Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(43,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.s (of order \(6\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.127 |
Dual form | 546.2.s.c.43.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.73205 | − | 3.00000i | −0.547723 | − | 0.948683i | ||||
\(11\) | −3.46410 | + | 2.00000i | −1.04447 | + | 0.603023i | −0.921095 | − | 0.389338i | \(-0.872704\pi\) |
−0.123371 | + | 0.992361i | \(0.539370\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.59808 | − | 2.50000i | −0.720577 | − | 0.693375i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 3.00000 | − | 1.73205i | 0.774597 | − | 0.447214i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.232051 | + | 0.401924i | −0.0562806 | + | 0.0974808i | −0.892793 | − | 0.450467i | \(-0.851257\pi\) |
0.836512 | + | 0.547948i | \(0.184591\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −0.464102 | − | 0.267949i | −0.106472 | − | 0.0614718i | 0.445818 | − | 0.895123i | \(-0.352913\pi\) |
−0.552291 | + | 0.833652i | \(0.686246\pi\) | |||||||
\(20\) | 3.00000 | + | 1.73205i | 0.670820 | + | 0.387298i | ||||
\(21\) | − | 1.00000i | − | 0.218218i | ||||||
\(22\) | 2.00000 | − | 3.46410i | 0.426401 | − | 0.738549i | ||||
\(23\) | 1.13397 | + | 1.96410i | 0.236450 | + | 0.409543i | 0.959693 | − | 0.281050i | \(-0.0906827\pi\) |
−0.723243 | + | 0.690594i | \(0.757349\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 3.50000 | + | 0.866025i | 0.686406 | + | 0.169842i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.866025 | − | 0.500000i | 0.163663 | − | 0.0944911i | ||||
\(29\) | −4.00000 | − | 6.92820i | −0.742781 | − | 1.28654i | −0.951224 | − | 0.308500i | \(-0.900173\pi\) |
0.208443 | − | 0.978035i | \(-0.433160\pi\) | |||||||
\(30\) | −1.73205 | + | 3.00000i | −0.316228 | + | 0.547723i | ||||
\(31\) | 0.464102i | 0.0833551i | 0.999131 | + | 0.0416776i | \(0.0132702\pi\) | ||||
−0.999131 | + | 0.0416776i | \(0.986730\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 3.46410 | + | 2.00000i | 0.603023 | + | 0.348155i | ||||
\(34\) | − | 0.464102i | − | 0.0795928i | ||||||
\(35\) | −1.73205 | + | 3.00000i | −0.292770 | + | 0.507093i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −7.73205 | + | 4.46410i | −1.27114 | + | 0.733894i | −0.975203 | − | 0.221313i | \(-0.928966\pi\) |
−0.295939 | + | 0.955207i | \(0.595632\pi\) | |||||||
\(38\) | 0.535898 | 0.0869342 | ||||||||
\(39\) | −0.866025 | + | 3.50000i | −0.138675 | + | 0.560449i | ||||
\(40\) | −3.46410 | −0.547723 | ||||||||
\(41\) | −6.00000 | + | 3.46410i | −0.937043 | + | 0.541002i | −0.889032 | − | 0.457845i | \(-0.848621\pi\) |
−0.0480106 | + | 0.998847i | \(0.515288\pi\) | |||||||
\(42\) | 0.500000 | + | 0.866025i | 0.0771517 | + | 0.133631i | ||||
\(43\) | −1.23205 | + | 2.13397i | −0.187886 | + | 0.325428i | −0.944545 | − | 0.328381i | \(-0.893497\pi\) |
0.756659 | + | 0.653809i | \(0.226830\pi\) | |||||||
\(44\) | 4.00000i | 0.603023i | ||||||||
\(45\) | −3.00000 | − | 1.73205i | −0.447214 | − | 0.258199i | ||||
\(46\) | −1.96410 | − | 1.13397i | −0.289591 | − | 0.167195i | ||||
\(47\) | 7.46410i | 1.08875i | 0.838842 | + | 0.544376i | \(0.183233\pi\) | ||||
−0.838842 | + | 0.544376i | \(0.816767\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 6.06218 | − | 3.50000i | 0.857321 | − | 0.494975i | ||||
\(51\) | 0.464102 | 0.0649872 | ||||||||
\(52\) | −3.46410 | + | 1.00000i | −0.480384 | + | 0.138675i | ||||
\(53\) | −11.7321 | −1.61152 | −0.805761 | − | 0.592241i | \(-0.798243\pi\) | ||||
−0.805761 | + | 0.592241i | \(0.798243\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | −6.92820 | − | 12.0000i | −0.934199 | − | 1.61808i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | 0.535898i | 0.0709815i | ||||||||
\(58\) | 6.92820 | + | 4.00000i | 0.909718 | + | 0.525226i | ||||
\(59\) | 8.42820 | + | 4.86603i | 1.09726 | + | 0.633503i | 0.935500 | − | 0.353328i | \(-0.114950\pi\) |
0.161759 | + | 0.986830i | \(0.448283\pi\) | |||||||
\(60\) | − | 3.46410i | − | 0.447214i | ||||||
\(61\) | −2.59808 | + | 4.50000i | −0.332650 | + | 0.576166i | −0.983030 | − | 0.183442i | \(-0.941276\pi\) |
0.650381 | + | 0.759608i | \(0.274609\pi\) | |||||||
\(62\) | −0.232051 | − | 0.401924i | −0.0294705 | − | 0.0510444i | ||||
\(63\) | −0.866025 | + | 0.500000i | −0.109109 | + | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 8.66025 | − | 9.00000i | 1.07417 | − | 1.11631i | ||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 2.76795 | − | 1.59808i | 0.338159 | − | 0.195236i | −0.321299 | − | 0.946978i | \(-0.604119\pi\) |
0.659458 | + | 0.751742i | \(0.270786\pi\) | |||||||
\(68\) | 0.232051 | + | 0.401924i | 0.0281403 | + | 0.0487404i | ||||
\(69\) | 1.13397 | − | 1.96410i | 0.136514 | − | 0.236450i | ||||
\(70\) | − | 3.46410i | − | 0.414039i | ||||||
\(71\) | 10.3301 | + | 5.96410i | 1.22596 | + | 0.707809i | 0.966182 | − | 0.257860i | \(-0.0830172\pi\) |
0.259778 | + | 0.965668i | \(0.416351\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | − | 2.92820i | − | 0.342720i | −0.985208 | − | 0.171360i | \(-0.945184\pi\) | ||
0.985208 | − | 0.171360i | \(-0.0548162\pi\) | |||||||
\(74\) | 4.46410 | − | 7.73205i | 0.518941 | − | 0.898833i | ||||
\(75\) | 3.50000 | + | 6.06218i | 0.404145 | + | 0.700000i | ||||
\(76\) | −0.464102 | + | 0.267949i | −0.0532361 | + | 0.0307359i | ||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | −1.00000 | − | 3.46410i | −0.113228 | − | 0.392232i | ||||
\(79\) | −2.53590 | −0.285311 | −0.142655 | − | 0.989772i | \(-0.545564\pi\) | ||||
−0.142655 | + | 0.989772i | \(0.545564\pi\) | |||||||
\(80\) | 3.00000 | − | 1.73205i | 0.335410 | − | 0.193649i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.46410 | − | 6.00000i | 0.382546 | − | 0.662589i | ||||
\(83\) | − | 1.73205i | − | 0.190117i | −0.995472 | − | 0.0950586i | \(-0.969696\pi\) | ||
0.995472 | − | 0.0950586i | \(-0.0303039\pi\) | |||||||
\(84\) | −0.866025 | − | 0.500000i | −0.0944911 | − | 0.0545545i | ||||
\(85\) | −1.39230 | − | 0.803848i | −0.151017 | − | 0.0871895i | ||||
\(86\) | − | 2.46410i | − | 0.265711i | ||||||
\(87\) | −4.00000 | + | 6.92820i | −0.428845 | + | 0.742781i | ||||
\(88\) | −2.00000 | − | 3.46410i | −0.213201 | − | 0.369274i | ||||
\(89\) | 7.16025 | − | 4.13397i | 0.758985 | − | 0.438200i | −0.0699459 | − | 0.997551i | \(-0.522283\pi\) |
0.828931 | + | 0.559350i | \(0.188949\pi\) | |||||||
\(90\) | 3.46410 | 0.365148 | ||||||||
\(91\) | −1.00000 | − | 3.46410i | −0.104828 | − | 0.363137i | ||||
\(92\) | 2.26795 | 0.236450 | ||||||||
\(93\) | 0.401924 | − | 0.232051i | 0.0416776 | − | 0.0240625i | ||||
\(94\) | −3.73205 | − | 6.46410i | −0.384932 | − | 0.666721i | ||||
\(95\) | 0.928203 | − | 1.60770i | 0.0952316 | − | 0.164946i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 7.26795 | + | 4.19615i | 0.737948 | + | 0.426055i | 0.821323 | − | 0.570464i | \(-0.193236\pi\) |
−0.0833745 | + | 0.996518i | \(0.526570\pi\) | |||||||
\(98\) | −0.866025 | − | 0.500000i | −0.0874818 | − | 0.0505076i | ||||
\(99\) | − | 4.00000i | − | 0.402015i | ||||||
\(100\) | −3.50000 | + | 6.06218i | −0.350000 | + | 0.606218i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | −0.401924 | + | 0.232051i | −0.0397964 | + | 0.0229765i | ||||
\(103\) | 6.66025 | 0.656254 | 0.328127 | − | 0.944634i | \(-0.393583\pi\) | ||||
0.328127 | + | 0.944634i | \(0.393583\pi\) | |||||||
\(104\) | 2.50000 | − | 2.59808i | 0.245145 | − | 0.254762i | ||||
\(105\) | 3.46410 | 0.338062 | ||||||||
\(106\) | 10.1603 | − | 5.86603i | 0.986851 | − | 0.569759i | ||||
\(107\) | −7.73205 | − | 13.3923i | −0.747486 | − | 1.29468i | −0.949024 | − | 0.315202i | \(-0.897928\pi\) |
0.201539 | − | 0.979481i | \(-0.435406\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | − | 12.0000i | − | 1.14939i | −0.818367 | − | 0.574696i | \(-0.805120\pi\) | ||
0.818367 | − | 0.574696i | \(-0.194880\pi\) | |||||||
\(110\) | 12.0000 | + | 6.92820i | 1.14416 | + | 0.660578i | ||||
\(111\) | 7.73205 | + | 4.46410i | 0.733894 | + | 0.423714i | ||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | −8.19615 | + | 14.1962i | −0.771029 | + | 1.33546i | 0.165970 | + | 0.986131i | \(0.446924\pi\) |
−0.936999 | + | 0.349331i | \(0.886409\pi\) | |||||||
\(114\) | −0.267949 | − | 0.464102i | −0.0250957 | − | 0.0434671i | ||||
\(115\) | −6.80385 | + | 3.92820i | −0.634462 | + | 0.366307i | ||||
\(116\) | −8.00000 | −0.742781 | ||||||||
\(117\) | 3.46410 | − | 1.00000i | 0.320256 | − | 0.0924500i | ||||
\(118\) | −9.73205 | −0.895908 | ||||||||
\(119\) | −0.401924 | + | 0.232051i | −0.0368443 | + | 0.0212721i | ||||
\(120\) | 1.73205 | + | 3.00000i | 0.158114 | + | 0.273861i | ||||
\(121\) | 2.50000 | − | 4.33013i | 0.227273 | − | 0.393648i | ||||
\(122\) | − | 5.19615i | − | 0.470438i | ||||||
\(123\) | 6.00000 | + | 3.46410i | 0.541002 | + | 0.312348i | ||||
\(124\) | 0.401924 | + | 0.232051i | 0.0360938 | + | 0.0208388i | ||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0.500000 | − | 0.866025i | 0.0445435 | − | 0.0771517i | ||||
\(127\) | 9.46410 | + | 16.3923i | 0.839803 | + | 1.45458i | 0.890059 | + | 0.455845i | \(0.150663\pi\) |
−0.0502557 | + | 0.998736i | \(0.516004\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 2.46410 | 0.216952 | ||||||||
\(130\) | −3.00000 | + | 12.1244i | −0.263117 | + | 1.06338i | ||||
