Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(143,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([27, 34]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.bb (of order \(36\), degree \(12\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{36})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 793.2 | ||
Character | \(\chi\) | \(=\) | 950.793 |
Dual form | 950.2.bb.a.357.2 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{7}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.906308 | + | 0.422618i | 0.640856 | + | 0.298836i | ||||
\(3\) | 1.85075 | + | 2.64314i | 1.06853 | + | 1.52602i | 0.832303 | + | 0.554321i | \(0.187022\pi\) |
0.236227 | + | 0.971698i | \(0.424089\pi\) | |||||||
\(4\) | 0.642788 | + | 0.766044i | 0.321394 | + | 0.383022i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.560307 | + | 3.17766i | 0.228745 | + | 1.29727i | ||||
\(7\) | −3.57554 | − | 0.958062i | −1.35143 | − | 0.362113i | −0.490765 | − | 0.871292i | \(-0.663282\pi\) |
−0.860661 | + | 0.509179i | \(0.829949\pi\) | |||||||
\(8\) | 0.258819 | + | 0.965926i | 0.0915064 | + | 0.341506i | ||||
\(9\) | −2.53487 | + | 6.96451i | −0.844958 | + | 2.32150i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.03209 | + | 1.78763i | −0.311187 | + | 0.538991i | −0.978620 | − | 0.205679i | \(-0.934060\pi\) |
0.667433 | + | 0.744670i | \(0.267393\pi\) | |||||||
\(12\) | −0.835127 | + | 3.11674i | −0.241080 | + | 0.899724i | ||||
\(13\) | 1.78968 | + | 1.25315i | 0.496367 | + | 0.347560i | 0.794801 | − | 0.606870i | \(-0.207575\pi\) |
−0.298434 | + | 0.954430i | \(0.596464\pi\) | |||||||
\(14\) | −2.83564 | − | 2.37939i | −0.757857 | − | 0.635917i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.173648 | + | 0.984808i | −0.0434120 | + | 0.246202i | ||||
\(17\) | −0.543308 | + | 1.16513i | −0.131771 | + | 0.282585i | −0.961112 | − | 0.276159i | \(-0.910939\pi\) |
0.829341 | + | 0.558743i | \(0.188716\pi\) | |||||||
\(18\) | −5.24070 | + | 5.24070i | −1.23525 | + | 1.23525i | ||||
\(19\) | 1.10359 | − | 4.21688i | 0.253181 | − | 0.967419i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.08512 | − | 11.2238i | −0.891447 | − | 2.44923i | ||||
\(22\) | −1.69088 | + | 1.18396i | −0.360496 | + | 0.252422i | ||||
\(23\) | −3.68758 | − | 0.322621i | −0.768914 | − | 0.0672712i | −0.304053 | − | 0.952655i | \(-0.598340\pi\) |
−0.464861 | + | 0.885384i | \(0.653896\pi\) | |||||||
\(24\) | −2.07407 | + | 2.47178i | −0.423368 | + | 0.504550i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.09240 | + | 1.89209i | 0.214237 | + | 0.371069i | ||||
\(27\) | −13.7494 | + | 3.68414i | −2.64607 | + | 0.709013i | ||||
\(28\) | −1.56439 | − | 3.35485i | −0.295642 | − | 0.634007i | ||||
\(29\) | 7.40333 | + | 2.69459i | 1.37476 | + | 0.500373i | 0.920587 | − | 0.390538i | \(-0.127711\pi\) |
0.454178 | + | 0.890911i | \(0.349933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.91147 | − | 4.56769i | 1.42094 | − | 0.820382i | 0.424563 | − | 0.905398i | \(-0.360428\pi\) |
0.996380 | + | 0.0850167i | \(0.0270944\pi\) | |||||||
\(32\) | −0.573576 | + | 0.819152i | −0.101395 | + | 0.144807i | ||||
\(33\) | −6.63510 | + | 0.580496i | −1.15502 | + | 0.101051i | ||||
\(34\) | −0.984808 | + | 0.826352i | −0.168893 | + | 0.141718i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.96451 | + | 2.53487i | −1.16075 | + | 0.422479i | ||||
\(37\) | 4.90984 | + | 4.90984i | 0.807173 | + | 0.807173i | 0.984205 | − | 0.177032i | \(-0.0566497\pi\) |
−0.177032 | + | 0.984205i | \(0.556650\pi\) | |||||||
\(38\) | 2.78232 | − | 3.35540i | 0.451352 | − | 0.544317i | ||||
\(39\) | 7.04963i | 1.12884i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.67752 | − | 1.35375i | −1.19903 | − | 0.211421i | −0.461749 | − | 0.887011i | \(-0.652778\pi\) |
−0.737278 | + | 0.675590i | \(0.763889\pi\) | |||||||
\(42\) | 1.04100 | − | 11.8986i | 0.160629 | − | 1.83600i | ||||
\(43\) | 0.866836 | + | 9.90798i | 0.132191 | + | 1.51095i | 0.715448 | + | 0.698666i | \(0.246222\pi\) |
−0.583257 | + | 0.812288i | \(0.698222\pi\) | |||||||
\(44\) | −2.03282 | + | 0.358441i | −0.306459 | + | 0.0540370i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.20574 | − | 1.85083i | −0.472660 | − | 0.272890i | ||||
\(47\) | 8.82464 | − | 4.11500i | 1.28721 | − | 0.600234i | 0.346054 | − | 0.938215i | \(-0.387522\pi\) |
0.941153 | + | 0.337980i | \(0.109744\pi\) | |||||||
\(48\) | −2.92437 | + | 1.36365i | −0.422096 | + | 0.196827i | ||||
\(49\) | 5.80439 | + | 3.35117i | 0.829199 | + | 0.478738i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.08512 | + | 0.720317i | −0.572032 | + | 0.100865i | ||||
\(52\) | 0.190417 | + | 2.17648i | 0.0264061 | + | 0.301823i | ||||
\(53\) | −0.791938 | + | 9.05189i | −0.108781 | + | 1.24337i | 0.724012 | + | 0.689788i | \(0.242296\pi\) |
−0.832793 | + | 0.553585i | \(0.813259\pi\) | |||||||
\(54\) | −14.0182 | − | 2.47178i | −1.90763 | − | 0.336367i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 3.70167i | − | 0.494656i | ||||||
\(57\) | 13.1883 | − | 4.88744i | 1.74683 | − | 0.647357i | ||||
\(58\) | 5.57091 | + | 5.57091i | 0.731497 | + | 0.731497i | ||||
\(59\) | 1.99654 | − | 0.726682i | 0.259928 | − | 0.0946059i | −0.208769 | − | 0.977965i | \(-0.566946\pi\) |
0.468697 | + | 0.883359i | \(0.344724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.62108 | − | 7.23395i | 1.10382 | − | 0.926212i | 0.106141 | − | 0.994351i | \(-0.466151\pi\) |
0.997676 | + | 0.0681392i | \(0.0217062\pi\) | |||||||
\(62\) | 9.10062 | − | 0.796201i | 1.15578 | − | 0.101118i | ||||
\(63\) | 15.7360 | − | 22.4733i | 1.98254 | − | 2.83137i | ||||
\(64\) | −0.866025 | + | 0.500000i | −0.108253 | + | 0.0625000i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.25877 | − | 2.27801i | −0.770401 | − | 0.280403i | ||||
\(67\) | −1.07953 | − | 2.31505i | −0.131885 | − | 0.282829i | 0.829265 | − | 0.558856i | \(-0.188760\pi\) |
−0.961150 | + | 0.276028i | \(0.910982\pi\) | |||||||
\(68\) | −1.24177 | + | 0.332731i | −0.150587 | + | 0.0403496i | ||||
\(69\) | −5.97205 | − | 10.3439i | −0.718950 | − | 1.24526i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.53209 | + | 3.01763i | −0.300504 | + | 0.358126i | −0.895074 | − | 0.445917i | \(-0.852878\pi\) |
0.594571 | + | 0.804043i | \(0.297322\pi\) | |||||||
\(72\) | −7.38327 | − | 0.645953i | −0.870127 | − | 0.0761262i | ||||
\(73\) | −4.33934 | + | 3.03844i | −0.507882 | + | 0.355623i | −0.799260 | − | 0.600985i | \(-0.794775\pi\) |
0.291378 | + | 0.956608i | \(0.405886\pi\) | |||||||
\(74\) | 2.37484 | + | 6.52481i | 0.276069 | + | 0.758494i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.93969 | − | 1.86516i | 0.451914 | − | 0.213949i | ||||
\(77\) | 5.40293 | − | 5.40293i | 0.615721 | − | 0.615721i | ||||
\(78\) | −2.97930 | + | 6.38913i | −0.337340 | + | 0.723427i | ||||
\(79\) | −0.385920 | + | 2.18866i | −0.0434194 | + | 0.246244i | −0.998791 | − | 0.0491638i | \(-0.984344\pi\) |
0.955371 | + | 0.295408i | \(0.0954555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −18.1518 | − | 15.2312i | −2.01687 | − | 1.69235i | ||||
\(82\) | −6.38607 | − | 4.47158i | −0.705224 | − | 0.493803i | ||||
\(83\) | 3.67656 | − | 13.7211i | 0.403555 | − | 1.50609i | −0.403151 | − | 0.915133i | \(-0.632085\pi\) |
0.806706 | − | 0.590953i | \(-0.201248\pi\) | |||||||
\(84\) | 5.97205 | − | 10.3439i | 0.651604 | − | 1.12861i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.40167 | + | 9.34602i | −0.366812 | + | 1.00781i | ||||
\(87\) | 6.57951 | + | 24.5551i | 0.705398 | + | 2.63258i | ||||
\(88\) | −1.99384 | − | 0.534249i | −0.212544 | − | 0.0569511i | ||||
\(89\) | −0.335316 | − | 1.90167i | −0.0355435 | − | 0.201577i | 0.961865 | − | 0.273525i | \(-0.0881896\pi\) |
−0.997408 | + | 0.0719479i | \(0.977078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.19846 | − | 6.19529i | −0.544947 | − | 0.649443i | ||||
\(92\) | −2.12319 | − | 3.03223i | −0.221358 | − | 0.316132i | ||||
\(93\) | 26.7152 | + | 12.4575i | 2.77024 | + | 1.29178i | ||||
\(94\) | 9.73692 | 1.00429 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.22668 | −0.329322 | ||||||||
\(97\) | −4.66105 | − | 2.17348i | −0.473258 | − | 0.220684i | 0.171330 | − | 0.985214i | \(-0.445193\pi\) |
−0.644589 | + | 0.764530i | \(0.722971\pi\) | |||||||
\(98\) | 3.84430 | + | 5.49023i | 0.388333 | + | 0.554597i | ||||
\(99\) | −9.83375 | − | 11.7194i | −0.988329 | − | 1.17784i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00727 | − | 5.71253i | −0.100228 | − | 0.568418i | −0.993020 | − | 0.117949i | \(-0.962368\pi\) |
0.892792 | − | 0.450469i | \(-0.148743\pi\) | |||||||
\(102\) | −4.00680 | − | 1.07362i | −0.396732 | − | 0.106304i | ||||
\(103\) | 0.530483 | + | 1.97979i | 0.0522701 | + | 0.195075i | 0.987124 | − | 0.159959i | \(-0.0511362\pi\) |
−0.934854 | + | 0.355033i | \(0.884469\pi\) | |||||||
\(104\) | −0.747243 | + | 2.05303i | −0.0732732 | + | 0.201316i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.54323 | + | 7.86911i | −0.441278 | + | 0.764316i | ||||
\(107\) | 3.86768 | − | 14.4344i | 0.373903 | − | 1.39542i | −0.481039 | − | 0.876699i | \(-0.659740\pi\) |
0.854942 | − | 0.518724i | \(-0.173593\pi\) | |||||||
\(108\) | −11.6602 | − | 8.16453i | −1.12200 | − | 0.785632i | ||||
\(109\) | −7.50016 | − | 6.29339i | −0.718386 | − | 0.602797i | 0.208553 | − | 0.978011i | \(-0.433125\pi\) |
−0.926938 | + | 0.375214i | \(0.877569\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.89053 | + | 22.0643i | −0.369273 | + | 2.09425i | ||||
\(112\) | 1.56439 | − | 3.35485i | 0.147821 | − | 0.317003i | ||||
