Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.0898194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.49 |
Dual form | 375.2.i.c.199.2 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0527945 | + | 0.0726655i | −0.0373314 | + | 0.0513822i | −0.827275 | − | 0.561798i | \(-0.810110\pi\) |
0.789943 | + | 0.613180i | \(0.210110\pi\) | |||||||
\(3\) | −0.951057 | + | 0.309017i | −0.549093 | + | 0.178411i | ||||
\(4\) | 0.615541 | + | 1.89444i | 0.307770 | + | 0.947220i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0277557 | − | 0.0854234i | 0.0113312 | − | 0.0348739i | ||||
\(7\) | 4.36070i | 1.64819i | 0.566451 | + | 0.824095i | \(0.308316\pi\) | ||||
−0.566451 | + | 0.824095i | \(0.691684\pi\) | |||||||
\(8\) | −0.341004 | − | 0.110799i | −0.120563 | − | 0.0391734i | ||||
\(9\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.55235 | − | 2.58093i | −1.07107 | − | 0.778180i | −0.0949680 | − | 0.995480i | \(-0.530275\pi\) |
−0.976105 | + | 0.217300i | \(0.930275\pi\) | |||||||
\(12\) | −1.17083 | − | 1.61151i | −0.337989 | − | 0.465202i | ||||
\(13\) | −1.16479 | − | 1.60319i | −0.323054 | − | 0.444646i | 0.616343 | − | 0.787478i | \(-0.288614\pi\) |
−0.939397 | + | 0.342832i | \(0.888614\pi\) | |||||||
\(14\) | −0.316872 | − | 0.230221i | −0.0846877 | − | 0.0615292i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.19696 | + | 2.32273i | −0.799240 | + | 0.580682i | ||||
\(17\) | 0.948224 | + | 0.308097i | 0.229978 | + | 0.0747244i | 0.421739 | − | 0.906717i | \(-0.361420\pi\) |
−0.191761 | + | 0.981442i | \(0.561420\pi\) | |||||||
\(18\) | 0.0898194i | 0.0211706i | ||||||||
\(19\) | −0.417468 | + | 1.28484i | −0.0957738 | + | 0.294761i | −0.987455 | − | 0.157903i | \(-0.949527\pi\) |
0.891681 | + | 0.452665i | \(0.149527\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34753 | − | 4.14727i | −0.294055 | − | 0.905009i | ||||
\(22\) | 0.375089 | − | 0.121874i | 0.0799692 | − | 0.0259836i | ||||
\(23\) | −1.38512 | + | 1.90646i | −0.288818 | + | 0.397524i | −0.928630 | − | 0.371008i | \(-0.879012\pi\) |
0.639812 | + | 0.768532i | \(0.279012\pi\) | |||||||
\(24\) | 0.358553 | 0.0731893 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.177991 | 0.0349069 | ||||||||
\(27\) | −0.587785 | + | 0.809017i | −0.113119 | + | 0.155695i | ||||
\(28\) | −8.26109 | + | 2.68419i | −1.56120 | + | 0.507264i | ||||
\(29\) | 2.46551 | + | 7.58806i | 0.457834 | + | 1.40907i | 0.867776 | + | 0.496955i | \(0.165549\pi\) |
−0.409942 | + | 0.912111i | \(0.634451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.13645 | + | 3.49762i | −0.204112 | + | 0.628191i | 0.795637 | + | 0.605774i | \(0.207136\pi\) |
−0.999749 | + | 0.0224173i | \(0.992864\pi\) | |||||||
\(32\) | − | 1.07204i | − | 0.189512i | ||||||
\(33\) | 4.17603 | + | 1.35688i | 0.726954 | + | 0.236202i | ||||
\(34\) | −0.0724490 | + | 0.0526373i | −0.0124249 | + | 0.00902722i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.61151 | + | 1.17083i | 0.268585 | + | 0.195138i | ||||
\(37\) | 0.844681 | + | 1.16260i | 0.138865 | + | 0.191131i | 0.872785 | − | 0.488105i | \(-0.162312\pi\) |
−0.733920 | + | 0.679235i | \(0.762312\pi\) | |||||||
\(38\) | −0.0713231 | − | 0.0981678i | −0.0115701 | − | 0.0159249i | ||||
\(39\) | 1.60319 | + | 1.16479i | 0.256716 | + | 0.186515i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.83992 | − | 3.51641i | 0.755869 | − | 0.549171i | −0.141771 | − | 0.989899i | \(-0.545280\pi\) |
0.897641 | + | 0.440728i | \(0.145280\pi\) | |||||||
\(42\) | 0.372506 | + | 0.121034i | 0.0574789 | + | 0.0186760i | ||||
\(43\) | − | 2.68554i | − | 0.409541i | −0.978810 | − | 0.204770i | \(-0.934355\pi\) | ||
0.978810 | − | 0.204770i | \(-0.0656447\pi\) | |||||||
\(44\) | 2.70280 | − | 8.31838i | 0.407463 | − | 1.25404i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0654066 | − | 0.201301i | −0.00964368 | − | 0.0296802i | ||||
\(47\) | −10.4039 | + | 3.38042i | −1.51756 | + | 0.493086i | −0.945082 | − | 0.326833i | \(-0.894018\pi\) |
−0.572480 | + | 0.819919i | \(0.694018\pi\) | |||||||
\(48\) | 2.32273 | − | 3.19696i | 0.335257 | − | 0.461441i | ||||
\(49\) | −12.0157 | −1.71653 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.997022 | −0.139611 | ||||||||
\(52\) | 2.32018 | − | 3.19345i | 0.321751 | − | 0.442852i | ||||
\(53\) | 10.5102 | − | 3.41496i | 1.44368 | − | 0.469081i | 0.520639 | − | 0.853777i | \(-0.325694\pi\) |
0.923043 | + | 0.384696i | \(0.125694\pi\) | |||||||
\(54\) | −0.0277557 | − | 0.0854234i | −0.00377708 | − | 0.0116246i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.483161 | − | 1.48702i | 0.0645652 | − | 0.198711i | ||||
\(57\) | − | 1.35096i | − | 0.178938i | ||||||
\(58\) | −0.681555 | − | 0.221451i | −0.0894926 | − | 0.0290779i | ||||
\(59\) | 5.41147 | − | 3.93167i | 0.704514 | − | 0.511859i | −0.176885 | − | 0.984231i | \(-0.556602\pi\) |
0.881399 | + | 0.472372i | \(0.156602\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.64982 | + | 5.55792i | 0.979460 | + | 0.711619i | 0.957588 | − | 0.288142i | \(-0.0930374\pi\) |
0.0218719 | + | 0.999761i | \(0.493037\pi\) | |||||||
\(62\) | −0.194158 | − | 0.267235i | −0.0246581 | − | 0.0339389i | ||||
\(63\) | 2.56316 | + | 3.52788i | 0.322927 | + | 0.444471i | ||||
\(64\) | −6.31602 | − | 4.58886i | −0.789502 | − | 0.573607i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.319070 | + | 0.231818i | −0.0392748 | + | 0.0285348i | ||||
\(67\) | 12.2894 | + | 3.99307i | 1.50139 | + | 0.487831i | 0.940423 | − | 0.340006i | \(-0.110429\pi\) |
0.560968 | + | 0.827838i | \(0.310429\pi\) | |||||||
\(68\) | 1.98600i | 0.240838i | ||||||||
\(69\) | 0.728201 | − | 2.24117i | 0.0876651 | − | 0.269806i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.26280 | + | 6.96418i | 0.268545 | + | 0.826496i | 0.990856 | + | 0.134927i | \(0.0430800\pi\) |
−0.722311 | + | 0.691569i | \(0.756920\pi\) | |||||||
\(72\) | −0.341004 | + | 0.110799i | −0.0401877 | + | 0.0130578i | ||||
\(73\) | 0.249694 | − | 0.343674i | 0.0292244 | − | 0.0402240i | −0.794155 | − | 0.607716i | \(-0.792086\pi\) |
0.823379 | + | 0.567492i | \(0.192086\pi\) | |||||||
\(74\) | −0.129076 | −0.0150047 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.69101 | −0.308680 | ||||||||
\(77\) | 11.2547 | − | 15.4907i | 1.28259 | − | 1.76533i | ||||
\(78\) | −0.169280 | + | 0.0550023i | −0.0191671 | + | 0.00622778i | ||||
\(79\) | 1.96390 | + | 6.04425i | 0.220956 | + | 0.680032i | 0.998677 | + | 0.0514225i | \(0.0163755\pi\) |
−0.777721 | + | 0.628609i | \(0.783624\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 0.537343i | 0.0593396i | ||||||||
\(83\) | −0.700939 | − | 0.227749i | −0.0769381 | − | 0.0249987i | 0.270295 | − | 0.962778i | \(-0.412879\pi\) |
−0.347233 | + | 0.937779i | \(0.612879\pi\) | |||||||
\(84\) | 7.02730 | − | 5.10563i | 0.766742 | − | 0.557070i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.195146 | + | 0.141782i | 0.0210431 | + | 0.0152887i | ||||
\(87\) | −4.68968 | − | 6.45479i | −0.502786 | − | 0.692026i | ||||
\(88\) | 0.925401 | + | 1.27370i | 0.0986481 | + | 0.135777i | ||||
\(89\) | −7.91814 | − | 5.75286i | −0.839321 | − | 0.609802i | 0.0828599 | − | 0.996561i | \(-0.473595\pi\) |
−0.922181 | + | 0.386759i | \(0.873595\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.99105 | − | 5.07929i | 0.732861 | − | 0.532455i | ||||
\(92\) | −4.46427 | − | 1.45053i | −0.465432 | − | 0.151228i | ||||
\(93\) | − | 3.67761i | − | 0.381351i | ||||||
\(94\) | 0.303628 | − | 0.934470i | 0.0313168 | − | 0.0963833i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.331279 | + | 1.01957i | 0.0338110 | + | 0.104060i | ||||
\(97\) | −0.0320583 | + | 0.0104164i | −0.00325503 | + | 0.00105762i | −0.310644 | − | 0.950526i | \(-0.600545\pi\) |
0.307389 | + | 0.951584i | \(0.400545\pi\) | |||||||
\(98\) | 0.634365 | − | 0.873128i | 0.0640805 | − | 0.0881992i | ||||
\(99\) | −4.39094 | −0.441306 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.19390 | 0.317805 | 0.158902 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158902 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(102\) | 0.0526373 | − | 0.0724490i | 0.00521187 | − | 0.00717352i | ||||
\(103\) | 8.13479 | − | 2.64315i | 0.801544 | − | 0.260438i | 0.120532 | − | 0.992709i | \(-0.461540\pi\) |
0.681012 | + | 0.732272i | \(0.261540\pi\) | |||||||
\(104\) | 0.219565 | + | 0.675753i | 0.0215302 | + | 0.0662630i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.306730 | + | 0.944017i | −0.0297922 | + | 0.0916910i | ||||
\(107\) | 2.22136i | 0.214747i | 0.994219 | + | 0.107373i | \(0.0342440\pi\) | ||||
−0.994219 | + | 0.107373i | \(0.965756\pi\) | |||||||
\(108\) | −1.89444 | − | 0.615541i | −0.182293 | − | 0.0592305i | ||||
\(109\) | 8.90108 | − | 6.46701i | 0.852569 | − | 0.619427i | −0.0732844 | − | 0.997311i | \(-0.523348\pi\) |
0.925853 | + | 0.377884i | \(0.123348\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.16260 | − | 0.844681i | −0.110349 | − | 0.0801735i | ||||
\(112\) | −10.1287 | − | 13.9410i | −0.957074 | − | 1.31730i | ||||
\(113\) | 1.00524 | + | 1.38359i | 0.0945646 | + | 0.130157i | 0.853678 | − | 0.520802i | \(-0.174367\pi\) |
−0.759113 | + | 0.650959i | \(0.774367\pi\) | |||||||
\(114\) | 0.0981678 | + | 0.0713231i | 0.00919426 | + | 0.00668002i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.8575 | + | 9.34152i | −1.19379 | + | 0.867338i | ||||