\(131\) | 19.0000 | 1.66004 | 0.830019 | − | 0.557735i | \(-0.188330\pi\) | ||||
0.830019 | + | 0.557735i | \(0.188330\pi\) | |||||||
\(132\) | 3.46410 | − | 2.00000i | 0.301511 | − | 0.174078i | ||||
\(133\) | −0.267949 | − | 0.464102i | −0.0232341 | − | 0.0402427i | ||||
\(134\) | −1.59808 | + | 2.76795i | −0.138053 | + | 0.239114i | ||||
\(135\) | 3.46410i | 0.298142i | ||||||||
\(136\) | −0.401924 | − | 0.232051i | −0.0344647 | − | 0.0198982i | ||||
\(137\) | −12.0000 | − | 6.92820i | −1.02523 | − | 0.591916i | −0.109615 | − | 0.993974i | \(-0.534962\pi\) |
−0.915614 | + | 0.402058i | \(0.868295\pi\) | |||||||
\(138\) | 2.26795i | 0.193061i | ||||||||
\(139\) | 5.46410 | − | 9.46410i | 0.463459 | − | 0.802735i | −0.535671 | − | 0.844426i | \(-0.679941\pi\) |
0.999131 | + | 0.0416919i | \(0.0132748\pi\) | |||||||
\(140\) | 1.73205 | + | 3.00000i | 0.146385 | + | 0.253546i | ||||
\(141\) | 6.46410 | − | 3.73205i | 0.544376 | − | 0.314295i | ||||
\(142\) | −11.9282 | −1.00099 | ||||||||
\(143\) | 14.0000 | + | 3.46410i | 1.17074 | + | 0.289683i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 24.0000 | − | 13.8564i | 1.99309 | − | 1.15071i | ||||
\(146\) | 1.46410 | + | 2.53590i | 0.121170 | + | 0.209872i | ||||
\(147\) | 0.500000 | − | 0.866025i | 0.0412393 | − | 0.0714286i | ||||
\(148\) | 8.92820i | 0.733894i | ||||||||
\(149\) | 15.9904 | + | 9.23205i | 1.30998 | + | 0.756319i | 0.982093 | − | 0.188397i | \(-0.0603291\pi\) |
0.327890 | + | 0.944716i | \(0.393662\pi\) | |||||||
\(150\) | −6.06218 | − | 3.50000i | −0.494975 | − | 0.285774i | ||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | 0.267949 | − | 0.464102i | 0.0217335 | − | 0.0376436i | ||||
\(153\) | −0.232051 | − | 0.401924i | −0.0187602 | − | 0.0324936i | ||||
\(154\) | 3.46410 | − | 2.00000i | 0.279145 | − | 0.161165i | ||||
\(155\) | −1.60770 | −0.129133 | ||||||||
\(156\) | 2.59808 | + | 2.50000i | 0.208013 | + | 0.200160i | ||||
\(157\) | 10.9282 | 0.872166 | 0.436083 | − | 0.899907i | \(-0.356365\pi\) | ||||
0.436083 | + | 0.899907i | \(0.356365\pi\) | |||||||
\(158\) | 2.19615 | − | 1.26795i | 0.174717 | − | 0.100873i | ||||
\(159\) | 5.86603 | + | 10.1603i | 0.465206 | + | 0.805761i | ||||
\(160\) | −1.73205 | + | 3.00000i | −0.136931 | + | 0.237171i | ||||
\(161\) | 2.26795i | 0.178739i | ||||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | −16.1603 | − | 9.33013i | −1.26577 | − | 0.730792i | −0.291584 | − | 0.956545i | \(-0.594182\pi\) |
−0.974185 | + | 0.225753i | \(0.927516\pi\) | |||||||
\(164\) | 6.92820i | 0.541002i | ||||||||
\(165\) | −6.92820 | + | 12.0000i | −0.539360 | + | 0.934199i | ||||
\(166\) | 0.866025 | + | 1.50000i | 0.0672166 | + | 0.116423i | ||||
\(167\) | −17.3205 | + | 10.0000i | −1.34030 | + | 0.773823i | −0.986851 | − | 0.161630i | \(-0.948325\pi\) |
−0.353450 | + | 0.935454i | \(0.614991\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0.500000 | + | 12.9904i | 0.0384615 | + | 0.999260i | ||||
\(170\) | 1.60770 | 0.123305 | ||||||||
\(171\) | 0.464102 | − | 0.267949i | 0.0354907 | − | 0.0204906i | ||||
\(172\) | 1.23205 | + | 2.13397i | 0.0939430 | + | 0.162714i | ||||
\(173\) | 7.46410 | − | 12.9282i | 0.567485 | − | 0.982913i | −0.429329 | − | 0.903148i | \(-0.641250\pi\) |
0.996814 | − | 0.0797647i | \(-0.0254169\pi\) | |||||||
\(174\) | − | 8.00000i | − | 0.606478i | ||||||
\(175\) | −6.06218 | − | 3.50000i | −0.458258 | − | 0.264575i | ||||
\(176\) | 3.46410 | + | 2.00000i | 0.261116 | + | 0.150756i | ||||
\(177\) | − | 9.73205i | − | 0.731506i | ||||||
\(178\) | −4.13397 | + | 7.16025i | −0.309854 | + | 0.536684i | ||||
\(179\) | −1.53590 | − | 2.66025i | −0.114798 | − | 0.198837i | 0.802901 | − | 0.596113i | \(-0.203289\pi\) |
−0.917699 | + | 0.397276i | \(0.869956\pi\) | |||||||
\(180\) | −3.00000 | + | 1.73205i | −0.223607 | + | 0.129099i | ||||
\(181\) | 16.7846 | 1.24759 | 0.623795 | − | 0.781588i | \(-0.285590\pi\) | ||||
0.623795 | + | 0.781588i | \(0.285590\pi\) | |||||||
\(182\) | 2.59808 | + | 2.50000i | 0.192582 | + | 0.185312i | ||||
\(183\) | 5.19615 | 0.384111 | ||||||||
\(184\) | −1.96410 | + | 1.13397i | −0.144795 | + | 0.0835977i | ||||
\(185\) | −15.4641 | − | 26.7846i | −1.13694 | − | 1.96924i | ||||
\(186\) | −0.232051 | + | 0.401924i | −0.0170148 | + | 0.0294705i | ||||
\(187\) | − | 1.85641i | − | 0.135754i | ||||||
\(188\) | 6.46410 | + | 3.73205i | 0.471443 | + | 0.272188i | ||||
\(189\) | 0.866025 | + | 0.500000i | 0.0629941 | + | 0.0363696i | ||||
\(190\) | 1.85641i | 0.134678i | ||||||||
\(191\) | −9.25833 | + | 16.0359i | −0.669909 | + | 1.16032i | 0.308020 | + | 0.951380i | \(0.400334\pi\) |
−0.977929 | + | 0.208937i | \(0.933000\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 8.53590 | − | 4.92820i | 0.614427 | − | 0.354740i | −0.160269 | − | 0.987073i | \(-0.551236\pi\) |
0.774696 | + | 0.632334i | \(0.217903\pi\) | |||||||
\(194\) | −8.39230 | −0.602532 | ||||||||
\(195\) | −12.1244 | − | 3.00000i | −0.868243 | − | 0.214834i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −20.2583 | + | 11.6962i | −1.44335 | + | 0.833316i | −0.998071 | − | 0.0620775i | \(-0.980227\pi\) |
−0.445275 | + | 0.895394i | \(0.646894\pi\) | |||||||
\(198\) | 2.00000 | + | 3.46410i | 0.142134 | + | 0.246183i | ||||
\(199\) | 1.06218 | − | 1.83975i | 0.0752958 | − | 0.130416i | −0.825919 | − | 0.563789i | \(-0.809343\pi\) |
0.901215 | + | 0.433373i | \(0.142677\pi\) | |||||||
\(200\) | − | 7.00000i | − | 0.494975i | ||||||
\(201\) | −2.76795 | − | 1.59808i | −0.195236 | − | 0.112720i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 8.00000i | − | 0.561490i | ||||||
\(204\) | 0.232051 | − | 0.401924i | 0.0162468 | − | 0.0281403i | ||||
\(205\) | −12.0000 | − | 20.7846i | −0.838116 | − | 1.45166i | ||||
\(206\) | −5.76795 | + | 3.33013i | −0.401872 | + | 0.232021i | ||||
\(207\) | −2.26795 | −0.157633 | ||||||||
\(208\) | −0.866025 | + | 3.50000i | −0.0600481 | + | 0.242681i | ||||
\(209\) | 2.14359 | 0.148275 | ||||||||
\(210\) | −3.00000 | + | 1.73205i | −0.207020 | + | 0.119523i | ||||
\(211\) | 11.4641 | + | 19.8564i | 0.789221 | + | 1.36697i | 0.926445 | + | 0.376431i | \(0.122849\pi\) |
−0.137223 | + | 0.990540i | \(0.543818\pi\) | |||||||
\(212\) | −5.86603 | + | 10.1603i | −0.402880 | + | 0.697809i | ||||
\(213\) | − | 11.9282i | − | 0.817307i | ||||||
\(214\) | 13.3923 | + | 7.73205i | 0.915479 | + | 0.528552i | ||||
\(215\) | −7.39230 | − | 4.26795i | −0.504151 | − | 0.291072i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −0.232051 | + | 0.401924i | −0.0157526 | + | 0.0272844i | ||||
\(218\) | 6.00000 | + | 10.3923i | 0.406371 | + | 0.703856i | ||||
\(219\) | −2.53590 | + | 1.46410i | −0.171360 | + | 0.0989348i | ||||
\(220\) | −13.8564 | −0.934199 | ||||||||
\(221\) | 1.60770 | − | 0.464102i | 0.108145 | − | 0.0312189i | ||||
\(222\) | −8.92820 | −0.599222 | ||||||||
\(223\) | 12.5263 | − | 7.23205i | 0.838822 | − | 0.484294i | −0.0180418 | − | 0.999837i | \(-0.505743\pi\) |
0.856864 | + | 0.515543i | \(0.172410\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 3.50000 | − | 6.06218i | 0.233333 | − | 0.404145i | ||||
\(226\) | − | 16.3923i | − | 1.09040i | ||||||
\(227\) | −18.4641 | − | 10.6603i | −1.22551 | − | 0.707546i | −0.259419 | − | 0.965765i | \(-0.583531\pi\) |
−0.966086 | + | 0.258219i | \(0.916864\pi\) | |||||||
\(228\) | 0.464102 | + | 0.267949i | 0.0307359 | + | 0.0177454i | ||||
\(229\) | − | 6.07180i | − | 0.401236i | −0.979670 | − | 0.200618i | \(-0.935705\pi\) | ||
0.979670 | − | 0.200618i | \(-0.0642949\pi\) | |||||||
\(230\) | 3.92820 | − | 6.80385i | 0.259018 | − | 0.448632i | ||||
\(231\) | 2.00000 | + | 3.46410i | 0.131590 | + | 0.227921i | ||||
\(232\) | 6.92820 | − | 4.00000i | 0.454859 | − | 0.262613i | ||||
\(233\) | −6.53590 | −0.428181 | −0.214090 | − | 0.976814i | \(-0.568679\pi\) | ||||
−0.214090 | + | 0.976814i | \(0.568679\pi\) | |||||||
\(234\) | −2.50000 | + | 2.59808i | −0.163430 | + | 0.169842i | ||||
\(235\) | −25.8564 | −1.68669 | ||||||||
\(236\) | 8.42820 | − | 4.86603i | 0.548629 | − | 0.316751i | ||||
\(237\) | 1.26795 | + | 2.19615i | 0.0823622 | + | 0.142655i | ||||
\(238\) | 0.232051 | − | 0.401924i | 0.0150416 | − | 0.0260528i | ||||
\(239\) | − | 14.8564i | − | 0.960981i | −0.877000 | − | 0.480491i | \(-0.840459\pi\) | ||
0.877000 | − | 0.480491i | \(-0.159541\pi\) | |||||||
\(240\) | −3.00000 | − | 1.73205i | −0.193649 | − | 0.111803i | ||||
\(241\) | 10.2679 | + | 5.92820i | 0.661417 | + | 0.381869i | 0.792817 | − | 0.609460i | \(-0.208614\pi\) |
−0.131400 | + | 0.991329i | \(0.541947\pi\) | |||||||
\(242\) | 5.00000i | 0.321412i | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 2.59808 | + | 4.50000i | 0.166325 | + | 0.288083i | ||||
\(245\) | −3.00000 | + | 1.73205i | −0.191663 | + | 0.110657i | ||||
\(246\) | −6.92820 | −0.441726 | ||||||||
\(247\) | 0.535898 | + | 1.85641i | 0.0340984 | + | 0.118120i | ||||
\(248\) | −0.464102 | −0.0294705 | ||||||||
\(249\) | −1.50000 | + | 0.866025i | −0.0950586 | + | 0.0548821i | ||||
\(250\) | 3.46410 | + | 6.00000i | 0.219089 | + | 0.379473i | ||||
\(251\) | −11.9641 | + | 20.7224i | −0.755167 | + | 1.30799i | 0.190124 | + | 0.981760i | \(0.439111\pi\) |
−0.945291 | + | 0.326228i | \(0.894222\pi\) | |||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | −7.85641 | − | 4.53590i | −0.493928 | − | 0.285169i | ||||
