Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(121,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.l (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Character | \(\chi\) | \(=\) | 315.121 |
Dual form | 315.2.l.b.151.2 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.71927 | −1.21571 | −0.607854 | − | 0.794049i | \(-0.707969\pi\) | ||||
−0.607854 | + | 0.794049i | \(0.707969\pi\) | |||||||
\(3\) | −0.324473 | − | 1.70139i | −0.187334 | − | 0.982296i | ||||
\(4\) | 0.955889 | 0.477944 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0.557856 | + | 2.92514i | 0.227744 | + | 1.19418i | ||||
\(7\) | −2.52983 | − | 0.774581i | −0.956185 | − | 0.292764i | ||||
\(8\) | 1.79511 | 0.634667 | ||||||||
\(9\) | −2.78943 | + | 1.10411i | −0.929812 | + | 0.368036i | ||||
\(10\) | −0.859635 | − | 1.48893i | −0.271840 | − | 0.470841i | ||||
\(11\) | −2.30123 | + | 3.98585i | −0.693848 | + | 1.20178i | 0.276720 | + | 0.960951i | \(0.410753\pi\) |
−0.970568 | + | 0.240829i | \(0.922581\pi\) | |||||||
\(12\) | −0.310160 | − | 1.62634i | −0.0895354 | − | 0.469483i | ||||
\(13\) | 0.944711 | − | 1.63629i | 0.262016 | − | 0.453825i | −0.704762 | − | 0.709444i | \(-0.748946\pi\) |
0.966777 | + | 0.255619i | \(0.0822794\pi\) | |||||||
\(14\) | 4.34945 | + | 1.33171i | 1.16244 | + | 0.355916i | ||||
\(15\) | 1.31121 | − | 1.13170i | 0.338552 | − | 0.292202i | ||||
\(16\) | −4.99805 | −1.24951 | ||||||||
\(17\) | 0.371733 | + | 0.643861i | 0.0901585 | + | 0.156159i | 0.907578 | − | 0.419884i | \(-0.137929\pi\) |
−0.817419 | + | 0.576043i | \(0.804596\pi\) | |||||||
\(18\) | 4.79579 | − | 1.89826i | 1.13038 | − | 0.447424i | ||||
\(19\) | −0.518230 | + | 0.897600i | −0.118890 | + | 0.205924i | −0.919328 | − | 0.393492i | \(-0.871267\pi\) |
0.800438 | + | 0.599415i | \(0.204600\pi\) | |||||||
\(20\) | 0.477944 | + | 0.827824i | 0.106872 | + | 0.185107i | ||||
\(21\) | −0.497003 | + | 4.55554i | −0.108455 | + | 0.994101i | ||||
\(22\) | 3.95644 | − | 6.85276i | 0.843516 | − | 1.46101i | ||||
\(23\) | 2.38562 | + | 4.13202i | 0.497437 | + | 0.861586i | 0.999996 | − | 0.00295696i | \(-0.000941229\pi\) |
−0.502559 | + | 0.864543i | \(0.667608\pi\) | |||||||
\(24\) | −0.582464 | − | 3.05418i | −0.118895 | − | 0.623431i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −1.62421 | + | 2.81322i | −0.318535 | + | 0.551718i | ||||
\(27\) | 2.78361 | + | 4.38766i | 0.535706 | + | 0.844405i | ||||
\(28\) | −2.41823 | − | 0.740414i | −0.457003 | − | 0.139925i | ||||
\(29\) | 4.71667 | + | 8.16951i | 0.875864 | + | 1.51704i | 0.855840 | + | 0.517241i | \(0.173041\pi\) |
0.0200242 | + | 0.999799i | \(0.493626\pi\) | |||||||
\(30\) | −2.25432 | + | 1.94569i | −0.411581 | + | 0.355233i | ||||
\(31\) | 1.17974 | 0.211888 | 0.105944 | − | 0.994372i | \(-0.466214\pi\) | ||||
0.105944 | + | 0.994372i | \(0.466214\pi\) | |||||||
\(32\) | 5.00279 | 0.884376 | ||||||||
\(33\) | 7.52817 | + | 2.62199i | 1.31049 | + | 0.456429i | ||||
\(34\) | −0.639110 | − | 1.10697i | −0.109606 | − | 0.189844i | ||||
\(35\) | −0.594106 | − | 2.57818i | −0.100422 | − | 0.435793i | ||||
\(36\) | −2.66639 | + | 1.05540i | −0.444398 | + | 0.175901i | ||||
\(37\) | −2.82154 | + | 4.88706i | −0.463859 | + | 0.803427i | −0.999149 | − | 0.0412409i | \(-0.986869\pi\) |
0.535290 | + | 0.844668i | \(0.320202\pi\) | |||||||
\(38\) | 0.890976 | − | 1.54322i | 0.144535 | − | 0.250343i | ||||
\(39\) | −3.09049 | − | 1.07639i | −0.494875 | − | 0.172360i | ||||
\(40\) | 0.897555 | + | 1.55461i | 0.141916 | + | 0.245805i | ||||
\(41\) | −3.72949 | + | 6.45966i | −0.582448 | + | 1.00883i | 0.412741 | + | 0.910849i | \(0.364572\pi\) |
−0.995188 | + | 0.0979806i | \(0.968762\pi\) | |||||||
\(42\) | 0.854482 | − | 7.83221i | 0.131849 | − | 1.20854i | ||||
\(43\) | −1.26959 | − | 2.19900i | −0.193611 | − | 0.335344i | 0.752833 | − | 0.658211i | \(-0.228687\pi\) |
−0.946444 | + | 0.322867i | \(0.895353\pi\) | |||||||
\(44\) | −2.19972 | + | 3.81003i | −0.331621 | + | 0.574384i | ||||
\(45\) | −2.35090 | − | 1.86367i | −0.350452 | − | 0.277819i | ||||
\(46\) | −4.10153 | − | 7.10406i | −0.604738 | − | 1.04744i | ||||
\(47\) | −1.91984 | −0.280037 | −0.140019 | − | 0.990149i | \(-0.544716\pi\) | ||||
−0.140019 | + | 0.990149i | \(0.544716\pi\) | |||||||
\(48\) | 1.62173 | + | 8.50362i | 0.234077 | + | 1.22739i | ||||
\(49\) | 5.80005 | + | 3.91911i | 0.828578 | + | 0.559873i | ||||
\(50\) | 0.859635 | − | 1.48893i | 0.121571 | − | 0.210567i | ||||
\(51\) | 0.974839 | − | 0.841377i | 0.136505 | − | 0.117816i | ||||
\(52\) | 0.903039 | − | 1.56411i | 0.125229 | − | 0.216903i | ||||
\(53\) | −3.94471 | − | 6.83244i | −0.541848 | − | 0.938507i | −0.998798 | − | 0.0490154i | \(-0.984392\pi\) |
0.456950 | − | 0.889492i | \(-0.348942\pi\) | |||||||
\(54\) | −4.78577 | − | 7.54356i | −0.651261 | − | 1.02655i | ||||
\(55\) | −4.60247 | −0.620596 | ||||||||
\(56\) | −4.54132 | − | 1.39046i | −0.606859 | − | 0.185808i | ||||
\(57\) | 1.69532 | + | 0.590462i | 0.224550 | + | 0.0782086i | ||||
\(58\) | −8.10923 | − | 14.0456i | −1.06479 | − | 1.84428i | ||||
\(59\) | −5.10165 | −0.664178 | −0.332089 | − | 0.943248i | \(-0.607753\pi\) | ||||
−0.332089 | + | 0.943248i | \(0.607753\pi\) | |||||||
\(60\) | 1.25337 | − | 1.08177i | 0.161809 | − | 0.139656i | ||||
\(61\) | 4.07757 | 0.522080 | 0.261040 | − | 0.965328i | \(-0.415935\pi\) | ||||
0.261040 | + | 0.965328i | \(0.415935\pi\) | |||||||
\(62\) | −2.02829 | −0.257594 | ||||||||
\(63\) | 7.91201 | − | 0.632556i | 0.996819 | − | 0.0796945i | ||||
\(64\) | 1.39497 | 0.174371 | ||||||||
\(65\) | 1.88942 | 0.234354 | ||||||||
\(66\) | −12.9429 | − | 4.50790i | −1.59317 | − | 0.554885i | ||||
\(67\) | −7.45782 | −0.911117 | −0.455559 | − | 0.890206i | \(-0.650560\pi\) | ||||
−0.455559 | + | 0.890206i | \(0.650560\pi\) | |||||||
\(68\) | 0.355335 | + | 0.615459i | 0.0430908 | + | 0.0746354i | ||||
\(69\) | 6.25610 | − | 5.39960i | 0.753146 | − | 0.650035i | ||||
\(70\) | 1.02143 | + | 4.43260i | 0.122084 | + | 0.529797i | ||||
\(71\) | −6.30656 | −0.748451 | −0.374225 | − | 0.927338i | \(-0.622091\pi\) | ||||
−0.374225 | + | 0.927338i | \(0.622091\pi\) | |||||||
\(72\) | −5.00734 | + | 1.98199i | −0.590121 | + | 0.233580i | ||||
\(73\) | 3.33632 | + | 5.77867i | 0.390486 | + | 0.676342i | 0.992514 | − | 0.122133i | \(-0.0389736\pi\) |
−0.602027 | + | 0.798475i | \(0.705640\pi\) | |||||||
\(74\) | 4.85100 | − | 8.40217i | 0.563917 | − | 0.976732i | ||||
\(75\) | 1.63568 | + | 0.569692i | 0.188872 | + | 0.0657824i | ||||
\(76\) | −0.495370 | + | 0.858006i | −0.0568228 | + | 0.0984200i | ||||
\(77\) | 8.90909 | − | 8.30103i | 1.01528 | − | 0.945990i | ||||
\(78\) | 5.31339 | + | 1.85060i | 0.601623 | + | 0.209540i | ||||
\(79\) | −5.21220 | −0.586418 | −0.293209 | − | 0.956048i | \(-0.594723\pi\) | ||||
−0.293209 | + | 0.956048i | \(0.594723\pi\) | |||||||
\(80\) | −2.49903 | − | 4.32844i | −0.279400 | − | 0.483935i | ||||
\(81\) | 6.56189 | − | 6.15967i | 0.729099 | − | 0.684408i | ||||
\(82\) | 6.41199 | − | 11.1059i | 0.708086 | − | 1.22644i | ||||
\(83\) | −8.45847 | − | 14.6505i | −0.928438 | − | 1.60810i | −0.785937 | − | 0.618307i | \(-0.787819\pi\) |
−0.142501 | − | 0.989795i | \(-0.545514\pi\) | |||||||
\(84\) | −0.475079 | + | 4.35459i | −0.0518354 | + | 0.475125i | ||||
\(85\) | −0.371733 | + | 0.643861i | −0.0403201 | + | 0.0698365i | ||||
\(86\) | 2.18277 | + | 3.78067i | 0.235374 | + | 0.407681i | ||||
\(87\) | 12.3691 | − | 10.6757i | 1.32610 | − | 1.14455i | ||||
\(88\) | −4.13096 | + | 7.15504i | −0.440362 | + | 0.762730i | ||||
\(89\) | 8.48148 | − | 14.6904i | 0.899035 | − | 1.55717i | 0.0703049 | − | 0.997526i | \(-0.477603\pi\) |
0.828730 | − | 0.559649i | \(-0.189064\pi\) | |||||||
\(90\) | 4.04184 | + | 3.20415i | 0.426047 | + | 0.337747i | ||||
\(91\) | −3.65739 | + | 3.40777i | −0.383399 | + | 0.357231i | ||||
\(92\) | 2.28039 | + | 3.94975i | 0.237747 | + | 0.411790i | ||||
\(93\) | −0.382794 | − | 2.00720i | −0.0396939 | − | 0.208137i | ||||
\(94\) | 3.30072 | 0.340444 | ||||||||
\(95\) | −1.03646 | −0.106338 | ||||||||
\(96\) | −1.62327 | − | 8.51167i | −0.165674 | − | 0.868719i | ||||
\(97\) | 5.80321 | + | 10.0515i | 0.589227 | + | 1.02057i | 0.994334 | + | 0.106302i | \(0.0339009\pi\) |
−0.405107 | + | 0.914269i | \(0.632766\pi\) | |||||||
\(98\) | −9.97185 | − | 6.73801i | −1.00731 | − | 0.680642i | ||||
\(99\) | 2.01833 | − | 13.6591i | 0.202850 | − | 1.37279i | ||||
\(100\) | −0.477944 | + | 0.827824i | −0.0477944 | + | 0.0827824i | ||||
\(101\) | −9.46492 | + | 16.3937i | −0.941794 | + | 1.63124i | −0.179749 | + | 0.983713i | \(0.557528\pi\) |
−0.762046 | + | 0.647523i | \(0.775805\pi\) | |||||||
\(102\) | −1.67601 | + | 1.44655i | −0.165950 | + | 0.143230i | ||||
\(103\) | −4.16009 | − | 7.20549i | −0.409906 | − | 0.709978i | 0.584973 | − | 0.811053i | \(-0.301105\pi\) |
−0.994879 | + | 0.101075i | \(0.967772\pi\) | |||||||
\(104\) | 1.69586 | − | 2.93732i | 0.166293 | − | 0.288028i | ||||
\(105\) | −4.19372 | + | 1.84736i | −0.409265 | + | 0.180283i | ||||
\(106\) | 6.78202 | + | 11.7468i | 0.658728 | + | 1.14095i | ||||
\(107\) | −4.96262 | + | 8.59551i | −0.479754 | + | 0.830959i | −0.999730 | − | 0.0232218i | \(-0.992608\pi\) |
0.519976 | + | 0.854181i | \(0.325941\pi\) | |||||||
\(108\) | 2.66082 | + | 4.19411i | 0.256038 | + | 0.403578i | ||||
\(109\) | −2.68358 | − | 4.64809i | −0.257040 | − | 0.445206i | 0.708408 | − | 0.705803i | \(-0.249414\pi\) |
−0.965448 | + | 0.260597i | \(0.916081\pi\) | |||||||
\(110\) | 7.91288 | 0.754464 | ||||||||
\(111\) | 9.23029 | + | 3.21482i | 0.876100 | + | 0.305137i | ||||
\(112\) | 12.6442 | + | 3.87140i | 1.19477 | + | 0.365813i | ||||
\(113\) | −7.54586 | + | 13.0698i | −0.709855 | + | 1.22951i | 0.255055 | + | 0.966926i | \(0.417906\pi\) |
−0.964911 | + | 0.262579i | \(0.915427\pi\) | |||||||
\(114\) | −2.91471 | − | 1.01516i | −0.272987 | − | 0.0950788i | ||||
\(115\) | −2.38562 | + | 4.13202i | −0.222461 | + | 0.385313i | ||||
