Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (of order \(4\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1273.6 | ||
Root | \(2.21573 - 0.300921i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1273 |
Dual form | 1470.2.m.f.97.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.569907 | − | 2.16222i | 0.254870 | − | 0.966975i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.12594 | − | 1.93191i | −0.356053 | − | 0.610923i | ||||
\(11\) | −2.01606 | −0.607864 | −0.303932 | − | 0.952694i | \(-0.598300\pi\) | ||||
−0.303932 | + | 0.952694i | \(0.598300\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −3.44007 | + | 3.44007i | −0.954105 | + | 0.954105i | −0.998992 | − | 0.0448871i | \(-0.985707\pi\) |
0.0448871 | + | 0.998992i | \(0.485707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.12594 | + | 1.93191i | 0.290716 | + | 0.498816i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.40102 | − | 3.40102i | −0.824868 | − | 0.824868i | 0.161933 | − | 0.986802i | \(-0.448227\pi\) |
−0.986802 | + | 0.161933i | \(0.948227\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | −6.72400 | −1.54259 | −0.771296 | − | 0.636477i | \(-0.780391\pi\) | ||||
−0.771296 | + | 0.636477i | \(0.780391\pi\) | |||||||
\(20\) | −2.16222 | − | 0.569907i | −0.483488 | − | 0.127435i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.42557 | + | 1.42557i | −0.303932 | + | 0.303932i | ||||
\(23\) | 4.65016 | + | 4.65016i | 0.969625 | + | 0.969625i | 0.999552 | − | 0.0299268i | \(-0.00952742\pi\) |
−0.0299268 | + | 0.999552i | \(0.509527\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.35041 | − | 2.46453i | −0.870082 | − | 0.492906i | ||||
\(26\) | 4.86500i | 0.954105i | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.60303i | − | 0.297675i | −0.988862 | − | 0.148837i | \(-0.952447\pi\) | ||
0.988862 | − | 0.148837i | \(-0.0475531\pi\) | |||||||
\(30\) | 2.16222 | + | 0.569907i | 0.394766 | + | 0.104050i | ||||
\(31\) | 6.25097i | 1.12271i | 0.827576 | + | 0.561353i | \(0.189719\pi\) | ||||
−0.827576 | + | 0.561353i | \(0.810281\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.42557 | − | 1.42557i | 0.248159 | − | 0.248159i | ||||
\(34\) | −4.80977 | −0.824868 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 3.63458 | − | 3.63458i | 0.597521 | − | 0.597521i | −0.342131 | − | 0.939652i | \(-0.611149\pi\) |
0.939652 | + | 0.342131i | \(0.111149\pi\) | |||||||
\(38\) | −4.75459 | + | 4.75459i | −0.771296 | + | 0.771296i | ||||
\(39\) | − | 4.86500i | − | 0.779023i | ||||||
\(40\) | −1.93191 | + | 1.12594i | −0.305461 | + | 0.178026i | ||||
\(41\) | 4.94376i | 0.772086i | 0.922481 | + | 0.386043i | \(0.126158\pi\) | ||||
−0.922481 | + | 0.386043i | \(0.873842\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.68143 | − | 4.68143i | −0.713912 | − | 0.713912i | 0.253439 | − | 0.967351i | \(-0.418438\pi\) |
−0.967351 | + | 0.253439i | \(0.918438\pi\) | |||||||
\(44\) | 2.01606i | 0.303932i | ||||||||
\(45\) | −2.16222 | − | 0.569907i | −0.322325 | − | 0.0849568i | ||||
\(46\) | 6.57632 | 0.969625 | ||||||||
\(47\) | 1.07805 | + | 1.07805i | 0.157250 | + | 0.157250i | 0.781347 | − | 0.624097i | \(-0.214533\pi\) |
−0.624097 | + | 0.781347i | \(0.714533\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.81889 | + | 1.33352i | −0.681494 | + | 0.188588i | ||||
\(51\) | 4.80977 | 0.673502 | ||||||||
\(52\) | 3.44007 | + | 3.44007i | 0.477052 | + | 0.477052i | ||||
\(53\) | 1.42923 | + | 1.42923i | 0.196320 | + | 0.196320i | 0.798421 | − | 0.602100i | \(-0.205669\pi\) |
−0.602100 | + | 0.798421i | \(0.705669\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.14896 | + | 4.35916i | −0.154926 | + | 0.587789i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.75459 | − | 4.75459i | 0.629760 | − | 0.629760i | ||||
\(58\) | −1.13351 | − | 1.13351i | −0.148837 | − | 0.148837i | ||||
\(59\) | −12.8185 | −1.66883 | −0.834413 | − | 0.551140i | \(-0.814193\pi\) | ||||
−0.834413 | + | 0.551140i | \(0.814193\pi\) | |||||||
\(60\) | 1.93191 | − | 1.12594i | 0.249408 | − | 0.145358i | ||||
\(61\) | − | 9.00341i | − | 1.15277i | −0.817179 | − | 0.576384i | \(-0.804463\pi\) | ||
0.817179 | − | 0.576384i | \(-0.195537\pi\) | |||||||
\(62\) | 4.42010 | + | 4.42010i | 0.561353 | + | 0.561353i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 5.47768 | + | 9.39873i | 0.679423 | + | 1.16577i | ||||
\(66\) | − | 2.01606i | − | 0.248159i | ||||||
\(67\) | −1.19011 | + | 1.19011i | −0.145395 | + | 0.145395i | −0.776057 | − | 0.630662i | \(-0.782783\pi\) |
0.630662 | + | 0.776057i | \(0.282783\pi\) | |||||||
\(68\) | −3.40102 | + | 3.40102i | −0.412434 | + | 0.412434i | ||||
\(69\) | −6.57632 | −0.791696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.49027 | −0.414219 | −0.207110 | − | 0.978318i | \(-0.566406\pi\) | ||||
−0.207110 | + | 0.978318i | \(0.566406\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | −5.97245 | + | 5.97245i | −0.699023 | + | 0.699023i | −0.964200 | − | 0.265177i | \(-0.914570\pi\) |
0.265177 | + | 0.964200i | \(0.414570\pi\) | |||||||
\(74\) | − | 5.14007i | − | 0.597521i | ||||||
\(75\) | 4.81889 | − | 1.33352i | 0.556438 | − | 0.153981i | ||||
\(76\) | 6.72400i | 0.771296i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.44007 | − | 3.44007i | −0.389512 | − | 0.389512i | ||||
\(79\) | 13.9865i | 1.57361i | 0.617203 | + | 0.786804i | \(0.288266\pi\) | ||||
−0.617203 | + | 0.786804i | \(0.711734\pi\) | |||||||
\(80\) | −0.569907 | + | 2.16222i | −0.0637176 | + | 0.241744i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 3.49577 | + | 3.49577i | 0.386043 | + | 0.386043i | ||||
\(83\) | 8.59652 | − | 8.59652i | 0.943590 | − | 0.943590i | −0.0549015 | − | 0.998492i | \(-0.517484\pi\) |
0.998492 | + | 0.0549015i | \(0.0174845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.29202 | + | 5.41549i | −1.00786 | + | 0.587393i | ||||
\(86\) | −6.62055 | −0.713912 | ||||||||
\(87\) | 1.13351 | + | 1.13351i | 0.121525 | + | 0.121525i | ||||
\(88\) | 1.42557 | + | 1.42557i | 0.151966 | + | 0.151966i | ||||
\(89\) | −2.40171 | −0.254581 | −0.127290 | − | 0.991865i | \(-0.540628\pi\) | ||||
−0.127290 | + | 0.991865i | \(0.540628\pi\) | |||||||
\(90\) | −1.93191 | + | 1.12594i | −0.203641 | + | 0.118684i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.65016 | − | 4.65016i | 0.484813 | − | 0.484813i | ||||
\(93\) | −4.42010 | − | 4.42010i | −0.458343 | − | 0.458343i | ||||
\(94\) | 1.52460 | 0.157250 | ||||||||
\(95\) | −3.83206 | + | 14.5388i | −0.393161 | + | 1.49165i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −13.1830 | − | 13.1830i | −1.33854 | − | 1.33854i | −0.897480 | − | 0.441055i | \(-0.854604\pi\) |
−0.441055 | − | 0.897480i | \(-0.645396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.01606i | 0.202621i | ||||||||
\(100\) | −2.46453 | + | 4.35041i | −0.246453 | + | 0.435041i | ||||
\(101\) | 13.9054i | 1.38364i | 0.722069 | + | 0.691821i | \(0.243191\pi\) | ||||
−0.722069 | + | 0.691821i | \(0.756809\pi\) | |||||||
\(102\) | 3.40102 | − | 3.40102i | 0.336751 | − | 0.336751i | ||||
\(103\) | 1.68753 | − | 1.68753i | 0.166278 | − | 0.166278i | −0.619063 | − | 0.785341i | \(-0.712488\pi\) |
0.785341 | + | 0.619063i | \(0.212488\pi\) | |||||||
\(104\) | 4.86500 | 0.477052 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.02124 | 0.196320 | ||||||||
\(107\) | 8.03115 | − | 8.03115i | 0.776400 | − | 0.776400i | −0.202816 | − | 0.979217i | \(-0.565009\pi\) |
0.979217 | + | 0.202816i | \(0.0650094\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 15.8201i | − | 1.51529i | −0.652664 | − | 0.757647i | \(-0.726349\pi\) | ||
0.652664 | − | 0.757647i | \(-0.273651\pi\) | |||||||
\(110\) | 2.26995 | + | 3.89483i | 0.216431 | + | 0.371358i | ||||
\(111\) | 5.14007i | 0.487874i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.9390 | − | 10.9390i | −1.02905 | − | 1.02905i | −0.999565 | − | 0.0294854i | \(-0.990613\pi\) |
−0.0294854 | − | 0.999565i | \(-0.509387\pi\) | |||||||
\(114\) | − | 6.72400i | − | 0.629760i | ||||||
\(115\) | 12.7048 | − | 7.40452i | 1.18473 | − | 0.690475i | ||||
\(116\) | −1.60303 | −0.148837 | ||||||||
\(117\) | 3.44007 | + | 3.44007i | 0.318035 | + | 0.318035i | ||||
\(118\) | −9.06404 | + | 9.06404i | −0.834413 | + | 0.834413i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.569907 | − | 2.16222i | 0.0520252 | − | 0.197383i | ||||
\(121\) | −6.93552 | −0.630502 | ||||||||
\(122\) | −6.36637 | − | 6.36637i | −0.576384 | − | 0.576384i | ||||
\(123\) | −3.49577 | − | 3.49577i | −0.315203 | − | 0.315203i | ||||
\(124\) | 6.25097 | 0.561353 | ||||||||