\(254\) | −16.3923 | − | 9.46410i | −1.02854 | − | 0.593831i | ||||
\(255\) | 1.60770i | 0.100678i | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.23205 | − | 5.59808i | −0.201610 | − | 0.349198i | 0.747437 | − | 0.664332i | \(-0.231284\pi\) |
−0.949047 | + | 0.315134i | \(0.897951\pi\) | |||||||
\(258\) | −2.13397 | + | 1.23205i | −0.132855 | + | 0.0767041i | ||||
\(259\) | −8.92820 | −0.554772 | ||||||||
\(260\) | −3.46410 | − | 12.0000i | −0.214834 | − | 0.744208i | ||||
\(261\) | 8.00000 | 0.495188 | ||||||||
\(262\) | −16.4545 | + | 9.50000i | −1.01656 | + | 0.586912i | ||||
\(263\) | −8.66025 | − | 15.0000i | −0.534014 | − | 0.924940i | −0.999210 | − | 0.0397320i | \(-0.987350\pi\) |
0.465196 | − | 0.885208i | \(-0.345984\pi\) | |||||||
\(264\) | −2.00000 | + | 3.46410i | −0.123091 | + | 0.213201i | ||||
\(265\) | − | 40.6410i | − | 2.49656i | ||||||
\(266\) | 0.464102 | + | 0.267949i | 0.0284559 | + | 0.0164290i | ||||
\(267\) | −7.16025 | − | 4.13397i | −0.438200 | − | 0.252995i | ||||
\(268\) | − | 3.19615i | − | 0.195236i | ||||||
\(269\) | −0.803848 | + | 1.39230i | −0.0490115 | + | 0.0848903i | −0.889490 | − | 0.456954i | \(-0.848940\pi\) |
0.840479 | + | 0.541844i | \(0.182274\pi\) | |||||||
\(270\) | −1.73205 | − | 3.00000i | −0.105409 | − | 0.182574i | ||||
\(271\) | −4.79423 | + | 2.76795i | −0.291229 | + | 0.168141i | −0.638496 | − | 0.769625i | \(-0.720443\pi\) |
0.347267 | + | 0.937766i | \(0.387110\pi\) | |||||||
\(272\) | 0.464102 | 0.0281403 | ||||||||
\(273\) | −2.50000 | + | 2.59808i | −0.151307 | + | 0.157243i | ||||
\(274\) | 13.8564 | 0.837096 | ||||||||
\(275\) | 24.2487 | − | 14.0000i | 1.46225 | − | 0.844232i | ||||
\(276\) | −1.13397 | − | 1.96410i | −0.0682572 | − | 0.118225i | ||||
\(277\) | −13.6603 | + | 23.6603i | −0.820765 | + | 1.42161i | 0.0843481 | + | 0.996436i | \(0.473119\pi\) |
−0.905113 | + | 0.425171i | \(0.860214\pi\) | |||||||
\(278\) | 10.9282i | 0.655430i | ||||||||
\(279\) | −0.401924 | − | 0.232051i | −0.0240625 | − | 0.0138925i | ||||
\(280\) | −3.00000 | − | 1.73205i | −0.179284 | − | 0.103510i | ||||
\(281\) | − | 18.3923i | − | 1.09719i | −0.836087 | − | 0.548596i | \(-0.815162\pi\) | ||
0.836087 | − | 0.548596i | \(-0.184838\pi\) | |||||||
\(282\) | −3.73205 | + | 6.46410i | −0.222240 | + | 0.384932i | ||||
\(283\) | −2.26795 | − | 3.92820i | −0.134816 | − | 0.233507i | 0.790711 | − | 0.612189i | \(-0.209711\pi\) |
−0.925527 | + | 0.378682i | \(0.876378\pi\) | |||||||
\(284\) | 10.3301 | − | 5.96410i | 0.612980 | − | 0.353904i | ||||
\(285\) | −1.85641 | −0.109964 | ||||||||
\(286\) | −13.8564 | + | 4.00000i | −0.819346 | + | 0.236525i | ||||
\(287\) | −6.92820 | −0.408959 | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | 8.39230 | + | 14.5359i | 0.493665 | + | 0.855053i | ||||
\(290\) | −13.8564 | + | 24.0000i | −0.813676 | + | 1.40933i | ||||
\(291\) | − | 8.39230i | − | 0.491966i | ||||||
\(292\) | −2.53590 | − | 1.46410i | −0.148402 | − | 0.0856801i | ||||
\(293\) | 22.9808 | + | 13.2679i | 1.34255 | + | 0.775122i | 0.987181 | − | 0.159604i | \(-0.0510218\pi\) |
0.355369 | + | 0.934726i | \(0.384355\pi\) | |||||||
\(294\) | 1.00000i | 0.0583212i | ||||||||
\(295\) | −16.8564 | + | 29.1962i | −0.981418 | + | 1.69987i | ||||
\(296\) | −4.46410 | − | 7.73205i | −0.259471 | − | 0.449416i | ||||
\(297\) | −3.46410 | + | 2.00000i | −0.201008 | + | 0.116052i | ||||
\(298\) | −18.4641 | −1.06960 | ||||||||
\(299\) | 1.96410 | − | 7.93782i | 0.113587 | − | 0.459056i | ||||
\(300\) | 7.00000 | 0.404145 | ||||||||
\(301\) | −2.13397 | + | 1.23205i | −0.123000 | + | 0.0710142i | ||||
\(302\) | −6.00000 | − | 10.3923i | −0.345261 | − | 0.598010i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.535898i | 0.0307359i | ||||||||
\(305\) | −15.5885 | − | 9.00000i | −0.892592 | − | 0.515339i | ||||
\(306\) | 0.401924 | + | 0.232051i | 0.0229765 | + | 0.0132655i | ||||
\(307\) | 22.0000i | 1.25561i | 0.778372 | + | 0.627803i | \(0.216046\pi\) | ||||
−0.778372 | + | 0.627803i | \(0.783954\pi\) | |||||||
\(308\) | −2.00000 | + | 3.46410i | −0.113961 | + | 0.197386i | ||||
\(309\) | −3.33013 | − | 5.76795i | −0.189444 | − | 0.328127i | ||||
\(310\) | 1.39230 | − | 0.803848i | 0.0790776 | − | 0.0456555i | ||||
\(311\) | 21.3205 | 1.20898 | 0.604488 | − | 0.796615i | \(-0.293378\pi\) | ||||
0.604488 | + | 0.796615i | \(0.293378\pi\) | |||||||
\(312\) | −3.50000 | − | 0.866025i | −0.198148 | − | 0.0490290i | ||||
\(313\) | 35.3205 | 1.99643 | 0.998217 | − | 0.0596964i | \(-0.0190133\pi\) | ||||
0.998217 | + | 0.0596964i | \(0.0190133\pi\) | |||||||
\(314\) | −9.46410 | + | 5.46410i | −0.534090 | + | 0.308357i | ||||
\(315\) | −1.73205 | − | 3.00000i | −0.0975900 | − | 0.169031i | ||||
\(316\) | −1.26795 | + | 2.19615i | −0.0713277 | + | 0.123543i | ||||
\(317\) | 9.53590i | 0.535589i | 0.963476 | + | 0.267795i | \(0.0862949\pi\) | ||||
−0.963476 | + | 0.267795i | \(0.913705\pi\) | |||||||
\(318\) | −10.1603 | − | 5.86603i | −0.569759 | − | 0.328950i | ||||
\(319\) | 27.7128 | + | 16.0000i | 1.55162 | + | 0.895828i | ||||
\(320\) | − | 3.46410i | − | 0.193649i | ||||||
\(321\) | −7.73205 | + | 13.3923i | −0.431561 | + | 0.747486i | ||||
\(322\) | −1.13397 | − | 1.96410i | −0.0631939 | − | 0.109455i | ||||
\(323\) | 0.215390 | − | 0.124356i | 0.0119846 | − | 0.00691933i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 18.1865 | + | 17.5000i | 1.00881 | + | 0.970725i | ||||
\(326\) | 18.6603 | 1.03350 | ||||||||
\(327\) | −10.3923 | + | 6.00000i | −0.574696 | + | 0.331801i | ||||
\(328\) | −3.46410 | − | 6.00000i | −0.191273 | − | 0.331295i | ||||
\(329\) | −3.73205 | + | 6.46410i | −0.205755 | + | 0.356377i | ||||
\(330\) | − | 13.8564i | − | 0.762770i | ||||||
\(331\) | 11.5359 | + | 6.66025i | 0.634070 | + | 0.366081i | 0.782327 | − | 0.622868i | \(-0.214033\pi\) |
−0.148256 | + | 0.988949i | \(0.547366\pi\) | |||||||
\(332\) | −1.50000 | − | 0.866025i | −0.0823232 | − | 0.0475293i | ||||
\(333\) | − | 8.92820i | − | 0.489263i | ||||||
\(334\) | 10.0000 | − | 17.3205i | 0.547176 | − | 0.947736i | ||||
\(335\) | 5.53590 | + | 9.58846i | 0.302458 | + | 0.523873i | ||||
\(336\) | −0.866025 | + | 0.500000i | −0.0472456 | + | 0.0272772i | ||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | −6.92820 | − | 11.0000i | −0.376845 | − | 0.598321i | ||||
\(339\) | 16.3923 | 0.890308 | ||||||||
\(340\) | −1.39230 | + | 0.803848i | −0.0755083 | + | 0.0435948i | ||||
\(341\) | −0.928203 | − | 1.60770i | −0.0502650 | − | 0.0870616i | ||||
\(342\) | −0.267949 | + | 0.464102i | −0.0144890 | + | 0.0250957i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −2.13397 | − | 1.23205i | −0.115056 | − | 0.0664277i | ||||
\(345\) | 6.80385 | + | 3.92820i | 0.366307 | + | 0.211487i | ||||
\(346\) | 14.9282i | 0.802545i | ||||||||
\(347\) | 14.8564 | − | 25.7321i | 0.797534 | − | 1.38137i | −0.123684 | − | 0.992322i | \(-0.539471\pi\) |
0.921218 | − | 0.389047i | \(-0.127196\pi\) | |||||||
\(348\) | 4.00000 | + | 6.92820i | 0.214423 | + | 0.371391i | ||||
\(349\) | −29.1340 | + | 16.8205i | −1.55951 | + | 0.900381i | −0.562202 | + | 0.827000i | \(0.690046\pi\) |
−0.997304 | + | 0.0733812i | \(0.976621\pi\) | |||||||
\(350\) | 7.00000 | 0.374166 | ||||||||
\(351\) | −2.59808 | − | 2.50000i | −0.138675 | − | 0.133440i | ||||
\(352\) | −4.00000 | −0.213201 | ||||||||
\(353\) | −23.0885 | + | 13.3301i | −1.22887 | + | 0.709491i | −0.966795 | − | 0.255555i | \(-0.917742\pi\) |
−0.262080 | + | 0.965046i | \(0.584408\pi\) | |||||||
\(354\) | 4.86603 | + | 8.42820i | 0.258626 | + | 0.447954i | ||||
\(355\) | −20.6603 | + | 35.7846i | −1.09653 | + | 1.89925i | ||||
\(356\) | − | 8.26795i | − | 0.438200i | ||||||
\(357\) | 0.401924 | + | 0.232051i | 0.0212721 | + | 0.0122814i | ||||
\(358\) | 2.66025 | + | 1.53590i | 0.140599 | + | 0.0811748i | ||||
\(359\) | 8.00000i | 0.422224i | 0.977462 | + | 0.211112i | \(0.0677085\pi\) | ||||
−0.977462 | + | 0.211112i | \(0.932292\pi\) | |||||||
\(360\) | 1.73205 | − | 3.00000i | 0.0912871 | − | 0.158114i | ||||
\(361\) | −9.35641 | − | 16.2058i | −0.492442 | − | 0.852935i | ||||
\(362\) | −14.5359 | + | 8.39230i | −0.763990 | + | 0.441090i | ||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | −3.50000 | − | 0.866025i | −0.183450 | − | 0.0453921i | ||||
\(365\) | 10.1436 | 0.530940 | ||||||||
\(366\) | −4.50000 | + | 2.59808i | −0.235219 | + | 0.135804i | ||||
\(367\) | −2.52628 | − | 4.37564i | −0.131871 | − | 0.228407i | 0.792527 | − | 0.609837i | \(-0.208765\pi\) |
−0.924398 | + | 0.381430i | \(0.875432\pi\) | |||||||
\(368\) | 1.13397 | − | 1.96410i | 0.0591125 | − | 0.102386i | ||||
\(369\) | − | 6.92820i | − | 0.360668i | ||||||
\(370\) | 26.7846 | + | 15.4641i | 1.39247 | + | 0.803940i | ||||
\(371\) | −10.1603 | − | 5.86603i | −0.527494 | − | 0.304549i | ||||
\(372\) | − | 0.464102i | − | 0.0240625i | ||||||
\(373\) | −11.1244 | + | 19.2679i | −0.575997 | + | 0.997657i | 0.419935 | + | 0.907554i | \(0.362053\pi\) |
−0.995932 | + | 0.0901025i | \(0.971281\pi\) | |||||||
\(374\) | 0.928203 | + | 1.60770i | 0.0479962 | + | 0.0831319i | ||||
\(375\) | −6.00000 | + | 3.46410i | −0.309839 | + | 0.178885i | ||||
\(376\) | −7.46410 | −0.384932 | ||||||||