\(116\) | 4.50861 | + | 7.80915i | 0.418614 | + | 0.725061i | ||||
\(117\) | −0.828574 | + | 5.60738i | −0.0766017 | + | 0.518403i | ||||
\(118\) | 8.77111 | 0.807446 | ||||||||
\(119\) | −0.441698 | − | 1.91679i | −0.0404904 | − | 0.175712i | ||||
\(120\) | 2.35376 | − | 2.03152i | 0.214868 | − | 0.185451i | ||||
\(121\) | −5.09135 | − | 8.81847i | −0.462850 | − | 0.801680i | ||||
\(122\) | −7.01045 | −0.634696 | ||||||||
\(123\) | 12.2005 | + | 4.24932i | 1.10008 | + | 0.383148i | ||||
\(124\) | 1.12770 | 0.101271 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −13.6029 | + | 1.08753i | −1.21184 | + | 0.0968852i | ||||
\(127\) | −21.1638 | −1.87798 | −0.938991 | − | 0.343940i | \(-0.888238\pi\) | ||||
−0.938991 | + | 0.343940i | \(0.888238\pi\) | |||||||
\(128\) | −12.4039 | −1.09636 | ||||||||
\(129\) | −3.32940 | + | 2.87358i | −0.293137 | + | 0.253005i | ||||
\(130\) | −3.24843 | −0.284906 | ||||||||
\(131\) | 7.11044 | + | 12.3156i | 0.621242 | + | 1.07602i | 0.989255 | + | 0.146202i | \(0.0467048\pi\) |
−0.368013 | + | 0.929821i | \(0.619962\pi\) | |||||||
\(132\) | 7.19609 | + | 2.50633i | 0.626339 | + | 0.218148i | ||||
\(133\) | 2.00630 | − | 1.86936i | 0.173968 | − | 0.162094i | ||||
\(134\) | 12.8220 | 1.10765 | ||||||||
\(135\) | −2.40802 | + | 4.60450i | −0.207249 | + | 0.396293i | ||||
\(136\) | 0.667302 | + | 1.15580i | 0.0572206 | + | 0.0991090i | ||||
\(137\) | 0.279292 | − | 0.483748i | 0.0238615 | − | 0.0413293i | −0.853848 | − | 0.520522i | \(-0.825737\pi\) |
0.877710 | + | 0.479193i | \(0.159071\pi\) | |||||||
\(138\) | −10.7559 | + | 9.28337i | −0.915605 | + | 0.790253i | ||||
\(139\) | −6.91228 | + | 11.9724i | −0.586292 | + | 1.01549i | 0.408421 | + | 0.912794i | \(0.366080\pi\) |
−0.994713 | + | 0.102694i | \(0.967254\pi\) | |||||||
\(140\) | −0.567899 | − | 2.46446i | −0.0479963 | − | 0.208285i | ||||
\(141\) | 0.622936 | + | 3.26639i | 0.0524606 | + | 0.275080i | ||||
\(142\) | 10.8427 | 0.909897 | ||||||||
\(143\) | 4.34800 | + | 7.53096i | 0.363598 | + | 0.629771i | ||||
\(144\) | 13.9417 | − | 5.51839i | 1.16181 | − | 0.459866i | ||||
\(145\) | −4.71667 | + | 8.16951i | −0.391698 | + | 0.678441i | ||||
\(146\) | −5.73603 | − | 9.93509i | −0.474717 | − | 0.822234i | ||||
\(147\) | 4.78597 | − | 11.1398i | 0.394740 | − | 0.918793i | ||||
\(148\) | −2.69708 | + | 4.67148i | −0.221699 | + | 0.383994i | ||||
\(149\) | −2.95113 | − | 5.11150i | −0.241766 | − | 0.418751i | 0.719451 | − | 0.694543i | \(-0.244393\pi\) |
−0.961217 | + | 0.275792i | \(0.911060\pi\) | |||||||
\(150\) | −2.81218 | − | 0.979454i | −0.229613 | − | 0.0799721i | ||||
\(151\) | 10.1855 | − | 17.6417i | 0.828881 | − | 1.43566i | −0.0700359 | − | 0.997544i | \(-0.522311\pi\) |
0.898917 | − | 0.438119i | \(-0.144355\pi\) | |||||||
\(152\) | −0.930279 | + | 1.61129i | −0.0754556 | + | 0.130693i | ||||
\(153\) | −1.74782 | − | 1.38557i | −0.141303 | − | 0.112017i | ||||
\(154\) | −15.3171 | + | 14.2717i | −1.23429 | + | 1.15005i | ||||
\(155\) | 0.589871 | + | 1.02169i | 0.0473796 | + | 0.0820638i | ||||
\(156\) | −2.95417 | − | 1.02891i | −0.236523 | − | 0.0823786i | ||||
\(157\) | 19.4336 | 1.55097 | 0.775486 | − | 0.631365i | \(-0.217505\pi\) | ||||
0.775486 | + | 0.631365i | \(0.217505\pi\) | |||||||
\(158\) | 8.96118 | 0.712913 | ||||||||
\(159\) | −10.3447 | + | 8.92842i | −0.820386 | + | 0.708070i | ||||
\(160\) | 2.50139 | + | 4.33254i | 0.197752 | + | 0.342517i | ||||
\(161\) | −2.83463 | − | 12.3012i | −0.223400 | − | 0.969467i | ||||
\(162\) | −11.2817 | + | 10.5901i | −0.886372 | + | 0.832040i | ||||
\(163\) | 9.70630 | − | 16.8118i | 0.760256 | − | 1.31680i | −0.182462 | − | 0.983213i | \(-0.558407\pi\) |
0.942718 | − | 0.333590i | \(-0.108260\pi\) | |||||||
\(164\) | −3.56497 | + | 6.17471i | −0.278378 | + | 0.482164i | ||||
\(165\) | 1.49337 | + | 7.83058i | 0.116259 | + | 0.609610i | ||||
\(166\) | 14.5424 | + | 25.1882i | 1.12871 | + | 1.95498i | ||||
\(167\) | −2.54026 | + | 4.39986i | −0.196571 | + | 0.340471i | −0.947414 | − | 0.320009i | \(-0.896314\pi\) |
0.750843 | + | 0.660480i | \(0.229647\pi\) | |||||||
\(168\) | −0.892174 | + | 8.17770i | −0.0688328 | + | 0.630923i | ||||
\(169\) | 4.71504 | + | 8.16669i | 0.362695 | + | 0.628207i | ||||
\(170\) | 0.639110 | − | 1.10697i | 0.0490175 | − | 0.0849007i | ||||
\(171\) | 0.454521 | − | 3.07598i | 0.0347581 | − | 0.235226i | ||||
\(172\) | −1.21359 | − | 2.10200i | −0.0925353 | − | 0.160276i | ||||
\(173\) | 11.2759 | 0.857294 | 0.428647 | − | 0.903472i | \(-0.358990\pi\) | ||||
0.428647 | + | 0.903472i | \(0.358990\pi\) | |||||||
\(174\) | −21.2658 | + | 18.3544i | −1.61215 | + | 1.39144i | ||||
\(175\) | 1.93572 | − | 1.80360i | 0.146327 | − | 0.136340i | ||||
\(176\) | 11.5017 | − | 19.9215i | 0.866972 | − | 1.50164i | ||||
\(177\) | 1.65534 | + | 8.67987i | 0.124423 | + | 0.652419i | ||||
\(178\) | −14.5819 | + | 25.2567i | −1.09296 | + | 1.89307i | ||||
\(179\) | 4.78541 | + | 8.28858i | 0.357679 | + | 0.619517i | 0.987573 | − | 0.157164i | \(-0.0502350\pi\) |
−0.629894 | + | 0.776681i | \(0.716902\pi\) | |||||||
\(180\) | −2.24720 | − | 1.78146i | −0.167496 | − | 0.132782i | ||||
\(181\) | 0.422168 | 0.0313795 | 0.0156898 | − | 0.999877i | \(-0.495006\pi\) | ||||
0.0156898 | + | 0.999877i | \(0.495006\pi\) | |||||||
\(182\) | 6.28805 | − | 5.85888i | 0.466101 | − | 0.434289i | ||||
\(183\) | −1.32306 | − | 6.93753i | −0.0978035 | − | 0.512837i | ||||
\(184\) | 4.28246 | + | 7.41743i | 0.315707 | + | 0.546820i | ||||
\(185\) | −5.64309 | −0.414888 | ||||||||
\(186\) | 0.658126 | + | 3.45091i | 0.0482562 | + | 0.253033i | ||||
\(187\) | −3.42178 | −0.250225 | ||||||||
\(188\) | −1.83515 | −0.133842 | ||||||||
\(189\) | −3.64345 | − | 13.2561i | −0.265022 | − | 0.964242i | ||||
\(190\) | 1.78195 | 0.129276 | ||||||||
\(191\) | 8.95130 | 0.647693 | 0.323847 | − | 0.946110i | \(-0.395024\pi\) | ||||
0.323847 | + | 0.946110i | \(0.395024\pi\) | |||||||
\(192\) | −0.452630 | − | 2.37338i | −0.0326657 | − | 0.171284i | ||||
\(193\) | −22.7000 | −1.63398 | −0.816990 | − | 0.576651i | \(-0.804359\pi\) | ||||
−0.816990 | + | 0.576651i | \(0.804359\pi\) | |||||||
\(194\) | −9.97729 | − | 17.2812i | −0.716327 | − | 1.24072i | ||||
\(195\) | −0.613066 | − | 3.21464i | −0.0439026 | − | 0.230205i | ||||
\(196\) | 5.54420 | + | 3.74624i | 0.396014 | + | 0.267588i | ||||
\(197\) | 3.56585 | 0.254056 | 0.127028 | − | 0.991899i | \(-0.459456\pi\) | ||||
0.127028 | + | 0.991899i | \(0.459456\pi\) | |||||||
\(198\) | −3.47006 | + | 23.4837i | −0.246606 | + | 1.66891i | ||||
\(199\) | 8.23861 | + | 14.2697i | 0.584020 | + | 1.01155i | 0.994997 | + | 0.0999063i | \(0.0318543\pi\) |
−0.410977 | + | 0.911646i | \(0.634812\pi\) | |||||||
\(200\) | −0.897555 | + | 1.55461i | −0.0634667 | + | 0.109928i | ||||
\(201\) | 2.41986 | + | 12.6886i | 0.170684 | + | 0.894987i | ||||
\(202\) | 16.2727 | − | 28.1852i | 1.14495 | − | 1.98311i | ||||
\(203\) | −5.60441 | − | 24.3209i | −0.393352 | − | 1.70699i | ||||
\(204\) | 0.931837 | − | 0.804263i | 0.0652417 | − | 0.0563097i | ||||
\(205\) | −7.45897 | −0.520957 | ||||||||
\(206\) | 7.15232 | + | 12.3882i | 0.498326 | + | 0.863125i | ||||
\(207\) | −11.2167 | − | 8.89202i | −0.779617 | − | 0.618038i | ||||
\(208\) | −4.72172 | + | 8.17826i | −0.327392 | + | 0.567060i | ||||
\(209\) | −2.38513 | − | 4.13117i | −0.164983 | − | 0.285759i | ||||
\(210\) | 7.21013 | − | 3.17610i | 0.497547 | − | 0.219172i | ||||
\(211\) | 13.1358 | − | 22.7518i | 0.904304 | − | 1.56630i | 0.0824548 | − | 0.996595i | \(-0.473724\pi\) |
0.821849 | − | 0.569705i | \(-0.192943\pi\) | |||||||
\(212\) | −3.77070 | − | 6.53105i | −0.258973 | − | 0.448554i | ||||
\(213\) | 2.04631 | + | 10.7299i | 0.140211 | + | 0.735200i | ||||
\(214\) | 8.53208 | − | 14.7780i | 0.583241 | − | 1.01020i | ||||
\(215\) | 1.26959 | − | 2.19900i | 0.0865855 | − | 0.149971i | ||||
\(216\) | 4.99688 | + | 7.87632i | 0.339995 | + | 0.535916i | ||||
\(217\) | −2.98454 | − | 0.913806i | −0.202604 | − | 0.0620332i | ||||
\(218\) | 4.61379 | + | 7.99132i | 0.312485 | + | 0.541240i | ||||
\(219\) | 8.74921 | − | 7.55138i | 0.591217 | − | 0.510275i | ||||
\(220\) | −4.39945 | −0.296611 | ||||||||
\(221\) | 1.40472 | 0.0944918 | ||||||||
\(222\) | −15.8694 | − | 5.52715i | −1.06508 | − | 0.370958i | ||||
\(223\) | 1.65477 | + | 2.86615i | 0.110812 | + | 0.191932i | 0.916098 | − | 0.400955i | \(-0.131322\pi\) |
−0.805286 | + | 0.592886i | \(0.797988\pi\) | |||||||
\(224\) | −12.6562 | − | 3.87506i | −0.845627 | − | 0.258914i | ||||
\(225\) | 0.438533 | − | 2.96778i | 0.0292355 | − | 0.197852i | ||||
\(226\) | 12.9734 | − | 22.4705i | 0.862976 | − | 1.49472i | ||||
\(227\) | −8.60251 | + | 14.9000i | −0.570968 | + | 0.988946i | 0.425498 | + | 0.904959i | \(0.360099\pi\) |
−0.996467 | + | 0.0839872i | \(0.973235\pi\) | |||||||
\(228\) | 1.62053 | + | 0.564416i | 0.107322 | + | 0.0373794i | ||||
\(229\) | 2.03962 | + | 3.53273i | 0.134782 | + | 0.233450i | 0.925514 | − | 0.378713i | \(-0.123633\pi\) |
−0.790732 | + | 0.612162i | \(0.790300\pi\) | |||||||
\(230\) | 4.10153 | − | 7.10406i | 0.270447 | − | 0.468428i | ||||
\(231\) | −17.0140 | − | 12.4644i | −1.11944 | − | 0.820094i | ||||
\(232\) | 8.46694 | + | 14.6652i | 0.555882 | + | 0.962816i | ||||
\(233\) | 9.57801 | − | 16.5896i | 0.627476 | − | 1.08682i | −0.360580 | − | 0.932728i | \(-0.617421\pi\) |
0.988056 | − | 0.154092i | \(-0.0492453\pi\) | |||||||
\(234\) | 1.42454 | − | 9.64060i | 0.0931252 | − | 0.630226i | ||||
\(235\) | −0.959920 | − | 1.66263i | −0.0626183 | − | 0.108458i | ||||
\(236\) | −4.87661 | −0.317440 | ||||||||
\(237\) | 1.69122 | + | 8.86797i | 0.109856 | + | 0.576036i | ||||
\(238\) | 0.759398 | + | 3.29549i | 0.0492245 | + | 0.213615i | ||||
\(239\) | −0.0833779 | + | 0.144415i | −0.00539327 | + | 0.00934141i | −0.868709 | − | 0.495322i | \(-0.835050\pi\) |
0.863316 | + | 0.504663i | \(0.168383\pi\) | |||||||
\(240\) | −6.55349 | + | 5.65627i | −0.423026 | + | 0.365111i | ||||
