Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 379.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.379 |
Dual form | 462.2.j.d.295.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | ||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −0.190983 | + | 0.587785i | −0.0854102 | + | 0.262866i | −0.984636 | − | 0.174619i | \(-0.944131\pi\) |
0.899226 | + | 0.437485i | \(0.144131\pi\) | |||||||
\(6\) | 0.309017 | − | 0.951057i | 0.126156 | − | 0.388267i | ||||
\(7\) | −0.809017 | + | 0.587785i | −0.305780 | + | 0.222162i | ||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0.618034 | 0.195440 | ||||||||
\(11\) | 0.309017 | + | 3.30220i | 0.0931721 | + | 0.995650i | ||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.618034 | + | 1.90211i | 0.171412 | + | 0.527551i | 0.999451 | − | 0.0331183i | \(-0.0105438\pi\) |
−0.828040 | + | 0.560670i | \(0.810544\pi\) | |||||||
\(14\) | 0.809017 | + | 0.587785i | 0.216219 | + | 0.157092i | ||||
\(15\) | −0.500000 | + | 0.363271i | −0.129099 | + | 0.0937962i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 0.118034 | − | 0.363271i | 0.0286274 | − | 0.0881062i | −0.935722 | − | 0.352738i | \(-0.885251\pi\) |
0.964349 | + | 0.264632i | \(0.0852506\pi\) | |||||||
\(18\) | 0.809017 | − | 0.587785i | 0.190687 | − | 0.138542i | ||||
\(19\) | 3.92705 | + | 2.85317i | 0.900927 | + | 0.654562i | 0.938704 | − | 0.344724i | \(-0.112028\pi\) |
−0.0377767 | + | 0.999286i | \(0.512028\pi\) | |||||||
\(20\) | −0.190983 | − | 0.587785i | −0.0427051 | − | 0.131433i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 3.04508 | − | 1.31433i | 0.649214 | − | 0.280216i | ||||
\(23\) | −4.85410 | −1.01215 | −0.506075 | − | 0.862489i | \(-0.668904\pi\) | ||||
−0.506075 | + | 0.862489i | \(0.668904\pi\) | |||||||
\(24\) | 0.309017 | + | 0.951057i | 0.0630778 | + | 0.194134i | ||||
\(25\) | 3.73607 | + | 2.71441i | 0.747214 | + | 0.542882i | ||||
\(26\) | 1.61803 | − | 1.17557i | 0.317323 | − | 0.230548i | ||||
\(27\) | −0.309017 | + | 0.951057i | −0.0594703 | + | 0.183031i | ||||
\(28\) | 0.309017 | − | 0.951057i | 0.0583987 | − | 0.179733i | ||||
\(29\) | 2.00000 | − | 1.45309i | 0.371391 | − | 0.269831i | −0.386397 | − | 0.922333i | \(-0.626280\pi\) |
0.757787 | + | 0.652502i | \(0.226280\pi\) | |||||||
\(30\) | 0.500000 | + | 0.363271i | 0.0912871 | + | 0.0663240i | ||||
\(31\) | 1.42705 | + | 4.39201i | 0.256306 | + | 0.788829i | 0.993570 | + | 0.113223i | \(0.0361176\pi\) |
−0.737264 | + | 0.675605i | \(0.763882\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.69098 | + | 2.85317i | −0.294362 | + | 0.496673i | ||||
\(34\) | −0.381966 | −0.0655066 | ||||||||
\(35\) | −0.190983 | − | 0.587785i | −0.0322820 | − | 0.0993538i | ||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | −3.11803 | + | 2.26538i | −0.512602 | + | 0.372427i | −0.813810 | − | 0.581132i | \(-0.802610\pi\) |