\(113\) | −7.12192 | + | 7.12192i | −0.669974 | + | 0.669974i | −0.957710 | − | 0.287736i | \(-0.907098\pi\) |
0.287736 | + | 0.957710i | \(0.407098\pi\) | |||||||
\(114\) | 14.0182 | + | 1.14409i | 1.31292 | + | 0.107153i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.69459 | + | 7.40333i | 0.250187 | + | 0.687382i | ||||
\(117\) | −13.2641 | + | 9.28766i | −1.22627 | + | 0.858644i | ||||
\(118\) | 2.11659 | + | 0.185178i | 0.194848 | + | 0.0170470i | ||||
\(119\) | 3.05888 | − | 3.64543i | 0.280407 | − | 0.334176i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.36959 | + | 5.83629i | 0.306326 | + | 0.530572i | ||||
\(122\) | 10.8706 | − | 2.91276i | 0.984173 | − | 0.263708i | ||||
\(123\) | −10.6310 | − | 22.7982i | −0.958564 | − | 2.05565i | ||||
\(124\) | 8.58445 | + | 3.12449i | 0.770907 | + | 0.280587i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 23.7592 | − | 13.7174i | 2.11664 | − | 1.22204i | ||||
\(127\) | 1.91549 | − | 2.73560i | 0.169972 | − | 0.242746i | −0.725124 | − | 0.688618i | \(-0.758218\pi\) |
0.895096 | + | 0.445873i | \(0.147107\pi\) | |||||||
\(128\) | −0.996195 | + | 0.0871557i | −0.0880520 | + | 0.00770355i | ||||
\(129\) | −24.5839 | + | 20.6284i | −2.16449 | + | 1.81623i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.7738 | − | 6.10516i | 1.46553 | − | 0.533410i | 0.518649 | − | 0.854987i | \(-0.326435\pi\) |
0.946883 | + | 0.321577i | \(0.104213\pi\) | |||||||
\(132\) | −4.70965 | − | 4.70965i | −0.409922 | − | 0.409922i | ||||
\(133\) | −7.98596 | + | 14.0203i | −0.692470 | + | 1.21571i | ||||
\(134\) | − | 2.55438i | − | 0.220665i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.26604 | − | 0.223238i | −0.108562 | − | 0.0191425i | ||||
\(137\) | −1.31925 | + | 15.0791i | −0.112711 | + | 1.28829i | 0.703565 | + | 0.710631i | \(0.251590\pi\) |
−0.816276 | + | 0.577662i | \(0.803965\pi\) | |||||||
\(138\) | −1.04100 | − | 11.8986i | −0.0886155 | − | 1.01288i | ||||
\(139\) | 21.7702 | − | 3.83868i | 1.84653 | − | 0.325592i | 0.862839 | − | 0.505479i | \(-0.168684\pi\) |
0.983687 | + | 0.179886i | \(0.0575730\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.2087 | + | 15.7090i | 2.29139 | + | 1.32293i | ||||
\(142\) | −3.57016 | + | 1.66479i | −0.299601 | + | 0.139706i | ||||
\(143\) | −4.08727 | + | 1.90592i | −0.341794 | + | 0.159381i | ||||
\(144\) | −6.41852 | − | 3.70574i | −0.534877 | − | 0.308811i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.21688 | + | 0.919877i | −0.431752 | + | 0.0761296i | ||||
\(147\) | 1.88486 | + | 21.5440i | 0.155460 | + | 1.77692i | ||||
\(148\) | −0.605171 | + | 6.91714i | −0.0497448 | + | 0.568585i | ||||
\(149\) | −15.1025 | − | 2.66297i | −1.23724 | − | 0.218159i | −0.483508 | − | 0.875340i | \(-0.660638\pi\) |
−0.753733 | + | 0.657181i | \(0.771749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.33012i | − | 0.515138i | −0.966260 | − | 0.257569i | \(-0.917078\pi\) | ||
0.966260 | − | 0.257569i | \(-0.0829215\pi\) | |||||||
\(152\) | 4.35882 | − | 0.0254230i | 0.353547 | − | 0.00206208i | ||||
\(153\) | −6.73732 | − | 6.73732i | −0.544680 | − | 0.544680i | ||||
\(154\) | 7.18009 | − | 2.61334i | 0.578589 | − | 0.210589i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.40033 | + | 4.53141i | −0.432372 | + | 0.362804i | ||||
\(157\) | 3.49465 | − | 0.305743i | 0.278904 | − | 0.0244009i | 0.0531542 | − | 0.998586i | \(-0.483073\pi\) |
0.225749 | + | 0.974185i | \(0.427517\pi\) | |||||||
\(158\) | −1.27473 | + | 1.82051i | −0.101412 | + | 0.144832i | ||||
\(159\) | −25.3911 | + | 14.6596i | −2.01365 | + | 1.16258i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.8760 | + | 4.68647i | 1.01477 | + | 0.369346i | ||||
\(162\) | −10.0142 | − | 21.4754i | −0.786787 | − | 1.68727i | ||||
\(163\) | 13.6561 | − | 3.65915i | 1.06963 | − | 0.286607i | 0.319290 | − | 0.947657i | \(-0.396556\pi\) |
0.750341 | + | 0.661050i | \(0.229889\pi\) | |||||||
\(164\) | −3.89798 | − | 6.75150i | −0.304381 | − | 0.527203i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.13088 | − | 10.8818i | 0.708694 | − | 0.844588i | ||||
\(167\) | −4.38698 | − | 0.383811i | −0.339474 | − | 0.0297002i | −0.0838559 | − | 0.996478i | \(-0.526724\pi\) |
−0.255618 | + | 0.966778i | \(0.582279\pi\) | |||||||
\(168\) | 9.78403 | − | 6.85085i | 0.754855 | − | 0.528555i | ||||
\(169\) | −2.81369 | − | 7.73055i | −0.216438 | − | 0.594658i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.5710 | + | 18.3752i | 2.03194 | + | 1.40519i | ||||
\(172\) | −7.03276 | + | 7.03276i | −0.536243 | + | 0.536243i | ||||
\(173\) | −9.59154 | + | 20.5691i | −0.729232 | + | 1.56384i | 0.0936344 | + | 0.995607i | \(0.470152\pi\) |
−0.822866 | + | 0.568236i | \(0.807626\pi\) | |||||||
\(174\) | −4.41436 | + | 25.0351i | −0.334652 | + | 1.89790i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.58125 | − | 1.32683i | −0.119191 | − | 0.100013i | ||||
\(177\) | 5.61582 | + | 3.93224i | 0.422111 | + | 0.295565i | ||||
\(178\) | 0.499782 | − | 1.86521i | 0.0374603 | − | 0.139804i | ||||
\(179\) | 4.85586 | − | 8.41060i | 0.362944 | − | 0.628638i | −0.625500 | − | 0.780224i | \(-0.715105\pi\) |
0.988444 | + | 0.151587i | \(0.0484383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.32501 | + | 9.13538i | −0.247146 | + | 0.679028i | 0.752642 | + | 0.658430i | \(0.228779\pi\) |
−0.999788 | + | 0.0205977i | \(0.993443\pi\) | |||||||
\(182\) | −2.09317 | − | 7.81180i | −0.155156 | − | 0.579049i | ||||
\(183\) | 35.0758 | + | 9.39853i | 2.59288 | + | 0.694760i | ||||
\(184\) | −0.642788 | − | 3.64543i | −0.0473869 | − | 0.268745i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 18.9474 | + | 22.5807i | 1.38929 | + | 1.65570i | ||||
\(187\) | −1.52207 | − | 2.17375i | −0.111305 | − | 0.158960i | ||||
\(188\) | 8.82464 | + | 4.11500i | 0.643603 | + | 0.300117i | ||||
\(189\) | 52.6911 | 3.83271 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.7469 | −1.13941 | −0.569703 | − | 0.821850i | \(-0.692942\pi\) | ||||
−0.569703 | + | 0.821850i | \(0.692942\pi\) | |||||||
\(192\) | −2.92437 | − | 1.36365i | −0.211048 | − | 0.0984133i | ||||
\(193\) | −5.51698 | − | 7.87906i | −0.397121 | − | 0.567147i | 0.569942 | − | 0.821685i | \(-0.306966\pi\) |
−0.967063 | + | 0.254538i | \(0.918077\pi\) | |||||||
\(194\) | −3.30579 | − | 3.93969i | −0.237342 | − | 0.282853i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.16385 | + | 6.60051i | 0.0831320 | + | 0.471465i | ||||
\(197\) | 1.09199 | + | 0.292599i | 0.0778014 | + | 0.0208468i | 0.297510 | − | 0.954719i | \(-0.403844\pi\) |
−0.219708 | + | 0.975566i | \(0.570511\pi\) | |||||||
\(198\) | −3.95957 | − | 14.7773i | −0.281394 | − | 1.05018i | ||||
\(199\) | 1.33883 | − | 3.67840i | 0.0949069 | − | 0.260755i | −0.883151 | − | 0.469089i | \(-0.844582\pi\) |
0.978058 | + | 0.208335i | \(0.0668044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.12108 | − | 7.13792i | 0.290679 | − | 0.503470i | ||||
\(202\) | 1.50132 | − | 5.60301i | 0.105633 | − | 0.394226i | ||||
\(203\) | −23.8893 | − | 16.7275i | −1.67670 | − | 1.17404i | ||||
\(204\) | −3.17766 | − | 2.66637i | −0.222481 | − | 0.186684i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.355914 | + | 2.01849i | −0.0247977 | + | 0.140635i | ||||
\(207\) | 11.5944 | − | 24.8644i | 0.805870 | − | 1.72819i | ||||
\(208\) | −1.54488 | + | 1.54488i | −0.107118 | + | 0.107118i | ||||
\(209\) | 6.39922 | + | 6.32501i | 0.442643 | + | 0.437510i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.33022 | − | 9.14971i | −0.229262 | − | 0.629892i | 0.770711 | − | 0.637184i | \(-0.219901\pi\) |
−0.999973 | + | 0.00729228i | \(0.997679\pi\) | |||||||
\(212\) | −7.44320 | + | 5.21178i | −0.511201 | + | 0.357947i | ||||
\(213\) | −12.6623 | − | 1.10781i | −0.867605 | − | 0.0759056i | ||||
\(214\) | 9.60554 | − | 11.4474i | 0.656621 | − | 0.782530i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.11721 | − | 12.3274i | −0.484265 | − | 0.838771i | ||||
\(217\) | −32.6639 | + | 8.75226i | −2.21737 | + | 0.594142i | ||||
\(218\) | −4.13776 | − | 8.87345i | −0.280244 | − | 0.600986i | ||||
\(219\) | −16.0621 | − | 5.84611i | −1.08537 | − | 0.395044i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.43242 | + | 1.40436i | −0.163622 | + | 0.0944673i | ||||
\(222\) | −12.8508 | + | 18.3528i | −0.862488 | + | 1.23176i | ||||
\(223\) | −3.13866 | + | 0.274597i | −0.210180 | + | 0.0183884i | −0.191759 | − | 0.981442i | \(-0.561419\pi\) |
−0.0184205 | + | 0.999830i | \(0.505864\pi\) | |||||||
\(224\) | 2.83564 | − | 2.37939i | 0.189464 | − | 0.158979i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.46451 | + | 3.44480i | −0.629570 | + | 0.229145i | ||||
\(227\) | −0.863822 | − | 0.863822i | −0.0573339 | − | 0.0573339i | 0.677858 | − | 0.735192i | \(-0.262908\pi\) |
−0.735192 | + | 0.677858i | \(0.762908\pi\) | |||||||
\(228\) | 12.2213 | + | 6.96123i | 0.809373 | + | 0.461019i | ||||
\(229\) | − | 23.2344i | − | 1.53537i | −0.640825 | − | 0.767687i | \(-0.721408\pi\) | ||
0.640825 | − | 0.767687i | \(-0.278592\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.2802 | + | 4.28125i | 1.59752 | + | 0.281686i | ||||
\(232\) | −0.686653 | + | 7.84848i | −0.0450810 | + | 0.515278i | ||||
\(233\) | 0.367557 | + | 4.20119i | 0.0240794 | + | 0.275229i | 0.998684 | + | 0.0512945i | \(0.0163347\pi\) |
−0.974604 | + | 0.223935i | \(0.928110\pi\) | |||||||
\(234\) | −15.9465 | + | 2.81180i | −1.04246 | + | 0.183813i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.84002 | + | 1.06234i | 0.119775 | + | 0.0691523i | ||||
\(237\) | −6.49919 | + | 3.03062i | −0.422168 | + | 0.196860i | ||||
\(238\) | 4.31291 | − | 2.01114i | 0.279564 | − | 0.130363i | ||||