\(241\) | 11.3477 | − | 19.6548i | 0.730969 | − | 1.26608i | −0.225500 | − | 0.974243i | \(-0.572402\pi\) |
0.956469 | − | 0.291832i | \(-0.0942650\pi\) | |||||||
\(242\) | 8.75340 | + | 15.1613i | 0.562690 | + | 0.974608i | ||||
\(243\) | −12.6091 | − | 9.16568i | −0.808877 | − | 0.587978i | ||||
\(244\) | 3.89771 | 0.249525 | ||||||||
\(245\) | −0.494028 | + | 6.98255i | −0.0315623 | + | 0.446098i | ||||
\(246\) | −20.9759 | − | 7.30572i | −1.33738 | − | 0.465796i | ||||
\(247\) | 0.979155 | + | 1.69595i | 0.0623021 | + | 0.107910i | ||||
\(248\) | 2.11777 | 0.134478 | ||||||||
\(249\) | −22.1816 | + | 19.1448i | −1.40570 | + | 1.21325i | ||||
\(250\) | 1.71927 | 0.108736 | ||||||||
\(251\) | 13.3004 | 0.839511 | 0.419756 | − | 0.907637i | \(-0.362116\pi\) | ||||
0.419756 | + | 0.907637i | \(0.362116\pi\) | |||||||
\(252\) | 7.56300 | − | 0.604653i | 0.476424 | − | 0.0380895i | ||||
\(253\) | −21.9595 | −1.38058 | ||||||||
\(254\) | 36.3863 | 2.28308 | ||||||||
\(255\) | 1.21607 | + | 0.423547i | 0.0761535 | + | 0.0265235i | ||||
\(256\) | 18.5357 | 1.15848 | ||||||||
\(257\) | −6.23155 | − | 10.7934i | −0.388713 | − | 0.673271i | 0.603563 | − | 0.797315i | \(-0.293747\pi\) |
−0.992277 | + | 0.124044i | \(0.960414\pi\) | |||||||
\(258\) | 5.72414 | − | 4.94047i | 0.356369 | − | 0.307580i | ||||
\(259\) | 10.9234 | − | 10.1779i | 0.678750 | − | 0.632424i | ||||
\(260\) | 1.80608 | 0.112008 | ||||||||
\(261\) | −22.1769 | − | 17.5806i | −1.37271 | − | 1.08821i | ||||
\(262\) | −12.2248 | − | 21.1739i | −0.755248 | − | 1.30813i | ||||
\(263\) | −2.69633 | + | 4.67018i | −0.166263 | + | 0.287976i | −0.937103 | − | 0.349053i | \(-0.886503\pi\) |
0.770840 | + | 0.637029i | \(0.219837\pi\) | |||||||
\(264\) | 13.5139 | + | 4.70675i | 0.831722 | + | 0.289681i | ||||
\(265\) | 3.94471 | − | 6.83244i | 0.242322 | − | 0.419713i | ||||
\(266\) | −3.44936 | + | 3.21394i | −0.211494 | + | 0.197059i | ||||
\(267\) | −27.7460 | − | 9.66366i | −1.69803 | − | 0.591406i | ||||
\(268\) | −7.12884 | −0.435463 | ||||||||
\(269\) | 11.5676 | + | 20.0357i | 0.705289 | + | 1.22160i | 0.966587 | + | 0.256339i | \(0.0825162\pi\) |
−0.261298 | + | 0.965258i | \(0.584150\pi\) | |||||||
\(270\) | 4.14003 | − | 7.91638i | 0.251954 | − | 0.481776i | ||||
\(271\) | −3.01396 | + | 5.22033i | −0.183085 | + | 0.317113i | −0.942930 | − | 0.332992i | \(-0.891942\pi\) |
0.759845 | + | 0.650105i | \(0.225275\pi\) | |||||||
\(272\) | −1.85794 | − | 3.21805i | −0.112654 | − | 0.195123i | ||||
\(273\) | 6.98466 | + | 5.11692i | 0.422731 | + | 0.309690i | ||||
\(274\) | −0.480178 | + | 0.831693i | −0.0290086 | + | 0.0502444i | ||||
\(275\) | −2.30123 | − | 3.98585i | −0.138770 | − | 0.240356i | ||||
\(276\) | 5.98013 | − | 5.16141i | 0.359962 | − | 0.310681i | ||||
\(277\) | −4.98378 | + | 8.63216i | −0.299446 | + | 0.518656i | −0.976009 | − | 0.217728i | \(-0.930135\pi\) |
0.676563 | + | 0.736385i | \(0.263469\pi\) | |||||||
\(278\) | 11.8841 | − | 20.5838i | 0.712760 | − | 1.23454i | ||||
\(279\) | −3.29081 | + | 1.30256i | −0.197016 | + | 0.0779823i | ||||
\(280\) | −1.06649 | − | 4.62812i | −0.0637347 | − | 0.276583i | ||||
\(281\) | −11.8821 | − | 20.5804i | −0.708828 | − | 1.22773i | −0.965292 | − | 0.261173i | \(-0.915891\pi\) |
0.256464 | − | 0.966554i | \(-0.417443\pi\) | |||||||
\(282\) | −1.07099 | − | 5.61581i | −0.0637768 | − | 0.334416i | ||||
\(283\) | 18.0998 | 1.07592 | 0.537961 | − | 0.842970i | \(-0.319195\pi\) | ||||
0.537961 | + | 0.842970i | \(0.319195\pi\) | |||||||
\(284\) | −6.02837 | −0.357718 | ||||||||
\(285\) | 0.336303 | + | 1.76342i | 0.0199209 | + | 0.104456i | ||||
\(286\) | −7.47539 | − | 12.9478i | −0.442029 | − | 0.765617i | ||||
\(287\) | 14.4385 | − | 13.4530i | 0.852277 | − | 0.794107i | ||||
\(288\) | −13.9549 | + | 5.52361i | −0.822303 | + | 0.325482i | ||||
\(289\) | 8.22363 | − | 14.2437i | 0.483743 | − | 0.837867i | ||||
\(290\) | 8.10923 | − | 14.0456i | 0.476190 | − | 0.824786i | ||||
\(291\) | 15.2184 | − | 13.1349i | 0.892120 | − | 0.769983i | ||||
\(292\) | 3.18915 | + | 5.52376i | 0.186631 | + | 0.323254i | ||||
\(293\) | −10.7702 | + | 18.6545i | −0.629200 | + | 1.08981i | 0.358513 | + | 0.933525i | \(0.383284\pi\) |
−0.987713 | + | 0.156281i | \(0.950049\pi\) | |||||||
\(294\) | −8.22838 | + | 19.1523i | −0.479889 | + | 1.11698i | ||||
\(295\) | −2.55082 | − | 4.41816i | −0.148515 | − | 0.257235i | ||||
\(296\) | −5.06498 | + | 8.77280i | −0.294396 | + | 0.509909i | ||||
\(297\) | −23.8943 | + | 0.998037i | −1.38649 | + | 0.0579120i | ||||
\(298\) | 5.07379 | + | 8.78806i | 0.293917 | + | 0.509078i | ||||
\(299\) | 9.01491 | 0.521345 | ||||||||
\(300\) | 1.56353 | + | 0.544562i | 0.0902704 | + | 0.0314403i | ||||
\(301\) | 1.50855 | + | 6.54649i | 0.0869512 | + | 0.377333i | ||||
\(302\) | −17.5116 | + | 30.3309i | −1.00768 | + | 1.74535i | ||||
\(303\) | 30.9632 | + | 10.7842i | 1.77879 | + | 0.619535i | ||||
\(304\) | 2.59014 | − | 4.48625i | 0.148555 | − | 0.257304i | ||||
\(305\) | 2.03879 | + | 3.53128i | 0.116741 | + | 0.202201i | ||||
\(306\) | 3.00497 | + | 2.38218i | 0.171783 | + | 0.136180i | ||||
\(307\) | 4.40118 | 0.251189 | 0.125594 | − | 0.992082i | \(-0.459916\pi\) | ||||
0.125594 | + | 0.992082i | \(0.459916\pi\) | |||||||
\(308\) | 8.51610 | − | 7.93486i | 0.485250 | − | 0.452130i | ||||
\(309\) | −10.9095 | + | 9.41591i | −0.620619 | + | 0.535652i | ||||
\(310\) | −1.01415 | − | 1.75655i | −0.0575997 | − | 0.0997656i | ||||
\(311\) | −14.1325 | −0.801380 | −0.400690 | − | 0.916214i | \(-0.631230\pi\) | ||||
−0.400690 | + | 0.916214i | \(0.631230\pi\) | |||||||
\(312\) | −5.54777 | − | 1.93224i | −0.314081 | − | 0.109391i | ||||
\(313\) | −8.26589 | −0.467216 | −0.233608 | − | 0.972331i | \(-0.575053\pi\) | ||||
−0.233608 | + | 0.972331i | \(0.575053\pi\) | |||||||
\(314\) | −33.4116 | −1.88553 | ||||||||
\(315\) | 4.50381 | + | 6.53572i | 0.253761 | + | 0.368246i | ||||
\(316\) | −4.98228 | −0.280275 | ||||||||
\(317\) | 0.134195 | 0.00753715 | 0.00376858 | − | 0.999993i | \(-0.498800\pi\) | ||||
0.00376858 | + | 0.999993i | \(0.498800\pi\) | |||||||
\(318\) | 17.7853 | − | 15.3504i | 0.997349 | − | 0.860805i | ||||
\(319\) | −43.4166 | −2.43087 | ||||||||
\(320\) | 0.697485 | + | 1.20808i | 0.0389906 | + | 0.0675337i | ||||
\(321\) | 16.2345 | + | 5.65433i | 0.906122 | + | 0.315594i | ||||
\(322\) | 4.87349 | + | 21.1490i | 0.271589 | + | 1.17859i | ||||
\(323\) | −0.770572 | −0.0428758 | ||||||||
\(324\) | 6.27244 | − | 5.88796i | 0.348469 | − | 0.327109i | ||||
\(325\) | 0.944711 | + | 1.63629i | 0.0524032 | + | 0.0907649i | ||||
\(326\) | −16.6878 | + | 28.9040i | −0.924249 | + | 1.60085i | ||||
\(327\) | −7.03745 | + | 6.07398i | −0.389172 | + | 0.335892i | ||||
\(328\) | −6.69483 | + | 11.5958i | −0.369660 | + | 0.640271i | ||||
\(329\) | 4.85686 | + | 1.48707i | 0.267768 | + | 0.0819850i | ||||
\(330\) | −2.56751 | − | 13.4629i | −0.141337 | − | 0.741107i | ||||
\(331\) | 0.441708 | 0.0242785 | 0.0121392 | − | 0.999926i | \(-0.496136\pi\) | ||||
0.0121392 | + | 0.999926i | \(0.496136\pi\) | |||||||
\(332\) | −8.08536 | − | 14.0042i | −0.443742 | − | 0.768583i | ||||
\(333\) | 2.47468 | − | 16.7474i | 0.135612 | − | 0.917753i | ||||
\(334\) | 4.36739 | − | 7.56454i | 0.238973 | − | 0.413913i | ||||
\(335\) | −3.72891 | − | 6.45866i | −0.203732 | − | 0.352874i | ||||
\(336\) | 2.48405 | − | 22.7689i | 0.135516 | − | 1.24214i | ||||
\(337\) | −6.10063 | + | 10.5666i | −0.332323 | + | 0.575600i | −0.982967 | − | 0.183783i | \(-0.941166\pi\) |
0.650644 | + | 0.759383i | \(0.274499\pi\) | |||||||
\(338\) | −8.10643 | − | 14.0407i | −0.440931 | − | 0.763716i | ||||
\(339\) | 24.6852 | + | 8.59763i | 1.34072 | + | 0.466959i | ||||
\(340\) | −0.355335 | + | 0.615459i | −0.0192708 | + | 0.0333780i | ||||
\(341\) | −2.71486 | + | 4.70228i | −0.147018 | + | 0.254643i | ||||
\(342\) | −0.781444 | + | 5.28844i | −0.0422557 | + | 0.285966i | ||||
\(343\) | −11.6374 | − | 14.4073i | −0.628363 | − | 0.777920i | ||||
\(344\) | −2.27906 | − | 3.94744i | −0.122879 | − | 0.212832i | ||||
\(345\) | 7.80424 | + | 2.71814i | 0.420166 | + | 0.146340i | ||||
\(346\) | −19.3864 | −1.04222 | ||||||||
\(347\) | 4.82105 | 0.258808 | 0.129404 | − | 0.991592i | \(-0.458694\pi\) | ||||
0.129404 | + | 0.991592i | \(0.458694\pi\) | |||||||
\(348\) | 11.8235 | − | 10.2047i | 0.633804 | − | 0.547032i | ||||
\(349\) | −6.69861 | − | 11.6023i | −0.358569 | − | 0.621059i | 0.629153 | − | 0.777281i | \(-0.283402\pi\) |
−0.987722 | + | 0.156222i | \(0.950068\pi\) | |||||||
\(350\) | −3.32803 | + | 3.10088i | −0.177890 | + | 0.165749i | ||||
\(351\) | 9.80918 | − | 0.409718i | 0.523575 | − | 0.0218691i | ||||
\(352\) | −11.5126 | + | 19.9404i | −0.613622 | + | 1.06283i | ||||
\(353\) | 16.2099 | − | 28.0764i | 0.862767 | − | 1.49436i | −0.00648100 | − | 0.999979i | \(-0.502063\pi\) |
0.869248 | − | 0.494377i | \(-0.164604\pi\) | |||||||
\(354\) | −2.84598 | − | 14.9230i | −0.151262 | − | 0.793151i | ||||
\(355\) | −3.15328 | − | 5.46164i | −0.167359 | − | 0.289874i | ||||
\(356\) | 8.10735 | − | 14.0423i | 0.429689 | − | 0.744243i | ||||
\(357\) | −3.11789 | + | 1.37345i | −0.165016 | + | 0.0726905i | ||||
\(358\) | −8.22742 | − | 14.2503i | −0.434832 | − | 0.753152i | ||||
\(359\) | −17.6749 | + | 30.6138i | −0.932846 | + | 1.61574i | −0.154416 | + | 0.988006i | \(0.549350\pi\) |
−0.778430 | + | 0.627731i | \(0.783984\pi\) | |||||||
\(360\) | −4.22013 | − | 3.34549i | −0.222420 | − | 0.176323i | ||||
\(361\) | 8.96288 | + | 15.5242i | 0.471730 | + | 0.817061i | ||||
\(362\) | −0.725821 | −0.0381483 | ||||||||
\(363\) | −13.3516 | + | 11.5237i | −0.700779 | + | 0.604838i | ||||
\(364\) | −3.49606 | + | 3.25745i | −0.183243 | + | 0.170737i | ||||
\(365\) | −3.33632 | + | 5.77867i | −0.174631 | + | 0.302469i | ||||
\(366\) | 2.27470 | + | 11.9275i | 0.118900 | + | 0.623460i | ||||
\(367\) | 9.33497 | − | 16.1686i | 0.487282 | − | 0.843996i | −0.512611 | − | 0.858621i | \(-0.671322\pi\) |
