Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.64000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(0.831254 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.161 |
Dual form | 363.2.f.a.239.2 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 0.587785i | −0.572061 | − | 0.415627i | 0.263792 | − | 0.964580i | \(-0.415027\pi\) |
−0.835853 | + | 0.548953i | \(0.815027\pi\) | |||||||
\(3\) | 1.65401 | − | 0.514040i | 0.954945 | − | 0.296781i | ||||
\(4\) | −0.309017 | − | 0.951057i | −0.154508 | − | 0.475528i | ||||
\(5\) | −1.66251 | − | 2.28825i | −0.743496 | − | 1.02333i | −0.998410 | − | 0.0563708i | \(-0.982047\pi\) |
0.254914 | − | 0.966964i | \(-0.417953\pi\) | |||||||
\(6\) | −1.64027 | − | 0.556338i | −0.669638 | − | 0.227124i | ||||
\(7\) | 1.34500 | − | 0.437016i | 0.508361 | − | 0.165177i | −0.0435957 | − | 0.999049i | \(-0.513881\pi\) |
0.551957 | + | 0.833873i | \(0.313881\pi\) | |||||||
\(8\) | −0.927051 | + | 2.85317i | −0.327762 | + | 1.00875i | ||||
\(9\) | 2.47152 | − | 1.70046i | 0.823842 | − | 0.566820i | ||||
\(10\) | 2.82843i | 0.894427i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | − | 1.41421i | −0.288675 | − | 0.408248i | ||||
\(13\) | 2.49376 | − | 3.43237i | 0.691645 | − | 0.951968i | −0.308355 | − | 0.951271i | \(-0.599778\pi\) |
1.00000 | 0.000696272i | \(-0.000221630\pi\) | ||||||||
\(14\) | −1.34500 | − | 0.437016i | −0.359466 | − | 0.116797i | ||||
\(15\) | −3.92606 | − | 2.93019i | −1.01370 | − | 0.756573i | ||||
\(16\) | 0.809017 | − | 0.587785i | 0.202254 | − | 0.146946i | ||||
\(17\) | −4.85410 | + | 3.52671i | −1.17729 | + | 0.855353i | −0.991864 | − | 0.127304i | \(-0.959367\pi\) |
−0.185429 | + | 0.982658i | \(0.559367\pi\) | |||||||
\(18\) | −2.99901 | − | 0.0770245i | −0.706874 | − | 0.0181548i | ||||
\(19\) | −4.03499 | − | 1.31105i | −0.925690 | − | 0.300775i | −0.192891 | − | 0.981220i | \(-0.561786\pi\) |
−0.732799 | + | 0.680445i | \(0.761786\pi\) | |||||||
\(20\) | −1.66251 | + | 2.28825i | −0.371748 | + | 0.511667i | ||||
\(21\) | 2.00000 | − | 1.41421i | 0.436436 | − | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −0.0667106 | + | 5.19572i | −0.0136173 | + | 1.06057i | ||||
\(25\) | −0.927051 | + | 2.85317i | −0.185410 | + | 0.570634i | ||||
\(26\) | −4.03499 | + | 1.31105i | −0.791327 | + | 0.257118i | ||||
\(27\) | 3.21383 | − | 4.08305i | 0.618502 | − | 0.785783i | ||||
\(28\) | −0.831254 | − | 1.14412i | −0.157092 | − | 0.216219i | ||||
\(29\) | −0.618034 | − | 1.90211i | −0.114766 | − | 0.353214i | 0.877132 | − | 0.480249i | \(-0.159454\pi\) |
−0.991898 | + | 0.127036i | \(0.959454\pi\) | |||||||
\(30\) | 1.45393 | + | 4.67826i | 0.265449 | + | 0.854129i | ||||
\(31\) | 1.61803 | + | 1.17557i | 0.290607 | + | 0.211139i | 0.723531 | − | 0.690292i | \(-0.242518\pi\) |
−0.432923 | + | 0.901431i | \(0.642518\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −3.23607 | − | 2.35114i | −0.546995 | − | 0.397415i | ||||
\(36\) | −2.38098 | − | 1.82509i | −0.396830 | − | 0.304181i | ||||
\(37\) | 2.47214 | + | 7.60845i | 0.406417 | + | 1.25082i | 0.919707 | + | 0.392607i | \(0.128427\pi\) |
−0.513290 | + | 0.858215i | \(0.671573\pi\) | |||||||
\(38\) | 2.49376 | + | 3.43237i | 0.404542 | + | 0.556804i | ||||
\(39\) | 2.36034 | − | 6.95908i | 0.377957 | − | 1.11434i | ||||
\(40\) | 8.06998 | − | 2.62210i | 1.27598 | − | 0.414590i | ||||
\(41\) | 1.85410 | − | 5.70634i | 0.289562 | − | 0.891180i | −0.695432 | − | 0.718592i | \(-0.744787\pi\) |
0.984994 | − | 0.172588i | \(-0.0552131\pi\) | |||||||
\(42\) | −2.44929 | − | 0.0314477i | −0.377933 | − | 0.00485249i | ||||
\(43\) | − | 4.24264i | − | 0.646997i | −0.946229 | − | 0.323498i | \(-0.895141\pi\) | ||
0.946229 | − | 0.323498i | \(-0.104859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.00000 | − | 2.82843i | −1.19257 | − | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.68999 | + | 0.874032i | 0.392376 | + | 0.127491i | 0.498559 | − | 0.866856i | \(-0.333863\pi\) |
−0.106183 | + | 0.994347i | \(0.533863\pi\) | |||||||
\(48\) | 1.03598 | − | 1.38807i | 0.149531 | − | 0.200351i | ||||
\(49\) | −4.04508 | + | 2.93893i | −0.577869 | + | 0.419847i | ||||
\(50\) | 2.42705 | − | 1.76336i | 0.343237 | − | 0.249376i | ||||
\(51\) | −6.21588 | + | 8.32844i | −0.870397 | + | 1.16621i | ||||
\(52\) | −4.03499 | − | 1.31105i | −0.559553 | − | 0.181810i | ||||
\(53\) | 3.32502 | − | 4.57649i | 0.456726 | − | 0.628629i | −0.517100 | − | 0.855925i | \(-0.672988\pi\) |
0.973826 | + | 0.227296i | \(0.0729884\pi\) | |||||||
\(54\) | −5.00000 | + | 1.41421i | −0.680414 | + | 0.192450i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.24264i | 0.566947i | ||||||||
\(57\) | −7.34786 | − | 0.0943431i | −0.973248 | − | 0.0124960i | ||||
\(58\) | −0.618034 | + | 1.90211i | −0.0811518 | + | 0.249760i | ||||
\(59\) | 10.7600 | − | 3.49613i | 1.40083 | − | 0.455157i | 0.491371 | − | 0.870951i | \(-0.336496\pi\) |
0.909459 | + | 0.415794i | \(0.136496\pi\) | |||||||
\(60\) | −1.57356 | + | 4.63939i | −0.203146 | + | 0.598942i | ||||
\(61\) | 5.81878 | + | 8.00886i | 0.745018 | + | 1.02543i | 0.998314 | + | 0.0580406i | \(0.0184853\pi\) |
−0.253296 | + | 0.967389i | \(0.581515\pi\) | |||||||
\(62\) | −0.618034 | − | 1.90211i | −0.0784904 | − | 0.241569i | ||||
\(63\) | 2.58107 | − | 3.36721i | 0.325184 | − | 0.424229i | ||||
\(64\) | −5.66312 | − | 4.11450i | −0.707890 | − | 0.514312i | ||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 4.85410 | + | 3.52671i | 0.588646 | + | 0.427677i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.23607 | + | 3.80423i | 0.147738 | + | 0.454692i | ||||
\(71\) | −1.66251 | − | 2.28825i | −0.197303 | − | 0.271565i | 0.698889 | − | 0.715230i | \(-0.253678\pi\) |
−0.896193 | + | 0.443665i | \(0.853678\pi\) | |||||||
\(72\) | 2.56047 | + | 8.62809i | 0.301755 | + | 1.01683i | ||||
\(73\) | 1.34500 | − | 0.437016i | 0.157420 | − | 0.0511489i | −0.229247 | − | 0.973368i | \(-0.573626\pi\) |
0.386667 | + | 0.922219i | \(0.373626\pi\) | |||||||
\(74\) | 2.47214 | − | 7.60845i | 0.287380 | − | 0.884465i | ||||
\(75\) | −0.0667106 | + | 5.19572i | −0.00770308 | + | 0.599951i | ||||
\(76\) | 4.24264i | 0.486664i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | + | 4.24264i | −0.679366 | + | 0.480384i | ||||
\(79\) | 2.49376 | − | 3.43237i | 0.280570 | − | 0.386172i | −0.645353 | − | 0.763885i | \(-0.723290\pi\) |
0.925923 | + | 0.377713i | \(0.123290\pi\) | |||||||
\(80\) | −2.68999 | − | 0.874032i | −0.300750 | − | 0.0977198i | ||||
\(81\) | 3.21687 | − | 8.40546i | 0.357430 | − | 0.933940i | ||||
\(82\) | −4.85410 | + | 3.52671i | −0.536046 | + | 0.389460i | ||||
\(83\) | 12.9443 | − | 9.40456i | 1.42082 | − | 1.03229i | 0.429183 | − | 0.903218i | \(-0.358802\pi\) |
0.991636 | − | 0.129067i | \(-0.0411983\pi\) | |||||||
\(84\) | −1.96303 | − | 1.46510i | −0.214184 | − | 0.159855i | ||||
\(85\) | 16.1400 | + | 5.24419i | 1.75062 | + | 0.568813i | ||||
\(86\) | −2.49376 | + | 3.43237i | −0.268909 | + | 0.370122i | ||||
\(87\) | −2.00000 | − | 2.82843i | −0.214423 | − | 0.303239i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 4.80963 | + | 6.99053i | 0.506979 | + | 0.736866i | ||||
\(91\) | 1.85410 | − | 5.70634i | 0.194363 | − | 0.598187i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.28054 | + | 1.11268i | 0.340176 | + | 0.115379i | ||||
\(94\) | −1.66251 | − | 2.28825i | −0.171475 | − | 0.236015i | ||||
\(95\) | 3.70820 | + | 11.4127i | 0.380454 | + | 1.17092i | ||||
\(96\) | 8.27007 | − | 2.57020i | 0.844060 | − | 0.262320i | ||||
\(97\) | 1.61803 | + | 1.17557i | 0.164286 | + | 0.119361i | 0.666891 | − | 0.745155i | \(-0.267625\pi\) |
−0.502604 | + | 0.864517i | \(0.667625\pi\) | |||||||
\(98\) | 5.00000 | 0.505076 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | 8.09017 | + | 5.87785i | 0.805002 | + | 0.584868i | 0.912377 | − | 0.409350i | \(-0.134245\pi\) |
−0.107375 | + | 0.994219i | \(0.534245\pi\) | |||||||
\(102\) | 9.92408 | − | 3.08424i | 0.982631 | − | 0.305386i | ||||
\(103\) | 2.47214 | + | 7.60845i | 0.243587 | + | 0.749683i | 0.995866 | + | 0.0908382i | \(0.0289546\pi\) |
−0.752279 | + | 0.658845i | \(0.771045\pi\) | |||||||
\(104\) | 7.48128 | + | 10.2971i | 0.733600 | + | 1.00971i | ||||
\(105\) | −6.56108 | − | 2.22535i | −0.640296 | − | 0.217172i | ||||
\(106\) | −5.37999 | + | 1.74806i | −0.522551 | + | 0.169787i | ||||
\(107\) | −4.94427 | + | 15.2169i | −0.477981 | + | 1.47107i | 0.363914 | + | 0.931432i | \(0.381440\pi\) |
−0.841895 | + | 0.539641i | \(0.818560\pi\) | |||||||
\(108\) | −4.87634 | − | 1.79480i | −0.469226 | − | 0.172705i | ||||
\(109\) | − | 4.24264i | − | 0.406371i | −0.979140 | − | 0.203186i | \(-0.934871\pi\) | ||
0.979140 | − | 0.203186i | \(-0.0651295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | + | 11.3137i | 0.759326 | + | 1.07385i | ||||
\(112\) | 0.831254 | − | 1.14412i | 0.0785461 | − | 0.108109i | ||||
\(113\) | 2.68999 | + | 0.874032i | 0.253053 | + | 0.0822220i | 0.432797 | − | 0.901492i | \(-0.357527\pi\) |
−0.179743 | + | 0.983714i | \(0.557527\pi\) | |||||||
\(114\) | 5.88909 | + | 4.39529i | 0.551564 | + | 0.411657i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.61803 | + | 1.17557i | −0.150231 | + | 0.109149i | ||||
\(117\) | 0.326787 | − | 12.7237i | 0.0302115 | − | 1.17631i | ||||
\(118\) | −10.7600 | − | 3.49613i | −0.990536 | − | 0.321845i | ||||