\(117\) | −1.88467 | − | 0.612365i | −0.174237 | − | 0.0566132i | ||||
\(118\) | 0.600798i | 0.0553079i | ||||||||
\(119\) | −1.34352 | + | 4.13492i | −0.123160 | + | 0.379048i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.55877 | + | 7.87510i | 0.232616 | + | 0.715918i | ||||
\(122\) | −0.807738 | + | 0.262450i | −0.0731292 | + | 0.0237611i | ||||
\(123\) | −3.51641 | + | 4.83992i | −0.317064 | + | 0.436401i | ||||
\(124\) | −7.32556 | −0.657855 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.391676 | −0.0348933 | ||||||||
\(127\) | −7.38079 | + | 10.1588i | −0.654939 | + | 0.901447i | −0.999301 | − | 0.0373905i | \(-0.988095\pi\) |
0.344361 | + | 0.938837i | \(0.388095\pi\) | |||||||
\(128\) | 2.70605 | − | 0.879248i | 0.239183 | − | 0.0777153i | ||||
\(129\) | 0.829877 | + | 2.55410i | 0.0730666 | + | 0.224876i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.09006 | − | 15.6656i | 0.444721 | − | 1.36871i | −0.438069 | − | 0.898942i | \(-0.644337\pi\) |
0.882790 | − | 0.469769i | \(-0.155663\pi\) | |||||||
\(132\) | 8.74646i | 0.761282i | ||||||||
\(133\) | −5.60278 | − | 1.82046i | −0.485823 | − | 0.157853i | ||||
\(134\) | −0.938972 | + | 0.682203i | −0.0811149 | + | 0.0589334i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.289212 | − | 0.210125i | −0.0247997 | − | 0.0180180i | ||||
\(137\) | 5.68231 | + | 7.82102i | 0.485472 | + | 0.668195i | 0.979545 | − | 0.201225i | \(-0.0644923\pi\) |
−0.494073 | + | 0.869421i | \(0.664492\pi\) | |||||||
\(138\) | 0.124411 | + | 0.171237i | 0.0105906 | + | 0.0145766i | ||||
\(139\) | 10.9482 | + | 7.95430i | 0.928611 | + | 0.674675i | 0.945652 | − | 0.325180i | \(-0.105425\pi\) |
−0.0170416 | + | 0.999855i | \(0.505425\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.85007 | − | 6.42995i | 0.745310 | − | 0.541499i | ||||
\(142\) | −0.625518 | − | 0.203243i | −0.0524923 | − | 0.0170558i | ||||
\(143\) | 8.70133i | 0.727642i | ||||||||
\(144\) | −1.22113 | + | 3.75825i | −0.101761 | + | 0.313188i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0117907 | + | 0.0362882i | 0.000975809 | + | 0.00300323i | ||||
\(147\) | 11.4276 | − | 3.71306i | 0.942535 | − | 0.306248i | ||||
\(148\) | −1.68255 | + | 2.31583i | −0.138304 | + | 0.190360i | ||||
\(149\) | −13.6843 | −1.12106 | −0.560529 | − | 0.828134i | \(-0.689402\pi\) | ||||
−0.560529 | + | 0.828134i | \(0.689402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3204 | −0.921237 | −0.460619 | − | 0.887598i | \(-0.652372\pi\) | ||||
−0.460619 | + | 0.887598i | \(0.652372\pi\) | |||||||
\(152\) | 0.284717 | − | 0.391879i | 0.0230936 | − | 0.0317856i | ||||
\(153\) | 0.948224 | − | 0.308097i | 0.0766594 | − | 0.0249081i | ||||
\(154\) | 0.531455 | + | 1.63565i | 0.0428259 | + | 0.131805i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.21979 | + | 3.75413i | −0.0976614 | + | 0.300571i | ||||
\(157\) | 8.56070i | 0.683219i | 0.939842 | + | 0.341609i | \(0.110972\pi\) | ||||
−0.939842 | + | 0.341609i | \(0.889028\pi\) | |||||||
\(158\) | −0.542892 | − | 0.176396i | −0.0431901 | − | 0.0140333i | ||||
\(159\) | −8.94048 | + | 6.49564i | −0.709026 | + | 0.515138i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.31349 | − | 6.04010i | −0.655194 | − | 0.476027i | ||||
\(162\) | 0.0527945 | + | 0.0726655i | 0.00414793 | + | 0.00570914i | ||||
\(163\) | 2.69505 | + | 3.70942i | 0.211093 | + | 0.290544i | 0.901413 | − | 0.432959i | \(-0.142531\pi\) |
−0.690321 | + | 0.723503i | \(0.742531\pi\) | |||||||
\(164\) | 9.64080 | + | 7.00445i | 0.752820 | + | 0.546956i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0535552 | − | 0.0389102i | 0.00415669 | − | 0.00302001i | ||||
\(167\) | 6.86465 | + | 2.23046i | 0.531203 | + | 0.172598i | 0.562323 | − | 0.826917i | \(-0.309908\pi\) |
−0.0311206 | + | 0.999516i | \(0.509908\pi\) | |||||||
\(168\) | 1.56354i | 0.120630i | ||||||||
\(169\) | 2.80372 | − | 8.62898i | 0.215671 | − | 0.663767i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.417468 | + | 1.28484i | 0.0319246 | + | 0.0982538i | ||||
\(172\) | 5.08759 | − | 1.65306i | 0.387925 | − | 0.126045i | ||||
\(173\) | 2.73326 | − | 3.76201i | 0.207806 | − | 0.286020i | −0.692374 | − | 0.721539i | \(-0.743435\pi\) |
0.900180 | + | 0.435519i | \(0.143435\pi\) | |||||||
\(174\) | 0.716629 | 0.0543275 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.3515 | 1.30792 | ||||||||
\(177\) | −3.93167 | + | 5.41147i | −0.295522 | + | 0.406751i | ||||
\(178\) | 0.836069 | − | 0.271655i | 0.0626660 | − | 0.0203614i | ||||
\(179\) | 2.22597 | + | 6.85082i | 0.166377 | + | 0.512055i | 0.999135 | − | 0.0415819i | \(-0.0132397\pi\) |
−0.832758 | + | 0.553636i | \(0.813240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.17557 | + | 3.61804i | −0.0873797 | + | 0.268927i | −0.985193 | − | 0.171449i | \(-0.945155\pi\) |
0.897813 | + | 0.440376i | \(0.145155\pi\) | |||||||
\(182\) | 0.776167i | 0.0575333i | ||||||||
\(183\) | −8.99291 | − | 2.92197i | −0.664775 | − | 0.215998i | ||||
\(184\) | 0.683566 | − | 0.496640i | 0.0503931 | − | 0.0366128i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.267235 | + | 0.194158i | 0.0195947 | + | 0.0142364i | ||||
\(187\) | −2.57324 | − | 3.54177i | −0.188174 | − | 0.259000i | ||||
\(188\) | −12.8080 | − | 17.6287i | −0.934121 | − | 1.28571i | ||||
\(189\) | −3.52788 | − | 2.56316i | −0.256616 | − | 0.186442i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.4377 | + | 12.6692i | −1.26174 | + | 0.916711i | −0.998842 | − | 0.0481112i | \(-0.984680\pi\) |
−0.262903 | + | 0.964822i | \(0.584680\pi\) | |||||||
\(192\) | 7.42493 | + | 2.41250i | 0.535848 | + | 0.174108i | ||||
\(193\) | − | 3.15029i | − | 0.226763i | −0.993552 | − | 0.113381i | \(-0.963832\pi\) | ||
0.993552 | − | 0.113381i | \(-0.0361682\pi\) | |||||||
\(194\) | 0.000935592 | − | 0.00287946i | 6.71716e−5 | − | 0.000206733i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.39617 | − | 22.7631i | −0.528298 | − | 1.62593i | ||||
\(197\) | −24.8071 | + | 8.06032i | −1.76743 | + | 0.574274i | −0.997927 | − | 0.0643637i | \(-0.979498\pi\) |
−0.769507 | + | 0.638638i | \(0.779498\pi\) | |||||||
\(198\) | 0.231818 | − | 0.319070i | 0.0164746 | − | 0.0226753i | ||||
\(199\) | 24.2662 | 1.72018 | 0.860092 | − | 0.510139i | \(-0.170406\pi\) | ||||
0.860092 | + | 0.510139i | \(0.170406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9219 | −0.911437 | ||||||||
\(202\) | −0.168620 | + | 0.232086i | −0.0118641 | + | 0.0163295i | ||||
\(203\) | −33.0893 | + | 10.7514i | −2.32241 | + | 0.754597i | ||||
\(204\) | −0.613708 | − | 1.88880i | −0.0429681 | − | 0.132242i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.237406 | + | 0.730662i | −0.0165409 | + | 0.0509076i | ||||
\(207\) | 2.35651i | 0.163789i | ||||||||
\(208\) | 7.44756 | + | 2.41986i | 0.516395 | + | 0.167787i | ||||
\(209\) | 4.79906 | − | 3.48672i | 0.331958 | − | 0.241182i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.2503 | − | 9.62694i | −0.912192 | − | 0.662746i | 0.0293766 | − | 0.999568i | \(-0.490648\pi\) |
−0.941568 | + | 0.336822i | \(0.890648\pi\) | |||||||
\(212\) | 12.9389 | + | 17.8088i | 0.888645 | + | 1.22312i | ||||
\(213\) | −4.30410 | − | 5.92408i | −0.294912 | − | 0.405911i | ||||
\(214\) | −0.161416 | − | 0.117276i | −0.0110342 | − | 0.00801680i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.290076 | − | 0.210752i | 0.0197371 | − | 0.0143399i | ||||
\(217\) | −15.2521 | − | 4.95570i | −1.03538 | − | 0.336415i | ||||
\(218\) | 0.988224i | 0.0669310i | ||||||||
\(219\) | −0.131272 | + | 0.404013i | −0.00887052 | + | 0.0273006i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.610541 | − | 1.87905i | −0.0410695 | − | 0.126399i | ||||
\(222\) | 0.122758 | − | 0.0398866i | 0.00823899 | − | 0.00267701i | ||||
\(223\) | 3.34035 | − | 4.59760i | 0.223687 | − | 0.307878i | −0.682393 | − | 0.730985i | \(-0.739061\pi\) |
0.906080 | + | 0.423107i | \(0.139061\pi\) | |||||||
\(224\) | 4.67486 | 0.312352 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.153610 | −0.0102180 | ||||||||
\(227\) | 2.14174 | − | 2.94785i | 0.142152 | − | 0.195656i | −0.732004 | − | 0.681300i | \(-0.761415\pi\) |
0.874157 | + | 0.485644i | \(0.161415\pi\) | |||||||
\(228\) | 2.55931 | − | 0.831569i | 0.169494 | − | 0.0550720i | ||||
\(229\) | −0.513355 | − | 1.57994i | −0.0339235 | − | 0.104406i | 0.932661 | − | 0.360754i | \(-0.117481\pi\) |
−0.966584 | + | 0.256348i | \(0.917481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.91693 | + | 18.2104i | −0.389305 | + | 1.19816i | ||||
\(232\) | − | 2.86074i | − | 0.187817i | ||||||
\(233\) | −7.47434 | − | 2.42856i | −0.489661 | − | 0.159100i | 0.0537719 | − | 0.998553i | \(-0.482876\pi\) |
−0.543432 | + | 0.839453i | \(0.682876\pi\) | |||||||
\(234\) | 0.143998 | − | 0.104621i | 0.00941344 | − | 0.00683926i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.7793 | + | 7.83161i | 0.701672 | + | 0.509795i | ||||
\(237\) | −3.73555 | − | 5.14155i | −0.242650 | − | 0.333980i | ||||
\(238\) | −0.229536 | − | 0.315929i | −0.0148786 | − | 0.0204786i | ||||
\(239\) | −0.458956 | − | 0.333451i | −0.0296874 | − | 0.0215691i | 0.572843 | − | 0.819665i | \(-0.305841\pi\) |
−0.602530 | + | 0.798096i | \(0.705841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.3779 | − | 11.1727i | 0.990578 | − | 0.719697i | 0.0305304 | − | 0.999534i | \(-0.490280\pi\) |
0.960048 | + | 0.279837i | \(0.0902804\pi\) | |||||||