\(239\) | 22.1552 | + | 12.7913i | 1.43310 | + | 0.827402i | 0.997356 | − | 0.0726674i | \(-0.0231512\pi\) |
0.435746 | + | 0.900070i | \(0.356485\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.5103 | + | 3.08753i | −1.12794 | + | 0.198885i | −0.706322 | − | 0.707890i | \(-0.749647\pi\) |
−0.421613 | + | 0.906776i | \(0.638536\pi\) | |||||||
\(242\) | 0.587357 | + | 6.71353i | 0.0377568 | + | 0.431562i | ||||
\(243\) | 2.94191 | − | 33.6262i | 0.188724 | − | 2.15712i | ||||
\(244\) | 11.0830 | + | 1.95424i | 0.709519 | + | 0.125107i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 25.1551i | − | 1.60383i | ||||||
\(247\) | 7.25944 | − | 6.16390i | 0.461907 | − | 0.392199i | ||||
\(248\) | 6.45969 | + | 6.45969i | 0.410191 | + | 0.410191i | ||||
\(249\) | 43.0712 | − | 15.6766i | 2.72953 | − | 0.993467i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0719 | + | 8.45134i | −0.635734 | + | 0.533444i | −0.902705 | − | 0.430261i | \(-0.858422\pi\) |
0.266971 | + | 0.963705i | \(0.413977\pi\) | |||||||
\(252\) | 27.3304 | − | 2.39110i | 1.72165 | − | 0.150625i | ||||
\(253\) | 4.38264 | − | 6.25906i | 0.275534 | − | 0.393504i | ||||
\(254\) | 2.89214 | − | 1.66978i | 0.181469 | − | 0.104771i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.939693 | − | 0.342020i | −0.0587308 | − | 0.0213763i | ||||
\(257\) | 5.51174 | + | 11.8200i | 0.343813 | + | 0.737309i | 0.999848 | − | 0.0174210i | \(-0.00554556\pi\) |
−0.656035 | + | 0.754730i | \(0.727768\pi\) | |||||||
\(258\) | −30.9985 | + | 8.30603i | −1.92988 | + | 0.517111i | ||||
\(259\) | −12.8514 | − | 22.2592i | −0.798546 | − | 1.38312i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −37.5330 | + | 44.7301i | −2.32324 | + | 2.76872i | ||||
\(262\) | 17.7824 | + | 1.55576i | 1.09860 | + | 0.0961149i | ||||
\(263\) | 5.17817 | − | 3.62579i | 0.319299 | − | 0.223576i | −0.402928 | − | 0.915232i | \(-0.632007\pi\) |
0.722227 | + | 0.691656i | \(0.243119\pi\) | |||||||
\(264\) | −2.27801 | − | 6.25877i | −0.140202 | − | 0.385201i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −13.1630 | + | 9.33170i | −0.807074 | + | 0.572163i | ||||
\(267\) | 4.40581 | − | 4.40581i | 0.269631 | − | 0.269631i | ||||
\(268\) | 1.07953 | − | 2.31505i | 0.0659426 | − | 0.141414i | ||||
\(269\) | 0.753138 | − | 4.27126i | 0.0459196 | − | 0.260423i | −0.953202 | − | 0.302335i | \(-0.902234\pi\) |
0.999121 | + | 0.0419120i | \(0.0133449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.70755 | + | 8.14560i | 0.589692 | + | 0.494810i | 0.888114 | − | 0.459624i | \(-0.152016\pi\) |
−0.298422 | + | 0.954434i | \(0.596460\pi\) | |||||||
\(272\) | −1.05308 | − | 0.737376i | −0.0638524 | − | 0.0447100i | ||||
\(273\) | 6.75398 | − | 25.2062i | 0.408770 | − | 1.52555i | ||||
\(274\) | −7.56834 | + | 13.1088i | −0.457220 | + | 0.791929i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.08512 | − | 11.2238i | 0.245895 | − | 0.675592i | ||||
\(277\) | −0.578676 | − | 2.15965i | −0.0347693 | − | 0.129761i | 0.946360 | − | 0.323115i | \(-0.104730\pi\) |
−0.981129 | + | 0.193354i | \(0.938063\pi\) | |||||||
\(278\) | 21.3528 | + | 5.72147i | 1.28066 | + | 0.343151i | ||||
\(279\) | 11.7571 | + | 66.6780i | 0.703881 | + | 3.99191i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.12449 | − | 7.29888i | −0.365356 | − | 0.435415i | 0.551779 | − | 0.833990i | \(-0.313949\pi\) |
−0.917135 | + | 0.398576i | \(0.869505\pi\) | |||||||
\(282\) | 18.0206 | + | 25.7361i | 1.07311 | + | 1.53256i | ||||
\(283\) | −24.1389 | − | 11.2561i | −1.43491 | − | 0.669108i | −0.459230 | − | 0.888318i | \(-0.651875\pi\) |
−0.975678 | + | 0.219209i | \(0.929652\pi\) | |||||||
\(284\) | −3.93923 | −0.233750 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.50980 | −0.266670 | ||||||||
\(287\) | 26.1543 | + | 12.1959i | 1.54384 | + | 0.719903i | ||||
\(288\) | −4.25105 | − | 6.07112i | −0.250495 | − | 0.357744i | ||||
\(289\) | 9.86505 | + | 11.7567i | 0.580297 | + | 0.691571i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.88161 | − | 16.3424i | −0.168923 | − | 0.958009i | ||||
\(292\) | −5.11686 | − | 1.37106i | −0.299441 | − | 0.0802351i | ||||
\(293\) | 1.64034 | + | 6.12185i | 0.0958299 | + | 0.357642i | 0.997144 | − | 0.0755241i | \(-0.0240630\pi\) |
−0.901314 | + | 0.433166i | \(0.857396\pi\) | |||||||
\(294\) | −7.39663 | + | 20.3221i | −0.431380 | + | 1.18521i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.47178 | + | 6.01330i | −0.201793 | + | 0.349516i | ||||
\(297\) | 7.60472 | − | 28.3812i | 0.441271 | − | 1.64684i | ||||
\(298\) | −12.5621 | − | 8.79605i | −0.727700 | − | 0.509541i | ||||
\(299\) | −6.19529 | − | 5.19846i | −0.358283 | − | 0.300635i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.39306 | − | 36.2568i | 0.368490 | − | 2.08981i | ||||
\(302\) | 2.67523 | − | 5.73704i | 0.153942 | − | 0.330130i | ||||
\(303\) | 13.2348 | − | 13.2348i | 0.760321 | − | 0.760321i | ||||
\(304\) | 3.96118 | + | 1.81908i | 0.227189 | + | 0.104331i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.25877 | − | 8.95340i | −0.186292 | − | 0.511832i | ||||
\(307\) | −7.36823 | + | 5.15929i | −0.420527 | + | 0.294456i | −0.764622 | − | 0.644478i | \(-0.777075\pi\) |
0.344095 | + | 0.938935i | \(0.388186\pi\) | |||||||
\(308\) | 7.61182 | + | 0.665948i | 0.433724 | + | 0.0379459i | ||||
\(309\) | −4.25108 | + | 5.06624i | −0.241835 | + | 0.288208i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.97952 | + | 8.62479i | 0.282363 | + | 0.489067i | 0.971966 | − | 0.235120i | \(-0.0755485\pi\) |
−0.689603 | + | 0.724187i | \(0.742215\pi\) | |||||||
\(312\) | −6.80942 | + | 1.82458i | −0.385507 | + | 0.103296i | ||||
\(313\) | −9.31017 | − | 19.9657i | −0.526242 | − | 1.12853i | −0.972345 | − | 0.233548i | \(-0.924966\pi\) |
0.446103 | − | 0.894981i | \(-0.352811\pi\) | |||||||
\(314\) | 3.29644 | + | 1.19981i | 0.186029 | + | 0.0677090i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.92468 | + | 1.11121i | −0.108272 | + | 0.0625106i | ||||
\(317\) | 15.2579 | − | 21.7905i | 0.856968 | − | 1.22388i | −0.116071 | − | 0.993241i | \(-0.537030\pi\) |
0.973040 | − | 0.230637i | \(-0.0740810\pi\) | |||||||
\(318\) | −29.2076 | + | 2.55533i | −1.63788 | + | 0.143296i | ||||
\(319\) | −12.4578 | + | 10.4534i | −0.697505 | + | 0.585276i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.3102 | − | 16.4916i | 2.52897 | − | 0.920470i | ||||
\(322\) | 9.68901 | + | 9.68901i | 0.539948 | + | 0.539948i | ||||
\(323\) | 4.31361 | + | 3.57689i | 0.240016 | + | 0.199023i | ||||
\(324\) | − | 23.6955i | − | 1.31642i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.9231 | + | 2.45502i | 0.771128 | + | 0.135971i | ||||
\(327\) | 2.75340 | − | 31.4715i | 0.152263 | − | 1.74038i | ||||
\(328\) | −0.679462 | − | 7.76629i | −0.0375170 | − | 0.428822i | ||||
\(329\) | −35.4953 | + | 6.25877i | −1.95692 | + | 0.345057i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.7001 | − | 13.1059i | −1.24771 | − | 0.720366i | −0.277059 | − | 0.960853i | \(-0.589360\pi\) |
−0.970652 | + | 0.240487i | \(0.922693\pi\) | |||||||
\(332\) | 12.8742 | − | 6.00335i | 0.706565 | − | 0.329476i | ||||
\(333\) | −46.6404 | + | 21.7488i | −2.55588 | + | 1.19183i | ||||
\(334\) | −3.81374 | − | 2.20187i | −0.208679 | − | 0.120481i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 11.7626 | − | 2.07407i | 0.641705 | − | 0.113150i | ||||
\(337\) | −2.08234 | − | 23.8013i | −0.113432 | − | 1.29654i | −0.813123 | − | 0.582092i | \(-0.802234\pi\) |
0.699691 | − | 0.714446i | \(-0.253321\pi\) | |||||||
\(338\) | 0.717003 | − | 8.19538i | 0.0389998 | − | 0.445770i | ||||
\(339\) | −32.0051 | − | 5.64337i | −1.73828 | − | 0.306506i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.8571i | 1.02117i | ||||||||
\(342\) | 16.3158 | + | 27.8830i | 0.882259 | + | 1.50774i | ||||
\(343\) | 0.779134 | + | 0.779134i | 0.0420693 | + | 0.0420693i | ||||
\(344\) | −9.34602 | + | 3.40167i | −0.503904 | + | 0.183406i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.3858 | + | 14.5884i | −0.934665 | + | 0.784277i | ||||
\(347\) | −11.8602 | + | 1.03763i | −0.636688 | + | 0.0557030i | −0.400930 | − | 0.916109i | \(-0.631313\pi\) |
−0.235758 | + | 0.971812i | \(0.575757\pi\) | |||||||
\(348\) | −14.5811 | + | 20.8239i | −0.781626 | + | 1.11628i | ||||
\(349\) | 13.6519 | − | 7.88191i | 0.730768 | − | 0.421909i | −0.0879351 | − | 0.996126i | \(-0.528027\pi\) |
0.818703 | + | 0.574217i | \(0.194693\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.2237 | − | 10.6366i | −1.55985 | − | 0.567738i | ||||
\(352\) | −0.872359 | − | 1.87078i | −0.0464969 | − | 0.0997129i | ||||
\(353\) | −12.1278 | + | 3.24962i | −0.645496 | + | 0.172960i | −0.566692 | − | 0.823930i | \(-0.691777\pi\) |
−0.0788042 | + | 0.996890i | \(0.525110\pi\) | |||||||
\(354\) | 3.42782 | + | 5.93717i | 0.182187 | + | 0.315557i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.24123 | − | 1.47924i | 0.0657850 | − | 0.0783995i | ||||
\(357\) | 15.2966 | + | 1.33828i | 0.809582 | + | 0.0708293i | ||||
\(358\) | 7.95538 | − | 5.57041i | 0.420455 | − | 0.294406i | ||||
\(359\) | −5.60575 | − | 15.4017i | −0.295860 | − | 0.812869i | −0.995180 | − | 0.0980607i | \(-0.968736\pi\) |
0.699320 | − | 0.714809i | \(-0.253486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5642 | − | 9.30742i | −0.871799 | − | 0.489864i | ||||
\(362\) | −6.87426 | + | 6.87426i | −0.361303 | + | 0.361303i | ||||
\(363\) | −9.18990 | + | 19.7078i | −0.482345 | + | 1.03439i | ||||
\(364\) | 1.40436 | − | 7.96451i | 0.0736083 | − | 0.417454i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 27.8175 | + | 23.3416i | 1.45404 | + | 1.22009i | ||||