0.999893 | + | 0.0146242i | \(0.00465521\pi\) | |||||||
\(368\) | −11.9235 | − | 20.6521i | −0.621554 | − | 1.07656i | ||||
\(369\) | 3.27100 | − | 22.1365i | 0.170282 | − | 1.15238i | ||||
\(370\) | 9.70199 | 0.504382 | ||||||||
\(371\) | 4.68715 | + | 20.3404i | 0.243345 | + | 1.05602i | ||||
\(372\) | −0.365909 | − | 1.91866i | −0.0189715 | − | 0.0994778i | ||||
\(373\) | 5.80962 | + | 10.0626i | 0.300811 | + | 0.521020i | 0.976320 | − | 0.216332i | \(-0.0694094\pi\) |
−0.675509 | + | 0.737352i | \(0.736076\pi\) | |||||||
\(374\) | 5.88296 | 0.304201 | ||||||||
\(375\) | 0.324473 | + | 1.70139i | 0.0167557 | + | 0.0878592i | ||||
\(376\) | −3.44632 | −0.177731 | ||||||||
\(377\) | 17.8236 | 0.917961 | ||||||||
\(378\) | 6.26408 | + | 22.7909i | 0.322189 | + | 1.17224i | ||||
\(379\) | 30.8650 | 1.58543 | 0.792714 | − | 0.609593i | \(-0.208667\pi\) | ||||
0.792714 | + | 0.609593i | \(0.208667\pi\) | |||||||
\(380\) | −0.990739 | −0.0508239 | ||||||||
\(381\) | 6.86707 | + | 36.0078i | 0.351811 | + | 1.84474i | ||||
\(382\) | −15.3897 | −0.787405 | ||||||||
\(383\) | 13.7713 | + | 23.8527i | 0.703683 | + | 1.21881i | 0.967165 | + | 0.254150i | \(0.0817957\pi\) |
−0.263482 | + | 0.964664i | \(0.584871\pi\) | |||||||
\(384\) | 4.02473 | + | 21.1038i | 0.205386 | + | 1.07695i | ||||
\(385\) | 11.6434 | + | 3.56498i | 0.593405 | + | 0.181688i | ||||
\(386\) | 39.0274 | 1.98644 | ||||||||
\(387\) | 5.96938 | + | 4.73220i | 0.303441 | + | 0.240551i | ||||
\(388\) | 5.54722 | + | 9.60807i | 0.281618 | + | 0.487776i | ||||
\(389\) | −9.56351 | + | 16.5645i | −0.484889 | + | 0.839853i | −0.999849 | − | 0.0173614i | \(-0.994473\pi\) |
0.514960 | + | 0.857214i | \(0.327807\pi\) | |||||||
\(390\) | 1.05403 | + | 5.52683i | 0.0533727 | + | 0.279862i | ||||
\(391\) | −1.77363 | + | 3.07202i | −0.0896964 | + | 0.155359i | ||||
\(392\) | 10.4117 | + | 7.03524i | 0.525871 | + | 0.355333i | ||||
\(393\) | 18.6465 | − | 16.0937i | 0.940593 | − | 0.811819i | ||||
\(394\) | −6.13065 | −0.308858 | ||||||||
\(395\) | −2.60610 | − | 4.51390i | −0.131127 | − | 0.227119i | ||||
\(396\) | 1.92930 | − | 13.0566i | 0.0969510 | − | 0.656117i | ||||
\(397\) | −5.02935 | + | 8.71109i | −0.252416 | + | 0.437197i | −0.964190 | − | 0.265211i | \(-0.914558\pi\) |
0.711775 | + | 0.702408i | \(0.247892\pi\) | |||||||
\(398\) | −14.1644 | − | 24.5335i | −0.709997 | − | 1.22975i | ||||
\(399\) | −3.83150 | − | 2.80693i | −0.191815 | − | 0.140522i | ||||
\(400\) | 2.49903 | − | 4.32844i | 0.124951 | − | 0.216422i | ||||
\(401\) | 7.85979 | + | 13.6135i | 0.392499 | + | 0.679828i | 0.992778 | − | 0.119962i | \(-0.0382773\pi\) |
−0.600279 | + | 0.799790i | \(0.704944\pi\) | |||||||
\(402\) | −4.16039 | − | 21.8152i | −0.207501 | − | 1.08804i | ||||
\(403\) | 1.11452 | − | 1.93040i | 0.0555180 | − | 0.0961600i | ||||
\(404\) | −9.04741 | + | 15.6706i | −0.450125 | + | 0.779640i | ||||
\(405\) | 8.61538 | + | 2.60293i | 0.428102 | + | 0.129341i | ||||
\(406\) | 9.63549 | + | 41.8142i | 0.478201 | + | 2.07520i | ||||
\(407\) | −12.9861 | − | 22.4925i | −0.643695 | − | 1.11491i | ||||
\(408\) | 1.74994 | − | 1.51036i | 0.0866350 | − | 0.0747741i | ||||
\(409\) | −12.4895 | −0.617566 | −0.308783 | − | 0.951132i | \(-0.599922\pi\) | ||||
−0.308783 | + | 0.951132i | \(0.599922\pi\) | |||||||
\(410\) | 12.8240 | 0.633331 | ||||||||
\(411\) | −0.913664 | − | 0.318220i | −0.0450677 | − | 0.0156967i | ||||
\(412\) | −3.97658 | − | 6.88764i | −0.195912 | − | 0.339330i | ||||
\(413\) | 12.9063 | + | 3.95164i | 0.635077 | + | 0.194448i | ||||
\(414\) | 19.2846 | + | 15.2878i | 0.947786 | + | 0.751354i | ||||
\(415\) | 8.45847 | − | 14.6505i | 0.415210 | − | 0.719165i | ||||
\(416\) | 4.72619 | − | 8.18600i | 0.231720 | − | 0.401352i | ||||
\(417\) | 22.6126 | + | 7.87574i | 1.10734 | + | 0.385677i | ||||
\(418\) | 4.10069 | + | 7.10260i | 0.200571 | + | 0.347400i | ||||
\(419\) | 1.57397 | − | 2.72619i | 0.0768934 | − | 0.133183i | −0.825015 | − | 0.565111i | \(-0.808833\pi\) |
0.901908 | + | 0.431928i | \(0.142167\pi\) | |||||||
\(420\) | −4.00873 | + | 1.76587i | −0.195606 | + | 0.0861654i | ||||
\(421\) | 2.08259 | + | 3.60716i | 0.101499 | + | 0.175802i | 0.912303 | − | 0.409517i | \(-0.134303\pi\) |
−0.810803 | + | 0.585319i | \(0.800969\pi\) | |||||||
\(422\) | −22.5839 | + | 39.1165i | −1.09937 | + | 1.90416i | ||||
\(423\) | 5.35527 | − | 2.11971i | 0.260382 | − | 0.103064i | ||||
\(424\) | −7.08118 | − | 12.2650i | −0.343893 | − | 0.595640i | ||||
\(425\) | −0.743466 | −0.0360634 | ||||||||
\(426\) | −3.51815 | − | 18.4476i | −0.170455 | − | 0.893788i | ||||
\(427\) | −10.3156 | − | 3.15841i | −0.499205 | − | 0.152846i | ||||
\(428\) | −4.74371 | + | 8.21635i | −0.229296 | + | 0.397152i | ||||
\(429\) | 11.4023 | − | 9.84123i | 0.550507 | − | 0.475139i | ||||
\(430\) | −2.18277 | + | 3.78067i | −0.105263 | + | 0.182320i | ||||
\(431\) | 5.66305 | + | 9.80869i | 0.272780 | + | 0.472468i | 0.969573 | − | 0.244804i | \(-0.0787237\pi\) |
−0.696793 | + | 0.717272i | \(0.745390\pi\) | |||||||
\(432\) | −13.9126 | − | 21.9297i | −0.669372 | − | 1.05510i | ||||
\(433\) | 40.8240 | 1.96188 | 0.980938 | − | 0.194319i | \(-0.0622497\pi\) | ||||
0.980938 | + | 0.194319i | \(0.0622497\pi\) | |||||||
\(434\) | 5.13124 | + | 1.57108i | 0.246307 | + | 0.0754142i | ||||
\(435\) | 15.4299 | + | 5.37410i | 0.739809 | + | 0.257668i | ||||
\(436\) | −2.56520 | − | 4.44306i | −0.122851 | − | 0.212784i | ||||
\(437\) | −4.94520 | −0.236561 | ||||||||
\(438\) | −15.0422 | + | 12.9829i | −0.718746 | + | 0.620345i | ||||
\(439\) | −16.9278 | −0.807918 | −0.403959 | − | 0.914777i | \(-0.632366\pi\) | ||||
−0.403959 | + | 0.914777i | \(0.632366\pi\) | |||||||
\(440\) | −8.26193 | −0.393872 | ||||||||
\(441\) | −20.5060 | − | 4.52824i | −0.976475 | − | 0.215630i | ||||
\(442\) | −2.41510 | −0.114874 | ||||||||
\(443\) | 9.33503 | 0.443521 | 0.221760 | − | 0.975101i | \(-0.428820\pi\) | ||||
0.221760 | + | 0.975101i | \(0.428820\pi\) | |||||||
\(444\) | 8.82313 | + | 3.07301i | 0.418727 | + | 0.145839i | ||||
\(445\) | 16.9630 | 0.804121 | ||||||||
\(446\) | −2.84500 | − | 4.92768i | −0.134715 | − | 0.233333i | ||||
\(447\) | −7.73909 | + | 6.67955i | −0.366046 | + | 0.315932i | ||||
\(448\) | −3.52903 | − | 1.08052i | −0.166731 | − | 0.0510497i | ||||
\(449\) | −35.6523 | −1.68254 | −0.841268 | − | 0.540618i | \(-0.818191\pi\) | ||||
−0.841268 | + | 0.540618i | \(0.818191\pi\) | |||||||
\(450\) | −0.753956 | + | 5.10241i | −0.0355418 | + | 0.240530i | ||||
\(451\) | −17.1648 | − | 29.7304i | −0.808260 | − | 1.39995i | ||||
\(452\) | −7.21301 | + | 12.4933i | −0.339271 | + | 0.587635i | ||||
\(453\) | −33.3203 | − | 11.6051i | −1.56553 | − | 0.545257i | ||||
\(454\) | 14.7900 | − | 25.6171i | 0.694131 | − | 1.20227i | ||||
\(455\) | −4.77991 | − | 1.46351i | −0.224086 | − | 0.0686105i | ||||
\(456\) | 3.04328 | + | 1.05994i | 0.142515 | + | 0.0496364i | ||||
\(457\) | −12.8930 | −0.603108 | −0.301554 | − | 0.953449i | \(-0.597505\pi\) | ||||
−0.301554 | + | 0.953449i | \(0.597505\pi\) | |||||||
\(458\) | −3.50667 | − | 6.07372i | −0.163856 | − | 0.283806i | ||||
\(459\) | −1.79028 | + | 3.42329i | −0.0835631 | + | 0.159786i | ||||
\(460\) | −2.28039 | + | 3.94975i | −0.106324 | + | 0.184158i | ||||
\(461\) | −18.5507 | − | 32.1308i | −0.863992 | − | 1.49648i | −0.868044 | − | 0.496487i | \(-0.834623\pi\) |
0.00405225 | − | 0.999992i | \(-0.498710\pi\) | |||||||
\(462\) | 29.2517 | + | 21.4296i | 1.36091 | + | 0.996994i | ||||
\(463\) | −11.4001 | + | 19.7456i | −0.529810 | + | 0.917658i | 0.469585 | + | 0.882887i | \(0.344403\pi\) |
−0.999395 | + | 0.0347706i | \(0.988930\pi\) | |||||||
\(464\) | −23.5742 | − | 40.8317i | −1.09440 | − | 1.89556i | ||||
\(465\) | 1.54689 | − | 1.33511i | 0.0717352 | − | 0.0619142i | ||||
\(466\) | −16.4672 | + | 28.5220i | −0.762827 | + | 1.32126i | ||||
\(467\) | 5.78367 | − | 10.0176i | 0.267636 | − | 0.463559i | −0.700615 | − | 0.713540i | \(-0.747091\pi\) |
0.968251 | + | 0.249980i | \(0.0804242\pi\) | |||||||
\(468\) | −0.792024 | + | 5.36003i | −0.0366113 | + | 0.247768i | ||||
\(469\) | 18.8670 | + | 5.77669i | 0.871196 | + | 0.266743i | ||||
\(470\) | 1.65036 | + | 2.85851i | 0.0761255 | + | 0.131853i | ||||
\(471\) | −6.30568 | − | 33.0641i | −0.290550 | − | 1.52351i | ||||
\(472\) | −9.15801 | −0.421532 | ||||||||
\(473\) | 11.6865 | 0.537347 | ||||||||
\(474\) | −2.90766 | − | 15.2464i | −0.133553 | − | 0.700292i | ||||
\(475\) | −0.518230 | − | 0.897600i | −0.0237780 | − | 0.0411847i | ||||
\(476\) | −0.422214 | − | 1.83224i | −0.0193521 | − | 0.0839806i | ||||
\(477\) | 18.5473 | + | 14.7033i | 0.849220 | + | 0.673216i | ||||
\(478\) | 0.143349 | − | 0.248288i | 0.00655664 | − | 0.0113564i | ||||
\(479\) | −2.74988 | + | 4.76294i | −0.125645 | + | 0.217624i | −0.921985 | − | 0.387225i | \(-0.873434\pi\) |
0.796340 | + | 0.604850i | \(0.206767\pi\) | |||||||
\(480\) | 6.55969 | − | 5.66163i | 0.299408 | − | 0.258417i | ||||
\(481\) | 5.33109 | + | 9.23372i | 0.243077 | + | 0.421021i | ||||
\(482\) | −19.5097 | + | 33.7919i | −0.888644 | + | 1.53918i | ||||
\(483\) | −20.0093 | + | 8.81419i | −0.910453 | + | 0.401060i | ||||
\(484\) | −4.86676 | − | 8.42948i | −0.221216 | − | 0.383158i | ||||
\(485\) | −5.80321 | + | 10.0515i | −0.263510 | + | 0.456413i | ||||
\(486\) | 21.6785 | + | 15.7583i | 0.983357 | + | 0.714810i | ||||
\(487\) | 0.825893 | + | 1.43049i | 0.0374248 | + | 0.0648217i | 0.884131 | − | 0.467239i | \(-0.154751\pi\) |
−0.846706 | + | 0.532061i | \(0.821418\pi\) | |||||||
\(488\) | 7.31969 | 0.331347 | ||||||||
\(489\) | −31.7528 | − | 11.0592i | −1.43591 | − | 0.500114i | ||||
\(490\) | 0.849368 | − | 12.0049i | 0.0383705 | − | 0.542325i | ||||
\(491\) | 4.06248 | − | 7.03643i | 0.183337 | − | 0.317549i | −0.759678 | − | 0.650300i | \(-0.774643\pi\) |
0.943015 | + | 0.332750i | \(0.107977\pi\) | |||||||
\(492\) | 11.6623 | + | 4.06187i | 0.525778 | + | 0.183123i | ||||
