 | − | 0.842872i | −0.170322 | − | 0.985389i | \(-0.554481\pi\) |
−0.989792 | + | 0.142516i | \(0.954481\pi\) | |||||||
\(888\) | 3.38988 | − | 2.46289i | 0.113757 | − | 0.0826492i | ||||
\(889\) | 4.43351 | − | 13.6449i | 0.148695 | − | 0.457637i | ||||
\(890\) | 9.34136 | 0.313123 | ||||||||
\(891\) | −22.2188 | + | 9.23524i | −0.744358 | + | 0.309392i | ||||
\(892\) | 23.1754 | 0.775971 | ||||||||
\(893\) | −3.85792 | + | 11.8735i | −0.129100 | + | 0.397330i | ||||
\(894\) | −17.3550 | + | 12.6091i | −0.580438 | + | 0.421713i | ||||
\(895\) | −20.0750 | − | 14.5854i | −0.671034 | − | 0.487535i | ||||
\(896\) | 0.479152 | + | 1.47468i | 0.0160073 | + | 0.0492655i | ||||
\(897\) | 2.77604 | + | 8.54376i | 0.0926892 | + | 0.285268i | ||||
\(898\) | 11.7625 | + | 8.54596i | 0.392520 | + | 0.285182i | ||||
\(899\) | 14.9742 | − | 10.8794i | 0.499416 | − | 0.362847i | ||||
\(900\) | −0.273202 | + | 0.840829i | −0.00910673 | + | 0.0280276i | ||||
\(901\) | 1.58938 | 0.0529500 | ||||||||
\(902\) | −24.3495 | − | 5.81424i | −0.810748 | − | 0.193593i | ||||
\(903\) | 14.3659 | 0.478068 | ||||||||
\(904\) | 2.73632 | − | 8.42152i | 0.0910086 | − | 0.280096i | ||||
\(905\) | −40.7051 | + | 29.5740i | −1.35308 | + | 0.983074i | ||||
\(906\) | −13.8848 | − | 10.0879i | −0.461291 | − | 0.335148i | ||||
\(907\) | 2.65727 | + | 8.17823i | 0.0882331 | + | 0.271554i | 0.985431 | − | 0.170075i | \(-0.0544009\pi\) |
−0.897198 | + | 0.441628i | \(0.854401\pi\) | |||||||
\(908\) | 2.84927 | + | 8.76915i | 0.0945563 | + | 0.291014i | ||||
\(909\) | −1.01407 | − | 0.736768i | −0.0336347 | − | 0.0244371i | ||||
\(910\) | −7.50541 | + | 5.45300i | −0.248802 | + | 0.180765i | ||||
\(911\) | −9.20664 | + | 28.3351i | −0.305030 | + | 0.938785i | 0.674637 | + | 0.738150i | \(0.264300\pi\) |
−0.979666 | + | 0.200635i | \(0.935700\pi\) | |||||||
\(912\) | 1.58152 | 0.0523695 | ||||||||
\(913\) | 52.5724 | + | 12.5534i | 1.73989 | + | 0.415457i | ||||
\(914\) | 2.89135 | 0.0956373 | ||||||||
\(915\) | 16.5574 | − | 50.9585i | 0.547371 | − | 1.68464i | ||||
\(916\) | 13.1744 | − | 9.57176i | 0.435294 | − | 0.316260i | ||||
\(917\) | 15.1934 | + | 11.0386i | 0.501729 | + | 0.364528i | ||||
\(918\) | −0.363003 | − | 1.11721i | −0.0119809 | − | 0.0368733i | ||||
\(919\) | 12.9936 | + | 39.9901i | 0.428619 | + | 1.31915i | 0.899486 | + | 0.436949i | \(0.143941\pi\) |
−0.470868 | + | 0.882204i | \(0.656059\pi\) | |||||||
\(920\) | −5.20174 | − | 3.77929i | −0.171496 | − | 0.124599i | ||||
\(921\) | −24.2211 | + | 17.5976i | −0.798111 | + | 0.579862i | ||||
\(922\) | 7.07360 | − | 21.7703i | 0.232957 | − | 0.716967i | ||||
\(923\) | 15.6830 | 0.516214 | ||||||||
\(924\) | 7.51030 | − | 3.12166i | 0.247071 | − | 0.102695i | ||||
\(925\) | −4.69615 | −0.154408 | ||||||||
\(926\) | 12.1040 | − | 37.2523i | 0.397762 | − | 1.22419i | ||||
\(927\) | 2.73314 | − | 1.98575i | 0.0897682 | − | 0.0652204i | ||||
\(928\) | −3.79183 | − | 2.75492i | −0.124473 | − | 0.0904348i | ||||