\(242\) | −0.707337 | − | 0.229828i | −0.0454693 | − | 0.0147739i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −5.82037 | + | 17.9133i | −0.372611 | + | 1.14678i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.166048 | − | 0.511043i | −0.0105868 | − | 0.0325829i | ||||
\(247\) | 2.54610 | − | 0.827278i | 0.162005 | − | 0.0526385i | ||||
\(248\) | 0.775065 | − | 1.06679i | 0.0492167 | − | 0.0677410i | ||||
\(249\) | 0.737011 | 0.0467062 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.02533 | 0.190957 | 0.0954787 | − | 0.995431i | \(-0.469562\pi\) | ||||
0.0954787 | + | 0.995431i | \(0.469562\pi\) | |||||||
\(252\) | −5.10563 | + | 7.02730i | −0.321625 | + | 0.442678i | ||||
\(253\) | 9.84086 | − | 3.19749i | 0.618690 | − | 0.201024i | ||||
\(254\) | −0.348527 | − | 1.07266i | −0.0218686 | − | 0.0673045i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.74604 | − | 14.6068i | 0.296627 | − | 0.912925i | ||||
\(257\) | − | 19.8613i | − | 1.23891i | −0.785032 | − | 0.619456i | \(-0.787353\pi\) | ||
0.785032 | − | 0.619456i | \(-0.212647\pi\) | |||||||
\(258\) | −0.229408 | − | 0.0745391i | −0.0142823 | − | 0.00464060i | ||||
\(259\) | −5.06977 | + | 3.68340i | −0.315020 | + | 0.228875i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.45479 | + | 4.68968i | 0.399541 | + | 0.290284i | ||||
\(262\) | 0.869621 | + | 1.19693i | 0.0537253 | + | 0.0739466i | ||||
\(263\) | 13.4191 | + | 18.4698i | 0.827456 | + | 1.13890i | 0.988391 | + | 0.151930i | \(0.0485489\pi\) |
−0.160935 | + | 0.986965i | \(0.551451\pi\) | |||||||
\(264\) | −1.27370 | − | 0.925401i | −0.0783911 | − | 0.0569545i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.428081 | − | 0.311019i | 0.0262473 | − | 0.0190698i | ||||
\(267\) | 9.30833 | + | 3.02446i | 0.569661 | + | 0.185094i | ||||
\(268\) | 25.7395i | 1.57229i | ||||||||
\(269\) | −4.58346 | + | 14.1065i | −0.279459 | + | 0.860086i | 0.708546 | + | 0.705664i | \(0.249351\pi\) |
−0.988005 | + | 0.154421i | \(0.950649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.98920 | − | 6.12214i | −0.120835 | − | 0.371893i | 0.872284 | − | 0.489000i | \(-0.162638\pi\) |
−0.993119 | + | 0.117106i | \(0.962638\pi\) | |||||||
\(272\) | −3.74706 | + | 1.21749i | −0.227199 | + | 0.0738214i | ||||
\(273\) | −5.07929 | + | 6.99105i | −0.307413 | + | 0.423117i | ||||
\(274\) | −0.868313 | −0.0524567 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.69401 | 0.282546 | ||||||||
\(277\) | 3.94390 | − | 5.42831i | 0.236966 | − | 0.326155i | −0.673927 | − | 0.738798i | \(-0.735394\pi\) |
0.910893 | + | 0.412642i | \(0.135394\pi\) | |||||||
\(278\) | −1.15601 | + | 0.375609i | −0.0693326 | + | 0.0225275i | ||||
\(279\) | 1.13645 | + | 3.49762i | 0.0680372 | + | 0.209397i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.33074 | + | 19.4840i | −0.377661 | + | 1.16232i | 0.564006 | + | 0.825771i | \(0.309260\pi\) |
−0.941666 | + | 0.336549i | \(0.890740\pi\) | |||||||
\(282\) | 0.982560i | 0.0585106i | ||||||||
\(283\) | 10.8589 | + | 3.52828i | 0.645496 | + | 0.209734i | 0.613427 | − | 0.789751i | \(-0.289790\pi\) |
0.0320688 | + | 0.999486i | \(0.489790\pi\) | |||||||
\(284\) | −11.8004 | + | 8.57347i | −0.700223 | + | 0.508742i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.632286 | − | 0.459383i | −0.0373879 | − | 0.0271639i | ||||
\(287\) | 15.3340 | + | 21.1055i | 0.905139 | + | 1.24582i | ||||
\(288\) | −0.630131 | − | 0.867300i | −0.0371308 | − | 0.0511062i | ||||
\(289\) | −12.9491 | − | 9.40806i | −0.761711 | − | 0.553415i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0272704 | − | 0.0198131i | 0.00159862 | − | 0.00116147i | ||||
\(292\) | 0.804766 | + | 0.261484i | 0.0470954 | + | 0.0153022i | ||||
\(293\) | − | 28.5505i | − | 1.66794i | −0.551812 | − | 0.833968i | \(-0.686063\pi\) | ||
0.551812 | − | 0.833968i | \(-0.313937\pi\) | |||||||
\(294\) | −0.333505 | + | 1.02642i | −0.0194504 | + | 0.0598622i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.159224 | − | 0.490042i | −0.00925473 | − | 0.0284831i | ||||
\(297\) | 4.17603 | − | 1.35688i | 0.242318 | − | 0.0787339i | ||||
\(298\) | 0.722455 | − | 0.994374i | 0.0418507 | − | 0.0576025i | ||||
\(299\) | 4.66979 | 0.270061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7108 | 0.675001 | ||||||||
\(302\) | 0.597653 | − | 0.822598i | 0.0343910 | − | 0.0473352i | ||||
\(303\) | −3.03758 | + | 0.986969i | −0.174504 | + | 0.0566999i | ||||
\(304\) | −1.64969 | − | 5.07723i | −0.0946164 | − | 0.291199i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0276731 | + | 0.0851689i | −0.00158196 | + | 0.00486878i | ||||
\(307\) | − | 20.5417i | − | 1.17238i | −0.810175 | − | 0.586188i | \(-0.800628\pi\) | ||
0.810175 | − | 0.586188i | \(-0.199372\pi\) | |||||||
\(308\) | 36.2740 | + | 11.7861i | 2.06690 | + | 0.671577i | ||||
\(309\) | −6.91986 | + | 5.02758i | −0.393657 | + | 0.286009i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1979 | − | 10.3154i | −0.805090 | − | 0.584932i | 0.107313 | − | 0.994225i | \(-0.465775\pi\) |
−0.912403 | + | 0.409293i | \(0.865775\pi\) | |||||||
\(312\) | −0.417638 | − | 0.574830i | −0.0236441 | − | 0.0325433i | ||||
\(313\) | −1.75491 | − | 2.41543i | −0.0991935 | − | 0.136528i | 0.756535 | − | 0.653953i | \(-0.226891\pi\) |
−0.855729 | + | 0.517425i | \(0.826891\pi\) | |||||||
\(314\) | −0.622067 | − | 0.451958i | −0.0351053 | − | 0.0255055i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.2416 | + | 7.44097i | −0.576136 | + | 0.418587i | ||||
\(317\) | −15.3794 | − | 4.99706i | −0.863791 | − | 0.280663i | −0.156580 | − | 0.987665i | \(-0.550047\pi\) |
−0.707211 | + | 0.707003i | \(0.750047\pi\) | |||||||
\(318\) | − | 0.992598i | − | 0.0556621i | ||||||
\(319\) | 10.8259 | − | 33.3187i | 0.606134 | − | 1.86549i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.686438 | − | 2.11264i | −0.0383132 | − | 0.117916i | ||||
\(322\) | 0.877813 | − | 0.285219i | 0.0489186 | − | 0.0158946i | ||||
\(323\) | −0.791707 | + | 1.08969i | −0.0440518 | + | 0.0606320i | ||||
\(324\) | 1.99193 | 0.110663 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.411830 | −0.0228092 | ||||||||
\(327\) | −6.46701 | + | 8.90108i | −0.357627 | + | 0.492231i | ||||
\(328\) | −2.04005 | + | 0.662852i | −0.112643 | + | 0.0365999i | ||||
\(329\) | −14.7410 | − | 45.3682i | −0.812699 | − | 2.50123i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.03900 | + | 12.4307i | −0.222003 | + | 0.683256i | 0.776579 | + | 0.630020i | \(0.216953\pi\) |
−0.998582 | + | 0.0532356i | \(0.983047\pi\) | |||||||
\(332\) | − | 1.46808i | − | 0.0805711i | ||||||
\(333\) | 1.36672 | + | 0.444075i | 0.0748959 | + | 0.0243352i | ||||
\(334\) | −0.524494 | + | 0.381067i | −0.0286990 | + | 0.0208511i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 13.9410 | + | 10.1287i | 0.760543 | + | 0.552567i | ||||
\(337\) | −15.7555 | − | 21.6856i | −0.858257 | − | 1.18129i | −0.981982 | − | 0.188973i | \(-0.939484\pi\) |
0.123725 | − | 0.992317i | \(-0.460516\pi\) | |||||||
\(338\) | 0.479007 | + | 0.659297i | 0.0260545 | + | 0.0358610i | ||||
\(339\) | −1.38359 | − | 1.00524i | −0.0751462 | − | 0.0545969i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.0642 | − | 9.49167i | 0.707464 | − | 0.514003i | ||||
\(342\) | −0.115403 | − | 0.0374968i | −0.00624029 | − | 0.00202759i | ||||
\(343\) | − | 21.8721i | − | 1.18098i | ||||||
\(344\) | −0.297555 | + | 0.915780i | −0.0160431 | + | 0.0493755i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.129067 | + | 0.397227i | 0.00693867 | + | 0.0213550i | ||||
\(347\) | 24.2385 | − | 7.87558i | 1.30119 | − | 0.422783i | 0.425196 | − | 0.905101i | \(-0.360205\pi\) |
0.875996 | + | 0.482318i | \(0.160205\pi\) | |||||||
\(348\) | 9.34152 | − | 12.8575i | 0.500758 | − | 0.689234i | ||||
\(349\) | 28.0435 | 1.50113 | 0.750566 | − | 0.660795i | \(-0.229781\pi\) | ||||
0.750566 | + | 0.660795i | \(0.229781\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.98166 | 0.105773 | ||||||||
\(352\) | −2.76687 | + | 3.80826i | −0.147474 | + | 0.202981i | ||||
\(353\) | 13.9489 | − | 4.53226i | 0.742423 | − | 0.241228i | 0.0867054 | − | 0.996234i | \(-0.472366\pi\) |
0.655718 | + | 0.755006i | \(0.272366\pi\) | |||||||
\(354\) | −0.185657 | − | 0.571393i | −0.00986754 | − | 0.0303692i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.02452 | − | 18.5416i | 0.319299 | − | 0.982701i | ||||
\(357\) | − | 4.34771i | − | 0.230105i | ||||||
\(358\) | −0.615337 | − | 0.199935i | −0.0325216 | − | 0.0105669i | ||||
\(359\) | −11.8283 | + | 8.59373i | −0.624272 | + | 0.453560i | −0.854411 | − | 0.519598i | \(-0.826082\pi\) |
0.230139 | + | 0.973158i | \(0.426082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.8948 | + | 10.0952i | 0.731305 | + | 0.531324i | ||||
\(362\) | −0.200843 | − | 0.276437i | −0.0105561 | − | 0.0145292i | ||||
\(363\) | −4.86708 | − | 6.69896i | −0.255455 | − | 0.351604i | ||||
\(364\) | 13.9257 | + | 10.1176i | 0.729905 | + | 0.530307i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.687103 | − | 0.499210i | 0.0359154 | − | 0.0260941i | ||||
\(367\) | −16.8279 | − | 5.46773i | −0.878412 | − | 0.285413i | −0.165114 | − | 0.986274i | \(-0.552799\pi\) |
−0.713298 | + | 0.700861i | \(0.752799\pi\) | |||||||
\(368\) | − | 9.31212i | − | 0.485428i | ||||||
\(369\) | 1.84869 | − | 5.68967i | 0.0962388 | − | 0.296193i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.8916 | + | 45.8317i | 0.773134 | + | 2.37946i | ||||