\(119\) | −4.98752 | + | 6.86474i | −0.457206 | + | 0.629289i | ||||
\(120\) | 12.0000 | − | 8.48528i | 1.09545 | − | 0.774597i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 9.89949i | − | 0.896258i | ||||||
\(123\) | 0.133421 | − | 10.3914i | 0.0120302 | − | 0.936965i | ||||
\(124\) | 0.618034 | − | 1.90211i | 0.0555011 | − | 0.170815i | ||||
\(125\) | −5.37999 | + | 1.74806i | −0.481201 | + | 0.156352i | ||||
\(126\) | −4.06732 | + | 1.20702i | −0.362346 | + | 0.107530i | ||||
\(127\) | 5.81878 | + | 8.00886i | 0.516333 | + | 0.710671i | 0.984971 | − | 0.172719i | \(-0.0552552\pi\) |
−0.468638 | + | 0.883390i | \(0.655255\pi\) | |||||||
\(128\) | −0.927051 | − | 2.85317i | −0.0819405 | − | 0.252187i | ||||
\(129\) | −2.18089 | − | 7.01739i | −0.192017 | − | 0.617846i | ||||
\(130\) | 9.70820 | + | 7.05342i | 0.851466 | + | 0.618626i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | −0.520266 | ||||||||
\(134\) | −1.61803 | − | 1.17557i | −0.139777 | − | 0.101554i | ||||
\(135\) | −14.6860 | − | 0.565934i | −1.26397 | − | 0.0487079i | ||||
\(136\) | −5.56231 | − | 17.1190i | −0.476964 | − | 1.46794i | ||||
\(137\) | −1.66251 | − | 2.28825i | −0.142038 | − | 0.195498i | 0.732071 | − | 0.681228i | \(-0.238554\pi\) |
−0.874109 | + | 0.485730i | \(0.838554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.34500 | − | 0.437016i | 0.114081 | − | 0.0370672i | −0.251420 | − | 0.967878i | \(-0.580898\pi\) |
0.365501 | + | 0.930811i | \(0.380898\pi\) | |||||||
\(140\) | −1.23607 | + | 3.80423i | −0.104467 | + | 0.321516i | ||||
\(141\) | 4.89858 | + | 0.0628954i | 0.412534 | + | 0.00529675i | ||||
\(142\) | 2.82843i | 0.237356i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | − | 2.82843i | 0.0833333 | − | 0.235702i | ||||
\(145\) | −3.32502 | + | 4.57649i | −0.276128 | + | 0.380057i | ||||
\(146\) | −1.34500 | − | 0.437016i | −0.111313 | − | 0.0361677i | ||||
\(147\) | −5.17990 | + | 6.94036i | −0.427231 | + | 0.572431i | ||||
\(148\) | 6.47214 | − | 4.70228i | 0.532006 | − | 0.386525i | ||||
\(149\) | −4.85410 | + | 3.52671i | −0.397664 | + | 0.288919i | −0.768589 | − | 0.639743i | \(-0.779041\pi\) |
0.370925 | + | 0.928663i | \(0.379041\pi\) | |||||||
\(150\) | 3.10794 | − | 4.16422i | 0.253762 | − | 0.340007i | ||||
\(151\) | −4.03499 | − | 1.31105i | −0.328363 | − | 0.106692i | 0.140196 | − | 0.990124i | \(-0.455227\pi\) |
−0.468559 | + | 0.883432i | \(0.655227\pi\) | |||||||
\(152\) | 7.48128 | − | 10.2971i | 0.606812 | − | 0.835206i | ||||
\(153\) | −6.00000 | + | 16.9706i | −0.485071 | + | 1.37199i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.65685i | − | 0.454369i | ||||||
\(156\) | −7.34786 | − | 0.0943431i | −0.588300 | − | 0.00755349i | ||||
\(157\) | −6.18034 | + | 19.0211i | −0.493245 | + | 1.51805i | 0.326429 | + | 0.945222i | \(0.394154\pi\) |
−0.819674 | + | 0.572830i | \(0.805846\pi\) | |||||||
\(158\) | −4.03499 | + | 1.31105i | −0.321007 | + | 0.104301i | ||||
\(159\) | 3.14712 | − | 9.27877i | 0.249583 | − | 0.735855i | ||||
\(160\) | −8.31254 | − | 11.4412i | −0.657164 | − | 0.904508i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.54311 | + | 4.90933i | −0.592642 | + | 0.385714i | ||||
\(163\) | −16.1803 | − | 11.7557i | −1.26734 | − | 0.920778i | −0.268249 | − | 0.963350i | \(-0.586445\pi\) |
−0.999093 | + | 0.0425718i | \(0.986445\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.0000 | −1.24184 | ||||||||
\(167\) | −9.70820 | − | 7.05342i | −0.751243 | − | 0.545810i | 0.144969 | − | 0.989436i | \(-0.453692\pi\) |
−0.896212 | + | 0.443626i | \(0.853692\pi\) | |||||||
\(168\) | 2.18089 | + | 7.01739i | 0.168259 | + | 0.541403i | ||||
\(169\) | −1.54508 | − | 4.75528i | −0.118853 | − | 0.365791i | ||||
\(170\) | −9.97505 | − | 13.7295i | −0.765051 | − | 1.05300i | ||||
\(171\) | −12.2020 | + | 3.62105i | −0.933108 | + | 0.276909i | ||||
\(172\) | −4.03499 | + | 1.31105i | −0.307665 | + | 0.0999665i | ||||
\(173\) | 1.85410 | − | 5.70634i | 0.140965 | − | 0.433845i | −0.855505 | − | 0.517794i | \(-0.826753\pi\) |
0.996470 | + | 0.0839492i | \(0.0267533\pi\) | |||||||
\(174\) | −0.0444738 | + | 3.46382i | −0.00337155 | + | 0.262591i | ||||
\(175\) | 4.24264i | 0.320713i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000 | − | 11.3137i | 1.20263 | − | 0.850390i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.68999 | + | 0.874032i | 0.201060 | + | 0.0653282i | 0.407816 | − | 0.913064i | \(-0.366291\pi\) |
−0.206756 | + | 0.978393i | \(0.566291\pi\) | |||||||
\(180\) | −0.217858 | + | 8.48248i | −0.0162382 | + | 0.632247i | ||||
\(181\) | 8.09017 | − | 5.87785i | 0.601338 | − | 0.436897i | −0.245016 | − | 0.969519i | \(-0.578793\pi\) |
0.846353 | + | 0.532622i | \(0.178793\pi\) | |||||||
\(182\) | −4.85410 | + | 3.52671i | −0.359810 | + | 0.261417i | ||||
\(183\) | 13.7412 | + | 10.2557i | 1.01578 | + | 0.758122i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.3001 | − | 18.3060i | 0.977840 | − | 1.34588i | ||||
\(186\) | −2.00000 | − | 2.82843i | −0.146647 | − | 0.207390i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 2.82843i | − | 0.206284i | ||||||
\(189\) | 2.53824 | − | 6.89618i | 0.184629 | − | 0.501624i | ||||
\(190\) | 3.70820 | − | 11.4127i | 0.269021 | − | 0.827963i | ||||
\(191\) | −18.8300 | + | 6.11822i | −1.36249 | + | 0.442699i | −0.896873 | − | 0.442288i | \(-0.854167\pi\) |
−0.465615 | + | 0.884987i | \(0.654167\pi\) | |||||||
\(192\) | −11.4819 | − | 3.89436i | −0.828634 | − | 0.281051i | ||||
\(193\) | −12.4688 | − | 17.1618i | −0.897524 | − | 1.23534i | −0.971251 | − | 0.238058i | \(-0.923489\pi\) |
0.0737265 | − | 0.997278i | \(-0.476511\pi\) | |||||||
\(194\) | −0.618034 | − | 1.90211i | −0.0443723 | − | 0.136564i | ||||
\(195\) | −19.8482 | + | 6.16849i | −1.42136 | + | 0.441734i | ||||
\(196\) | 4.04508 | + | 2.93893i | 0.288935 | + | 0.209923i | ||||
\(197\) | 22.0000 | 1.56744 | 0.783718 | − | 0.621117i | \(-0.213321\pi\) | ||||
0.783718 | + | 0.621117i | \(0.213321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | −7.28115 | − | 5.29007i | −0.514855 | − | 0.374064i | ||||
\(201\) | 3.30803 | − | 1.02808i | 0.233330 | − | 0.0725152i | ||||
\(202\) | −3.09017 | − | 9.51057i | −0.217424 | − | 0.669161i | ||||
\(203\) | −1.66251 | − | 2.28825i | −0.116685 | − | 0.160603i | ||||
\(204\) | 9.84163 | + | 3.33803i | 0.689052 | + | 0.233709i | ||||
\(205\) | −16.1400 | + | 5.24419i | −1.12726 | + | 0.366270i | ||||
\(206\) | 2.47214 | − | 7.60845i | 0.172242 | − | 0.530106i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.24264i | − | 0.294174i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.00000 | + | 5.65685i | 0.276026 | + | 0.390360i | ||||
\(211\) | −15.7938 | + | 21.7383i | −1.08729 | + | 1.49653i | −0.236060 | + | 0.971738i | \(0.575856\pi\) |
−0.851232 | + | 0.524790i | \(0.824144\pi\) | |||||||
\(212\) | −5.37999 | − | 1.74806i | −0.369499 | − | 0.120058i | ||||
\(213\) | −3.92606 | − | 2.93019i | −0.269009 | − | 0.200774i | ||||
\(214\) | 12.9443 | − | 9.40456i | 0.884852 | − | 0.642883i | ||||
\(215\) | −9.70820 | + | 7.05342i | −0.662094 | + | 0.481039i | ||||
\(216\) | 8.67025 | + | 12.9548i | 0.589936 | + | 0.881462i | ||||
\(217\) | 2.68999 | + | 0.874032i | 0.182609 | + | 0.0593332i | ||||
\(218\) | −2.49376 | + | 3.43237i | −0.168899 | + | 0.232469i | ||||
\(219\) | 2.00000 | − | 1.41421i | 0.135147 | − | 0.0955637i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.4558i | 1.71235i | ||||||||
\(222\) | 0.177895 | − | 13.8553i | 0.0119395 | − | 0.929904i | ||||
\(223\) | 7.41641 | − | 22.8254i | 0.496639 | − | 1.52850i | −0.317747 | − | 0.948176i | \(-0.602926\pi\) |
0.814386 | − | 0.580323i | \(-0.197074\pi\) | |||||||
\(224\) | 6.72499 | − | 2.18508i | 0.449332 | − | 0.145997i | ||||
\(225\) | 2.56047 | + | 8.62809i | 0.170698 | + | 0.575206i | ||||
\(226\) | −1.66251 | − | 2.28825i | −0.110588 | − | 0.152212i | ||||
\(227\) | −7.41641 | − | 22.8254i | −0.492244 | − | 1.51497i | −0.821208 | − | 0.570629i | \(-0.806699\pi\) |
0.328963 | − | 0.944343i | \(-0.393301\pi\) | |||||||
\(228\) | 2.18089 | + | 7.01739i | 0.144433 | + | 0.464738i | ||||
\(229\) | 19.4164 | + | 14.1068i | 1.28307 | + | 0.932207i | 0.999641 | − | 0.0267860i | \(-0.00852726\pi\) |
0.283431 | + | 0.958993i | \(0.408527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | 8.09017 | + | 5.87785i | 0.530005 | + | 0.385071i | 0.820360 | − | 0.571848i | \(-0.193773\pi\) |
−0.290355 | + | 0.956919i | \(0.593773\pi\) | |||||||
\(234\) | −7.74320 | + | 10.1016i | −0.506188 | + | 0.660364i | ||||
\(235\) | −2.47214 | − | 7.60845i | −0.161264 | − | 0.496321i | ||||
\(236\) | −6.65003 | − | 9.15298i | −0.432880 | − | 0.595808i | ||||
\(237\) | 2.36034 | − | 6.95908i | 0.153321 | − | 0.452041i | ||||
\(238\) | 8.06998 | − | 2.62210i | 0.523099 | − | 0.169965i | ||||
\(239\) | −4.94427 | + | 15.2169i | −0.319818 | + | 0.984300i | 0.653907 | + | 0.756575i | \(0.273129\pi\) |
−0.973726 | + | 0.227725i | \(0.926871\pi\) | |||||||
\(240\) | −4.89858 | − | 0.0628954i | −0.316202 | − | 0.00405988i | ||||
\(241\) | − | 4.24264i | − | 0.273293i | −0.990620 | − | 0.136646i | \(-0.956368\pi\) | ||
0.990620 | − | 0.136646i | \(-0.0436324\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 5.81878 | − | 8.00886i | 0.372509 | − | 0.512715i | ||||
\(245\) | 13.4500 | + | 4.37016i | 0.859287 | + | 0.279199i | ||||