\(929\) | −16.8144 | − | 51.7494i | −0.551663 | − | 1.69784i | −0.704597 | − | 0.709608i | \(-0.748872\pi\) |
0.152934 | − | 0.988236i | \(-0.451128\pi\) | |||||||
\(930\) | 5.02258 | + | 15.4579i | 0.164697 | + | 0.506885i | ||||
\(931\) | −3.71803 | − | 2.70131i | −0.121854 | − | 0.0885318i | ||||
\(932\) | 12.6876 | − | 9.21810i | 0.415597 | − | 0.301949i | ||||
\(933\) | −8.22072 | + | 25.3008i | −0.269134 | + | 0.828310i | ||||
\(934\) | 27.7227 | 0.907115 | ||||||||
\(935\) | −0.146002 | − | 1.82651i | −0.00477478 | − | 0.0597334i | ||||
\(936\) | 1.14673 | 0.0374821 | ||||||||
\(937\) | 10.7812 | − | 33.1812i | 0.352207 | − | 1.08398i | −0.605405 | − | 0.795918i | \(-0.706989\pi\) |
0.957611 | − | 0.288063i | \(-0.0930113\pi\) | |||||||
\(938\) | 11.2531 | − | 8.17585i | 0.367427 | − | 0.266951i | ||||
\(939\) | −31.5791 | − | 22.9436i | −1.03055 | − | 0.748736i | ||||
\(940\) | 10.0399 | + | 30.8996i | 0.327465 | + | 1.00783i | ||||
\(941\) | −3.94810 | − | 12.1510i | −0.128704 | − | 0.396111i | 0.865854 | − | 0.500298i | \(-0.166776\pi\) |
−0.994558 | + | 0.104187i | \(0.966776\pi\) | |||||||
\(942\) | −6.61939 | − | 4.80927i | −0.215671 | − | 0.156694i | ||||
\(943\) | −15.0872 | + | 10.9615i | −0.491306 | + | 0.356955i | ||||
\(944\) | 1.29269 | − | 3.97849i | 0.0420735 | − | 0.129489i | ||||
\(945\) | −22.3284 | −0.726344 | ||||||||
\(946\) | −12.6366 | − | 14.7589i | −0.410852 | − | 0.479853i | ||||
\(947\) | 2.31945 | 0.0753720 | 0.0376860 | − | 0.999290i | \(-0.488001\pi\) | ||||
0.0376860 | + | 0.999290i | \(0.488001\pi\) | |||||||
\(948\) | −4.38932 | + | 13.5089i | −0.142559 | + | 0.438750i | ||||
\(949\) | 15.7212 | − | 11.4221i | 0.510331 | − | 0.370777i | ||||
\(950\) | −1.43400 | − | 1.04186i | −0.0465250 | − | 0.0338024i | ||||
\(951\) | −11.4647 | − | 35.2848i | −0.371769 | − | 1.14419i | ||||
\(952\) | 0.101720 | + | 0.313063i | 0.00329677 | + | 0.0101464i | ||||
\(953\) | 5.76745 | + | 4.19030i | 0.186826 | + | 0.135737i | 0.677267 | − | 0.735737i | \(-0.263164\pi\) |
−0.490441 | + | 0.871475i | \(0.663164\pi\) | |||||||
\(954\) | −3.02108 | + | 2.19494i | −0.0978111 | + | 0.0710639i | ||||
\(955\) | −1.68008 | + | 5.17074i | −0.0543660 | + | 0.167321i | ||||
\(956\) | −23.9513 | −0.774640 | ||||||||
\(957\) | −12.8197 | + | 20.9775i | −0.414403 | + | 0.678107i | ||||
\(958\) | −16.8581 | −0.544660 | ||||||||
\(959\) | 4.67157 | − | 14.3776i | 0.150853 | − | 0.464278i | ||||
\(960\) | 3.32973 | − | 2.41919i | 0.107466 | − | 0.0780789i | ||||
\(961\) | 12.4628 | + | 9.05478i | 0.402027 | + | 0.292090i | ||||
\(962\) | 1.88228 | + | 5.79306i | 0.0606871 | + | 0.186776i | ||||
\(963\) | 2.02467 | + | 6.23129i | 0.0652440 | + | 0.200800i | ||||
\(964\) | 3.08105 | + | 2.23851i | 0.0992339 | + | 0.0720976i | ||||
\(965\) | 15.9334 | − | 11.5763i | 0.512915 | − | 0.372655i | ||||
\(966\) | 1.87225 | − | 5.76221i | 0.0602388 | − | 0.185396i | ||||
\(967\) | −14.9561 | −0.480957 | −0.240478 | − | 0.970654i | \(-0.577304\pi\) | ||||
−0.240478 | + | 0.970654i | \(0.577304\pi\) | |||||||