\(125\) | −7.80820 | + | 8.00200i | −0.698386 | + | 0.715721i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.559216 | + | 0.559216i | −0.0496224 | + | 0.0496224i | −0.731483 | − | 0.681860i | \(-0.761171\pi\) |
0.681860 | + | 0.731483i | \(0.261171\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 6.62055 | 0.582907 | ||||||||
\(130\) | 10.5192 | + | 2.77260i | 0.922596 | + | 0.243173i | ||||
\(131\) | − | 15.7930i | − | 1.37984i | −0.723885 | − | 0.689920i | \(-0.757646\pi\) | ||
0.723885 | − | 0.689920i | \(-0.242354\pi\) | |||||||
\(132\) | −1.42557 | − | 1.42557i | −0.124080 | − | 0.124080i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.68307i | 0.145395i | ||||||||
\(135\) | 1.93191 | − | 1.12594i | 0.166272 | − | 0.0969052i | ||||
\(136\) | 4.80977i | 0.412434i | ||||||||
\(137\) | −9.99143 | + | 9.99143i | −0.853625 | + | 0.853625i | −0.990578 | − | 0.136952i | \(-0.956269\pi\) |
0.136952 | + | 0.990578i | \(0.456269\pi\) | |||||||
\(138\) | −4.65016 | + | 4.65016i | −0.395848 | + | 0.395848i | ||||
\(139\) | 4.06459 | 0.344754 | 0.172377 | − | 0.985031i | \(-0.444855\pi\) | ||||
0.172377 | + | 0.985031i | \(0.444855\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.52460 | −0.128394 | ||||||||
\(142\) | −2.46800 | + | 2.46800i | −0.207110 | + | 0.207110i | ||||
\(143\) | 6.93538 | − | 6.93538i | 0.579966 | − | 0.579966i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −3.46610 | − | 0.913577i | −0.287844 | − | 0.0758684i | ||||
\(146\) | 8.44633i | 0.699023i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.63458 | − | 3.63458i | −0.298760 | − | 0.298760i | ||||
\(149\) | 10.4743i | 0.858092i | 0.903283 | + | 0.429046i | \(0.141150\pi\) | ||||
−0.903283 | + | 0.429046i | \(0.858850\pi\) | |||||||
\(150\) | 2.46453 | − | 4.35041i | 0.201228 | − | 0.355210i | ||||
\(151\) | −10.5250 | −0.856516 | −0.428258 | − | 0.903656i | \(-0.640873\pi\) | ||||
−0.428258 | + | 0.903656i | \(0.640873\pi\) | |||||||
\(152\) | 4.75459 | + | 4.75459i | 0.385648 | + | 0.385648i | ||||
\(153\) | −3.40102 | + | 3.40102i | −0.274956 | + | 0.274956i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.5160 | + | 3.56247i | 1.08563 | + | 0.286145i | ||||
\(156\) | −4.86500 | −0.389512 | ||||||||
\(157\) | 5.51100 | + | 5.51100i | 0.439826 | + | 0.439826i | 0.891953 | − | 0.452128i | \(-0.149335\pi\) |
−0.452128 | + | 0.891953i | \(0.649335\pi\) | |||||||
\(158\) | 9.88997 | + | 9.88997i | 0.786804 | + | 0.786804i | ||||
\(159\) | −2.02124 | −0.160295 | ||||||||
\(160\) | 1.12594 | + | 1.93191i | 0.0890131 | + | 0.152731i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | −3.18264 | − | 3.18264i | −0.249283 | − | 0.249283i | 0.571393 | − | 0.820676i | \(-0.306403\pi\) |
−0.820676 | + | 0.571393i | \(0.806403\pi\) | |||||||
\(164\) | 4.94376 | 0.386043 | ||||||||
\(165\) | −2.26995 | − | 3.89483i | −0.176715 | − | 0.303212i | ||||
\(166\) | − | 12.1573i | − | 0.943590i | ||||||
\(167\) | 3.06894 | + | 3.06894i | 0.237482 | + | 0.237482i | 0.815806 | − | 0.578325i | \(-0.196293\pi\) |
−0.578325 | + | 0.815806i | \(0.696293\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.6682i | − | 0.820632i | ||||||
\(170\) | −2.74112 | + | 10.3998i | −0.210234 | + | 0.797627i | ||||
\(171\) | 6.72400i | 0.514197i | ||||||||
\(172\) | −4.68143 | + | 4.68143i | −0.356956 | + | 0.356956i | ||||
\(173\) | 12.4162 | − | 12.4162i | 0.943986 | − | 0.943986i | −0.0545259 | − | 0.998512i | \(-0.517365\pi\) |
0.998512 | + | 0.0545259i | \(0.0173647\pi\) | |||||||
\(174\) | 1.60303 | 0.121525 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.01606 | 0.151966 | ||||||||
\(177\) | 9.06404 | − | 9.06404i | 0.681295 | − | 0.681295i | ||||
\(178\) | −1.69827 | + | 1.69827i | −0.127290 | + | 0.127290i | ||||
\(179\) | 21.3788i | 1.59792i | 0.601382 | + | 0.798961i | \(0.294617\pi\) | ||||
−0.601382 | + | 0.798961i | \(0.705383\pi\) | |||||||
\(180\) | −0.569907 | + | 2.16222i | −0.0424784 | + | 0.161163i | ||||
\(181\) | − | 17.6702i | − | 1.31341i | −0.754146 | − | 0.656707i | \(-0.771949\pi\) | ||
0.754146 | − | 0.656707i | \(-0.228051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.36637 | + | 6.36637i | 0.470616 | + | 0.470616i | ||||
\(184\) | − | 6.57632i | − | 0.484813i | ||||||
\(185\) | −5.78739 | − | 9.93014i | −0.425498 | − | 0.730078i | ||||
\(186\) | −6.25097 | −0.458343 | ||||||||
\(187\) | 6.85664 | + | 6.85664i | 0.501407 | + | 0.501407i | ||||
\(188\) | 1.07805 | − | 1.07805i | 0.0786251 | − | 0.0786251i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.57080 | + | 12.9901i | 0.549244 | + | 0.942404i | ||||
\(191\) | −3.33512 | −0.241321 | −0.120660 | − | 0.992694i | \(-0.538501\pi\) | ||||
−0.120660 | + | 0.992694i | \(0.538501\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | −14.8727 | − | 14.8727i | −1.07056 | − | 1.07056i | −0.997314 | − | 0.0732463i | \(-0.976664\pi\) |
−0.0732463 | − | 0.997314i | \(-0.523336\pi\) | |||||||
\(194\) | −18.6436 | −1.33854 | ||||||||
\(195\) | −10.5192 | − | 2.77260i | −0.753296 | − | 0.198550i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.84201 | − | 6.84201i | 0.487473 | − | 0.487473i | −0.420035 | − | 0.907508i | \(-0.637982\pi\) |
0.907508 | + | 0.420035i | \(0.137982\pi\) | |||||||
\(198\) | 1.42557 | + | 1.42557i | 0.101311 | + | 0.101311i | ||||
\(199\) | 17.8747 | 1.26710 | 0.633551 | − | 0.773701i | \(-0.281597\pi\) | ||||
0.633551 | + | 0.773701i | \(0.281597\pi\) | |||||||
\(200\) | 1.33352 | + | 4.81889i | 0.0942940 | + | 0.340747i | ||||
\(201\) | − | 1.68307i | − | 0.118715i | ||||||
\(202\) | 9.83263 | + | 9.83263i | 0.691821 | + | 0.691821i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 4.80977i | − | 0.336751i | ||||||
\(205\) | 10.6895 | + | 2.81749i | 0.746588 | + | 0.196782i | ||||
\(206\) | − | 2.38653i | − | 0.166278i | ||||||
\(207\) | 4.65016 | − | 4.65016i | 0.323208 | − | 0.323208i | ||||
\(208\) | 3.44007 | − | 3.44007i | 0.238526 | − | 0.238526i | ||||
\(209\) | 13.5560 | 0.937685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.70108 | 0.599007 | 0.299504 | − | 0.954095i | \(-0.403179\pi\) | ||||
0.299504 | + | 0.954095i | \(0.403179\pi\) | |||||||
\(212\) | 1.42923 | − | 1.42923i | 0.0981602 | − | 0.0981602i | ||||
\(213\) | 2.46800 | − | 2.46800i | 0.169104 | − | 0.169104i | ||||
\(214\) | − | 11.3578i | − | 0.776400i | ||||||
\(215\) | −12.7903 | + | 7.45432i | −0.872290 | + | 0.508380i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.1865 | − | 11.1865i | −0.757647 | − | 0.757647i | ||||
\(219\) | − | 8.44633i | − | 0.570750i | ||||||
\(220\) | 4.35916 | + | 1.14896i | 0.293895 | + | 0.0774632i | ||||
\(221\) | 23.3995 | 1.57402 | ||||||||
\(222\) | 3.63458 | + | 3.63458i | 0.243937 | + | 0.243937i | ||||
\(223\) | 17.0152 | − | 17.0152i | 1.13942 | − | 1.13942i | 0.150867 | − | 0.988554i | \(-0.451793\pi\) |
0.988554 | − | 0.150867i | \(-0.0482065\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46453 | + | 4.35041i | −0.164302 | + | 0.290027i | ||||
\(226\) | −15.4700 | −1.02905 | ||||||||
\(227\) | −5.71327 | − | 5.71327i | −0.379203 | − | 0.379203i | 0.491611 | − | 0.870815i | \(-0.336408\pi\) |
−0.870815 | + | 0.491611i | \(0.836408\pi\) | |||||||
\(228\) | −4.75459 | − | 4.75459i | −0.314880 | − | 0.314880i | ||||
\(229\) | 6.23842 | 0.412246 | 0.206123 | − | 0.978526i | \(-0.433915\pi\) | ||||
0.206123 | + | 0.978526i | \(0.433915\pi\) | |||||||
\(230\) | 3.74789 | − | 14.2195i | 0.247129 | − | 0.937604i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.13351 | + | 1.13351i | −0.0744187 | + | 0.0744187i | ||||
\(233\) | −6.88051 | − | 6.88051i | −0.450757 | − | 0.450757i | 0.444849 | − | 0.895606i | \(-0.353257\pi\) |
−0.895606 | + | 0.444849i | \(0.853257\pi\) | |||||||
\(234\) | 4.86500 | 0.318035 | ||||||||
\(235\) | 2.94538 | − | 1.71660i | 0.192135 | − | 0.111979i | ||||
\(236\) | 12.8185i | 0.834413i | ||||||||
\(237\) | −9.88997 | − | 9.88997i | −0.642423 | − | 0.642423i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6330i | 0.687792i | 0.939008 | + | 0.343896i | \(0.111747\pi\) | ||||
−0.939008 | + | 0.343896i | \(0.888253\pi\) | |||||||
\(240\) | −1.12594 | − | 1.93191i | −0.0726789 | − | 0.124704i | ||||
\(241\) | − | 8.44540i | − | 0.544016i | −0.962295 | − | 0.272008i | \(-0.912312\pi\) | ||
0.962295 | − | 0.272008i | \(-0.0876878\pi\) | |||||||
\(242\) | −4.90415 | + | 4.90415i | −0.315251 | + | 0.315251i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −9.00341 | −0.576384 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.94376 | −0.315203 | ||||||||
\(247\) | 23.1311 | − | 23.1311i | 1.47179 | − | 1.47179i | ||||