0.301208 | + | 0.953558i | \(0.402610\pi\) | |||||||
\(38\) | 1.50000 | − | 4.61653i | 0.243332 | − | 0.748899i | ||||
\(39\) | −0.618034 | + | 1.90211i | −0.0989646 | + | 0.304582i | ||||
\(40\) | −0.500000 | + | 0.363271i | −0.0790569 | + | 0.0574382i | ||||
\(41\) | −2.11803 | − | 1.53884i | −0.330781 | − | 0.240327i | 0.409981 | − | 0.912094i | \(-0.365535\pi\) |
−0.740762 | + | 0.671767i | \(0.765535\pi\) | |||||||
\(42\) | 0.309017 | + | 0.951057i | 0.0476824 | + | 0.146751i | ||||
\(43\) | 10.0000 | 1.52499 | 0.762493 | − | 0.646997i | \(-0.223975\pi\) | ||||
0.762493 | + | 0.646997i | \(0.223975\pi\) | |||||||
\(44\) | −2.19098 | − | 2.48990i | −0.330303 | − | 0.375366i | ||||
\(45\) | −0.618034 | −0.0921311 | ||||||||
\(46\) | 1.50000 | + | 4.61653i | 0.221163 | + | 0.680670i | ||||
\(47\) | −5.23607 | − | 3.80423i | −0.763759 | − | 0.554903i | 0.136302 | − | 0.990667i | \(-0.456478\pi\) |
−0.900061 | + | 0.435764i | \(0.856478\pi\) | |||||||
\(48\) | 0.809017 | − | 0.587785i | 0.116772 | − | 0.0848395i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 1.42705 | − | 4.39201i | 0.201815 | − | 0.621124i | ||||
\(51\) | 0.309017 | − | 0.224514i | 0.0432710 | − | 0.0314382i | ||||
\(52\) | −1.61803 | − | 1.17557i | −0.224381 | − | 0.163022i | ||||
\(53\) | 0.145898 | + | 0.449028i | 0.0200406 | + | 0.0616787i | 0.960577 | − | 0.278015i | \(-0.0896765\pi\) |
−0.940536 | + | 0.339694i | \(0.889677\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.00000 | − | 0.449028i | −0.269680 | − | 0.0605469i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.50000 | + | 4.61653i | 0.198680 | + | 0.611474i | ||||
\(58\) | −2.00000 | − | 1.45309i | −0.262613 | − | 0.190799i | ||||
\(59\) | 4.23607 | − | 3.07768i | 0.551489 | − | 0.400680i | −0.276845 | − | 0.960915i | \(-0.589289\pi\) |
0.828334 | + | 0.560234i | \(0.189289\pi\) | |||||||
\(60\) | 0.190983 | − | 0.587785i | 0.0246558 | − | 0.0758827i | ||||
\(61\) | 3.76393 | − | 11.5842i | 0.481922 | − | 1.48320i | −0.354467 | − | 0.935068i | \(-0.615338\pi\) |
0.836390 | − | 0.548135i | \(-0.184662\pi\) | |||||||
\(62\) | 3.73607 | − | 2.71441i | 0.474481 | − | 0.344731i | ||||
\(63\) | −0.809017 | − | 0.587785i | −0.101927 | − | 0.0740540i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | −1.23607 | −0.153315 | ||||||||
\(66\) | 3.23607 | + | 0.726543i | 0.398332 | + | 0.0894312i | ||||
\(67\) | −12.1803 | −1.48807 | −0.744033 | − | 0.668143i | \(-0.767089\pi\) | ||||
−0.744033 | + | 0.668143i | \(0.767089\pi\) | |||||||
\(68\) | 0.118034 | + | 0.363271i | 0.0143137 | + | 0.0440531i | ||||
\(69\) | −3.92705 | − | 2.85317i | −0.472761 | − | 0.343481i | ||||
\(70\) | −0.500000 | + | 0.363271i | −0.0597614 | + | 0.0434192i | ||||
\(71\) | 2.00000 | − | 6.15537i | 0.237356 | − | 0.730508i | −0.759444 | − | 0.650573i | \(-0.774529\pi\) |
