Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (of order \(6\), degree \(2\), not 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.7 | ||
Root | \(0.599547 + 0.346149i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.79 |
Dual form | 1470.2.n.k.949.7 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.0918501 | − | 2.23418i | −0.0410766 | − | 0.999156i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.03755 | − | 1.98078i | 0.328101 | − | 0.626378i | ||||
\(11\) | −0.489528 | − | 0.847888i | −0.147598 | − | 0.255648i | 0.782741 | − | 0.622348i | \(-0.213821\pi\) |
−0.930339 | + | 0.366700i | \(0.880488\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 0.435157i | 0.120691i | 0.998178 | + | 0.0603455i | \(0.0192202\pi\) | ||||
−0.998178 | + | 0.0603455i | \(0.980780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.19663 | − | 1.88893i | −0.308970 | − | 0.487720i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.42384 | − | 1.39940i | 0.587867 | − | 0.339405i | −0.176386 | − | 0.984321i | \(-0.556441\pi\) |
0.764254 | + | 0.644916i | \(0.223108\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 3.67135 | − | 6.35897i | 0.842266 | − | 1.45885i | −0.0457080 | − | 0.998955i | \(-0.514554\pi\) |
0.887974 | − | 0.459893i | \(-0.152112\pi\) | |||||||
\(20\) | 1.88893 | − | 1.19663i | 0.422378 | − | 0.267576i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.979056i | − | 0.208735i | ||||||
\(23\) | 2.89487 | + | 1.67135i | 0.603622 | + | 0.348501i | 0.770465 | − | 0.637482i | \(-0.220024\pi\) |
−0.166843 | + | 0.985983i | \(0.553357\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −4.98313 | + | 0.410420i | −0.996625 | + | 0.0820839i | ||||
\(26\) | −0.217579 | + | 0.376857i | −0.0426707 | + | 0.0739078i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.74825 | −0.696032 | −0.348016 | − | 0.937489i | \(-0.613144\pi\) | ||||
−0.348016 | + | 0.937489i | \(0.613144\pi\) | |||||||
\(30\) | −0.0918501 | − | 2.23418i | −0.0167695 | − | 0.407904i | ||||
\(31\) | −2.48953 | − | 4.31199i | −0.447132 | − | 0.774456i | 0.551066 | − | 0.834462i | \(-0.314221\pi\) |
−0.998198 | + | 0.0600058i | \(0.980888\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −0.847888 | − | 0.489528i | −0.147598 | − | 0.0852159i | ||||
\(34\) | 2.79881 | 0.479992 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.01482 | + | 2.31796i | 0.660032 | + | 0.381069i | 0.792289 | − | 0.610146i | \(-0.208889\pi\) |
−0.132257 | + | 0.991215i | \(0.542223\pi\) | |||||||
\(38\) | 6.35897 | − | 3.67135i | 1.03156 | − | 0.595572i | ||||
\(39\) | 0.217579 | + | 0.376857i | 0.0348405 | + | 0.0603455i | ||||
\(40\) | 2.23418 | − | 0.0918501i | 0.353255 | − | 0.0145228i | ||||
\(41\) | 4.94944 | 0.772972 | 0.386486 | − | 0.922295i | \(-0.373689\pi\) | ||||
0.386486 | + | 0.922295i | \(0.373689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.97862i | − | 1.52172i | −0.648913 | − | 0.760862i | \(-0.724776\pi\) | ||
0.648913 | − | 0.760862i | \(-0.275224\pi\) | |||||||
\(44\) | 0.489528 | − | 0.847888i | 0.0737991 | − | 0.127824i | ||||
\(45\) | −1.98078 | − | 1.03755i | −0.295278 | − | 0.154668i | ||||
\(46\) | 1.67135 | + | 2.89487i | 0.246428 | + | 0.426825i | ||||
\(47\) | 3.81531 | + | 2.20277i | 0.556520 | + | 0.321307i | 0.751748 | − | 0.659451i | \(-0.229211\pi\) |
−0.195228 | + | 0.980758i | \(0.562545\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.52072 | − | 2.13613i | −0.639327 | − | 0.302094i | ||||
\(51\) | 1.39940 | − | 2.42384i | 0.195956 | − | 0.339405i | ||||
\(52\) | −0.376857 | + | 0.217579i | −0.0522607 | + | 0.0301727i | ||||
\(53\) | 0.569232 | − | 0.328646i | 0.0781901 | − | 0.0451431i | −0.460395 | − | 0.887714i | \(-0.652292\pi\) |
0.538585 | + | 0.842571i | \(0.318959\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −1.84937 | + | 1.17157i | −0.249369 | + | 0.157975i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.34271i | − | 0.972565i | ||||||
\(58\) | −3.24608 | − | 1.87412i | −0.426231 | − | 0.246084i | ||||
\(59\) | 4.13613 | + | 7.16399i | 0.538478 | + | 0.932672i | 0.998986 | + | 0.0450161i | \(0.0143339\pi\) |
−0.460508 | + | 0.887656i | \(0.652333\pi\) | |||||||
\(60\) | 1.03755 | − | 1.98078i | 0.133947 | − | 0.255718i | ||||
\(61\) | 5.66680 | − | 9.81518i | 0.725559 | − | 1.25670i | −0.233185 | − | 0.972432i | \(-0.574915\pi\) |
0.958744 | − | 0.284272i | \(-0.0917520\pi\) | |||||||
\(62\) | − | 4.97906i | − | 0.632341i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.972220 | − | 0.0399693i | 0.120589 | − | 0.00495758i | ||||
\(66\) | −0.489528 | − | 0.847888i | −0.0602567 | − | 0.104368i | ||||
\(67\) | −2.04698 | + | 1.18183i | −0.250079 | + | 0.144383i | −0.619800 | − | 0.784760i | \(-0.712786\pi\) |
0.369722 | + | 0.929143i | \(0.379453\pi\) | |||||||
\(68\) | 2.42384 | + | 1.39940i | 0.293934 | + | 0.169703i | ||||
\(69\) | 3.34271 | 0.402415 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1119 | −1.67477 | −0.837387 | − | 0.546610i | \(-0.815918\pi\) | ||||
−0.837387 | + | 0.546610i | \(0.815918\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −13.3306 | + | 7.69642i | −1.56023 | + | 0.900797i | −0.562993 | + | 0.826461i | \(0.690350\pi\) |
−0.997233 | + | 0.0743360i | \(0.976316\pi\) | |||||||
\(74\) | 2.31796 | + | 4.01482i | 0.269457 | + | 0.466713i | ||||
\(75\) | −4.11030 | + | 2.84700i | −0.474617 | + | 0.328743i | ||||
\(76\) | 7.34271 | 0.842266 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.435157i | 0.0492719i | ||||||||
\(79\) | −1.44383 | + | 2.50079i | −0.162444 | + | 0.281361i | −0.935745 | − | 0.352678i | \(-0.885271\pi\) |
0.773301 | + | 0.634039i | \(0.218604\pi\) | |||||||
\(80\) | 1.98078 | + | 1.03755i | 0.221458 | + | 0.116001i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.28634 | + | 2.47472i | 0.473347 | + | 0.273287i | ||||
\(83\) | 14.3842i | 1.57887i | 0.613837 | + | 0.789433i | \(0.289625\pi\) | ||||
−0.613837 | + | 0.789433i | \(0.710375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.34915 | − | 5.28676i | −0.363266 | − | 0.573430i | ||||
\(86\) | 4.98931 | − | 8.64174i | 0.538011 | − | 0.931862i | ||||
\(87\) | −3.24608 | + | 1.87412i | −0.348016 | + | 0.200927i | ||||
\(88\) | 0.847888 | − | 0.489528i | 0.0903851 | − | 0.0521839i | ||||
\(89\) | 5.06051 | − | 8.76505i | 0.536412 | − | 0.929094i | −0.462681 | − | 0.886525i | \(-0.653112\pi\) |
0.999094 | − | 0.0425688i | \(-0.0135542\pi\) | |||||||
\(90\) | −1.19663 | − | 1.88893i | −0.126136 | − | 0.199111i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.34271i | 0.348501i | ||||||||
\(93\) | −4.31199 | − | 2.48953i | −0.447132 | − | 0.258152i | ||||
\(94\) | 2.20277 | + | 3.81531i | 0.227198 | + | 0.393519i | ||||
\(95\) | −14.5443 | − | 7.61840i | −1.49221 | − | 0.781631i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 10.6655i | − | 1.08292i | −0.840726 | − | 0.541460i | \(-0.817872\pi\) | ||
0.840726 | − | 0.541460i | \(-0.182128\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.979056 | −0.0983989 | ||||||||
\(100\) | −2.84700 | − | 4.11030i | −0.284700 | − | 0.411030i | ||||
\(101\) | −7.01639 | − | 12.1527i | −0.698157 | − | 1.20924i | −0.969105 | − | 0.246649i | \(-0.920671\pi\) |
0.270948 | − | 0.962594i | \(-0.412663\pi\) | |||||||
\(102\) | 2.42384 | − | 1.39940i | 0.239996 | − | 0.138562i | ||||
\(103\) | 8.99294 | + | 5.19208i | 0.886101 | + | 0.511591i | 0.872665 | − | 0.488319i | \(-0.162390\pi\) |
0.0134358 | + | 0.999910i | \(0.495723\pi\) | |||||||
\(104\) | −0.435157 | −0.0426707 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.657293 | 0.0638419 | ||||||||
\(107\) | 17.3560 | + | 10.0205i | 1.67787 | + | 0.968719i | 0.963016 | + | 0.269446i | \(0.0868405\pi\) |
0.714855 | + | 0.699273i | \(0.246493\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 9.32821 | + | 16.1569i | 0.893480 | + | 1.54755i | 0.835674 | + | 0.549225i | \(0.185077\pi\) |
0.0578060 | + | 0.998328i | \(0.481590\pi\) | |||||||
\(110\) | −2.18739 | + | 0.0899264i | −0.208559 | + | 0.00857415i | ||||
\(111\) | 4.63591 | 0.440021 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.4132i | 0.979587i | 0.871838 | + | 0.489794i | \(0.162928\pi\) | ||||
−0.871838 | + | 0.489794i | \(0.837072\pi\) | |||||||
\(114\) | 3.67135 | − | 6.35897i | 0.343854 | − | 0.595572i | ||||
\(115\) | 3.46821 | − | 6.62118i | 0.323412 | − | 0.617428i | ||||
\(116\) | −1.87412 | − | 3.24608i | −0.174008 | − | 0.301391i | ||||
\(117\) | 0.376857 | + | 0.217579i | 0.0348405 | + | 0.0201152i | ||||
\(118\) | 8.27226i | 0.761523i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.88893 | − | 1.19663i | 0.172435 | − | 0.109237i | ||||
\(121\) | 5.02072 | − | 8.69615i | 0.456429 | − | 0.790559i | ||||
\(122\) | 9.81518 | − | 5.66680i | 0.888625 | − | 0.513048i | ||||
\(123\) | 4.28634 | − | 2.47472i | 0.386486 | − | 0.223138i | ||||
\(124\) | 2.48953 | − | 4.31199i | 0.223566 | − | 0.387228i | ||||
\(125\) | 1.37465 | + | 11.0955i | 0.122953 | + | 0.992413i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6987i | 1.03810i | 0.854745 | + | 0.519048i | \(0.173713\pi\) | ||||