\(248\) | 4.42010 | − | 4.42010i | 0.280677 | − | 0.280677i | ||||
\(249\) | 12.1573i | 0.770438i | ||||||||
\(250\) | 0.137040 | + | 11.1795i | 0.00866720 | + | 0.707054i | ||||
\(251\) | − | 11.8182i | − | 0.745957i | −0.927840 | − | 0.372979i | \(-0.878337\pi\) | ||
0.927840 | − | 0.372979i | \(-0.121663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.37498 | − | 9.37498i | −0.589400 | − | 0.589400i | ||||
\(254\) | 0.790851i | 0.0496224i | ||||||||
\(255\) | 2.74112 | − | 10.3998i | 0.171656 | − | 0.651260i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.7015 | + | 10.7015i | 0.667540 | + | 0.667540i | 0.957146 | − | 0.289606i | \(-0.0935244\pi\) |
−0.289606 | + | 0.957146i | \(0.593524\pi\) | |||||||
\(258\) | 4.68143 | − | 4.68143i | 0.291453 | − | 0.291453i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.39873 | − | 5.47768i | 0.582884 | − | 0.339711i | ||||
\(261\) | −1.60303 | −0.0992249 | ||||||||
\(262\) | −11.1673 | − | 11.1673i | −0.689920 | − | 0.689920i | ||||
\(263\) | 12.5956 | + | 12.5956i | 0.776679 | + | 0.776679i | 0.979265 | − | 0.202586i | \(-0.0649345\pi\) |
−0.202586 | + | 0.979265i | \(0.564934\pi\) | |||||||
\(264\) | −2.01606 | −0.124080 | ||||||||
\(265\) | 3.90485 | − | 2.27579i | 0.239873 | − | 0.139801i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.69827 | − | 1.69827i | 0.103932 | − | 0.103932i | ||||
\(268\) | 1.19011 | + | 1.19011i | 0.0726976 | + | 0.0726976i | ||||
\(269\) | −18.8098 | −1.14685 | −0.573426 | − | 0.819257i | \(-0.694386\pi\) | ||||
−0.573426 | + | 0.819257i | \(0.694386\pi\) | |||||||
\(270\) | 0.569907 | − | 2.16222i | 0.0346834 | − | 0.131589i | ||||
\(271\) | − | 5.82286i | − | 0.353713i | −0.984237 | − | 0.176857i | \(-0.943407\pi\) | ||
0.984237 | − | 0.176857i | \(-0.0565929\pi\) | |||||||
\(272\) | 3.40102 | + | 3.40102i | 0.206217 | + | 0.206217i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.1300i | 0.853625i | ||||||||
\(275\) | 8.77067 | + | 4.96863i | 0.528891 | + | 0.299620i | ||||
\(276\) | 6.57632i | 0.395848i | ||||||||
\(277\) | 5.08820 | − | 5.08820i | 0.305720 | − | 0.305720i | −0.537527 | − | 0.843247i | \(-0.680641\pi\) |
0.843247 | + | 0.537527i | \(0.180641\pi\) | |||||||
\(278\) | 2.87410 | − | 2.87410i | 0.172377 | − | 0.172377i | ||||
\(279\) | 6.25097 | 0.374236 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5943 | 1.34786 | 0.673930 | − | 0.738795i | \(-0.264605\pi\) | ||||
0.673930 | + | 0.738795i | \(0.264605\pi\) | |||||||
\(282\) | −1.07805 | + | 1.07805i | −0.0641971 | + | 0.0641971i | ||||
\(283\) | 5.22535 | − | 5.22535i | 0.310615 | − | 0.310615i | −0.534533 | − | 0.845148i | \(-0.679512\pi\) |
0.845148 | + | 0.534533i | \(0.179512\pi\) | |||||||
\(284\) | 3.49027i | 0.207110i | ||||||||
\(285\) | −7.57080 | − | 12.9901i | −0.448455 | − | 0.769470i | ||||
\(286\) | − | 9.80811i | − | 0.579966i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 6.13386i | 0.360815i | ||||||||
\(290\) | −3.09690 | + | 1.80491i | −0.181856 | + | 0.105988i | ||||
\(291\) | 18.6436 | 1.09291 | ||||||||
\(292\) | 5.97245 | + | 5.97245i | 0.349511 | + | 0.349511i | ||||
\(293\) | 16.8432 | − | 16.8432i | 0.983990 | − | 0.983990i | −0.0158834 | − | 0.999874i | \(-0.505056\pi\) |
0.999874 | + | 0.0158834i | \(0.00505604\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.30535 | + | 27.7164i | −0.425334 | + | 1.61371i | ||||
\(296\) | −5.14007 | −0.298760 | ||||||||
\(297\) | −1.42557 | − | 1.42557i | −0.0827198 | − | 0.0827198i | ||||
\(298\) | 7.40648 | + | 7.40648i | 0.429046 | + | 0.429046i | ||||
\(299\) | −31.9938 | −1.85025 | ||||||||
\(300\) | −1.33352 | − | 4.81889i | −0.0769907 | − | 0.278219i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.44233 | + | 7.44233i | −0.428258 | + | 0.428258i | ||||
\(303\) | −9.83263 | − | 9.83263i | −0.564870 | − | 0.564870i | ||||
\(304\) | 6.72400 | 0.385648 | ||||||||
\(305\) | −19.4674 | − | 5.13111i | −1.11470 | − | 0.293806i | ||||
\(306\) | 4.80977i | 0.274956i | ||||||||
\(307\) | 20.0279 | + | 20.0279i | 1.14305 | + | 1.14305i | 0.987889 | + | 0.155164i | \(0.0495907\pi\) |
0.155164 | + | 0.987889i | \(0.450409\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.38653i | 0.135765i | ||||||||
\(310\) | 12.0763 | − | 7.03819i | 0.685887 | − | 0.399743i | ||||
\(311\) | 22.8400i | 1.29514i | 0.762007 | + | 0.647568i | \(0.224214\pi\) | ||||
−0.762007 | + | 0.647568i | \(0.775786\pi\) | |||||||
\(312\) | −3.44007 | + | 3.44007i | −0.194756 | + | 0.194756i | ||||
\(313\) | −15.2546 | + | 15.2546i | −0.862244 | + | 0.862244i | −0.991598 | − | 0.129355i | \(-0.958709\pi\) |
0.129355 | + | 0.991598i | \(0.458709\pi\) | |||||||
\(314\) | 7.79373 | 0.439826 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.9865 | 0.786804 | ||||||||
\(317\) | −16.9641 | + | 16.9641i | −0.952798 | + | 0.952798i | −0.998935 | − | 0.0461374i | \(-0.985309\pi\) |
0.0461374 | + | 0.998935i | \(0.485309\pi\) | |||||||
\(318\) | −1.42923 | + | 1.42923i | −0.0801475 | + | 0.0801475i | ||||
\(319\) | 3.23179i | 0.180946i | ||||||||
\(320\) | 2.16222 | + | 0.569907i | 0.120872 | + | 0.0318588i | ||||
\(321\) | 11.3578i | 0.633928i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.8685 | + | 22.8685i | 1.27243 | + | 1.27243i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | 23.4439 | − | 6.48756i | 1.30043 | − | 0.359865i | ||||
\(326\) | −4.50093 | −0.249283 | ||||||||
\(327\) | 11.1865 | + | 11.1865i | 0.618617 | + | 0.618617i | ||||
\(328\) | 3.49577 | − | 3.49577i | 0.193022 | − | 0.193022i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.35916 | − | 1.14896i | −0.239964 | − | 0.0632484i | ||||
\(331\) | −21.9108 | −1.20432 | −0.602162 | − | 0.798374i | \(-0.705694\pi\) | ||||
−0.602162 | + | 0.798374i | \(0.705694\pi\) | |||||||
\(332\) | −8.59652 | − | 8.59652i | −0.471795 | − | 0.471795i | ||||
\(333\) | −3.63458 | − | 3.63458i | −0.199174 | − | 0.199174i | ||||
\(334\) | 4.34013 | 0.237482 | ||||||||
\(335\) | 1.89503 | + | 3.25154i | 0.103537 | + | 0.177651i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6311 | − | 21.6311i | 1.17832 | − | 1.17832i | 0.198147 | − | 0.980172i | \(-0.436508\pi\) |
0.980172 | − | 0.198147i | \(-0.0634922\pi\) | |||||||
\(338\) | −7.54357 | − | 7.54357i | −0.410316 | − | 0.410316i | ||||
\(339\) | 15.4700 | 0.840216 | ||||||||
\(340\) | 5.41549 | + | 9.29202i | 0.293696 | + | 0.503931i | ||||
\(341\) | − | 12.6023i | − | 0.682453i | ||||||
\(342\) | 4.75459 | + | 4.75459i | 0.257099 | + | 0.257099i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.62055i | 0.356956i | ||||||||
\(345\) | −3.74789 | + | 14.2195i | −0.201780 | + | 0.765550i | ||||
\(346\) | − | 17.5592i | − | 0.943986i | ||||||
\(347\) | 18.8604 | − | 18.8604i | 1.01248 | − | 1.01248i | 0.0125582 | − | 0.999921i | \(-0.496003\pi\) |
0.999921 | − | 0.0125582i | \(-0.00399750\pi\) | |||||||
\(348\) | 1.13351 | − | 1.13351i | 0.0607626 | − | 0.0607626i | ||||
\(349\) | −17.0176 | −0.910933 | −0.455467 | − | 0.890253i | \(-0.650528\pi\) | ||||
−0.455467 | + | 0.890253i | \(0.650528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.86500 | −0.259674 | ||||||||
\(352\) | 1.42557 | − | 1.42557i | 0.0759830 | − | 0.0759830i | ||||
\(353\) | −9.74603 | + | 9.74603i | −0.518729 | + | 0.518729i | −0.917187 | − | 0.398458i | \(-0.869545\pi\) |
0.398458 | + | 0.917187i | \(0.369545\pi\) | |||||||
\(354\) | − | 12.8185i | − | 0.681295i | ||||||
\(355\) | −1.98913 | + | 7.54675i | −0.105572 | + | 0.400540i | ||||
\(356\) | 2.40171i | 0.127290i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.1171 | + | 15.1171i | 0.798961 | + | 0.798961i | ||||
\(359\) | − | 1.60107i | − | 0.0845013i | −0.999107 | − | 0.0422507i | \(-0.986547\pi\) | ||
0.999107 | − | 0.0422507i | \(-0.0134528\pi\) | |||||||
\(360\) | 1.12594 | + | 1.93191i | 0.0593421 | + | 0.101820i | ||||
\(361\) | 26.2122 | 1.37959 | ||||||||
\(362\) | −12.4947 | − | 12.4947i | −0.656707 | − | 0.656707i | ||||
\(363\) | 4.90415 | − | 4.90415i | 0.257401 | − | 0.257401i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.51003 | + | 16.3175i | 0.497778 | + | 0.854098i | ||||
\(366\) | 9.00341 | 0.470616 | ||||||||
\(367\) | −17.6900 | − | 17.6900i | −0.923411 | − | 0.923411i | 0.0738577 | − | 0.997269i | \(-0.476469\pi\) |
−0.997269 | + | 0.0738577i | \(0.976469\pi\) | |||||||
\(368\) | −4.65016 | − | 4.65016i | −0.242406 | − | 0.242406i | ||||
\(369\) | 4.94376 | 0.257362 | ||||||||
\(370\) | −11.1140 | − | 2.92936i | −0.577788 | − | 0.152290i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.42010 | + | 4.42010i | −0.229172 | + | 0.229172i | ||||