\(372\) | 6.96702 | − | 2.26372i | 0.361223 | − | 0.117369i | ||||
\(373\) | −7.18821 | + | 9.89372i | −0.372191 | + | 0.512278i | −0.953495 | − | 0.301409i | \(-0.902543\pi\) |
0.581303 | + | 0.813687i | \(0.302543\pi\) | |||||||
\(374\) | 0.393217 | 0.0203328 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.92231 | 0.202278 | ||||||||
\(377\) | 9.29333 | − | 12.7912i | 0.478631 | − | 0.658779i | ||||
\(378\) | 0.372506 | − | 0.121034i | 0.0191596 | − | 0.00622534i | ||||
\(379\) | −8.68186 | − | 26.7200i | −0.445957 | − | 1.37251i | −0.881431 | − | 0.472313i | \(-0.843419\pi\) |
0.435474 | − | 0.900201i | \(-0.356581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.88031 | − | 11.9424i | 0.198794 | − | 0.611826i | ||||
\(382\) | − | 1.93598i | − | 0.0990533i | ||||||
\(383\) | −32.7481 | − | 10.6405i | −1.67335 | − | 0.543705i | −0.689748 | − | 0.724049i | \(-0.742279\pi\) |
−0.983603 | + | 0.180345i | \(0.942279\pi\) | |||||||
\(384\) | −2.30190 | + | 1.67243i | −0.117468 | + | 0.0853458i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.228917 | + | 0.166318i | 0.0116516 | + | 0.00846536i | ||||
\(387\) | −1.57852 | − | 2.17265i | −0.0802406 | − | 0.110442i | ||||
\(388\) | −0.0394664 | − | 0.0543208i | −0.00200360 | − | 0.00275772i | ||||
\(389\) | 10.9399 | + | 7.94834i | 0.554677 | + | 0.402997i | 0.829507 | − | 0.558496i | \(-0.188622\pi\) |
−0.274830 | + | 0.961493i | \(0.588622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.90078 | + | 1.38100i | −0.0961265 | + | 0.0698400i | ||||
\(392\) | 4.09741 | + | 1.33133i | 0.206951 | + | 0.0672423i | ||||
\(393\) | 16.4718i | 0.830892i | ||||||||
\(394\) | 0.723974 | − | 2.22816i | 0.0364733 | − | 0.112253i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.70280 | − | 8.31838i | −0.135821 | − | 0.418014i | ||||
\(397\) | 34.2136 | − | 11.1167i | 1.71713 | − | 0.557931i | 0.725639 | − | 0.688076i | \(-0.241544\pi\) |
0.991495 | + | 0.130145i | \(0.0415444\pi\) | |||||||
\(398\) | −1.28112 | + | 1.76331i | −0.0642169 | + | 0.0883869i | ||||
\(399\) | 5.89112 | 0.294925 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.35977 | 0.217717 | 0.108858 | − | 0.994057i | \(-0.465281\pi\) | ||||
0.108858 | + | 0.994057i | \(0.465281\pi\) | |||||||
\(402\) | 0.682203 | − | 0.938972i | 0.0340252 | − | 0.0468317i | ||||
\(403\) | 6.93108 | − | 2.25204i | 0.345261 | − | 0.112182i | ||||
\(404\) | 1.96598 | + | 6.05065i | 0.0978110 | + | 0.301031i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.965680 | − | 2.97206i | 0.0479259 | − | 0.147501i | ||||
\(407\) | − | 6.31003i | − | 0.312777i | ||||||
\(408\) | 0.339989 | + | 0.110469i | 0.0168319 | + | 0.00546903i | ||||
\(409\) | −14.6543 | + | 10.6470i | −0.724610 | + | 0.526460i | −0.887854 | − | 0.460126i | \(-0.847804\pi\) |
0.163243 | + | 0.986586i | \(0.447804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.82102 | − | 5.68231i | −0.385783 | − | 0.280288i | ||||
\(412\) | 10.0146 | + | 13.7839i | 0.493383 | + | 0.679084i | ||||
\(413\) | 17.1448 | + | 23.5978i | 0.843642 | + | 1.16117i | ||||
\(414\) | −0.171237 | − | 0.124411i | −0.00841583 | − | 0.00611446i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.71869 | + | 1.24870i | −0.0842657 | + | 0.0612226i | ||||
\(417\) | −12.8703 | − | 4.18182i | −0.630263 | − | 0.204785i | ||||
\(418\) | 0.532806i | 0.0260604i | ||||||||
\(419\) | −0.163120 | + | 0.502031i | −0.00796892 | + | 0.0245258i | −0.954962 | − | 0.296728i | \(-0.904104\pi\) |
0.946993 | + | 0.321254i | \(0.104104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.76583 | + | 17.7454i | 0.281009 | + | 0.864857i | 0.987567 | + | 0.157201i | \(0.0502472\pi\) |
−0.706557 | + | 0.707656i | \(0.749753\pi\) | |||||||
\(422\) | 1.39909 | − | 0.454593i | 0.0681067 | − | 0.0221292i | ||||
\(423\) | −6.42995 | + | 8.85007i | −0.312635 | + | 0.430305i | ||||
\(424\) | −3.96239 | −0.192430 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.657709 | 0.0318661 | ||||||||
\(427\) | −24.2364 | + | 33.3586i | −1.17288 | + | 1.61434i | ||||
\(428\) | −4.20823 | + | 1.36734i | −0.203413 | + | 0.0660928i | ||||
\(429\) | −2.68886 | − | 8.27546i | −0.129819 | − | 0.399543i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.48668 | − | 19.9640i | 0.312453 | − | 0.961630i | −0.664338 | − | 0.747432i | \(-0.731286\pi\) |
0.976790 | − | 0.214198i | \(-0.0687136\pi\) | |||||||
\(432\) | − | 3.95166i | − | 0.190124i | ||||||
\(433\) | 12.9952 | + | 4.22239i | 0.624508 | + | 0.202915i | 0.604141 | − | 0.796877i | \(-0.293516\pi\) |
0.0203675 | + | 0.999793i | \(0.493516\pi\) | |||||||
\(434\) | 1.16533 | − | 0.846665i | 0.0559378 | − | 0.0406412i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.7303 | + | 12.8819i | 0.849130 | + | 0.616929i | ||||
\(437\) | −1.87124 | − | 2.57554i | −0.0895134 | − | 0.123205i | ||||
\(438\) | −0.0224273 | − | 0.0308686i | −0.00107162 | − | 0.00147496i | ||||
\(439\) | −3.50578 | − | 2.54710i | −0.167322 | − | 0.121567i | 0.500973 | − | 0.865463i | \(-0.332976\pi\) |
−0.668295 | + | 0.743896i | \(0.732976\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.72092 | + | 7.06266i | −0.462901 | + | 0.336317i | ||||
\(442\) | 0.168776 | + | 0.0548385i | 0.00802783 | + | 0.00260840i | ||||
\(443\) | 1.60742i | 0.0763707i | 0.999271 | + | 0.0381854i | \(0.0121577\pi\) | ||||
−0.999271 | + | 0.0381854i | \(0.987842\pi\) | |||||||
\(444\) | 0.884567 | − | 2.72242i | 0.0419797 | − | 0.129200i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.157734 | + | 0.485456i | 0.00746894 | + | 0.0229870i | ||||
\(447\) | 13.0145 | − | 4.22867i | 0.615565 | − | 0.200009i | ||||
\(448\) | 20.0106 | − | 27.5423i | 0.945414 | − | 1.30125i | ||||
\(449\) | 13.8291 | 0.652634 | 0.326317 | − | 0.945260i | \(-0.394192\pi\) | ||||
0.326317 | + | 0.945260i | \(0.394192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.2687 | −1.23694 | ||||||||
\(452\) | −2.00236 | + | 2.75601i | −0.0941832 | + | 0.129632i | ||||
\(453\) | 10.7663 | − | 3.49818i | 0.505845 | − | 0.164359i | ||||
\(454\) | 0.101135 | + | 0.311261i | 0.00474649 | + | 0.0146082i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.149685 | + | 0.460682i | −0.00700962 | + | 0.0215734i | ||||
\(457\) | 20.1345i | 0.941850i | 0.882173 | + | 0.470925i | \(0.156080\pi\) | ||||
−0.882173 | + | 0.470925i | \(0.843920\pi\) | |||||||
\(458\) | 0.141910 | + | 0.0461093i | 0.00663101 | + | 0.00215455i | ||||
\(459\) | −0.806607 | + | 0.586035i | −0.0376492 | + | 0.0273538i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.5054 | − | 18.5308i | −1.18791 | − | 0.863064i | −0.194865 | − | 0.980830i | \(-0.562427\pi\) |
−0.993041 | + | 0.117766i | \(0.962427\pi\) | |||||||
\(462\) | −1.01089 | − | 1.39137i | −0.0470308 | − | 0.0647323i | ||||
\(463\) | −0.0265501 | − | 0.0365431i | −0.00123389 | − | 0.00169830i | 0.808400 | − | 0.588634i | \(-0.200334\pi\) |
−0.809633 | + | 0.586936i | \(0.800334\pi\) | |||||||
\(464\) | −25.5071 | − | 18.5320i | −1.18414 | − | 0.860327i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.571077 | − | 0.414912i | 0.0264546 | − | 0.0192204i | ||||
\(467\) | −31.2278 | − | 10.1465i | −1.44505 | − | 0.469525i | −0.521582 | − | 0.853201i | \(-0.674658\pi\) |
−0.923468 | + | 0.383676i | \(0.874658\pi\) | |||||||
\(468\) | − | 3.94732i | − | 0.182465i | ||||||
\(469\) | −17.4126 | + | 53.5905i | −0.804039 | + | 2.47458i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.64540 | − | 8.14171i | −0.121894 | − | 0.375150i | ||||
\(472\) | −2.28096 | + | 0.741129i | −0.104990 | + | 0.0341132i | ||||
\(473\) | −6.93119 | + | 9.53996i | −0.318696 | + | 0.438648i | ||||
\(474\) | 0.570830 | 0.0262191 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.66035 | −0.396947 | ||||||||
\(477\) | 6.49564 | − | 8.94048i | 0.297415 | − | 0.409356i | ||||
\(478\) | 0.0484607 | − | 0.0157458i | 0.00221654 | − | 0.000720198i | ||||
\(479\) | −2.31323 | − | 7.11938i | −0.105694 | − | 0.325293i | 0.884199 | − | 0.467111i | \(-0.154705\pi\) |
−0.989893 | + | 0.141818i | \(0.954705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.880003 | − | 2.70837i | 0.0401247 | − | 0.123491i | ||||
\(482\) | 1.70730i | 0.0777654i | ||||||||
\(483\) | 9.77309 | + | 3.17547i | 0.444691 | + | 0.144489i | ||||
\(484\) | −13.3439 | + | 9.69489i | −0.606540 | + | 0.440677i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.0726655 | − | 0.0527945i | −0.00329617 | − | 0.00239481i | ||||
\(487\) | 14.9471 | + | 20.5729i | 0.677316 | + | 0.932246i | 0.999898 | − | 0.0142956i | \(-0.00455060\pi\) |
−0.322581 | + | 0.946542i | \(0.604551\pi\) | |||||||
\(488\) | −1.99281 | − | 2.74287i | −0.0902103 | − | 0.124164i | ||||
\(489\) | −3.70942 | − | 2.69505i | −0.167746 | − | 0.121874i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.95323 | − | 6.50490i | 0.404053 | − | 0.293562i | −0.367137 | − | 0.930167i | \(-0.619662\pi\) |
0.771190 | + | 0.636605i | \(0.219662\pi\) | |||||||
\(492\) | −11.3334 | − | 3.68246i | −0.510951 | − | 0.166018i | ||||
\(493\) | 7.95479i | 0.358266i | ||||||||
\(494\) | −0.0743057 | + | 0.228689i | −0.00334317 | + | 0.0102892i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.49084 | − | 13.8214i | −0.201645 | − | 0.620599i | ||||
\(497\) | −30.3687 | + | 9.86739i | −1.36222 | + | 0.442613i | ||||