\(377\) | −6.92820 | + | 28.0000i | −0.356821 | + | 1.44207i | ||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 26.3205 | − | 15.1962i | 1.35199 | − | 0.780574i | 0.363465 | − | 0.931608i | \(-0.381594\pi\) |
0.988529 | + | 0.151034i | \(0.0482603\pi\) | |||||||
\(380\) | −0.928203 | − | 1.60770i | −0.0476158 | − | 0.0824730i | ||||
\(381\) | 9.46410 | − | 16.3923i | 0.484861 | − | 0.839803i | ||||
\(382\) | − | 18.5167i | − | 0.947395i | ||||||
\(383\) | 23.6603 | + | 13.6603i | 1.20898 | + | 0.698006i | 0.962537 | − | 0.271150i | \(-0.0874040\pi\) |
0.246445 | + | 0.969157i | \(0.420737\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | − | 13.8564i | − | 0.706188i | ||||||
\(386\) | −4.92820 | + | 8.53590i | −0.250839 | + | 0.434466i | ||||
\(387\) | −1.23205 | − | 2.13397i | −0.0626287 | − | 0.108476i | ||||
\(388\) | 7.26795 | − | 4.19615i | 0.368974 | − | 0.213027i | ||||
\(389\) | −2.66025 | −0.134880 | −0.0674401 | − | 0.997723i | \(-0.521483\pi\) | ||||
−0.0674401 | + | 0.997723i | \(0.521483\pi\) | |||||||
\(390\) | 12.0000 | − | 3.46410i | 0.607644 | − | 0.175412i | ||||
\(391\) | −1.05256 | −0.0532302 | ||||||||
\(392\) | −0.866025 | + | 0.500000i | −0.0437409 | + | 0.0252538i | ||||
\(393\) | −9.50000 | − | 16.4545i | −0.479212 | − | 0.830019i | ||||
\(394\) | 11.6962 | − | 20.2583i | 0.589244 | − | 1.02060i | ||||
\(395\) | − | 8.78461i | − | 0.442002i | ||||||
\(396\) | −3.46410 | − | 2.00000i | −0.174078 | − | 0.100504i | ||||
\(397\) | −10.2058 | − | 5.89230i | −0.512213 | − | 0.295726i | 0.221530 | − | 0.975154i | \(-0.428895\pi\) |
−0.733743 | + | 0.679427i | \(0.762228\pi\) | |||||||
\(398\) | 2.12436i | 0.106484i | ||||||||
\(399\) | −0.267949 | + | 0.464102i | −0.0134142 | + | 0.0232341i | ||||
\(400\) | 3.50000 | + | 6.06218i | 0.175000 | + | 0.303109i | ||||
\(401\) | −3.80385 | + | 2.19615i | −0.189955 | + | 0.109671i | −0.591962 | − | 0.805966i | \(-0.701646\pi\) |
0.402006 | + | 0.915637i | \(0.368313\pi\) | |||||||
\(402\) | 3.19615 | 0.159410 | ||||||||
\(403\) | 1.16025 | − | 1.20577i | 0.0577964 | − | 0.0600637i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.00000 | − | 1.73205i | 0.149071 | − | 0.0860663i | ||||
\(406\) | 4.00000 | + | 6.92820i | 0.198517 | + | 0.343841i | ||||
\(407\) | 17.8564 | − | 30.9282i | 0.885109 | − | 1.53305i | ||||
\(408\) | 0.464102i | 0.0229765i | ||||||||
\(409\) | 12.4641 | + | 7.19615i | 0.616310 | + | 0.355827i | 0.775431 | − | 0.631432i | \(-0.217533\pi\) |
−0.159121 | + | 0.987259i | \(0.550866\pi\) | |||||||
\(410\) | 20.7846 | + | 12.0000i | 1.02648 | + | 0.592638i | ||||
\(411\) | 13.8564i | 0.683486i | ||||||||
\(412\) | 3.33013 | − | 5.76795i | 0.164064 | − | 0.284166i | ||||
\(413\) | 4.86603 | + | 8.42820i | 0.239441 | + | 0.414725i | ||||
\(414\) | 1.96410 | − | 1.13397i | 0.0965303 | − | 0.0557318i | ||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −1.00000 | − | 3.46410i | −0.0490290 | − | 0.169842i | ||||
\(417\) | −10.9282 | −0.535156 | ||||||||
\(418\) | −1.85641 | + | 1.07180i | −0.0907998 | + | 0.0524233i | ||||
\(419\) | 2.50000 | + | 4.33013i | 0.122133 | + | 0.211541i | 0.920609 | − | 0.390487i | \(-0.127693\pi\) |
−0.798476 | + | 0.602027i | \(0.794360\pi\) | |||||||
\(420\) | 1.73205 | − | 3.00000i | 0.0845154 | − | 0.146385i | ||||
\(421\) | − | 22.3923i | − | 1.09133i | −0.838002 | − | 0.545667i | \(-0.816276\pi\) | ||
0.838002 | − | 0.545667i | \(-0.183724\pi\) | |||||||
\(422\) | −19.8564 | − | 11.4641i | −0.966595 | − | 0.558064i | ||||
\(423\) | −6.46410 | − | 3.73205i | −0.314295 | − | 0.181459i | ||||
\(424\) | − | 11.7321i | − | 0.569759i | ||||||
\(425\) | 1.62436 | − | 2.81347i | 0.0787928 | − | 0.136473i | ||||
\(426\) | 5.96410 | + | 10.3301i | 0.288962 | + | 0.500496i | ||||
\(427\) | −4.50000 | + | 2.59808i | −0.217770 | + | 0.125730i | ||||
\(428\) | −15.4641 | −0.747486 | ||||||||
\(429\) | −4.00000 | − | 13.8564i | −0.193122 | − | 0.668994i | ||||
\(430\) | 8.53590 | 0.411638 | ||||||||
\(431\) | 19.7942 | − | 11.4282i | 0.953454 | − | 0.550477i | 0.0593021 | − | 0.998240i | \(-0.481112\pi\) |
0.894152 | + | 0.447763i | \(0.147779\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −8.92820 | + | 15.4641i | −0.429062 | + | 0.743157i | −0.996790 | − | 0.0800589i | \(-0.974489\pi\) |
0.567728 | + | 0.823216i | \(0.307823\pi\) | |||||||
\(434\) | − | 0.464102i | − | 0.0222776i | ||||||
\(435\) | −24.0000 | − | 13.8564i | −1.15071 | − | 0.664364i | ||||
\(436\) | −10.3923 | − | 6.00000i | −0.497701 | − | 0.287348i | ||||
\(437\) | − | 1.21539i | − | 0.0581400i | ||||||
\(438\) | 1.46410 | − | 2.53590i | 0.0699575 | − | 0.121170i | ||||
\(439\) | −17.1962 | − | 29.7846i | −0.820728 | − | 1.42154i | −0.905141 | − | 0.425111i | \(-0.860235\pi\) |
0.0844136 | − | 0.996431i | \(-0.473098\pi\) | |||||||
\(440\) | 12.0000 | − | 6.92820i | 0.572078 | − | 0.330289i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | −1.16025 | + | 1.20577i | −0.0551877 | + | 0.0573527i | ||||
\(443\) | −1.60770 | −0.0763839 | −0.0381920 | − | 0.999270i | \(-0.512160\pi\) | ||||
−0.0381920 | + | 0.999270i | \(0.512160\pi\) | |||||||
\(444\) | 7.73205 | − | 4.46410i | 0.366947 | − | 0.211857i | ||||
\(445\) | 14.3205 | + | 24.8038i | 0.678857 | + | 1.17582i | ||||
\(446\) | −7.23205 | + | 12.5263i | −0.342448 | + | 0.593137i | ||||
\(447\) | − | 18.4641i | − | 0.873322i | ||||||
\(448\) | −0.866025 | − | 0.500000i | −0.0409159 | − | 0.0236228i | ||||
\(449\) | −15.5885 | − | 9.00000i | −0.735665 | − | 0.424736i | 0.0848262 | − | 0.996396i | \(-0.472967\pi\) |
−0.820491 | + | 0.571660i | \(0.806300\pi\) | |||||||
\(450\) | 7.00000i | 0.329983i | ||||||||
\(451\) | 13.8564 | − | 24.0000i | 0.652473 | − | 1.13012i | ||||
\(452\) | 8.19615 | + | 14.1962i | 0.385515 | + | 0.667731i | ||||
\(453\) | 10.3923 | − | 6.00000i | 0.488273 | − | 0.281905i | ||||
\(454\) | 21.3205 | 1.00062 | ||||||||
\(455\) | 12.0000 | − | 3.46410i | 0.562569 | − | 0.162400i | ||||
\(456\) | −0.535898 | −0.0250957 | ||||||||
\(457\) | 7.96410 | − | 4.59808i | 0.372545 | − | 0.215089i | −0.302025 | − | 0.953300i | \(-0.597663\pi\) |
0.674570 | + | 0.738211i | \(0.264329\pi\) | |||||||
\(458\) | 3.03590 | + | 5.25833i | 0.141858 | + | 0.245706i | ||||
\(459\) | −0.232051 | + | 0.401924i | −0.0108312 | + | 0.0187602i | ||||
\(460\) | 7.85641i | 0.366307i | ||||||||
\(461\) | 16.3923 | + | 9.46410i | 0.763466 | + | 0.440787i | 0.830539 | − | 0.556961i | \(-0.188033\pi\) |
−0.0670730 | + | 0.997748i | \(0.521366\pi\) | |||||||
\(462\) | −3.46410 | − | 2.00000i | −0.161165 | − | 0.0930484i | ||||
\(463\) | 40.2487i | 1.87052i | 0.353966 | + | 0.935258i | \(0.384833\pi\) | ||||
−0.353966 | + | 0.935258i | \(0.615167\pi\) | |||||||
\(464\) | −4.00000 | + | 6.92820i | −0.185695 | + | 0.321634i | ||||
\(465\) | 0.803848 | + | 1.39230i | 0.0372775 | + | 0.0645666i | ||||
\(466\) | 5.66025 | − | 3.26795i | 0.262206 | − | 0.151385i | ||||
\(467\) | −29.6410 | −1.37162 | −0.685811 | − | 0.727779i | \(-0.740552\pi\) | ||||
−0.685811 | + | 0.727779i | \(0.740552\pi\) | |||||||
\(468\) | 0.866025 | − | 3.50000i | 0.0400320 | − | 0.161788i | ||||
\(469\) | 3.19615 | 0.147585 | ||||||||
\(470\) | 22.3923 | − | 12.9282i | 1.03288 | − | 0.596334i | ||||
\(471\) | −5.46410 | − | 9.46410i | −0.251773 | − | 0.436083i | ||||
\(472\) | −4.86603 | + | 8.42820i | −0.223977 | + | 0.387939i | ||||
\(473\) | − | 9.85641i | − | 0.453198i | ||||||
\(474\) | −2.19615 | − | 1.26795i | −0.100873 | − | 0.0582388i | ||||
\(475\) | 3.24871 | + | 1.87564i | 0.149061 | + | 0.0860605i | ||||
\(476\) | 0.464102i | 0.0212721i | ||||||||
\(477\) | 5.86603 | − | 10.1603i | 0.268587 | − | 0.465206i | ||||
\(478\) | 7.42820 | + | 12.8660i | 0.339758 | + | 0.588478i | ||||
\(479\) | −14.1962 | + | 8.19615i | −0.648639 | + | 0.374492i | −0.787935 | − | 0.615759i | \(-0.788849\pi\) |
0.139296 | + | 0.990251i | \(0.455516\pi\) | |||||||
\(480\) | 3.46410 | 0.158114 | ||||||||
\(481\) | 31.2487 | + | 7.73205i | 1.42482 | + | 0.352551i | ||||
\(482\) | −11.8564 | −0.540045 | ||||||||
\(483\) | 1.96410 | − | 1.13397i | 0.0893697 | − | 0.0515976i | ||||
\(484\) | −2.50000 | − | 4.33013i | −0.113636 | − | 0.196824i | ||||
\(485\) | −14.5359 | + | 25.1769i | −0.660041 | + | 1.14322i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 17.6603 | + | 10.1962i | 0.800262 | + | 0.462032i | 0.843563 | − | 0.537030i | \(-0.180454\pi\) |
−0.0433004 | + | 0.999062i | \(0.513787\pi\) | |||||||
\(488\) | −4.50000 | − | 2.59808i | −0.203705 | − | 0.117609i | ||||
\(489\) | 18.6603i | 0.843846i | ||||||||
\(490\) | 1.73205 | − | 3.00000i | 0.0782461 | − | 0.135526i | ||||
\(491\) | 8.92820 | + | 15.4641i | 0.402924 | + | 0.697885i | 0.994077 | − | 0.108674i | \(-0.0346605\pi\) |
−0.591153 | + | 0.806559i | \(0.701327\pi\) | |||||||
\(492\) | 6.00000 | − | 3.46410i | 0.270501 | − | 0.156174i | ||||
\(493\) | 3.71281 | 0.167217 | ||||||||
\(494\) | −1.39230 | − | 1.33975i | −0.0626428 | − | 0.0602780i | ||||
\(495\) | 13.8564 | 0.622799 | ||||||||
\(496\) | 0.401924 | − | 0.232051i | 0.0180469 | − | 0.0104194i | ||||
\(497\) | 5.96410 | + | 10.3301i | 0.267527 | + | 0.463370i | ||||
\(498\) | 0.866025 | − | 1.50000i | 0.0388075 | − | 0.0672166i | ||||
\(499\) | − | 3.73205i | − | 0.167070i | −0.996505 | − | 0.0835348i | \(-0.973379\pi\) | ||
0.996505 | − | 0.0835348i | \(-0.0266210\pi\) | |||||||
\(500\) | −6.00000 | − | 3.46410i | −0.268328 | − | 0.154919i | ||||