\(373\) | −19.8270 | − | 19.8270i | −1.02660 | − | 1.02660i | −0.999636 | − | 0.0269674i | \(-0.991415\pi\) |
−0.0269674 | − | 0.999636i | \(-0.508585\pi\) | |||||||
\(374\) | 9.69676 | 0.501407 | ||||||||
\(375\) | −0.137040 | − | 11.1795i | −0.00707674 | − | 0.577307i | ||||
\(376\) | − | 1.52460i | − | 0.0786251i | ||||||
\(377\) | 5.51453 | + | 5.51453i | 0.284013 | + | 0.284013i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.69997i | − | 0.190055i | −0.995475 | − | 0.0950275i | \(-0.969706\pi\) | ||
0.995475 | − | 0.0950275i | \(-0.0302939\pi\) | |||||||
\(380\) | 14.5388 | + | 3.83206i | 0.745824 | + | 0.196580i | ||||
\(381\) | − | 0.790851i | − | 0.0405165i | ||||||
\(382\) | −2.35828 | + | 2.35828i | −0.120660 | + | 0.120660i | ||||
\(383\) | 9.22741 | − | 9.22741i | 0.471499 | − | 0.471499i | −0.430901 | − | 0.902399i | \(-0.641804\pi\) |
0.902399 | + | 0.430901i | \(0.141804\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.0332 | −1.07056 | ||||||||
\(387\) | −4.68143 | + | 4.68143i | −0.237971 | + | 0.237971i | ||||
\(388\) | −13.1830 | + | 13.1830i | −0.669268 | + | 0.669268i | ||||
\(389\) | 13.5526i | 0.687147i | 0.939126 | + | 0.343573i | \(0.111637\pi\) | ||||
−0.939126 | + | 0.343573i | \(0.888363\pi\) | |||||||
\(390\) | −9.39873 | + | 5.47768i | −0.475923 | + | 0.277373i | ||||
\(391\) | − | 31.6306i | − | 1.59963i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.1673 | + | 11.1673i | 0.563318 | + | 0.563318i | ||||
\(394\) | − | 9.67606i | − | 0.487473i | ||||||
\(395\) | 30.2420 | + | 7.97102i | 1.52164 | + | 0.401066i | ||||
\(396\) | 2.01606 | 0.101311 | ||||||||
\(397\) | −1.18143 | − | 1.18143i | −0.0592943 | − | 0.0592943i | 0.676838 | − | 0.736132i | \(-0.263350\pi\) |
−0.736132 | + | 0.676838i | \(0.763350\pi\) | |||||||
\(398\) | 12.6393 | − | 12.6393i | 0.633551 | − | 0.633551i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.35041 | + | 2.46453i | 0.217521 | + | 0.123227i | ||||
\(401\) | 5.26427 | 0.262885 | 0.131443 | − | 0.991324i | \(-0.458039\pi\) | ||||
0.131443 | + | 0.991324i | \(0.458039\pi\) | |||||||
\(402\) | −1.19011 | − | 1.19011i | −0.0593574 | − | 0.0593574i | ||||
\(403\) | −21.5038 | − | 21.5038i | −1.07118 | − | 1.07118i | ||||
\(404\) | 13.9054 | 0.691821 | ||||||||
\(405\) | −0.569907 | + | 2.16222i | −0.0283189 | + | 0.107442i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.32751 | + | 7.32751i | −0.363211 | + | 0.363211i | ||||
\(408\) | −3.40102 | − | 3.40102i | −0.168376 | − | 0.168376i | ||||
\(409\) | −30.8758 | −1.52671 | −0.763355 | − | 0.645979i | \(-0.776449\pi\) | ||||
−0.763355 | + | 0.645979i | \(0.776449\pi\) | |||||||
\(410\) | 9.55089 | − | 5.56636i | 0.471685 | − | 0.274903i | ||||
\(411\) | − | 14.1300i | − | 0.696982i | ||||||
\(412\) | −1.68753 | − | 1.68753i | −0.0831388 | − | 0.0831388i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 6.57632i | − | 0.323208i | ||||||
\(415\) | −13.6884 | − | 23.4868i | −0.671935 | − | 1.15292i | ||||
\(416\) | − | 4.86500i | − | 0.238526i | ||||||
\(417\) | −2.87410 | + | 2.87410i | −0.140745 | + | 0.140745i | ||||
\(418\) | 9.58551 | − | 9.58551i | 0.468843 | − | 0.468843i | ||||
\(419\) | 27.7914 | 1.35770 | 0.678850 | − | 0.734277i | \(-0.262479\pi\) | ||||
0.678850 | + | 0.734277i | \(0.262479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.3633 | −1.86971 | −0.934855 | − | 0.355029i | \(-0.884471\pi\) | ||||
−0.934855 | + | 0.355029i | \(0.884471\pi\) | |||||||
\(422\) | 6.15259 | − | 6.15259i | 0.299504 | − | 0.299504i | ||||
\(423\) | 1.07805 | − | 1.07805i | 0.0524167 | − | 0.0524167i | ||||
\(424\) | − | 2.02124i | − | 0.0981602i | ||||||
\(425\) | 6.41391 | + | 23.1778i | 0.311120 | + | 1.12429i | ||||
\(426\) | − | 3.49027i | − | 0.169104i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.03115 | − | 8.03115i | −0.388200 | − | 0.388200i | ||||
\(429\) | 9.80811i | 0.473540i | ||||||||
\(430\) | −3.77310 | + | 14.3151i | −0.181955 | + | 0.690335i | ||||
\(431\) | −28.2654 | −1.36150 | −0.680748 | − | 0.732518i | \(-0.738345\pi\) | ||||
−0.680748 | + | 0.732518i | \(0.738345\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −20.1385 | + | 20.1385i | −0.967796 | + | 0.967796i | −0.999497 | − | 0.0317009i | \(-0.989908\pi\) |
0.0317009 | + | 0.999497i | \(0.489908\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.09690 | − | 1.80491i | 0.148485 | − | 0.0865387i | ||||
\(436\) | −15.8201 | −0.757647 | ||||||||
\(437\) | −31.2677 | − | 31.2677i | −1.49574 | − | 1.49574i | ||||
\(438\) | −5.97245 | − | 5.97245i | −0.285375 | − | 0.285375i | ||||
\(439\) | −4.59353 | −0.219237 | −0.109619 | − | 0.993974i | \(-0.534963\pi\) | ||||
−0.109619 | + | 0.993974i | \(0.534963\pi\) | |||||||
\(440\) | 3.89483 | − | 2.26995i | 0.185679 | − | 0.108216i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.5460 | − | 16.5460i | 0.787011 | − | 0.787011i | ||||
\(443\) | −26.3918 | − | 26.3918i | −1.25391 | − | 1.25391i | −0.953953 | − | 0.299957i | \(-0.903028\pi\) |
−0.299957 | − | 0.953953i | \(-0.596972\pi\) | |||||||
\(444\) | 5.14007 | 0.243937 | ||||||||
\(445\) | −1.36875 | + | 5.19304i | −0.0648851 | + | 0.246173i | ||||
\(446\) | − | 24.0631i | − | 1.13942i | ||||||
\(447\) | −7.40648 | − | 7.40648i | −0.350314 | − | 0.350314i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.5778i | 0.829549i | 0.909924 | + | 0.414775i | \(0.136140\pi\) | ||||
−0.909924 | + | 0.414775i | \(0.863860\pi\) | |||||||
\(450\) | 1.33352 | + | 4.81889i | 0.0628626 | + | 0.227165i | ||||
\(451\) | − | 9.96690i | − | 0.469323i | ||||||
\(452\) | −10.9390 | + | 10.9390i | −0.514525 | + | 0.514525i | ||||
\(453\) | 7.44233 | − | 7.44233i | 0.349671 | − | 0.349671i | ||||
\(454\) | −8.07979 | −0.379203 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.72400 | −0.314880 | ||||||||
\(457\) | 22.3868 | − | 22.3868i | 1.04721 | − | 1.04721i | 0.0483833 | − | 0.998829i | \(-0.484593\pi\) |
0.998829 | − | 0.0483833i | \(-0.0154069\pi\) | |||||||
\(458\) | 4.41123 | − | 4.41123i | 0.206123 | − | 0.206123i | ||||
\(459\) | − | 4.80977i | − | 0.224501i | ||||||
\(460\) | −7.40452 | − | 12.7048i | −0.345238 | − | 0.592366i | ||||
\(461\) | 7.25807i | 0.338042i | 0.985612 | + | 0.169021i | \(0.0540606\pi\) | ||||
−0.985612 | + | 0.169021i | \(0.945939\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.8885 | − | 14.8885i | −0.691926 | − | 0.691926i | 0.270730 | − | 0.962655i | \(-0.412735\pi\) |
−0.962655 | + | 0.270730i | \(0.912735\pi\) | |||||||
\(464\) | 1.60303i | 0.0744187i | ||||||||
\(465\) | −12.0763 | + | 7.03819i | −0.560024 | + | 0.326388i | ||||
\(466\) | −9.73051 | −0.450757 | ||||||||
\(467\) | 7.66720 | + | 7.66720i | 0.354796 | + | 0.354796i | 0.861890 | − | 0.507095i | \(-0.169281\pi\) |
−0.507095 | + | 0.861890i | \(0.669281\pi\) | |||||||
\(468\) | 3.44007 | − | 3.44007i | 0.159017 | − | 0.159017i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.868879 | − | 3.29652i | 0.0400784 | − | 0.152057i | ||||
\(471\) | −7.79373 | −0.359116 | ||||||||
\(472\) | 9.06404 | + | 9.06404i | 0.417206 | + | 0.417206i | ||||
\(473\) | 9.43803 | + | 9.43803i | 0.433961 | + | 0.433961i | ||||
\(474\) | −13.9865 | −0.642423 | ||||||||
\(475\) | 29.2522 | + | 16.5715i | 1.34218 | + | 0.760353i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.42923 | − | 1.42923i | 0.0654402 | − | 0.0654402i | ||||
\(478\) | 7.51867 | + | 7.51867i | 0.343896 | + | 0.343896i | ||||
\(479\) | 26.8377 | 1.22625 | 0.613123 | − | 0.789987i | \(-0.289913\pi\) | ||||
0.613123 | + | 0.789987i | \(0.289913\pi\) | |||||||
\(480\) | −2.16222 | − | 0.569907i | −0.0986915 | − | 0.0260126i | ||||
\(481\) | 25.0064i | 1.14020i | ||||||||
\(482\) | −5.97180 | − | 5.97180i | −0.272008 | − | 0.272008i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.93552i | 0.315251i | ||||||||
\(485\) | −36.0178 | + | 20.9916i | −1.63548 | + | 0.953178i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −12.3064 | + | 12.3064i | −0.557658 | + | 0.557658i | −0.928640 | − | 0.370982i | \(-0.879021\pi\) |
0.370982 | + | 0.928640i | \(0.379021\pi\) | |||||||
\(488\) | −6.36637 | + | 6.36637i | −0.288192 | + | 0.288192i | ||||
\(489\) | 4.50093 | 0.203539 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.9347 | −1.26067 | −0.630337 | − | 0.776322i | \(-0.717083\pi\) | ||||
−0.630337 | + | 0.776322i | \(0.717083\pi\) | |||||||
\(492\) | −3.49577 | + | 3.49577i | −0.157601 | + | 0.157601i | ||||
\(493\) | −5.45192 | + | 5.45192i | −0.245542 | + | 0.245542i | ||||
\(494\) | − | 32.7123i | − | 1.47179i | ||||||
\(495\) | 4.35916 | + | 1.14896i | 0.195930 | + | 0.0516421i | ||||