\(493\) | −3.50669 | + | 6.07376i | −0.157933 | + | 0.273548i | ||||
\(494\) | −1.68343 | − | 2.91579i | −0.0757412 | − | 0.131188i | ||||
\(495\) | 12.8383 | − | 5.08162i | 0.577038 | − | 0.228402i | ||||
\(496\) | −5.89642 | −0.264757 | ||||||||
\(497\) | 15.9545 | + | 4.88494i | 0.715657 | + | 0.219120i | ||||
\(498\) | 38.1362 | − | 32.9151i | 1.70892 | − | 1.47496i | ||||
\(499\) | −5.83729 | − | 10.1105i | −0.261313 | − | 0.452607i | 0.705278 | − | 0.708931i | \(-0.250822\pi\) |
−0.966591 | + | 0.256323i | \(0.917489\pi\) | |||||||
\(500\) | −0.955889 | −0.0427486 | ||||||||
\(501\) | 8.31010 | + | 2.89433i | 0.371268 | + | 0.129309i | ||||
\(502\) | −22.8669 | −1.02060 | ||||||||
\(503\) | 5.08007 | 0.226509 | 0.113255 | − | 0.993566i | \(-0.463872\pi\) | ||||
0.113255 | + | 0.993566i | \(0.463872\pi\) | |||||||
\(504\) | 14.2029 | − | 1.13551i | 0.632648 | − | 0.0505795i | ||||
\(505\) | −18.9298 | −0.842367 | ||||||||
\(506\) | 37.7543 | 1.67838 | ||||||||
\(507\) | 12.3648 | − | 10.6720i | 0.549140 | − | 0.473959i | ||||
\(508\) | −20.2302 | −0.897571 | ||||||||
\(509\) | 10.3876 | + | 17.9919i | 0.460424 | + | 0.797478i | 0.998982 | − | 0.0451108i | \(-0.0143641\pi\) |
−0.538558 | + | 0.842588i | \(0.681031\pi\) | |||||||
\(510\) | −2.09076 | − | 0.728191i | −0.0925803 | − | 0.0322448i | ||||
\(511\) | −3.96425 | − | 17.2033i | −0.175368 | − | 0.761028i | ||||
\(512\) | −7.06009 | −0.312015 | ||||||||
\(513\) | −5.38091 | + | 0.224754i | −0.237573 | + | 0.00992315i | ||||
\(514\) | 10.7137 | + | 18.5567i | 0.472562 | + | 0.818501i | ||||
\(515\) | 4.16009 | − | 7.20549i | 0.183315 | − | 0.317512i | ||||
\(516\) | −3.18254 | + | 2.74683i | −0.140103 | + | 0.120922i | ||||
\(517\) | 4.41800 | − | 7.65220i | 0.194303 | − | 0.336543i | ||||
\(518\) | −18.7803 | + | 17.4985i | −0.825161 | + | 0.768842i | ||||
\(519\) | −3.65874 | − | 19.1847i | −0.160601 | − | 0.842117i | ||||
\(520\) | 3.39172 | 0.148737 | ||||||||
\(521\) | −7.15028 | − | 12.3846i | −0.313259 | − | 0.542581i | 0.665807 | − | 0.746124i | \(-0.268088\pi\) |
−0.979066 | + | 0.203543i | \(0.934754\pi\) | |||||||
\(522\) | 38.1280 | + | 30.2258i | 1.66882 | + | 1.32295i | ||||
\(523\) | −9.31897 | + | 16.1409i | −0.407490 | + | 0.705794i | −0.994608 | − | 0.103708i | \(-0.966929\pi\) |
0.587118 | + | 0.809502i | \(0.300263\pi\) | |||||||
\(524\) | 6.79679 | + | 11.7724i | 0.296919 | + | 0.514279i | ||||
\(525\) | −3.69672 | − | 2.70819i | −0.161338 | − | 0.118195i | ||||
\(526\) | 4.63572 | − | 8.02930i | 0.202127 | − | 0.350094i | ||||
\(527\) | 0.438549 | + | 0.759590i | 0.0191035 | + | 0.0330882i | ||||
\(528\) | −37.6262 | − | 13.1048i | −1.63747 | − | 0.570315i | ||||
\(529\) | 0.117595 | − | 0.203681i | 0.00511283 | − | 0.00885568i | ||||
\(530\) | −6.78202 | + | 11.7468i | −0.294592 | + | 0.510249i | ||||
\(531\) | 14.2307 | − | 5.63276i | 0.617560 | − | 0.244441i | ||||
\(532\) | 1.91779 | − | 1.78690i | 0.0831469 | − | 0.0774720i | ||||
\(533\) | 7.04658 | + | 12.2050i | 0.305221 | + | 0.528658i | ||||
\(534\) | 47.7028 | + | 16.6144i | 2.06430 | + | 0.718977i | ||||
\(535\) | −9.92524 | −0.429105 | ||||||||
\(536\) | −13.3876 | −0.578256 | ||||||||
\(537\) | 12.5493 | − | 10.8313i | 0.541544 | − | 0.467403i | ||||
\(538\) | −19.8878 | − | 34.4467i | −0.857425 | − | 1.48510i | ||||
\(539\) | −28.9683 | + | 14.0993i | −1.24775 | + | 0.607302i | ||||
\(540\) | −2.30180 | + | 4.40139i | −0.0990535 | + | 0.189406i | ||||
\(541\) | −14.3876 | + | 24.9200i | −0.618570 | + | 1.07139i | 0.371177 | + | 0.928562i | \(0.378954\pi\) |
−0.989747 | + | 0.142832i | \(0.954379\pi\) | |||||||
\(542\) | 5.18181 | − | 8.97516i | 0.222578 | − | 0.385516i | ||||
\(543\) | −0.136982 | − | 0.718272i | −0.00587846 | − | 0.0308240i | ||||
\(544\) | 1.85970 | + | 3.22110i | 0.0797340 | + | 0.138103i | ||||
\(545\) | 2.68358 | − | 4.64809i | 0.114952 | − | 0.199102i | ||||
\(546\) | −12.0085 | − | 8.79736i | −0.513917 | − | 0.376492i | ||||
\(547\) | 16.5643 | + | 28.6902i | 0.708239 | + | 1.22671i | 0.965510 | + | 0.260367i | \(0.0838434\pi\) |
−0.257271 | + | 0.966339i | \(0.582823\pi\) | |||||||
\(548\) | 0.266972 | − | 0.462409i | 0.0114045 | − | 0.0197531i | ||||
\(549\) | −11.3741 | + | 4.50208i | −0.485436 | + | 0.192144i | ||||
\(550\) | 3.95644 | + | 6.85276i | 0.168703 | + | 0.292203i | ||||
\(551\) | −9.77727 | −0.416526 | ||||||||
\(552\) | 11.2304 | − | 9.69287i | 0.477997 | − | 0.412556i | ||||
\(553\) | 13.1860 | + | 4.03727i | 0.560724 | + | 0.171682i | ||||
\(554\) | 8.56846 | − | 14.8410i | 0.364039 | − | 0.630534i | ||||
\(555\) | 1.83103 | + | 9.60108i | 0.0777228 | + | 0.407543i | ||||
\(556\) | −6.60737 | + | 11.4443i | −0.280215 | + | 0.485347i | ||||
\(557\) | −3.56430 | − | 6.17354i | −0.151024 | − | 0.261581i | 0.780580 | − | 0.625056i | \(-0.214924\pi\) |
−0.931604 | + | 0.363474i | \(0.881590\pi\) | |||||||
\(558\) | 5.65780 | − | 2.23946i | 0.239514 | − | 0.0948037i | ||||
\(559\) | −4.79760 | −0.202917 | ||||||||
\(560\) | 2.96938 | + | 12.8859i | 0.125479 | + | 0.544529i | ||||
\(561\) | 1.11027 | + | 5.82177i | 0.0468758 | + | 0.245795i | ||||
\(562\) | 20.4286 | + | 35.3833i | 0.861728 | + | 1.49256i | ||||
\(563\) | 29.0206 | 1.22307 | 0.611537 | − | 0.791216i | \(-0.290552\pi\) | ||||
0.611537 | + | 0.791216i | \(0.290552\pi\) | |||||||
\(564\) | 0.595457 | + | 3.12231i | 0.0250733 | + | 0.131473i | ||||
\(565\) | −15.0917 | −0.634914 | ||||||||
\(566\) | −31.1184 | −1.30801 | ||||||||
\(567\) | −21.3716 | + | 10.5002i | −0.897524 | + | 0.440966i | ||||
\(568\) | −11.3210 | −0.475017 | ||||||||
\(569\) | −21.2762 | −0.891943 | −0.445971 | − | 0.895047i | \(-0.647142\pi\) | ||||
−0.445971 | + | 0.895047i | \(0.647142\pi\) | |||||||
\(570\) | −0.578195 | − | 3.03179i | −0.0242179 | − | 0.126988i | ||||
\(571\) | −10.6504 | −0.445705 | −0.222853 | − | 0.974852i | \(-0.571537\pi\) | ||||
−0.222853 | + | 0.974852i | \(0.571537\pi\) | |||||||
\(572\) | 4.15621 | + | 7.19876i | 0.173780 | + | 0.300995i | ||||
\(573\) | −2.90445 | − | 15.2296i | −0.121335 | − | 0.636227i | ||||
\(574\) | −24.8236 | + | 23.1294i | −1.03612 | + | 0.965402i | ||||
\(575\) | −4.77125 | −0.198975 | ||||||||
\(576\) | −3.89118 | + | 1.54020i | −0.162132 | + | 0.0641749i | ||||
\(577\) | −10.2383 | − | 17.7333i | −0.426227 | − | 0.738248i | 0.570307 | − | 0.821432i | \(-0.306824\pi\) |
−0.996534 | + | 0.0831842i | \(0.973491\pi\) | |||||||
\(578\) | −14.1386 | + | 24.4888i | −0.588090 | + | 1.01860i | ||||
\(579\) | 7.36552 | + | 38.6215i | 0.306101 | + | 1.60505i | ||||
\(580\) | −4.50861 | + | 7.80915i | −0.187210 | + | 0.324257i | ||||
\(581\) | 10.0505 | + | 43.6150i | 0.416963 | + | 1.80946i | ||||
\(582\) | −26.1646 | + | 22.5825i | −1.08456 | + | 0.936074i | ||||
\(583\) | 36.3108 | 1.50384 | ||||||||
\(584\) | 5.98905 | + | 10.3733i | 0.247829 | + | 0.429252i | ||||
\(585\) | −5.27042 | + | 2.08613i | −0.217905 | + | 0.0862507i | ||||
\(586\) | 18.5168 | − | 32.0721i | 0.764923 | − | 1.32489i | ||||
\(587\) | 6.61348 | + | 11.4549i | 0.272967 | + | 0.472794i | 0.969620 | − | 0.244615i | \(-0.0786615\pi\) |
−0.696653 | + | 0.717408i | \(0.745328\pi\) | |||||||
\(588\) | 4.57486 | − | 10.6484i | 0.188664 | − | 0.439132i | ||||
\(589\) | −0.611377 | + | 1.05894i | −0.0251914 | + | 0.0436327i | ||||
\(590\) | 4.38555 | + | 7.59600i | 0.180550 | + | 0.312722i | ||||
\(591\) | −1.15702 | − | 6.06689i | −0.0475935 | − | 0.249558i | ||||
\(592\) | 14.1022 | − | 24.4258i | 0.579598 | − | 1.00389i | ||||
\(593\) | 6.01696 | − | 10.4217i | 0.247087 | − | 0.427967i | −0.715629 | − | 0.698480i | \(-0.753860\pi\) |
0.962716 | + | 0.270513i | \(0.0871934\pi\) | |||||||
\(594\) | 41.0807 | − | 1.71589i | 1.68556 | − | 0.0704040i | ||||
\(595\) | 1.43914 | − | 1.34092i | 0.0589991 | − | 0.0549723i | ||||
\(596\) | −2.82095 | − | 4.88603i | −0.115551 | − | 0.200140i | ||||
\(597\) | 21.6051 | − | 18.6472i | 0.884237 | − | 0.763179i | ||||
\(598\) | −15.4991 | −0.633804 | ||||||||
\(599\) | 24.7789 | 1.01244 | 0.506220 | − | 0.862404i | \(-0.331042\pi\) | ||||
0.506220 | + | 0.862404i | \(0.331042\pi\) | |||||||
\(600\) | 2.93623 | + | 1.02266i | 0.119871 | + | 0.0417499i | ||||
\(601\) | −11.2423 | − | 19.4722i | −0.458581 | − | 0.794286i | 0.540305 | − | 0.841469i | \(-0.318309\pi\) |
−0.998886 | + | 0.0471831i | \(0.984976\pi\) | |||||||
\(602\) | −2.59360 | − | 11.2552i | −0.105707 | − | 0.458727i | ||||
\(603\) | 20.8031 | − | 8.23423i | 0.847167 | − | 0.335324i | ||||
\(604\) | 9.73616 | − | 16.8635i | 0.396159 | − | 0.686167i | ||||
\(605\) | 5.09135 | − | 8.81847i | 0.206993 | − | 0.358522i | ||||
\(606\) | −53.2340 | − | 18.5409i | −2.16248 | − | 0.753173i | ||||
\(607\) | −7.23803 | − | 12.5366i | −0.293782 | − | 0.508846i | 0.680918 | − | 0.732359i | \(-0.261581\pi\) |
−0.974701 | + | 0.223513i | \(0.928247\pi\) | |||||||
\(608\) | −2.59259 | + | 4.49050i | −0.105143 | + | 0.182114i | ||||
\(609\) | −39.5608 | + | 17.4267i | −1.60308 | + | 0.706167i | ||||
\(610\) | −3.50522 | − | 6.07123i | −0.141922 | − | 0.245817i | ||||
\(611\) | −1.81369 | + | 3.14141i | −0.0733742 | + | 0.127088i | ||||
\(612\) | −1.67072 | − | 1.32445i | −0.0675348 | − | 0.0535379i | ||||
\(613\) | 16.3703 | + | 28.3542i | 0.661190 | + | 1.14521i | 0.980303 | + | 0.197498i | \(0.0632815\pi\) |
−0.319114 | + | 0.947716i | \(0.603385\pi\) | |||||||
\(614\) | −7.56681 | −0.305372 | ||||||||
\(615\) | 2.42023 | + | 12.6906i | 0.0975932 | + | 0.511734i | ||||
\(616\) | 15.9928 | − | 14.9012i | 0.644368 | − | 0.600388i | ||||
\(617\) | 13.8291 | − | 23.9527i | 0.556738 | − | 0.964299i | −0.441028 | − | 0.897494i | \(-0.645386\pi\) |
0.997766 | − | 0.0668057i | \(-0.0212808\pi\) | |||||||
\(618\) | 18.7564 | − | 16.1885i | 0.754491 | − | 0.651196i | ||||
\(619\) | 11.4743 | − | 19.8740i | 0.461190 | − | 0.798805i | −0.537830 | − | 0.843053i | \(-0.680756\pi\) |
0.999021 | + | 0.0442479i | \(0.0140892\pi\) | |||||||
\(620\) | 0.563851 | + | 0.976619i | 0.0226448 | + | 0.0392219i | ||||