−0.854745 | + | 0.519048i | \(0.826287\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −4.98931 | − | 8.64174i | −0.439284 | − | 0.760862i | ||||
\(130\) | 0.861952 | + | 0.451496i | 0.0755982 | + | 0.0395988i | ||||
\(131\) | −2.69230 | + | 4.66320i | −0.235227 | + | 0.407425i | −0.959339 | − | 0.282258i | \(-0.908917\pi\) |
0.724112 | + | 0.689683i | \(0.242250\pi\) | |||||||
\(132\) | − | 0.979056i | − | 0.0852159i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.36365 | −0.204188 | ||||||||
\(135\) | −2.23418 | + | 0.0918501i | −0.192288 | + | 0.00790520i | ||||
\(136\) | 1.39940 | + | 2.42384i | 0.119998 | + | 0.207842i | ||||
\(137\) | −3.19204 | + | 1.84293i | −0.272715 | + | 0.157452i | −0.630121 | − | 0.776497i | \(-0.716995\pi\) |
0.357406 | + | 0.933949i | \(0.383661\pi\) | |||||||
\(138\) | 2.89487 | + | 1.67135i | 0.246428 | + | 0.142275i | ||||
\(139\) | −8.15378 | −0.691595 | −0.345797 | − | 0.938309i | \(-0.612392\pi\) | ||||
−0.345797 | + | 0.938309i | \(0.612392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.40554 | 0.371013 | ||||||||
\(142\) | −12.2213 | − | 7.05595i | −1.02559 | − | 0.592122i | ||||
\(143\) | 0.368964 | − | 0.213022i | 0.0308544 | − | 0.0178138i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0.344277 | + | 8.37426i | 0.0285906 | + | 0.695444i | ||||
\(146\) | −15.3928 | −1.27392 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.63591i | 0.381069i | ||||||||
\(149\) | −7.83868 | + | 13.5770i | −0.642170 | + | 1.11227i | 0.342778 | + | 0.939417i | \(0.388632\pi\) |
−0.984947 | + | 0.172854i | \(0.944701\pi\) | |||||||
\(150\) | −4.98313 | + | 0.410420i | −0.406871 | + | 0.0335106i | ||||
\(151\) | −2.13613 | − | 3.69989i | −0.173836 | − | 0.301092i | 0.765922 | − | 0.642934i | \(-0.222283\pi\) |
−0.939758 | + | 0.341841i | \(0.888950\pi\) | |||||||
\(152\) | 6.35897 | + | 3.67135i | 0.515781 | + | 0.297786i | ||||
\(153\) | − | 2.79881i | − | 0.226270i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.40510 | + | 5.95811i | −0.755436 | + | 0.478567i | ||||
\(156\) | −0.217579 | + | 0.376857i | −0.0174202 | + | 0.0301727i | ||||
\(157\) | −13.2067 | + | 7.62491i | −1.05401 | + | 0.608534i | −0.923770 | − | 0.382948i | \(-0.874909\pi\) |
−0.130242 | + | 0.991482i | \(0.541575\pi\) | |||||||
\(158\) | −2.50079 | + | 1.44383i | −0.198952 | + | 0.114865i | ||||
\(159\) | 0.328646 | − | 0.569232i | 0.0260634 | − | 0.0451431i | ||||
\(160\) | 1.19663 | + | 1.88893i | 0.0946023 | + | 0.149333i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 6.47439 | + | 3.73799i | 0.507114 | + | 0.292782i | 0.731646 | − | 0.681684i | \(-0.238752\pi\) |
−0.224533 | + | 0.974467i | \(0.572086\pi\) | |||||||
\(164\) | 2.47472 | + | 4.28634i | 0.193243 | + | 0.334707i | ||||
\(165\) | −1.01582 | + | 1.93930i | −0.0790811 | + | 0.150974i | ||||
\(166\) | −7.19208 | + | 12.4570i | −0.558214 | + | 0.966854i | ||||
\(167\) | 12.6640i | 0.979972i | 0.871730 | + | 0.489986i | \(0.162998\pi\) | ||||
−0.871730 | + | 0.489986i | \(0.837002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8106 | 0.985434 | ||||||||
\(170\) | −0.257071 | − | 6.25304i | −0.0197164 | − | 0.479587i | ||||
\(171\) | −3.67135 | − | 6.35897i | −0.280755 | − | 0.486283i | ||||
\(172\) | 8.64174 | − | 4.98931i | 0.658926 | − | 0.380431i | ||||
\(173\) | −6.16660 | − | 3.56029i | −0.468838 | − | 0.270684i | 0.246915 | − | 0.969037i | \(-0.420583\pi\) |
−0.715753 | + | 0.698354i | \(0.753916\pi\) | |||||||
\(174\) | −3.74825 | −0.284154 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.979056 | 0.0737991 | ||||||||
\(177\) | 7.16399 | + | 4.13613i | 0.538478 | + | 0.310891i | ||||
\(178\) | 8.76505 | − | 5.06051i | 0.656968 | − | 0.379301i | ||||
\(179\) | 1.63210 | + | 2.82688i | 0.121989 | + | 0.211291i | 0.920552 | − | 0.390620i | \(-0.127739\pi\) |
−0.798563 | + | 0.601911i | \(0.794406\pi\) | |||||||
\(180\) | −0.0918501 | − | 2.23418i | −0.00684610 | − | 0.166526i | ||||
\(181\) | 1.93823 | 0.144067 | 0.0720337 | − | 0.997402i | \(-0.477051\pi\) | ||||
0.0720337 | + | 0.997402i | \(0.477051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.3336i | − | 0.837803i | ||||||
\(184\) | −1.67135 | + | 2.89487i | −0.123214 | + | 0.213413i | ||||
\(185\) | 4.80997 | − | 9.18273i | 0.353636 | − | 0.675128i | ||||
\(186\) | −2.48953 | − | 4.31199i | −0.182541 | − | 0.316170i | ||||
\(187\) | −2.37307 | − | 1.37010i | −0.173536 | − | 0.100191i | ||||
\(188\) | 4.40554i | 0.321307i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.78654 | − | 13.8699i | −0.637443 | − | 1.00623i | ||||
\(191\) | −4.03500 | + | 6.98883i | −0.291963 | + | 0.505694i | −0.974274 | − | 0.225368i | \(-0.927642\pi\) |
0.682311 | + | 0.731062i | \(0.260975\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 1.69578 | − | 0.979056i | 0.122065 | − | 0.0704740i | −0.437725 | − | 0.899109i | \(-0.644215\pi\) |
0.559789 | + | 0.828635i | \(0.310882\pi\) | |||||||
\(194\) | 5.33276 | − | 9.23662i | 0.382870 | − | 0.663151i | ||||
\(195\) | 0.821983 | − | 0.520724i | 0.0588634 | − | 0.0372899i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.3418i | 1.23555i | 0.786353 | + | 0.617777i | \(0.211967\pi\) | ||||
−0.786353 | + | 0.617777i | \(0.788033\pi\) | |||||||
\(198\) | −0.847888 | − | 0.489528i | −0.0602567 | − | 0.0347892i | ||||
\(199\) | 1.29745 | + | 2.24725i | 0.0919738 | + | 0.159303i | 0.908342 | − | 0.418229i | \(-0.137349\pi\) |
−0.816368 | + | 0.577532i | \(0.804016\pi\) | |||||||
\(200\) | −0.410420 | − | 4.98313i | −0.0290210 | − | 0.352360i | ||||
\(201\) | −1.18183 | + | 2.04698i | −0.0833595 | + | 0.144383i | ||||
\(202\) | − | 14.0328i | − | 0.987343i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.79881 | 0.195956 | ||||||||
\(205\) | −0.454606 | − | 11.0579i | −0.0317511 | − | 0.772320i | ||||
\(206\) | 5.19208 | + | 8.99294i | 0.361749 | + | 0.626568i | ||||
\(207\) | 2.89487 | − | 1.67135i | 0.201207 | − | 0.116167i | ||||
\(208\) | −0.376857 | − | 0.217579i | −0.0261304 | − | 0.0150864i | ||||
\(209\) | −7.18892 | −0.497268 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4127 | 1.06106 | 0.530528 | − | 0.847668i | \(-0.321994\pi\) | ||||
0.530528 | + | 0.847668i | \(0.321994\pi\) | |||||||
\(212\) | 0.569232 | + | 0.328646i | 0.0390950 | + | 0.0225715i | ||||
\(213\) | −12.2213 | + | 7.05595i | −0.837387 | + | 0.483466i | ||||
\(214\) | 10.0205 | + | 17.3560i | 0.684988 | + | 1.18643i | ||||
\(215\) | −22.2940 | + | 0.916537i | −1.52044 | + | 0.0625073i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.6564i | 1.26357i | ||||||||
\(219\) | −7.69642 | + | 13.3306i | −0.520076 | + | 0.900797i | ||||
\(220\) | −1.93930 | − | 1.01582i | −0.130747 | − | 0.0684863i | ||||
\(221\) | 0.608961 | + | 1.05475i | 0.0409631 | + | 0.0709502i | ||||
\(222\) | 4.01482 | + | 2.31796i | 0.269457 | + | 0.155571i | ||||
\(223\) | 7.61497i | 0.509936i | 0.966950 | + | 0.254968i | \(0.0820649\pi\) | ||||
−0.966950 | + | 0.254968i | \(0.917935\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13613 | + | 4.52072i | −0.142409 | + | 0.301382i | ||||
\(226\) | −5.20658 | + | 9.01806i | −0.346336 | + | 0.599872i | ||||
\(227\) | 7.22462 | − | 4.17113i | 0.479515 | − | 0.276848i | −0.240700 | − | 0.970600i | \(-0.577377\pi\) |
0.720214 | + | 0.693752i | \(0.244044\pi\) | |||||||
\(228\) | 6.35897 | − | 3.67135i | 0.421133 | − | 0.243141i | ||||
\(229\) | 9.34503 | − | 16.1861i | 0.617537 | − | 1.06961i | −0.372396 | − | 0.928074i | \(-0.621464\pi\) |
0.989934 | − | 0.141532i | \(-0.0452028\pi\) | |||||||
\(230\) | 6.31415 | − | 4.00000i | 0.416343 | − | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 3.74825i | − | 0.246084i | ||||||
\(233\) | −17.3923 | − | 10.0414i | −1.13941 | − | 0.657837i | −0.193124 | − | 0.981174i | \(-0.561862\pi\) |
−0.946284 | + | 0.323337i | \(0.895195\pi\) | |||||||
\(234\) | 0.217579 | + | 0.376857i | 0.0142236 | + | 0.0246359i | ||||
\(235\) | 4.57095 | − | 8.72641i | 0.298176 | − | 0.569248i | ||||
\(236\) | −4.13613 | + | 7.16399i | −0.269239 | + | 0.466336i | ||||
\(237\) | 2.88767i | 0.187574i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.2714 | 1.44062 | 0.720308 | − | 0.693654i | \(-0.244000\pi\) | ||||
0.720308 | + | 0.693654i | \(0.244000\pi\) | |||||||
\(240\) | 2.23418 | − | 0.0918501i | 0.144216 | − | 0.00592890i | ||||
\(241\) | 3.10038 | + | 5.37001i | 0.199713 | + | 0.345913i | 0.948435 | − | 0.316971i | \(-0.102666\pi\) |
−0.748722 | + | 0.662884i | \(0.769332\pi\) | |||||||
\(242\) | 8.69615 | − | 5.02072i | 0.559010 | − | 0.322744i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 11.3336 | 0.725559 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.94944 | 0.315565 | ||||||||
\(247\) | 2.76715 | + | 1.59762i | 0.176070 | + | 0.101654i | ||||
\(248\) | 4.31199 | − | 2.48953i | 0.273812 | − | 0.158085i | ||||
\(249\) | 7.19208 | + | 12.4570i | 0.455779 | + | 0.789433i | ||||
\(250\) | −4.35727 | + | 10.2963i | −0.275578 | + | 0.651196i | ||||
\(251\) | −27.6560 | −1.74563 | −0.872815 | − | 0.488051i | \(-0.837708\pi\) | ||||
−0.872815 | + | 0.488051i | \(0.837708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.27270i | − | 0.205753i | ||||||