\(496\) | − | 6.25097i | − | 0.280677i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.59652 | + | 8.59652i | 0.385219 | + | 0.385219i | ||||
\(499\) | 29.2011i | 1.30722i | 0.756831 | + | 0.653610i | \(0.226746\pi\) | ||||
−0.756831 | + | 0.653610i | \(0.773254\pi\) | |||||||
\(500\) | 8.00200 | + | 7.80820i | 0.357860 | + | 0.349193i | ||||
\(501\) | −4.34013 | −0.193903 | ||||||||
\(502\) | −8.35672 | − | 8.35672i | −0.372979 | − | 0.372979i | ||||
\(503\) | −17.8373 | + | 17.8373i | −0.795326 | + | 0.795326i | −0.982354 | − | 0.187028i | \(-0.940114\pi\) |
0.187028 | + | 0.982354i | \(0.440114\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.0666 | + | 7.92481i | 1.33795 | + | 0.352649i | ||||
\(506\) | −13.2582 | −0.589400 | ||||||||
\(507\) | 7.54357 | + | 7.54357i | 0.335022 | + | 0.335022i | ||||
\(508\) | 0.559216 | + | 0.559216i | 0.0248112 | + | 0.0248112i | ||||
\(509\) | −21.1693 | −0.938312 | −0.469156 | − | 0.883115i | \(-0.655442\pi\) | ||||
−0.469156 | + | 0.883115i | \(0.655442\pi\) | |||||||
\(510\) | −5.41549 | − | 9.29202i | −0.239802 | − | 0.411458i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −4.75459 | − | 4.75459i | −0.209920 | − | 0.209920i | ||||
\(514\) | 15.1342 | 0.667540 | ||||||||
\(515\) | −2.68709 | − | 4.61056i | −0.118407 | − | 0.203166i | ||||
\(516\) | − | 6.62055i | − | 0.291453i | ||||||
\(517\) | −2.17341 | − | 2.17341i | −0.0955867 | − | 0.0955867i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.5592i | 0.770762i | ||||||||
\(520\) | 2.77260 | − | 10.5192i | 0.121586 | − | 0.461298i | ||||
\(521\) | 12.3957i | 0.543066i | 0.962429 | + | 0.271533i | \(0.0875306\pi\) | ||||
−0.962429 | + | 0.271533i | \(0.912469\pi\) | |||||||
\(522\) | −1.13351 | + | 1.13351i | −0.0496124 | + | 0.0496124i | ||||
\(523\) | −6.44681 | + | 6.44681i | −0.281899 | + | 0.281899i | −0.833866 | − | 0.551967i | \(-0.813878\pi\) |
0.551967 | + | 0.833866i | \(0.313878\pi\) | |||||||
\(524\) | −15.7930 | −0.689920 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.8129 | 0.776679 | ||||||||
\(527\) | 21.2597 | − | 21.2597i | 0.926085 | − | 0.926085i | ||||
\(528\) | −1.42557 | + | 1.42557i | −0.0620398 | + | 0.0620398i | ||||
\(529\) | 20.2480i | 0.880346i | ||||||||
\(530\) | 1.15192 | − | 4.37038i | 0.0500362 | − | 0.189837i | ||||
\(531\) | 12.8185i | 0.556275i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.0069 | − | 17.0069i | −0.736651 | − | 0.736651i | ||||
\(534\) | − | 2.40171i | − | 0.103932i | ||||||
\(535\) | −12.7881 | − | 21.9421i | −0.552879 | − | 0.948641i | ||||
\(536\) | 1.68307 | 0.0726976 | ||||||||
\(537\) | −15.1171 | − | 15.1171i | −0.652349 | − | 0.652349i | ||||
\(538\) | −13.3005 | + | 13.3005i | −0.573426 | + | 0.573426i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.12594 | − | 1.93191i | −0.0484526 | − | 0.0831361i | ||||
\(541\) | 15.8888 | 0.683112 | 0.341556 | − | 0.939861i | \(-0.389046\pi\) | ||||
0.341556 | + | 0.939861i | \(0.389046\pi\) | |||||||
\(542\) | −4.11738 | − | 4.11738i | −0.176857 | − | 0.176857i | ||||
\(543\) | 12.4947 | + | 12.4947i | 0.536199 | + | 0.536199i | ||||
\(544\) | 4.80977 | 0.206217 | ||||||||
\(545\) | −34.2067 | − | 9.01601i | −1.46525 | − | 0.386204i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.25721 | + | 8.25721i | −0.353053 | + | 0.353053i | −0.861244 | − | 0.508191i | \(-0.830314\pi\) |
0.508191 | + | 0.861244i | \(0.330314\pi\) | |||||||
\(548\) | 9.99143 | + | 9.99143i | 0.426813 | + | 0.426813i | ||||
\(549\) | −9.00341 | −0.384256 | ||||||||
\(550\) | 9.71516 | − | 2.68845i | 0.414256 | − | 0.114636i | ||||
\(551\) | 10.7788i | 0.459190i | ||||||||
\(552\) | 4.65016 | + | 4.65016i | 0.197924 | + | 0.197924i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 7.19579i | − | 0.305720i | ||||||
\(555\) | 11.1140 | + | 2.92936i | 0.471762 | + | 0.124345i | ||||
\(556\) | − | 4.06459i | − | 0.172377i | ||||||
\(557\) | 20.3695 | − | 20.3695i | 0.863082 | − | 0.863082i | −0.128613 | − | 0.991695i | \(-0.541052\pi\) |
0.991695 | + | 0.128613i | \(0.0410524\pi\) | |||||||
\(558\) | 4.42010 | − | 4.42010i | 0.187118 | − | 0.187118i | ||||
\(559\) | 32.2090 | 1.36229 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.69676 | −0.409397 | ||||||||
\(562\) | 15.9766 | − | 15.9766i | 0.673930 | − | 0.673930i | ||||
\(563\) | 13.6409 | − | 13.6409i | 0.574895 | − | 0.574895i | −0.358598 | − | 0.933492i | \(-0.616745\pi\) |
0.933492 | + | 0.358598i | \(0.116745\pi\) | |||||||
\(564\) | 1.52460i | 0.0641971i | ||||||||
\(565\) | −29.8867 | + | 17.4183i | −1.25734 | + | 0.732792i | ||||
\(566\) | − | 7.38976i | − | 0.310615i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.46800 | + | 2.46800i | 0.103555 | + | 0.103555i | ||||
\(569\) | 23.8046i | 0.997941i | 0.866619 | + | 0.498971i | \(0.166288\pi\) | ||||
−0.866619 | + | 0.498971i | \(0.833712\pi\) | |||||||
\(570\) | −14.5388 | − | 3.83206i | −0.608963 | − | 0.160507i | ||||
\(571\) | 27.8052 | 1.16361 | 0.581805 | − | 0.813329i | \(-0.302347\pi\) | ||||
0.581805 | + | 0.813329i | \(0.302347\pi\) | |||||||
\(572\) | −6.93538 | − | 6.93538i | −0.289983 | − | 0.289983i | ||||
\(573\) | 2.35828 | − | 2.35828i | 0.0985187 | − | 0.0985187i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.76964 | − | 31.6906i | −0.365719 | − | 1.32159i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 23.1463 | + | 23.1463i | 0.963593 | + | 0.963593i | 0.999360 | − | 0.0357671i | \(-0.0113874\pi\) |
−0.0357671 | + | 0.999360i | \(0.511387\pi\) | |||||||
\(578\) | 4.33729 | + | 4.33729i | 0.180408 | + | 0.180408i | ||||
\(579\) | 21.0332 | 0.874109 | ||||||||
\(580\) | −0.913577 | + | 3.46610i | −0.0379342 | + | 0.143922i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 13.1830 | − | 13.1830i | 0.546455 | − | 0.546455i | ||||
\(583\) | −2.88142 | − | 2.88142i | −0.119336 | − | 0.119336i | ||||
\(584\) | 8.44633 | 0.349511 | ||||||||
\(585\) | 9.39873 | − | 5.47768i | 0.388590 | − | 0.226474i | ||||
\(586\) | − | 23.8199i | − | 0.983990i | ||||||
\(587\) | −10.2376 | − | 10.2376i | −0.422551 | − | 0.422551i | 0.463530 | − | 0.886081i | \(-0.346583\pi\) |
−0.886081 | + | 0.463530i | \(0.846583\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 42.0315i | − | 1.73188i | ||||||
\(590\) | 14.4328 | + | 24.7641i | 0.594189 | + | 1.01952i | ||||
\(591\) | 9.67606i | 0.398020i | ||||||||
\(592\) | −3.63458 | + | 3.63458i | −0.149380 | + | 0.149380i | ||||
\(593\) | 13.4975 | − | 13.4975i | 0.554278 | − | 0.554278i | −0.373395 | − | 0.927673i | \(-0.621806\pi\) |
0.927673 | + | 0.373395i | \(0.121806\pi\) | |||||||
\(594\) | −2.01606 | −0.0827198 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.4743 | 0.429046 | ||||||||
\(597\) | −12.6393 | + | 12.6393i | −0.517293 | + | 0.517293i | ||||
\(598\) | −22.6230 | + | 22.6230i | −0.925124 | + | 0.925124i | ||||
\(599\) | 14.4212i | 0.589233i | 0.955616 | + | 0.294616i | \(0.0951919\pi\) | ||||
−0.955616 | + | 0.294616i | \(0.904808\pi\) | |||||||
\(600\) | −4.35041 | − | 2.46453i | −0.177605 | − | 0.100614i | ||||
\(601\) | − | 33.8262i | − | 1.37980i | −0.723906 | − | 0.689899i | \(-0.757655\pi\) | ||
0.723906 | − | 0.689899i | \(-0.242345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.19011 | + | 1.19011i | 0.0484651 | + | 0.0484651i | ||||
\(604\) | 10.5250i | 0.428258i | ||||||||
\(605\) | −3.95260 | + | 14.9961i | −0.160696 | + | 0.609680i | ||||
\(606\) | −13.9054 | −0.564870 | ||||||||
\(607\) | 2.25227 | + | 2.25227i | 0.0914168 | + | 0.0914168i | 0.751336 | − | 0.659919i | \(-0.229410\pi\) |
−0.659919 | + | 0.751336i | \(0.729410\pi\) | |||||||
\(608\) | 4.75459 | − | 4.75459i | 0.192824 | − | 0.192824i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.3938 | + | 10.1373i | −0.704252 | + | 0.410446i | ||||
\(611\) | −7.41716 | −0.300066 | ||||||||
\(612\) | 3.40102 | + | 3.40102i | 0.137478 | + | 0.137478i | ||||
\(613\) | 12.7193 | + | 12.7193i | 0.513726 | + | 0.513726i | 0.915666 | − | 0.401940i | \(-0.131664\pi\) |
−0.401940 | + | 0.915666i | \(0.631664\pi\) | |||||||
\(614\) | 28.3237 | 1.14305 | ||||||||
\(615\) | −9.55089 | + | 5.56636i | −0.385129 | + | 0.224457i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.92028 | − | 1.92028i | 0.0773075 | − | 0.0773075i | −0.667396 | − | 0.744703i | \(-0.732591\pi\) |
0.744703 | + | 0.667396i | \(0.232591\pi\) | |||||||
\(618\) | 1.68753 | + | 1.68753i | 0.0678826 | + | 0.0678826i | ||||
\(619\) | 2.09236 | 0.0840992 | 0.0420496 | − | 0.999116i | \(-0.486611\pi\) | ||||
0.0420496 | + | 0.999116i | \(0.486611\pi\) | |||||||
\(620\) | 3.56247 | − | 13.5160i | 0.143072 | − | 0.542815i | ||||
\(621\) | 6.57632i | 0.263899i | ||||||||