0.996800 | − | 0.0799347i | \(-0.0254712\pi\) | |||||||
\(72\) | −0.309017 | + | 0.951057i | −0.0364180 | + | 0.112083i | ||||
\(73\) | 8.23607 | − | 5.98385i | 0.963959 | − | 0.700357i | 0.00989205 | − | 0.999951i | \(-0.496851\pi\) |
0.954067 | + | 0.299594i | \(0.0968512\pi\) | |||||||
\(74\) | 3.11803 | + | 2.26538i | 0.362464 | + | 0.263346i | ||||
\(75\) | 1.42705 | + | 4.39201i | 0.164782 | + | 0.507146i | ||||
\(76\) | −4.85410 | −0.556804 | ||||||||
\(77\) | −2.19098 | − | 2.48990i | −0.249686 | − | 0.283750i | ||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | 4.47214 | + | 13.7638i | 0.503155 | + | 1.54855i | 0.803851 | + | 0.594831i | \(0.202781\pi\) |
−0.300696 | + | 0.953720i | \(0.597219\pi\) | |||||||
\(80\) | 0.500000 | + | 0.363271i | 0.0559017 | + | 0.0406150i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −0.809017 | + | 2.48990i | −0.0893410 | + | 0.274963i | ||||
\(83\) | 0.854102 | − | 2.62866i | 0.0937499 | − | 0.288532i | −0.893176 | − | 0.449707i | \(-0.851528\pi\) |
0.986926 | + | 0.161175i | \(0.0515283\pi\) | |||||||
\(84\) | 0.809017 | − | 0.587785i | 0.0882710 | − | 0.0641326i | ||||
\(85\) | 0.190983 | + | 0.138757i | 0.0207150 | + | 0.0150503i | ||||
\(86\) | −3.09017 | − | 9.51057i | −0.333222 | − | 1.02555i | ||||
\(87\) | 2.47214 | 0.265041 | ||||||||
\(88\) | −1.69098 | + | 2.85317i | −0.180259 | + | 0.304149i | ||||
\(89\) | −15.7984 | −1.67462 | −0.837312 | − | 0.546725i | \(-0.815874\pi\) | ||||
−0.837312 | + | 0.546725i | \(0.815874\pi\) | |||||||
\(90\) | 0.190983 | + | 0.587785i | 0.0201314 | + | 0.0619580i | ||||
\(91\) | −1.61803 | − | 1.17557i | −0.169616 | − | 0.123233i | ||||
\(92\) | 3.92705 | − | 2.85317i | 0.409423 | − | 0.297463i | ||||
\(93\) | −1.42705 | + | 4.39201i | −0.147978 | + | 0.455430i | ||||
\(94\) | −2.00000 | + | 6.15537i | −0.206284 | + | 0.634878i | ||||
\(95\) | −2.42705 | + | 1.76336i | −0.249010 | + | 0.180916i | ||||
\(96\) | −0.809017 | − | 0.587785i | −0.0825700 | − | 0.0599906i | ||||
\(97\) | −3.14590 | − | 9.68208i | −0.319418 | − | 0.983066i | −0.973898 | − | 0.226987i | \(-0.927113\pi\) |
0.654480 | − | 0.756079i | \(-0.272887\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −3.04508 | + | 1.31433i | −0.306043 | + | 0.132095i | ||||
\(100\) | −4.61803 | −0.461803 | ||||||||
\(101\) | −3.51722 | − | 10.8249i | −0.349977 | − | 1.07712i | −0.958865 | − | 0.283861i | \(-0.908384\pi\) |
0.608889 | − | 0.793256i | \(-0.291616\pi\) | |||||||
\(102\) | −0.309017 | − | 0.224514i | −0.0305972 | − | 0.0222302i | ||||
\(103\) | −6.92705 | + | 5.03280i | −0.682543 | + | 0.495896i | −0.874200 | − | 0.485566i | \(-0.838614\pi\) |
0.191658 | + | 0.981462i | \(0.438614\pi\) | |||||||
\(104\) | −0.618034 | + | 1.90211i | −0.0606032 | + | 0.186518i | ||||
\(105\) | 0.190983 | − | 0.587785i | 0.0186380 | − | 0.0573620i | ||||