\(501\) | 17.3205 | + | 10.0000i | 0.773823 | + | 0.446767i | ||||
\(502\) | − | 23.9282i | − | 1.06797i | ||||||
\(503\) | −3.46410 | + | 6.00000i | −0.154457 | + | 0.267527i | −0.932861 | − | 0.360236i | \(-0.882696\pi\) |
0.778404 | + | 0.627763i | \(0.216029\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.07180 | 0.403291 | ||||||||
\(507\) | 11.0000 | − | 6.92820i | 0.488527 | − | 0.307692i | ||||
\(508\) | 18.9282 | 0.839803 | ||||||||
\(509\) | −12.3397 | + | 7.12436i | −0.546950 | + | 0.315782i | −0.747891 | − | 0.663822i | \(-0.768933\pi\) |
0.200941 | + | 0.979603i | \(0.435600\pi\) | |||||||
\(510\) | −0.803848 | − | 1.39230i | −0.0355950 | − | 0.0616523i | ||||
\(511\) | 1.46410 | − | 2.53590i | 0.0647680 | − | 0.112182i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −0.464102 | − | 0.267949i | −0.0204906 | − | 0.0118302i | ||||
\(514\) | 5.59808 | + | 3.23205i | 0.246921 | + | 0.142560i | ||||
\(515\) | 23.0718i | 1.01666i | ||||||||
\(516\) | 1.23205 | − | 2.13397i | 0.0542380 | − | 0.0939430i | ||||
\(517\) | −14.9282 | − | 25.8564i | −0.656542 | − | 1.13716i | ||||
\(518\) | 7.73205 | − | 4.46410i | 0.339727 | − | 0.196141i | ||||
\(519\) | −14.9282 | −0.655275 | ||||||||
\(520\) | 9.00000 | + | 8.66025i | 0.394676 | + | 0.379777i | ||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | −6.92820 | + | 4.00000i | −0.303239 | + | 0.175075i | ||||
\(523\) | −0.535898 | − | 0.928203i | −0.0234332 | − | 0.0405875i | 0.854071 | − | 0.520156i | \(-0.174126\pi\) |
−0.877504 | + | 0.479569i | \(0.840793\pi\) | |||||||
\(524\) | 9.50000 | − | 16.4545i | 0.415009 | − | 0.718817i | ||||
\(525\) | 7.00000i | 0.305505i | ||||||||
\(526\) | 15.0000 | + | 8.66025i | 0.654031 | + | 0.377605i | ||||
\(527\) | −0.186533 | − | 0.107695i | −0.00812553 | − | 0.00469127i | ||||
\(528\) | − | 4.00000i | − | 0.174078i | ||||||
\(529\) | 8.92820 | − | 15.4641i | 0.388183 | − | 0.672352i | ||||
\(530\) | 20.3205 | + | 35.1962i | 0.882666 | + | 1.52882i | ||||
\(531\) | −8.42820 | + | 4.86603i | −0.365753 | + | 0.211168i | ||||
\(532\) | −0.535898 | −0.0232341 | ||||||||
\(533\) | 24.2487 | + | 6.00000i | 1.05033 | + | 0.259889i | ||||
\(534\) | 8.26795 | 0.357789 | ||||||||
\(535\) | 46.3923 | − | 26.7846i | 2.00571 | − | 1.15800i | ||||
\(536\) | 1.59808 | + | 2.76795i | 0.0690264 | + | 0.119557i | ||||
\(537\) | −1.53590 | + | 2.66025i | −0.0662789 | + | 0.114798i | ||||
\(538\) | − | 1.60770i | − | 0.0693127i | ||||||
\(539\) | −3.46410 | − | 2.00000i | −0.149209 | − | 0.0861461i | ||||
\(540\) | 3.00000 | + | 1.73205i | 0.129099 | + | 0.0745356i | ||||
\(541\) | − | 17.3205i | − | 0.744667i | −0.928099 | − | 0.372333i | \(-0.878558\pi\) | ||
0.928099 | − | 0.372333i | \(-0.121442\pi\) | |||||||
\(542\) | 2.76795 | − | 4.79423i | 0.118894 | − | 0.205930i | ||||
\(543\) | −8.39230 | − | 14.5359i | −0.360148 | − | 0.623795i | ||||
\(544\) | −0.401924 | + | 0.232051i | −0.0172323 | + | 0.00994910i | ||||
\(545\) | 41.5692 | 1.78063 | ||||||||
\(546\) | 0.866025 | − | 3.50000i | 0.0370625 | − | 0.149786i | ||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | −12.0000 | + | 6.92820i | −0.512615 | + | 0.295958i | ||||
\(549\) | −2.59808 | − | 4.50000i | −0.110883 | − | 0.192055i | ||||
\(550\) | −14.0000 | + | 24.2487i | −0.596962 | + | 1.03397i | ||||
\(551\) | 4.28719i | 0.182640i | ||||||||
\(552\) | 1.96410 | + | 1.13397i | 0.0835977 | + | 0.0482652i | ||||
\(553\) | −2.19615 | − | 1.26795i | −0.0933899 | − | 0.0539187i | ||||
\(554\) | − | 27.3205i | − | 1.16074i | ||||||
\(555\) | −15.4641 | + | 26.7846i | −0.656415 | + | 1.13694i | ||||
\(556\) | −5.46410 | − | 9.46410i | −0.231730 | − | 0.401367i | ||||
\(557\) | −39.3109 | + | 22.6962i | −1.66566 | + | 0.961667i | −0.695718 | + | 0.718315i | \(0.744914\pi\) |
−0.969938 | + | 0.243351i | \(0.921753\pi\) | |||||||
\(558\) | 0.464102 | 0.0196470 | ||||||||
\(559\) | 8.53590 | − | 2.46410i | 0.361030 | − | 0.104220i | ||||
\(560\) | 3.46410 | 0.146385 | ||||||||
\(561\) | −1.60770 | + | 0.928203i | −0.0678769 | + | 0.0391888i | ||||
\(562\) | 9.19615 | + | 15.9282i | 0.387916 | + | 0.671891i | ||||
\(563\) | 6.92820 | − | 12.0000i | 0.291989 | − | 0.505740i | −0.682291 | − | 0.731081i | \(-0.739016\pi\) |
0.974280 | + | 0.225341i | \(0.0723496\pi\) | |||||||
\(564\) | − | 7.46410i | − | 0.314295i | ||||||
\(565\) | −49.1769 | − | 28.3923i | −2.06889 | − | 1.19447i | ||||
\(566\) | 3.92820 | + | 2.26795i | 0.165115 | + | 0.0953290i | ||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | −5.96410 | + | 10.3301i | −0.250248 | + | 0.433443i | ||||
\(569\) | 4.26795 | + | 7.39230i | 0.178922 | + | 0.309902i | 0.941511 | − | 0.336981i | \(-0.109406\pi\) |
−0.762590 | + | 0.646882i | \(0.776072\pi\) | |||||||
\(570\) | 1.60770 | − | 0.928203i | 0.0673389 | − | 0.0388782i | ||||
\(571\) | −17.3923 | −0.727845 | −0.363923 | − | 0.931429i | \(-0.618563\pi\) | ||||
−0.363923 | + | 0.931429i | \(0.618563\pi\) | |||||||
\(572\) | 10.0000 | − | 10.3923i | 0.418121 | − | 0.434524i | ||||
\(573\) | 18.5167 | 0.773545 | ||||||||
\(574\) | 6.00000 | − | 3.46410i | 0.250435 | − | 0.144589i | ||||
\(575\) | −7.93782 | − | 13.7487i | −0.331030 | − | 0.573361i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 42.7846i | 1.78115i | 0.454840 | + | 0.890573i | \(0.349697\pi\) | ||||
−0.454840 | + | 0.890573i | \(0.650303\pi\) | |||||||
\(578\) | −14.5359 | − | 8.39230i | −0.604614 | − | 0.349074i | ||||
\(579\) | −8.53590 | − | 4.92820i | −0.354740 | − | 0.204809i | ||||
\(580\) | − | 27.7128i | − | 1.15071i | ||||||
\(581\) | 0.866025 | − | 1.50000i | 0.0359288 | − | 0.0622305i | ||||
\(582\) | 4.19615 | + | 7.26795i | 0.173936 | + | 0.301266i | ||||
\(583\) | 40.6410 | − | 23.4641i | 1.68318 | − | 0.971784i | ||||
\(584\) | 2.92820 | 0.121170 | ||||||||
\(585\) | 3.46410 | + | 12.0000i | 0.143223 | + | 0.496139i | ||||
\(586\) | −26.5359 | −1.09619 | ||||||||
\(587\) | 13.9641 | − | 8.06218i | 0.576360 | − | 0.332762i | −0.183325 | − | 0.983052i | \(-0.558686\pi\) |
0.759686 | + | 0.650291i | \(0.225353\pi\) | |||||||
\(588\) | −0.500000 | − | 0.866025i | −0.0206197 | − | 0.0357143i | ||||
\(589\) | 0.124356 | − | 0.215390i | 0.00512399 | − | 0.00887500i | ||||
\(590\) | − | 33.7128i | − | 1.38793i | ||||||
\(591\) | 20.2583 | + | 11.6962i | 0.833316 | + | 0.481115i | ||||
\(592\) | 7.73205 | + | 4.46410i | 0.317785 | + | 0.183473i | ||||
\(593\) | − | 7.73205i | − | 0.317517i | −0.987317 | − | 0.158759i | \(-0.949251\pi\) | ||
0.987317 | − | 0.158759i | \(-0.0507492\pi\) | |||||||
\(594\) | 2.00000 | − | 3.46410i | 0.0820610 | − | 0.142134i | ||||
\(595\) | −0.803848 | − | 1.39230i | −0.0329545 | − | 0.0570789i | ||||
\(596\) | 15.9904 | − | 9.23205i | 0.654992 | − | 0.378160i | ||||
\(597\) | −2.12436 | −0.0869441 | ||||||||
\(598\) | 2.26795 | + | 7.85641i | 0.0927433 | + | 0.321272i | ||||
\(599\) | 19.0526 | 0.778466 | 0.389233 | − | 0.921139i | \(-0.372740\pi\) | ||||
0.389233 | + | 0.921139i | \(0.372740\pi\) | |||||||
\(600\) | −6.06218 | + | 3.50000i | −0.247487 | + | 0.142887i | ||||
\(601\) | −12.1244 | − | 21.0000i | −0.494563 | − | 0.856608i | 0.505418 | − | 0.862875i | \(-0.331338\pi\) |
−0.999980 | + | 0.00626702i | \(0.998005\pi\) | |||||||
\(602\) | 1.23205 | − | 2.13397i | 0.0502146 | − | 0.0869743i | ||||
\(603\) | 3.19615i | 0.130157i | ||||||||
\(604\) | 10.3923 | + | 6.00000i | 0.422857 | + | 0.244137i | ||||
\(605\) | 15.0000 | + | 8.66025i | 0.609837 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.40192 | − | 4.16025i | 0.0974911 | − | 0.168860i | −0.813154 | − | 0.582048i | \(-0.802252\pi\) |
0.910646 | + | 0.413188i | \(0.135585\pi\) | |||||||
\(608\) | −0.267949 | − | 0.464102i | −0.0108668 | − | 0.0188218i | ||||
\(609\) | −6.92820 | + | 4.00000i | −0.280745 | + | 0.162088i | ||||
\(610\) | 18.0000 | 0.728799 | ||||||||
\(611\) | 18.6603 | − | 19.3923i | 0.754913 | − | 0.784529i | ||||
\(612\) | −0.464102 | −0.0187602 | ||||||||
\(613\) | −11.7846 | + | 6.80385i | −0.475976 | + | 0.274805i | −0.718738 | − | 0.695281i | \(-0.755280\pi\) |
0.242762 | + | 0.970086i | \(0.421947\pi\) | |||||||
\(614\) | −11.0000 | − | 19.0526i | −0.443924 | − | 0.768899i | ||||
\(615\) | −12.0000 | + | 20.7846i | −0.483887 | + | 0.838116i | ||||
\(616\) | − | 4.00000i | − | 0.161165i | ||||||
\(617\) | −18.9282 | − | 10.9282i | −0.762021 | − | 0.439953i | 0.0680000 | − | 0.997685i | \(-0.478338\pi\) |
−0.830021 | + | 0.557732i | \(0.811672\pi\) | |||||||
\(618\) | 5.76795 | + | 3.33013i | 0.232021 | + | 0.133957i | ||||
\(619\) | 10.7846i | 0.433470i | 0.976230 | + | 0.216735i | \(0.0695408\pi\) | ||||
−0.976230 | + | 0.216735i | \(0.930459\pi\) | |||||||
\(620\) | −0.803848 | + | 1.39230i | −0.0322833 | + | 0.0559163i | ||||
\(621\) | 1.13397 | + | 1.96410i | 0.0455048 | + | 0.0788167i | ||||
\(622\) | −18.4641 | + | 10.6603i | −0.740343 | + | 0.427437i | ||||
\(623\) | 8.26795 | 0.331248 | ||||||||
\(624\) | 3.46410 | − | 1.00000i | 0.138675 | − | 0.0400320i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −30.5885 | + | 17.6603i | −1.22256 | + | 0.705846i | ||||
\(627\) | −1.07180 | − | 1.85641i | −0.0428034 | − | 0.0741377i | ||||
\(628\) | 5.46410 | − | 9.46410i | 0.218041 | − | 0.377659i | ||||
\(629\) | − | 4.14359i | − | 0.165216i | ||||||
\(630\) | 3.00000 | + | 1.73205i | 0.119523 | + | 0.0690066i | ||||