\(622\) | 16.1503 | + | 16.1503i | 0.647568 | + | 0.647568i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.86500i | 0.194756i | ||||||||
\(625\) | 12.8522 | + | 21.4435i | 0.514086 | + | 0.857738i | ||||
\(626\) | 21.5733i | 0.862244i | ||||||||
\(627\) | −9.58551 | + | 9.58551i | −0.382808 | + | 0.382808i | ||||
\(628\) | 5.51100 | − | 5.51100i | 0.219913 | − | 0.219913i | ||||
\(629\) | −24.7225 | −0.985752 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9051 | 0.792410 | 0.396205 | − | 0.918162i | \(-0.370327\pi\) | ||||
0.396205 | + | 0.918162i | \(0.370327\pi\) | |||||||
\(632\) | 9.88997 | − | 9.88997i | 0.393402 | − | 0.393402i | ||||
\(633\) | −6.15259 | + | 6.15259i | −0.244544 | + | 0.244544i | ||||
\(634\) | 23.9908i | 0.952798i | ||||||||
\(635\) | 0.890448 | + | 1.52785i | 0.0353364 | + | 0.0606309i | ||||
\(636\) | 2.02124i | 0.0801475i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.28522 | + | 2.28522i | 0.0904728 | + | 0.0904728i | ||||
\(639\) | 3.49027i | 0.138073i | ||||||||
\(640\) | 1.93191 | − | 1.12594i | 0.0763653 | − | 0.0445066i | ||||
\(641\) | −17.5462 | −0.693032 | −0.346516 | − | 0.938044i | \(-0.612635\pi\) | ||||
−0.346516 | + | 0.938044i | \(0.612635\pi\) | |||||||
\(642\) | 8.03115 | + | 8.03115i | 0.316964 | + | 0.316964i | ||||
\(643\) | −24.0108 | + | 24.0108i | −0.946895 | + | 0.946895i | −0.998659 | − | 0.0517644i | \(-0.983516\pi\) |
0.0517644 | + | 0.998659i | \(0.483516\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.77310 | − | 14.3151i | 0.148566 | − | 0.563656i | ||||
\(646\) | 32.3409 | 1.27243 | ||||||||
\(647\) | −1.70120 | − | 1.70120i | −0.0668810 | − | 0.0668810i | 0.672875 | − | 0.739756i | \(-0.265059\pi\) |
−0.739756 | + | 0.672875i | \(0.765059\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | 25.8428 | 1.01442 | ||||||||
\(650\) | 11.9899 | − | 21.1648i | 0.470284 | − | 0.830150i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.18264 | + | 3.18264i | −0.124642 | + | 0.124642i | ||||
\(653\) | 22.7164 | + | 22.7164i | 0.888962 | + | 0.888962i | 0.994423 | − | 0.105462i | \(-0.0336320\pi\) |
−0.105462 | + | 0.994423i | \(0.533632\pi\) | |||||||
\(654\) | 15.8201 | 0.618617 | ||||||||
\(655\) | −34.1480 | − | 9.00054i | −1.33427 | − | 0.351680i | ||||
\(656\) | − | 4.94376i | − | 0.193022i | ||||||
\(657\) | 5.97245 | + | 5.97245i | 0.233008 | + | 0.233008i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.3970i | 0.794552i | 0.917699 | + | 0.397276i | \(0.130045\pi\) | ||||
−0.917699 | + | 0.397276i | \(0.869955\pi\) | |||||||
\(660\) | −3.89483 | + | 2.26995i | −0.151606 | + | 0.0883577i | ||||
\(661\) | − | 18.4521i | − | 0.717702i | −0.933395 | − | 0.358851i | \(-0.883169\pi\) | ||
0.933395 | − | 0.358851i | \(-0.116831\pi\) | |||||||
\(662\) | −15.4933 | + | 15.4933i | −0.602162 | + | 0.602162i | ||||
\(663\) | −16.5460 | + | 16.5460i | −0.642592 | + | 0.642592i | ||||
\(664\) | −12.1573 | −0.471795 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.14007 | −0.199174 | ||||||||
\(667\) | 7.45433 | − | 7.45433i | 0.288633 | − | 0.288633i | ||||
\(668\) | 3.06894 | − | 3.06894i | 0.118741 | − | 0.118741i | ||||
\(669\) | 24.0631i | 0.930333i | ||||||||
\(670\) | 3.63918 | + | 0.959195i | 0.140594 | + | 0.0370569i | ||||
\(671\) | 18.1514i | 0.700726i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.5335 | − | 31.5335i | −1.21553 | − | 1.21553i | −0.969182 | − | 0.246344i | \(-0.920771\pi\) |
−0.246344 | − | 0.969182i | \(-0.579229\pi\) | |||||||
\(674\) | − | 30.5909i | − | 1.17832i | ||||||
\(675\) | −1.33352 | − | 4.81889i | −0.0513271 | − | 0.185479i | ||||
\(676\) | −10.6682 | −0.410316 | ||||||||
\(677\) | 9.14781 | + | 9.14781i | 0.351579 | + | 0.351579i | 0.860697 | − | 0.509118i | \(-0.170028\pi\) |
−0.509118 | + | 0.860697i | \(0.670028\pi\) | |||||||
\(678\) | 10.9390 | − | 10.9390i | 0.420108 | − | 0.420108i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.3998 | + | 2.74112i | 0.398814 | + | 0.105117i | ||||
\(681\) | 8.07979 | 0.309618 | ||||||||
\(682\) | −8.91117 | − | 8.91117i | −0.341226 | − | 0.341226i | ||||
\(683\) | −13.1956 | − | 13.1956i | −0.504916 | − | 0.504916i | 0.408046 | − | 0.912962i | \(-0.366210\pi\) |
−0.912962 | + | 0.408046i | \(0.866210\pi\) | |||||||
\(684\) | 6.72400 | 0.257099 | ||||||||
\(685\) | 15.9095 | + | 27.2979i | 0.607871 | + | 1.04300i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.41123 | + | 4.41123i | −0.168299 | + | 0.168299i | ||||
\(688\) | 4.68143 | + | 4.68143i | 0.178478 | + | 0.178478i | ||||
\(689\) | −9.83335 | −0.374621 | ||||||||
\(690\) | 7.40452 | + | 12.7048i | 0.281885 | + | 0.483665i | ||||
\(691\) | 41.3069i | 1.57139i | 0.618615 | + | 0.785694i | \(0.287694\pi\) | ||||
−0.618615 | + | 0.785694i | \(0.712306\pi\) | |||||||
\(692\) | −12.4162 | − | 12.4162i | −0.471993 | − | 0.471993i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 26.6726i | − | 1.01248i | ||||||
\(695\) | 2.31644 | − | 8.78854i | 0.0878675 | − | 0.333368i | ||||
\(696\) | − | 1.60303i | − | 0.0607626i | ||||||
\(697\) | 16.8138 | − | 16.8138i | 0.636869 | − | 0.636869i | ||||
\(698\) | −12.0333 | + | 12.0333i | −0.455467 | + | 0.455467i | ||||
\(699\) | 9.73051 | 0.368042 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.7798 | −1.46469 | −0.732347 | − | 0.680931i | \(-0.761575\pi\) | ||||
−0.732347 | + | 0.680931i | \(0.761575\pi\) | |||||||
\(702\) | −3.44007 | + | 3.44007i | −0.129837 | + | 0.129837i | ||||
\(703\) | −24.4389 | + | 24.4389i | −0.921731 | + | 0.921731i | ||||
\(704\) | − | 2.01606i | − | 0.0759830i | ||||||
\(705\) | −0.868879 | + | 3.29652i | −0.0327239 | + | 0.124154i | ||||
\(706\) | 13.7830i | 0.518729i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.06404 | − | 9.06404i | −0.340647 | − | 0.340647i | ||||
\(709\) | 38.8263i | 1.45815i | 0.684432 | + | 0.729077i | \(0.260050\pi\) | ||||
−0.684432 | + | 0.729077i | \(0.739950\pi\) | |||||||
\(710\) | 3.92983 | + | 6.74289i | 0.147484 | + | 0.253056i | ||||
\(711\) | 13.9865 | 0.524536 | ||||||||
\(712\) | 1.69827 | + | 1.69827i | 0.0636452 | + | 0.0636452i | ||||
\(713\) | −29.0680 | + | 29.0680i | −1.08860 | + | 1.08860i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0433 | − | 18.9484i | −0.412996 | − | 0.708629i | ||||
\(716\) | 21.3788 | 0.798961 | ||||||||
\(717\) | −7.51867 | − | 7.51867i | −0.280790 | − | 0.280790i | ||||
\(718\) | −1.13213 | − | 1.13213i | −0.0422507 | − | 0.0422507i | ||||
\(719\) | 35.2226 | 1.31358 | 0.656791 | − | 0.754073i | \(-0.271913\pi\) | ||||
0.656791 | + | 0.754073i | \(0.271913\pi\) | |||||||
\(720\) | 2.16222 | + | 0.569907i | 0.0805813 | + | 0.0212392i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.5348 | − | 18.5348i | 0.689794 | − | 0.689794i | ||||
\(723\) | 5.97180 | + | 5.97180i | 0.222094 | + | 0.222094i | ||||
\(724\) | −17.6702 | −0.656707 | ||||||||
\(725\) | −3.95071 | + | 6.97383i | −0.146726 | + | 0.259001i | ||||
\(726\) | − | 6.93552i | − | 0.257401i | ||||||
\(727\) | 5.41810 | + | 5.41810i | 0.200946 | + | 0.200946i | 0.800405 | − | 0.599459i | \(-0.204618\pi\) |
−0.599459 | + | 0.800405i | \(0.704618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 18.2628 | + | 4.81362i | 0.675938 | + | 0.178160i | ||||
\(731\) | 31.8433i | 1.17777i | ||||||||
\(732\) | 6.36637 | − | 6.36637i | 0.235308 | − | 0.235308i | ||||
\(733\) | 21.5955 | − | 21.5955i | 0.797647 | − | 0.797647i | −0.185077 | − | 0.982724i | \(-0.559253\pi\) |
0.982724 | + | 0.185077i | \(0.0592534\pi\) | |||||||
\(734\) | −25.0175 | −0.923411 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.57632 | −0.242406 | ||||||||
\(737\) | 2.39933 | − | 2.39933i | 0.0883805 | − | 0.0883805i | ||||
\(738\) | 3.49577 | − | 3.49577i | 0.128681 | − | 0.128681i | ||||
\(739\) | 25.0262i | 0.920603i | 0.887763 | + | 0.460302i | \(0.152259\pi\) | ||||
−0.887763 | + | 0.460302i | \(0.847741\pi\) | |||||||
\(740\) | −9.93014 | + | 5.78739i | −0.365039 | + | 0.212749i | ||||
\(741\) | 32.7123i | 1.20171i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.3224 | + | 12.3224i | 0.452064 | + | 0.452064i | 0.896039 | − | 0.443975i | \(-0.146432\pi\) |
−0.443975 | + | 0.896039i | \(0.646432\pi\) | |||||||
\(744\) | 6.25097i | 0.229172i | ||||||||
\(745\) | 22.6479 | + | 5.96940i | 0.829753 | + | 0.218702i | ||||
\(746\) | −28.0396 | −1.02660 | ||||||||
\(747\) | −8.59652 | − | 8.59652i | −0.314530 | − | 0.314530i | ||||
\(748\) | 6.85664 | − | 6.85664i | 0.250704 | − | 0.250704i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.00200 | − | 7.80820i | −0.292192 | − | 0.285115i | ||||
\(751\) | −51.8620 | −1.89247 | −0.946235 | − | 0.323479i | \(-0.895147\pi\) | ||||