\(621\) | −11.4892 | + | 21.9692i | −0.461048 | + | 0.881595i | ||||
\(622\) | 24.2976 | 0.974243 | ||||||||
\(623\) | −32.8355 | + | 30.5945i | −1.31553 | + | 1.22574i | ||||
\(624\) | 15.4464 | + | 5.37985i | 0.618353 | + | 0.215366i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 14.2113 | 0.567998 | ||||||||
\(627\) | −6.25481 | + | 5.39849i | −0.249793 | + | 0.215595i | ||||
\(628\) | 18.5764 | 0.741278 | ||||||||
\(629\) | −4.19545 | −0.167283 | ||||||||
\(630\) | −7.74327 | − | 11.2367i | −0.308499 | − | 0.447680i | ||||
\(631\) | 11.7247 | 0.466755 | 0.233377 | − | 0.972386i | \(-0.425022\pi\) | ||||
0.233377 | + | 0.972386i | \(0.425022\pi\) | |||||||
\(632\) | −9.35647 | −0.372180 | ||||||||
\(633\) | −42.9719 | − | 14.9667i | −1.70798 | − | 0.594872i | ||||
\(634\) | −0.230718 | −0.00916297 | ||||||||
\(635\) | −10.5819 | − | 18.3284i | −0.419930 | − | 0.727340i | ||||
\(636\) | −9.88835 | + | 8.53457i | −0.392099 | + | 0.338418i | ||||
\(637\) | 11.8922 | − | 5.78812i | 0.471185 | − | 0.229334i | ||||
\(638\) | 74.6449 | 2.95522 | ||||||||
\(639\) | 17.5917 | − | 6.96311i | 0.695918 | − | 0.275457i | ||||
\(640\) | −6.20195 | − | 10.7421i | −0.245154 | − | 0.424619i | ||||
\(641\) | 10.2353 | − | 17.7281i | 0.404271 | − | 0.700217i | −0.589966 | − | 0.807428i | \(-0.700859\pi\) |
0.994236 | + | 0.107211i | \(0.0341921\pi\) | |||||||
\(642\) | −27.9115 | − | 9.72131i | −1.10158 | − | 0.383670i | ||||
\(643\) | −6.02670 | + | 10.4386i | −0.237670 | + | 0.411656i | −0.960045 | − | 0.279845i | \(-0.909717\pi\) |
0.722375 | + | 0.691501i | \(0.243050\pi\) | |||||||
\(644\) | −2.70959 | − | 11.7585i | −0.106773 | − | 0.463351i | ||||
\(645\) | −4.15330 | − | 1.44655i | −0.163536 | − | 0.0569580i | ||||
\(646\) | 1.32482 | 0.0521244 | ||||||||
\(647\) | −1.33773 | − | 2.31702i | −0.0525916 | − | 0.0910913i | 0.838531 | − | 0.544854i | \(-0.183415\pi\) |
−0.891123 | + | 0.453762i | \(0.850081\pi\) | |||||||
\(648\) | 11.7793 | − | 11.0573i | 0.462735 | − | 0.434371i | ||||
\(649\) | 11.7401 | − | 20.3344i | 0.460838 | − | 0.798196i | ||||
\(650\) | −1.62421 | − | 2.81322i | −0.0637069 | − | 0.110344i | ||||
\(651\) | −0.586335 | + | 5.37437i | −0.0229803 | + | 0.210638i | ||||
\(652\) | 9.27814 | − | 16.0702i | 0.363360 | − | 0.629358i | ||||
\(653\) | 2.28406 | + | 3.95611i | 0.0893822 | + | 0.154814i | 0.907250 | − | 0.420591i | \(-0.138177\pi\) |
−0.817868 | + | 0.575406i | \(0.804844\pi\) | |||||||
\(654\) | 12.0993 | − | 10.4428i | 0.473119 | − | 0.408346i | ||||
\(655\) | −7.11044 | + | 12.3156i | −0.277828 | + | 0.481212i | ||||
\(656\) | 18.6402 | − | 32.2857i | 0.727776 | − | 1.26055i | ||||
\(657\) | −15.6867 | − | 12.4356i | −0.611997 | − | 0.485158i | ||||
\(658\) | −8.35026 | − | 2.55668i | −0.325527 | − | 0.0996697i | ||||
\(659\) | 9.40458 | + | 16.2892i | 0.366350 | + | 0.634537i | 0.988992 | − | 0.147970i | \(-0.0472738\pi\) |
−0.622641 | + | 0.782507i | \(0.713940\pi\) | |||||||
\(660\) | 1.42750 | + | 7.48516i | 0.0555654 | + | 0.291359i | ||||
\(661\) | −2.89274 | −0.112515 | −0.0562573 | − | 0.998416i | \(-0.517917\pi\) | ||||
−0.0562573 | + | 0.998416i | \(0.517917\pi\) | |||||||
\(662\) | −0.759416 | −0.0295155 | ||||||||
\(663\) | −0.455794 | − | 2.38998i | −0.0177016 | − | 0.0928190i | ||||
\(664\) | −15.1839 | − | 26.2992i | −0.589249 | − | 1.02061i | ||||
\(665\) | 2.62206 | + | 0.802822i | 0.101679 | + | 0.0311321i | ||||
\(666\) | −4.25464 | + | 28.7933i | −0.164864 | + | 1.11572i | ||||
\(667\) | −22.5044 | + | 38.9788i | −0.871374 | + | 1.50926i | ||||
\(668\) | −2.42820 | + | 4.20577i | −0.0939500 | + | 0.162726i | ||||
\(669\) | 4.33950 | − | 3.74539i | 0.167775 | − | 0.144805i | ||||
\(670\) | 6.41100 | + | 11.1042i | 0.247678 | + | 0.428992i | ||||
\(671\) | −9.38345 | + | 16.2526i | −0.362244 | + | 0.627425i | ||||
\(672\) | −2.48640 | + | 22.7904i | −0.0959149 | + | 0.879159i | ||||
\(673\) | −12.6582 | − | 21.9247i | −0.487939 | − | 0.845136i | 0.511965 | − | 0.859007i | \(-0.328918\pi\) |
−0.999904 | + | 0.0138710i | \(0.995585\pi\) | |||||||
\(674\) | 10.4886 | − | 18.1669i | 0.404007 | − | 0.699761i | ||||
\(675\) | −5.19163 | + | 0.216848i | −0.199826 | + | 0.00834649i | ||||
\(676\) | 4.50705 | + | 7.80645i | 0.173348 | + | 0.300248i | ||||
\(677\) | 2.69033 | 0.103398 | 0.0516989 | − | 0.998663i | \(-0.483536\pi\) | ||||
0.0516989 | + | 0.998663i | \(0.483536\pi\) | |||||||
\(678\) | −42.4406 | − | 14.7817i | −1.62992 | − | 0.567686i | ||||
\(679\) | −6.89545 | − | 29.9235i | −0.264623 | − | 1.14836i | ||||
\(680\) | −0.667302 | + | 1.15580i | −0.0255898 | + | 0.0443229i | ||||
\(681\) | 28.1419 | + | 9.80156i | 1.07840 | + | 0.375596i | ||||
\(682\) | 4.66758 | − | 8.08449i | 0.178731 | − | 0.309571i | ||||
\(683\) | −6.32531 | − | 10.9558i | −0.242031 | − | 0.419210i | 0.719262 | − | 0.694739i | \(-0.244480\pi\) |
−0.961293 | + | 0.275529i | \(0.911147\pi\) | |||||||
\(684\) | 0.434472 | − | 2.94029i | 0.0166124 | − | 0.112425i | ||||
\(685\) | 0.558584 | 0.0213424 | ||||||||
\(686\) | 20.0079 | + | 24.7700i | 0.763905 | + | 0.945723i | ||||
\(687\) | 5.34874 | − | 4.61647i | 0.204067 | − | 0.176129i | ||||
\(688\) | 6.34549 | + | 10.9907i | 0.241920 | + | 0.419017i | ||||
\(689\) | −14.9065 | −0.567891 | ||||||||
\(690\) | −13.4176 | − | 4.67322i | −0.510799 | − | 0.177906i | ||||
\(691\) | 20.6396 | 0.785166 | 0.392583 | − | 0.919717i | \(-0.371582\pi\) | ||||
0.392583 | + | 0.919717i | \(0.371582\pi\) | |||||||
\(692\) | 10.7785 | 0.409739 | ||||||||
\(693\) | −15.6861 | + | 32.9918i | −0.595866 | + | 1.25325i | ||||
\(694\) | −8.28869 | −0.314634 | ||||||||
\(695\) | −13.8246 | −0.524396 | ||||||||
\(696\) | 22.2038 | − | 19.1640i | 0.841634 | − | 0.726409i | ||||
\(697\) | −5.54549 | −0.210051 | ||||||||
\(698\) | 11.5167 | + | 19.9476i | 0.435915 | + | 0.755026i | ||||
\(699\) | −31.3331 | − | 10.9130i | −1.18513 | − | 0.412768i | ||||
\(700\) | 1.85033 | − | 1.72404i | 0.0699360 | − | 0.0651627i | ||||
\(701\) | −19.3708 | −0.731626 | −0.365813 | − | 0.930688i | \(-0.619209\pi\) | ||||
−0.365813 | + | 0.930688i | \(0.619209\pi\) | |||||||
\(702\) | −16.8646 | + | 0.704416i | −0.636514 | + | 0.0265865i | ||||
\(703\) | −2.92442 | − | 5.06524i | −0.110296 | − | 0.191039i | ||||
\(704\) | −3.21015 | + | 5.56015i | −0.120987 | + | 0.209556i | ||||
\(705\) | −2.51731 | + | 2.17267i | −0.0948074 | + | 0.0818276i | ||||
\(706\) | −27.8692 | + | 48.2709i | −1.04887 | + | 1.81670i | ||||
\(707\) | 36.6429 | − | 34.1419i | 1.37810 | − | 1.28404i | ||||
\(708\) | 1.58233 | + | 8.29699i | 0.0594674 | + | 0.311820i | ||||
\(709\) | 14.1845 | 0.532711 | 0.266355 | − | 0.963875i | \(-0.414181\pi\) | ||||
0.266355 | + | 0.963875i | \(0.414181\pi\) | |||||||
\(710\) | 5.42134 | + | 9.39003i | 0.203459 | + | 0.352402i | ||||
\(711\) | 14.5391 | − | 5.75483i | 0.545258 | − | 0.215823i | ||||
\(712\) | 15.2252 | − | 26.3708i | 0.570588 | − | 0.988287i | ||||
\(713\) | 2.81442 | + | 4.87472i | 0.105401 | + | 0.182560i | ||||
\(714\) | 5.36049 | − | 2.36132i | 0.200611 | − | 0.0883704i | ||||
\(715\) | −4.34800 | + | 7.53096i | −0.162606 | + | 0.281642i | ||||
\(716\) | 4.57432 | + | 7.92296i | 0.170950 | + | 0.296095i | ||||
\(717\) | 0.272759 | + | 0.0949994i | 0.0101864 | + | 0.00354782i | ||||
\(718\) | 30.3879 | − | 52.6335i | 1.13407 | − | 1.96426i | ||||
\(719\) | 1.47355 | − | 2.55226i | 0.0549542 | − | 0.0951834i | −0.837240 | − | 0.546836i | \(-0.815832\pi\) |
0.892194 | + | 0.451653i | \(0.149165\pi\) | |||||||
\(720\) | 11.7499 | + | 9.31471i | 0.437894 | + | 0.347139i | ||||
\(721\) | 4.94307 | + | 21.4510i | 0.184090 | + | 0.798876i | ||||
\(722\) | −15.4096 | − | 26.6902i | −0.573486 | − | 0.993307i | ||||
\(723\) | −37.1224 | − | 12.9294i | −1.38060 | − | 0.480849i | ||||
\(724\) | 0.403546 | 0.0149977 | ||||||||
\(725\) | −9.43334 | −0.350346 | ||||||||
\(726\) | 22.9551 | − | 19.8124i | 0.851942 | − | 0.735306i | ||||
\(727\) | −7.45252 | − | 12.9082i | −0.276399 | − | 0.478737i | 0.694088 | − | 0.719890i | \(-0.255808\pi\) |
−0.970487 | + | 0.241153i | \(0.922474\pi\) | |||||||
\(728\) | −6.56542 | + | 6.11732i | −0.243331 | + | 0.226723i | ||||
\(729\) | −11.5030 | + | 24.4270i | −0.426039 | + | 0.904705i | ||||
\(730\) | 5.73603 | − | 9.93509i | 0.212300 | − | 0.367714i | ||||
\(731\) | 0.943900 | − | 1.63488i | 0.0349114 | − | 0.0604683i | ||||
\(732\) | −1.26470 | − | 6.63151i | −0.0467446 | − | 0.245108i | ||||
\(733\) | 0.648040 | + | 1.12244i | 0.0239359 | + | 0.0414582i | 0.877745 | − | 0.479128i | \(-0.159047\pi\) |
−0.853809 | + | 0.520586i | \(0.825714\pi\) | |||||||
\(734\) | −16.0493 | + | 27.7983i | −0.592392 | + | 1.02605i | ||||
\(735\) | 12.0403 | − | 1.42511i | 0.444114 | − | 0.0525661i | ||||
\(736\) | 11.9348 | + | 20.6716i | 0.439921 | + | 0.761966i | ||||
\(737\) | 17.1622 | − | 29.7258i | 0.632177 | − | 1.09496i | ||||
\(738\) | −5.62374 | + | 38.0587i | −0.207013 | + | 1.40096i | ||||
\(739\) | 8.55467 | + | 14.8171i | 0.314689 | + | 0.545057i | 0.979371 | − | 0.202069i | \(-0.0647665\pi\) |
−0.664683 | + | 0.747126i | \(0.731433\pi\) | |||||||
\(740\) | −5.39416 | −0.198293 | ||||||||
\(741\) | 2.56775 | − | 2.21621i | 0.0943287 | − | 0.0814145i | ||||
\(742\) | −8.05848 | − | 34.9706i | −0.295836 | − | 1.28381i | ||||
\(743\) | −1.23227 | + | 2.13436i | −0.0452076 | + | 0.0783019i | −0.887744 | − | 0.460338i | \(-0.847728\pi\) |
0.842536 | + | 0.538640i | \(0.181062\pi\) | |||||||
\(744\) | −0.687157 | − | 3.60314i | −0.0251924 | − | 0.132097i | ||||
\(745\) | 2.95113 | − | 5.11150i | 0.108121 | − | 0.187271i | ||||
\(746\) | −9.98831 | − | 17.3003i | −0.365698 | − | 0.633407i | ||||
\(747\) | 39.7701 | + | 31.5276i | 1.45511 | + | 1.15353i | ||||
\(748\) | −3.27084 | −0.119594 | ||||||||
\(749\) | 19.2125 | − | 17.9012i | 0.702009 | − | 0.654095i | ||||
\(750\) | −0.557856 | − | 2.92514i | −0.0203700 | − | 0.106811i | ||||
\(751\) | −16.1069 | − | 27.8980i | −0.587751 | − | 1.01801i | −0.994526 | − | 0.104486i | \(-0.966680\pi\) |