\(631\) | −18.2487 | − | 10.5359i | −0.726470 | − | 0.419427i | 0.0906596 | − | 0.995882i | \(-0.471102\pi\) |
−0.817129 | + | 0.576454i | \(0.804436\pi\) | |||||||
\(632\) | − | 2.53590i | − | 0.100873i | ||||||
\(633\) | 11.4641 | − | 19.8564i | 0.455657 | − | 0.789221i | ||||
\(634\) | −4.76795 | − | 8.25833i | −0.189359 | − | 0.327980i | ||||
\(635\) | −56.7846 | + | 32.7846i | −2.25343 | + | 1.30102i | ||||
\(636\) | 11.7321 | 0.465206 | ||||||||
\(637\) | 0.866025 | − | 3.50000i | 0.0343132 | − | 0.138675i | ||||
\(638\) | −32.0000 | −1.26689 | ||||||||
\(639\) | −10.3301 | + | 5.96410i | −0.408654 | + | 0.235936i | ||||
\(640\) | 1.73205 | + | 3.00000i | 0.0684653 | + | 0.118585i | ||||
\(641\) | 21.3205 | − | 36.9282i | 0.842109 | − | 1.45858i | −0.0459986 | − | 0.998942i | \(-0.514647\pi\) |
0.888108 | − | 0.459635i | \(-0.152020\pi\) | |||||||
\(642\) | − | 15.4641i | − | 0.610319i | ||||||
\(643\) | −24.4641 | − | 14.1244i | −0.964770 | − | 0.557010i | −0.0671322 | − | 0.997744i | \(-0.521385\pi\) |
−0.897638 | + | 0.440734i | \(0.854718\pi\) | |||||||
\(644\) | 1.96410 | + | 1.13397i | 0.0773964 | + | 0.0446849i | ||||
\(645\) | 8.53590i | 0.336101i | ||||||||
\(646\) | −0.124356 | + | 0.215390i | −0.00489271 | + | 0.00847442i | ||||
\(647\) | 1.33975 | + | 2.32051i | 0.0526708 | + | 0.0912286i | 0.891159 | − | 0.453692i | \(-0.149893\pi\) |
−0.838488 | + | 0.544920i | \(0.816560\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −38.9282 | −1.52807 | ||||||||
\(650\) | −24.5000 | − | 6.06218i | −0.960969 | − | 0.237778i | ||||
\(651\) | 0.464102 | 0.0181896 | ||||||||
\(652\) | −16.1603 | + | 9.33013i | −0.632884 | + | 0.365396i | ||||
\(653\) | 3.20577 | + | 5.55256i | 0.125452 | + | 0.217288i | 0.921909 | − | 0.387406i | \(-0.126629\pi\) |
−0.796458 | + | 0.604694i | \(0.793295\pi\) | |||||||
\(654\) | 6.00000 | − | 10.3923i | 0.234619 | − | 0.406371i | ||||
\(655\) | 65.8179i | 2.57172i | ||||||||
\(656\) | 6.00000 | + | 3.46410i | 0.234261 | + | 0.135250i | ||||
\(657\) | 2.53590 | + | 1.46410i | 0.0989348 | + | 0.0571200i | ||||
\(658\) | − | 7.46410i | − | 0.290981i | ||||||
\(659\) | −11.1962 | + | 19.3923i | −0.436140 | + | 0.755417i | −0.997388 | − | 0.0722309i | \(-0.976988\pi\) |
0.561248 | + | 0.827648i | \(0.310321\pi\) | |||||||
\(660\) | 6.92820 | + | 12.0000i | 0.269680 | + | 0.467099i | ||||
\(661\) | 4.08142 | − | 2.35641i | 0.158749 | − | 0.0916536i | −0.418521 | − | 0.908207i | \(-0.637451\pi\) |
0.577270 | + | 0.816553i | \(0.304118\pi\) | |||||||
\(662\) | −13.3205 | −0.517716 | ||||||||
\(663\) | −1.20577 | − | 1.16025i | −0.0468283 | − | 0.0450605i | ||||
\(664\) | 1.73205 | 0.0672166 | ||||||||
\(665\) | 1.60770 | − | 0.928203i | 0.0623437 | − | 0.0359942i | ||||
\(666\) | 4.46410 | + | 7.73205i | 0.172980 | + | 0.299611i | ||||
\(667\) | 9.07180 | − | 15.7128i | 0.351261 | − | 0.608403i | ||||
\(668\) | 20.0000i | 0.773823i | ||||||||
\(669\) | −12.5263 | − | 7.23205i | −0.484294 | − | 0.279607i | ||||
\(670\) | −9.58846 | − | 5.53590i | −0.370434 | − | 0.213870i | ||||
\(671\) | − | 20.7846i | − | 0.802381i | ||||||
\(672\) | 0.500000 | − | 0.866025i | 0.0192879 | − | 0.0334077i | ||||
\(673\) | −14.8205 | − | 25.6699i | −0.571289 | − | 0.989501i | −0.996434 | − | 0.0843758i | \(-0.973110\pi\) |
0.425145 | − | 0.905125i | \(-0.360223\pi\) | |||||||
\(674\) | 5.19615 | − | 3.00000i | 0.200148 | − | 0.115556i | ||||
\(675\) | −7.00000 | −0.269430 | ||||||||
\(676\) | 11.5000 | + | 6.06218i | 0.442308 | + | 0.233161i | ||||
\(677\) | 14.9282 | 0.573737 | 0.286869 | − | 0.957970i | \(-0.407386\pi\) | ||||
0.286869 | + | 0.957970i | \(0.407386\pi\) | |||||||
\(678\) | −14.1962 | + | 8.19615i | −0.545200 | + | 0.314771i | ||||
\(679\) | 4.19615 | + | 7.26795i | 0.161034 | + | 0.278918i | ||||
\(680\) | 0.803848 | − | 1.39230i | 0.0308261 | − | 0.0533925i | ||||
\(681\) | 21.3205i | 0.817004i | ||||||||
\(682\) | 1.60770 | + | 0.928203i | 0.0615618 | + | 0.0355427i | ||||
\(683\) | 9.67949 | + | 5.58846i | 0.370375 | + | 0.213836i | 0.673622 | − | 0.739076i | \(-0.264737\pi\) |
−0.303247 | + | 0.952912i | \(0.598071\pi\) | |||||||
\(684\) | − | 0.535898i | − | 0.0204906i | ||||||
\(685\) | 24.0000 | − | 41.5692i | 0.916993 | − | 1.58828i | ||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | −5.25833 | + | 3.03590i | −0.200618 | + | 0.115827i | ||||
\(688\) | 2.46410 | 0.0939430 | ||||||||
\(689\) | 30.4808 | + | 29.3301i | 1.16122 | + | 1.11739i | ||||
\(690\) | −7.85641 | −0.299088 | ||||||||
\(691\) | −18.3397 | + | 10.5885i | −0.697677 | + | 0.402804i | −0.806482 | − | 0.591259i | \(-0.798631\pi\) |
0.108805 | + | 0.994063i | \(0.465298\pi\) | |||||||
\(692\) | −7.46410 | − | 12.9282i | −0.283743 | − | 0.491457i | ||||
\(693\) | 2.00000 | − | 3.46410i | 0.0759737 | − | 0.131590i | ||||
\(694\) | 29.7128i | 1.12788i | ||||||||
\(695\) | 32.7846 | + | 18.9282i | 1.24359 | + | 0.717988i | ||||
\(696\) | −6.92820 | − | 4.00000i | −0.262613 | − | 0.151620i | ||||
\(697\) | − | 3.21539i | − | 0.121792i | ||||||
\(698\) | 16.8205 | − | 29.1340i | 0.636666 | − | 1.10274i | ||||
\(699\) | 3.26795 | + | 5.66025i | 0.123605 | + | 0.214090i | ||||
\(700\) | −6.06218 | + | 3.50000i | −0.229129 | + | 0.132288i | ||||
\(701\) | −22.1244 | −0.835625 | −0.417813 | − | 0.908533i | \(-0.637203\pi\) | ||||
−0.417813 | + | 0.908533i | \(0.637203\pi\) | |||||||
\(702\) | 3.50000 | + | 0.866025i | 0.132099 | + | 0.0326860i | ||||
\(703\) | 4.78461 | 0.180455 | ||||||||
\(704\) | 3.46410 | − | 2.00000i | 0.130558 | − | 0.0753778i | ||||
\(705\) | 12.9282 | + | 22.3923i | 0.486904 | + | 0.843343i | ||||
\(706\) | 13.3301 | − | 23.0885i | 0.501686 | − | 0.868946i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.42820 | − | 4.86603i | −0.316751 | − | 0.182876i | ||||
\(709\) | −41.3205 | − | 23.8564i | −1.55182 | − | 0.895946i | −0.997993 | − | 0.0633169i | \(-0.979832\pi\) |
−0.553831 | − | 0.832629i | \(-0.686835\pi\) | |||||||
\(710\) | − | 41.3205i | − | 1.55073i | ||||||
\(711\) | 1.26795 | − | 2.19615i | 0.0475518 | − | 0.0823622i | ||||
\(712\) | 4.13397 | + | 7.16025i | 0.154927 | + | 0.268342i | ||||
\(713\) | −0.911543 | + | 0.526279i | −0.0341375 | + | 0.0197093i | ||||
\(714\) | −0.464102 | −0.0173686 | ||||||||
\(715\) | −12.0000 | + | 48.4974i | −0.448775 | + | 1.81370i | ||||
\(716\) | −3.07180 | −0.114798 | ||||||||
\(717\) | −12.8660 | + | 7.42820i | −0.480491 | + | 0.277411i | ||||
\(718\) | −4.00000 | − | 6.92820i | −0.149279 | − | 0.258558i | ||||
\(719\) | 20.7321 | − | 35.9090i | 0.773175 | − | 1.33918i | −0.162639 | − | 0.986686i | \(-0.552001\pi\) |
0.935814 | − | 0.352493i | \(-0.114666\pi\) | |||||||
\(720\) | 3.46410i | 0.129099i | ||||||||
\(721\) | 5.76795 | + | 3.33013i | 0.214810 | + | 0.124020i | ||||
\(722\) | 16.2058 | + | 9.35641i | 0.603116 | + | 0.348209i | ||||
\(723\) | − | 11.8564i | − | 0.440945i | ||||||
\(724\) | 8.39230 | − | 14.5359i | 0.311898 | − | 0.540222i | ||||
\(725\) | 28.0000 | + | 48.4974i | 1.03989 | + | 1.80115i | ||||
\(726\) | 4.33013 | − | 2.50000i | 0.160706 | − | 0.0927837i | ||||
\(727\) | −42.9090 | −1.59141 | −0.795703 | − | 0.605687i | \(-0.792898\pi\) | ||||
−0.795703 | + | 0.605687i | \(0.792898\pi\) | |||||||
\(728\) | 3.46410 | − | 1.00000i | 0.128388 | − | 0.0370625i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.78461 | + | 5.07180i | −0.325133 | + | 0.187716i | ||||
\(731\) | −0.571797 | − | 0.990381i | −0.0211487 | − | 0.0366306i | ||||
\(732\) | 2.59808 | − | 4.50000i | 0.0960277 | − | 0.166325i | ||||
\(733\) | − | 22.8564i | − | 0.844221i | −0.906544 | − | 0.422110i | \(-0.861289\pi\) | ||
0.906544 | − | 0.422110i | \(-0.138711\pi\) | |||||||
\(734\) | 4.37564 | + | 2.52628i | 0.161508 | + | 0.0932467i | ||||
\(735\) | 3.00000 | + | 1.73205i | 0.110657 | + | 0.0638877i | ||||
\(736\) | 2.26795i | 0.0835977i | ||||||||
\(737\) | −6.39230 | + | 11.0718i | −0.235464 | + | 0.407835i | ||||
\(738\) | 3.46410 | + | 6.00000i | 0.127515 | + | 0.220863i | ||||
\(739\) | −3.69615 | + | 2.13397i | −0.135965 | + | 0.0784995i | −0.566440 | − | 0.824103i | \(-0.691680\pi\) |
0.430474 | + | 0.902603i | \(0.358346\pi\) | |||||||
\(740\) | −30.9282 | −1.13694 | ||||||||
\(741\) | 1.33975 | − | 1.39230i | 0.0492168 | − | 0.0511476i | ||||
\(742\) | 11.7321 | 0.430697 | ||||||||
\(743\) | 34.4545 | − | 19.8923i | 1.26401 | − | 0.729778i | 0.290164 | − | 0.956977i | \(-0.406290\pi\) |
0.973848 | + | 0.227199i | \(0.0729568\pi\) | |||||||
\(744\) | 0.232051 | + | 0.401924i | 0.00850740 | + | 0.0147352i | ||||
\(745\) | −31.9808 | + | 55.3923i | −1.17168 | + | 2.02942i | ||||
\(746\) | − | 22.2487i | − | 0.814583i | ||||||
\(747\) | 1.50000 | + | 0.866025i | 0.0548821 | + | 0.0316862i | ||||
\(748\) | −1.60770 | − | 0.928203i | −0.0587832 | − | 0.0339385i | ||||
\(749\) | − | 15.4641i | − | 0.565046i | ||||||
\(750\) | 3.46410 | − | 6.00000i | 0.126491 | − | 0.219089i | ||||
\(751\) | −2.66025 | − | 4.60770i | −0.0970740 | − | 0.168137i | 0.813398 | − | 0.581707i | \(-0.197615\pi\) |
−0.910472 | + | 0.413570i | \(0.864282\pi\) | |||||||
\(752\) | 6.46410 | − | 3.73205i | 0.235722 | − | 0.136094i | ||||
\(753\) | 23.9282 | 0.871992 | ||||||||
\(754\) | −8.00000 | − | 27.7128i | −0.291343 | − | 1.00924i | ||||
\(755\) | −41.5692 | −1.51286 | ||||||||