−0.946235 | + | 0.323479i | \(0.895147\pi\) | |||||||
\(752\) | −1.07805 | − | 1.07805i | −0.0393125 | − | 0.0393125i | ||||
\(753\) | 8.35672 | + | 8.35672i | 0.304536 | + | 0.304536i | ||||
\(754\) | 7.79873 | 0.284013 | ||||||||
\(755\) | −5.99830 | + | 22.7575i | −0.218301 | + | 0.828230i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0109 | + | 15.0109i | −0.545581 | + | 0.545581i | −0.925160 | − | 0.379578i | \(-0.876069\pi\) |
0.379578 | + | 0.925160i | \(0.376069\pi\) | |||||||
\(758\) | −2.61628 | − | 2.61628i | −0.0950275 | − | 0.0950275i | ||||
\(759\) | 13.2582 | 0.481243 | ||||||||
\(760\) | 12.9901 | − | 7.57080i | 0.471202 | − | 0.274622i | ||||
\(761\) | 31.8137i | 1.15325i | 0.817010 | + | 0.576623i | \(0.195630\pi\) | ||||
−0.817010 | + | 0.576623i | \(0.804370\pi\) | |||||||
\(762\) | −0.559216 | − | 0.559216i | −0.0202583 | − | 0.0202583i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.33512i | 0.120660i | ||||||||
\(765\) | 5.41549 | + | 9.29202i | 0.195798 | + | 0.335954i | ||||
\(766\) | − | 13.0495i | − | 0.471499i | ||||||
\(767\) | 44.0966 | − | 44.0966i | 1.59223 | − | 1.59223i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | −40.6705 | −1.46662 | −0.733308 | − | 0.679896i | \(-0.762025\pi\) | ||||
−0.733308 | + | 0.679896i | \(0.762025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.1342 | −0.545044 | ||||||||
\(772\) | −14.8727 | + | 14.8727i | −0.535280 | + | 0.535280i | ||||
\(773\) | 25.2031 | − | 25.2031i | 0.906493 | − | 0.906493i | −0.0894947 | − | 0.995987i | \(-0.528525\pi\) |
0.995987 | + | 0.0894947i | \(0.0285252\pi\) | |||||||
\(774\) | 6.62055i | 0.237971i | ||||||||
\(775\) | 15.4057 | − | 27.1943i | 0.553389 | − | 0.976847i | ||||
\(776\) | 18.6436i | 0.669268i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.58317 | + | 9.58317i | 0.343573 | + | 0.343573i | ||||
\(779\) | − | 33.2419i | − | 1.19101i | ||||||
\(780\) | −2.77260 | + | 10.5192i | −0.0992749 | + | 0.376648i | ||||
\(781\) | 7.03659 | 0.251789 | ||||||||
\(782\) | −22.3662 | − | 22.3662i | −0.799813 | − | 0.799813i | ||||
\(783\) | 1.13351 | − | 1.13351i | 0.0405084 | − | 0.0405084i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.0568 | − | 8.77525i | 0.537399 | − | 0.313202i | ||||
\(786\) | 15.7930 | 0.563318 | ||||||||
\(787\) | 5.04970 | + | 5.04970i | 0.180003 | + | 0.180003i | 0.791357 | − | 0.611354i | \(-0.209375\pi\) |
−0.611354 | + | 0.791357i | \(0.709375\pi\) | |||||||
\(788\) | −6.84201 | − | 6.84201i | −0.243736 | − | 0.243736i | ||||
\(789\) | −17.8129 | −0.634156 | ||||||||
\(790\) | 27.0207 | − | 15.7479i | 0.961353 | − | 0.560287i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.42557 | − | 1.42557i | 0.0506553 | − | 0.0506553i | ||||
\(793\) | 30.9724 | + | 30.9724i | 1.09986 | + | 1.09986i | ||||
\(794\) | −1.67080 | −0.0592943 | ||||||||
\(795\) | −1.15192 | + | 4.37038i | −0.0408544 | + | 0.155001i | ||||
\(796\) | − | 17.8747i | − | 0.633551i | ||||||
\(797\) | 6.34127 | + | 6.34127i | 0.224619 | + | 0.224619i | 0.810440 | − | 0.585821i | \(-0.199228\pi\) |
−0.585821 | + | 0.810440i | \(0.699228\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.33295i | − | 0.259421i | ||||||
\(800\) | 4.81889 | − | 1.33352i | 0.170374 | − | 0.0471470i | ||||
\(801\) | 2.40171i | 0.0848603i | ||||||||
\(802\) | 3.72240 | − | 3.72240i | 0.131443 | − | 0.131443i | ||||
\(803\) | 12.0408 | − | 12.0408i | 0.424911 | − | 0.424911i | ||||
\(804\) | −1.68307 | −0.0593574 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30.4110 | −1.07118 | ||||||||
\(807\) | 13.3005 | − | 13.3005i | 0.468201 | − | 0.468201i | ||||
\(808\) | 9.83263 | − | 9.83263i | 0.345911 | − | 0.345911i | ||||
\(809\) | − | 35.0348i | − | 1.23176i | −0.787840 | − | 0.615880i | \(-0.788801\pi\) | ||
0.787840 | − | 0.615880i | \(-0.211199\pi\) | |||||||
\(810\) | 1.12594 | + | 1.93191i | 0.0395614 | + | 0.0678803i | ||||
\(811\) | 11.8588i | 0.416417i | 0.978084 | + | 0.208209i | \(0.0667633\pi\) | ||||
−0.978084 | + | 0.208209i | \(0.933237\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.11738 | + | 4.11738i | 0.144403 | + | 0.144403i | ||||
\(814\) | 10.3627i | 0.363211i | ||||||||
\(815\) | −8.69538 | + | 5.06776i | −0.304586 | + | 0.177516i | ||||
\(816\) | −4.80977 | −0.168376 | ||||||||
\(817\) | 31.4780 | + | 31.4780i | 1.10127 | + | 1.10127i | ||||
\(818\) | −21.8325 | + | 21.8325i | −0.763355 | + | 0.763355i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.81749 | − | 10.6895i | 0.0983909 | − | 0.373294i | ||||
\(821\) | 40.9820 | 1.43028 | 0.715141 | − | 0.698980i | \(-0.246362\pi\) | ||||
0.715141 | + | 0.698980i | \(0.246362\pi\) | |||||||
\(822\) | −9.99143 | − | 9.99143i | −0.348491 | − | 0.348491i | ||||
\(823\) | 4.17227 | + | 4.17227i | 0.145436 | + | 0.145436i | 0.776076 | − | 0.630640i | \(-0.217207\pi\) |
−0.630640 | + | 0.776076i | \(0.717207\pi\) | |||||||
\(824\) | −2.38653 | −0.0831388 | ||||||||
\(825\) | −9.71516 | + | 2.68845i | −0.338238 | + | 0.0935997i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.5494 | − | 23.5494i | 0.818893 | − | 0.818893i | −0.167054 | − | 0.985948i | \(-0.553426\pi\) |
0.985948 | + | 0.167054i | \(0.0534255\pi\) | |||||||
\(828\) | −4.65016 | − | 4.65016i | −0.161604 | − | 0.161604i | ||||
\(829\) | −38.6065 | −1.34086 | −0.670430 | − | 0.741973i | \(-0.733890\pi\) | ||||
−0.670430 | + | 0.741973i | \(0.733890\pi\) | |||||||
\(830\) | −26.2868 | − | 6.92854i | −0.912428 | − | 0.240493i | ||||
\(831\) | 7.19579i | 0.249619i | ||||||||
\(832\) | −3.44007 | − | 3.44007i | −0.119263 | − | 0.119263i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.06459i | 0.140745i | ||||||||
\(835\) | 8.38474 | − | 4.88672i | 0.290166 | − | 0.169112i | ||||
\(836\) | − | 13.5560i | − | 0.468843i | ||||||
\(837\) | −4.42010 | + | 4.42010i | −0.152781 | + | 0.152781i | ||||
\(838\) | 19.6515 | − | 19.6515i | 0.678850 | − | 0.678850i | ||||
\(839\) | −30.3854 | −1.04902 | −0.524510 | − | 0.851404i | \(-0.675752\pi\) | ||||
−0.524510 | + | 0.851404i | \(0.675752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4303 | 0.911390 | ||||||||
\(842\) | −27.1269 | + | 27.1269i | −0.934855 | + | 0.934855i | ||||
\(843\) | −15.9766 | + | 15.9766i | −0.550262 | + | 0.550262i | ||||
\(844\) | − | 8.70108i | − | 0.299504i | ||||||
\(845\) | −23.0671 | − | 6.07990i | −0.793531 | − | 0.209155i | ||||
\(846\) | − | 1.52460i | − | 0.0524167i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.42923 | − | 1.42923i | −0.0490801 | − | 0.0490801i | ||||
\(849\) | 7.38976i | 0.253616i | ||||||||
\(850\) | 20.9245 | + | 11.8538i | 0.717703 | + | 0.406583i | ||||
\(851\) | 33.8027 | 1.15874 | ||||||||
\(852\) | −2.46800 | − | 2.46800i | −0.0845522 | − | 0.0845522i | ||||
\(853\) | −16.1195 | + | 16.1195i | −0.551920 | + | 0.551920i | −0.926995 | − | 0.375074i | \(-0.877617\pi\) |
0.375074 | + | 0.926995i | \(0.377617\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.5388 | + | 3.83206i | 0.497216 | + | 0.131054i | ||||
\(856\) | −11.3578 | −0.388200 | ||||||||
\(857\) | 30.9961 | + | 30.9961i | 1.05881 | + | 1.05881i | 0.998159 | + | 0.0606487i | \(0.0193169\pi\) |
0.0606487 | + | 0.998159i | \(0.480683\pi\) | |||||||
\(858\) | 6.93538 | + | 6.93538i | 0.236770 | + | 0.236770i | ||||
\(859\) | −21.2260 | −0.724221 | −0.362110 | − | 0.932135i | \(-0.617944\pi\) | ||||
−0.362110 | + | 0.932135i | \(0.617944\pi\) | |||||||
\(860\) | 7.45432 | + | 12.7903i | 0.254190 | + | 0.436145i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.9866 | + | 19.9866i | −0.680748 | + | 0.680748i | ||||
\(863\) | −9.89635 | − | 9.89635i | −0.336876 | − | 0.336876i | 0.518315 | − | 0.855190i | \(-0.326560\pi\) |
−0.855190 | + | 0.518315i | \(0.826560\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −19.7705 | − | 33.9227i | −0.672217 | − | 1.15341i | ||||
\(866\) | 28.4802i | 0.967796i | ||||||||
\(867\) | −4.33729 | − | 4.33729i | −0.147302 | − | 0.147302i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 28.1976i | − | 0.956539i | ||||||
\(870\) | 0.913577 | − | 3.46610i | 0.0309732 | − | 0.117512i | ||||
\(871\) | − | 8.18814i | − | 0.277445i | ||||||
\(872\) | −11.1865 | + | 11.1865i | −0.378824 | + | 0.378824i | ||||
\(873\) | −13.1830 | + | 13.1830i | −0.446178 | + | 0.446178i | ||||
\(874\) | −44.2192 | −1.49574 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.44633 | −0.285375 | ||||||||
\(877\) | −18.4262 | + | 18.4262i | −0.622208 | + | 0.622208i | −0.946096 | − | 0.323888i | \(-0.895010\pi\) |
0.323888 | + | 0.946096i | \(0.395010\pi\) | |||||||
\(878\) | −3.24812 | + | 3.24812i | −0.109619 | + | 0.109619i | ||||