\(254\) | −5.84937 | + | 10.1314i | −0.367022 | + | 0.635701i | ||||
\(255\) | −5.54383 | − | 2.90389i | −0.347168 | − | 0.181849i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.1915 | − | 5.88407i | −0.635728 | − | 0.367038i | 0.147239 | − | 0.989101i | \(-0.452961\pi\) |
−0.782967 | + | 0.622063i | \(0.786295\pi\) | |||||||
\(258\) | − | 9.97862i | − | 0.621242i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.520724 | + | 0.821983i | 0.0322940 | + | 0.0509772i | ||||
\(261\) | −1.87412 | + | 3.24608i | −0.116005 | + | 0.200927i | ||||
\(262\) | −4.66320 | + | 2.69230i | −0.288093 | + | 0.166331i | ||||
\(263\) | −0.394078 | + | 0.227521i | −0.0242999 | + | 0.0140295i | −0.512101 | − | 0.858925i | \(-0.671133\pi\) |
0.487801 | + | 0.872955i | \(0.337799\pi\) | |||||||
\(264\) | 0.489528 | − | 0.847888i | 0.0301284 | − | 0.0521839i | ||||
\(265\) | −0.786540 | − | 1.24158i | −0.0483167 | − | 0.0762698i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.1210i | − | 0.619396i | ||||||
\(268\) | −2.04698 | − | 1.18183i | −0.125039 | − | 0.0721915i | ||||
\(269\) | 13.0687 | + | 22.6357i | 0.796815 | + | 1.38012i | 0.921680 | + | 0.387951i | \(0.126817\pi\) |
−0.124865 | + | 0.992174i | \(0.539850\pi\) | |||||||
\(270\) | −1.98078 | − | 1.03755i | −0.120547 | − | 0.0631430i | ||||
\(271\) | −8.38840 | + | 14.5291i | −0.509559 | + | 0.882582i | 0.490380 | + | 0.871509i | \(0.336858\pi\) |
−0.999939 | + | 0.0110734i | \(0.996475\pi\) | |||||||
\(272\) | 2.79881i | 0.169703i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.68585 | −0.222671 | ||||||||
\(275\) | 2.78737 | + | 4.02422i | 0.168085 | + | 0.242670i | ||||
\(276\) | 1.67135 | + | 2.89487i | 0.100604 | + | 0.174251i | ||||
\(277\) | 17.9681 | − | 10.3739i | 1.07960 | − | 0.623307i | 0.148812 | − | 0.988866i | \(-0.452455\pi\) |
0.930789 | + | 0.365558i | \(0.119122\pi\) | |||||||
\(278\) | −7.06138 | − | 4.07689i | −0.423514 | − | 0.244516i | ||||
\(279\) | −4.97906 | −0.298088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.3141 | −1.09253 | −0.546265 | − | 0.837612i | \(-0.683951\pi\) | ||||
−0.546265 | + | 0.837612i | \(0.683951\pi\) | |||||||
\(282\) | 3.81531 | + | 2.20277i | 0.227198 | + | 0.131173i | ||||
\(283\) | −10.2646 | + | 5.92626i | −0.610166 | + | 0.352280i | −0.773031 | − | 0.634369i | \(-0.781260\pi\) |
0.162864 | + | 0.986649i | \(0.447927\pi\) | |||||||
\(284\) | −7.05595 | − | 12.2213i | −0.418693 | − | 0.725198i | ||||
\(285\) | −16.4049 | + | 0.674429i | −0.971744 | + | 0.0399497i | ||||
\(286\) | 0.426043 | 0.0251925 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −4.58334 | + | 7.93857i | −0.269608 | + | 0.466975i | ||||
\(290\) | −3.88898 | + | 7.42446i | −0.228369 | + | 0.435979i | ||||
\(291\) | −5.33276 | − | 9.23662i | −0.312612 | − | 0.541460i | ||||
\(292\) | −13.3306 | − | 7.69642i | −0.780113 | − | 0.450399i | ||||
\(293\) | − | 14.4770i | − | 0.845758i | −0.906186 | − | 0.422879i | \(-0.861020\pi\) | ||
0.906186 | − | 0.422879i | \(-0.138980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.6257 | − | 9.89887i | 0.909766 | − | 0.576335i | ||||
\(296\) | −2.31796 | + | 4.01482i | −0.134728 | + | 0.233356i | ||||
\(297\) | −0.847888 | + | 0.489528i | −0.0491994 | + | 0.0284053i | ||||
\(298\) | −13.5770 | + | 7.83868i | −0.786494 | + | 0.454083i | ||||
\(299\) | −0.727302 | + | 1.25972i | −0.0420609 | + | 0.0728517i | ||||
\(300\) | −4.52072 | − | 2.13613i | −0.261004 | − | 0.123330i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 4.27226i | − | 0.245841i | ||||||
\(303\) | −12.1527 | − | 7.01639i | −0.698157 | − | 0.403081i | ||||
\(304\) | 3.67135 | + | 6.35897i | 0.210567 | + | 0.364712i | ||||
\(305\) | −22.4494 | − | 11.7591i | −1.28545 | − | 0.673325i | ||||
\(306\) | 1.39940 | − | 2.42384i | 0.0799986 | − | 0.138562i | ||||
\(307\) | − | 30.4252i | − | 1.73646i | −0.496165 | − | 0.868228i | \(-0.665259\pi\) | ||
0.496165 | − | 0.868228i | \(-0.334741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.3842 | 0.590734 | ||||||||
\(310\) | −11.1241 | + | 0.457327i | −0.631807 | + | 0.0259744i | ||||
\(311\) | 4.51428 | + | 7.81896i | 0.255981 | + | 0.443373i | 0.965162 | − | 0.261655i | \(-0.0842681\pi\) |
−0.709180 | + | 0.705027i | \(0.750935\pi\) | |||||||
\(312\) | −0.376857 | + | 0.217579i | −0.0213353 | + | 0.0123180i | ||||
\(313\) | −14.8725 | − | 8.58662i | −0.840641 | − | 0.485344i | 0.0168412 | − | 0.999858i | \(-0.494639\pi\) |
−0.857482 | + | 0.514514i | \(0.827972\pi\) | |||||||
\(314\) | −15.2498 | −0.860597 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.88767 | −0.162444 | ||||||||
\(317\) | 2.26501 | + | 1.30770i | 0.127215 | + | 0.0734479i | 0.562257 | − | 0.826962i | \(-0.309933\pi\) |
−0.435042 | + | 0.900410i | \(0.643266\pi\) | |||||||
\(318\) | 0.569232 | − | 0.328646i | 0.0319210 | − | 0.0184296i | ||||
\(319\) | 1.83487 | + | 3.17809i | 0.102733 | + | 0.177939i | ||||
\(320\) | 0.0918501 | + | 2.23418i | 0.00513458 | + | 0.124894i | ||||
\(321\) | 20.0410 | 1.11858 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 20.5508i | − | 1.14348i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −0.178597 | − | 2.16844i | −0.00990678 | − | 0.120284i | ||||
\(326\) | 3.73799 | + | 6.47439i | 0.207028 | + | 0.358584i | ||||
\(327\) | 16.1569 | + | 9.32821i | 0.893480 | + | 0.515851i | ||||
\(328\) | 4.94944i | 0.273287i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.84937 | + | 1.17157i | −0.101805 | + | 0.0644930i | ||||
\(331\) | 8.87793 | − | 15.3770i | 0.487975 | − | 0.845198i | −0.511929 | − | 0.859028i | \(-0.671069\pi\) |
0.999904 | + | 0.0138298i | \(0.00440231\pi\) | |||||||
\(332\) | −12.4570 | + | 7.19208i | −0.683669 | + | 0.394717i | ||||
\(333\) | 4.01482 | − | 2.31796i | 0.220011 | − | 0.127023i | ||||
\(334\) | −6.33202 | + | 10.9674i | −0.346472 | + | 0.600108i | ||||
\(335\) | 2.82843 | + | 4.46478i | 0.154533 | + | 0.243937i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.2304i | 1.31991i | 0.751304 | + | 0.659956i | \(0.229425\pi\) | ||||
−0.751304 | + | 0.659956i | \(0.770575\pi\) | |||||||
\(338\) | 11.0943 | + | 6.40532i | 0.603452 | + | 0.348403i | ||||
\(339\) | 5.20658 | + | 9.01806i | 0.282782 | + | 0.489794i | ||||
\(340\) | 2.90389 | − | 5.54383i | 0.157486 | − | 0.300656i | ||||
\(341\) | −2.43739 | + | 4.22168i | −0.131992 | + | 0.228617i | ||||
\(342\) | − | 7.34271i | − | 0.397048i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.97862 | 0.538011 | ||||||||
\(345\) | −0.307028 | − | 7.46821i | −0.0165298 | − | 0.402075i | ||||
\(346\) | −3.56029 | − | 6.16660i | −0.191402 | − | 0.331518i | ||||
\(347\) | −26.3490 | + | 15.2126i | −1.41449 | + | 0.816654i | −0.995807 | − | 0.0914797i | \(-0.970840\pi\) |
−0.418680 | + | 0.908134i | \(0.637507\pi\) | |||||||
\(348\) | −3.24608 | − | 1.87412i | −0.174008 | − | 0.100464i | ||||
\(349\) | −30.2623 | −1.61990 | −0.809951 | − | 0.586497i | \(-0.800506\pi\) | ||||
−0.809951 | + | 0.586497i | \(0.800506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.435157 | 0.0232270 | ||||||||
\(352\) | 0.847888 | + | 0.489528i | 0.0451926 | + | 0.0260919i | ||||
\(353\) | 3.78617 | − | 2.18594i | 0.201517 | − | 0.116346i | −0.395846 | − | 0.918317i | \(-0.629549\pi\) |
0.597363 | + | 0.801971i | \(0.296215\pi\) | |||||||
\(354\) | 4.13613 | + | 7.16399i | 0.219833 | + | 0.380762i | ||||
\(355\) | 1.29618 | + | 31.5285i | 0.0687941 | + | 1.67336i | ||||
\(356\) | 10.1210 | 0.536412 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.26420i | 0.172519i | ||||||||
\(359\) | −7.84249 | + | 13.5836i | −0.413911 | + | 0.716914i | −0.995313 | − | 0.0967016i | \(-0.969171\pi\) |
0.581403 | + | 0.813616i | \(0.302504\pi\) | |||||||
\(360\) | 1.03755 | − | 1.98078i | 0.0546835 | − | 0.104396i | ||||
\(361\) | −17.4577 | − | 30.2376i | −0.918825 | − | 1.59145i | ||||
\(362\) | 1.67855 | + | 0.969114i | 0.0882229 | + | 0.0509355i | ||||
\(363\) | − | 10.0414i | − | 0.527039i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.4196 | + | 29.0760i | 0.964126 | + | 1.52191i | ||||
\(366\) | 5.66680 | − | 9.81518i | 0.296208 | − | 0.513048i | ||||
\(367\) | 4.28231 | − | 2.47239i | 0.223535 | − | 0.129058i | −0.384051 | − | 0.923312i | \(-0.625471\pi\) |
0.607586 | + | 0.794254i | \(0.292138\pi\) | |||||||
\(368\) | −2.89487 | + | 1.67135i | −0.150905 | + | 0.0871253i | ||||
\(369\) | 2.47472 | − | 4.28634i | 0.128829 | − | 0.223138i | ||||
\(370\) | 8.75692 | − | 5.54749i | 0.455251 | − | 0.288400i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 4.97906i | − | 0.258152i | ||||||
\(373\) | 5.21467 | + | 3.01069i | 0.270005 | + | 0.155888i | 0.628890 | − | 0.777494i | \(-0.283510\pi\) |
−0.358885 | + | 0.933382i | \(0.616843\pi\) | |||||||
\(374\) | −1.37010 | − | 2.37307i | −0.0708459 | − | 0.122709i | ||||
\(375\) | 6.73824 | + | 8.92167i | 0.347961 | + | 0.460713i | ||||
\(376\) | −2.20277 | + | 3.81531i | −0.113599 | + | 0.196759i | ||||
\(377\) | − | 1.63108i | − | 0.0840047i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.8030 | 1.89044 | 0.945222 | − | 0.326429i | \(-0.105845\pi\) | ||||