\(246\) | −6.21588 | + | 8.32844i | −0.396310 | + | 0.531002i | ||||
\(247\) | −14.5623 | + | 10.5801i | −0.926577 | + | 0.673198i | ||||
\(248\) | −4.85410 | + | 3.52671i | −0.308236 | + | 0.223946i | ||||
\(249\) | 16.5757 | − | 22.2092i | 1.05044 | − | 1.40745i | ||||
\(250\) | 5.37999 | + | 1.74806i | 0.340260 | + | 0.110557i | ||||
\(251\) | −14.9626 | + | 20.5942i | −0.944429 | + | 1.29990i | 0.00952890 | + | 0.999955i | \(0.496967\pi\) |
−0.953958 | + | 0.299940i | \(0.903033\pi\) | |||||||
\(252\) | −4.00000 | − | 1.41421i | −0.251976 | − | 0.0890871i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 9.89949i | − | 0.621150i | ||||||
\(255\) | 29.3915 | + | 0.377372i | 1.84056 | + | 0.0236320i | ||||
\(256\) | −5.25329 | + | 16.1680i | −0.328331 | + | 1.01050i | ||||
\(257\) | 10.7600 | − | 3.49613i | 0.671189 | − | 0.218082i | 0.0464552 | − | 0.998920i | \(-0.485208\pi\) |
0.624734 | + | 0.780838i | \(0.285208\pi\) | |||||||
\(258\) | −2.36034 | + | 6.95908i | −0.146948 | + | 0.433253i | ||||
\(259\) | 6.65003 | + | 9.15298i | 0.413213 | + | 0.568739i | ||||
\(260\) | 3.70820 | + | 11.4127i | 0.229973 | + | 0.707784i | ||||
\(261\) | −4.76195 | − | 3.65018i | −0.294758 | − | 0.225940i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0000 | −0.982872 | ||||||||
\(266\) | 4.85410 | + | 3.52671i | 0.297624 | + | 0.216237i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.618034 | − | 1.90211i | −0.0377524 | − | 0.116190i | ||||
\(269\) | 16.6251 | + | 22.8825i | 1.01365 | + | 1.39517i | 0.916562 | + | 0.399892i | \(0.130952\pi\) |
0.0970866 | + | 0.995276i | \(0.469048\pi\) | |||||||
\(270\) | 11.5486 | + | 9.09009i | 0.702826 | + | 0.553205i | ||||
\(271\) | −28.2449 | + | 9.17734i | −1.71576 | + | 0.557483i | −0.991275 | − | 0.131809i | \(-0.957921\pi\) |
−0.724483 | + | 0.689293i | \(0.757921\pi\) | |||||||
\(272\) | −1.85410 | + | 5.70634i | −0.112421 | + | 0.345998i | ||||
\(273\) | 0.133421 | − | 10.3914i | 0.00807502 | − | 0.628919i | ||||
\(274\) | 2.82843i | 0.170872i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.49376 | − | 3.43237i | 0.149836 | − | 0.206231i | −0.727501 | − | 0.686107i | \(-0.759318\pi\) |
0.877336 | + | 0.479876i | \(0.159318\pi\) | |||||||
\(278\) | −1.34500 | − | 0.437016i | −0.0806676 | − | 0.0262105i | ||||
\(279\) | 5.99802 | + | 0.154049i | 0.359092 | + | 0.00922267i | ||||
\(280\) | 9.70820 | − | 7.05342i | 0.580176 | − | 0.421523i | ||||
\(281\) | −4.85410 | + | 3.52671i | −0.289571 | + | 0.210386i | −0.723081 | − | 0.690763i | \(-0.757275\pi\) |
0.433510 | + | 0.901149i | \(0.357275\pi\) | |||||||
\(282\) | −3.92606 | − | 2.93019i | −0.233794 | − | 0.174491i | ||||
\(283\) | 25.5549 | + | 8.30330i | 1.51908 | + | 0.493580i | 0.945515 | − | 0.325577i | \(-0.105559\pi\) |
0.573568 | + | 0.819158i | \(0.305559\pi\) | |||||||
\(284\) | −1.66251 | + | 2.28825i | −0.0986517 | + | 0.135782i | ||||
\(285\) | 12.0000 | + | 16.9706i | 0.710819 | + | 1.00525i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8.48528i | − | 0.500870i | ||||||
\(288\) | 12.3576 | − | 8.50230i | 0.728180 | − | 0.501003i | ||||
\(289\) | 5.87132 | − | 18.0701i | 0.345372 | − | 1.06295i | ||||
\(290\) | 5.37999 | − | 1.74806i | 0.315924 | − | 0.102650i | ||||
\(291\) | 3.28054 | + | 1.11268i | 0.192309 | + | 0.0652262i | ||||
\(292\) | −0.831254 | − | 1.14412i | −0.0486455 | − | 0.0669547i | ||||
\(293\) | −0.618034 | − | 1.90211i | −0.0361059 | − | 0.111123i | 0.931379 | − | 0.364051i | \(-0.118606\pi\) |
−0.967485 | + | 0.252928i | \(0.918606\pi\) | |||||||
\(294\) | 8.27007 | − | 2.57020i | 0.482320 | − | 0.149897i | ||||
\(295\) | −25.8885 | − | 18.8091i | −1.50729 | − | 1.09511i | ||||
\(296\) | −24.0000 | −1.39497 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.96204 | − | 1.54212i | 0.286484 | − | 0.0890344i | ||||
\(301\) | −1.85410 | − | 5.70634i | −0.106869 | − | 0.328908i | ||||
\(302\) | 2.49376 | + | 3.43237i | 0.143500 | + | 0.197511i | ||||
\(303\) | 16.4027 | + | 5.56338i | 0.942311 | + | 0.319608i | ||||
\(304\) | −4.03499 | + | 1.31105i | −0.231423 | + | 0.0751938i | ||||
\(305\) | 8.65248 | − | 26.6296i | 0.495439 | − | 1.52481i | ||||
\(306\) | 14.8291 | − | 10.2028i | 0.847726 | − | 0.583253i | ||||
\(307\) | − | 4.24264i | − | 0.242140i | −0.992644 | − | 0.121070i | \(-0.961367\pi\) | ||
0.992644 | − | 0.121070i | \(-0.0386326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | + | 11.3137i | 0.455104 | + | 0.643614i | ||||
\(310\) | −3.32502 | + | 4.57649i | −0.188848 | + | 0.259927i | ||||
\(311\) | −26.8999 | − | 8.74032i | −1.52536 | − | 0.495618i | −0.578064 | − | 0.815991i | \(-0.696192\pi\) |
−0.947291 | + | 0.320373i | \(0.896192\pi\) | |||||||
\(312\) | 17.6673 | + | 13.1859i | 1.00021 | + | 0.746503i | ||||
\(313\) | −9.70820 | + | 7.05342i | −0.548740 | + | 0.398683i | −0.827321 | − | 0.561730i | \(-0.810136\pi\) |
0.278581 | + | 0.960413i | \(0.410136\pi\) | |||||||
\(314\) | 16.1803 | − | 11.7557i | 0.913109 | − | 0.663413i | ||||
\(315\) | −11.9960 | − | 0.308098i | −0.675901 | − | 0.0173593i | ||||
\(316\) | −4.03499 | − | 1.31105i | −0.226986 | − | 0.0737522i | ||||
\(317\) | −14.9626 | + | 20.5942i | −0.840382 | + | 1.15669i | 0.145519 | + | 0.989355i | \(0.453515\pi\) |
−0.985901 | + | 0.167331i | \(0.946485\pi\) | |||||||
\(318\) | −8.00000 | + | 5.65685i | −0.448618 | + | 0.317221i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 19.7990i | 1.10680i | ||||||||
\(321\) | −0.355790 | + | 27.7105i | −0.0198583 | + | 1.54665i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.2099 | − | 7.86629i | 1.34708 | − | 0.437692i | ||||
\(324\) | −8.98813 | − | 0.461994i | −0.499341 | − | 0.0256664i | ||||
\(325\) | 7.48128 | + | 10.2971i | 0.414987 | + | 0.571181i | ||||
\(326\) | 6.18034 | + | 19.0211i | 0.342297 | + | 1.05348i | ||||
\(327\) | −2.18089 | − | 7.01739i | −0.120603 | − | 0.388062i | ||||
\(328\) | 14.5623 | + | 10.5801i | 0.804069 | + | 0.584190i | ||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | −12.9443 | − | 9.40456i | −0.710409 | − | 0.516143i | ||||
\(333\) | 19.0478 | + | 14.6007i | 1.04381 | + | 0.800114i | ||||
\(334\) | 3.70820 | + | 11.4127i | 0.202904 | + | 0.624474i | ||||
\(335\) | −3.32502 | − | 4.57649i | −0.181665 | − | 0.250040i | ||||
\(336\) | 0.786780 | − | 2.31969i | 0.0429224 | − | 0.126550i | ||||
\(337\) | 30.9349 | − | 10.0514i | 1.68513 | − | 0.547533i | 0.699237 | − | 0.714890i | \(-0.253523\pi\) |
0.985896 | + | 0.167357i | \(0.0535233\pi\) | |||||||
\(338\) | −1.54508 | + | 4.75528i | −0.0840415 | + | 0.258653i | ||||
\(339\) | 4.89858 | + | 0.0628954i | 0.266054 | + | 0.00341601i | ||||
\(340\) | − | 16.9706i | − | 0.920358i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.0000 | + | 4.24264i | 0.648886 | + | 0.229416i | ||||
\(343\) | −9.97505 | + | 13.7295i | −0.538602 | + | 0.741322i | ||||
\(344\) | 12.1050 | + | 3.93314i | 0.652656 | + | 0.212061i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.85410 | + | 3.52671i | −0.260958 | + | 0.189597i | ||||
\(347\) | 12.9443 | − | 9.40456i | 0.694885 | − | 0.504863i | −0.183377 | − | 0.983043i | \(-0.558703\pi\) |
0.878262 | + | 0.478179i | \(0.158703\pi\) | |||||||
\(348\) | −2.07196 | + | 2.77615i | −0.111069 | + | 0.148817i | ||||
\(349\) | −4.03499 | − | 1.31105i | −0.215988 | − | 0.0701788i | 0.199024 | − | 0.979995i | \(-0.436223\pi\) |
−0.415012 | + | 0.909816i | \(0.636223\pi\) | |||||||
\(350\) | 2.49376 | − | 3.43237i | 0.133297 | − | 0.183468i | ||||
\(351\) | −6.00000 | − | 21.2132i | −0.320256 | − | 1.13228i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | −19.5943 | − | 0.251582i | −1.04143 | − | 0.0133714i | ||||
\(355\) | −2.47214 | + | 7.60845i | −0.131207 | + | 0.403815i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.72068 | + | 13.9182i | −0.249845 | + | 0.736627i | ||||
\(358\) | −1.66251 | − | 2.28825i | −0.0878663 | − | 0.120938i | ||||
\(359\) | 6.18034 | + | 19.0211i | 0.326186 | + | 1.00390i | 0.970902 | + | 0.239475i | \(0.0769754\pi\) |
−0.644717 | + | 0.764422i | \(0.723025\pi\) | |||||||
\(360\) | 15.4864 | − | 20.2033i | 0.816204 | − | 1.06481i | ||||
\(361\) | −0.809017 | − | 0.587785i | −0.0425798 | − | 0.0309361i | ||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.00000 | −0.314485 | ||||||||
\(365\) | −3.23607 | − | 2.35114i | −0.169384 | − | 0.123064i | ||||
\(366\) | −5.08874 | − | 16.3739i | −0.265993 | − | 0.855878i | ||||
\(367\) | 2.47214 | + | 7.60845i | 0.129044 | + | 0.397158i | 0.994616 | − | 0.103627i | \(-0.0330448\pi\) |
−0.865572 | + | 0.500785i | \(0.833045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.12094 | − | 17.2562i | −0.266586 | − | 0.898321i | ||||
\(370\) | −21.5200 | + | 6.99226i | −1.11877 | + | 0.363510i | ||||
\(371\) | 2.47214 | − | 7.60845i | 0.128347 | − | 0.395011i | ||||
\(372\) | 0.0444738 | − | 3.46382i | 0.00230586 | − | 0.179590i | ||||
\(373\) | − | 4.24264i | − | 0.219676i | −0.993950 | − | 0.109838i | \(-0.964967\pi\) | ||
0.993950 | − | 0.109838i | \(-0.0350331\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.00000 | + | 5.65685i | −0.413118 | + | 0.292119i | ||||
\(376\) | −4.98752 | + | 6.86474i | −0.257212 | + | 0.354022i | ||||
\(377\) | −8.06998 | − | 2.62210i | −0.415625 | − | 0.135045i | ||||
\(378\) | −6.10695 | + | 4.08719i | −0.314108 | + | 0.210223i | ||||