\(968\) | −9.81328 | − | 4.96986i | −0.315411 | − | 0.159737i | ||||
\(969\) | 0.335746 | 0.0107857 | ||||||||
\(970\) | 1.19773 | − | 3.68622i | 0.0384567 | − | 0.118357i | ||||
\(971\) | 36.1716 | − | 26.2802i | 1.16080 | − | 0.843372i | 0.170923 | − | 0.985284i | \(-0.445325\pi\) |
0.989879 | + | 0.141912i | \(0.0453250\pi\) | |||||||
\(972\) | 4.14740 | + | 3.01326i | 0.133028 | + | 0.0966505i | ||||
\(973\) | −6.09324 | − | 18.7531i | −0.195340 | − | 0.601195i | ||||
\(974\) | 8.51256 | + | 26.1990i | 0.272760 | + | 0.839469i | ||||
\(975\) | 5.21405 | + | 3.78823i | 0.166983 | + | 0.121320i | ||||
\(976\) | 10.5321 | − | 7.65205i | 0.337126 | − | 0.244936i | ||||
\(977\) | −13.4055 | + | 41.2580i | −0.428881 | + | 1.31996i | 0.470348 | + | 0.882481i | \(0.344128\pi\) |
−0.899229 | + | 0.437478i | \(0.855872\pi\) | |||||||
\(978\) | −1.89784 | −0.0606863 | ||||||||
\(979\) | 6.20793 | − | 10.1583i | 0.198406 | − | 0.324662i | ||||
\(980\) | −11.9600 | −0.382048 | ||||||||
\(981\) | 0.420168 | − | 1.29315i | 0.0134149 | − | 0.0412870i | ||||
\(982\) | 16.2475 | − | 11.8045i | 0.518478 | − | 0.376697i | ||||
\(983\) | −34.0915 | − | 24.7689i | −1.08735 | − | 0.790007i | −0.108401 | − | 0.994107i | \(-0.534573\pi\) |
−0.978950 | + | 0.204101i | \(0.934573\pi\) | |||||||
\(984\) | −3.68886 | − | 11.3531i | −0.117597 | − | 0.361925i | ||||
\(985\) | 1.33253 | + | 4.10110i | 0.0424579 | + | 0.130672i | ||||
\(986\) | −0.804977 | − | 0.584850i | −0.0256357 | − | 0.0186254i | ||||
\(987\) | −24.7682 | + | 17.9952i | −0.788381 | + | 0.572792i | ||||
\(988\) | −0.710450 | + | 2.18654i | −0.0226024 | + | 0.0695631i | ||||
\(989\) | −14.4738 | −0.460241 | ||||||||
\(990\) | 2.79994 | + | 3.27019i | 0.0889880 | + | 0.103933i | ||||
\(991\) | 55.5865 | 1.76576 | 0.882881 | − | 0.469596i | \(-0.155600\pi\) | ||||
0.882881 | + | 0.469596i | \(0.155600\pi\) | |||||||
\(992\) | −1.22033 | + | 3.75578i | −0.0387454 | + | 0.119246i | ||||
\(993\) | 21.3096 | − | 15.4823i | 0.676240 | − | 0.491317i | ||||
\(994\) | −8.55712 | − | 6.21711i | −0.271415 | − | 0.197195i | ||||
\(995\) | −2.96204 | − | 9.11622i | −0.0939030 | − | 0.289004i | ||||
\(996\) | 7.96454 | + | 24.5123i | 0.252366 | + | 0.776703i | ||||
\(997\) | 3.05604 | + | 2.22035i | 0.0967859 | + | 0.0703191i | 0.635126 | − | 0.772409i | \(-0.280948\pi\) |
−0.538340 | + | 0.842728i | \(0.680948\pi\) | |||||||
\(998\) | −13.4352 | + | 9.76122i | −0.425283 | + | 0.308986i | ||||
\(999\) | −4.53029 | + | 13.9428i | −0.143332 | + | 0.441131i |
(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 | 418.2.f.h.229.4 | yes | 20 | |
11.4 | even | 5 | 4598.2.a.cc.1.3 | 10 | |||
11.5 | even | 5 | inner | 418.2.f.h.115.4 | ✓ | 20 | |
11.7 | odd | 10 | 4598.2.a.cd.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.h.115.4 | ✓ | 20 | 11.5 | even | 5 | inner | |
418.2.f.h.229.4 | yes | 20 | 1.1 | even | 1 | trivial | |
4598.2.a.cc.1.3 | 10 | 11.4 | even | 5 | |||
4598.2.a.cd.1.3 | 10 | 11.7 | odd | 10 |