0.945222 | + | 0.326429i | \(0.105845\pi\) | |||||||
\(380\) | −0.674429 | − | 16.4049i | −0.0345975 | − | 0.841555i | ||||
\(381\) | 5.84937 | + | 10.1314i | 0.299672 | + | 0.519048i | ||||
\(382\) | −6.98883 | + | 4.03500i | −0.357580 | + | 0.206449i | ||||
\(383\) | −7.82353 | − | 4.51692i | −0.399764 | − | 0.230804i | 0.286618 | − | 0.958045i | \(-0.407469\pi\) |
−0.686382 | + | 0.727241i | \(0.740802\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.95811 | 0.0996653 | ||||||||
\(387\) | −8.64174 | − | 4.98931i | −0.439284 | − | 0.253621i | ||||
\(388\) | 9.23662 | − | 5.33276i | 0.468918 | − | 0.270730i | ||||
\(389\) | 16.7823 | + | 29.0678i | 0.850896 | + | 1.47380i | 0.880401 | + | 0.474231i | \(0.157274\pi\) |
−0.0295047 | + | 0.999565i | \(0.509393\pi\) | |||||||
\(390\) | 0.972220 | − | 0.0399693i | 0.0492303 | − | 0.00202392i | ||||
\(391\) | 9.35560 | 0.473133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.38459i | 0.271617i | ||||||||
\(394\) | −8.67091 | + | 15.0185i | −0.436834 | + | 0.756619i | ||||
\(395\) | 5.71984 | + | 2.99608i | 0.287796 | + | 0.150749i | ||||
\(396\) | −0.489528 | − | 0.847888i | −0.0245997 | − | 0.0426080i | ||||
\(397\) | −29.4269 | − | 16.9896i | −1.47689 | − | 0.852685i | −0.477233 | − | 0.878777i | \(-0.658360\pi\) |
−0.999660 | + | 0.0260921i | \(0.991694\pi\) | |||||||
\(398\) | 2.59490i | 0.130071i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.13613 | − | 4.52072i | 0.106806 | − | 0.226036i | ||||
\(401\) | 2.13613 | − | 3.69989i | 0.106673 | − | 0.184763i | −0.807747 | − | 0.589529i | \(-0.799313\pi\) |
0.914421 | + | 0.404765i | \(0.132647\pi\) | |||||||
\(402\) | −2.04698 | + | 1.18183i | −0.102094 | + | 0.0589441i | ||||
\(403\) | 1.87639 | − | 1.08334i | 0.0934698 | − | 0.0539648i | ||||
\(404\) | 7.01639 | − | 12.1527i | 0.349078 | − | 0.604621i | ||||
\(405\) | −1.88893 | + | 1.19663i | −0.0938618 | + | 0.0594613i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.53882i | − | 0.224981i | ||||||
\(408\) | 2.42384 | + | 1.39940i | 0.119998 | + | 0.0692808i | ||||
\(409\) | 1.81944 | + | 3.15137i | 0.0899656 | + | 0.155825i | 0.907496 | − | 0.420060i | \(-0.137991\pi\) |
−0.817531 | + | 0.575885i | \(0.804658\pi\) | |||||||
\(410\) | 5.13527 | − | 9.80376i | 0.253613 | − | 0.484173i | ||||
\(411\) | −1.84293 | + | 3.19204i | −0.0909049 | + | 0.157452i | ||||
\(412\) | 10.3842i | 0.511591i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.34271 | 0.164285 | ||||||||
\(415\) | 32.1368 | − | 1.32119i | 1.57753 | − | 0.0648545i | ||||
\(416\) | −0.217579 | − | 0.376857i | −0.0106677 | − | 0.0184769i | ||||
\(417\) | −7.06138 | + | 4.07689i | −0.345797 | + | 0.199646i | ||||
\(418\) | −6.22579 | − | 3.59446i | −0.304513 | − | 0.175811i | ||||
\(419\) | 26.6274 | 1.30083 | 0.650417 | − | 0.759577i | \(-0.274594\pi\) | ||||
0.650417 | + | 0.759577i | \(0.274594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1880 | −0.740220 | −0.370110 | − | 0.928988i | \(-0.620680\pi\) | ||||
−0.370110 | + | 0.928988i | \(0.620680\pi\) | |||||||
\(422\) | 13.3478 | + | 7.70636i | 0.649761 | + | 0.375140i | ||||
\(423\) | 3.81531 | − | 2.20277i | 0.185507 | − | 0.107102i | ||||
\(424\) | 0.328646 | + | 0.569232i | 0.0159605 | + | 0.0276444i | ||||
\(425\) | −11.5040 | + | 7.96820i | −0.558024 | + | 0.386514i | ||||
\(426\) | −14.1119 | −0.683724 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 20.0410i | 0.968719i | ||||||||
\(429\) | 0.213022 | − | 0.368964i | 0.0102848 | − | 0.0178138i | ||||
\(430\) | −19.7655 | − | 10.3533i | −0.953176 | − | 0.499279i | ||||
\(431\) | 2.11562 | + | 3.66437i | 0.101906 | + | 0.176506i | 0.912470 | − | 0.409144i | \(-0.134173\pi\) |
−0.810564 | + | 0.585650i | \(0.800839\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 33.9352i | − | 1.63082i | −0.578882 | − | 0.815412i | \(-0.696511\pi\) | ||
0.578882 | − | 0.815412i | \(-0.303489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.48528 | + | 7.08018i | 0.215053 | + | 0.339469i | ||||
\(436\) | −9.32821 | + | 16.1569i | −0.446740 | + | 0.773777i | ||||
\(437\) | 21.2562 | − | 12.2723i | 1.01682 | − | 0.587062i | ||||
\(438\) | −13.3306 | + | 7.69642i | −0.636960 | + | 0.367749i | ||||
\(439\) | 2.74128 | − | 4.74804i | 0.130834 | − | 0.226612i | −0.793164 | − | 0.609008i | \(-0.791568\pi\) |
0.923998 | + | 0.382396i | \(0.124901\pi\) | |||||||
\(440\) | −1.17157 | − | 1.84937i | −0.0558525 | − | 0.0881653i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.21792i | 0.0579306i | ||||||||
\(443\) | −1.06591 | − | 0.615405i | −0.0506431 | − | 0.0292388i | 0.474465 | − | 0.880275i | \(-0.342642\pi\) |
−0.525108 | + | 0.851036i | \(0.675975\pi\) | |||||||
\(444\) | 2.31796 | + | 4.01482i | 0.110005 | + | 0.190535i | ||||
\(445\) | −20.0475 | − | 10.5010i | −0.950344 | − | 0.497796i | ||||
\(446\) | −3.80748 | + | 6.59475i | −0.180290 | + | 0.312271i | ||||
\(447\) | 15.6774i | 0.741514i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.6435 | −0.691071 | −0.345535 | − | 0.938406i | \(-0.612303\pi\) | ||||
−0.345535 | + | 0.938406i | \(0.612303\pi\) | |||||||
\(450\) | −4.11030 | + | 2.84700i | −0.193762 | + | 0.134209i | ||||
\(451\) | −2.42289 | − | 4.19657i | −0.114089 | − | 0.197609i | ||||
\(452\) | −9.01806 | + | 5.20658i | −0.424174 | + | 0.244897i | ||||
\(453\) | −3.69989 | − | 2.13613i | −0.173836 | − | 0.100364i | ||||
\(454\) | 8.34227 | 0.391522 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.34271 | 0.343854 | ||||||||
\(457\) | −27.1317 | − | 15.6645i | −1.26917 | − | 0.732753i | −0.294335 | − | 0.955702i | \(-0.595098\pi\) |
−0.974830 | + | 0.222949i | \(0.928432\pi\) | |||||||
\(458\) | 16.1861 | − | 9.34503i | 0.756325 | − | 0.436665i | ||||
\(459\) | −1.39940 | − | 2.42384i | −0.0653186 | − | 0.113135i | ||||
\(460\) | 7.46821 | − | 0.307028i | 0.348207 | − | 0.0143153i | ||||
\(461\) | −12.7667 | −0.594602 | −0.297301 | − | 0.954784i | \(-0.596087\pi\) | ||||
−0.297301 | + | 0.954784i | \(0.596087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.7112i | − | 1.24137i | −0.784058 | − | 0.620687i | \(-0.786854\pi\) | ||
0.784058 | − | 0.620687i | \(-0.213146\pi\) | |||||||
\(464\) | 1.87412 | − | 3.24608i | 0.0870040 | − | 0.150695i | ||||
\(465\) | −5.16600 | + | 9.86243i | −0.239567 | + | 0.457359i | ||||
\(466\) | −10.0414 | − | 17.3923i | −0.465161 | − | 0.805683i | ||||
\(467\) | 32.5748 | + | 18.8070i | 1.50738 | + | 0.870286i | 0.999963 | + | 0.00858551i | \(0.00273289\pi\) |
0.507417 | + | 0.861701i | \(0.330600\pi\) | |||||||
\(468\) | 0.435157i | 0.0201152i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.32176 | − | 5.27182i | 0.383854 | − | 0.243171i | ||||
\(471\) | −7.62491 | + | 13.2067i | −0.351337 | + | 0.608534i | ||||
\(472\) | −7.16399 | + | 4.13613i | −0.329749 | + | 0.190381i | ||||
\(473\) | −8.46075 | + | 4.88481i | −0.389026 | + | 0.224604i | ||||
\(474\) | −1.44383 | + | 2.50079i | −0.0663174 | + | 0.114865i | ||||
\(475\) | −15.6850 | + | 33.1944i | −0.719676 | + | 1.52306i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 0.657293i | − | 0.0300954i | ||||||
\(478\) | 19.2876 | + | 11.1357i | 0.882194 | + | 0.509335i | ||||
\(479\) | 11.9118 | + | 20.6318i | 0.544262 | + | 0.942690i | 0.998653 | + | 0.0518875i | \(0.0165237\pi\) |
−0.454391 | + | 0.890803i | \(0.650143\pi\) | |||||||
\(480\) | 1.98078 | + | 1.03755i | 0.0904099 | + | 0.0473573i | ||||
\(481\) | −1.00868 | + | 1.74708i | −0.0459916 | + | 0.0796598i | ||||
\(482\) | 6.20075i | 0.282437i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.0414 | 0.456429 | ||||||||
\(485\) | −23.8287 | + | 0.979630i | −1.08201 | + | 0.0444827i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 3.25343 | − | 1.87837i | 0.147427 | − | 0.0851170i | −0.424472 | − | 0.905441i | \(-0.639540\pi\) |
0.571899 | + | 0.820324i | \(0.306207\pi\) | |||||||
\(488\) | 9.81518 | + | 5.66680i | 0.444312 | + | 0.256524i | ||||
\(489\) | 7.47599 | 0.338076 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00762 | 0.0906025 | 0.0453012 | − | 0.998973i | \(-0.485575\pi\) | ||||
0.0453012 | + | 0.998973i | \(0.485575\pi\) | |||||||
\(492\) | 4.28634 | + | 2.47472i | 0.193243 | + | 0.111569i | ||||
\(493\) | −9.08514 | + | 5.24531i | −0.409174 | + | 0.236237i | ||||
\(494\) | 1.59762 | + | 2.76715i | 0.0718802 | + | 0.124500i | ||||
\(495\) | 0.0899264 | + | 2.18739i | 0.00404189 | + | 0.0983158i | ||||
\(496\) | 4.97906 | 0.223566 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.3842i | 0.644569i | ||||||||
\(499\) | −0.314147 | + | 0.544119i | −0.0140632 | + | 0.0243581i | −0.872971 | − | 0.487772i | \(-0.837810\pi\) |
0.858908 | + | 0.512130i | \(0.171143\pi\) | |||||||
\(500\) | −8.92167 | + | 6.73824i | −0.398989 | + | 0.301343i | ||||
\(501\) | 6.33202 | + | 10.9674i | 0.282894 | + | 0.489986i | ||||
\(502\) | −23.9508 | − | 13.8280i | −1.06898 | − | 0.617173i | ||||
\(503\) | − | 28.9911i | − | 1.29265i | −0.763063 | − | 0.646324i | \(-0.776305\pi\) | ||
0.763063 | − | 0.646324i | \(-0.223695\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.5070 | + | 16.7921i | −1.17954 | + | 0.747239i | ||||