\(498\) | −0.0389102 | + | 0.0535552i | −0.00174361 | + | 0.00239987i | ||||
\(499\) | −4.68157 | −0.209576 | −0.104788 | − | 0.994495i | \(-0.533416\pi\) | ||||
−0.104788 | + | 0.994495i | \(0.533416\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.21792 | −0.322473 | ||||||||
\(502\) | −0.159721 | + | 0.219837i | −0.00712870 | + | 0.00981182i | ||||
\(503\) | 10.2985 | − | 3.34618i | 0.459187 | − | 0.149199i | −0.0702839 | − | 0.997527i | \(-0.522391\pi\) |
0.529471 | + | 0.848328i | \(0.322391\pi\) | |||||||
\(504\) | −0.483161 | − | 1.48702i | −0.0215217 | − | 0.0662371i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.287197 | + | 0.883901i | −0.0127675 | + | 0.0392942i | ||||
\(507\) | 9.07304i | 0.402948i | ||||||||
\(508\) | −23.7884 | − | 7.72932i | −1.05544 | − | 0.342933i | ||||
\(509\) | 9.30422 | − | 6.75991i | 0.412402 | − | 0.299628i | −0.362171 | − | 0.932112i | \(-0.617964\pi\) |
0.774574 | + | 0.632484i | \(0.217964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.49866 | + | 1.08884i | 0.0662967 | + | 0.0481674i | ||||
\(512\) | 4.15570 | + | 5.71984i | 0.183658 | + | 0.252783i | ||||
\(513\) | −0.794072 | − | 1.09295i | −0.0350591 | − | 0.0482548i | ||||
\(514\) | 1.44323 | + | 1.04857i | 0.0636580 | + | 0.0462503i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.32776 | + | 3.14430i | −0.190519 | + | 0.138420i | ||||
\(517\) | 45.6828 | + | 14.8432i | 2.00913 | + | 0.652805i | ||||
\(518\) | − | 0.562860i | − | 0.0247307i | ||||||
\(519\) | −1.43696 | + | 4.42250i | −0.0630755 | + | 0.194126i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.246536 | + | 0.758759i | 0.0108009 | + | 0.0332418i | 0.956312 | − | 0.292349i | \(-0.0944368\pi\) |
−0.945511 | + | 0.325591i | \(0.894437\pi\) | |||||||
\(522\) | −0.681555 | + | 0.221451i | −0.0298309 | + | 0.00969263i | ||||
\(523\) | −23.5954 | + | 32.4763i | −1.03175 | + | 1.42009i | −0.128133 | + | 0.991757i | \(0.540898\pi\) |
−0.903622 | + | 0.428331i | \(0.859102\pi\) | |||||||
\(524\) | 32.8107 | 1.43334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.05057 | −0.0894090 | ||||||||
\(527\) | −2.15521 | + | 2.96639i | −0.0938824 | + | 0.129218i | ||||
\(528\) | −16.5023 | + | 5.36191i | −0.718169 | + | 0.233347i | ||||
\(529\) | 5.39138 | + | 16.5930i | 0.234408 | + | 0.721433i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.06700 | − | 6.36157i | 0.0897001 | − | 0.276069i | ||||
\(532\) | − | 11.7347i | − | 0.508764i | ||||||
\(533\) | −11.2750 | − | 3.66346i | −0.488373 | − | 0.158682i | ||||
\(534\) | −0.711203 | + | 0.516719i | −0.0307768 | + | 0.0223606i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.74831 | − | 2.72331i | −0.161903 | − | 0.117629i | ||||
\(537\) | −4.23404 | − | 5.82766i | −0.182712 | − | 0.251482i | ||||
\(538\) | −0.783070 | − | 1.07780i | −0.0337605 | − | 0.0464674i | ||||
\(539\) | 42.6840 | + | 31.0117i | 1.83853 | + | 1.33577i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.14085 | + | 0.828873i | −0.0490488 | + | 0.0356360i | −0.612040 | − | 0.790827i | \(-0.709651\pi\) |
0.562991 | + | 0.826463i | \(0.309651\pi\) | |||||||
\(542\) | 0.549887 | + | 0.178669i | 0.0236197 | + | 0.00767449i | ||||
\(543\) | − | 3.80424i | − | 0.163255i | ||||||
\(544\) | 0.330293 | − | 1.01654i | 0.0141612 | − | 0.0435836i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.239849 | − | 0.738178i | −0.0102646 | − | 0.0315911i | ||||
\(547\) | −14.7053 | + | 4.77804i | −0.628753 | + | 0.204294i | −0.606023 | − | 0.795447i | \(-0.707236\pi\) |
−0.0227302 | + | 0.999742i | \(0.507236\pi\) | |||||||
\(548\) | −11.3188 | + | 15.5790i | −0.483514 | + | 0.665500i | ||||
\(549\) | 9.45570 | 0.403560 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.7787 | −0.459187 | ||||||||
\(552\) | −0.496640 | + | 0.683566i | −0.0211384 | + | 0.0290945i | ||||
\(553\) | −26.3572 | + | 8.56397i | −1.12082 | + | 0.364177i | ||||
\(554\) | 0.186234 | + | 0.573170i | 0.00791234 | + | 0.0243517i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.32991 | + | 25.6368i | −0.353267 | + | 1.08724i | ||||
\(557\) | − | 18.0445i | − | 0.764568i | −0.924045 | − | 0.382284i | \(-0.875138\pi\) | ||
0.924045 | − | 0.382284i | \(-0.124862\pi\) | |||||||
\(558\) | −0.314154 | − | 0.102075i | −0.0132992 | − | 0.00432117i | ||||
\(559\) | −4.30543 | + | 3.12808i | −0.182100 | + | 0.132304i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.54177 | + | 2.57324i | 0.149533 | + | 0.108642i | ||||
\(562\) | −1.08159 | − | 1.48868i | −0.0456240 | − | 0.0627960i | ||||
\(563\) | −16.7711 | − | 23.0834i | −0.706816 | − | 0.972849i | −0.999860 | − | 0.0167502i | \(-0.994668\pi\) |
0.293043 | − | 0.956099i | \(-0.405332\pi\) | |||||||
\(564\) | 17.6287 | + | 12.8080i | 0.742304 | + | 0.539315i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.829676 | + | 0.602795i | −0.0348739 | + | 0.0253374i | ||||
\(567\) | 4.14727 | + | 1.34753i | 0.174169 | + | 0.0565910i | ||||
\(568\) | − | 2.62553i | − | 0.110165i | ||||||
\(569\) | −5.07011 | + | 15.6042i | −0.212550 | + | 0.654162i | 0.786768 | + | 0.617248i | \(0.211753\pi\) |
−0.999318 | + | 0.0369135i | \(0.988247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.57938 | − | 7.93852i | −0.107944 | − | 0.332217i | 0.882466 | − | 0.470376i | \(-0.155882\pi\) |
−0.990410 | + | 0.138159i | \(0.955882\pi\) | |||||||
\(572\) | −16.4842 | + | 5.35603i | −0.689237 | + | 0.223947i | ||||
\(573\) | 12.6692 | − | 17.4377i | 0.529263 | − | 0.728469i | ||||
\(574\) | −2.34319 | −0.0978029 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.80703 | −0.325293 | ||||||||
\(577\) | 4.95815 | − | 6.82431i | 0.206411 | − | 0.284100i | −0.693243 | − | 0.720704i | \(-0.743819\pi\) |
0.899654 | + | 0.436604i | \(0.143819\pi\) | |||||||
\(578\) | 1.36728 | − | 0.444257i | 0.0568714 | − | 0.0184786i | ||||
\(579\) | 0.973492 | + | 2.99610i | 0.0404570 | + | 0.124514i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.993145 | − | 3.05659i | 0.0412026 | − | 0.126809i | ||||
\(582\) | 0.00302764i | 0.000125500i | ||||||||
\(583\) | −46.1495 | − | 14.9949i | −1.91132 | − | 0.621025i | ||||
\(584\) | −0.123225 | + | 0.0895284i | −0.00509910 | + | 0.00370471i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.07463 | + | 1.50731i | 0.0857023 | + | 0.0622664i | ||||
\(587\) | 14.2745 | + | 19.6471i | 0.589171 | + | 0.810925i | 0.994663 | − | 0.103174i | \(-0.0328998\pi\) |
−0.405492 | + | 0.914099i | \(0.632900\pi\) | |||||||
\(588\) | 14.0684 | + | 19.3634i | 0.580169 | + | 0.798534i | ||||
\(589\) | −4.01943 | − | 2.92029i | −0.165618 | − | 0.120328i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.1022 | − | 15.3316i | 0.868028 | − | 0.630659i | ||||
\(592\) | −5.40082 | − | 1.75483i | −0.221972 | − | 0.0721232i | ||||
\(593\) | 28.4653i | 1.16893i | 0.811418 | + | 0.584466i | \(0.198696\pi\) | ||||
−0.811418 | + | 0.584466i | \(0.801304\pi\) | |||||||
\(594\) | −0.121874 | + | 0.375089i | −0.00500054 | + | 0.0153901i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.42323 | − | 25.9240i | −0.345029 | − | 1.06189i | ||||
\(597\) | −23.0785 | + | 7.49866i | −0.944541 | + | 0.306900i | ||||
\(598\) | −0.246539 | + | 0.339332i | −0.0100817 | + | 0.0138763i | ||||
\(599\) | −16.0387 | −0.655323 | −0.327662 | − | 0.944795i | \(-0.606261\pi\) | ||||
−0.327662 | + | 0.944795i | \(0.606261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.09005 | −0.330000 | −0.165000 | − | 0.986294i | \(-0.552762\pi\) | ||||
−0.165000 | + | 0.986294i | \(0.552762\pi\) | |||||||
\(602\) | −0.618268 | + | 0.850973i | −0.0251987 | + | 0.0346831i | ||||
\(603\) | 12.2894 | − | 3.99307i | 0.500464 | − | 0.162610i | ||||
\(604\) | −6.96814 | − | 21.4457i | −0.283530 | − | 0.872614i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.0886490 | − | 0.272834i | 0.00360112 | − | 0.0110831i | ||||
\(607\) | − | 0.434608i | − | 0.0176402i | −0.999961 | − | 0.00882010i | \(-0.997192\pi\) | ||
0.999961 | − | 0.00882010i | \(-0.00280756\pi\) | |||||||
\(608\) | 1.37740 | + | 0.447544i | 0.0558609 | + | 0.0181503i | ||||
\(609\) | 28.1474 | − | 20.4503i | 1.14059 | − | 0.828687i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.5378 | + | 12.7419i | 0.709503 | + | 0.515484i | ||||
\(612\) | 1.16734 | + | 1.60671i | 0.0471870 | + | 0.0649473i | ||||
\(613\) | −23.1565 | − | 31.8722i | −0.935282 | − | 1.28731i | −0.957763 | − | 0.287558i | \(-0.907156\pi\) |
0.0224808 | − | 0.999747i | \(-0.492844\pi\) | |||||||
\(614\) | 1.49267 | + | 1.08449i | 0.0602393 | + | 0.0437664i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.55425 | + | 4.03540i | −0.223787 | + | 0.162591i | ||||
\(617\) | 14.6602 | + | 4.76337i | 0.590196 | + | 0.191766i | 0.588863 | − | 0.808233i | \(-0.299576\pi\) |
0.00133273 | + | 0.999999i | \(0.499576\pi\) | |||||||
\(618\) | − | 0.768264i | − | 0.0309041i | ||||||
\(619\) | 3.29776 | − | 10.1495i | 0.132548 | − | 0.407942i | −0.862652 | − | 0.505797i | \(-0.831198\pi\) |
0.995201 | + | 0.0978556i | \(0.0311983\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.728201 | − | 2.24117i | −0.0292217 | − | 0.0899352i | ||||
\(622\) | 1.49914 | − | 0.487102i | 0.0601102 | − | 0.0195310i | ||||
\(623\) | 25.0865 | − | 34.5286i | 1.00507 | − | 1.38336i | ||||
\(624\) | −7.83083 | −0.313484 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.268168 | 0.0107182 | ||||||||
\(627\) | −3.48672 | + | 4.79906i | −0.139246 | + | 0.191656i | ||||