\(879\) | 23.8199i | 0.803425i | ||||||||
\(880\) | 1.14896 | − | 4.35916i | 0.0387316 | − | 0.146947i | ||||
\(881\) | 21.4410i | 0.722367i | 0.932495 | + | 0.361184i | \(0.117627\pi\) | ||||
−0.932495 | + | 0.361184i | \(0.882373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.4356 | + | 28.4356i | 0.956934 | + | 0.956934i | 0.999110 | − | 0.0421764i | \(-0.0134292\pi\) |
−0.0421764 | + | 0.999110i | \(0.513429\pi\) | |||||||
\(884\) | − | 23.3995i | − | 0.787011i | ||||||
\(885\) | −14.4328 | − | 24.7641i | −0.485154 | − | 0.832437i | ||||
\(886\) | −37.3236 | −1.25391 | ||||||||
\(887\) | 14.4859 | + | 14.4859i | 0.486388 | + | 0.486388i | 0.907164 | − | 0.420776i | \(-0.138242\pi\) |
−0.420776 | + | 0.907164i | \(0.638242\pi\) | |||||||
\(888\) | 3.63458 | − | 3.63458i | 0.121968 | − | 0.121968i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.70418 | + | 4.63988i | 0.0906442 | + | 0.155529i | ||||
\(891\) | 2.01606 | 0.0675404 | ||||||||
\(892\) | −17.0152 | − | 17.0152i | −0.569711 | − | 0.569711i | ||||
\(893\) | −7.24883 | − | 7.24883i | −0.242573 | − | 0.242573i | ||||
\(894\) | −10.4743 | −0.350314 | ||||||||
\(895\) | 46.2256 | + | 12.1839i | 1.54515 | + | 0.407263i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.6230 | − | 22.6230i | 0.755361 | − | 0.755361i | ||||
\(898\) | 12.4294 | + | 12.4294i | 0.414775 | + | 0.414775i | ||||
\(899\) | 10.0205 | 0.334201 | ||||||||
\(900\) | 4.35041 | + | 2.46453i | 0.145014 | + | 0.0821511i | ||||
\(901\) | − | 9.72171i | − | 0.323877i | ||||||
\(902\) | −7.04766 | − | 7.04766i | −0.234662 | − | 0.234662i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.4700i | 0.514525i | ||||||||
\(905\) | −38.2069 | − | 10.0704i | −1.27004 | − | 0.334750i | ||||
\(906\) | − | 10.5250i | − | 0.349671i | ||||||
\(907\) | −30.4690 | + | 30.4690i | −1.01170 | + | 1.01170i | −0.0117742 | + | 0.999931i | \(0.503748\pi\) |
−0.999931 | + | 0.0117742i | \(0.996252\pi\) | |||||||
\(908\) | −5.71327 | + | 5.71327i | −0.189602 | + | 0.189602i | ||||
\(909\) | 13.9054 | 0.461214 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.8475 | −1.15455 | −0.577275 | − | 0.816550i | \(-0.695884\pi\) | ||||
−0.577275 | + | 0.816550i | \(0.695884\pi\) | |||||||
\(912\) | −4.75459 | + | 4.75459i | −0.157440 | + | 0.157440i | ||||
\(913\) | −17.3311 | + | 17.3311i | −0.573574 | + | 0.573574i | ||||
\(914\) | − | 31.6598i | − | 1.04721i | ||||||
\(915\) | 17.3938 | − | 10.1373i | 0.575020 | − | 0.335128i | ||||
\(916\) | − | 6.23842i | − | 0.206123i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.40102 | − | 3.40102i | −0.112250 | − | 0.112250i | ||||
\(919\) | 4.08697i | 0.134817i | 0.997725 | + | 0.0674084i | \(0.0214731\pi\) | ||||
−0.997725 | + | 0.0674084i | \(0.978527\pi\) | |||||||
\(920\) | −14.2195 | − | 3.74789i | −0.468802 | − | 0.123564i | ||||
\(921\) | −28.3237 | −0.933299 | ||||||||
\(922\) | 5.13223 | + | 5.13223i | 0.169021 | + | 0.169021i | ||||
\(923\) | 12.0068 | − | 12.0068i | 0.395209 | − | 0.395209i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.7694 | + | 6.85437i | −0.814414 | + | 0.225370i | ||||
\(926\) | −21.0555 | −0.691926 | ||||||||
\(927\) | −1.68753 | − | 1.68753i | −0.0554259 | − | 0.0554259i | ||||
\(928\) | 1.13351 | + | 1.13351i | 0.0372093 | + | 0.0372093i | ||||
\(929\) | −10.8143 | −0.354805 | −0.177403 | − | 0.984138i | \(-0.556769\pi\) | ||||
−0.177403 | + | 0.984138i | \(0.556769\pi\) | |||||||
\(930\) | −3.56247 | + | 13.5160i | −0.116818 | + | 0.443206i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.88051 | + | 6.88051i | −0.225379 | + | 0.225379i | ||||
\(933\) | −16.1503 | − | 16.1503i | −0.528737 | − | 0.528737i | ||||
\(934\) | 10.8431 | 0.354796 | ||||||||
\(935\) | 18.7332 | − | 10.9179i | 0.612642 | − | 0.357055i | ||||
\(936\) | − | 4.86500i | − | 0.159017i | ||||||
\(937\) | 5.40732 | + | 5.40732i | 0.176649 | + | 0.176649i | 0.789894 | − | 0.613244i | \(-0.210136\pi\) |
−0.613244 | + | 0.789894i | \(0.710136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 21.5733i | − | 0.704019i | ||||||
\(940\) | −1.71660 | − | 2.94538i | −0.0559893 | − | 0.0960677i | ||||
\(941\) | − | 45.9833i | − | 1.49901i | −0.661997 | − | 0.749507i | \(-0.730291\pi\) | ||
0.661997 | − | 0.749507i | \(-0.269709\pi\) | |||||||
\(942\) | −5.51100 | + | 5.51100i | −0.179558 | + | 0.179558i | ||||
\(943\) | −22.9893 | + | 22.9893i | −0.748634 | + | 0.748634i | ||||
\(944\) | 12.8185 | 0.417206 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.3474 | 0.433961 | ||||||||
\(947\) | 1.91345 | − | 1.91345i | 0.0621786 | − | 0.0621786i | −0.675334 | − | 0.737512i | \(-0.736000\pi\) |
0.737512 | + | 0.675334i | \(0.236000\pi\) | |||||||
\(948\) | −9.88997 | + | 9.88997i | −0.321211 | + | 0.321211i | ||||
\(949\) | − | 41.0914i | − | 1.33388i | ||||||
\(950\) | 32.4022 | − | 8.96658i | 1.05127 | − | 0.290914i | ||||
\(951\) | − | 23.9908i | − | 0.777956i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.34628 | − | 8.34628i | −0.270363 | − | 0.270363i | 0.558884 | − | 0.829246i | \(-0.311230\pi\) |
−0.829246 | + | 0.558884i | \(0.811230\pi\) | |||||||
\(954\) | − | 2.02124i | − | 0.0654402i | ||||||
\(955\) | −1.90071 | + | 7.21126i | −0.0615054 | + | 0.233351i | ||||
\(956\) | 10.6330 | 0.343896 | ||||||||
\(957\) | −2.28522 | − | 2.28522i | −0.0738707 | − | 0.0738707i | ||||
\(958\) | 18.9771 | − | 18.9771i | 0.613123 | − | 0.613123i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.93191 | + | 1.12594i | −0.0623520 | + | 0.0363395i | ||||
\(961\) | −8.07459 | −0.260471 | ||||||||
\(962\) | 17.6822 | + | 17.6822i | 0.570098 | + | 0.570098i | ||||
\(963\) | −8.03115 | − | 8.03115i | −0.258800 | − | 0.258800i | ||||
\(964\) | −8.44540 | −0.272008 | ||||||||
\(965\) | −40.6341 | + | 23.6820i | −1.30806 | + | 0.762351i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.8242 | + | 15.8242i | −0.508871 | + | 0.508871i | −0.914180 | − | 0.405309i | \(-0.867164\pi\) |
0.405309 | + | 0.914180i | \(0.367164\pi\) | |||||||
\(968\) | 4.90415 | + | 4.90415i | 0.157625 | + | 0.157625i | ||||
\(969\) | −32.3409 | −1.03894 | ||||||||
\(970\) | −10.6251 | + | 40.3117i | −0.341153 | + | 1.29433i | ||||
\(971\) | − | 29.2160i | − | 0.937587i | −0.883308 | − | 0.468793i | \(-0.844689\pi\) | ||
0.883308 | − | 0.468793i | \(-0.155311\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17.4039i | 0.557658i | ||||||||
\(975\) | −11.9899 | + | 21.1648i | −0.383986 | + | 0.677814i | ||||
\(976\) | 9.00341i | 0.288192i | ||||||||
\(977\) | 3.83196 | − | 3.83196i | 0.122595 | − | 0.122595i | −0.643147 | − | 0.765742i | \(-0.722372\pi\) |
0.765742 | + | 0.643147i | \(0.222372\pi\) | |||||||
\(978\) | 3.18264 | − | 3.18264i | 0.101770 | − | 0.101770i | ||||
\(979\) | 4.84198 | 0.154751 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.8201 | −0.505098 | ||||||||
\(982\) | −19.7528 | + | 19.7528i | −0.630337 | + | 0.630337i | ||||
\(983\) | 15.3737 | − | 15.3737i | 0.490344 | − | 0.490344i | −0.418071 | − | 0.908415i | \(-0.637294\pi\) |
0.908415 | + | 0.418071i | \(0.137294\pi\) | |||||||
\(984\) | 4.94376i | 0.157601i | ||||||||
\(985\) | −10.8946 | − | 18.6932i | −0.347132 | − | 0.595616i | ||||
\(986\) | 7.71019i | 0.245542i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23.1311 | − | 23.1311i | −0.735897 | − | 0.735897i | ||||
\(989\) | − | 43.5388i | − | 1.38445i | ||||||
\(990\) | 3.89483 | − | 2.26995i | 0.123786 | − | 0.0721438i | ||||
\(991\) | 14.6567 | 0.465585 | 0.232792 | − | 0.972526i | \(-0.425214\pi\) | ||||
0.232792 | + | 0.972526i | \(0.425214\pi\) | |||||||
\(992\) | −4.42010 | − | 4.42010i | −0.140338 | − | 0.140338i | ||||
\(993\) | 15.4933 | − | 15.4933i | 0.491663 | − | 0.491663i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.1869 | − | 38.6490i | 0.322947 | − | 1.22526i | ||||
\(996\) | 12.1573 | 0.385219 | ||||||||
\(997\) | 18.4510 | + | 18.4510i | 0.584350 | + | 0.584350i | 0.936096 | − | 0.351745i | \(-0.114412\pi\) |
−0.351745 | + | 0.936096i | \(0.614412\pi\) | |||||||
\(998\) | 20.6483 | + | 20.6483i | 0.653610 | + | 0.653610i | ||||
\(999\) | 5.14007 | 0.162625 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1470.2.m.f.1273.6 | yes | 16 | |
5.2 | odd | 4 | 1470.2.m.c.97.7 | ✓ | 16 | ||
7.6 | odd | 2 | 1470.2.m.c.1273.7 | yes | 16 | ||
35.27 | even | 4 | inner | 1470.2.m.f.97.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.m.c.97.7 | ✓ | 16 | 5.2 | odd | 4 | ||
1470.2.m.c.1273.7 | yes | 16 | 7.6 | odd | 2 | ||
1470.2.m.f.97.6 | yes | 16 | 35.27 | even | 4 | inner | |
1470.2.m.f.1273.6 | yes | 16 | 1.1 | even | 1 | trivial |