\(506\) | 1.63635 | − | 2.83424i | 0.0727446 | − | 0.125997i | ||||
\(507\) | 11.0943 | − | 6.40532i | 0.492717 | − | 0.284470i | ||||
\(508\) | −10.1314 | + | 5.84937i | −0.449509 | + | 0.259524i | ||||
\(509\) | 7.75280 | − | 13.4282i | 0.343637 | − | 0.595197i | −0.641468 | − | 0.767150i | \(-0.721674\pi\) |
0.985105 | + | 0.171953i | \(0.0550077\pi\) | |||||||
\(510\) | −3.34915 | − | 5.28676i | −0.148303 | − | 0.234102i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −6.35897 | − | 3.67135i | −0.280755 | − | 0.162094i | ||||
\(514\) | −5.88407 | − | 10.1915i | −0.259535 | − | 0.449528i | ||||
\(515\) | 10.7740 | − | 20.5688i | 0.474761 | − | 0.906368i | ||||
\(516\) | 4.98931 | − | 8.64174i | 0.219642 | − | 0.380431i | ||||
\(517\) | − | 4.31327i | − | 0.189697i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.12057 | −0.312558 | ||||||||
\(520\) | 0.0399693 | + | 0.972220i | 0.00175277 | + | 0.0426347i | ||||
\(521\) | −6.77660 | − | 11.7374i | −0.296888 | − | 0.514225i | 0.678534 | − | 0.734569i | \(-0.262616\pi\) |
−0.975422 | + | 0.220343i | \(0.929282\pi\) | |||||||
\(522\) | −3.24608 | + | 1.87412i | −0.142077 | + | 0.0820281i | ||||
\(523\) | 19.4459 | + | 11.2271i | 0.850309 | + | 0.490926i | 0.860755 | − | 0.509019i | \(-0.169992\pi\) |
−0.0104462 | + | 0.999945i | \(0.503325\pi\) | |||||||
\(524\) | −5.38459 | −0.235227 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.455042 | −0.0198408 | ||||||||
\(527\) | −12.0684 | − | 6.96771i | −0.525709 | − | 0.303518i | ||||
\(528\) | 0.847888 | − | 0.489528i | 0.0368996 | − | 0.0213040i | ||||
\(529\) | −5.91315 | − | 10.2419i | −0.257094 | − | 0.445299i | ||||
\(530\) | −0.0603724 | − | 1.46851i | −0.00262241 | − | 0.0637880i | ||||
\(531\) | 8.27226 | 0.358985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.15378i | 0.0932907i | ||||||||
\(534\) | 5.06051 | − | 8.76505i | 0.218989 | − | 0.379301i | ||||
\(535\) | 20.7935 | − | 39.6969i | 0.898980 | − | 1.71625i | ||||
\(536\) | −1.18183 | − | 2.04698i | −0.0510471 | − | 0.0884161i | ||||
\(537\) | 2.82688 | + | 1.63210i | 0.121989 | + | 0.0704304i | ||||
\(538\) | 26.1375i | 1.12687i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.19663 | − | 1.88893i | −0.0514950 | − | 0.0812867i | ||||
\(541\) | −5.40554 | + | 9.36267i | −0.232402 | + | 0.402532i | −0.958515 | − | 0.285044i | \(-0.907992\pi\) |
0.726112 | + | 0.687576i | \(0.241325\pi\) | |||||||
\(542\) | −14.5291 | + | 8.38840i | −0.624080 | + | 0.360313i | ||||
\(543\) | 1.67855 | − | 0.969114i | 0.0720337 | − | 0.0415887i | ||||
\(544\) | −1.39940 | + | 2.42384i | −0.0599990 | + | 0.103921i | ||||
\(545\) | 35.2407 | − | 22.3249i | 1.50955 | − | 0.956294i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.1881i | 1.03421i | 0.855923 | + | 0.517103i | \(0.172990\pi\) | ||||
−0.855923 | + | 0.517103i | \(0.827010\pi\) | |||||||
\(548\) | −3.19204 | − | 1.84293i | −0.136357 | − | 0.0787259i | ||||
\(549\) | −5.66680 | − | 9.81518i | −0.241853 | − | 0.418902i | ||||
\(550\) | 0.401824 | + | 4.87876i | 0.0171338 | + | 0.208031i | ||||
\(551\) | −13.7611 | + | 23.8350i | −0.586244 | + | 1.01540i | ||||
\(552\) | 3.34271i | 0.142275i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.7478 | 0.881490 | ||||||||
\(555\) | −0.425809 | − | 10.3575i | −0.0180746 | − | 0.439650i | ||||
\(556\) | −4.07689 | − | 7.06138i | −0.172899 | − | 0.299469i | ||||
\(557\) | 22.6491 | − | 13.0765i | 0.959672 | − | 0.554067i | 0.0636002 | − | 0.997975i | \(-0.479742\pi\) |
0.896072 | + | 0.443908i | \(0.146408\pi\) | |||||||
\(558\) | −4.31199 | − | 2.48953i | −0.182541 | − | 0.105390i | ||||
\(559\) | 4.34227 | 0.183658 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.74019 | −0.115691 | ||||||||
\(562\) | −15.8605 | − | 9.15707i | −0.669036 | − | 0.386268i | ||||
\(563\) | −9.16810 | + | 5.29320i | −0.386389 | + | 0.223082i | −0.680594 | − | 0.732660i | \(-0.738278\pi\) |
0.294205 | + | 0.955742i | \(0.404945\pi\) | |||||||
\(564\) | 2.20277 | + | 3.81531i | 0.0927533 | + | 0.160653i | ||||
\(565\) | 23.2649 | − | 0.956449i | 0.978760 | − | 0.0402381i | ||||
\(566\) | −11.8525 | −0.498199 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 14.1119i | − | 0.592122i | ||||||
\(569\) | 7.82198 | − | 13.5481i | 0.327915 | − | 0.567965i | −0.654183 | − | 0.756336i | \(-0.726988\pi\) |
0.982098 | + | 0.188371i | \(0.0603208\pi\) | |||||||
\(570\) | −14.5443 | − | 7.61840i | −0.609194 | − | 0.319099i | ||||
\(571\) | −4.25491 | − | 7.36972i | −0.178062 | − | 0.308413i | 0.763154 | − | 0.646216i | \(-0.223650\pi\) |
−0.941217 | + | 0.337803i | \(0.890316\pi\) | |||||||
\(572\) | 0.368964 | + | 0.213022i | 0.0154272 | + | 0.00890689i | ||||
\(573\) | 8.07001i | 0.337129i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.1115 | − | 7.14046i | −0.630191 | − | 0.297778i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −8.38138 | + | 4.83899i | −0.348921 | + | 0.201450i | −0.664210 | − | 0.747546i | \(-0.731232\pi\) |
0.315289 | + | 0.948996i | \(0.397899\pi\) | |||||||
\(578\) | −7.93857 | + | 4.58334i | −0.330201 | + | 0.190642i | ||||
\(579\) | 0.979056 | − | 1.69578i | 0.0406882 | − | 0.0704740i | ||||
\(580\) | −7.08018 | + | 4.48528i | −0.293989 | + | 0.186241i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 10.6655i | − | 0.442100i | ||||||
\(583\) | −0.557310 | − | 0.321763i | −0.0230814 | − | 0.0133261i | ||||
\(584\) | −7.69642 | − | 13.3306i | −0.318480 | − | 0.551623i | ||||
\(585\) | 0.451496 | − | 0.861952i | 0.0186670 | − | 0.0356373i | ||||
\(586\) | 7.23852 | − | 12.5375i | 0.299021 | − | 0.517919i | ||||
\(587\) | 16.3013i | 0.672825i | 0.941715 | + | 0.336412i | \(0.109214\pi\) | ||||
−0.941715 | + | 0.336412i | \(0.890786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.5598 | −1.50642 | ||||||||
\(590\) | 18.4817 | − | 0.759808i | 0.760880 | − | 0.0312808i | ||||
\(591\) | 8.67091 | + | 15.0185i | 0.356674 | + | 0.617777i | ||||
\(592\) | −4.01482 | + | 2.31796i | −0.165008 | + | 0.0952674i | ||||
\(593\) | 10.8082 | + | 6.24010i | 0.443838 | + | 0.256250i | 0.705224 | − | 0.708984i | \(-0.250846\pi\) |
−0.261386 | + | 0.965234i | \(0.584180\pi\) | |||||||
\(594\) | −0.979056 | −0.0401712 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.6774 | −0.642170 | ||||||||
\(597\) | 2.24725 | + | 1.29745i | 0.0919738 | + | 0.0531011i | ||||
\(598\) | −1.25972 | + | 0.727302i | −0.0515139 | + | 0.0297416i | ||||
\(599\) | 20.3773 | + | 35.2945i | 0.832593 | + | 1.44209i | 0.895975 | + | 0.444104i | \(0.146478\pi\) |
−0.0633826 | + | 0.997989i | \(0.520189\pi\) | |||||||
\(600\) | −2.84700 | − | 4.11030i | −0.116228 | − | 0.167802i | ||||
\(601\) | −4.94541 | −0.201727 | −0.100864 | − | 0.994900i | \(-0.532161\pi\) | ||||
−0.100864 | + | 0.994900i | \(0.532161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.36365i | 0.0962553i | ||||||||
\(604\) | 2.13613 | − | 3.69989i | 0.0869179 | − | 0.150546i | ||||
\(605\) | −19.8899 | − | 10.4185i | −0.808640 | − | 0.423571i | ||||
\(606\) | −7.01639 | − | 12.1527i | −0.285021 | − | 0.493671i | ||||
\(607\) | −0.754789 | − | 0.435778i | −0.0306359 | − | 0.0176877i | 0.484604 | − | 0.874734i | \(-0.338964\pi\) |
−0.515240 | + | 0.857046i | \(0.672297\pi\) | |||||||
\(608\) | 7.34271i | 0.297786i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.5622 | − | 21.4084i | −0.549116 | − | 0.866800i | ||||
\(611\) | −0.958551 | + | 1.66026i | −0.0387788 | + | 0.0671669i | ||||
\(612\) | 2.42384 | − | 1.39940i | 0.0979779 | − | 0.0565676i | ||||
\(613\) | 31.9570 | − | 18.4504i | 1.29073 | − | 0.745203i | 0.311946 | − | 0.950100i | \(-0.399019\pi\) |
0.978784 | + | 0.204897i | \(0.0656860\pi\) | |||||||
\(614\) | 15.2126 | − | 26.3490i | 0.613930 | − | 1.06336i | ||||
\(615\) | −5.92267 | − | 9.34915i | −0.238825 | − | 0.376994i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.6911i | − | 1.15506i | −0.816369 | − | 0.577530i | \(-0.804016\pi\) | ||
0.816369 | − | 0.577530i | \(-0.195984\pi\) | |||||||
\(618\) | 8.99294 | + | 5.19208i | 0.361749 | + | 0.208856i | ||||
\(619\) | 3.15707 | + | 5.46821i | 0.126894 | + | 0.219786i | 0.922472 | − | 0.386065i | \(-0.126166\pi\) |
−0.795578 | + | 0.605851i | \(0.792833\pi\) | |||||||
\(620\) | −9.86243 | − | 5.16600i | −0.396085 | − | 0.207472i | ||||
\(621\) | 1.67135 | − | 2.89487i | 0.0670691 | − | 0.116167i | ||||
\(622\) | 9.02856i | 0.362012i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.435157 | −0.0174202 | ||||||||
\(625\) | 24.6631 | − | 4.09035i | 0.986524 | − | 0.163614i | ||||
\(626\) | −8.58662 | − | 14.8725i | −0.343190 | − | 0.594423i | ||||
\(627\) | −6.22579 | + | 3.59446i | −0.248634 | + | 0.143549i | ||||
\(628\) | −13.2067 | − | 7.62491i | −0.527006 | − | 0.304267i | ||||
\(629\) | 12.9750 | 0.517348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.237559 | −0.00945707 | −0.00472853 | − | 0.999989i | \(-0.501505\pi\) | ||||
−0.00472853 | + | 0.999989i | \(0.501505\pi\) | |||||||
\(632\) | −2.50079 | − | 1.44383i | −0.0994761 | − | 0.0574326i | ||||
\(633\) | 13.3478 | − | 7.70636i | 0.530528 | − | 0.306300i | ||||
\(634\) | 1.30770 | + | 2.26501i | 0.0519355 | + | 0.0899549i | ||||