\(628\) | −16.2177 | + | 5.26946i | −0.647158 | + | 0.210275i | ||||
\(629\) | 0.442752 | + | 1.36265i | 0.0176537 | + | 0.0543325i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.69664 | + | 17.5324i | −0.226780 | + | 0.697956i | 0.771327 | + | 0.636440i | \(0.219594\pi\) |
−0.998106 | + | 0.0615162i | \(0.980406\pi\) | |||||||
\(632\) | − | 2.27871i | − | 0.0906424i | ||||||
\(633\) | 15.5767 | + | 5.06118i | 0.619119 | + | 0.201164i | ||||
\(634\) | 1.17506 | − | 0.853731i | 0.0466676 | − | 0.0339060i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −17.8088 | − | 12.9389i | −0.706166 | − | 0.513060i | ||||
\(637\) | 13.9958 | + | 19.2635i | 0.554533 | + | 0.763249i | ||||
\(638\) | 1.84957 | + | 2.54572i | 0.0732252 | + | 0.100786i | ||||
\(639\) | 5.92408 | + | 4.30410i | 0.234353 | + | 0.170267i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.0546 | + | 7.30508i | −0.397132 | + | 0.288533i | −0.768372 | − | 0.640004i | \(-0.778933\pi\) |
0.371240 | + | 0.928537i | \(0.378933\pi\) | |||||||
\(642\) | 0.189756 | + | 0.0616554i | 0.00748907 | + | 0.00243335i | ||||
\(643\) | 1.84657i | 0.0728218i | 0.999337 | + | 0.0364109i | \(0.0115925\pi\) | ||||
−0.999337 | + | 0.0364109i | \(0.988407\pi\) | |||||||
\(644\) | 6.32532 | − | 19.4673i | 0.249253 | − | 0.767120i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.0373851 | − | 0.115059i | −0.00147090 | − | 0.00452695i | ||||
\(647\) | 37.0683 | − | 12.0442i | 1.45731 | − | 0.473508i | 0.530061 | − | 0.847960i | \(-0.322169\pi\) |
0.927246 | + | 0.374452i | \(0.122169\pi\) | |||||||
\(648\) | −0.210752 | + | 0.290076i | −0.00827913 | + | 0.0113952i | ||||
\(649\) | −29.3708 | −1.15290 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0370 | 0.628539 | ||||||||
\(652\) | −5.36836 | + | 7.38891i | −0.210241 | + | 0.289372i | ||||
\(653\) | 26.9519 | − | 8.75719i | 1.05471 | − | 0.342695i | 0.270193 | − | 0.962806i | \(-0.412912\pi\) |
0.784514 | + | 0.620111i | \(0.212912\pi\) | |||||||
\(654\) | −0.305378 | − | 0.939857i | −0.0119412 | − | 0.0367513i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.30538 | + | 22.4836i | −0.285227 | + | 0.877839i | ||||
\(657\) | − | 0.424804i | − | 0.0165732i | ||||||
\(658\) | 4.07495 | + | 1.32403i | 0.158858 | + | 0.0516161i | ||||
\(659\) | −18.0864 | + | 13.1406i | −0.704547 | + | 0.511883i | −0.881410 | − | 0.472352i | \(-0.843405\pi\) |
0.176863 | + | 0.984236i | \(0.443405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6349 | − | 17.1717i | −0.919290 | − | 0.667903i | 0.0240570 | − | 0.999711i | \(-0.492342\pi\) |
−0.943347 | + | 0.331807i | \(0.892342\pi\) | |||||||
\(662\) | −0.690049 | − | 0.949771i | −0.0268195 | − | 0.0369139i | ||||
\(663\) | 1.16132 | + | 1.59842i | 0.0451019 | + | 0.0620774i | ||||
\(664\) | 0.213789 | + | 0.155327i | 0.00829662 | + | 0.00602785i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.104424 | + | 0.0758687i | −0.00404636 | + | 0.00293985i | ||||
\(667\) | −17.8813 | − | 5.81000i | −0.692368 | − | 0.224964i | ||||
\(668\) | 14.3776i | 0.556287i | ||||||||
\(669\) | −1.75613 | + | 5.40480i | −0.0678958 | + | 0.208962i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.8302 | − | 39.4873i | −0.495305 | − | 1.52439i | ||||
\(672\) | −4.44605 | + | 1.44461i | −0.171510 | + | 0.0557270i | ||||
\(673\) | −1.89000 | + | 2.60136i | −0.0728542 | + | 0.100275i | −0.843889 | − | 0.536518i | \(-0.819739\pi\) |
0.771035 | + | 0.636793i | \(0.219739\pi\) | |||||||
\(674\) | 2.40760 | 0.0927372 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.0729 | 0.695111 | ||||||||
\(677\) | −27.7711 | + | 38.2236i | −1.06733 | + | 1.46905i | −0.194579 | + | 0.980887i | \(0.562334\pi\) |
−0.872751 | + | 0.488166i | \(0.837666\pi\) | |||||||
\(678\) | 0.146092 | − | 0.0474681i | 0.00561062 | − | 0.00182300i | ||||
\(679\) | −0.0454227 | − | 0.139797i | −0.00174316 | − | 0.00536490i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.12598 | + | 3.46541i | −0.0431476 | + | 0.132795i | ||||
\(682\) | 1.45042i | 0.0555395i | ||||||||
\(683\) | 35.4294 | + | 11.5117i | 1.35567 | + | 0.440483i | 0.894595 | − | 0.446879i | \(-0.147464\pi\) |
0.461074 | + | 0.887362i | \(0.347464\pi\) | |||||||
\(684\) | −2.17708 | + | 1.58174i | −0.0832426 | + | 0.0604793i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.58934 | + | 1.15473i | 0.0606814 | + | 0.0440876i | ||||
\(687\) | 0.976460 | + | 1.34398i | 0.0372543 | + | 0.0512761i | ||||
\(688\) | 6.23777 | + | 8.58556i | 0.237813 | + | 0.327321i | ||||
\(689\) | −17.7170 | − | 12.8721i | −0.674962 | − | 0.490389i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.88522 | − | 6.45549i | 0.338010 | − | 0.245578i | −0.405812 | − | 0.913957i | \(-0.633011\pi\) |
0.743822 | + | 0.668378i | \(0.233011\pi\) | |||||||
\(692\) | 8.80933 | + | 2.86232i | 0.334880 | + | 0.108809i | ||||
\(693\) | − | 19.1476i | − | 0.727357i | ||||||
\(694\) | −0.707380 | + | 2.17709i | −0.0268518 | + | 0.0826412i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.884016 | + | 2.72072i | 0.0335085 | + | 0.103129i | ||||
\(697\) | 5.67273 | − | 1.84318i | 0.214870 | − | 0.0698154i | ||||
\(698\) | −1.48054 | + | 2.03779i | −0.0560394 | + | 0.0771316i | ||||
\(699\) | 7.85899 | 0.297254 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.4086 | 0.846361 | 0.423180 | − | 0.906046i | \(-0.360914\pi\) | ||||
0.423180 | + | 0.906046i | \(0.360914\pi\) | |||||||
\(702\) | −0.104621 | + | 0.143998i | −0.00394865 | + | 0.00543485i | ||||
\(703\) | −1.84638 | + | 0.599926i | −0.0696376 | + | 0.0226266i | ||||
\(704\) | 10.5932 | + | 32.6024i | 0.399245 | + | 1.22875i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.407085 | + | 1.25288i | −0.0153209 | + | 0.0471527i | ||||
\(707\) | 13.9276i | 0.523803i | ||||||||
\(708\) | −12.6718 | − | 4.11732i | −0.476236 | − | 0.154738i | ||||
\(709\) | −11.8357 | + | 8.59914i | −0.444499 | + | 0.322948i | −0.787420 | − | 0.616417i | \(-0.788584\pi\) |
0.342921 | + | 0.939364i | \(0.388584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.14155 | + | 3.73555i | 0.192823 | + | 0.140094i | ||||
\(712\) | 2.06271 | + | 2.83907i | 0.0773032 | + | 0.106399i | ||||
\(713\) | −5.09394 | − | 7.01121i | −0.190770 | − | 0.262572i | ||||
\(714\) | 0.315929 | + | 0.229536i | 0.0118233 | + | 0.00859015i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.6083 | + | 8.43392i | −0.433823 | + | 0.315191i | ||||
\(717\) | 0.539535 | + | 0.175305i | 0.0201493 | + | 0.00654690i | ||||
\(718\) | − | 1.31321i | − | 0.0490085i | ||||||
\(719\) | 8.80627 | − | 27.1029i | 0.328419 | − | 1.01077i | −0.641455 | − | 0.767160i | \(-0.721669\pi\) |
0.969874 | − | 0.243608i | \(-0.0783310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5260 | + | 35.4734i | 0.429251 | + | 1.32110i | ||||
\(722\) | −1.46714 | + | 0.476702i | −0.0546013 | + | 0.0177410i | ||||
\(723\) | −11.1727 | + | 15.3779i | −0.415517 | + | 0.571910i | ||||
\(724\) | −7.57778 | −0.281626 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.743738 | 0.0276027 | ||||||||
\(727\) | 25.8663 | − | 35.6019i | 0.959329 | − | 1.32040i | 0.0120725 | − | 0.999927i | \(-0.496157\pi\) |
0.947257 | − | 0.320476i | \(-0.103843\pi\) | |||||||
\(728\) | −2.94676 | + | 0.957460i | −0.109214 | + | 0.0354858i | ||||
\(729\) | −0.309017 | − | 0.951057i | −0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.827405 | − | 2.54649i | 0.0306027 | − | 0.0941854i | ||||
\(732\) | − | 18.8351i | − | 0.696166i | ||||||
\(733\) | 25.9854 | + | 8.44317i | 0.959793 | + | 0.311856i | 0.746689 | − | 0.665174i | \(-0.231643\pi\) |
0.213104 | + | 0.977029i | \(0.431643\pi\) | |||||||
\(734\) | 1.28574 | − | 0.934144i | 0.0474575 | − | 0.0344799i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.04380 | + | 1.48491i | 0.0753355 | + | 0.0547344i | ||||
\(737\) | −33.3504 | − | 45.9029i | −1.22848 | − | 1.69086i | ||||
\(738\) | 0.315842 | + | 0.434719i | 0.0116263 | + | 0.0160022i | ||||
\(739\) | 13.3227 | + | 9.67951i | 0.490083 | + | 0.356066i | 0.805216 | − | 0.592981i | \(-0.202049\pi\) |
−0.315133 | + | 0.949048i | \(0.602049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.16584 | + | 1.57358i | −0.0795642 | + | 0.0578068i | ||||
\(742\) | −4.11658 | − | 1.33756i | −0.151124 | − | 0.0491033i | ||||
\(743\) | 35.6012i | 1.30608i | 0.757322 | + | 0.653041i | \(0.226507\pi\) | ||||
−0.757322 | + | 0.653041i | \(0.773493\pi\) | |||||||
\(744\) | −0.407476 | + | 1.25408i | −0.0149388 | + | 0.0459769i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.339434 | − | 1.04467i | −0.0124275 | − | 0.0382481i | ||||
\(747\) | −0.700939 | + | 0.227749i | −0.0256460 | + | 0.00833290i | ||||
\(748\) | 5.12573 | − | 7.05496i | 0.187415 | − | 0.257955i | ||||
\(749\) | −9.68668 | −0.353944 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.0748 | 1.68129 | 0.840647 | − | 0.541583i | \(-0.182175\pi\) | ||||
0.840647 | + | 0.541583i | \(0.182175\pi\) | |||||||
\(752\) | 25.4090 | − | 34.9725i | 0.926570 | − | 1.27531i | ||||
\(753\) | −2.87726 | + | 0.934879i | −0.104853 | + | 0.0340689i | ||||
\(754\) | 0.438839 | + | 1.35061i | 0.0159816 | + | 0.0491862i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.68419 | − | 8.26109i | 0.0976231 | − | 0.300453i | ||||
\(757\) | 36.6482i | 1.33200i | 0.745951 | + | 0.666000i | \(0.231995\pi\) | ||||
−0.745951 | + | 0.666000i | \(0.768005\pi\) | |||||||