\(379\) | −9.70820 | + | 7.05342i | −0.498677 | + | 0.362310i | −0.808511 | − | 0.588481i | \(-0.799726\pi\) |
0.309834 | + | 0.950791i | \(0.399726\pi\) | |||||||
\(380\) | 9.70820 | − | 7.05342i | 0.498020 | − | 0.361833i | ||||
\(381\) | 13.7412 | + | 10.2557i | 0.703984 | + | 0.525414i | ||||
\(382\) | 18.8300 | + | 6.11822i | 0.963424 | + | 0.313036i | ||||
\(383\) | 3.32502 | − | 4.57649i | 0.169900 | − | 0.233848i | −0.715573 | − | 0.698538i | \(-0.753834\pi\) |
0.885473 | + | 0.464690i | \(0.153834\pi\) | |||||||
\(384\) | −3.00000 | − | 4.24264i | −0.153093 | − | 0.216506i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.2132i | 1.07972i | ||||||||
\(387\) | −7.21444 | − | 10.4858i | −0.366731 | − | 0.533023i | ||||
\(388\) | 0.618034 | − | 1.90211i | 0.0313759 | − | 0.0965652i | ||||
\(389\) | −18.8300 | + | 6.11822i | −0.954717 | + | 0.310206i | −0.744631 | − | 0.667477i | \(-0.767374\pi\) |
−0.210086 | + | 0.977683i | \(0.567374\pi\) | |||||||
\(390\) | 19.6833 | + | 6.67605i | 0.996700 | + | 0.338055i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.63525 | − | 14.2658i | −0.234116 | − | 0.720534i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.7984 | − | 12.9313i | −0.896669 | − | 0.651468i | ||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | −1.61803 | − | 1.17557i | −0.0811047 | − | 0.0589260i | ||||
\(399\) | −9.92408 | + | 3.08424i | −0.496826 | + | 0.154405i | ||||
\(400\) | 0.927051 | + | 2.85317i | 0.0463525 | + | 0.142658i | ||||
\(401\) | −1.66251 | − | 2.28825i | −0.0830217 | − | 0.114270i | 0.765486 | − | 0.643452i | \(-0.222499\pi\) |
−0.848508 | + | 0.529183i | \(0.822499\pi\) | |||||||
\(402\) | −3.28054 | − | 1.11268i | −0.163619 | − | 0.0554952i | ||||
\(403\) | 8.06998 | − | 2.62210i | 0.401994 | − | 0.130616i | ||||
\(404\) | 3.09017 | − | 9.51057i | 0.153742 | − | 0.473168i | ||||
\(405\) | −24.5818 | + | 6.61316i | −1.22148 | + | 0.328610i | ||||
\(406\) | 2.82843i | 0.140372i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.0000 | − | 25.4558i | −0.891133 | − | 1.26025i | ||||
\(409\) | 2.49376 | − | 3.43237i | 0.123309 | − | 0.169720i | −0.742900 | − | 0.669403i | \(-0.766550\pi\) |
0.866208 | + | 0.499683i | \(0.166550\pi\) | |||||||
\(410\) | 16.1400 | + | 5.24419i | 0.797096 | + | 0.258992i | ||||
\(411\) | −3.92606 | − | 2.93019i | −0.193658 | − | 0.144536i | ||||
\(412\) | 6.47214 | − | 4.70228i | 0.318859 | − | 0.231665i | ||||
\(413\) | 12.9443 | − | 9.40456i | 0.636946 | − | 0.462768i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −43.0399 | − | 13.9845i | −2.11275 | − | 0.686473i | ||||
\(416\) | 12.4688 | − | 17.1618i | 0.611334 | − | 0.841429i | ||||
\(417\) | 2.00000 | − | 1.41421i | 0.0979404 | − | 0.0692543i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 31.1127i | − | 1.51995i | −0.649950 | − | 0.759977i | \(-0.725210\pi\) | ||
0.649950 | − | 0.759977i | \(-0.274790\pi\) | |||||||
\(420\) | −0.0889475 | + | 6.92763i | −0.00434019 | + | 0.338034i | ||||
\(421\) | −6.18034 | + | 19.0211i | −0.301211 | + | 0.927033i | 0.679853 | + | 0.733349i | \(0.262044\pi\) |
−0.981064 | + | 0.193684i | \(0.937956\pi\) | |||||||
\(422\) | 25.5549 | − | 8.30330i | 1.24400 | − | 0.404199i | ||||
\(423\) | 8.13464 | − | 2.41404i | 0.395520 | − | 0.117374i | ||||
\(424\) | 9.97505 | + | 13.7295i | 0.484431 | + | 0.666762i | ||||
\(425\) | −5.56231 | − | 17.1190i | −0.269811 | − | 0.830394i | ||||
\(426\) | 1.45393 | + | 4.67826i | 0.0704429 | + | 0.226662i | ||||
\(427\) | 11.3262 | + | 8.22899i | 0.548115 | + | 0.398229i | ||||
\(428\) | 16.0000 | 0.773389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | 0.578691 | ||||||||
\(431\) | 25.8885 | + | 18.8091i | 1.24701 | + | 0.906004i | 0.998044 | − | 0.0625092i | \(-0.0199103\pi\) |
0.248963 | + | 0.968513i | \(0.419910\pi\) | |||||||
\(432\) | 0.200088 | − | 5.19230i | 0.00962674 | − | 0.249815i | ||||
\(433\) | 9.27051 | + | 28.5317i | 0.445512 | + | 1.37115i | 0.881921 | + | 0.471397i | \(0.156250\pi\) |
−0.436409 | + | 0.899749i | \(0.643750\pi\) | |||||||
\(434\) | −1.66251 | − | 2.28825i | −0.0798029 | − | 0.109839i | ||||
\(435\) | −3.14712 | + | 9.27877i | −0.150893 | + | 0.444883i | ||||
\(436\) | −4.03499 | + | 1.31105i | −0.193241 | + | 0.0627878i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −2.44929 | − | 0.0314477i | −0.117032 | − | 0.00150263i | ||||
\(439\) | 26.8701i | 1.28244i | 0.767358 | + | 0.641219i | \(0.221571\pi\) | ||||
−0.767358 | + | 0.641219i | \(0.778429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 14.1421i | −0.238095 | + | 0.673435i | ||||
\(442\) | 14.9626 | − | 20.5942i | 0.711697 | − | 0.979567i | ||||
\(443\) | −26.8999 | − | 8.74032i | −1.27805 | − | 0.415265i | −0.410160 | − | 0.912014i | \(-0.634527\pi\) |
−0.867895 | + | 0.496748i | \(0.834527\pi\) | |||||||
\(444\) | 8.28784 | − | 11.1046i | 0.393323 | − | 0.527000i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.4164 | + | 14.1068i | −0.919394 | + | 0.667979i | ||||
\(447\) | −6.21588 | + | 8.32844i | −0.294001 | + | 0.393921i | ||||
\(448\) | −9.41498 | − | 3.05911i | −0.444816 | − | 0.144529i | ||||
\(449\) | 3.32502 | − | 4.57649i | 0.156917 | − | 0.215978i | −0.723319 | − | 0.690514i | \(-0.757384\pi\) |
0.880236 | + | 0.474536i | \(0.157384\pi\) | |||||||
\(450\) | 3.00000 | − | 8.48528i | 0.141421 | − | 0.400000i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 2.82843i | − | 0.133038i | ||||||
\(453\) | −7.34786 | − | 0.0943431i | −0.345233 | − | 0.00443263i | ||||
\(454\) | −7.41641 | + | 22.8254i | −0.348069 | + | 1.07125i | ||||
\(455\) | −16.1400 | + | 5.24419i | −0.756653 | + | 0.245852i | ||||
\(456\) | 7.08102 | − | 20.8772i | 0.331599 | − | 0.977666i | ||||
\(457\) | 5.81878 | + | 8.00886i | 0.272191 | + | 0.374639i | 0.923128 | − | 0.384493i | \(-0.125624\pi\) |
−0.650937 | + | 0.759132i | \(0.725624\pi\) | |||||||
\(458\) | −7.41641 | − | 22.8254i | −0.346546 | − | 1.06656i | ||||
\(459\) | −1.20053 | + | 31.1538i | −0.0560358 | + | 1.45413i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0000 | 1.02464 | 0.512321 | − | 0.858794i | \(-0.328786\pi\) | ||||
0.512321 | + | 0.858794i | \(0.328786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(464\) | −1.61803 | − | 1.17557i | −0.0751153 | − | 0.0545745i | ||||
\(465\) | −2.90785 | − | 9.35652i | −0.134848 | − | 0.433898i | ||||
\(466\) | −3.09017 | − | 9.51057i | −0.143149 | − | 0.440568i | ||||
\(467\) | 16.6251 | + | 22.8825i | 0.769317 | + | 1.05887i | 0.996381 | + | 0.0849941i | \(0.0270871\pi\) |
−0.227065 | + | 0.973880i | \(0.572913\pi\) | |||||||
\(468\) | −12.2020 | + | 3.62105i | −0.564036 | + | 0.167383i | ||||
\(469\) | 2.68999 | − | 0.874032i | 0.124212 | − | 0.0403591i | ||||
\(470\) | −2.47214 | + | 7.60845i | −0.114031 | + | 0.350952i | ||||
\(471\) | −0.444738 | + | 34.6382i | −0.0204924 | + | 1.59604i | ||||
\(472\) | 33.9411i | 1.56227i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.00000 | + | 4.24264i | −0.275589 | + | 0.194871i | ||||
\(475\) | 7.48128 | − | 10.2971i | 0.343265 | − | 0.472464i | ||||
\(476\) | 8.06998 | + | 2.62210i | 0.369887 | + | 0.120184i | ||||
\(477\) | 0.435716 | − | 16.9650i | 0.0199501 | − | 0.776773i | ||||
\(478\) | 12.9443 | − | 9.40456i | 0.592057 | − | 0.430155i | ||||
\(479\) | −22.6525 | + | 16.4580i | −1.03502 | + | 0.751985i | −0.969307 | − | 0.245854i | \(-0.920932\pi\) |
−0.0657112 | + | 0.997839i | \(0.520932\pi\) | |||||||
\(480\) | −19.6303 | − | 14.6510i | −0.895997 | − | 0.668722i | ||||
\(481\) | 32.2799 | + | 10.4884i | 1.47184 | + | 0.478229i | ||||
\(482\) | −2.49376 | + | 3.43237i | −0.113588 | + | 0.156340i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 5.65685i | − | 0.256865i | ||||||
\(486\) | −9.95281 | + | 11.9976i | −0.451469 | + | 0.544221i | ||||
\(487\) | 0.618034 | − | 1.90211i | 0.0280058 | − | 0.0861930i | −0.936077 | − | 0.351796i | \(-0.885571\pi\) |
0.964082 | + | 0.265603i | \(0.0855711\pi\) | |||||||
\(488\) | −28.2449 | + | 9.17734i | −1.27859 | + | 0.415439i | ||||
\(489\) | −32.8054 | − | 11.1268i | −1.48351 | − | 0.503169i | ||||
\(490\) | −8.31254 | − | 11.4412i | −0.375522 | − | 0.516862i | ||||
\(491\) | 6.18034 | + | 19.0211i | 0.278915 | + | 0.858412i | 0.988157 | + | 0.153447i | \(0.0490373\pi\) |
−0.709242 | + | 0.704965i | \(0.750963\pi\) | |||||||
\(492\) | −9.92408 | + | 3.08424i | −0.447412 | + | 0.139048i | ||||
\(493\) | 9.70820 | + | 7.05342i | 0.437236 | + | 0.317670i | ||||
\(494\) | 18.0000 | 0.809858 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −3.23607 | − | 2.35114i | −0.145157 | − | 0.105463i | ||||
\(498\) | −26.4642 | + | 8.22465i | −1.18589 | + | 0.368555i | ||||
\(499\) | −4.32624 | − | 13.3148i | −0.193669 | − | 0.596052i | −0.999990 | − | 0.00457310i | \(-0.998544\pi\) |
0.806321 | − | 0.591479i | \(-0.201456\pi\) | |||||||
\(500\) | 3.32502 | + | 4.57649i | 0.148699 | + | 0.204667i | ||||
\(501\) | −19.6833 | − | 6.67605i | −0.879383 | − | 0.298264i | ||||
\(502\) | 24.2099 | − | 7.86629i | 1.08054 | − | 0.351090i | ||||
\(503\) | −4.94427 | + | 15.2169i | −0.220454 | + | 0.678488i | 0.778267 | + | 0.627933i | \(0.216099\pi\) |
−0.998721 | + | 0.0505549i | \(0.983901\pi\) | |||||||
\(504\) | 7.21444 | + | 10.4858i | 0.321357 | + | 0.467074i | ||||
\(505\) | − | 28.2843i | − | 1.25863i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | − | 7.07107i | −0.222058 | − | 0.314037i | ||||