0.406776 | − | 0.913528i | \(-0.366653\pi\) | |||||||
\(752\) | 9.59546 | 0.349911 | ||||||||
\(753\) | −4.31560 | − | 22.6291i | −0.157269 | − | 0.824649i | ||||
\(754\) | −30.6435 | −1.11597 | ||||||||
\(755\) | 20.3709 | 0.741374 | ||||||||
\(756\) | −3.48273 | − | 12.6714i | −0.126666 | − | 0.460854i | ||||
\(757\) | 15.0178 | 0.545831 | 0.272915 | − | 0.962038i | \(-0.412012\pi\) | ||||
0.272915 | + | 0.962038i | \(0.412012\pi\) | |||||||
\(758\) | −53.0653 | −1.92742 | ||||||||
\(759\) | 7.12526 | + | 37.3616i | 0.258631 | + | 1.35614i | ||||
\(760\) | −1.86056 | −0.0674895 | ||||||||
\(761\) | −21.0710 | − | 36.4961i | −0.763825 | − | 1.32298i | −0.940866 | − | 0.338780i | \(-0.889986\pi\) |
0.177041 | − | 0.984203i | \(-0.443348\pi\) | |||||||
\(762\) | −11.8064 | − | 61.9071i | −0.427699 | − | 2.24266i | ||||
\(763\) | 3.18866 | + | 13.8375i | 0.115437 | + | 0.500951i | ||||
\(764\) | 8.55644 | 0.309561 | ||||||||
\(765\) | 0.326034 | − | 2.20644i | 0.0117878 | − | 0.0797740i | ||||
\(766\) | −23.6767 | − | 41.0092i | −0.855472 | − | 1.48172i | ||||
\(767\) | −4.81958 | + | 8.34776i | −0.174025 | + | 0.301420i | ||||
\(768\) | −6.01433 | − | 31.5364i | −0.217024 | − | 1.13797i | ||||
\(769\) | 14.9534 | − | 25.9000i | 0.539233 | − | 0.933979i | −0.459712 | − | 0.888068i | \(-0.652047\pi\) |
0.998946 | − | 0.0459114i | \(-0.0146192\pi\) | |||||||
\(770\) | −20.0182 | − | 6.12917i | −0.721407 | − | 0.220880i | ||||
\(771\) | −16.3417 | + | 14.1044i | −0.588533 | + | 0.507959i | ||||
\(772\) | −21.6987 | −0.780952 | ||||||||
\(773\) | 3.44462 | + | 5.96625i | 0.123894 | + | 0.214591i | 0.921300 | − | 0.388852i | \(-0.127128\pi\) |
−0.797406 | + | 0.603443i | \(0.793795\pi\) | |||||||
\(774\) | −10.2630 | − | 8.13593i | −0.368895 | − | 0.292440i | ||||
\(775\) | −0.589871 | + | 1.02169i | −0.0211888 | + | 0.0367001i | ||||
\(776\) | 10.4174 | + | 18.0435i | 0.373963 | + | 0.647723i | ||||
\(777\) | −20.8609 | − | 15.2826i | −0.748380 | − | 0.548259i | ||||
\(778\) | 16.4423 | − | 28.4788i | 0.589483 | − | 1.02102i | ||||
\(779\) | −3.86546 | − | 6.69517i | −0.138494 | − | 0.239879i | ||||
\(780\) | −0.586023 | − | 3.07284i | −0.0209830 | − | 0.110025i | ||||
\(781\) | 14.5129 | − | 25.1370i | 0.519311 | − | 0.899473i | ||||
\(782\) | 3.04935 | − | 5.28163i | 0.109045 | − | 0.188871i | ||||
\(783\) | −22.7156 | + | 43.4359i | −0.811791 | + | 1.55227i | ||||
\(784\) | −28.9890 | − | 19.5879i | −1.03532 | − | 0.699569i | ||||
\(785\) | 9.71681 | + | 16.8300i | 0.346808 | + | 0.600689i | ||||
\(786\) | −32.0584 | + | 27.6694i | −1.14349 | + | 0.986935i | ||||
\(787\) | −28.9946 | −1.03355 | −0.516774 | − | 0.856122i | \(-0.672867\pi\) | ||||
−0.516774 | + | 0.856122i | \(0.672867\pi\) | |||||||
\(788\) | 3.40855 | 0.121425 | ||||||||
\(789\) | 8.82067 | + | 3.07216i | 0.314024 | + | 0.109372i | ||||
\(790\) | 4.48059 | + | 7.76061i | 0.159412 | + | 0.276110i | ||||
\(791\) | 29.2134 | − | 27.2195i | 1.03871 | − | 0.967814i | ||||
\(792\) | 3.62313 | − | 24.5195i | 0.128742 | − | 0.871264i | ||||
\(793\) | 3.85213 | − | 6.67209i | 0.136793 | − | 0.236933i | ||||
\(794\) | 8.64681 | − | 14.9767i | 0.306864 | − | 0.531504i | ||||
\(795\) | −12.9046 | − | 4.49454i | −0.457678 | − | 0.159405i | ||||
\(796\) | 7.87520 | + | 13.6402i | 0.279129 | + | 0.483466i | ||||
\(797\) | 18.2990 | − | 31.6948i | 0.648184 | − | 1.12269i | −0.335372 | − | 0.942086i | \(-0.608862\pi\) |
0.983556 | − | 0.180602i | \(-0.0578047\pi\) | |||||||
\(798\) | 6.58737 | + | 4.82587i | 0.233191 | + | 0.170834i | ||||
\(799\) | −0.713668 | − | 1.23611i | −0.0252478 | − | 0.0437304i | ||||
\(800\) | −2.50139 | + | 4.33254i | −0.0884376 | + | 0.153178i | ||||
\(801\) | −7.43881 | + | 50.3422i | −0.262837 | + | 1.77876i | ||||
\(802\) | −13.5131 | − | 23.4054i | −0.477164 | − | 0.826472i | ||||
\(803\) | −30.7106 | −1.08375 | ||||||||
\(804\) | 2.31311 | + | 12.1289i | 0.0815773 | + | 0.427754i | ||||
\(805\) | 9.23580 | − | 8.60544i | 0.325519 | − | 0.303302i | ||||
\(806\) | −1.91615 | + | 3.31888i | −0.0674936 | + | 0.116902i | ||||
\(807\) | 30.3351 | − | 26.1820i | 1.06784 | − | 0.921650i | ||||
\(808\) | −16.9906 | + | 29.4285i | −0.597726 | + | 1.03529i | ||||
\(809\) | −6.95113 | − | 12.0397i | −0.244389 | − | 0.423294i | 0.717571 | − | 0.696485i | \(-0.245254\pi\) |
−0.961960 | + | 0.273192i | \(0.911921\pi\) | |||||||
\(810\) | −14.8122 | − | 4.47514i | −0.520446 | − | 0.157241i | ||||
\(811\) | 23.2445 | 0.816224 | 0.408112 | − | 0.912932i | \(-0.366187\pi\) | ||||
0.408112 | + | 0.912932i | \(0.366187\pi\) | |||||||
\(812\) | −5.35719 | − | 23.2481i | −0.188001 | − | 0.815847i | ||||
\(813\) | 9.85975 | + | 3.43406i | 0.345797 | + | 0.120438i | ||||
\(814\) | 22.3265 | + | 38.6707i | 0.782545 | + | 1.35541i | ||||
\(815\) | 19.4126 | 0.679994 | ||||||||
\(816\) | −4.87230 | + | 4.20525i | −0.170565 | + | 0.147213i | ||||
\(817\) | 2.63176 | 0.0920737 | ||||||||
\(818\) | 21.4728 | 0.750780 | ||||||||
\(819\) | 6.43952 | − | 13.5439i | 0.225015 | − | 0.473262i | ||||
\(820\) | −7.12995 | −0.248989 | ||||||||
\(821\) | 40.8589 | 1.42598 | 0.712992 | − | 0.701172i | \(-0.247339\pi\) | ||||
0.712992 | + | 0.701172i | \(0.247339\pi\) | |||||||
\(822\) | 1.57084 | + | 0.547107i | 0.0547892 | + | 0.0190825i | ||||
\(823\) | −16.7182 | −0.582760 | −0.291380 | − | 0.956607i | \(-0.594114\pi\) | ||||
−0.291380 | + | 0.956607i | \(0.594114\pi\) | |||||||
\(824\) | −7.46782 | − | 12.9346i | −0.260154 | − | 0.450599i | ||||
\(825\) | −6.03479 | + | 5.20859i | −0.210104 | + | 0.181340i | ||||
\(826\) | −22.1894 | − | 6.79394i | −0.772067 | − | 0.236391i | ||||
\(827\) | 4.44830 | 0.154682 | 0.0773412 | − | 0.997005i | \(-0.475357\pi\) | ||||
0.0773412 | + | 0.997005i | \(0.475357\pi\) | |||||||
\(828\) | −10.7220 | − | 8.49978i | −0.372614 | − | 0.295388i | ||||
\(829\) | 18.5305 | + | 32.0957i | 0.643590 | + | 1.11473i | 0.984625 | + | 0.174680i | \(0.0558890\pi\) |
−0.341036 | + | 0.940050i | \(0.610778\pi\) | |||||||
\(830\) | −14.5424 | + | 25.1882i | −0.504774 | + | 0.874294i | ||||
\(831\) | 16.3037 | + | 5.67844i | 0.565571 | + | 0.196983i | ||||
\(832\) | 1.31784 | − | 2.28257i | 0.0456880 | − | 0.0791340i | ||||
\(833\) | −0.367293 | + | 5.19129i | −0.0127260 | + | 0.179867i | ||||
\(834\) | −38.8771 | − | 13.5405i | −1.34620 | − | 0.468870i | ||||
\(835\) | −5.08052 | −0.175818 | ||||||||
\(836\) | −2.27992 | − | 3.94894i | −0.0788528 | − | 0.136577i | ||||
\(837\) | 3.28394 | + | 5.17630i | 0.113510 | + | 0.178919i | ||||
\(838\) | −2.70608 | + | 4.68706i | −0.0934798 | + | 0.161912i | ||||
\(839\) | 0.692323 | + | 1.19914i | 0.0239016 | + | 0.0413988i | 0.877729 | − | 0.479158i | \(-0.159058\pi\) |
−0.853827 | + | 0.520557i | \(0.825724\pi\) | |||||||
\(840\) | −7.52818 | + | 3.31620i | −0.259747 | + | 0.114420i | ||||
\(841\) | −29.9940 | + | 51.9511i | −1.03427 | + | 1.79142i | ||||
\(842\) | −3.58054 | − | 6.20168i | −0.123394 | − | 0.213724i | ||||
\(843\) | −31.1599 | + | 26.8939i | −1.07320 | + | 0.926275i | ||||
\(844\) | 12.5563 | − | 21.7482i | 0.432207 | − | 0.748604i | ||||
\(845\) | −4.71504 | + | 8.16669i | −0.162202 | + | 0.280943i | ||||
\(846\) | −9.20715 | + | 3.64435i | −0.316548 | + | 0.125295i | ||||
\(847\) | 6.04960 | + | 26.2529i | 0.207867 | + | 0.902060i | ||||
\(848\) | 19.7159 | + | 34.1489i | 0.677046 | + | 1.17268i | ||||
\(849\) | −5.87289 | − | 30.7948i | −0.201557 | − | 1.05687i | ||||
\(850\) | 1.27822 | 0.0438426 | ||||||||
\(851\) | −26.9246 | −0.922963 | ||||||||
\(852\) | 1.95604 | + | 10.2566i | 0.0670128 | + | 0.351385i | ||||
\(853\) | 15.3741 | + | 26.6288i | 0.526401 | + | 0.911752i | 0.999527 | + | 0.0307579i | \(0.00979208\pi\) |
−0.473126 | + | 0.880995i | \(0.656875\pi\) | |||||||
\(854\) | 17.7352 | + | 5.43016i | 0.606887 | + | 0.185816i | ||||
\(855\) | 2.89114 | − | 1.14436i | 0.0988747 | − | 0.0391364i | ||||
\(856\) | −8.90844 | + | 15.4299i | −0.304484 | + | 0.527382i | ||||
\(857\) | 7.13463 | − | 12.3575i | 0.243714 | − | 0.422126i | −0.718055 | − | 0.695986i | \(-0.754967\pi\) |
0.961769 | + | 0.273861i | \(0.0883007\pi\) | |||||||
\(858\) | −19.6036 | + | 16.9197i | −0.669255 | + | 0.577630i | ||||
\(859\) | 23.2027 | + | 40.1882i | 0.791665 | + | 1.37120i | 0.924935 | + | 0.380124i | \(0.124119\pi\) |
−0.133271 | + | 0.991080i | \(0.542548\pi\) | |||||||
\(860\) | 1.21359 | − | 2.10200i | 0.0413831 | − | 0.0716776i | ||||
\(861\) | −27.5737 | − | 20.2003i | −0.939709 | − | 0.688425i | ||||
\(862\) | −9.73631 | − | 16.8638i | −0.331620 | − | 0.574383i | ||||
\(863\) | −11.3378 | + | 19.6376i | −0.385943 | + | 0.668473i | −0.991900 | − | 0.127025i | \(-0.959457\pi\) |
0.605957 | + | 0.795498i | \(0.292791\pi\) | |||||||
\(864\) | 13.9258 | + | 21.9505i | 0.473765 | + | 0.746771i | ||||
\(865\) | 5.63797 | + | 9.76525i | 0.191697 | + | 0.332029i | ||||
\(866\) | −70.1875 | −2.38507 | ||||||||
\(867\) | −26.9025 | − | 9.36987i | −0.913655 | − | 0.318217i | ||||
\(868\) | −2.85289 | − | 0.873497i | −0.0968334 | − | 0.0296484i | ||||
\(869\) | 11.9945 | − | 20.7751i | 0.406885 | − | 0.704746i | ||||
\(870\) | −26.5282 | − | 9.23953i | −0.899391 | − | 0.313249i | ||||
\(871\) | −7.04548 | + | 12.2031i | −0.238727 | + | 0.413488i | ||||
\(872\) | −4.81731 | − | 8.34383i | −0.163135 | − | 0.282558i | ||||
\(873\) | −27.2856 | − | 21.6305i | −0.923477 | − | 0.732082i | ||||
\(874\) | 8.50214 | 0.287589 | ||||||||
\(875\) | 2.52983 | + | 0.774581i | 0.0855238 | + | 0.0261856i | ||||
\(876\) | 8.36327 | − | 7.21828i | 0.282569 | − | 0.243883i | ||||
\(877\) | 11.1131 | + | 19.2485i | 0.375264 | + | 0.649976i | 0.990366 | − | 0.138471i | \(-0.0442188\pi\) |
−0.615103 | + | 0.788447i | \(0.710885\pi\) | |||||||
\(878\) | 29.1034 | 0.982192 | ||||||||
\(879\) | 35.2331 | + | 12.2714i | 1.18838 | + | 0.413903i | ||||
\(880\) | 23.0034 | 0.775444 | ||||||||
\(881\) | −4.26806 | −0.143795 | −0.0718973 | − | 0.997412i | \(-0.522905\pi\) | ||||