\(367\) | −16.7223 | − | 11.7091i | −0.872896 | − | 0.611209i | 0.0489341 | − | 0.998802i | \(-0.484418\pi\) |
−0.921830 | + | 0.387593i | \(0.873306\pi\) | |||||||
\(368\) | 0.958062 | − | 3.57554i | 0.0499424 | − | 0.186388i | ||||
\(369\) | 28.8898 | − | 50.0385i | 1.50394 | − | 2.60490i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5039 | − | 31.6066i | 0.597251 | − | 1.64093i | ||||
\(372\) | 7.62920 | + | 28.4726i | 0.395556 | + | 1.47623i | ||||
\(373\) | 33.0754 | + | 8.86252i | 1.71258 | + | 0.458884i | 0.976054 | − | 0.217527i | \(-0.0697990\pi\) |
0.736524 | + | 0.676411i | \(0.236466\pi\) | |||||||
\(374\) | −0.460802 | − | 2.61334i | −0.0238275 | − | 0.135133i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.25877 | + | 7.45891i | 0.322771 | + | 0.384664i | ||||
\(377\) | 9.87286 | + | 14.0999i | 0.508478 | + | 0.726182i | ||||
\(378\) | 47.7543 | + | 22.2682i | 2.45622 | + | 1.14535i | ||||
\(379\) | 33.0656 | 1.69847 | 0.849234 | − | 0.528017i | \(-0.177064\pi\) | ||||
0.849234 | + | 0.528017i | \(0.177064\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.7757 | 0.552055 | ||||||||
\(382\) | −14.2715 | − | 6.65493i | −0.730196 | − | 0.340496i | ||||
\(383\) | −8.90050 | − | 12.7112i | −0.454794 | − | 0.649513i | 0.524629 | − | 0.851331i | \(-0.324204\pi\) |
−0.979423 | + | 0.201818i | \(0.935315\pi\) | |||||||
\(384\) | −2.07407 | − | 2.47178i | −0.105842 | − | 0.126138i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.67024 | − | 9.47243i | −0.0850132 | − | 0.482134i | ||||
\(387\) | −71.2015 | − | 19.0784i | −3.61938 | − | 0.969809i | ||||
\(388\) | −1.33108 | − | 4.96766i | −0.0675754 | − | 0.252195i | ||||
\(389\) | −4.15312 | + | 11.4106i | −0.210571 | + | 0.578540i | −0.999347 | − | 0.0361415i | \(-0.988493\pi\) |
0.788775 | + | 0.614682i | \(0.210716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.37939 | − | 4.12122i | 0.120331 | − | 0.208419i | ||||
\(392\) | −1.73469 | + | 6.47396i | −0.0876152 | + | 0.326984i | ||||
\(393\) | 47.1809 | + | 33.0364i | 2.37996 | + | 1.66647i | ||||
\(394\) | 0.866025 | + | 0.726682i | 0.0436297 | + | 0.0366097i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.65657 | − | 15.0662i | 0.133498 | − | 0.757104i | ||||
\(397\) | 5.65663 | − | 12.1307i | 0.283898 | − | 0.608822i | −0.711706 | − | 0.702477i | \(-0.752077\pi\) |
0.995605 | + | 0.0936552i | \(0.0298551\pi\) | |||||||
\(398\) | 2.76795 | − | 2.76795i | 0.138745 | − | 0.138745i | ||||
\(399\) | −51.8377 | + | 4.84002i | −2.59513 | + | 0.242304i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.46522 | + | 15.0156i | 0.272920 | + | 0.749842i | 0.998119 | + | 0.0613028i | \(0.0195255\pi\) |
−0.725199 | + | 0.688539i | \(0.758252\pi\) | |||||||
\(402\) | 6.75158 | − | 4.72751i | 0.336738 | − | 0.235787i | ||||
\(403\) | 19.8830 | + | 1.73953i | 0.990441 | + | 0.0866524i | ||||
\(404\) | 3.72859 | − | 4.44356i | 0.185504 | − | 0.221076i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.5817 | − | 25.2563i | −0.723679 | − | 1.25345i | ||||
\(407\) | −13.8444 | + | 3.70959i | −0.686240 | + | 0.183877i | ||||
\(408\) | −1.75308 | − | 3.75949i | −0.0867904 | − | 0.186123i | ||||
\(409\) | 9.39052 | + | 3.41787i | 0.464331 | + | 0.169003i | 0.563583 | − | 0.826060i | \(-0.309423\pi\) |
−0.0992514 | + | 0.995062i | \(0.531645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −42.2978 | + | 24.4206i | −2.08640 | + | 1.20458i | ||||
\(412\) | −1.17562 | + | 1.67896i | −0.0579186 | + | 0.0827163i | ||||
\(413\) | −7.83491 | + | 0.685466i | −0.385531 | + | 0.0337296i | ||||
\(414\) | 21.0163 | − | 17.6348i | 1.03289 | − | 0.866701i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.05303 | + | 0.747243i | −0.100658 | + | 0.0366366i | ||||
\(417\) | 50.4374 | + | 50.4374i | 2.46993 | + | 2.46993i | ||||
\(418\) | 3.12660 | + | 8.43683i | 0.152927 | + | 0.412659i | ||||
\(419\) | 21.6304i | 1.05671i | 0.849022 | + | 0.528357i | \(0.177192\pi\) | ||||
−0.849022 | + | 0.528357i | \(0.822808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8892 | + | 2.80169i | 0.774392 | + | 0.136546i | 0.546859 | − | 0.837224i | \(-0.315823\pi\) |
0.227532 | + | 0.973771i | \(0.426934\pi\) | |||||||
\(422\) | 0.848628 | − | 9.69987i | 0.0413106 | − | 0.472182i | ||||
\(423\) | 6.28959 | + | 71.8903i | 0.305810 | + | 3.49543i | ||||
\(424\) | −8.94842 | + | 1.57785i | −0.434574 | + | 0.0766271i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −11.0077 | − | 6.35532i | −0.533327 | − | 0.307916i | ||||
\(427\) | −37.7555 | + | 17.6057i | −1.82712 | + | 0.852000i | ||||
\(428\) | 13.5435 | − | 6.31542i | 0.654648 | − | 0.305267i | ||||
\(429\) | −12.6021 | − | 7.27584i | −0.608437 | − | 0.351281i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.309993 | + | 0.0546601i | −0.0149318 | + | 0.00263288i | −0.181109 | − | 0.983463i | \(-0.557969\pi\) |
0.166177 | + | 0.986096i | \(0.446858\pi\) | |||||||
\(432\) | −1.24061 | − | 14.1803i | −0.0596890 | − | 0.682248i | ||||
\(433\) | 0.581970 | − | 6.65195i | 0.0279677 | − | 0.319672i | −0.969305 | − | 0.245863i | \(-0.920929\pi\) |
0.997272 | − | 0.0738095i | \(-0.0235157\pi\) | |||||||
\(434\) | −33.3024 | − | 5.87211i | −1.59857 | − | 0.281870i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 9.79077i | − | 0.468893i | ||||||
\(437\) | −5.43003 | + | 15.1940i | −0.259754 | + | 0.726830i | ||||
\(438\) | −12.0865 | − | 12.0865i | −0.577515 | − | 0.577515i | ||||
\(439\) | 15.8102 | − | 5.75443i | 0.754579 | − | 0.274644i | 0.0640474 | − | 0.997947i | \(-0.479599\pi\) |
0.690531 | + | 0.723303i | \(0.257377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −38.0526 | + | 31.9299i | −1.81203 | + | 1.52047i | ||||
\(442\) | −2.79803 | + | 0.244796i | −0.133089 | + | 0.0116437i | ||||
\(443\) | −18.8721 | + | 26.9521i | −0.896640 | + | 1.28053i | 0.0626285 | + | 0.998037i | \(0.480052\pi\) |
−0.959268 | + | 0.282497i | \(0.908837\pi\) | |||||||
\(444\) | −19.4030 | + | 11.2023i | −0.920826 | + | 0.531639i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.96064 | − | 1.07758i | −0.140190 | − | 0.0510251i | ||||
\(447\) | −20.9122 | − | 44.8464i | −0.989115 | − | 2.12116i | ||||
\(448\) | 3.57554 | − | 0.958062i | 0.168928 | − | 0.0452642i | ||||
\(449\) | 4.17680 | + | 7.23442i | 0.197115 | + | 0.341414i | 0.947592 | − | 0.319483i | \(-0.103509\pi\) |
−0.750477 | + | 0.660897i | \(0.770176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3439 | − | 12.3274i | 0.487075 | − | 0.580473i | ||||
\(452\) | −10.0336 | − | 0.877826i | −0.471940 | − | 0.0412894i | ||||
\(453\) | 16.7314 | − | 11.7155i | 0.786111 | − | 0.550441i | ||||
\(454\) | −0.417822 | − | 1.14796i | −0.0196093 | − | 0.0538762i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.13429 | + | 11.4739i | 0.380923 | + | 0.537317i | ||||
\(457\) | 7.96206 | − | 7.96206i | 0.372450 | − | 0.372450i | −0.495919 | − | 0.868369i | \(-0.665169\pi\) |
0.868369 | + | 0.495919i | \(0.165169\pi\) | |||||||
\(458\) | 9.81929 | − | 21.0575i | 0.458825 | − | 0.983954i | ||||
\(459\) | 3.17766 | − | 18.0214i | 0.148321 | − | 0.841167i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.97384 | + | 5.85175i | 0.324804 | + | 0.272543i | 0.790579 | − | 0.612360i | \(-0.209780\pi\) |
−0.465775 | + | 0.884903i | \(0.654224\pi\) | |||||||
\(462\) | 20.1960 | + | 14.1414i | 0.939602 | + | 0.657917i | ||||
\(463\) | −1.39015 | + | 5.18810i | −0.0646056 | + | 0.241111i | −0.990676 | − | 0.136240i | \(-0.956498\pi\) |
0.926070 | + | 0.377351i | \(0.123165\pi\) | |||||||
\(464\) | −3.93923 | + | 6.82295i | −0.182874 | + | 0.316747i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.44238 | + | 3.96291i | −0.0668170 | + | 0.183578i | ||||
\(467\) | 2.39939 | + | 8.95465i | 0.111031 | + | 0.414372i | 0.998959 | − | 0.0456091i | \(-0.0145229\pi\) |
−0.887929 | + | 0.459981i | \(0.847856\pi\) | |||||||
\(468\) | −15.6408 | − | 4.19094i | −0.722996 | − | 0.193726i | ||||
\(469\) | 1.64192 | + | 9.31180i | 0.0758169 | + | 0.429979i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.27584 | + | 8.67101i | 0.335253 | + | 0.399539i | ||||
\(472\) | 1.21866 | + | 1.74043i | 0.0560935 | + | 0.0801099i | ||||
\(473\) | −18.6065 | − | 8.67634i | −0.855526 | − | 0.398938i | ||||
\(474\) | −7.17106 | −0.329378 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.75877 | 0.218118 | ||||||||
\(477\) | −61.0345 | − | 28.4609i | −2.79458 | − | 1.30313i | ||||
\(478\) | 14.6736 | + | 20.9561i | 0.671155 | + | 0.958509i | ||||
\(479\) | −9.08040 | − | 10.8216i | −0.414894 | − | 0.494452i | 0.517607 | − | 0.855618i | \(-0.326823\pi\) |
−0.932501 | + | 0.361167i | \(0.882379\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.63429 | + | 14.9398i | 0.120113 | + | 0.681195i | ||||
\(482\) | −17.1745 | − | 4.60190i | −0.782279 | − | 0.209611i | ||||
\(483\) | 11.4432 | + | 42.7065i | 0.520683 | + | 1.94322i | ||||
\(484\) | −2.30493 | + | 6.33275i | −0.104770 | + | 0.287852i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.8773 | − | 29.2324i | 0.765571 | − | 1.32601i | ||||
\(487\) | 1.05258 | − | 3.92829i | 0.0476971 | − | 0.178008i | −0.937968 | − | 0.346722i | \(-0.887295\pi\) |
0.985665 | + | 0.168714i | \(0.0539614\pi\) | |||||||
\(488\) | 9.21876 | + | 6.45504i | 0.417313 | + | 0.292206i | ||||
\(489\) | 34.9457 | + | 29.3229i | 1.58030 | + | 1.32603i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.489322 | + | 2.77509i | −0.0220828 | + | 0.125238i | −0.993856 | − | 0.110678i | \(-0.964698\pi\) |
0.971774 | + | 0.235916i | \(0.0758089\pi\) | |||||||