\(508\) | 5.81878 | − | 8.00886i | 0.258166 | − | 0.355336i | ||||
\(509\) | 32.2799 | + | 10.4884i | 1.43078 | + | 0.464889i | 0.919011 | − | 0.394232i | \(-0.128989\pi\) |
0.511772 | + | 0.859121i | \(0.328989\pi\) | |||||||
\(510\) | −23.5564 | − | 17.5812i | −1.04309 | − | 0.778507i | ||||
\(511\) | 1.61803 | − | 1.17557i | 0.0715776 | − | 0.0520042i | ||||
\(512\) | 8.89919 | − | 6.46564i | 0.393292 | − | 0.285744i | ||||
\(513\) | −18.3209 | + | 12.2616i | −0.808885 | + | 0.541362i | ||||
\(514\) | −10.7600 | − | 3.49613i | −0.474602 | − | 0.154208i | ||||
\(515\) | 13.3001 | − | 18.3060i | 0.586071 | − | 0.806657i | ||||
\(516\) | −6.00000 | + | 4.24264i | −0.264135 | + | 0.186772i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 11.3137i | − | 0.497096i | ||||||
\(519\) | 0.133421 | − | 10.3914i | 0.00585654 | − | 0.456134i | ||||
\(520\) | 11.1246 | − | 34.2380i | 0.487846 | − | 1.50144i | ||||
\(521\) | −18.8300 | + | 6.11822i | −0.824955 | + | 0.268044i | −0.690919 | − | 0.722932i | \(-0.742794\pi\) |
−0.134036 | + | 0.990976i | \(0.542794\pi\) | |||||||
\(522\) | 1.70698 | + | 5.75206i | 0.0747126 | + | 0.251761i | ||||
\(523\) | −12.4688 | − | 17.1618i | −0.545223 | − | 0.750435i | 0.444131 | − | 0.895962i | \(-0.353512\pi\) |
−0.989354 | + | 0.145527i | \(0.953512\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.18089 | + | 7.01739i | 0.0951818 | + | 0.306264i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 12.9443 | + | 9.40456i | 0.562263 | + | 0.408508i | ||||
\(531\) | 20.6485 | − | 26.9377i | 0.896069 | − | 1.16900i | ||||
\(532\) | 1.85410 | + | 5.70634i | 0.0803855 | + | 0.247401i | ||||
\(533\) | −14.9626 | − | 20.5942i | −0.648101 | − | 0.892034i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.0399 | − | 13.9845i | 1.86078 | − | 0.604603i | ||||
\(536\) | −1.85410 | + | 5.70634i | −0.0800850 | + | 0.246476i | ||||
\(537\) | 4.89858 | + | 0.0628954i | 0.211389 | + | 0.00271414i | ||||
\(538\) | − | 28.2843i | − | 1.21942i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.00000 | + | 14.1421i | 0.172133 | + | 0.608581i | ||||
\(541\) | 20.7813 | − | 28.6031i | 0.893460 | − | 1.22974i | −0.0790477 | − | 0.996871i | \(-0.525188\pi\) |
0.972508 | − | 0.232871i | \(-0.0748121\pi\) | |||||||
\(542\) | 28.2449 | + | 9.17734i | 1.21322 | + | 0.394200i | ||||
\(543\) | 10.3598 | − | 13.8807i | 0.444582 | − | 0.595679i | ||||
\(544\) | −24.2705 | + | 17.6336i | −1.04059 | + | 0.756033i | ||||
\(545\) | −9.70820 | + | 7.05342i | −0.415854 | + | 0.302135i | ||||
\(546\) | −6.21588 | + | 8.32844i | −0.266015 | + | 0.356424i | ||||
\(547\) | −33.6249 | − | 10.9254i | −1.43770 | − | 0.467136i | −0.516519 | − | 0.856276i | \(-0.672772\pi\) |
−0.921179 | + | 0.389139i | \(0.872772\pi\) | |||||||
\(548\) | −1.66251 | + | 2.28825i | −0.0710188 | + | 0.0977490i | ||||
\(549\) | 28.0000 | + | 9.89949i | 1.19501 | + | 0.422500i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.48528i | 0.361485i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.85410 | − | 5.70634i | 0.0788444 | − | 0.242658i | ||||
\(554\) | −4.03499 | + | 1.31105i | −0.171430 | + | 0.0557011i | ||||
\(555\) | 12.5885 | − | 37.1151i | 0.534351 | − | 1.57545i | ||||
\(556\) | −0.831254 | − | 1.14412i | −0.0352530 | − | 0.0485216i | ||||
\(557\) | −0.618034 | − | 1.90211i | −0.0261869 | − | 0.0805951i | 0.937109 | − | 0.349037i | \(-0.113491\pi\) |
−0.963296 | + | 0.268442i | \(0.913491\pi\) | |||||||
\(558\) | −4.76195 | − | 3.65018i | −0.201590 | − | 0.154524i | ||||
\(559\) | −14.5623 | − | 10.5801i | −0.615920 | − | 0.447492i | ||||
\(560\) | −4.00000 | −0.169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | −9.70820 | − | 7.05342i | −0.409152 | − | 0.297266i | 0.364106 | − | 0.931357i | \(-0.381374\pi\) |
−0.773258 | + | 0.634091i | \(0.781374\pi\) | |||||||
\(564\) | −1.45393 | − | 4.67826i | −0.0612213 | − | 0.196990i | ||||
\(565\) | −2.47214 | − | 7.60845i | −0.104004 | − | 0.320090i | ||||
\(566\) | −15.7938 | − | 21.7383i | −0.663864 | − | 0.913730i | ||||
\(567\) | 0.653359 | − | 12.7111i | 0.0274385 | − | 0.533818i | ||||
\(568\) | 8.06998 | − | 2.62210i | 0.338609 | − | 0.110021i | ||||
\(569\) | −11.7426 | + | 36.1401i | −0.492277 | + | 1.51507i | 0.328880 | + | 0.944372i | \(0.393329\pi\) |
−0.821157 | + | 0.570702i | \(0.806671\pi\) | |||||||
\(570\) | 0.266843 | − | 20.7829i | 0.0111768 | − | 0.870500i | ||||
\(571\) | 26.8701i | 1.12448i | 0.826975 | + | 0.562238i | \(0.190060\pi\) | ||||
−0.826975 | + | 0.562238i | \(0.809940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.0000 | + | 19.7990i | −1.16972 | + | 0.827115i | ||||
\(574\) | −4.98752 | + | 6.86474i | −0.208175 | + | 0.286529i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −20.9931 | − | 0.539171i | −0.874712 | − | 0.0224655i | ||||
\(577\) | 25.8885 | − | 18.8091i | 1.07775 | − | 0.783034i | 0.100464 | − | 0.994941i | \(-0.467967\pi\) |
0.977290 | + | 0.211906i | \(0.0679672\pi\) | |||||||
\(578\) | −15.3713 | + | 11.1679i | −0.639363 | + | 0.464524i | ||||
\(579\) | −29.4455 | − | 21.9765i | −1.22371 | − | 0.913310i | ||||
\(580\) | 5.37999 | + | 1.74806i | 0.223392 | + | 0.0725844i | ||||
\(581\) | 13.3001 | − | 18.3060i | 0.551780 | − | 0.759459i | ||||
\(582\) | −2.00000 | − | 2.82843i | −0.0829027 | − | 0.117242i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.24264i | 0.175562i | ||||||||
\(585\) | −29.6583 | + | 20.4055i | −1.22622 | + | 0.843665i | ||||
\(586\) | −0.618034 | + | 1.90211i | −0.0255307 | + | 0.0785756i | ||||
\(587\) | 10.7600 | − | 3.49613i | 0.444112 | − | 0.144301i | −0.0784201 | − | 0.996920i | \(-0.524988\pi\) |
0.522532 | + | 0.852620i | \(0.324988\pi\) | |||||||
\(588\) | 8.20135 | + | 2.78169i | 0.338218 | + | 0.114715i | ||||
\(589\) | −4.98752 | − | 6.86474i | −0.205507 | − | 0.282857i | ||||
\(590\) | 9.88854 | + | 30.4338i | 0.407105 | + | 1.25294i | ||||
\(591\) | 36.3883 | − | 11.3089i | 1.49681 | − | 0.465186i | ||||
\(592\) | 6.47214 | + | 4.70228i | 0.266003 | + | 0.193263i | ||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | 0.983904 | ||||||||
\(596\) | 4.85410 | + | 3.52671i | 0.198832 | + | 0.144460i | ||||
\(597\) | 3.30803 | − | 1.02808i | 0.135389 | − | 0.0420766i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.9501 | − | 27.4589i | −0.815139 | − | 1.12194i | −0.990510 | − | 0.137440i | \(-0.956113\pi\) |
0.175371 | − | 0.984502i | \(-0.443887\pi\) | |||||||
\(600\) | −14.7624 | − | 5.00704i | −0.602674 | − | 0.204411i | ||||
\(601\) | −28.2449 | + | 9.17734i | −1.15214 | + | 0.374351i | −0.821947 | − | 0.569564i | \(-0.807112\pi\) |
−0.330188 | + | 0.943915i | \(0.607112\pi\) | |||||||
\(602\) | −1.85410 | + | 5.70634i | −0.0755676 | + | 0.232573i | ||||
\(603\) | 4.94305 | − | 3.40092i | 0.201297 | − | 0.138496i | ||||
\(604\) | 4.24264i | 0.172631i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.0000 | − | 14.1421i | −0.406222 | − | 0.574485i | ||||
\(607\) | 2.49376 | − | 3.43237i | 0.101219 | − | 0.139316i | −0.755403 | − | 0.655260i | \(-0.772559\pi\) |
0.856622 | + | 0.515945i | \(0.172559\pi\) | |||||||
\(608\) | −20.1750 | − | 6.55524i | −0.818202 | − | 0.265850i | ||||
\(609\) | −3.92606 | − | 2.93019i | −0.159092 | − | 0.118737i | ||||
\(610\) | −22.6525 | + | 16.4580i | −0.917172 | + | 0.666364i | ||||
\(611\) | 9.70820 | − | 7.05342i | 0.392752 | − | 0.285351i | ||||
\(612\) | 17.9941 | + | 0.462147i | 0.727367 | + | 0.0186812i | ||||
\(613\) | −4.03499 | − | 1.31105i | −0.162972 | − | 0.0529527i | 0.226395 | − | 0.974036i | \(-0.427306\pi\) |
−0.389367 | + | 0.921083i | \(0.627306\pi\) | |||||||
\(614\) | −2.49376 | + | 3.43237i | −0.100640 | + | 0.138519i | ||||
\(615\) | −24.0000 | + | 16.9706i | −0.967773 | + | 0.684319i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 31.1127i | − | 1.25255i | −0.779602 | − | 0.626275i | \(-0.784579\pi\) | ||
0.779602 | − | 0.626275i | \(-0.215421\pi\) | |||||||
\(618\) | 0.177895 | − | 13.8553i | 0.00715599 | − | 0.557340i | ||||
\(619\) | −6.18034 | + | 19.0211i | −0.248409 | + | 0.764524i | 0.746648 | + | 0.665219i | \(0.231662\pi\) |
−0.995057 | + | 0.0993047i | \(0.968338\pi\) | |||||||
\(620\) | −5.37999 | + | 1.74806i | −0.216066 | + | 0.0702039i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.6251 | + | 22.8825i | 0.666605 | + | 0.917503i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.18089 | − | 7.01739i | −0.0873054 | − | 0.280920i | ||||
\(625\) | 25.0795 | + | 18.2213i | 1.00318 | + | 0.728854i | ||||
\(626\) | 12.0000 | 0.479616 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.0000 | 0.798087 | ||||||||
\(629\) | −38.8328 | − | 28.2137i | −1.54837 | − | 1.12495i | ||||
\(630\) | 9.52391 | + | 7.30035i | 0.379442 | + | 0.290853i | ||||
\(631\) | −4.32624 | − | 13.3148i | −0.172225 | − | 0.530053i | 0.827271 | − | 0.561803i | \(-0.189892\pi\) |
−0.999496 | + | 0.0317495i | \(0.989892\pi\) | |||||||
\(632\) | 7.48128 | + | 10.2971i | 0.297590 | + | 0.409597i | ||||
\(633\) | −14.9488 | + | 44.0742i | −0.594162 | + | 1.75179i | ||||
\(634\) | 24.2099 | − | 7.86629i | 0.961500 | − | 0.312410i | ||||
\(635\) | 8.65248 | − | 26.6296i | 0.343363 | − | 1.05676i | ||||
\(636\) | −9.79715 | − | 0.125791i | −0.388482 | − | 0.00498793i | ||||
\(637\) | 21.2132i | 0.840498i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | − | 2.82843i | −0.316475 | − | 0.111891i | ||||