−0.0718973 | + | 0.997412i | \(0.522905\pi\) | |||||||
\(882\) | 35.2553 | + | 7.78526i | 1.18711 | + | 0.262143i | ||||
\(883\) | −18.2078 | −0.612741 | −0.306370 | − | 0.951912i | \(-0.599115\pi\) | ||||
−0.306370 | + | 0.951912i | \(0.599115\pi\) | |||||||
\(884\) | 1.34276 | 0.0451618 | ||||||||
\(885\) | −6.68932 | + | 5.77351i | −0.224859 | + | 0.194074i | ||||
\(886\) | −16.0494 | −0.539191 | ||||||||
\(887\) | 13.1258 | + | 22.7346i | 0.440721 | + | 0.763352i | 0.997743 | − | 0.0671462i | \(-0.0213894\pi\) |
−0.557022 | + | 0.830498i | \(0.688056\pi\) | |||||||
\(888\) | 16.5694 | + | 5.77096i | 0.556032 | + | 0.193661i | ||||
\(889\) | 53.5407 | + | 16.3931i | 1.79570 | + | 0.549806i | ||||
\(890\) | −29.1639 | −0.977576 | ||||||||
\(891\) | 9.45109 | + | 40.3296i | 0.316623 | + | 1.35109i | ||||
\(892\) | 1.58178 | + | 2.73972i | 0.0529618 | + | 0.0917326i | ||||
\(893\) | 0.994918 | − | 1.72325i | 0.0332937 | − | 0.0576663i | ||||
\(894\) | 13.3056 | − | 11.4840i | 0.445005 | − | 0.384081i | ||||
\(895\) | −4.78541 | + | 8.28858i | −0.159959 | + | 0.277057i | ||||
\(896\) | 31.3797 | + | 9.60783i | 1.04832 | + | 0.320975i | ||||
\(897\) | −2.92509 | − | 15.3378i | −0.0976659 | − | 0.512116i | ||||
\(898\) | 61.2959 | 2.04547 | ||||||||
\(899\) | 5.56446 | + | 9.63792i | 0.185585 | + | 0.321443i | ||||
\(900\) | 0.419188 | − | 2.83686i | 0.0139729 | − | 0.0945621i | ||||
\(901\) | 2.93276 | − | 5.07969i | 0.0977044 | − | 0.169229i | ||||
\(902\) | 29.5110 | + | 51.1145i | 0.982608 | + | 1.70193i | ||||
\(903\) | 10.6486 | − | 4.69078i | 0.354364 | − | 0.156099i | ||||
\(904\) | −13.5456 | + | 23.4618i | −0.450522 | + | 0.780326i | ||||
\(905\) | 0.211084 | + | 0.365608i | 0.00701667 | + | 0.0121532i | ||||
\(906\) | 57.2866 | + | 19.9524i | 1.90322 | + | 0.662873i | ||||
\(907\) | −7.46852 | + | 12.9359i | −0.247988 | + | 0.429528i | −0.962968 | − | 0.269617i | \(-0.913103\pi\) |
0.714979 | + | 0.699146i | \(0.246436\pi\) | |||||||
\(908\) | −8.22304 | + | 14.2427i | −0.272891 | + | 0.472661i | ||||
\(909\) | 8.30135 | − | 56.1795i | 0.275338 | − | 1.86336i | ||||
\(910\) | 8.21796 | + | 2.51617i | 0.272423 | + | 0.0834103i | ||||
\(911\) | −9.19315 | − | 15.9230i | −0.304583 | − | 0.527553i | 0.672586 | − | 0.740019i | \(-0.265184\pi\) |
−0.977168 | + | 0.212467i | \(0.931850\pi\) | |||||||
\(912\) | −8.47328 | − | 2.95116i | −0.280578 | − | 0.0977228i | ||||
\(913\) | 77.8597 | 2.57678 | ||||||||
\(914\) | 22.1665 | 0.733203 | ||||||||
\(915\) | 5.34655 | − | 4.61457i | 0.176751 | − | 0.152553i | ||||
\(916\) | 1.94965 | + | 3.37690i | 0.0644184 | + | 0.111576i | ||||
\(917\) | −8.44871 | − | 36.6640i | −0.279001 | − | 1.21075i | ||||
\(918\) | 3.07797 | − | 5.88556i | 0.101588 | − | 0.194253i | ||||
\(919\) | −2.59097 | + | 4.48768i | −0.0854681 | + | 0.148035i | −0.905591 | − | 0.424153i | \(-0.860572\pi\) |
0.820122 | + | 0.572188i | \(0.193905\pi\) | |||||||
\(920\) | −4.28246 | + | 7.41743i | −0.141188 | + | 0.244545i | ||||
\(921\) | −1.42806 | − | 7.48811i | −0.0470563 | − | 0.246742i | ||||
\(922\) | 31.8937 | + | 55.2414i | 1.05036 | + | 1.81928i | ||||
\(923\) | −5.95788 | + | 10.3193i | −0.196106 | + | 0.339665i | ||||
\(924\) | −16.2635 | − | 11.9145i | −0.535030 | − | 0.391959i | ||||
\(925\) | −2.82154 | − | 4.88706i | −0.0927718 | − | 0.160685i | ||||
\(926\) | 19.5999 | − | 33.9481i | 0.644094 | − | 1.11560i | ||||
\(927\) | 19.5599 | + | 15.5061i | 0.642432 | + | 0.509286i | ||||
\(928\) | 23.5965 | + | 40.8703i | 0.774593 | + | 1.34163i | ||||
\(929\) | 25.8879 | 0.849354 | 0.424677 | − | 0.905345i | \(-0.360388\pi\) | ||||
0.424677 | + | 0.905345i | \(0.360388\pi\) | |||||||
\(930\) | −2.65952 | + | 2.29541i | −0.0872090 | + | 0.0752695i | ||||
\(931\) | −6.52355 | + | 3.17512i | −0.213801 | + | 0.104060i | ||||
\(932\) | 9.15551 | − | 15.8578i | 0.299899 | − | 0.519440i | ||||
\(933\) | 4.58561 | + | 24.0448i | 0.150126 | + | 0.787192i | ||||
\(934\) | −9.94368 | + | 17.2230i | −0.325367 | + | 0.563553i | ||||
\(935\) | −1.71089 | − | 2.96335i | −0.0559521 | − | 0.0969118i | ||||
\(936\) | −1.48738 | + | 10.0659i | −0.0486165 | + | 0.329013i | ||||
\(937\) | 45.6581 | 1.49158 | 0.745792 | − | 0.666178i | \(-0.232071\pi\) | ||||
0.745792 | + | 0.666178i | \(0.232071\pi\) | |||||||
\(938\) | −32.4374 | − | 9.93168i | −1.05912 | − | 0.324281i | ||||
\(939\) | 2.68206 | + | 14.0635i | 0.0875256 | + | 0.458944i | ||||
\(940\) | −0.917577 | − | 1.58929i | −0.0299280 | − | 0.0518369i | ||||
\(941\) | −39.5929 | −1.29069 | −0.645346 | − | 0.763890i | \(-0.723287\pi\) | ||||
−0.645346 | + | 0.763890i | \(0.723287\pi\) | |||||||
\(942\) | 10.8412 | + | 56.8461i | 0.353224 | + | 1.85215i | ||||
\(943\) | −35.5886 | −1.15892 | ||||||||
\(944\) | 25.4983 | 0.829899 | ||||||||
\(945\) | 9.65843 | − | 9.78339i | 0.314189 | − | 0.318254i | ||||
\(946\) | −20.0923 | −0.653256 | ||||||||
\(947\) | −47.2360 | −1.53496 | −0.767482 | − | 0.641070i | \(-0.778491\pi\) | ||||
−0.767482 | + | 0.641070i | \(0.778491\pi\) | |||||||
\(948\) | 1.61661 | + | 8.47679i | 0.0525052 | + | 0.275313i | ||||
\(949\) | 12.6074 | 0.409254 | ||||||||
\(950\) | 0.890976 | + | 1.54322i | 0.0289071 | + | 0.0500686i | ||||
\(951\) | −0.0435427 | − | 0.228318i | −0.00141197 | − | 0.00740371i | ||||
\(952\) | −0.792896 | − | 3.44085i | −0.0256979 | − | 0.111519i | ||||
\(953\) | −61.6657 | −1.99755 | −0.998773 | − | 0.0495191i | \(-0.984231\pi\) | ||||
−0.998773 | + | 0.0495191i | \(0.984231\pi\) | |||||||
\(954\) | −31.8877 | − | 25.2789i | −1.03240 | − | 0.818434i | ||||
\(955\) | 4.47565 | + | 7.75205i | 0.144829 | + | 0.250850i | ||||
\(956\) | −0.0797000 | + | 0.138044i | −0.00257768 | + | 0.00446468i | ||||
\(957\) | 14.0875 | + | 73.8685i | 0.455385 | + | 2.38783i | ||||
\(958\) | 4.72779 | − | 8.18878i | 0.152748 | − | 0.264567i | ||||
\(959\) | −1.08126 | + | 1.00746i | −0.0349158 | + | 0.0325327i | ||||
\(960\) | 1.82910 | − | 1.57868i | 0.0590338 | − | 0.0509517i | ||||
\(961\) | −29.6082 | −0.955104 | ||||||||
\(962\) | −9.16558 | − | 15.8753i | −0.295510 | − | 0.511839i | ||||
\(963\) | 4.35254 | − | 29.4559i | 0.140259 | − | 0.949202i | ||||
\(964\) | 10.8471 | − | 18.7878i | 0.349362 | − | 0.605114i | ||||
\(965\) | −11.3500 | − | 19.6588i | −0.365369 | − | 0.632838i | ||||
\(966\) | 34.4013 | − | 15.1540i | 1.10684 | − | 0.487571i | ||||
\(967\) | 21.1947 | − | 36.7103i | 0.681576 | − | 1.18052i | −0.292924 | − | 0.956136i | \(-0.594628\pi\) |
0.974500 | − | 0.224389i | \(-0.0720385\pi\) | |||||||
\(968\) | −9.13953 | − | 15.8301i | −0.293756 | − | 0.508799i | ||||
\(969\) | 0.250030 | + | 1.31104i | 0.00803211 | + | 0.0421167i | ||||
\(970\) | 9.97729 | − | 17.2812i | 0.320351 | − | 0.554865i | ||||
\(971\) | 1.17376 | − | 2.03301i | 0.0376677 | − | 0.0652424i | −0.846577 | − | 0.532266i | \(-0.821340\pi\) |
0.884245 | + | 0.467024i | \(0.154674\pi\) | |||||||
\(972\) | −12.0529 | − | 8.76137i | −0.386598 | − | 0.281021i | ||||
\(973\) | 26.7605 | − | 24.9340i | 0.857902 | − | 0.799349i | ||||
\(974\) | −1.41993 | − | 2.45940i | −0.0454976 | − | 0.0788042i | ||||
\(975\) | 2.47743 | − | 2.13825i | 0.0793411 | − | 0.0684788i | ||||
\(976\) | −20.3799 | −0.652346 | ||||||||
\(977\) | 4.45628 | 0.142569 | 0.0712846 | − | 0.997456i | \(-0.477290\pi\) | ||||
0.0712846 | + | 0.997456i | \(0.477290\pi\) | |||||||
\(978\) | 54.5917 | + | 19.0138i | 1.74565 | + | 0.607993i | ||||
\(979\) | 39.0357 | + | 67.6119i | 1.24759 | + | 2.16088i | ||||
\(980\) | −0.472236 | + | 6.67454i | −0.0150850 | + | 0.213210i | ||||
\(981\) | 12.6176 | + | 10.0026i | 0.402850 | + | 0.319358i | ||||
\(982\) | −6.98450 | + | 12.0975i | −0.222884 | + | 0.386047i | ||||
\(983\) | 10.8186 | − | 18.7383i | 0.345059 | − | 0.597660i | −0.640305 | − | 0.768120i | \(-0.721192\pi\) |
0.985365 | + | 0.170460i | \(0.0545255\pi\) | |||||||
\(984\) | 21.9012 | + | 7.62798i | 0.698185 | + | 0.243171i | ||||
\(985\) | 1.78292 | + | 3.08811i | 0.0568087 | + | 0.0983955i | ||||
\(986\) | 6.02894 | − | 10.4424i | 0.192001 | − | 0.332555i | ||||
\(987\) | 0.954166 | − | 8.74592i | 0.0303714 | − | 0.278386i | ||||
\(988\) | 0.935963 | + | 1.62114i | 0.0297769 | + | 0.0515752i | ||||
\(989\) | 6.05754 | − | 10.4920i | 0.192619 | − | 0.333625i | ||||
\(990\) | −22.0725 | + | 8.73667i | −0.701509 | + | 0.277670i | ||||
\(991\) | 26.4853 | + | 45.8739i | 0.841333 | + | 1.45723i | 0.888768 | + | 0.458357i | \(0.151562\pi\) |
−0.0474349 | + | 0.998874i | \(0.515105\pi\) | |||||||
\(992\) | 5.90200 | 0.187389 | ||||||||
\(993\) | −0.143322 | − | 0.751517i | −0.00454820 | − | 0.0238487i | ||||
\(994\) | −27.4301 | − | 8.39853i | −0.870029 | − | 0.266385i | ||||
\(995\) | −8.23861 | + | 14.2697i | −0.261182 | + | 0.452380i | ||||
\(996\) | −21.2032 | + | 18.3003i | −0.671848 | + | 0.579868i | ||||
\(997\) | −13.5044 | + | 23.3903i | −0.427688 | + | 0.740777i | −0.996667 | − | 0.0815748i | \(-0.974005\pi\) |
0.568979 | + | 0.822352i | \(0.307338\pi\) | |||||||
\(998\) | 10.0359 | + | 17.3826i | 0.317680 | + | 0.550238i | ||||
\(999\) | −29.2968 | + | 1.22369i | −0.926910 | + | 0.0387160i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.2.l.b.121.2 | yes | 24 | |
3.2 | odd | 2 | 945.2.l.b.226.11 | 24 | |||
7.4 | even | 3 | 315.2.k.b.256.11 | yes | 24 | ||
9.2 | odd | 6 | 945.2.k.b.856.2 | 24 | |||
9.7 | even | 3 | 315.2.k.b.16.11 | ✓ | 24 | ||
21.11 | odd | 6 | 945.2.k.b.361.2 | 24 | |||
63.11 | odd | 6 | 945.2.l.b.46.11 | 24 | |||
63.25 | even | 3 | inner | 315.2.l.b.151.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.k.b.16.11 | ✓ | 24 | 9.7 | even | 3 | ||
315.2.k.b.256.11 | yes | 24 | 7.4 | even | 3 | ||
315.2.l.b.121.2 | yes | 24 | 1.1 | even | 1 | trivial | |
315.2.l.b.151.2 | yes | 24 | 63.25 | even | 3 | inner | |
945.2.k.b.361.2 | 24 | 21.11 | odd | 6 | |||
945.2.k.b.856.2 | 24 | 9.2 | odd | 6 | |||
945.2.l.b.46.11 | 24 | 63.11 | odd | 6 | |||
945.2.l.b.226.11 | 24 | 3.2 | odd | 2 |