\(756\) | 0.866025 | − | 0.500000i | 0.0314970 | − | 0.0181848i | ||||
\(757\) | 3.92820 | + | 6.80385i | 0.142773 | + | 0.247290i | 0.928540 | − | 0.371233i | \(-0.121065\pi\) |
−0.785767 | + | 0.618523i | \(0.787731\pi\) | |||||||
\(758\) | −15.1962 | + | 26.3205i | −0.551949 | + | 0.956004i | ||||
\(759\) | 9.07180i | 0.329285i | ||||||||
\(760\) | 1.60770 | + | 0.928203i | 0.0583172 | + | 0.0336695i | ||||
\(761\) | 6.00000 | + | 3.46410i | 0.217500 | + | 0.125574i | 0.604792 | − | 0.796383i | \(-0.293256\pi\) |
−0.387292 | + | 0.921957i | \(0.626590\pi\) | |||||||
\(762\) | 18.9282i | 0.685696i | ||||||||
\(763\) | 6.00000 | − | 10.3923i | 0.217215 | − | 0.376227i | ||||
\(764\) | 9.25833 | + | 16.0359i | 0.334955 | + | 0.580158i | ||||
\(765\) | 1.39230 | − | 0.803848i | 0.0503389 | − | 0.0290632i | ||||
\(766\) | −27.3205 | −0.987130 | ||||||||
\(767\) | −9.73205 | − | 33.7128i | −0.351404 | − | 1.21730i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 23.0718 | − | 13.3205i | 0.831990 | − | 0.480350i | −0.0225434 | − | 0.999746i | \(-0.507176\pi\) |
0.854534 | + | 0.519396i | \(0.173843\pi\) | |||||||
\(770\) | 6.92820 | + | 12.0000i | 0.249675 | + | 0.432450i | ||||
\(771\) | −3.23205 | + | 5.59808i | −0.116399 | + | 0.201610i | ||||
\(772\) | − | 9.85641i | − | 0.354740i | ||||||
\(773\) | 0.803848 | + | 0.464102i | 0.0289124 | + | 0.0166926i | 0.514387 | − | 0.857558i | \(-0.328020\pi\) |
−0.485474 | + | 0.874251i | \(0.661353\pi\) | |||||||
\(774\) | 2.13397 | + | 1.23205i | 0.0767041 | + | 0.0442852i | ||||
\(775\) | − | 3.24871i | − | 0.116697i | ||||||
\(776\) | −4.19615 | + | 7.26795i | −0.150633 | + | 0.260904i | ||||
\(777\) | 4.46410 | + | 7.73205i | 0.160149 | + | 0.277386i | ||||
\(778\) | 2.30385 | − | 1.33013i | 0.0825969 | − | 0.0476874i | ||||
\(779\) | 3.71281 | 0.133025 | ||||||||
\(780\) | −8.66025 | + | 9.00000i | −0.310087 | + | 0.322252i | ||||
\(781\) | −47.7128 | −1.70730 | ||||||||
\(782\) | 0.911543 | − | 0.526279i | 0.0325967 | − | 0.0188197i | ||||
\(783\) | −4.00000 | − | 6.92820i | −0.142948 | − | 0.247594i | ||||
\(784\) | 0.500000 | − | 0.866025i | 0.0178571 | − | 0.0309295i | ||||
\(785\) | 37.8564i | 1.35115i | ||||||||
\(786\) | 16.4545 | + | 9.50000i | 0.586912 | + | 0.338854i | ||||
\(787\) | −10.7321 | − | 6.19615i | −0.382556 | − | 0.220869i | 0.296374 | − | 0.955072i | \(-0.404223\pi\) |
−0.678930 | + | 0.734203i | \(0.737556\pi\) | |||||||
\(788\) | 23.3923i | 0.833316i | ||||||||
\(789\) | −8.66025 | + | 15.0000i | −0.308313 | + | 0.534014i | ||||
\(790\) | 4.39230 | + | 7.60770i | 0.156271 | + | 0.270670i | ||||
\(791\) | −14.1962 | + | 8.19615i | −0.504757 | + | 0.291422i | ||||
\(792\) | 4.00000 | 0.142134 | ||||||||
\(793\) | 18.0000 | − | 5.19615i | 0.639199 | − | 0.184521i | ||||
\(794\) | 11.7846 | 0.418220 | ||||||||
\(795\) | −35.1962 | + | 20.3205i | −1.24828 | + | 0.720694i | ||||
\(796\) | −1.06218 | − | 1.83975i | −0.0376479 | − | 0.0652081i | ||||
\(797\) | −3.12436 | + | 5.41154i | −0.110670 | + | 0.191687i | −0.916041 | − | 0.401085i | \(-0.868633\pi\) |
0.805370 | + | 0.592772i | \(0.201966\pi\) | |||||||
\(798\) | − | 0.535898i | − | 0.0189706i | ||||||
\(799\) | −3.00000 | − | 1.73205i | −0.106132 | − | 0.0612756i | ||||
\(800\) | −6.06218 | − | 3.50000i | −0.214330 | − | 0.123744i | ||||
\(801\) | 8.26795i | 0.292134i | ||||||||
\(802\) | 2.19615 | − | 3.80385i | 0.0775488 | − | 0.134319i | ||||
\(803\) | 5.85641 | + | 10.1436i | 0.206668 | + | 0.357960i | ||||
\(804\) | −2.76795 | + | 1.59808i | −0.0976180 | + | 0.0563598i | ||||
\(805\) | −7.85641 | −0.276902 | ||||||||
\(806\) | −0.401924 | + | 1.62436i | −0.0141572 | + | 0.0572155i | ||||
\(807\) | 1.60770 | 0.0565935 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.8564 | + | 34.3923i | 0.698114 | + | 1.20917i | 0.969120 | + | 0.246591i | \(0.0793105\pi\) |
−0.271006 | + | 0.962578i | \(0.587356\pi\) | |||||||
\(810\) | −1.73205 | + | 3.00000i | −0.0608581 | + | 0.105409i | ||||
\(811\) | 29.8564i | 1.04840i | 0.851595 | + | 0.524200i | \(0.175636\pi\) | ||||
−0.851595 | + | 0.524200i | \(0.824364\pi\) | |||||||
\(812\) | −6.92820 | − | 4.00000i | −0.243132 | − | 0.140372i | ||||
\(813\) | 4.79423 | + | 2.76795i | 0.168141 | + | 0.0970762i | ||||
\(814\) | 35.7128i | 1.25173i | ||||||||
\(815\) | 32.3205 | − | 55.9808i | 1.13214 | − | 1.96092i | ||||
\(816\) | −0.232051 | − | 0.401924i | −0.00812340 | − | 0.0140701i | ||||
\(817\) | 1.14359 | − | 0.660254i | 0.0400093 | − | 0.0230994i | ||||
\(818\) | −14.3923 | −0.503215 | ||||||||
\(819\) | 3.50000 | + | 0.866025i | 0.122300 | + | 0.0302614i | ||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | 14.9378 | − | 8.62436i | 0.521334 | − | 0.300992i | −0.216147 | − | 0.976361i | \(-0.569349\pi\) |
0.737480 | + | 0.675369i | \(0.236016\pi\) | |||||||
\(822\) | −6.92820 | − | 12.0000i | −0.241649 | − | 0.418548i | ||||
\(823\) | 22.1962 | − | 38.4449i | 0.773709 | − | 1.34010i | −0.161808 | − | 0.986822i | \(-0.551732\pi\) |
0.935517 | − | 0.353281i | \(-0.114934\pi\) | |||||||
\(824\) | 6.66025i | 0.232021i | ||||||||
\(825\) | −24.2487 | − | 14.0000i | −0.844232 | − | 0.487417i | ||||
\(826\) | −8.42820 | − | 4.86603i | −0.293255 | − | 0.169311i | ||||
\(827\) | − | 15.6077i | − | 0.542733i | −0.962476 | − | 0.271366i | \(-0.912525\pi\) | ||
0.962476 | − | 0.271366i | \(-0.0874755\pi\) | |||||||
\(828\) | −1.13397 | + | 1.96410i | −0.0394083 | + | 0.0682572i | ||||
\(829\) | 24.3923 | + | 42.2487i | 0.847180 | + | 1.46736i | 0.883715 | + | 0.468026i | \(0.155035\pi\) |
−0.0365349 | + | 0.999332i | \(0.511632\pi\) | |||||||
\(830\) | −5.19615 | + | 3.00000i | −0.180361 | + | 0.104132i | ||||
\(831\) | 27.3205 | 0.947738 | ||||||||
\(832\) | 2.59808 | + | 2.50000i | 0.0900721 | + | 0.0866719i | ||||
\(833\) | −0.464102 | −0.0160802 | ||||||||
\(834\) | 9.46410 | − | 5.46410i | 0.327715 | − | 0.189206i | ||||
\(835\) | −34.6410 | − | 60.0000i | −1.19880 | − | 2.07639i | ||||
\(836\) | 1.07180 | − | 1.85641i | 0.0370689 | − | 0.0642052i | ||||
\(837\) | 0.464102i | 0.0160417i | ||||||||
\(838\) | −4.33013 | − | 2.50000i | −0.149582 | − | 0.0863611i | ||||
\(839\) | 19.3923 | + | 11.1962i | 0.669497 | + | 0.386534i | 0.795886 | − | 0.605447i | \(-0.207005\pi\) |
−0.126389 | + | 0.991981i | \(0.540339\pi\) | |||||||
\(840\) | 3.46410i | 0.119523i | ||||||||
\(841\) | −17.5000 | + | 30.3109i | −0.603448 | + | 1.04520i | ||||
\(842\) | 11.1962 | + | 19.3923i | 0.385845 | + | 0.668303i | ||||
\(843\) | −15.9282 | + | 9.19615i | −0.548596 | + | 0.316732i | ||||
\(844\) | 22.9282 | 0.789221 | ||||||||
\(845\) | −45.0000 | + | 1.73205i | −1.54805 | + | 0.0595844i | ||||
\(846\) | 7.46410 | 0.256621 | ||||||||
\(847\) | 4.33013 | − | 2.50000i | 0.148785 | − | 0.0859010i | ||||
\(848\) | 5.86603 | + | 10.1603i | 0.201440 | + | 0.348905i | ||||
\(849\) | −2.26795 | + | 3.92820i | −0.0778358 | + | 0.134816i | ||||
\(850\) | 3.24871i | 0.111430i | ||||||||
\(851\) | −17.5359 | − | 10.1244i | −0.601123 | − | 0.347058i | ||||
\(852\) | −10.3301 | − | 5.96410i | −0.353904 | − | 0.204327i | ||||
\(853\) | 21.6410i | 0.740974i | 0.928838 | + | 0.370487i | \(0.120809\pi\) | ||||
−0.928838 | + | 0.370487i | \(0.879191\pi\) | |||||||
\(854\) | 2.59808 | − | 4.50000i | 0.0889043 | − | 0.153987i | ||||
\(855\) | 0.928203 | + | 1.60770i | 0.0317439 | + | 0.0549820i | ||||
\(856\) | 13.3923 | − | 7.73205i | 0.457740 | − | 0.264276i | ||||
\(857\) | −21.7128 | −0.741696 | −0.370848 | − | 0.928694i | \(-0.620933\pi\) | ||||
−0.370848 | + | 0.928694i | \(0.620933\pi\) | |||||||
\(858\) | 10.3923 | + | 10.0000i | 0.354787 | + | 0.341394i | ||||
\(859\) | 11.8564 | 0.404535 | 0.202268 | − | 0.979330i | \(-0.435169\pi\) | ||||
0.202268 | + | 0.979330i | \(0.435169\pi\) | |||||||
\(860\) | −7.39230 | + | 4.26795i | −0.252076 | + | 0.145536i | ||||
\(861\) | 3.46410 | + | 6.00000i | 0.118056 | + | 0.204479i | ||||
\(862\) | −11.4282 | + | 19.7942i | −0.389246 | + | 0.674194i | ||||
\(863\) | 29.0718i | 0.989615i | 0.869002 | + | 0.494808i | \(0.164762\pi\) | ||||
−0.869002 | + | 0.494808i | \(0.835238\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 44.7846 | + | 25.8564i | 1.52272 | + | 0.879144i | ||||
\(866\) | − | 17.8564i | − | 0.606785i | ||||||
\(867\) | 8.39230 | − | 14.5359i | 0.285018 | − | 0.493665i | ||||
\(868\) | 0.232051 | + | 0.401924i | 0.00787632 | + | 0.0136422i | ||||
\(869\) | 8.78461 | − | 5.07180i | 0.297997 | − | 0.172049i | ||||
\(870\) | 27.7128 | 0.939552 | ||||||||
\(871\) | −11.1865 | − | 2.76795i | −0.379041 | − | 0.0937884i | ||||
\(872\) | 12.0000 | 0.406371 | ||||||||
\(873\) | −7.26795 | + | 4.19615i | −0.245983 | + | 0.142018i | ||||
\(874\) | 0.607695 | + | 1.05256i | 0.0205556 | + | 0.0356033i | ||||
\(875\) | 3.46410 | − | 6.00000i | 0.117108 | − | 0.202837i | ||||
\(876\) | 2.92820i | 0.0989348i | ||||||||
\(877\) | 25.7321 | + | 14.8564i | 0.868910 | + | 0.501665i | 0.866986 | − | 0.498333i | \(-0.166054\pi\) |
0.00192388 | + | 0.999998i | \(0.499388\pi\) | |||||||
\(878\) | 29.7846 | + | 17.1962i | 1.00518 | + | 0.580342i | ||||
\(879\) | − | 26.5359i | − | 0.895034i | ||||||
\(880\) | −6.92820 | + | 12.0000i | −0.233550 | + | 0.404520i | ||||
\(881\) | −29.0167 | − | 50.2583i | −0.977596 | − | 1.69325i | −0.671087 | − | 0.741378i | \(-0.734172\pi\) |
−0.306509 | − | 0.951868i | \(-0.599161\pi\) | |||||||