\(635\) | 26.1371 | − | 1.07453i | 1.03722 | − | 0.0426415i | ||||
\(636\) | 0.657293 | 0.0260634 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.66974i | 0.145287i | ||||||||
\(639\) | −7.05595 | + | 12.2213i | −0.279129 | + | 0.483466i | ||||
\(640\) | −1.03755 | + | 1.98078i | −0.0410126 | + | 0.0782973i | ||||
\(641\) | 7.67451 | + | 13.2926i | 0.303125 | + | 0.525028i | 0.976842 | − | 0.213962i | \(-0.0686367\pi\) |
−0.673717 | + | 0.738989i | \(0.735303\pi\) | |||||||
\(642\) | 17.3560 | + | 10.0205i | 0.684988 | + | 0.395478i | ||||
\(643\) | − | 8.77577i | − | 0.346083i | −0.984915 | − | 0.173041i | \(-0.944641\pi\) | ||
0.984915 | − | 0.173041i | \(-0.0553594\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.8489 | + | 11.9408i | −0.742176 | + | 0.470167i | ||||
\(646\) | 10.2754 | − | 17.7975i | 0.404281 | − | 0.700235i | ||||
\(647\) | −16.6714 | + | 9.62522i | −0.655419 | + | 0.378406i | −0.790529 | − | 0.612424i | \(-0.790194\pi\) |
0.135110 | + | 0.990831i | \(0.456861\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 4.04950 | − | 7.01395i | 0.158957 | − | 0.275321i | ||||
\(650\) | 0.929553 | − | 1.96723i | 0.0364600 | − | 0.0771610i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.47599i | 0.292782i | ||||||||
\(653\) | −6.45588 | − | 3.72730i | −0.252638 | − | 0.145861i | 0.368334 | − | 0.929694i | \(-0.379928\pi\) |
−0.620972 | + | 0.783833i | \(0.713262\pi\) | |||||||
\(654\) | 9.32821 | + | 16.1569i | 0.364762 | + | 0.631786i | ||||
\(655\) | 10.6657 | + | 5.58676i | 0.416744 | + | 0.218293i | ||||
\(656\) | −2.47472 | + | 4.28634i | −0.0966215 | + | 0.167353i | ||||
\(657\) | 15.3928i | 0.600532i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.93717 | −0.114416 | −0.0572079 | − | 0.998362i | \(-0.518220\pi\) | ||||
−0.0572079 | + | 0.998362i | \(0.518220\pi\) | |||||||
\(660\) | −2.18739 | + | 0.0899264i | −0.0851440 | + | 0.00350038i | ||||
\(661\) | 11.8180 | + | 20.4695i | 0.459669 | + | 0.796170i | 0.998943 | − | 0.0459604i | \(-0.0146348\pi\) |
−0.539275 | + | 0.842130i | \(0.681301\pi\) | |||||||
\(662\) | 15.3770 | − | 8.87793i | 0.597645 | − | 0.345051i | ||||
\(663\) | 1.05475 | + | 0.608961i | 0.0409631 | + | 0.0236501i | ||||
\(664\) | −14.3842 | −0.558214 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.63591 | 0.179638 | ||||||||
\(667\) | −10.8507 | − | 6.26464i | −0.420140 | − | 0.242568i | ||||
\(668\) | −10.9674 | + | 6.33202i | −0.424340 | + | 0.244993i | ||||
\(669\) | 3.80748 | + | 6.59475i | 0.147206 | + | 0.254968i | ||||
\(670\) | 0.217102 | + | 5.28082i | 0.00838737 | + | 0.204016i | ||||
\(671\) | −11.0962 | −0.428365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 50.9568i | − | 1.96424i | −0.188256 | − | 0.982120i | \(-0.560283\pi\) | ||
0.188256 | − | 0.982120i | \(-0.439717\pi\) | |||||||
\(674\) | −12.1152 | + | 20.9841i | −0.466660 | + | 0.808278i | ||||
\(675\) | 0.410420 | + | 4.98313i | 0.0157971 | + | 0.191801i | ||||
\(676\) | 6.40532 | + | 11.0943i | 0.246358 | + | 0.426705i | ||||
\(677\) | −4.53791 | − | 2.61996i | −0.174406 | − | 0.100693i | 0.410256 | − | 0.911971i | \(-0.365439\pi\) |
−0.584662 | + | 0.811277i | \(0.698773\pi\) | |||||||
\(678\) | 10.4132i | 0.399915i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.28676 | − | 3.34915i | 0.202738 | − | 0.128434i | ||||
\(681\) | 4.17113 | − | 7.22462i | 0.159838 | − | 0.276848i | ||||
\(682\) | −4.22168 | + | 2.43739i | −0.161656 | + | 0.0933324i | ||||
\(683\) | 27.9421 | − | 16.1324i | 1.06918 | − | 0.617289i | 0.141220 | − | 0.989978i | \(-0.454898\pi\) |
0.927956 | + | 0.372689i | \(0.121564\pi\) | |||||||
\(684\) | 3.67135 | − | 6.35897i | 0.140378 | − | 0.243141i | ||||
\(685\) | 4.41062 | + | 6.96233i | 0.168521 | + | 0.266017i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 18.6901i | − | 0.713071i | ||||||
\(688\) | 8.64174 | + | 4.98931i | 0.329463 | + | 0.190216i | ||||
\(689\) | 0.143013 | + | 0.247706i | 0.00544836 | + | 0.00943683i | ||||
\(690\) | 3.46821 | − | 6.62118i | 0.132033 | − | 0.252064i | ||||
\(691\) | 10.2235 | − | 17.7076i | 0.388920 | − | 0.673629i | −0.603385 | − | 0.797450i | \(-0.706182\pi\) |
0.992305 | + | 0.123821i | \(0.0395150\pi\) | |||||||
\(692\) | − | 7.12057i | − | 0.270684i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.4252 | −1.15492 | ||||||||
\(695\) | 0.748926 | + | 18.2170i | 0.0284084 | + | 0.691011i | ||||
\(696\) | −1.87412 | − | 3.24608i | −0.0710384 | − | 0.123042i | ||||
\(697\) | 11.9966 | − | 6.92626i | 0.454405 | − | 0.262351i | ||||
\(698\) | −26.2079 | − | 15.1311i | −0.991983 | − | 0.572722i | ||||
\(699\) | −20.0829 | −0.759605 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.4969 | −0.585311 | −0.292655 | − | 0.956218i | \(-0.594539\pi\) | ||||
−0.292655 | + | 0.956218i | \(0.594539\pi\) | |||||||
\(702\) | 0.376857 | + | 0.217579i | 0.0142236 | + | 0.00821198i | ||||
\(703\) | 29.4796 | − | 17.0201i | 1.11184 | − | 0.641924i | ||||
\(704\) | 0.489528 | + | 0.847888i | 0.0184498 | + | 0.0319560i | ||||
\(705\) | −0.404649 | − | 9.84277i | −0.0152400 | − | 0.370700i | ||||
\(706\) | 4.37189 | 0.164538 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.27226i | 0.310891i | ||||||||
\(709\) | 19.4606 | − | 33.7068i | 0.730859 | − | 1.26588i | −0.225658 | − | 0.974207i | \(-0.572453\pi\) |
0.956517 | − | 0.291678i | \(-0.0942134\pi\) | |||||||
\(710\) | −14.6417 | + | 27.9526i | −0.549495 | + | 1.04904i | ||||
\(711\) | 1.44383 | + | 2.50079i | 0.0541479 | + | 0.0937870i | ||||
\(712\) | 8.76505 | + | 5.06051i | 0.328484 | + | 0.189650i | ||||
\(713\) | − | 16.6435i | − | 0.623305i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.509819 | − | 0.804767i | −0.0190661 | − | 0.0300966i | ||||
\(716\) | −1.63210 | + | 2.82688i | −0.0609945 | + | 0.105646i | ||||
\(717\) | 19.2876 | − | 11.1357i | 0.720308 | − | 0.415870i | ||||
\(718\) | −13.5836 | + | 7.84249i | −0.506935 | + | 0.292679i | ||||
\(719\) | 1.76560 | − | 3.05810i | 0.0658456 | − | 0.114048i | −0.831223 | − | 0.555939i | \(-0.812359\pi\) |
0.897069 | + | 0.441891i | \(0.145692\pi\) | |||||||
\(720\) | 1.88893 | − | 1.19663i | 0.0703963 | − | 0.0445959i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 34.9153i | − | 1.29941i | ||||||
\(723\) | 5.37001 | + | 3.10038i | 0.199713 | + | 0.115304i | ||||
\(724\) | 0.969114 | + | 1.67855i | 0.0360168 | + | 0.0623830i | ||||
\(725\) | 18.6780 | − | 1.53835i | 0.693683 | − | 0.0571330i | ||||
\(726\) | 5.02072 | − | 8.69615i | 0.186337 | − | 0.322744i | ||||
\(727\) | 45.2934i | 1.67984i | 0.542712 | + | 0.839919i | \(0.317398\pi\) | ||||
−0.542712 | + | 0.839919i | \(0.682602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 1.41383 | + | 34.3904i | 0.0523283 | + | 1.27284i | ||||
\(731\) | −13.9641 | − | 24.1866i | −0.516482 | − | 0.894572i | ||||
\(732\) | 9.81518 | − | 5.66680i | 0.362779 | − | 0.209451i | ||||
\(733\) | 42.0422 | + | 24.2731i | 1.55286 | + | 0.896547i | 0.997907 | + | 0.0646687i | \(0.0205991\pi\) |
0.554958 | + | 0.831878i | \(0.312734\pi\) | |||||||
\(734\) | 4.94478 | 0.182515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.34271 | −0.123214 | ||||||||
\(737\) | 2.00411 | + | 1.15707i | 0.0738223 | + | 0.0426214i | ||||
\(738\) | 4.28634 | − | 2.47472i | 0.157782 | − | 0.0910957i | ||||
\(739\) | 12.8984 | + | 22.3407i | 0.474477 | + | 0.821818i | 0.999573 | − | 0.0292252i | \(-0.00930400\pi\) |
−0.525096 | + | 0.851043i | \(0.675971\pi\) | |||||||
\(740\) | 10.3575 | − | 0.425809i | 0.380748 | − | 0.0156530i | ||||
\(741\) | 3.19523 | 0.117380 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.7192i | − | 1.05361i | −0.849987 | − | 0.526803i | \(-0.823390\pi\) | ||
0.849987 | − | 0.526803i | \(-0.176610\pi\) | |||||||
\(744\) | 2.48953 | − | 4.31199i | 0.0912705 | − | 0.158085i | ||||
\(745\) | 31.0534 | + | 16.2660i | 1.13771 | + | 0.595939i | ||||
\(746\) | 3.01069 | + | 5.21467i | 0.110229 | + | 0.190923i | ||||
\(747\) | 12.4570 | + | 7.19208i | 0.455779 | + | 0.263144i | ||||
\(748\) | − | 2.74019i | − | 0.100191i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.37465 | + | 11.0955i | 0.0501952 | + | 0.405151i | ||||
\(751\) | 17.0938 | − | 29.6073i | 0.623762 | − | 1.08039i | −0.365017 | − | 0.931001i | \(-0.618937\pi\) |
0.988779 | − | 0.149386i | \(-0.0477298\pi\) | |||||||
\(752\) | −3.81531 | + | 2.20277i | −0.139130 | + | 0.0803267i | ||||
\(753\) | −23.9508 | + | 13.8280i | −0.872815 | + | 0.503920i | ||||
\(754\) | 0.815538 | − | 1.41255i | 0.0297002 | − | 0.0514422i | ||||
\(755\) | −8.07001 | + | 5.11233i | −0.293698 | + | 0.186057i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.4622i | 1.50697i | 0.657465 | + | 0.753485i | \(0.271629\pi\) | ||||
−0.657465 | + | 0.753485i | \(0.728371\pi\) | |||||||
\(758\) | 31.8723 | + | 18.4015i | 1.15766 | + | 0.668373i | ||||
\(759\) | −1.63635 | − | 2.83424i | −0.0593957 | − | 0.102876i | ||||
\(760\) | 7.61840 | − | 14.5443i | 0.276348 | − | 0.527577i | ||||
\(761\) | 13.8470 | − | 23.9838i | 0.501955 | − | 0.869412i | −0.498042 | − | 0.867153i | \(-0.665948\pi\) |