\(492\) | 10.6310 | − | 22.7982i | 0.479282 | − | 1.02782i | ||||
\(493\) | −7.16183 | + | 7.16183i | −0.322553 | + | 0.322553i | ||||
\(494\) | 9.18426 | − | 2.51842i | 0.413219 | − | 0.113309i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.12449 | + | 8.58445i | 0.140294 | + | 0.385453i | ||||
\(497\) | 11.9446 | − | 8.36373i | 0.535791 | − | 0.375165i | ||||
\(498\) | 45.6610 | + | 3.99482i | 2.04612 | + | 0.179012i | ||||
\(499\) | 1.67382 | − | 1.99479i | 0.0749306 | − | 0.0892989i | −0.727277 | − | 0.686344i | \(-0.759214\pi\) |
0.802207 | + | 0.597045i | \(0.203659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.10472 | − | 12.3057i | −0.317416 | − | 0.549780i | ||||
\(502\) | −12.7000 | + | 3.40294i | −0.566827 | + | 0.151881i | ||||
\(503\) | −3.62237 | − | 7.76819i | −0.161513 | − | 0.346367i | 0.808851 | − | 0.588014i | \(-0.200090\pi\) |
−0.970364 | + | 0.241647i | \(0.922312\pi\) | |||||||
\(504\) | 25.7803 | + | 9.38326i | 1.14835 | + | 0.417963i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.61721 | − | 3.82045i | 0.294171 | − | 0.169840i | ||||
\(507\) | 15.2255 | − | 21.7443i | 0.676189 | − | 0.965698i | ||||
\(508\) | 3.32685 | − | 0.291061i | 0.147605 | − | 0.0129138i | ||||
\(509\) | −16.4526 | + | 13.8054i | −0.729251 | + | 0.611914i | −0.929927 | − | 0.367744i | \(-0.880130\pi\) |
0.200677 | + | 0.979658i | \(0.435686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.4265 | − | 6.70669i | 0.815140 | − | 0.296687i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0.361882 | + | 62.0454i | 0.0159775 | + | 2.73937i | ||||
\(514\) | 13.0419i | 0.575253i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −31.6045 | − | 5.57272i | −1.39131 | − | 0.245325i | ||||
\(517\) | −1.75172 | + | 20.0222i | −0.0770405 | + | 0.880577i | ||||
\(518\) | −2.24014 | − | 25.6049i | −0.0984262 | − | 1.12502i | ||||
\(519\) | −72.1187 | + | 12.7165i | −3.16566 | + | 0.558191i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.1783 | − | 13.9593i | −1.05927 | − | 0.611570i | −0.134040 | − | 0.990976i | \(-0.542795\pi\) |
−0.925230 | + | 0.379406i | \(0.876128\pi\) | |||||||
\(522\) | −52.9202 | + | 24.6771i | −2.31626 | + | 1.08009i | ||||
\(523\) | 19.1582 | − | 8.93364i | 0.837732 | − | 0.390641i | 0.0440910 | − | 0.999028i | \(-0.485961\pi\) |
0.793641 | + | 0.608387i | \(0.208183\pi\) | |||||||
\(524\) | 15.4588 | + | 8.92514i | 0.675321 | + | 0.389897i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.22534 | − | 1.09769i | 0.271438 | − | 0.0478618i | ||||
\(527\) | 1.02358 | + | 11.6995i | 0.0445877 | + | 0.509640i | ||||
\(528\) | 0.580496 | − | 6.63510i | 0.0252628 | − | 0.288756i | ||||
\(529\) | −9.15641 | − | 1.61452i | −0.398105 | − | 0.0701966i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.7470i | 0.683360i | ||||||||
\(532\) | −15.8734 | + | 2.89448i | −0.688201 | + | 0.125491i | ||||
\(533\) | −12.0438 | − | 12.0438i | −0.521676 | − | 0.521676i | ||||
\(534\) | 5.85499 | − | 2.13104i | 0.253370 | − | 0.0922193i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.95677 | − | 1.64192i | 0.0845195 | − | 0.0709202i | ||||
\(537\) | 31.2174 | − | 2.73117i | 1.34713 | − | 0.117859i | ||||
\(538\) | 2.48769 | − | 3.55279i | 0.107252 | − | 0.153171i | ||||
\(539\) | −11.9813 | + | 6.91740i | −0.516071 | + | 0.297954i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.3020 | + | 5.20550i | 0.614891 | + | 0.223802i | 0.630642 | − | 0.776074i | \(-0.282792\pi\) |
−0.0157509 | + | 0.999876i | \(0.505014\pi\) | |||||||
\(542\) | 5.35555 | + | 11.4850i | 0.230040 | + | 0.493323i | ||||
\(543\) | −30.2999 | + | 8.11883i | −1.30029 | + | 0.348412i | ||||
\(544\) | −0.642788 | − | 1.11334i | −0.0275593 | − | 0.0477341i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.7738 | − | 19.9902i | 0.717852 | − | 0.855502i | ||||
\(547\) | −39.2080 | − | 3.43025i | −1.67641 | − | 0.146667i | −0.791107 | − | 0.611678i | \(-0.790495\pi\) |
−0.885305 | + | 0.465011i | \(0.846050\pi\) | |||||||
\(548\) | −12.3992 | + | 8.68205i | −0.529670 | + | 0.370879i | ||||
\(549\) | 28.5275 | + | 78.3787i | 1.21753 | + | 3.34512i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.5330 | − | 28.2452i | 0.832135 | − | 1.20329i | ||||
\(552\) | 8.44575 | − | 8.44575i | 0.359475 | − | 0.359475i | ||||
\(553\) | 3.47675 | − | 7.45591i | 0.147846 | − | 0.317057i | ||||
\(554\) | 0.388249 | − | 2.20187i | 0.0164951 | − | 0.0935484i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.9342 | + | 14.2095i | 0.718171 | + | 0.602617i | ||||
\(557\) | −8.14183 | − | 5.70097i | −0.344980 | − | 0.241558i | 0.388226 | − | 0.921564i | \(-0.373088\pi\) |
−0.733206 | + | 0.680007i | \(0.761977\pi\) | |||||||
\(558\) | −17.5238 | + | 65.3996i | −0.741840 | + | 2.76859i | ||||
\(559\) | −10.8648 | + | 18.8184i | −0.459532 | + | 0.795932i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.92855 | − | 8.04612i | 0.123643 | − | 0.339707i | ||||
\(562\) | −2.46603 | − | 9.20335i | −0.104023 | − | 0.388220i | ||||
\(563\) | 15.4508 | + | 4.14004i | 0.651175 | + | 0.174482i | 0.569260 | − | 0.822157i | \(-0.307230\pi\) |
0.0819150 | + | 0.996639i | \(0.473896\pi\) | |||||||
\(564\) | 5.45567 | + | 30.9406i | 0.229725 | + | 1.30284i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.1202 | − | 20.4031i | −0.719616 | − | 0.857605i | ||||
\(567\) | 50.3101 | + | 71.8502i | 2.11282 | + | 3.01743i | ||||
\(568\) | −3.57016 | − | 1.66479i | −0.149800 | − | 0.0698531i | ||||
\(569\) | −11.5163 | −0.482789 | −0.241395 | − | 0.970427i | \(-0.577605\pi\) | ||||
−0.241395 | + | 0.970427i | \(0.577605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.4593 | −1.86057 | −0.930283 | − | 0.366843i | \(-0.880439\pi\) | ||||
−0.930283 | + | 0.366843i | \(0.880439\pi\) | |||||||
\(572\) | −4.08727 | − | 1.90592i | −0.170897 | − | 0.0796907i | ||||
\(573\) | −29.1436 | − | 41.6213i | −1.21749 | − | 1.73876i | ||||
\(574\) | 18.5496 | + | 22.1065i | 0.774245 | + | 0.922709i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.28699 | − | 7.29888i | −0.0536245 | − | 0.304120i | ||||
\(577\) | 14.9109 | + | 3.99535i | 0.620747 | + | 0.166329i | 0.555467 | − | 0.831538i | \(-0.312539\pi\) |
0.0652797 | + | 0.997867i | \(0.479206\pi\) | |||||||
\(578\) | 3.97217 | + | 14.8243i | 0.165221 | + | 0.616612i | ||||
\(579\) | 10.6149 | − | 29.1643i | 0.441142 | − | 1.21203i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.2913 | + | 45.5379i | −1.09075 | + | 1.88923i | ||||
\(582\) | 4.29498 | − | 16.0291i | 0.178032 | − | 0.664426i | ||||
\(583\) | −15.3641 | − | 10.7580i | −0.636315 | − | 0.445553i | ||||
\(584\) | −4.05801 | − | 3.40508i | −0.167922 | − | 0.140903i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.10055 | + | 6.24152i | −0.0454632 | + | 0.257835i | ||||
\(587\) | −1.14200 | + | 2.44904i | −0.0471356 | + | 0.101083i | −0.928465 | − | 0.371419i | \(-0.878871\pi\) |
0.881330 | + | 0.472502i | \(0.156649\pi\) | |||||||
\(588\) | −15.2921 | + | 15.2921i | −0.630636 | + | 0.630636i | ||||
\(589\) | −10.5304 | − | 38.4026i | −0.433897 | − | 1.58235i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.24763 | + | 3.42782i | 0.0513205 | + | 0.141002i | ||||
\(592\) | −5.68783 | + | 3.98266i | −0.233769 | + | 0.163686i | ||||
\(593\) | −8.26288 | − | 0.722909i | −0.339316 | − | 0.0296863i | −0.0837754 | − | 0.996485i | \(-0.526698\pi\) |
−0.255540 | + | 0.966798i | \(0.582253\pi\) | |||||||
\(594\) | 18.8866 | − | 22.5082i | 0.774928 | − | 0.923523i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.66772 | − | 13.2809i | −0.314082 | − | 0.544006i | ||||
\(597\) | 12.2004 | − | 3.26908i | 0.499327 | − | 0.133794i | ||||
\(598\) | −3.41787 | − | 7.32965i | −0.139767 | − | 0.299732i | ||||
\(599\) | −0.193064 | − | 0.0702697i | −0.00788840 | − | 0.00287114i | 0.338073 | − | 0.941120i | \(-0.390225\pi\) |
−0.345961 | + | 0.938249i | \(0.612447\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.44175 | + | 0.832396i | −0.0588103 | + | 0.0339541i | −0.529117 | − | 0.848549i | \(-0.677477\pi\) |
0.470307 | + | 0.882503i | \(0.344143\pi\) | |||||||
\(602\) | 21.1169 | − | 30.1580i | 0.860659 | − | 1.22915i | ||||
\(603\) | 18.8597 | − | 1.65001i | 0.768025 | − | 0.0671935i | ||||
\(604\) | 4.84916 | − | 4.06893i | 0.197309 | − | 0.165562i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 17.5881 | − | 6.40155i | 0.714468 | − | 0.260045i | ||||
\(607\) | −14.3272 | − | 14.3272i | −0.581524 | − | 0.581524i | 0.353798 | − | 0.935322i | \(-0.384890\pi\) |
−0.935322 | + | 0.353798i | \(0.884890\pi\) | |||||||
\(608\) | 2.82127 | + | 3.32271i | 0.114418 | + | 0.134754i | ||||
\(609\) | − | 94.1011i | − | 3.81317i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.9500 | + | 3.69404i | 0.847545 | + | 0.149445i | ||||
\(612\) | 0.830421 | − | 9.49175i | 0.0335678 | − | 0.383681i | ||||
\(613\) | −2.18465 | − | 24.9707i | −0.0882373 | − | 1.00856i | −0.903250 | − | 0.429114i | \(-0.858826\pi\) |
0.815013 | − | 0.579443i | \(-0.196730\pi\) | |||||||
\(614\) | −8.85829 | + | 1.56196i | −0.357492 | + | 0.0630354i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.61721 | + | 3.82045i | 0.266615 | + | 0.153930i | ||||
\(617\) | 5.24969 | − | 2.44797i | 0.211345 | − | 0.0985516i | −0.314063 | − | 0.949402i | \(-0.601690\pi\) |
0.525408 | + | 0.850850i | \(0.323913\pi\) | |||||||
\(618\) | −5.99387 | + | 2.79499i | −0.241109 | + | 0.112431i | ||||
\(619\) | −26.0474 | − | 15.0385i | −1.04693 | − | 0.604448i | −0.125145 | − | 0.992138i | \(-0.539940\pi\) |
−0.921790 | + | 0.387691i | \(0.873273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 51.8906 | − | 9.14971i | 2.08230 | − | 0.367165i | ||||