\(882\) | 0.866025 | − | 0.500000i | 0.0291606 | − | 0.0168359i | ||||
\(883\) | −34.3205 | −1.15498 | −0.577489 | − | 0.816399i | \(-0.695967\pi\) | ||||
−0.577489 | + | 0.816399i | \(0.695967\pi\) | |||||||
\(884\) | 0.401924 | − | 1.62436i | 0.0135182 | − | 0.0546330i | ||||
\(885\) | 33.7128 | 1.13324 | ||||||||
\(886\) | 1.39230 | − | 0.803848i | 0.0467754 | − | 0.0270058i | ||||
\(887\) | 7.92820 | + | 13.7321i | 0.266203 | + | 0.461077i | 0.967878 | − | 0.251420i | \(-0.0808975\pi\) |
−0.701675 | + | 0.712497i | \(0.747564\pi\) | |||||||
\(888\) | −4.46410 | + | 7.73205i | −0.149805 | + | 0.259471i | ||||
\(889\) | 18.9282i | 0.634832i | ||||||||
\(890\) | −24.8038 | − | 14.3205i | −0.831427 | − | 0.480025i | ||||
\(891\) | 3.46410 | + | 2.00000i | 0.116052 | + | 0.0670025i | ||||
\(892\) | − | 14.4641i | − | 0.484294i | ||||||
\(893\) | 2.00000 | − | 3.46410i | 0.0669274 | − | 0.115922i | ||||
\(894\) | 9.23205 | + | 15.9904i | 0.308766 | + | 0.534798i | ||||
\(895\) | 9.21539 | − | 5.32051i | 0.308037 | − | 0.177845i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −7.85641 | + | 2.26795i | −0.262318 | + | 0.0757246i | ||||
\(898\) | 18.0000 | 0.600668 | ||||||||
\(899\) | 3.21539 | − | 1.85641i | 0.107239 | − | 0.0619146i | ||||
\(900\) | −3.50000 | − | 6.06218i | −0.116667 | − | 0.202073i | ||||
\(901\) | 2.72243 | − | 4.71539i | 0.0906974 | − | 0.157092i | ||||
\(902\) | 27.7128i | 0.922736i | ||||||||
\(903\) | 2.13397 | + | 1.23205i | 0.0710142 | + | 0.0410001i | ||||
\(904\) | −14.1962 | − | 8.19615i | −0.472157 | − | 0.272600i | ||||
\(905\) | 58.1436i | 1.93276i | ||||||||
\(906\) | −6.00000 | + | 10.3923i | −0.199337 | + | 0.345261i | ||||
\(907\) | −5.76795 | − | 9.99038i | −0.191522 | − | 0.331725i | 0.754233 | − | 0.656607i | \(-0.228009\pi\) |
−0.945755 | + | 0.324882i | \(0.894676\pi\) | |||||||
\(908\) | −18.4641 | + | 10.6603i | −0.612753 | + | 0.353773i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.66025 | + | 9.00000i | −0.287085 | + | 0.298347i | ||||
\(911\) | −35.1769 | −1.16546 | −0.582732 | − | 0.812665i | \(-0.698016\pi\) | ||||
−0.582732 | + | 0.812665i | \(0.698016\pi\) | |||||||
\(912\) | 0.464102 | − | 0.267949i | 0.0153679 | − | 0.00887268i | ||||
\(913\) | 3.46410 | + | 6.00000i | 0.114645 | + | 0.198571i | ||||
\(914\) | −4.59808 | + | 7.96410i | −0.152091 | + | 0.263429i | ||||
\(915\) | 18.0000i | 0.595062i | ||||||||
\(916\) | −5.25833 | − | 3.03590i | −0.173740 | − | 0.100309i | ||||
\(917\) | 16.4545 | + | 9.50000i | 0.543375 | + | 0.313718i | ||||
\(918\) | − | 0.464102i | − | 0.0153176i | ||||||
\(919\) | 13.0000 | − | 22.5167i | 0.428830 | − | 0.742756i | −0.567939 | − | 0.823071i | \(-0.692259\pi\) |
0.996770 | + | 0.0803145i | \(0.0255924\pi\) | |||||||
\(920\) | −3.92820 | − | 6.80385i | −0.129509 | − | 0.224316i | ||||
\(921\) | 19.0526 | − | 11.0000i | 0.627803 | − | 0.362462i | ||||
\(922\) | −18.9282 | −0.623367 | ||||||||
\(923\) | −11.9282 | − | 41.3205i | −0.392622 | − | 1.36008i | ||||
\(924\) | 4.00000 | 0.131590 | ||||||||
\(925\) | 54.1244 | − | 31.2487i | 1.77960 | − | 1.02745i | ||||
\(926\) | −20.1244 | − | 34.8564i | −0.661327 | − | 1.14545i | ||||
\(927\) | −3.33013 | + | 5.76795i | −0.109376 | + | 0.189444i | ||||
\(928\) | − | 8.00000i | − | 0.262613i | ||||||
\(929\) | −26.0885 | − | 15.0622i | −0.855935 | − | 0.494174i | 0.00671424 | − | 0.999977i | \(-0.497863\pi\) |
−0.862649 | + | 0.505803i | \(0.831196\pi\) | |||||||
\(930\) | −1.39230 | − | 0.803848i | −0.0456555 | − | 0.0263592i | ||||
\(931\) | − | 0.535898i | − | 0.0175634i | ||||||
\(932\) | −3.26795 | + | 5.66025i | −0.107045 | + | 0.185408i | ||||
\(933\) | −10.6603 | − | 18.4641i | −0.349001 | − | 0.604488i | ||||
\(934\) | 25.6699 | − | 14.8205i | 0.839944 | − | 0.484942i | ||||
\(935\) | 6.43078 | 0.210309 | ||||||||
\(936\) | 1.00000 | + | 3.46410i | 0.0326860 | + | 0.113228i | ||||
\(937\) | −31.0718 | −1.01507 | −0.507536 | − | 0.861631i | \(-0.669443\pi\) | ||||
−0.507536 | + | 0.861631i | \(0.669443\pi\) | |||||||
\(938\) | −2.76795 | + | 1.59808i | −0.0903767 | + | 0.0521790i | ||||
\(939\) | −17.6603 | − | 30.5885i | −0.576321 | − | 0.998217i | ||||
\(940\) | −12.9282 | + | 22.3923i | −0.421671 | + | 0.730356i | ||||
\(941\) | − | 40.3923i | − | 1.31675i | −0.752689 | − | 0.658376i | \(-0.771244\pi\) | ||
0.752689 | − | 0.658376i | \(-0.228756\pi\) | |||||||
\(942\) | 9.46410 | + | 5.46410i | 0.308357 | + | 0.178030i | ||||
\(943\) | −13.6077 | − | 7.85641i | −0.443128 | − | 0.255840i | ||||
\(944\) | − | 9.73205i | − | 0.316751i | ||||||
\(945\) | −1.73205 | + | 3.00000i | −0.0563436 | + | 0.0975900i | ||||
\(946\) | 4.92820 | + | 8.53590i | 0.160230 | + | 0.277526i | ||||
\(947\) | 15.8038 | − | 9.12436i | 0.513556 | − | 0.296502i | −0.220738 | − | 0.975333i | \(-0.570847\pi\) |
0.734294 | + | 0.678831i | \(0.237513\pi\) | |||||||
\(948\) | 2.53590 | 0.0823622 | ||||||||
\(949\) | −7.32051 | + | 7.60770i | −0.237634 | + | 0.246956i | ||||
\(950\) | −3.75129 | −0.121708 | ||||||||
\(951\) | 8.25833 | − | 4.76795i | 0.267795 | − | 0.154611i | ||||
\(952\) | −0.232051 | − | 0.401924i | −0.00752081 | − | 0.0130264i | ||||
\(953\) | 15.0000 | − | 25.9808i | 0.485898 | − | 0.841599i | −0.513971 | − | 0.857808i | \(-0.671826\pi\) |
0.999869 | + | 0.0162081i | \(0.00515944\pi\) | |||||||
\(954\) | 11.7321i | 0.379839i | ||||||||
\(955\) | −55.5500 | − | 32.0718i | −1.79756 | − | 1.03782i | ||||
\(956\) | −12.8660 | − | 7.42820i | −0.416117 | − | 0.240245i | ||||
\(957\) | − | 32.0000i | − | 1.03441i | ||||||
\(958\) | 8.19615 | − | 14.1962i | 0.264806 | − | 0.458657i | ||||
\(959\) | −6.92820 | − | 12.0000i | −0.223723 | − | 0.387500i | ||||
\(960\) | −3.00000 | + | 1.73205i | −0.0968246 | + | 0.0559017i | ||||
\(961\) | 30.7846 | 0.993052 | ||||||||
\(962\) | −30.9282 | + | 8.92820i | −0.997165 | + | 0.287857i | ||||
\(963\) | 15.4641 | 0.498324 | ||||||||
\(964\) | 10.2679 | − | 5.92820i | 0.330708 | − | 0.190935i | ||||
\(965\) | 17.0718 | + | 29.5692i | 0.549561 | + | 0.951867i | ||||
\(966\) | −1.13397 | + | 1.96410i | −0.0364850 | + | 0.0631939i | ||||
\(967\) | 23.4641i | 0.754555i | 0.926100 | + | 0.377277i | \(0.123140\pi\) | ||||
−0.926100 | + | 0.377277i | \(0.876860\pi\) | |||||||
\(968\) | 4.33013 | + | 2.50000i | 0.139176 | + | 0.0803530i | ||||
\(969\) | −0.215390 | − | 0.124356i | −0.00691933 | − | 0.00399488i | ||||
\(970\) | − | 29.0718i | − | 0.933439i | ||||||
\(971\) | −5.03590 | + | 8.72243i | −0.161610 | + | 0.279916i | −0.935446 | − | 0.353469i | \(-0.885002\pi\) |
0.773836 | + | 0.633385i | \(0.218335\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 9.46410 | − | 5.46410i | 0.303405 | − | 0.175171i | ||||
\(974\) | −20.3923 | −0.653412 | ||||||||
\(975\) | 6.06218 | − | 24.5000i | 0.194145 | − | 0.784628i | ||||
\(976\) | 5.19615 | 0.166325 | ||||||||
\(977\) | −1.60770 | + | 0.928203i | −0.0514347 | + | 0.0296959i | −0.525497 | − | 0.850796i | \(-0.676121\pi\) |
0.474062 | + | 0.880491i | \(0.342787\pi\) | |||||||
\(978\) | −9.33013 | − | 16.1603i | −0.298345 | − | 0.516748i | ||||
\(979\) | −16.5359 | + | 28.6410i | −0.528490 | + | 0.915371i | ||||
\(980\) | 3.46410i | 0.110657i | ||||||||
\(981\) | 10.3923 | + | 6.00000i | 0.331801 | + | 0.191565i | ||||
\(982\) | −15.4641 | − | 8.92820i | −0.493479 | − | 0.284910i | ||||
\(983\) | − | 32.9282i | − | 1.05025i | −0.851026 | − | 0.525123i | \(-0.824019\pi\) | ||
0.851026 | − | 0.525123i | \(-0.175981\pi\) | |||||||
\(984\) | −3.46410 | + | 6.00000i | −0.110432 | + | 0.191273i | ||||
\(985\) | −40.5167 | − | 70.1769i | −1.29097 | − | 2.23602i | ||||
\(986\) | −3.21539 | + | 1.85641i | −0.102399 | + | 0.0591200i | ||||
\(987\) | 7.46410 | 0.237585 | ||||||||
\(988\) | 1.87564 | + | 0.464102i | 0.0596722 | + | 0.0147650i | ||||
\(989\) | −5.58846 | −0.177703 | ||||||||
\(990\) | −12.0000 | + | 6.92820i | −0.381385 | + | 0.220193i | ||||
\(991\) | −13.9282 | − | 24.1244i | −0.442444 | − | 0.766335i | 0.555426 | − | 0.831566i | \(-0.312555\pi\) |
−0.997870 | + | 0.0652304i | \(0.979222\pi\) | |||||||
\(992\) | −0.232051 | + | 0.401924i | −0.00736762 | + | 0.0127611i | ||||
\(993\) | − | 13.3205i | − | 0.422714i | ||||||
\(994\) | −10.3301 | − | 5.96410i | −0.327652 | − | 0.189170i | ||||
\(995\) | 6.37307 | + | 3.67949i | 0.202040 | + | 0.116648i | ||||
\(996\) | 1.73205i | 0.0548821i | ||||||||
\(997\) | 8.99038 | − | 15.5718i | 0.284728 | − | 0.493164i | −0.687815 | − | 0.725886i | \(-0.741430\pi\) |
0.972543 | + | 0.232722i | \(0.0747633\pi\) | |||||||
\(998\) | 1.86603 | + | 3.23205i | 0.0590680 | + | 0.102309i | ||||
\(999\) | −7.73205 | + | 4.46410i | −0.244631 | + | 0.141238i |
(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 | 546.2.s.c.127.1 | yes | 4 | |
3.2 | odd | 2 | 1638.2.bj.e.127.2 | 4 | |||
13.2 | odd | 12 | 7098.2.a.bn.1.2 | 2 | |||
13.4 | even | 6 | inner | 546.2.s.c.43.1 | ✓ | 4 | |
13.11 | odd | 12 | 7098.2.a.bz.1.1 | 2 | |||
39.17 | odd | 6 | 1638.2.bj.e.1135.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.c.43.1 | ✓ | 4 | 13.4 | even | 6 | inner | |
546.2.s.c.127.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1638.2.bj.e.127.2 | 4 | 3.2 | odd | 2 | |||
1638.2.bj.e.1135.2 | 4 | 39.17 | odd | 6 | |||
7098.2.a.bn.1.2 | 2 | 13.2 | odd | 12 | |||
7098.2.a.bz.1.1 | 2 | 13.11 | odd | 12 |