\(640\) | −4.98752 | + | 6.86474i | −0.197149 | + | 0.271353i | ||||
\(641\) | −26.8999 | − | 8.74032i | −1.06248 | − | 0.345222i | −0.274928 | − | 0.961465i | \(-0.588654\pi\) |
−0.787556 | + | 0.616243i | \(0.788654\pi\) | |||||||
\(642\) | 16.5757 | − | 22.2092i | 0.654190 | − | 0.876526i | ||||
\(643\) | −9.70820 | + | 7.05342i | −0.382854 | + | 0.278160i | −0.762521 | − | 0.646963i | \(-0.776039\pi\) |
0.379667 | + | 0.925123i | \(0.376039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.4318 | + | 16.6569i | −0.489500 | + | 0.655864i | ||||
\(646\) | −24.2099 | − | 7.86629i | −0.952528 | − | 0.309495i | ||||
\(647\) | 3.32502 | − | 4.57649i | 0.130720 | − | 0.179920i | −0.738640 | − | 0.674100i | \(-0.764532\pi\) |
0.869360 | + | 0.494180i | \(0.164532\pi\) | |||||||
\(648\) | 21.0000 | + | 16.9706i | 0.824958 | + | 0.666667i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 12.7279i | − | 0.499230i | ||||||
\(651\) | 4.89858 | + | 0.0628954i | 0.191990 | + | 0.00246506i | ||||
\(652\) | −6.18034 | + | 19.0211i | −0.242041 | + | 0.744925i | ||||
\(653\) | 10.7600 | − | 3.49613i | 0.421070 | − | 0.136814i | −0.0908151 | − | 0.995868i | \(-0.528947\pi\) |
0.511885 | + | 0.859054i | \(0.328947\pi\) | |||||||
\(654\) | −2.36034 | + | 6.95908i | −0.0922966 | + | 0.272122i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.85410 | − | 5.70634i | −0.0723905 | − | 0.222795i | ||||
\(657\) | 2.58107 | − | 3.36721i | 0.100697 | − | 0.131367i | ||||
\(658\) | −3.23607 | − | 2.35114i | −0.126155 | − | 0.0916570i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0000 | −0.777910 | −0.388955 | − | 0.921257i | \(-0.627164\pi\) | ||||
−0.388955 | + | 0.921257i | \(0.627164\pi\) | |||||||
\(662\) | 16.1803 | + | 11.7557i | 0.628867 | + | 0.456898i | ||||
\(663\) | 13.0853 | + | 42.1043i | 0.508192 | + | 1.63520i | ||||
\(664\) | 14.8328 | + | 45.6507i | 0.575625 | + | 1.77159i | ||||
\(665\) | 9.97505 | + | 13.7295i | 0.386816 | + | 0.532406i | ||||
\(666\) | −6.82793 | − | 23.0082i | −0.264577 | − | 0.891551i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −3.70820 | + | 11.4127i | −0.143475 | + | 0.441570i | ||||
\(669\) | 0.533685 | − | 41.5658i | 0.0206335 | − | 1.60703i | ||||
\(670\) | 5.65685i | 0.218543i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 10.0000 | − | 7.07107i | 0.385758 | − | 0.272772i | ||||
\(673\) | 2.49376 | − | 3.43237i | 0.0961274 | − | 0.132308i | −0.758244 | − | 0.651971i | \(-0.773942\pi\) |
0.854371 | + | 0.519663i | \(0.173942\pi\) | |||||||
\(674\) | −30.9349 | − | 10.0514i | −1.19157 | − | 0.387164i | ||||
\(675\) | 8.67025 | + | 12.9548i | 0.333718 | + | 0.498630i | ||||
\(676\) | −4.04508 | + | 2.93893i | −0.155580 | + | 0.113036i | ||||
\(677\) | 30.7426 | − | 22.3358i | 1.18154 | − | 0.858436i | 0.189192 | − | 0.981940i | \(-0.439413\pi\) |
0.992344 | + | 0.123504i | \(0.0394132\pi\) | |||||||
\(678\) | −3.92606 | − | 2.93019i | −0.150780 | − | 0.112533i | ||||
\(679\) | 2.68999 | + | 0.874032i | 0.103232 | + | 0.0335423i | ||||
\(680\) | −29.9251 | + | 41.1884i | −1.14758 | + | 1.57950i | ||||
\(681\) | −24.0000 | − | 33.9411i | −0.919682 | − | 1.30063i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.1127i | 1.19049i | 0.803543 | + | 0.595247i | \(0.202946\pi\) | ||||
−0.803543 | + | 0.595247i | \(0.797054\pi\) | |||||||
\(684\) | 7.21444 | + | 10.4858i | 0.275851 | + | 0.400934i | ||||
\(685\) | −2.47214 | + | 7.60845i | −0.0944555 | + | 0.290704i | ||||
\(686\) | 16.1400 | − | 5.24419i | 0.616227 | − | 0.200224i | ||||
\(687\) | 39.3665 | + | 13.3521i | 1.50193 | + | 0.509414i | ||||
\(688\) | −2.49376 | − | 3.43237i | −0.0950738 | − | 0.130858i | ||||
\(689\) | −7.41641 | − | 22.8254i | −0.282543 | − | 0.869577i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.1803 | − | 11.7557i | −0.615529 | − | 0.447208i | 0.235828 | − | 0.971795i | \(-0.424220\pi\) |
−0.851357 | + | 0.524587i | \(0.824220\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | −3.23607 | − | 2.35114i | −0.122751 | − | 0.0891839i | ||||
\(696\) | 9.92408 | − | 3.08424i | 0.376171 | − | 0.116908i | ||||
\(697\) | 11.1246 | + | 34.2380i | 0.421375 | + | 1.29686i | ||||
\(698\) | 2.49376 | + | 3.43237i | 0.0943903 | + | 0.129917i | ||||
\(699\) | 16.4027 | + | 5.56338i | 0.620407 | + | 0.210426i | ||||
\(700\) | 4.03499 | − | 1.31105i | 0.152508 | − | 0.0495530i | ||||
\(701\) | 1.85410 | − | 5.70634i | 0.0700285 | − | 0.215525i | −0.909917 | − | 0.414790i | \(-0.863855\pi\) |
0.979946 | + | 0.199264i | \(0.0638552\pi\) | |||||||
\(702\) | −7.61471 | + | 20.6886i | −0.287399 | + | 0.780839i | ||||
\(703\) | − | 33.9411i | − | 1.28011i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | − | 11.3137i | −0.301297 | − | 0.426099i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.4500 | + | 4.37016i | 0.505838 | + | 0.164357i | ||||
\(708\) | −15.7042 | − | 11.7208i | −0.590202 | − | 0.440494i | ||||
\(709\) | 25.8885 | − | 18.8091i | 0.972265 | − | 0.706392i | 0.0162981 | − | 0.999867i | \(-0.494812\pi\) |
0.955967 | + | 0.293476i | \(0.0948119\pi\) | |||||||
\(710\) | 6.47214 | − | 4.70228i | 0.242895 | − | 0.176473i | ||||
\(711\) | 0.326787 | − | 12.7237i | 0.0122555 | − | 0.477177i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 12.0000 | − | 8.48528i | 0.449089 | − | 0.317554i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 2.82843i | − | 0.105703i | ||||||
\(717\) | −0.355790 | + | 27.7105i | −0.0132872 | + | 1.03487i | ||||
\(718\) | 6.18034 | − | 19.0211i | 0.230648 | − | 0.709862i | ||||
\(719\) | −18.8300 | + | 6.11822i | −0.702239 | + | 0.228171i | −0.638306 | − | 0.769783i | \(-0.720364\pi\) |
−0.0639332 | + | 0.997954i | \(0.520364\pi\) | |||||||
\(720\) | −8.13464 | + | 2.41404i | −0.303160 | + | 0.0899658i | ||||
\(721\) | 6.65003 | + | 9.15298i | 0.247660 | + | 0.340875i | ||||
\(722\) | 0.309017 | + | 0.951057i | 0.0115004 | + | 0.0353947i | ||||
\(723\) | −2.18089 | − | 7.01739i | −0.0811081 | − | 0.260979i | ||||
\(724\) | −8.09017 | − | 5.87785i | −0.300669 | − | 0.218449i | ||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | 0.0741759 | 0.0370879 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370879 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(728\) | 14.5623 | + | 10.5801i | 0.539715 | + | 0.392126i | ||||
\(729\) | −6.34258 | − | 26.2445i | −0.234910 | − | 0.972017i | ||||
\(730\) | 1.23607 | + | 3.80423i | 0.0457489 | + | 0.140801i | ||||
\(731\) | 14.9626 | + | 20.5942i | 0.553411 | + | 0.761704i | ||||
\(732\) | 5.50746 | − | 16.2379i | 0.203562 | − | 0.600168i | ||||
\(733\) | 1.34500 | − | 0.437016i | 0.0496786 | − | 0.0161416i | −0.284072 | − | 0.958803i | \(-0.591686\pi\) |
0.333751 | + | 0.942661i | \(0.391686\pi\) | |||||||
\(734\) | 2.47214 | − | 7.60845i | 0.0912482 | − | 0.280833i | ||||
\(735\) | 24.4929 | + | 0.314477i | 0.903433 | + | 0.0115997i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.00000 | + | 16.9706i | −0.220863 | + | 0.624695i | ||||
\(739\) | 2.49376 | − | 3.43237i | 0.0917345 | − | 0.126262i | −0.760683 | − | 0.649124i | \(-0.775136\pi\) |
0.852417 | + | 0.522862i | \(0.175136\pi\) | |||||||
\(740\) | −21.5200 | − | 6.99226i | −0.791089 | − | 0.257040i | ||||
\(741\) | −18.6476 | + | 24.9853i | −0.685038 | + | 0.917858i | ||||
\(742\) | −6.47214 | + | 4.70228i | −0.237600 | + | 0.172626i | ||||
\(743\) | 12.9443 | − | 9.40456i | 0.474879 | − | 0.345020i | −0.324461 | − | 0.945899i | \(-0.605183\pi\) |
0.799340 | + | 0.600879i | \(0.205183\pi\) | |||||||
\(744\) | −6.21588 | + | 8.32844i | −0.227885 | + | 0.305335i | ||||
\(745\) | 16.1400 | + | 5.24419i | 0.591323 | + | 0.192132i | ||||
\(746\) | −2.49376 | + | 3.43237i | −0.0913031 | + | 0.125668i | ||||
\(747\) | 16.0000 | − | 45.2548i | 0.585409 | − | 1.65579i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.6274i | 0.826788i | ||||||||
\(750\) | 9.79715 | + | 0.125791i | 0.357741 | + | 0.00459323i | ||||
\(751\) | 0.618034 | − | 1.90211i | 0.0225524 | − | 0.0694091i | −0.939147 | − | 0.343516i | \(-0.888382\pi\) |
0.961699 | + | 0.274107i | \(0.0883821\pi\) | |||||||
\(752\) | 2.68999 | − | 0.874032i | 0.0980940 | − | 0.0318727i | ||||
\(753\) | −14.1620 | + | 41.7545i | −0.516094 | + | 1.52162i | ||||
\(754\) | 4.98752 | + | 6.86474i | 0.181635 | + | 0.249999i | ||||
\(755\) | 3.70820 | + | 11.4127i | 0.134955 | + | 0.415350i | ||||
\(756\) | −7.34302 | − | 0.282967i | −0.267063 | − | 0.0102914i | ||||
\(757\) | −16.1803 | − | 11.7557i | −0.588084 | − | 0.427268i | 0.253545 | − | 0.967324i | \(-0.418403\pi\) |
−0.841630 | + | 0.540055i | \(0.818403\pi\) | |||||||
\(758\) | 12.0000 | 0.435860 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −36.0000 | −1.30586 | ||||||||
\(761\) | 8.09017 | + | 5.87785i | 0.293268 | + | 0.213072i | 0.724684 | − | 0.689081i | \(-0.241986\pi\) |
−0.431416 | + | 0.902153i | \(0.641986\pi\) | |||||||
\(762\) | −5.08874 | − | 16.3739i | −0.184346 | − | 0.593164i | ||||
\(763\) | −1.85410 | − | 5.70634i | −0.0671230 | − | 0.206583i | ||||
\(764\) | 11.6376 | + | 16.0177i | 0.421032 | + | 0.579501i | ||||
\(765\) | 48.8079 | − | 14.4842i | 1.76465 | − | 0.523678i | ||||
\(766\) | −5.37999 | + | 1.74806i | −0.194387 | + | 0.0631601i | ||||
\(767\) | 14.8328 | − | 45.6507i | 0.535582 | − | 1.64835i | ||||
\(768\) | −0.378027 | + | 29.4424i | −0.0136409 | + | 1.06241i | ||||