0.999997 | − | 0.00225889i | \(-0.000719027\pi\) | |||||||
\(762\) | 11.6987i | 0.423801i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.07001 | −0.291963 | ||||||||
\(765\) | −6.25304 | + | 0.257071i | −0.226079 | + | 0.00929442i | ||||
\(766\) | −4.51692 | − | 7.82353i | −0.163203 | − | 0.282676i | ||||
\(767\) | −3.11746 | + | 1.79987i | −0.112565 | + | 0.0649894i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 9.74001 | 0.351234 | 0.175617 | − | 0.984459i | \(-0.443808\pi\) | ||||
0.175617 | + | 0.984459i | \(0.443808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.7681 | −0.423819 | ||||||||
\(772\) | 1.69578 | + | 0.979056i | 0.0610323 | + | 0.0352370i | ||||
\(773\) | −26.5152 | + | 15.3085i | −0.953684 | + | 0.550610i | −0.894223 | − | 0.447621i | \(-0.852271\pi\) |
−0.0594605 | + | 0.998231i | \(0.518938\pi\) | |||||||
\(774\) | −4.98931 | − | 8.64174i | −0.179337 | − | 0.310621i | ||||
\(775\) | 14.1754 | + | 20.4654i | 0.509194 | + | 0.735140i | ||||
\(776\) | 10.6655 | 0.382870 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.5646i | 1.20335i | ||||||||
\(779\) | 18.1711 | − | 31.4733i | 0.651048 | − | 1.12765i | ||||
\(780\) | 0.861952 | + | 0.451496i | 0.0308628 | + | 0.0161661i | ||||
\(781\) | 6.90817 | + | 11.9653i | 0.247194 | + | 0.428152i | ||||
\(782\) | 8.10218 | + | 4.67780i | 0.289734 | + | 0.167278i | ||||
\(783\) | 3.74825i | 0.133951i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.2485 | + | 28.8059i | 0.651316 | + | 1.02813i | ||||
\(786\) | −2.69230 | + | 4.66320i | −0.0960311 | + | 0.166331i | ||||
\(787\) | 13.6813 | − | 7.89887i | 0.487684 | − | 0.281564i | −0.235929 | − | 0.971770i | \(-0.575813\pi\) |
0.723613 | + | 0.690206i | \(0.242480\pi\) | |||||||
\(788\) | −15.0185 | + | 8.67091i | −0.535011 | + | 0.308889i | ||||
\(789\) | −0.227521 | + | 0.394078i | −0.00809996 | + | 0.0140295i | ||||
\(790\) | 3.45548 | + | 5.45460i | 0.122940 | + | 0.194066i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 0.979056i | − | 0.0347892i | ||||||
\(793\) | 4.27115 | + | 2.46595i | 0.151673 | + | 0.0875684i | ||||
\(794\) | −16.9896 | − | 29.4269i | −0.602939 | − | 1.04432i | ||||
\(795\) | −1.30195 | − | 0.681971i | −0.0461756 | − | 0.0241870i | ||||
\(796\) | −1.29745 | + | 2.24725i | −0.0459869 | + | 0.0796516i | ||||
\(797\) | 47.6651i | 1.68838i | 0.536041 | + | 0.844192i | \(0.319919\pi\) | ||||
−0.536041 | + | 0.844192i | \(0.680081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.3303 | 0.436213 | ||||||||
\(800\) | 4.11030 | − | 2.84700i | 0.145321 | − | 0.100657i | ||||
\(801\) | −5.06051 | − | 8.76505i | −0.178804 | − | 0.309698i | ||||
\(802\) | 3.69989 | − | 2.13613i | 0.130647 | − | 0.0754294i | ||||
\(803\) | 13.0514 | + | 7.53522i | 0.460574 | + | 0.265912i | ||||
\(804\) | −2.36365 | −0.0833595 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.16667 | 0.0763178 | ||||||||
\(807\) | 22.6357 | + | 13.0687i | 0.796815 | + | 0.460041i | ||||
\(808\) | 12.1527 | − | 7.01639i | 0.427532 | − | 0.246836i | ||||
\(809\) | −8.63547 | − | 14.9571i | −0.303607 | − | 0.525863i | 0.673343 | − | 0.739330i | \(-0.264858\pi\) |
−0.976950 | + | 0.213467i | \(0.931524\pi\) | |||||||
\(810\) | −2.23418 | + | 0.0918501i | −0.0785011 | + | 0.00322728i | ||||
\(811\) | 14.7901 | 0.519351 | 0.259676 | − | 0.965696i | \(-0.416384\pi\) | ||||
0.259676 | + | 0.965696i | \(0.416384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.7768i | 0.588388i | ||||||||
\(814\) | 2.26941 | − | 3.93073i | 0.0795427 | − | 0.137772i | ||||
\(815\) | 7.75668 | − | 14.8083i | 0.271705 | − | 0.518712i | ||||
\(816\) | 1.39940 | + | 2.42384i | 0.0489889 | + | 0.0848513i | ||||
\(817\) | −63.4537 | − | 36.6350i | −2.21997 | − | 1.28170i | ||||
\(818\) | 3.63888i | 0.127231i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.34915 | − | 5.92267i | 0.326487 | − | 0.206829i | ||||
\(821\) | 22.8459 | − | 39.5702i | 0.797326 | − | 1.38101i | −0.124026 | − | 0.992279i | \(-0.539581\pi\) |
0.921352 | − | 0.388730i | \(-0.127086\pi\) | |||||||
\(822\) | −3.19204 | + | 1.84293i | −0.111335 | + | 0.0642794i | ||||
\(823\) | −4.32481 | + | 2.49693i | −0.150753 | + | 0.0870375i | −0.573479 | − | 0.819220i | \(-0.694407\pi\) |
0.422726 | + | 0.906258i | \(0.361073\pi\) | |||||||
\(824\) | −5.19208 | + | 8.99294i | −0.180875 | + | 0.313284i | ||||
\(825\) | 4.42604 | + | 2.09139i | 0.154095 | + | 0.0728129i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 53.5946i | − | 1.86367i | −0.362885 | − | 0.931834i | \(-0.618208\pi\) | ||
0.362885 | − | 0.931834i | \(-0.381792\pi\) | |||||||
\(828\) | 2.89487 | + | 1.67135i | 0.100604 | + | 0.0580836i | ||||
\(829\) | 0.583460 | + | 1.01058i | 0.0202644 | + | 0.0350990i | 0.875980 | − | 0.482348i | \(-0.160216\pi\) |
−0.855715 | + | 0.517447i | \(0.826883\pi\) | |||||||
\(830\) | 28.4919 | + | 14.9242i | 0.988968 | + | 0.518027i | ||||
\(831\) | 10.3739 | − | 17.9681i | 0.359867 | − | 0.623307i | ||||
\(832\) | − | 0.435157i | − | 0.0150864i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.15378 | −0.282342 | ||||||||
\(835\) | 28.2937 | − | 1.16319i | 0.979145 | − | 0.0402539i | ||||
\(836\) | −3.59446 | − | 6.22579i | −0.124317 | − | 0.215323i | ||||
\(837\) | −4.31199 | + | 2.48953i | −0.149044 | + | 0.0860507i | ||||
\(838\) | 23.0600 | + | 13.3137i | 0.796595 | + | 0.459914i | ||||
\(839\) | 31.2709 | 1.07959 | 0.539796 | − | 0.841796i | \(-0.318501\pi\) | ||||
0.539796 | + | 0.841796i | \(0.318501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.9507 | −0.515540 | ||||||||
\(842\) | −13.1532 | − | 7.59402i | −0.453290 | − | 0.261707i | ||||
\(843\) | −15.8605 | + | 9.15707i | −0.546265 | + | 0.315386i | ||||
\(844\) | 7.70636 | + | 13.3478i | 0.265264 | + | 0.459450i | ||||
\(845\) | −1.17666 | − | 28.6213i | −0.0404783 | − | 0.984602i | ||||
\(846\) | 4.40554 | 0.151466 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.657293i | 0.0225715i | ||||||||
\(849\) | −5.92626 | + | 10.2646i | −0.203389 | + | 0.352280i | ||||
\(850\) | −13.9468 | + | 1.14869i | −0.478372 | + | 0.0393996i | ||||
\(851\) | 7.74825 | + | 13.4204i | 0.265606 | + | 0.460044i | ||||
\(852\) | −12.2213 | − | 7.05595i | −0.418693 | − | 0.241733i | ||||
\(853\) | 11.3154i | 0.387431i | 0.981058 | + | 0.193715i | \(0.0620538\pi\) | ||||
−0.981058 | + | 0.193715i | \(0.937946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.8699 | + | 8.78654i | −0.474340 | + | 0.300493i | ||||
\(856\) | −10.0205 | + | 17.3560i | −0.342494 | + | 0.593217i | ||||
\(857\) | 31.9192 | − | 18.4286i | 1.09034 | − | 0.629508i | 0.156673 | − | 0.987650i | \(-0.449923\pi\) |
0.933667 | + | 0.358142i | \(0.116590\pi\) | |||||||
\(858\) | 0.368964 | − | 0.213022i | 0.0125962 | − | 0.00727244i | ||||
\(859\) | 9.34871 | − | 16.1924i | 0.318974 | − | 0.552479i | −0.661300 | − | 0.750121i | \(-0.729995\pi\) |
0.980274 | + | 0.197642i | \(0.0633284\pi\) | |||||||
\(860\) | −11.9408 | − | 18.8489i | −0.407177 | − | 0.642743i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.23125i | 0.144117i | ||||||||
\(863\) | −25.5810 | − | 14.7692i | −0.870787 | − | 0.502749i | −0.00317724 | − | 0.999995i | \(-0.501011\pi\) |
−0.867610 | + | 0.497246i | \(0.834345\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −7.38792 | + | 14.1043i | −0.251197 | + | 0.479561i | ||||
\(866\) | 16.9676 | − | 29.3888i | 0.576583 | − | 0.998671i | ||||
\(867\) | 9.16667i | 0.311317i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.82719 | 0.0959057 | ||||||||
\(870\) | 0.344277 | + | 8.37426i | 0.0116721 | + | 0.283914i | ||||
\(871\) | −0.514280 | − | 0.890759i | −0.0174257 | − | 0.0301822i | ||||
\(872\) | −16.1569 | + | 9.32821i | −0.547143 | + | 0.315893i | ||||
\(873\) | −9.23662 | − | 5.33276i | −0.312612 | − | 0.180487i | ||||
\(874\) | 24.5445 | 0.830231 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.3928 | −0.520076 | ||||||||
\(877\) | −12.3478 | − | 7.12903i | −0.416957 | − | 0.240730i | 0.276817 | − | 0.960923i | \(-0.410720\pi\) |
−0.693775 | + | 0.720192i | \(0.744054\pi\) | |||||||
\(878\) | 4.74804 | − | 2.74128i | 0.160239 | − | 0.0925138i | ||||
\(879\) | −7.23852 | − | 12.5375i | −0.244149 | − | 0.422879i | ||||
\(880\) | −0.0899264 | − | 2.18739i | −0.00303142 | − | 0.0737369i | ||||
\(881\) | 31.2744 | 1.05366 | 0.526830 | − | 0.849971i | \(-0.323380\pi\) | ||||
0.526830 | + | 0.849971i | \(0.323380\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.3566i | 1.12254i | 0.827633 | + | 0.561270i | \(0.189687\pi\) | ||||
−0.827633 | + | 0.561270i | \(0.810313\pi\) | |||||||
\(884\) | −0.608961 | + | 1.05475i | −0.0204816 | + | 0.0354751i | ||||
\(885\) | 8.58285 | − | 16.3855i | 0.288509 | − | 0.550794i | ||||
\(886\) | −0.615405 | − | 1.06591i | −0.0206749 | − | 0.0358101i | ||||
\(887\) | 36.4981 | + | 21.0722i | 1.22549 | + | 0.707535i | 0.966083 | − | 0.258233i | \(-0.0831403\pi\) |
0.259405 | + | 0.965769i | \(0.416474\pi\) | |||||||
\(888\) | 4.63591i | 0.155571i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.1112 | − | 19.1179i | −0.405967 | − | 0.640834i | ||||
\(891\) | −0.489528 | + | 0.847888i | −0.0163998 | + | 0.0284053i | ||||