\(622\) | 0.867988 | + | 9.92115i | 0.0348031 | + | 0.397802i | ||||
\(623\) | −0.622985 | + | 7.12076i | −0.0249594 | + | 0.285287i | ||||
\(624\) | −6.94253 | − | 1.22416i | −0.277924 | − | 0.0490054i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 22.0297i | − | 0.880486i | ||||||
\(627\) | −4.87455 | + | 28.6201i | −0.194671 | + | 1.14297i | ||||
\(628\) | 2.48053 | + | 2.48053i | 0.0989840 | + | 0.0989840i | ||||
\(629\) | −8.38814 | + | 3.05303i | −0.334457 | + | 0.121732i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.77584 | + | 6.52471i | −0.309551 | + | 0.259745i | −0.784307 | − | 0.620373i | \(-0.786981\pi\) |
0.474755 | + | 0.880118i | \(0.342537\pi\) | |||||||
\(632\) | −2.21397 | + | 0.193697i | −0.0880670 | + | 0.00770486i | ||||
\(633\) | 18.0206 | − | 25.7361i | 0.716254 | − | 1.02292i | ||||
\(634\) | 23.0374 | − | 13.3007i | 0.914933 | − | 0.528237i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −27.5510 | − | 10.0277i | −1.09247 | − | 0.397626i | ||||
\(637\) | 6.18849 | + | 13.2713i | 0.245197 | + | 0.525826i | ||||
\(638\) | −15.7084 | + | 4.20906i | −0.621902 | + | 0.166638i | ||||
\(639\) | −14.5978 | − | 25.2841i | −0.577478 | − | 1.00022i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.5903 | + | 13.8128i | −0.457791 | + | 0.545574i | −0.944725 | − | 0.327865i | \(-0.893671\pi\) |
0.486934 | + | 0.873439i | \(0.338115\pi\) | |||||||
\(642\) | 48.0346 | + | 4.20249i | 1.89578 | + | 0.165859i | ||||
\(643\) | −16.3163 | + | 11.4248i | −0.643450 | + | 0.450549i | −0.849211 | − | 0.528054i | \(-0.822922\pi\) |
0.205761 | + | 0.978602i | \(0.434033\pi\) | |||||||
\(644\) | 4.68647 | + | 12.8760i | 0.184673 | + | 0.507385i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.39780 | + | 5.06477i | 0.0943403 | + | 0.199271i | ||||
\(647\) | 2.68415 | − | 2.68415i | 0.105525 | − | 0.105525i | −0.652373 | − | 0.757898i | \(-0.726226\pi\) |
0.757898 | + | 0.652373i | \(0.226226\pi\) | |||||||
\(648\) | 10.0142 | − | 21.4754i | 0.393393 | − | 0.843635i | ||||
\(649\) | −0.761570 | + | 4.31908i | −0.0298942 | + | 0.169539i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −83.5861 | − | 70.1371i | −3.27600 | − | 2.74889i | ||||
\(652\) | 11.5811 | + | 8.10915i | 0.453550 | + | 0.317579i | ||||
\(653\) | 6.33751 | − | 23.6519i | 0.248006 | − | 0.925571i | −0.723843 | − | 0.689965i | \(-0.757626\pi\) |
0.971849 | − | 0.235606i | \(-0.0757075\pi\) | |||||||
\(654\) | 15.7958 | − | 27.3592i | 0.617667 | − | 1.06983i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.66637 | − | 7.32580i | 0.104104 | − | 0.286025i | ||||
\(657\) | −10.1616 | − | 37.9235i | −0.396440 | − | 1.47953i | ||||
\(658\) | −34.8147 | − | 9.32857i | −1.35722 | − | 0.363665i | ||||
\(659\) | 2.20718 | + | 12.5175i | 0.0859795 | + | 0.487614i | 0.997141 | + | 0.0755645i | \(0.0240759\pi\) |
−0.911161 | + | 0.412050i | \(0.864813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.46229 | + | 11.2767i | 0.368040 | + | 0.438613i | 0.918002 | − | 0.396577i | \(-0.129802\pi\) |
−0.549961 | + | 0.835190i | \(0.685358\pi\) | |||||||
\(662\) | −15.0345 | − | 21.4715i | −0.584332 | − | 0.834513i | ||||
\(663\) | −8.21371 | − | 3.83012i | −0.318994 | − | 0.148749i | ||||
\(664\) | 14.2051 | 0.551266 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −51.4620 | −1.99411 | ||||||||
\(667\) | −26.4311 | − | 12.3250i | −1.02341 | − | 0.477226i | ||||
\(668\) | −2.52588 | − | 3.60733i | −0.0977291 | − | 0.139572i | ||||
\(669\) | −6.53466 | − | 7.78770i | −0.252645 | − | 0.301090i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.03390 | + | 22.8774i | 0.155727 | + | 0.883172i | ||||
\(672\) | 11.5371 | + | 3.09136i | 0.445054 | + | 0.119252i | ||||
\(673\) | −5.05413 | − | 18.8623i | −0.194822 | − | 0.727087i | −0.992313 | − | 0.123755i | \(-0.960506\pi\) |
0.797491 | − | 0.603331i | \(-0.206160\pi\) | |||||||
\(674\) | 8.17161 | − | 22.4513i | 0.314759 | − | 0.864792i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.11334 | − | 7.12452i | 0.158205 | − | 0.274020i | ||||
\(677\) | −0.0241410 | + | 0.0900954i | −0.000927814 | + | 0.00346265i | −0.966388 | − | 0.257087i | \(-0.917237\pi\) |
0.965460 | + | 0.260550i | \(0.0839039\pi\) | |||||||
\(678\) | −26.6215 | − | 18.6406i | −1.02239 | − | 0.715887i | ||||
\(679\) | 14.5834 | + | 12.2369i | 0.559661 | + | 0.469611i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.684488 | − | 3.88192i | 0.0262296 | − | 0.148756i | ||||
\(682\) | −7.96934 | + | 17.0903i | −0.305162 | + | 0.654421i | ||||
\(683\) | 16.0864 | − | 16.0864i | 0.615529 | − | 0.615529i | −0.328852 | − | 0.944381i | \(-0.606662\pi\) |
0.944381 | + | 0.328852i | \(0.106662\pi\) | |||||||
\(684\) | 3.00330 | + | 32.1660i | 0.114834 | + | 1.22990i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.376859 | + | 1.03541i | 0.0143885 | + | 0.0395322i | ||||
\(687\) | 61.4119 | − | 43.0011i | 2.34301 | − | 1.64059i | ||||
\(688\) | −9.90798 | − | 0.866836i | −0.377738 | − | 0.0330478i | ||||
\(689\) | −12.7606 | + | 15.2075i | −0.486142 | + | 0.579361i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.42989 | − | 9.40485i | −0.206563 | − | 0.357777i | 0.744067 | − | 0.668105i | \(-0.232894\pi\) |
−0.950630 | + | 0.310328i | \(0.899561\pi\) | |||||||
\(692\) | −21.9222 | + | 5.87403i | −0.833357 | + | 0.223297i | ||||
\(693\) | 23.9330 | + | 51.3245i | 0.909140 | + | 1.94966i | ||||
\(694\) | −11.1875 | − | 4.07192i | −0.424672 | − | 0.154568i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −22.0155 | + | 12.7106i | −0.834495 | + | 0.481796i | ||||
\(697\) | 5.74855 | − | 8.20978i | 0.217742 | − | 0.310968i | ||||
\(698\) | 15.7038 | − | 1.37391i | 0.594399 | − | 0.0520032i | ||||
\(699\) | −10.4241 | + | 8.74685i | −0.394275 | + | 0.330836i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.1386 | − | 7.32986i | 0.760625 | − | 0.276845i | 0.0675556 | − | 0.997716i | \(-0.478480\pi\) |
0.693070 | + | 0.720871i | \(0.256258\pi\) | |||||||
\(702\) | −21.9905 | − | 21.9905i | −0.829978 | − | 0.829978i | ||||
\(703\) | 26.1227 | − | 15.2858i | 0.985235 | − | 0.576513i | ||||
\(704\) | − | 2.06418i | − | 0.0777966i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.3648 | − | 2.18025i | −0.465357 | − | 0.0820550i | ||||
\(707\) | −1.87142 | + | 21.3904i | −0.0703819 | + | 0.804469i | ||||
\(708\) | 0.597509 | + | 6.82956i | 0.0224558 | + | 0.256671i | ||||
\(709\) | −6.98551 | + | 1.23173i | −0.262346 | + | 0.0462587i | −0.303274 | − | 0.952903i | \(-0.598080\pi\) |
0.0409277 | + | 0.999162i | \(0.486969\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.2647 | − | 8.23573i | −0.534968 | − | 0.308864i | ||||
\(712\) | 1.75009 | − | 0.816080i | 0.0655874 | − | 0.0305839i | ||||
\(713\) | −30.6478 | + | 14.2913i | −1.14777 | + | 0.535214i | ||||
\(714\) | 13.2979 | + | 7.67752i | 0.497660 | + | 0.287324i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.56418 | − | 1.68642i | 0.357430 | − | 0.0630246i | ||||
\(717\) | 7.19445 | + | 82.2330i | 0.268682 | + | 3.07105i | ||||
\(718\) | 1.42849 | − | 16.3277i | 0.0533109 | − | 0.609346i | ||||
\(719\) | 29.8553 | + | 5.26429i | 1.11341 | + | 0.196325i | 0.699947 | − | 0.714194i | \(-0.253207\pi\) |
0.413466 | + | 0.910519i | \(0.364318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 7.58705i | − | 0.282556i | ||||||
\(722\) | −11.0788 | − | 15.4357i | −0.412309 | − | 0.574458i | ||||
\(723\) | −40.5679 | − | 40.5679i | −1.50874 | − | 1.50874i | ||||
\(724\) | −9.13538 | + | 3.32501i | −0.339514 | + | 0.123573i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −16.6578 | + | 13.9775i | −0.618227 | + | 0.518754i | ||||
\(727\) | −29.1194 | + | 2.54762i | −1.07998 | + | 0.0944860i | −0.613231 | − | 0.789904i | \(-0.710130\pi\) |
−0.466749 | + | 0.884390i | \(0.654575\pi\) | |||||||
\(728\) | 4.63873 | − | 6.62479i | 0.171923 | − | 0.245531i | ||||
\(729\) | 32.7608 | − | 18.9145i | 1.21336 | − | 0.700536i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0150 | − | 4.37311i | −0.444391 | − | 0.161745i | ||||
\(732\) | 15.3466 | + | 32.9109i | 0.567227 | + | 1.21642i | ||||
\(733\) | 47.5677 | − | 12.7457i | 1.75695 | − | 0.470774i | 0.770864 | − | 0.636999i | \(-0.219825\pi\) |
0.986088 | + | 0.166225i | \(0.0531579\pi\) | |||||||
\(734\) | −10.2071 | − | 17.6792i | −0.376750 | − | 0.652550i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.37939 | − | 2.83564i | 0.0877053 | − | 0.104523i | ||||
\(737\) | 5.25263 | + | 0.459545i | 0.193483 | + | 0.0169276i | ||||
\(738\) | 47.3302 | − | 33.1410i | 1.74225 | − | 1.21994i | ||||
\(739\) | 8.11338 | + | 22.2913i | 0.298455 | + | 0.820000i | 0.994759 | + | 0.102252i | \(0.0326047\pi\) |
−0.696303 | + | 0.717748i | \(0.745173\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.7275 | + | 7.77990i | 1.09207 | + | 0.285802i | ||||
\(742\) | 23.7836 | − | 23.7836i | 0.873123 | − | 0.873123i | ||||
\(743\) | 13.1579 | − | 28.2173i | 0.482718 | − | 1.03519i | −0.502609 | − | 0.864514i | \(-0.667626\pi\) |
0.985327 | − | 0.170678i | \(-0.0545959\pi\) | |||||||
\(744\) | −5.11862 | + | 29.0292i | −0.187658 | + | 1.06426i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.2310 | + | 22.0104i | 0.960386 | + | 0.805859i | ||||
\(747\) | 86.2411 | + | 60.3867i | 3.15540 | + | 2.20943i | ||||
\(748\) | 0.686817 | − | 2.56323i | 0.0251125 | − | 0.0937211i | ||||
\(749\) | −27.6580 | + | 47.9051i | −1.01060 | + | 1.75042i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.79339 | − | 4.92729i | 0.0654416 | − | 0.179799i | −0.902662 | − | 0.430351i | \(-0.858390\pi\) |