\(769\) | − | 35.3553i | − | 1.27495i | −0.770473 | − | 0.637473i | \(-0.779980\pi\) | ||
0.770473 | − | 0.637473i | \(-0.220020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0000 | − | 11.3137i | 0.576226 | − | 0.407453i | ||||
\(772\) | −12.4688 | + | 17.1618i | −0.448762 | + | 0.617668i | ||||
\(773\) | 32.2799 | + | 10.4884i | 1.16103 | + | 0.377241i | 0.825287 | − | 0.564713i | \(-0.191013\pi\) |
0.335741 | + | 0.941954i | \(0.391013\pi\) | |||||||
\(774\) | −0.326787 | + | 12.7237i | −0.0117461 | + | 0.457345i | ||||
\(775\) | −4.85410 | + | 3.52671i | −0.174364 | + | 0.126683i | ||||
\(776\) | −4.85410 | + | 3.52671i | −0.174252 | + | 0.126602i | ||||
\(777\) | 15.7042 | + | 11.7208i | 0.563387 | + | 0.420480i | ||||
\(778\) | 18.8300 | + | 6.11822i | 0.675087 | + | 0.219349i | ||||
\(779\) | −14.9626 | + | 20.5942i | −0.536090 | + | 0.737864i | ||||
\(780\) | 12.0000 | + | 16.9706i | 0.429669 | + | 0.607644i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.75268 | − | 3.58961i | −0.348532 | − | 0.128282i | ||||
\(784\) | −1.54508 | + | 4.75528i | −0.0551816 | + | 0.169832i | ||||
\(785\) | 53.7999 | − | 17.4806i | 1.92020 | − | 0.623911i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.4688 | − | 17.1618i | −0.444465 | − | 0.611754i | 0.526732 | − | 0.850031i | \(-0.323417\pi\) |
−0.971197 | + | 0.238278i | \(0.923417\pi\) | |||||||
\(788\) | −6.79837 | − | 20.9232i | −0.242182 | − | 0.745360i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.70820 | + | 7.05342i | 0.345402 | + | 0.250950i | ||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.0000 | 1.49146 | ||||||||
\(794\) | −1.61803 | − | 1.17557i | −0.0574219 | − | 0.0417194i | ||||
\(795\) | −26.4642 | + | 8.22465i | −0.938589 | + | 0.291698i | ||||
\(796\) | −0.618034 | − | 1.90211i | −0.0219056 | − | 0.0674186i | ||||
\(797\) | −1.66251 | − | 2.28825i | −0.0588890 | − | 0.0810538i | 0.778557 | − | 0.627574i | \(-0.215952\pi\) |
−0.837446 | + | 0.546520i | \(0.815952\pi\) | |||||||
\(798\) | 9.84163 | + | 3.33803i | 0.348390 | + | 0.118165i | ||||
\(799\) | −16.1400 | + | 5.24419i | −0.570991 | + | 0.185526i | ||||
\(800\) | −4.63525 | + | 14.2658i | −0.163881 | + | 0.504374i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.82843i | 0.0998752i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.00000 | − | 2.82843i | −0.0705346 | − | 0.0997509i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.06998 | − | 2.62210i | −0.284253 | − | 0.0923594i | ||||
\(807\) | 39.2606 | + | 29.3019i | 1.38204 | + | 1.03148i | ||||
\(808\) | −24.2705 | + | 17.6336i | −0.853834 | + | 0.620346i | ||||
\(809\) | −40.4508 | + | 29.3893i | −1.42218 | + | 1.03327i | −0.430769 | + | 0.902462i | \(0.641757\pi\) |
−0.991408 | + | 0.130809i | \(0.958243\pi\) | |||||||
\(810\) | 23.7742 | + | 9.09868i | 0.835341 | + | 0.319695i | ||||
\(811\) | 25.5549 | + | 8.30330i | 0.897355 | + | 0.291568i | 0.721145 | − | 0.692784i | \(-0.243616\pi\) |
0.176210 | + | 0.984353i | \(0.443616\pi\) | |||||||
\(812\) | −1.66251 | + | 2.28825i | −0.0583426 | + | 0.0803017i | ||||
\(813\) | −42.0000 | + | 29.6985i | −1.47300 | + | 1.04157i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 56.5685i | 1.98151i | ||||||||
\(816\) | −0.133421 | + | 10.3914i | −0.00467068 | + | 0.363773i | ||||
\(817\) | −5.56231 | + | 17.1190i | −0.194600 | + | 0.598919i | ||||
\(818\) | −4.03499 | + | 1.31105i | −0.141080 | + | 0.0458397i | ||||
\(819\) | −5.12094 | − | 17.2562i | −0.178940 | − | 0.602980i | ||||
\(820\) | 9.97505 | + | 13.7295i | 0.348344 | + | 0.479454i | ||||
\(821\) | 12.9787 | + | 39.9444i | 0.452960 | + | 1.39407i | 0.873513 | + | 0.486800i | \(0.161836\pi\) |
−0.420553 | + | 0.907268i | \(0.638164\pi\) | |||||||
\(822\) | 1.45393 | + | 4.67826i | 0.0507115 | + | 0.163173i | ||||
\(823\) | 19.4164 | + | 14.1068i | 0.676813 | + | 0.491734i | 0.872299 | − | 0.488973i | \(-0.162628\pi\) |
−0.195486 | + | 0.980707i | \(0.562628\pi\) | |||||||
\(824\) | −24.0000 | −0.836080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.0000 | −0.556711 | ||||||||
\(827\) | −9.70820 | − | 7.05342i | −0.337587 | − | 0.245272i | 0.406056 | − | 0.913848i | \(-0.366904\pi\) |
−0.743643 | + | 0.668577i | \(0.766904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.32624 | − | 13.3148i | −0.150256 | − | 0.462442i | 0.847393 | − | 0.530966i | \(-0.178171\pi\) |
−0.997649 | + | 0.0685244i | \(0.978171\pi\) | |||||||
\(830\) | 26.6001 | + | 36.6119i | 0.923304 | + | 1.27082i | ||||
\(831\) | 2.36034 | − | 6.95908i | 0.0818793 | − | 0.241408i | ||||
\(832\) | −28.2449 | + | 9.17734i | −0.979217 | + | 0.318167i | ||||
\(833\) | 9.27051 | − | 28.5317i | 0.321204 | − | 0.988565i | ||||
\(834\) | −2.44929 | − | 0.0314477i | −0.0848119 | − | 0.00108894i | ||||
\(835\) | 33.9411i | 1.17458i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0000 | − | 2.82843i | 0.345651 | − | 0.0977647i | ||||
\(838\) | −18.2876 | + | 25.1707i | −0.631734 | + | 0.869507i | ||||
\(839\) | 32.2799 | + | 10.4884i | 1.11443 | + | 0.362099i | 0.807638 | − | 0.589678i | \(-0.200745\pi\) |
0.306789 | + | 0.951778i | \(0.400745\pi\) | |||||||
\(840\) | 12.4318 | − | 16.6569i | 0.428936 | − | 0.574717i | ||||
\(841\) | 20.2254 | − | 14.6946i | 0.697428 | − | 0.506711i | ||||
\(842\) | 16.1803 | − | 11.7557i | 0.557611 | − | 0.405128i | ||||
\(843\) | −6.21588 | + | 8.32844i | −0.214086 | + | 0.286847i | ||||
\(844\) | 25.5549 | + | 8.30330i | 0.879637 | + | 0.285812i | ||||
\(845\) | −8.31254 | + | 11.4412i | −0.285960 | + | 0.393590i | ||||
\(846\) | −8.00000 | − | 2.82843i | −0.275046 | − | 0.0972433i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 5.65685i | − | 0.194257i | ||||||
\(849\) | 46.5365 | + | 0.597506i | 1.59713 | + | 0.0205064i | ||||
\(850\) | −5.56231 | + | 17.1190i | −0.190786 | + | 0.587177i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −1.57356 | + | 4.63939i | −0.0539093 | + | 0.158943i | ||||
\(853\) | 24.1064 | + | 33.1796i | 0.825386 | + | 1.13605i | 0.988764 | + | 0.149483i | \(0.0477609\pi\) |
−0.163378 | + | 0.986564i | \(0.552239\pi\) | |||||||
\(854\) | −4.32624 | − | 13.3148i | −0.148041 | − | 0.455623i | ||||
\(855\) | 28.5717 | + | 21.9011i | 0.977132 | + | 0.749001i | ||||
\(856\) | −38.8328 | − | 28.2137i | −1.32728 | − | 0.964324i | ||||
\(857\) | −22.0000 | −0.751506 | −0.375753 | − | 0.926720i | \(-0.622616\pi\) | ||||
−0.375753 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0000 | −0.682391 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(860\) | 9.70820 | + | 7.05342i | 0.331047 | + | 0.240520i | ||||
\(861\) | −4.36178 | − | 14.0348i | −0.148649 | − | 0.478304i | ||||
\(862\) | −9.88854 | − | 30.4338i | −0.336805 | − | 1.03658i | ||||
\(863\) | −19.9501 | − | 27.4589i | −0.679109 | − | 0.934713i | 0.320814 | − | 0.947142i | \(-0.396044\pi\) |
−0.999923 | + | 0.0124289i | \(0.996044\pi\) | |||||||
\(864\) | 16.0692 | − | 20.4152i | 0.546684 | − | 0.694541i | ||||
\(865\) | −16.1400 | + | 5.24419i | −0.548775 | + | 0.178308i | ||||
\(866\) | 9.27051 | − | 28.5317i | 0.315025 | − | 0.969546i | ||||
\(867\) | 0.422501 | − | 32.9063i | 0.0143489 | − | 1.11755i | ||||
\(868\) | − | 2.82843i | − | 0.0960031i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 8.00000 | − | 5.65685i | 0.271225 | − | 0.191785i | ||||
\(871\) | 4.98752 | − | 6.86474i | 0.168996 | − | 0.232603i | ||||
\(872\) | 12.1050 | + | 3.93314i | 0.409926 | + | 0.133193i | ||||
\(873\) | 5.99802 | + | 0.154049i | 0.203002 | + | 0.00521377i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.47214 | + | 4.70228i | −0.218798 | + | 0.158966i | ||||
\(876\) | −1.96303 | − | 1.46510i | −0.0663247 | − | 0.0495010i | ||||
\(877\) | −33.6249 | − | 10.9254i | −1.13543 | − | 0.368925i | −0.319795 | − | 0.947487i | \(-0.603614\pi\) |
−0.815638 | + | 0.578562i | \(0.803614\pi\) | |||||||
\(878\) | 15.7938 | − | 21.7383i | 0.533016 | − | 0.733633i | ||||
\(879\) | −2.00000 | − | 2.82843i | −0.0674583 | − | 0.0954005i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 31.1127i | − | 1.04821i | −0.851653 | − | 0.524107i | \(-0.824399\pi\) | ||
0.851653 | − | 0.524107i | \(-0.175601\pi\) | |||||||
\(882\) | 12.3576 | − | 8.50230i | 0.416103 | − | 0.286287i | ||||
\(883\) | 14.2148 | − | 43.7486i | 0.478365 | − | 1.47226i | −0.362999 | − | 0.931790i | \(-0.618247\pi\) |
0.841365 | − | 0.540468i | \(-0.181753\pi\) | |||||||
\(884\) | 24.2099 | − | 7.86629i | 0.814269 | − | 0.264572i | ||||
\(885\) | −52.4887 | − | 17.8028i | −1.76439 | − | 0.598435i | ||||
\(886\) | 16.6251 | + | 22.8825i | 0.558530 | + | 0.768751i | ||||
\(887\) | −7.41641 | − | 22.8254i | −0.249019 | − | 0.766400i | −0.994949 | − | 0.100377i | \(-0.967995\pi\) |
0.745931 | − | 0.666023i | \(-0.232005\pi\) | |||||||
\(888\) | −39.6963 | + | 12.3370i | −1.33212 | + | 0.414002i | ||||
\(889\) | 11.3262 | + | 8.22899i | 0.379870 | + | 0.275992i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.0000 | −0.803579 | ||||||||
\(893\) | −9.70820 | − | 7.05342i | −0.324873 | − | 0.236034i | ||||
\(894\) | 9.92408 | − | 3.08424i | 0.331911 | − | 0.103153i | ||||
\(895\) | −2.47214 | − | 7.60845i | −0.0826344 | − | 0.254323i | ||||
\(896\) | −2.49376 | − | 3.43237i | −0.0833107 | − | 0.114667i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.37999 | + | 1.74806i | −0.179533 | + | 0.0583337i | ||||