\(892\) | −6.59475 | + | 3.80748i | −0.220809 | + | 0.127484i | ||||
\(893\) | 28.0147 | − | 16.1743i | 0.937476 | − | 0.541252i | ||||
\(894\) | −7.83868 | + | 13.5770i | −0.262165 | + | 0.454083i | ||||
\(895\) | 6.16586 | − | 3.90606i | 0.206102 | − | 0.130565i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.45460i | 0.0485678i | ||||||||
\(898\) | −12.6817 | − | 7.32176i | −0.423193 | − | 0.244330i | ||||
\(899\) | 9.33136 | + | 16.1624i | 0.311218 | + | 0.539046i | ||||
\(900\) | −4.98313 | + | 0.410420i | −0.166104 | + | 0.0136807i | ||||
\(901\) | 0.919818 | − | 1.59317i | 0.0306436 | − | 0.0530763i | ||||
\(902\) | − | 4.84578i | − | 0.161347i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.4132 | −0.346336 | ||||||||
\(905\) | −0.178026 | − | 4.33035i | −0.00591780 | − | 0.143946i | ||||
\(906\) | −2.13613 | − | 3.69989i | −0.0709682 | − | 0.122920i | ||||
\(907\) | −48.4836 | + | 27.9920i | −1.60987 | + | 0.929460i | −0.620474 | + | 0.784227i | \(0.713060\pi\) |
−0.989397 | + | 0.145233i | \(0.953607\pi\) | |||||||
\(908\) | 7.22462 | + | 4.17113i | 0.239757 | + | 0.138424i | ||||
\(909\) | −14.0328 | −0.465438 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4389 | 1.00849 | 0.504243 | − | 0.863562i | \(-0.331771\pi\) | ||||
0.504243 | + | 0.863562i | \(0.331771\pi\) | |||||||
\(912\) | 6.35897 | + | 3.67135i | 0.210567 | + | 0.121571i | ||||
\(913\) | 12.1961 | − | 7.04145i | 0.403634 | − | 0.233038i | ||||
\(914\) | −15.6645 | − | 27.1317i | −0.518135 | − | 0.897436i | ||||
\(915\) | −25.3213 | + | 1.04099i | −0.837096 | + | 0.0344141i | ||||
\(916\) | 18.6901 | 0.617537 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 2.79881i | − | 0.0923744i | ||||||
\(919\) | −14.0769 | + | 24.3819i | −0.464354 | + | 0.804284i | −0.999172 | − | 0.0406827i | \(-0.987047\pi\) |
0.534818 | + | 0.844967i | \(0.320380\pi\) | |||||||
\(920\) | 6.62118 | + | 3.46821i | 0.218294 | + | 0.114344i | ||||
\(921\) | −15.2126 | − | 26.3490i | −0.501272 | − | 0.868228i | ||||
\(922\) | −11.0562 | − | 6.38333i | −0.364118 | − | 0.210224i | ||||
\(923\) | − | 6.14089i | − | 0.202130i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.9577 | − | 9.90291i | −0.689084 | − | 0.325606i | ||||
\(926\) | 13.3556 | − | 23.1326i | 0.438892 | − | 0.760183i | ||||
\(927\) | 8.99294 | − | 5.19208i | 0.295367 | − | 0.170530i | ||||
\(928\) | 3.24608 | − | 1.87412i | 0.106558 | − | 0.0615211i | ||||
\(929\) | −12.9477 | + | 22.4261i | −0.424801 | + | 0.735777i | −0.996402 | − | 0.0847546i | \(-0.972989\pi\) |
0.571601 | + | 0.820532i | \(0.306323\pi\) | |||||||
\(930\) | −9.40510 | + | 5.95811i | −0.308405 | + | 0.195374i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 20.0829i | − | 0.657837i | ||||||
\(933\) | 7.81896 | + | 4.51428i | 0.255981 | + | 0.147791i | ||||
\(934\) | 18.8070 | + | 32.5748i | 0.615385 | + | 1.06588i | ||||
\(935\) | −2.84307 | + | 5.42772i | −0.0929784 | + | 0.177505i | ||||
\(936\) | −0.217579 | + | 0.376857i | −0.00711178 | + | 0.0123180i | ||||
\(937\) | − | 48.1184i | − | 1.57196i | −0.618253 | − | 0.785979i | \(-0.712159\pi\) | ||
0.618253 | − | 0.785979i | \(-0.287841\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.1732 | −0.560427 | ||||||||
\(940\) | 9.84277 | − | 0.404649i | 0.321036 | − | 0.0131982i | ||||
\(941\) | −26.1033 | − | 45.2123i | −0.850944 | − | 1.47388i | −0.880358 | − | 0.474310i | \(-0.842698\pi\) |
0.0294144 | − | 0.999567i | \(-0.490636\pi\) | |||||||
\(942\) | −13.2067 | + | 7.62491i | −0.430299 | + | 0.248433i | ||||
\(943\) | 14.3280 | + | 8.27226i | 0.466583 | + | 0.269382i | ||||
\(944\) | −8.27226 | −0.269239 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.76963 | −0.317638 | ||||||||
\(947\) | −17.5799 | − | 10.1498i | −0.571270 | − | 0.329823i | 0.186387 | − | 0.982476i | \(-0.440322\pi\) |
−0.757656 | + | 0.652654i | \(0.773656\pi\) | |||||||
\(948\) | −2.50079 | + | 1.44383i | −0.0812219 | + | 0.0468935i | ||||
\(949\) | −3.34915 | − | 5.80090i | −0.108718 | − | 0.188305i | ||||
\(950\) | −30.1808 | + | 20.9047i | −0.979193 | + | 0.678237i | ||||
\(951\) | 2.61541 | 0.0848103 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.9511i | − | 0.549100i | −0.961573 | − | 0.274550i | \(-0.911471\pi\) | ||
0.961573 | − | 0.274550i | \(-0.0885289\pi\) | |||||||
\(954\) | 0.328646 | − | 0.569232i | 0.0106403 | − | 0.0184296i | ||||
\(955\) | 15.9849 | + | 8.37300i | 0.517260 | + | 0.270944i | ||||
\(956\) | 11.1357 | + | 19.2876i | 0.360154 | + | 0.623805i | ||||
\(957\) | 3.17809 | + | 1.83487i | 0.102733 | + | 0.0593130i | ||||
\(958\) | 23.8235i | 0.769703i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.19663 | + | 1.88893i | 0.0386212 | + | 0.0609650i | ||||
\(961\) | 3.10450 | − | 5.37715i | 0.100145 | − | 0.173456i | ||||
\(962\) | −1.74708 | + | 1.00868i | −0.0563280 | + | 0.0325210i | ||||
\(963\) | 17.3560 | − | 10.0205i | 0.559290 | − | 0.322906i | ||||
\(964\) | −3.10038 | + | 5.37001i | −0.0998564 | + | 0.172956i | ||||
\(965\) | −2.34315 | − | 3.69874i | −0.0754285 | − | 0.119067i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.0294i | 0.740577i | 0.928917 | + | 0.370288i | \(0.120741\pi\) | ||||
−0.928917 | + | 0.370288i | \(0.879259\pi\) | |||||||
\(968\) | 8.69615 | + | 5.02072i | 0.279505 | + | 0.161372i | ||||
\(969\) | −10.2754 | − | 17.7975i | −0.330094 | − | 0.571739i | ||||
\(970\) | −21.1261 | − | 11.0660i | −0.678318 | − | 0.355307i | ||||
\(971\) | −6.18848 | + | 10.7188i | −0.198598 | + | 0.343982i | −0.948074 | − | 0.318050i | \(-0.896972\pi\) |
0.749476 | + | 0.662031i | \(0.230305\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.75674 | 0.120374 | ||||||||
\(975\) | −1.23889 | − | 1.78863i | −0.0396763 | − | 0.0572820i | ||||
\(976\) | 5.66680 | + | 9.81518i | 0.181390 | + | 0.314176i | ||||
\(977\) | 0.871343 | − | 0.503070i | 0.0278767 | − | 0.0160946i | −0.485997 | − | 0.873961i | \(-0.661543\pi\) |
0.513874 | + | 0.857866i | \(0.328210\pi\) | |||||||
\(978\) | 6.47439 | + | 3.73799i | 0.207028 | + | 0.119528i | ||||
\(979\) | −9.90904 | −0.316694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.6564 | 0.595654 | ||||||||
\(982\) | 1.73865 | + | 1.00381i | 0.0554824 | + | 0.0320328i | ||||
\(983\) | −36.4981 | + | 21.0722i | −1.16411 | + | 0.672099i | −0.952285 | − | 0.305209i | \(-0.901274\pi\) |
−0.211824 | + | 0.977308i | \(0.567940\pi\) | |||||||
\(984\) | 2.47472 | + | 4.28634i | 0.0788911 | + | 0.136643i | ||||
\(985\) | 38.7448 | − | 1.59285i | 1.23451 | − | 0.0507524i | ||||
\(986\) | −10.4906 | −0.334089 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.19523i | 0.101654i | ||||||||
\(989\) | 16.6778 | − | 28.8868i | 0.530323 | − | 0.918547i | ||||
\(990\) | −1.01582 | + | 1.93930i | −0.0322847 | + | 0.0616349i | ||||
\(991\) | 17.0346 | + | 29.5047i | 0.541121 | + | 0.937249i | 0.998840 | + | 0.0481519i | \(0.0153332\pi\) |
−0.457719 | + | 0.889097i | \(0.651333\pi\) | |||||||
\(992\) | 4.31199 | + | 2.48953i | 0.136906 | + | 0.0790426i | ||||
\(993\) | − | 17.7559i | − | 0.563465i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.90159 | − | 3.10515i | 0.155391 | − | 0.0984398i | ||||
\(996\) | −7.19208 | + | 12.4570i | −0.227890 | + | 0.394717i | ||||
\(997\) | 5.21413 | − | 3.01038i | 0.165133 | − | 0.0953397i | −0.415156 | − | 0.909750i | \(-0.636273\pi\) |
0.580289 | + | 0.814411i | \(0.302940\pi\) | |||||||
\(998\) | −0.544119 | + | 0.314147i | −0.0172238 | + | 0.00994415i | ||||
\(999\) | 2.31796 | − | 4.01482i | 0.0733369 | − | 0.127023i |
(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 | 1470.2.n.k.79.7 | 16 | ||
5.4 | even | 2 | inner | 1470.2.n.k.79.4 | 16 | ||
7.2 | even | 3 | 1470.2.g.k.589.1 | yes | 8 | ||
7.3 | odd | 6 | 1470.2.n.l.949.1 | 16 | |||
7.4 | even | 3 | inner | 1470.2.n.k.949.4 | 16 | ||
7.5 | odd | 6 | 1470.2.g.j.589.4 | ✓ | 8 | ||
7.6 | odd | 2 | 1470.2.n.l.79.6 | 16 | |||
35.2 | odd | 12 | 7350.2.a.du.1.3 | 4 | |||
35.4 | even | 6 | inner | 1470.2.n.k.949.7 | 16 | ||
35.9 | even | 6 | 1470.2.g.k.589.5 | yes | 8 | ||
35.12 | even | 12 | 7350.2.a.dt.1.3 | 4 | |||
35.19 | odd | 6 | 1470.2.g.j.589.8 | yes | 8 | ||
35.23 | odd | 12 | 7350.2.a.dr.1.3 | 4 | |||
35.24 | odd | 6 | 1470.2.n.l.949.6 | 16 | |||
35.33 | even | 12 | 7350.2.a.ds.1.3 | 4 | |||
35.34 | odd | 2 | 1470.2.n.l.79.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.g.j.589.4 | ✓ | 8 | 7.5 | odd | 6 | ||
1470.2.g.j.589.8 | yes | 8 | 35.19 | odd | 6 | ||
1470.2.g.k.589.1 | yes | 8 | 7.2 | even | 3 | ||
1470.2.g.k.589.5 | yes | 8 | 35.9 | even | 6 | ||
1470.2.n.k.79.4 | 16 | 5.4 | even | 2 | inner | ||
1470.2.n.k.79.7 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.n.k.949.4 | 16 | 7.4 | even | 3 | inner | ||
1470.2.n.k.949.7 | 16 | 35.4 | even | 6 | inner | ||
1470.2.n.l.79.1 | 16 | 35.34 | odd | 2 | |||
1470.2.n.l.79.6 | 16 | 7.6 | odd | 2 | |||
1470.2.n.l.949.1 | 16 | 7.3 | odd | 6 | |||
1470.2.n.l.949.6 | 16 | 35.24 | odd | 6 | |||
7350.2.a.dr.1.3 | 4 | 35.23 | odd | 12 | |||
7350.2.a.ds.1.3 | 4 | 35.33 | even | 12 | |||
7350.2.a.dt.1.3 | 4 | 35.12 | even | 12 | |||
7350.2.a.du.1.3 | 4 | 35.2 | odd | 12 |