0.968103 | + | 0.250552i | \(0.0806120\pi\) | |||||||
\(752\) | 2.52010 | + | 9.40514i | 0.0918986 | + | 0.342970i | ||||
\(753\) | −40.9787 | − | 10.9802i | −1.49335 | − | 0.400141i | ||||
\(754\) | 2.98897 | + | 16.9513i | 0.108852 | + | 0.617330i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 33.8692 | + | 40.3637i | 1.23181 | + | 1.46801i | ||||
\(757\) | −13.6281 | − | 19.4630i | −0.495323 | − | 0.707395i | 0.491194 | − | 0.871050i | \(-0.336561\pi\) |
−0.986518 | + | 0.163655i | \(0.947672\pi\) | |||||||
\(758\) | 29.9676 | + | 13.9741i | 1.08847 | + | 0.507564i | ||||
\(759\) | 24.6547 | 0.894910 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.7347 | −1.15038 | −0.575191 | − | 0.818019i | \(-0.695072\pi\) | ||||
−0.575191 | + | 0.818019i | \(0.695072\pi\) | |||||||
\(762\) | 9.76608 | + | 4.55400i | 0.353788 | + | 0.164974i | ||||
\(763\) | 20.7877 | + | 29.6878i | 0.752563 | + | 1.07477i | ||||
\(764\) | −10.1219 | − | 12.0628i | −0.366198 | − | 0.436418i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.69459 | − | 15.2818i | −0.0973596 | − | 0.552154i | ||||
\(767\) | 4.48380 | + | 1.20143i | 0.161901 | + | 0.0433812i | ||||
\(768\) | −0.835127 | − | 3.11674i | −0.0301350 | − | 0.112465i | ||||
\(769\) | 8.86948 | − | 24.3687i | 0.319842 | − | 0.878758i | −0.670722 | − | 0.741708i | \(-0.734016\pi\) |
0.990564 | − | 0.137050i | \(-0.0437620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.0410 | + | 36.4441i | −0.757774 | + | 1.31250i | ||||
\(772\) | 2.48947 | − | 9.29081i | 0.0895978 | − | 0.334384i | ||||
\(773\) | 24.6447 | + | 17.2564i | 0.886409 | + | 0.620670i | 0.925576 | − | 0.378562i | \(-0.123581\pi\) |
−0.0391668 | + | 0.999233i | \(0.512470\pi\) | |||||||
\(774\) | −56.4676 | − | 47.3820i | −2.02969 | − | 1.70311i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.893056 | − | 5.06477i | 0.0320588 | − | 0.181815i | ||||
\(777\) | 35.0497 | − | 75.1643i | 1.25740 | − | 2.69650i | ||||
\(778\) | −8.58633 | + | 8.58633i | −0.307835 | + | 0.307835i | ||||
\(779\) | −14.1815 | + | 30.8812i | −0.508103 | + | 1.10643i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.78106 | − | 7.64090i | −0.0995141 | − | 0.273413i | ||||
\(782\) | 3.89816 | − | 2.72952i | 0.139398 | − | 0.0976074i | ||||
\(783\) | −111.719 | − | 9.77411i | −3.99250 | − | 0.349298i | ||||
\(784\) | −4.30818 | + | 5.13429i | −0.153863 | + | 0.183367i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 28.7986 | + | 49.8806i | 1.02721 | + | 1.77918i | ||||
\(787\) | 24.0457 | − | 6.44302i | 0.857136 | − | 0.229669i | 0.196619 | − | 0.980480i | \(-0.437004\pi\) |
0.660517 | + | 0.750811i | \(0.270337\pi\) | |||||||
\(788\) | 0.477777 | + | 1.02460i | 0.0170201 | + | 0.0364997i | ||||
\(789\) | 19.1670 | + | 6.97620i | 0.682362 | + | 0.248359i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.2879 | − | 18.6414i | 1.14803 | − | 0.662813i | ||||
\(792\) | 8.77492 | − | 12.5319i | 0.311803 | − | 0.445301i | ||||
\(793\) | 24.4941 | − | 2.14296i | 0.869812 | − | 0.0760987i | ||||
\(794\) | 10.2533 | − | 8.60354i | 0.363876 | − | 0.305328i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.67840 | − | 1.33883i | 0.130377 | − | 0.0474535i | ||||
\(797\) | 9.13482 | + | 9.13482i | 0.323572 | + | 0.323572i | 0.850136 | − | 0.526564i | \(-0.176520\pi\) |
−0.526564 | + | 0.850136i | \(0.676520\pi\) | |||||||
\(798\) | −49.0264 | − | 17.5210i | −1.73551 | − | 0.620236i | ||||
\(799\) | 12.5175i | 0.442839i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.0942 | + | 2.48519i | 0.497994 | + | 0.0878098i | ||||
\(802\) | −1.39268 | + | 15.9184i | −0.0491773 | + | 0.562100i | ||||
\(803\) | −0.953021 | − | 10.8931i | −0.0336314 | − | 0.384409i | ||||
\(804\) | 8.11695 | − | 1.43124i | 0.286263 | − | 0.0504758i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.2849 | + | 9.97946i | 0.608836 | + | 0.351511i | ||||
\(807\) | 12.6834 | − | 5.91437i | 0.446477 | − | 0.208196i | ||||
\(808\) | 5.25718 | − | 2.45146i | 0.184947 | − | 0.0862422i | ||||
\(809\) | 38.0948 | + | 21.9941i | 1.33934 | + | 0.773270i | 0.986710 | − | 0.162491i | \(-0.0519529\pi\) |
0.352634 | + | 0.935762i | \(0.385286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.36025 | + | 1.12148i | −0.223339 | + | 0.0393806i | −0.284198 | − | 0.958766i | \(-0.591727\pi\) |
0.0608589 | + | 0.998146i | \(0.480616\pi\) | |||||||
\(812\) | −2.54176 | − | 29.0525i | −0.0891983 | − | 1.01954i | ||||
\(813\) | −3.56375 | + | 40.7339i | −0.124986 | + | 1.42860i | ||||
\(814\) | −14.1150 | − | 2.48886i | −0.494731 | − | 0.0872343i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 4.14814i | − | 0.145214i | ||||||
\(817\) | 42.7374 | + | 7.27901i | 1.49519 | + | 0.254660i | ||||
\(818\) | 7.06625 | + | 7.06625i | 0.247066 | + | 0.247066i | ||||
\(819\) | 56.3246 | − | 20.5005i | 1.96814 | − | 0.716344i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2690 | − | 16.1686i | 0.672494 | − | 0.564290i | −0.241308 | − | 0.970448i | \(-0.577577\pi\) |
0.913802 | + | 0.406159i | \(0.133132\pi\) | |||||||
\(822\) | −48.6554 | + | 4.25680i | −1.69705 | + | 0.148473i | ||||
\(823\) | −24.9100 | + | 35.5752i | −0.868309 | + | 1.24007i | 0.101163 | + | 0.994870i | \(0.467744\pi\) |
−0.969472 | + | 0.245203i | \(0.921145\pi\) | |||||||
\(824\) | −1.77503 | + | 1.02481i | −0.0618362 | + | 0.0357011i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.39053 | − | 2.68993i | −0.257149 | − | 0.0935947i | ||||
\(827\) | −6.55512 | − | 14.0575i | −0.227944 | − | 0.488827i | 0.758757 | − | 0.651374i | \(-0.225807\pi\) |
−0.986701 | + | 0.162547i | \(0.948029\pi\) | |||||||
\(828\) | 26.5000 | − | 7.10065i | 0.920938 | − | 0.246765i | ||||
\(829\) | 22.3718 | + | 38.7490i | 0.777003 | + | 1.34581i | 0.933662 | + | 0.358156i | \(0.116595\pi\) |
−0.156658 | + | 0.987653i | \(0.550072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.63728 | − | 5.52649i | 0.160865 | − | 0.191712i | ||||
\(832\) | −2.17648 | − | 0.190417i | −0.0754558 | − | 0.00660153i | ||||
\(833\) | −7.05810 | + | 4.94214i | −0.244549 | + | 0.171235i | ||||
\(834\) | 24.3960 | + | 67.0276i | 0.844766 | + | 2.32097i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.731896 | + | 8.96773i | −0.0253132 | + | 0.310155i | ||||
\(837\) | −91.9500 | + | 91.9500i | −3.17826 | + | 3.17826i | ||||
\(838\) | −9.14141 | + | 19.6038i | −0.315785 | + | 0.677203i | ||||
\(839\) | −9.72552 | + | 55.1562i | −0.335762 | + | 1.90420i | 0.0838127 | + | 0.996482i | \(0.473290\pi\) |
−0.419575 | + | 0.907721i | \(0.637821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.3332 | + | 21.2571i | 0.873559 | + | 0.733003i | ||||
\(842\) | 13.2164 | + | 9.25426i | 0.455469 | + | 0.318923i | ||||
\(843\) | 7.95709 | − | 29.6963i | 0.274057 | − | 1.02279i | ||||
\(844\) | 4.86846 | − | 8.43242i | 0.167579 | − | 0.290256i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −24.6819 | + | 67.8128i | −0.848580 | + | 2.33145i | ||||
\(847\) | −6.45654 | − | 24.0961i | −0.221849 | − | 0.827953i | ||||
\(848\) | −8.77685 | − | 2.35175i | −0.301398 | − | 0.0807594i | ||||
\(849\) | −14.9234 | − | 84.6348i | −0.512170 | − | 2.90466i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.5214 | − | 19.6895i | −0.566347 | − | 0.674946i | ||||
\(852\) | −7.29053 | − | 10.4120i | −0.249769 | − | 0.356708i | ||||
\(853\) | −0.171300 | − | 0.0798783i | −0.00586519 | − | 0.00273498i | 0.419683 | − | 0.907671i | \(-0.362141\pi\) |
−0.425549 | + | 0.904936i | \(0.639919\pi\) | |||||||
\(854\) | −41.6586 | −1.42553 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.9436 | 0.510760 | ||||||||
\(857\) | −22.1305 | − | 10.3196i | −0.755963 | − | 0.352511i | 0.00612819 | − | 0.999981i | \(-0.498049\pi\) |
−0.762091 | + | 0.647470i | \(0.775827\pi\) | |||||||
\(858\) | −8.34651 | − | 11.9200i | −0.284945 | − | 0.406944i | ||||
\(859\) | −21.5057 | − | 25.6295i | −0.733766 | − | 0.874469i | 0.262124 | − | 0.965034i | \(-0.415577\pi\) |
−0.995890 | + | 0.0905656i | \(0.971133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.1694 | + | 91.7010i | 0.551051 | + | 3.12516i | ||||
\(862\) | −0.304049 | − | 0.0814698i | −0.0103560 | − | 0.00277487i | ||||
\(863\) | −2.26824 | − | 8.46520i | −0.0772119 | − | 0.288159i | 0.916514 | − | 0.400003i | \(-0.130991\pi\) |
−0.993726 | + | 0.111844i | \(0.964324\pi\) | |||||||
\(864\) | 4.86846 | − | 13.3760i | 0.165628 | − | 0.455060i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.33868 | − | 5.78276i | 0.113453 | − | 0.196506i | ||||
\(867\) | −12.8169 | + | 47.8335i | −0.435286 | + | 1.62451i | ||||
\(868\) | −27.7006 | − | 19.3961i | −0.940218 | − | 0.658348i | ||||
\(869\) | −3.51422 | − | 2.94878i | −0.119212 | − | 0.100030i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.969093 | − | 5.49600i | 0.0328365 | − | 0.186225i | ||||
\(872\) | 4.13776 | − | 8.87345i | 0.140122 | − | 0.300493i | ||||
\(873\) | 26.9524 | − | 26.9524i | 0.912202 | − | 0.912202i | ||||
\(874\) | −11.3426 | + | 11.4757i | −0.383668 | + | 0.388170i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.84611 | − | 16.0621i | −0.197522 | − | 0.542687i | ||||
\(877\) | −21.0549 | + | 14.7428i | −0.710973 | + | 0.497829i | −0.872237 | − | 0.489083i | \(-0.837332\pi\) |
0.161265 | + | 0.986911i | \(0.448443\pi\) | |||||||
\(878\) | 16.7608 | + | 1.46638i | 0.565650 | + | 0.0494880i | ||||
\(879\) | −13.1450 | + | 15.6657i | −0.443371 | + | 0.528390i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.8097 | + | 32.5794i | 0.633716 | + | 1.09763i | 0.986786 | + | 0.162032i | \(0.0518047\pi\) |
−0.353069 | + | 0.935597i | \(0.614862\pi\) | |||||||