\(758\) | 2.39998 | + | 0.779800i | 0.0871711 | + | 0.0283236i | ||||
\(759\) | −8.37114 | + | 6.08199i | −0.303853 | + | 0.220762i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.0116 | + | 15.9923i | 0.797919 | + | 0.579722i | 0.910303 | − | 0.413943i | \(-0.135849\pi\) |
−0.112384 | + | 0.993665i | \(0.535849\pi\) | |||||||
\(762\) | 0.662939 | + | 0.912457i | 0.0240157 | + | 0.0330548i | ||||
\(763\) | 28.2007 | + | 38.8149i | 1.02093 | + | 1.40520i | ||||
\(764\) | −34.7346 | − | 25.2362i | −1.25666 | − | 0.913013i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.50212 | − | 1.81790i | 0.0904053 | − | 0.0656833i | ||||
\(767\) | −12.6064 | − | 4.09608i | −0.455192 | − | 0.147901i | ||||
\(768\) | 15.3585i | 0.554202i | ||||||||
\(769\) | −8.19906 | + | 25.2341i | −0.295666 | + | 0.909965i | 0.687331 | + | 0.726344i | \(0.258782\pi\) |
−0.982997 | + | 0.183621i | \(0.941218\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.13747 | + | 18.8892i | 0.221035 | + | 0.680277i | ||||
\(772\) | 5.96803 | − | 1.93913i | 0.214794 | − | 0.0697908i | ||||
\(773\) | 16.9092 | − | 23.2736i | 0.608183 | − | 0.837092i | −0.388244 | − | 0.921557i | \(-0.626918\pi\) |
0.996426 | + | 0.0844651i | \(0.0269181\pi\) | |||||||
\(774\) | 0.241213 | 0.00867024 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.0120861 | 0.000433867 | ||||||||
\(777\) | 3.68340 | − | 5.06977i | 0.132141 | − | 0.181877i | ||||
\(778\) | −1.15514 | + | 0.375327i | −0.0414137 | + | 0.0134561i | ||||
\(779\) | 2.49749 | + | 7.68650i | 0.0894820 | + | 0.275397i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.93581 | − | 30.5793i | 0.355531 | − | 1.09421i | ||||
\(782\) | − | 0.211030i | − | 0.00754641i | ||||||
\(783\) | −7.58806 | − | 2.46551i | −0.271175 | − | 0.0881101i | ||||
\(784\) | 38.4138 | − | 27.9092i | 1.37192 | − | 0.996759i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.19693 | − | 0.869621i | −0.0426931 | − | 0.0310183i | ||||
\(787\) | −14.6160 | − | 20.1172i | −0.521005 | − | 0.717102i | 0.464721 | − | 0.885457i | \(-0.346155\pi\) |
−0.985726 | + | 0.168355i | \(0.946155\pi\) | |||||||
\(788\) | −30.5396 | − | 42.0341i | −1.08793 | − | 1.49740i | ||||
\(789\) | −18.4698 | − | 13.4191i | −0.657541 | − | 0.477732i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.03342 | + | 4.38353i | −0.214524 | + | 0.155861i | ||||
\(792\) | 1.49733 | + | 0.486512i | 0.0532053 | + | 0.0172875i | ||||
\(793\) | − | 18.7379i | − | 0.665404i | ||||||
\(794\) | −0.998495 | + | 3.07305i | −0.0354352 | + | 0.109058i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.9368 | + | 45.9708i | 0.529422 | + | 1.62939i | ||||
\(797\) | 29.8828 | − | 9.70951i | 1.05850 | − | 0.343928i | 0.272503 | − | 0.962155i | \(-0.412149\pi\) |
0.786000 | + | 0.618226i | \(0.212149\pi\) | |||||||
\(798\) | −0.311019 | + | 0.428081i | −0.0110099 | + | 0.0151539i | ||||
\(799\) | −10.9067 | −0.385851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.78736 | −0.345819 | ||||||||
\(802\) | −0.230172 | + | 0.316805i | −0.00812766 | + | 0.0111868i | ||||
\(803\) | −1.77400 | + | 0.576406i | −0.0626030 | + | 0.0203409i | ||||
\(804\) | −7.95393 | − | 24.4797i | −0.280513 | − | 0.863332i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.202277 | + | 0.622545i | −0.00712491 | + | 0.0219282i | ||||
\(807\) | − | 14.8324i | − | 0.522125i | ||||||
\(808\) | −1.08913 | − | 0.353881i | −0.0383156 | − | 0.0124495i | ||||
\(809\) | 40.8575 | − | 29.6847i | 1.43647 | − | 1.04366i | 0.447710 | − | 0.894179i | \(-0.352240\pi\) |
0.988765 | − | 0.149481i | \(-0.0477603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.3558 | − | 14.7894i | −0.714789 | − | 0.519325i | 0.169926 | − | 0.985457i | \(-0.445647\pi\) |
−0.884715 | + | 0.466132i | \(0.845647\pi\) | |||||||
\(812\) | −40.7356 | − | 56.0677i | −1.42954 | − | 1.96759i | ||||
\(813\) | 3.78369 | + | 5.20780i | 0.132700 | + | 0.182646i | ||||
\(814\) | 0.458521 | + | 0.333135i | 0.0160712 | + | 0.0116764i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.18744 | − | 2.31581i | 0.111583 | − | 0.0810696i | ||||
\(817\) | 3.45047 | + | 1.12113i | 0.120717 | + | 0.0392233i | ||||
\(818\) | − | 1.62697i | − | 0.0568856i | ||||||
\(819\) | 2.67034 | − | 8.21847i | 0.0933093 | − | 0.287177i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.37524 | − | 19.6210i | −0.222498 | − | 0.684777i | −0.998536 | − | 0.0540914i | \(-0.982774\pi\) |
0.776038 | − | 0.630686i | \(-0.217226\pi\) | |||||||
\(822\) | 0.825815 | − | 0.268324i | 0.0288036 | − | 0.00935886i | ||||
\(823\) | 21.0790 | − | 29.0128i | 0.734769 | − | 1.01132i | −0.264133 | − | 0.964486i | \(-0.585086\pi\) |
0.998903 | − | 0.0468368i | \(-0.0149141\pi\) | |||||||
\(824\) | −3.06686 | −0.106839 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.61990 | −0.0911580 | ||||||||
\(827\) | 2.78400 | − | 3.83184i | 0.0968090 | − | 0.133246i | −0.757865 | − | 0.652412i | \(-0.773757\pi\) |
0.854674 | + | 0.519166i | \(0.173757\pi\) | |||||||
\(828\) | −4.46427 | + | 1.45053i | −0.155144 | + | 0.0504093i | ||||
\(829\) | 8.79981 | + | 27.0830i | 0.305630 | + | 0.940632i | 0.979441 | + | 0.201729i | \(0.0646560\pi\) |
−0.673811 | + | 0.738903i | \(0.735344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.07343 | + | 6.38136i | −0.0719265 | + | 0.221367i | ||||
\(832\) | 15.4708i | 0.536355i | ||||||||
\(833\) | −11.3936 | − | 3.70200i | −0.394765 | − | 0.128267i | ||||
\(834\) | 0.983357 | − | 0.714451i | 0.0340509 | − | 0.0247394i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.55941 | + | 6.94532i | 0.330619 | + | 0.240209i | ||||
\(837\) | −2.16165 | − | 2.97525i | −0.0747175 | − | 0.102840i | ||||
\(838\) | −0.0278685 | − | 0.0383577i | −0.000962700 | − | 0.00132504i | ||||
\(839\) | −0.619476 | − | 0.450076i | −0.0213867 | − | 0.0155383i | 0.577041 | − | 0.816715i | \(-0.304207\pi\) |
−0.598427 | + | 0.801177i | \(0.704207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0384 | + | 20.3711i | −0.966841 | + | 0.702451i | ||||
\(842\) | −1.59388 | − | 0.517883i | −0.0549287 | − | 0.0178474i | ||||
\(843\) | − | 20.4867i | − | 0.705600i | ||||||
\(844\) | 10.0815 | − | 31.0278i | 0.347021 | − | 1.06802i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.303628 | − | 0.934470i | −0.0104389 | − | 0.0321278i | ||||
\(847\) | −34.3410 | + | 11.1581i | −1.17997 | + | 0.383395i | ||||
\(848\) | −25.6686 | + | 35.3297i | −0.881462 | + | 1.21323i | ||||
\(849\) | −11.4177 | −0.391856 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.38644 | −0.116086 | ||||||||
\(852\) | 8.57347 | − | 11.8004i | 0.293722 | − | 0.404274i | ||||
\(853\) | 33.0292 | − | 10.7318i | 1.13090 | − | 0.367451i | 0.316981 | − | 0.948432i | \(-0.397331\pi\) |
0.813917 | + | 0.580981i | \(0.197331\pi\) | |||||||
\(854\) | −1.14447 | − | 3.52230i | −0.0391628 | − | 0.120531i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.246124 | − | 0.757493i | 0.00841236 | − | 0.0258906i | ||||
\(857\) | 54.2561i | 1.85335i | 0.375860 | + | 0.926676i | \(0.377347\pi\) | ||||
−0.375860 | + | 0.926676i | \(0.622653\pi\) | |||||||
\(858\) | 0.743297 | + | 0.241512i | 0.0253757 | + | 0.00824508i | ||||
\(859\) | 12.8710 | − | 9.35134i | 0.439154 | − | 0.319064i | −0.346145 | − | 0.938181i | \(-0.612509\pi\) |
0.785299 | + | 0.619117i | \(0.212509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.1055 | − | 15.3340i | −0.719272 | − | 0.522582i | ||||
\(862\) | 1.10823 | + | 1.52535i | 0.0377464 | + | 0.0519535i | ||||
\(863\) | 13.2083 | + | 18.1797i | 0.449617 | + | 0.618845i | 0.972315 | − | 0.233673i | \(-0.0750744\pi\) |
−0.522698 | + | 0.852518i | \(0.675074\pi\) | |||||||
\(864\) | 0.867300 | + | 0.630131i | 0.0295062 | + | 0.0214375i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.992896 | + | 0.721381i | −0.0337400 | + | 0.0245135i | ||||
\(867\) | 15.2226 | + | 4.94611i | 0.516985 | + | 0.167979i | ||||
\(868\) | − | 31.9446i | − | 1.08427i | ||||||
\(869\) | 8.62336 | − | 26.5400i | 0.292527 | − | 0.900307i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.91289 | − | 24.3534i | −0.268118 | − | 0.825183i | ||||
\(872\) | −3.75184 | + | 1.21905i | −0.127053 | + | 0.0412822i | ||||
\(873\) | −0.0198131 | + | 0.0272704i | −0.000670572 | + | 0.000922963i | ||||
\(874\) | 0.285944 | 0.00967219 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.846181 | −0.0285898 | ||||||||
\(877\) | 15.9146 | − | 21.9046i | 0.537399 | − | 0.739667i | −0.450836 | − | 0.892607i | \(-0.648874\pi\) |
0.988235 | + | 0.152940i | \(0.0488741\pi\) | |||||||
\(878\) | 0.370173 | − | 0.120276i | 0.0124927 | − | 0.00405913i | ||||
\(879\) | 8.82258 | + | 27.1531i | 0.297578 | + | 0.915852i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.41440 | + | 7.43077i | −0.0813433 | + | 0.250349i | −0.983455 | − | 0.181154i | \(-0.942017\pi\) |
0.902111 | + | 0.431503i | \(0.142017\pi\) | |||||||
\(882\) | − | 1.07925i | − | 0.0363401i | ||||||
\(883\) | 55.4476 | + | 18.0160i | 1.86596 | + | 0.606287i | 0.992942 | + | 0.118599i | \(0.0378402\pi\) |
0.873018 | + | 0.487688i | \(0.162160\pi\) | |||||||
\(884\) | 3.18394 | − | 2.31327i | 0.107088 | − | 0.0778036i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.116804 | − | 0.0848629i | −0.00392410 | − | 0.00285102i | ||||
\(887\) | 5.08205 | + | 6.99484i | 0.170638 | + | 0.234864i | 0.885768 | − | 0.464128i | \(-0.153632\pi\) |