\(899\) | 1.23607 | − | 3.80423i | 0.0412252 | − | 0.126878i | ||||
\(900\) | 7.41457 | − | 5.10138i | 0.247152 | − | 0.170046i | ||||
\(901\) | 33.9411i | 1.13074i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00000 | − | 8.48528i | −0.199667 | − | 0.282372i | ||||
\(904\) | −4.98752 | + | 6.86474i | −0.165883 | + | 0.228318i | ||||
\(905\) | −26.8999 | − | 8.74032i | −0.894184 | − | 0.290538i | ||||
\(906\) | 5.88909 | + | 4.39529i | 0.195652 | + | 0.146024i | ||||
\(907\) | −9.70820 | + | 7.05342i | −0.322356 | + | 0.234205i | −0.737180 | − | 0.675696i | \(-0.763843\pi\) |
0.414824 | + | 0.909902i | \(0.363843\pi\) | |||||||
\(908\) | −19.4164 | + | 14.1068i | −0.644356 | + | 0.468152i | ||||
\(909\) | 29.9901 | + | 0.770245i | 0.994709 | + | 0.0255474i | ||||
\(910\) | 16.1400 | + | 5.24419i | 0.535035 | + | 0.173843i | ||||
\(911\) | 21.6126 | − | 29.7472i | 0.716057 | − | 0.985568i | −0.283588 | − | 0.958946i | \(-0.591525\pi\) |
0.999646 | − | 0.0266223i | \(-0.00847514\pi\) | |||||||
\(912\) | −6.00000 | + | 4.24264i | −0.198680 | + | 0.140488i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 9.89949i | − | 0.327446i | ||||||
\(915\) | 0.622633 | − | 48.4934i | 0.0205836 | − | 1.60314i | ||||
\(916\) | 7.41641 | − | 22.8254i | 0.245045 | − | 0.754171i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 19.2830 | − | 24.4983i | 0.636433 | − | 0.808564i | ||||
\(919\) | −12.4688 | − | 17.1618i | −0.411308 | − | 0.566117i | 0.552229 | − | 0.833693i | \(-0.313777\pi\) |
−0.963537 | + | 0.267576i | \(0.913777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.18089 | − | 7.01739i | −0.0718627 | − | 0.231231i | ||||
\(922\) | −17.7984 | − | 12.9313i | −0.586158 | − | 0.425869i | ||||
\(923\) | −12.0000 | −0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0000 | −0.789115 | ||||||||
\(926\) | −19.4164 | − | 14.1068i | −0.638063 | − | 0.463580i | ||||
\(927\) | 19.0478 | + | 14.6007i | 0.625612 | + | 0.479550i | ||||
\(928\) | −3.09017 | − | 9.51057i | −0.101440 | − | 0.312200i | ||||
\(929\) | −1.66251 | − | 2.28825i | −0.0545451 | − | 0.0750749i | 0.780873 | − | 0.624690i | \(-0.214775\pi\) |
−0.835418 | + | 0.549615i | \(0.814775\pi\) | |||||||
\(930\) | −3.14712 | + | 9.27877i | −0.103198 | + | 0.304263i | ||||
\(931\) | 20.1750 | − | 6.55524i | 0.661207 | − | 0.214839i | ||||
\(932\) | 3.09017 | − | 9.51057i | 0.101222 | − | 0.311529i | ||||
\(933\) | −48.9858 | − | 0.628954i | −1.60372 | − | 0.0205910i | ||||
\(934\) | − | 28.2843i | − | 0.925490i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 36.0000 | + | 12.7279i | 1.17670 | + | 0.416025i | ||||
\(937\) | 20.7813 | − | 28.6031i | 0.678897 | − | 0.934422i | −0.321023 | − | 0.947071i | \(-0.604027\pi\) |
0.999920 | + | 0.0126498i | \(0.00402667\pi\) | |||||||
\(938\) | −2.68999 | − | 0.874032i | −0.0878314 | − | 0.0285382i | ||||
\(939\) | −12.4318 | + | 16.6569i | −0.405695 | + | 0.543576i | ||||
\(940\) | −6.47214 | + | 4.70228i | −0.211098 | + | 0.153372i | ||||
\(941\) | 30.7426 | − | 22.3358i | 1.00218 | − | 0.728128i | 0.0396268 | − | 0.999215i | \(-0.487383\pi\) |
0.962555 | + | 0.271087i | \(0.0873831\pi\) | |||||||
\(942\) | 20.7196 | − | 27.7615i | 0.675081 | − | 0.904517i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 6.65003 | − | 9.15298i | 0.216440 | − | 0.297904i | ||||
\(945\) | −20.0000 | + | 5.65685i | −0.650600 | + | 0.184017i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.1127i | 1.01103i | 0.862819 | + | 0.505513i | \(0.168697\pi\) | ||||
−0.862819 | + | 0.505513i | \(0.831303\pi\) | |||||||
\(948\) | −7.34786 | − | 0.0943431i | −0.238648 | − | 0.00306412i | ||||
\(949\) | 1.85410 | − | 5.70634i | 0.0601867 | − | 0.185236i | ||||
\(950\) | −12.1050 | + | 3.93314i | −0.392737 | + | 0.127608i | ||||
\(951\) | −14.1620 | + | 41.7545i | −0.459236 | + | 1.35398i | ||||
\(952\) | −14.9626 | − | 20.5942i | −0.484940 | − | 0.667462i | ||||
\(953\) | −0.618034 | − | 1.90211i | −0.0200201 | − | 0.0616155i | 0.940547 | − | 0.339663i | \(-0.110313\pi\) |
−0.960567 | + | 0.278047i | \(0.910313\pi\) | |||||||
\(954\) | −10.3243 | + | 13.4688i | −0.334260 | + | 0.436070i | ||||
\(955\) | 45.3050 | + | 32.9160i | 1.46603 | + | 1.06514i | ||||
\(956\) | 16.0000 | 0.517477 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.0000 | 0.904639 | ||||||||
\(959\) | −3.23607 | − | 2.35114i | −0.104498 | − | 0.0759223i | ||||
\(960\) | 10.1775 | + | 32.7478i | 0.328477 | + | 1.05693i | ||||
\(961\) | −8.34346 | − | 25.6785i | −0.269144 | − | 0.828340i | ||||
\(962\) | −19.9501 | − | 27.4589i | −0.643217 | − | 0.885312i | ||||
\(963\) | 13.6559 | + | 46.0165i | 0.440054 | + | 1.48286i | ||||
\(964\) | −4.03499 | + | 1.31105i | −0.129958 | + | 0.0422260i | ||||
\(965\) | −18.5410 | + | 57.0634i | −0.596857 | + | 1.83694i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.24264i | − | 0.136434i | −0.997671 | − | 0.0682171i | \(-0.978269\pi\) | ||
0.997671 | − | 0.0682171i | \(-0.0217310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.0000 | − | 25.4558i | 1.15649 | − | 0.817760i | ||||
\(970\) | −3.32502 | + | 4.57649i | −0.106760 | + | 0.146942i | ||||
\(971\) | 32.2799 | + | 10.4884i | 1.03591 | + | 0.336588i | 0.777125 | − | 0.629346i | \(-0.216677\pi\) |
0.258787 | + | 0.965934i | \(0.416677\pi\) | |||||||
\(972\) | −15.1040 | + | 3.85612i | −0.484461 | + | 0.123685i | ||||
\(973\) | 1.61803 | − | 1.17557i | 0.0518718 | − | 0.0376871i | ||||
\(974\) | −1.61803 | + | 1.17557i | −0.0518452 | + | 0.0376677i | ||||
\(975\) | 17.6673 | + | 13.1859i | 0.565806 | + | 0.422286i | ||||
\(976\) | 9.41498 | + | 3.05911i | 0.301366 | + | 0.0979198i | ||||
\(977\) | −14.9626 | + | 20.5942i | −0.478695 | + | 0.658867i | −0.978253 | − | 0.207413i | \(-0.933496\pi\) |
0.499558 | + | 0.866280i | \(0.333496\pi\) | |||||||
\(978\) | 20.0000 | + | 28.2843i | 0.639529 | + | 0.904431i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 14.1421i | − | 0.451754i | ||||||
\(981\) | −7.21444 | − | 10.4858i | −0.230339 | − | 0.334786i | ||||
\(982\) | 6.18034 | − | 19.0211i | 0.197223 | − | 0.606989i | ||||
\(983\) | 10.7600 | − | 3.49613i | 0.343190 | − | 0.111509i | −0.132351 | − | 0.991203i | \(-0.542252\pi\) |
0.475541 | + | 0.879694i | \(0.342252\pi\) | |||||||
\(984\) | 29.5249 | + | 10.0141i | 0.941219 | + | 0.319237i | ||||
\(985\) | −36.5752 | − | 50.3414i | −1.16538 | − | 1.60401i | ||||
\(986\) | −3.70820 | − | 11.4127i | −0.118093 | − | 0.363454i | ||||
\(987\) | 6.61606 | − | 2.05616i | 0.210591 | − | 0.0654484i | ||||
\(988\) | 14.5623 | + | 10.5801i | 0.463289 | + | 0.336599i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.0000 | −1.33417 | −0.667087 | − | 0.744980i | \(-0.732459\pi\) | ||||
−0.667087 | + | 0.744980i | \(0.732459\pi\) | |||||||
\(992\) | 8.09017 | + | 5.87785i | 0.256863 | + | 0.186622i | ||||
\(993\) | −33.0803 | + | 10.2808i | −1.04977 | + | 0.326252i | ||||
\(994\) | 1.23607 | + | 3.80423i | 0.0392057 | + | 0.120663i | ||||
\(995\) | −3.32502 | − | 4.57649i | −0.105410 | − | 0.145085i | ||||
\(996\) | −26.2443 | − | 8.90140i | −0.831584 | − | 0.282052i | ||||
\(997\) | −28.2449 | + | 9.17734i | −0.894526 | + | 0.290649i | −0.719976 | − | 0.693999i | \(-0.755847\pi\) |
−0.174550 | + | 0.984648i | \(0.555847\pi\) | |||||||
\(998\) | −4.32624 | + | 13.3148i | −0.136945 | + | 0.421472i | ||||
\(999\) | 39.0107 | + | 14.3584i | 1.23424 | + | 0.454281i |
(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 | 363.2.f.a.161.2 | 8 | ||
3.2 | odd | 2 | 363.2.f.f.161.1 | 8 | |||
11.2 | odd | 10 | 363.2.f.f.215.2 | 8 | |||
11.3 | even | 5 | inner | 363.2.f.a.239.1 | 8 | ||
11.4 | even | 5 | inner | 363.2.f.a.233.1 | 8 | ||
11.5 | even | 5 | 363.2.d.b.362.2 | yes | 2 | ||
11.6 | odd | 10 | 363.2.d.a.362.2 | yes | 2 | ||
11.7 | odd | 10 | 363.2.f.f.233.1 | 8 | |||
11.8 | odd | 10 | 363.2.f.f.239.1 | 8 | |||
11.9 | even | 5 | inner | 363.2.f.a.215.2 | 8 | ||
11.10 | odd | 2 | 363.2.f.f.161.2 | 8 | |||
33.2 | even | 10 | inner | 363.2.f.a.215.1 | 8 | ||
33.5 | odd | 10 | 363.2.d.a.362.1 | ✓ | 2 | ||
33.8 | even | 10 | inner | 363.2.f.a.239.2 | 8 | ||
33.14 | odd | 10 | 363.2.f.f.239.2 | 8 | |||
33.17 | even | 10 | 363.2.d.b.362.1 | yes | 2 | ||
33.20 | odd | 10 | 363.2.f.f.215.1 | 8 | |||
33.26 | odd | 10 | 363.2.f.f.233.2 | 8 | |||
33.29 | even | 10 | inner | 363.2.f.a.233.2 | 8 | ||
33.32 | even | 2 | inner | 363.2.f.a.161.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.a.362.1 | ✓ | 2 | 33.5 | odd | 10 | ||
363.2.d.a.362.2 | yes | 2 | 11.6 | odd | 10 | ||
363.2.d.b.362.1 | yes | 2 | 33.17 | even | 10 | ||
363.2.d.b.362.2 | yes | 2 | 11.5 | even | 5 | ||
363.2.f.a.161.1 | 8 | 33.32 | even | 2 | inner | ||
363.2.f.a.161.2 | 8 | 1.1 | even | 1 | trivial | ||
363.2.f.a.215.1 | 8 | 33.2 | even | 10 | inner | ||
363.2.f.a.215.2 | 8 | 11.9 | even | 5 | inner | ||
363.2.f.a.233.1 | 8 | 11.4 | even | 5 | inner | ||
363.2.f.a.233.2 | 8 | 33.29 | even | 10 | inner | ||
363.2.f.a.239.1 | 8 | 11.3 | even | 5 | inner | ||
363.2.f.a.239.2 | 8 | 33.8 | even | 10 | inner | ||
363.2.f.f.161.1 | 8 | 3.2 | odd | 2 | |||
363.2.f.f.161.2 | 8 | 11.10 | odd | 2 | |||
363.2.f.f.215.1 | 8 | 33.20 | odd | 10 | |||
363.2.f.f.215.2 | 8 | 11.2 | odd | 10 | |||
363.2.f.f.233.1 | 8 | 11.7 | odd | 10 | |||
363.2.f.f.233.2 | 8 | 33.26 | odd | 10 | |||
363.2.f.f.239.1 | 8 | 11.8 | odd | 10 | |||
363.2.f.f.239.2 | 8 | 33.14 | odd | 10 |