\(882\) | −47.9816 | + | 12.8566i | −1.61562 | + | 0.432905i | ||||
\(883\) | −19.7033 | − | 42.2538i | −0.663067 | − | 1.42195i | −0.893589 | − | 0.448886i | \(-0.851821\pi\) |
0.230522 | − | 0.973067i | \(-0.425957\pi\) | |||||||
\(884\) | −2.63933 | − | 0.960637i | −0.0887702 | − | 0.0323097i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.4944 | + | 16.4512i | −0.957287 | + | 0.552690i | ||||
\(887\) | −9.61244 | + | 13.7280i | −0.322754 | + | 0.460940i | −0.947439 | − | 0.319936i | \(-0.896338\pi\) |
0.624685 | + | 0.780877i | \(0.285227\pi\) | |||||||
\(888\) | −22.3194 | + | 1.95270i | −0.748990 | + | 0.0655282i | ||||
\(889\) | −9.46978 | + | 7.94609i | −0.317606 | + | 0.266503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 45.9620 | − | 16.7288i | 1.53979 | − | 0.560436i | ||||
\(892\) | −2.22784 | − | 2.22784i | −0.0745937 | − | 0.0745937i | ||||
\(893\) | −7.61367 | − | 41.7538i | −0.254782 | − | 1.39724i | ||||
\(894\) | − | 49.4826i | − | 1.65494i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.64543 | + | 0.642788i | 0.121785 | + | 0.0214740i | ||||
\(897\) | 2.27436 | − | 25.9961i | 0.0759387 | − | 0.867984i | ||||
\(898\) | 0.728063 | + | 8.32180i | 0.0242958 | + | 0.277702i | ||||
\(899\) | 70.8793 | − | 12.4979i | 2.36396 | − | 0.416830i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.1163 | − | 5.84067i | −0.337024 | − | 0.194581i | ||||
\(902\) | 14.5845 | − | 6.80087i | 0.485611 | − | 0.226444i | ||||
\(903\) | 107.664 | − | 50.2045i | 3.58283 | − | 1.67070i | ||||
\(904\) | −8.72254 | − | 5.03596i | −0.290107 | − | 0.167494i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.1150 | − | 3.54682i | 0.668276 | − | 0.117835i | ||||
\(907\) | −3.62075 | − | 41.3854i | −0.120225 | − | 1.37418i | −0.781439 | − | 0.623981i | \(-0.785514\pi\) |
0.661214 | − | 0.750197i | \(-0.270041\pi\) | |||||||
\(908\) | 0.106472 | − | 1.21698i | 0.00353340 | − | 0.0403869i | ||||
\(909\) | 42.3383 | + | 7.46538i | 1.40427 | + | 0.247611i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 23.1584i | − | 0.767273i | −0.923484 | − | 0.383636i | \(-0.874672\pi\) | ||
0.923484 | − | 0.383636i | \(-0.125328\pi\) | |||||||
\(912\) | 2.52307 | + | 13.8366i | 0.0835471 | + | 0.458176i | ||||
\(913\) | 20.7337 | + | 20.7337i | 0.686186 | + | 0.686186i | ||||
\(914\) | 10.5810 | − | 3.85117i | 0.349988 | − | 0.127385i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.7986 | − | 14.9348i | 0.588082 | − | 0.493460i | ||||
\(917\) | −65.8244 | + | 5.75889i | −2.17371 | + | 0.190175i | ||||
\(918\) | 10.4961 | − | 14.9900i | 0.346423 | − | 0.494744i | ||||
\(919\) | 22.4279 | − | 12.9488i | 0.739829 | − | 0.427141i | −0.0821778 | − | 0.996618i | \(-0.526188\pi\) |
0.822007 | + | 0.569477i | \(0.192854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.2735 | − | 9.92674i | −0.898692 | − | 0.327097i | ||||
\(922\) | 3.84739 | + | 8.25076i | 0.126707 | + | 0.271724i | ||||
\(923\) | −8.31315 | + | 2.22750i | −0.273631 | + | 0.0733191i | ||||
\(924\) | 12.3274 | + | 21.3516i | 0.405541 | + | 0.702417i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.45249 | + | 4.11451i | −0.113456 | + | 0.135211i | ||||
\(927\) | −15.1330 | − | 1.32396i | −0.497032 | − | 0.0434847i | ||||
\(928\) | −6.45366 | + | 4.51890i | −0.211852 | + | 0.148340i | ||||
\(929\) | −8.24476 | − | 22.6523i | −0.270502 | − | 0.743198i | −0.998348 | − | 0.0574572i | \(-0.981701\pi\) |
0.727846 | − | 0.685740i | \(-0.240521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.5371 | − | 20.7781i | 0.673078 | − | 0.680975i | ||||
\(932\) | −2.98204 | + | 2.98204i | −0.0976799 | + | 0.0976799i | ||||
\(933\) | −13.5807 | + | 29.1239i | −0.444612 | + | 0.953474i | ||||
\(934\) | −1.60981 | + | 9.12970i | −0.0526747 | + | 0.298733i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.4042 | − | 10.4084i | −0.405444 | − | 0.340208i | ||||
\(937\) | 6.30034 | + | 4.41154i | 0.205823 | + | 0.144119i | 0.671943 | − | 0.740602i | \(-0.265460\pi\) |
−0.466120 | + | 0.884721i | \(0.654349\pi\) | |||||||
\(938\) | −2.44725 | + | 9.13327i | −0.0799056 | + | 0.298212i | ||||
\(939\) | 35.5415 | − | 61.5596i | 1.15985 | − | 2.00892i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.80706 | − | 15.9548i | 0.189305 | − | 0.520110i | −0.808339 | − | 0.588717i | \(-0.799633\pi\) |
0.997644 | + | 0.0686069i | \(0.0218554\pi\) | |||||||
\(942\) | 2.92963 | + | 10.9335i | 0.0954524 | + | 0.356233i | ||||
\(943\) | 27.8747 | + | 7.46901i | 0.907726 | + | 0.243224i | ||||
\(944\) | 0.368946 | + | 2.09240i | 0.0120082 | + | 0.0681017i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.1964 | − | 15.7269i | −0.429052 | − | 0.511324i | ||||
\(947\) | 17.3490 | + | 24.7769i | 0.563765 | + | 0.805140i | 0.995288 | − | 0.0969618i | \(-0.0309125\pi\) |
−0.431523 | + | 0.902102i | \(0.642024\pi\) | |||||||
\(948\) | −6.49919 | − | 3.03062i | −0.211084 | − | 0.0984300i | ||||
\(949\) | −11.5736 | −0.375696 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 85.8340 | 2.78336 | ||||||||
\(952\) | 4.31291 | + | 2.01114i | 0.139782 | + | 0.0651815i | ||||
\(953\) | 30.1701 | + | 43.0873i | 0.977304 | + | 1.39573i | 0.917594 | + | 0.397519i | \(0.130129\pi\) |
0.0597101 | + | 0.998216i | \(0.480982\pi\) | |||||||
\(954\) | −43.2880 | − | 51.5886i | −1.40150 | − | 1.67024i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.44238 | + | 25.1940i | 0.143677 | + | 0.814832i | ||||
\(957\) | −50.6860 | − | 13.5813i | −1.63845 | − | 0.439021i | ||||
\(958\) | −3.65623 | − | 13.6452i | −0.118128 | − | 0.440858i | ||||
\(959\) | 19.1637 | − | 52.6519i | 0.618829 | − | 1.70022i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.2276 | − | 45.4276i | 0.846052 | − | 1.46541i | ||||
\(962\) | −3.92635 | + | 14.6533i | −0.126591 | + | 0.472442i | ||||
\(963\) | 90.7242 | + | 63.5258i | 2.92355 | + | 2.04709i | ||||
\(964\) | −13.6206 | − | 11.4290i | −0.438689 | − | 0.368104i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.67752 | + | 43.5414i | −0.247020 | + | 1.40092i | ||||
\(967\) | −1.38978 | + | 2.98039i | −0.0446923 | + | 0.0958430i | −0.927386 | − | 0.374106i | \(-0.877950\pi\) |
0.882694 | + | 0.469949i | \(0.155728\pi\) | |||||||
\(968\) | −4.76531 | + | 4.76531i | −0.153163 | + | 0.153163i | ||||
\(969\) | −1.47081 | + | 18.0214i | −0.0472492 | + | 0.578931i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.7426 | + | 32.2626i | 0.376839 | + | 1.03536i | 0.972659 | + | 0.232238i | \(0.0746050\pi\) |
−0.595820 | + | 0.803118i | \(0.703173\pi\) | |||||||
\(972\) | 27.6502 | − | 19.3609i | 0.886880 | − | 0.621000i | ||||
\(973\) | −81.5179 | − | 7.13189i | −2.61334 | − | 0.228638i | ||||
\(974\) | 2.61413 | − | 3.11540i | 0.0837622 | − | 0.0998239i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.62701 | + | 9.74627i | 0.180116 | + | 0.311970i | ||||
\(977\) | −15.4183 | + | 4.13133i | −0.493276 | + | 0.132173i | −0.496878 | − | 0.867821i | \(-0.665520\pi\) |
0.00360160 | + | 0.999994i | \(0.498854\pi\) | |||||||
\(978\) | 19.2792 | + | 41.3443i | 0.616480 | + | 1.32205i | ||||
\(979\) | 3.74557 | + | 1.36327i | 0.119709 | + | 0.0435704i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 62.8423 | − | 36.2820i | 2.00640 | − | 1.15840i | ||||
\(982\) | −1.61628 | + | 2.30829i | −0.0515775 | + | 0.0736603i | ||||
\(983\) | −30.3910 | + | 2.65887i | −0.969323 | + | 0.0848048i | −0.560807 | − | 0.827946i | \(-0.689509\pi\) |
−0.408516 | + | 0.912751i | \(0.633954\pi\) | |||||||
\(984\) | 19.2699 | − | 16.1694i | 0.614302 | − | 0.515461i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.51754 | + | 3.46410i | −0.303100 | + | 0.110319i | ||||
\(987\) | −82.2356 | − | 82.2356i | −2.61759 | − | 2.61759i | ||||
\(988\) | 9.38810 | + | 1.59897i | 0.298675 | + | 0.0508701i | ||||
\(989\) | − | 36.8161i | − | 1.17069i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.3307 | − | 2.87954i | −0.518761 | − | 0.0914716i | −0.0918638 | − | 0.995772i | \(-0.529282\pi\) |
−0.426898 | + | 0.904300i | \(0.640394\pi\) | |||||||
\(992\) | −0.796201 | + | 9.10062i | −0.0252794 | + | 0.288945i | ||||
\(993\) | −7.37139 | − | 84.2554i | −0.233924 | − | 2.67376i | ||||
\(994\) | 14.3602 | − | 2.53209i | 0.455478 | − | 0.0803130i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 39.6946 | + | 22.9177i | 1.25777 | + | 0.726176i | ||||
\(997\) | 27.3622 | − | 12.7592i | 0.866570 | − | 0.404088i | 0.0620919 | − | 0.998070i | \(-0.480223\pi\) |
0.804478 | + | 0.593982i | \(0.202445\pi\) | |||||||
\(998\) | 2.36003 | − | 1.10050i | 0.0747055 | − | 0.0348358i | ||||
\(999\) | −85.5959 | − | 49.4188i | −2.70813 | − | 1.56354i |
(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 | 950.2.bb.a.793.2 | yes | 24 | |
5.2 | odd | 4 | inner | 950.2.bb.a.907.1 | yes | 24 | |
5.3 | odd | 4 | inner | 950.2.bb.a.907.2 | yes | 24 | |
5.4 | even | 2 | inner | 950.2.bb.a.793.1 | yes | 24 | |
19.15 | odd | 18 | inner | 950.2.bb.a.243.1 | ✓ | 24 | |
95.34 | odd | 18 | inner | 950.2.bb.a.243.2 | yes | 24 | |
95.53 | even | 36 | inner | 950.2.bb.a.357.1 | yes | 24 | |
95.72 | even | 36 | inner | 950.2.bb.a.357.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.bb.a.243.1 | ✓ | 24 | 19.15 | odd | 18 | inner | |
950.2.bb.a.243.2 | yes | 24 | 95.34 | odd | 18 | inner | |
950.2.bb.a.357.1 | yes | 24 | 95.53 | even | 36 | inner | |
950.2.bb.a.357.2 | yes | 24 | 95.72 | even | 36 | inner | |
950.2.bb.a.793.1 | yes | 24 | 5.4 | even | 2 | inner | |
950.2.bb.a.793.2 | yes | 24 | 1.1 | even | 1 | trivial | |
950.2.bb.a.907.1 | yes | 24 | 5.2 | odd | 4 | inner | |
950.2.bb.a.907.2 | yes | 24 | 5.3 | odd | 4 | inner |