−0.715130 | + | 0.698992i | \(0.753632\pi\) | |||||||
\(888\) | 0.302863 | + | 0.416855i | 0.0101634 | + | 0.0139887i | ||||
\(889\) | −44.2994 | − | 32.1854i | −1.48576 | − | 1.07946i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.55235 | + | 2.58093i | −0.119008 | + | 0.0864644i | ||||
\(892\) | 10.7660 | + | 3.49809i | 0.360472 | + | 0.117125i | ||||
\(893\) | − | 14.7785i | − | 0.494543i | ||||||
\(894\) | −0.379817 | + | 1.16896i | −0.0127030 | + | 0.0390957i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.83414 | + | 11.8003i | 0.128090 | + | 0.394219i | ||||
\(897\) | −4.44123 | + | 1.44304i | −0.148288 | + | 0.0481818i | ||||
\(898\) | −0.730099 | + | 1.00490i | −0.0243637 | + | 0.0335338i | ||||
\(899\) | −29.3420 | −0.978612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0181 | 0.367067 | ||||||||
\(902\) | 1.38684 | − | 1.90883i | 0.0461769 | − | 0.0635570i | ||||
\(903\) | −11.1377 | + | 3.61885i | −0.370638 | + | 0.120428i | ||||
\(904\) | −0.189490 | − | 0.583189i | −0.00630233 | − | 0.0193966i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.314205 | + | 0.967022i | −0.0104387 | + | 0.0321272i | ||||
\(907\) | − | 40.4367i | − | 1.34268i | −0.741151 | − | 0.671339i | \(-0.765720\pi\) | ||
0.741151 | − | 0.671339i | \(-0.234280\pi\) | |||||||
\(908\) | 6.90285 | + | 2.24287i | 0.229079 | + | 0.0744324i | ||||
\(909\) | 2.58392 | − | 1.87733i | 0.0857032 | − | 0.0622670i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.9074 | + | 29.7210i | 1.35532 | + | 0.984700i | 0.998727 | + | 0.0504407i | \(0.0160626\pi\) |
0.356596 | + | 0.934259i | \(0.383937\pi\) | |||||||
\(912\) | 3.13790 | + | 4.31895i | 0.103906 | + | 0.143015i | ||||
\(913\) | 1.90217 | + | 2.61812i | 0.0629528 | + | 0.0866471i | ||||
\(914\) | −1.46308 | − | 1.06299i | −0.0483944 | − | 0.0351606i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.67712 | − | 1.94504i | 0.0884545 | − | 0.0642660i | ||||
\(917\) | 68.3130 | + | 22.1962i | 2.25590 | + | 0.732985i | ||||
\(918\) | − | 0.0895519i | − | 0.00295565i | ||||||
\(919\) | 13.3979 | − | 41.2346i | 0.441957 | − | 1.36020i | −0.443831 | − | 0.896111i | \(-0.646381\pi\) |
0.885787 | − | 0.464092i | \(-0.153619\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.34773 | + | 19.5363i | 0.209165 | + | 0.643743i | ||||
\(922\) | 2.69309 | − | 0.875039i | 0.0886923 | − | 0.0288179i | ||||
\(923\) | 8.52924 | − | 11.7395i | 0.280743 | − | 0.386410i | ||||
\(924\) | −38.1407 | −1.25474 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.00405712 | 0.000133325 | ||||||||
\(927\) | 5.02758 | − | 6.91986i | 0.165127 | − | 0.227278i | ||||
\(928\) | 8.13472 | − | 2.64313i | 0.267035 | − | 0.0867650i | ||||
\(929\) | 10.5605 | + | 32.5020i | 0.346480 | + | 1.06636i | 0.960787 | + | 0.277289i | \(0.0894358\pi\) |
−0.614307 | + | 0.789067i | \(0.710564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.01618 | − | 15.4382i | 0.164399 | − | 0.505967i | ||||
\(932\) | − | 15.6546i | − | 0.512783i | ||||||
\(933\) | 16.6907 | + | 5.42312i | 0.546427 | + | 0.177545i | ||||
\(934\) | 2.38596 | − | 1.73350i | 0.0780710 | − | 0.0567219i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.574830 | + | 0.417638i | 0.0187889 | + | 0.0136509i | ||||
\(937\) | −16.3990 | − | 22.5713i | −0.535731 | − | 0.737371i | 0.452259 | − | 0.891887i | \(-0.350618\pi\) |
−0.987990 | + | 0.154516i | \(0.950618\pi\) | |||||||
\(938\) | −2.97489 | − | 4.09458i | −0.0971334 | − | 0.133693i | ||||
\(939\) | 2.41543 | + | 1.75491i | 0.0788246 | + | 0.0572694i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.9507 | − | 31.9321i | 1.43275 | − | 1.04096i | 0.443257 | − | 0.896395i | \(-0.353823\pi\) |
0.989496 | − | 0.144561i | \(-0.0461769\pi\) | |||||||
\(942\) | 0.731284 | + | 0.237609i | 0.0238265 | + | 0.00774171i | ||||
\(943\) | 14.0978i | 0.459086i | ||||||||
\(944\) | −8.16808 | + | 25.1388i | −0.265848 | + | 0.818197i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.327297 | − | 1.00732i | −0.0106413 | − | 0.0327507i | ||||
\(947\) | −4.02460 | + | 1.30767i | −0.130782 | + | 0.0424936i | −0.373677 | − | 0.927559i | \(-0.621903\pi\) |
0.242895 | + | 0.970053i | \(0.421903\pi\) | |||||||
\(948\) | 7.44097 | − | 10.2416i | 0.241672 | − | 0.332632i | ||||
\(949\) | −0.841815 | −0.0273265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1708 | 0.524375 | ||||||||
\(952\) | 0.916291 | − | 1.26117i | 0.0296971 | − | 0.0408746i | ||||
\(953\) | −45.5848 | + | 14.8114i | −1.47664 | + | 0.479788i | −0.933106 | − | 0.359601i | \(-0.882913\pi\) |
−0.543531 | + | 0.839389i | \(0.682913\pi\) | |||||||
\(954\) | 0.306730 | + | 0.944017i | 0.00993074 | + | 0.0305637i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.349197 | − | 1.07472i | 0.0112938 | − | 0.0347588i | ||||
\(957\) | 35.0334i | 1.13247i | ||||||||
\(958\) | 0.639459 | + | 0.207773i | 0.0206600 | + | 0.00671284i | ||||
\(959\) | −34.1052 | + | 24.7788i | −1.10131 | + | 0.800151i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1377 | + | 10.2716i | 0.456055 | + | 0.331343i | ||||
\(962\) | 0.150346 | + | 0.206933i | 0.00484734 | + | 0.00667179i | ||||
\(963\) | 1.30568 | + | 1.79712i | 0.0420750 | + | 0.0579113i | ||||
\(964\) | 30.6318 | + | 22.2553i | 0.986582 | + | 0.716794i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.746713 | + | 0.542518i | −0.0240251 | + | 0.0174552i | ||||
\(967\) | −19.8607 | − | 6.45312i | −0.638676 | − | 0.207518i | −0.0282614 | − | 0.999601i | \(-0.508997\pi\) |
−0.610414 | + | 0.792082i | \(0.708997\pi\) | |||||||
\(968\) | − | 2.96895i | − | 0.0954257i | ||||||
\(969\) | 0.416225 | − | 1.28101i | 0.0133711 | − | 0.0411519i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.96713 | + | 15.2872i | 0.159403 | + | 0.490591i | 0.998580 | − | 0.0532663i | \(-0.0169632\pi\) |
−0.839178 | + | 0.543857i | \(0.816963\pi\) | |||||||
\(972\) | −1.89444 | + | 0.615541i | −0.0607642 | + | 0.0197435i | ||||
\(973\) | −34.6863 | + | 47.7417i | −1.11199 | + | 1.53053i | ||||
\(974\) | −2.28406 | −0.0731860 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.3657 | −1.19605 | ||||||||
\(977\) | −20.9055 | + | 28.7739i | −0.668826 | + | 0.920560i | −0.999733 | − | 0.0231034i | \(-0.992645\pi\) |
0.330907 | + | 0.943663i | \(0.392645\pi\) | |||||||
\(978\) | 0.391674 | − | 0.127263i | 0.0125244 | − | 0.00406941i | ||||
\(979\) | 13.2802 | + | 40.8723i | 0.424438 | + | 1.30629i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.39991 | − | 10.4638i | 0.108551 | − | 0.334085i | ||||
\(982\) | 0.994014i | 0.0317202i | ||||||||
\(983\) | −17.5671 | − | 5.70790i | −0.560303 | − | 0.182054i | 0.0151542 | − | 0.999885i | \(-0.495176\pi\) |
−0.575458 | + | 0.817832i | \(0.695176\pi\) | |||||||
\(984\) | 1.73537 | − | 1.26082i | 0.0553216 | − | 0.0401935i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.578039 | − | 0.419970i | −0.0184085 | − | 0.0133746i | ||||
\(987\) | 28.0391 | + | 38.5925i | 0.892494 | + | 1.22841i | ||||
\(988\) | 3.13446 | + | 4.31421i | 0.0997204 | + | 0.137253i | ||||
\(989\) | 5.11986 | + | 3.71979i | 0.162802 | + | 0.118283i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.6476 | − | 24.4464i | 1.06885 | − | 0.776566i | 0.0931455 | − | 0.995653i | \(-0.470308\pi\) |
0.975705 | + | 0.219087i | \(0.0703078\pi\) | |||||||
\(992\) | 3.74959 | + | 1.21832i | 0.119050 | + | 0.0386816i | ||||
\(993\) | − | 13.0705i | − | 0.414779i | ||||||
\(994\) | 0.886283 | − | 2.72770i | 0.0281112 | − | 0.0865174i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.453660 | + | 1.39622i | 0.0143748 | + | 0.0442410i | ||||
\(997\) | −30.2792 | + | 9.83830i | −0.958952 | + | 0.311582i | −0.746348 | − | 0.665556i | \(-0.768194\pi\) |
−0.212604 | + | 0.977138i | \(0.568194\pi\) | |||||||
\(998\) | 0.247161 | − | 0.340189i | 0.00782376 | − | 0.0107685i | ||||
\(999\) | −1.43706 | −0.0454665 |
(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 | 375.2.i.c.49.2 | 16 | ||
5.2 | odd | 4 | 375.2.g.e.76.2 | 16 | |||
5.3 | odd | 4 | 375.2.g.d.76.3 | 16 | |||
5.4 | even | 2 | 75.2.i.a.34.3 | ✓ | 16 | ||
15.14 | odd | 2 | 225.2.m.b.109.2 | 16 | |||
25.2 | odd | 20 | 375.2.g.e.301.2 | 16 | |||
25.6 | even | 5 | 1875.2.b.h.1249.8 | 16 | |||
25.8 | odd | 20 | 1875.2.a.p.1.4 | 8 | |||
25.11 | even | 5 | 75.2.i.a.64.3 | yes | 16 | ||
25.14 | even | 10 | inner | 375.2.i.c.199.2 | 16 | ||
25.17 | odd | 20 | 1875.2.a.m.1.5 | 8 | |||
25.19 | even | 10 | 1875.2.b.h.1249.9 | 16 | |||
25.23 | odd | 20 | 375.2.g.d.301.3 | 16 | |||
75.8 | even | 20 | 5625.2.a.t.1.5 | 8 | |||
75.11 | odd | 10 | 225.2.m.b.64.2 | 16 | |||
75.17 | even | 20 | 5625.2.a.bd.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.34.3 | ✓ | 16 | 5.4 | even | 2 | ||
75.2.i.a.64.3 | yes | 16 | 25.11 | even | 5 | ||
225.2.m.b.64.2 | 16 | 75.11 | odd | 10 | |||
225.2.m.b.109.2 | 16 | 15.14 | odd | 2 | |||
375.2.g.d.76.3 | 16 | 5.3 | odd | 4 | |||
375.2.g.d.301.3 | 16 | 25.23 | odd | 20 | |||
375.2.g.e.76.2 | 16 | 5.2 | odd | 4 | |||
375.2.g.e.301.2 | 16 | 25.2 | odd | 20 | |||
375.2.i.c.49.2 | 16 | 1.1 | even | 1 | trivial | ||
375.2.i.c.199.2 | 16 | 25.14 | even | 10 | inner | ||
1875.2.a.m.1.5 | 8 | 25.17 | odd | 20 | |||
1875.2.a.p.1.4 | 8 | 25.8 | odd | 20 | |||
1875.2.b.h.1249.8 | 16 | 25.6 | even | 5 | |||
1875.2.b.h.1249.9 | 16 | 25.19 | even | 10 | |||
5625.2.a.t.1.5 | 8 | 75.8 | even | 20 | |||
5625.2.a.bd.1.4 | 8 | 75.17 | even | 20 |