\(106\) | 0.381966 | − | 0.277515i | 0.0370998 | − | 0.0269546i | ||||
\(107\) | −0.927051 | − | 0.673542i | −0.0896214 | − | 0.0651138i | 0.542072 | − | 0.840332i | \(-0.317640\pi\) |
−0.631694 | + | 0.775218i | \(0.717640\pi\) | |||||||
\(108\) | −0.309017 | − | 0.951057i | −0.0297352 | − | 0.0915155i | ||||
\(109\) | 4.14590 | 0.397105 | 0.198553 | − | 0.980090i | \(-0.436376\pi\) | ||||
0.198553 | + | 0.980090i | \(0.436376\pi\) | |||||||
\(110\) | 0.190983 | + | 2.04087i | 0.0182095 | + | 0.194589i | ||||
\(111\) | −3.85410 | −0.365815 | ||||||||
\(112\) | 0.309017 | + | 0.951057i | 0.0291994 | + | 0.0898664i | ||||
\(113\) | 9.32624 | + | 6.77591i | 0.877339 | + | 0.637424i | 0.932546 | − | 0.361051i | \(-0.117582\pi\) |
−0.0552074 | + | 0.998475i | \(0.517582\pi\) | |||||||
\(114\) | 3.92705 | − | 2.85317i | 0.367802 | − | 0.267224i | ||||
\(115\) | 0.927051 | − | 2.85317i | 0.0864479 | − | 0.266059i | ||||
\(116\) | −0.763932 | + | 2.35114i | −0.0709293 | + | 0.218298i | ||||
\(117\) | −1.61803 | + | 1.17557i | −0.149587 | + | 0.108682i | ||||
\(118\) | −4.23607 | − | 3.07768i | −0.389962 | − | 0.283324i | ||||
\(119\) | 0.118034 | + | 0.363271i | 0.0108202 | + | 0.0333010i | ||||
\(120\) | −0.618034 | −0.0564185 | ||||||||
\(121\) | −10.8090 | + | 2.04087i | −0.982638 | + | 0.185534i | ||||
\(122\) | −12.1803 | −1.10276 | ||||||||
\(123\) | −0.809017 | − | 2.48990i | −0.0729466 | − | 0.224507i | ||||
\(124\) | −3.73607 | − | 2.71441i | −0.335509 | − | 0.243761i | ||||
\(125\) | −4.80902 | + | 3.49396i | −0.430132 | + | 0.312509i | ||||
\(126\) | −0.309017 | + | 0.951057i | −0.0275294 | + | 0.0847268i | ||||
\(127\) | 1.52786 | − | 4.70228i | 0.135576 | − | 0.417260i | −0.860103 | − | 0.510120i | \(-0.829601\pi\) |
0.995679 | + | 0.0928601i | \(0.0296009\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | 8.09017 | + | 5.87785i | 0.712300 | + | 0.517516i | ||||
\(130\) | 0.381966 | + | 1.17557i | 0.0335006 | + | 0.103104i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −0.309017 | − | 3.30220i | −0.0268965 | − | 0.287419i | ||||
\(133\) | −4.85410 | −0.420904 | ||||||||
\(134\) | 3.76393 | + | 11.5842i | 0.325154 | + | 1.00072i | ||||
\(135\) | −0.500000 | − | 0.363271i | −0.0430331 | − | 0.0312654i | ||||
\(136\) | 0.309017 | − | 0.224514i | 0.0264980 | − | 0.0192519i | ||||
\(137\) | 1.61803 | − | 4.97980i | 0.138238 | − | 0.425453i | −0.857842 | − | 0.513914i | \(-0.828195\pi\) |
0.996080 | + | 0.0884614i | \(0.0281950\pi\) | |||||||
\(138\) | −1.50000 | + | 4.61653i | −0.127688 | + | 0.392985i | ||||
\(139\) | 1.30902 | − | 0.951057i | 0.111029 | − | 0.0806676i | −0.530885 | − | 0.847444i | \(-0.678140\pi\) |
0.641914 | + | 0.766776i | \(0.278140\pi\) | |||||||
\(140\) | 0.500000 | + | 0.363271i | 0.0422577 | + | 0.0307020i | ||||
\(141\) | −2.00000 | − | 6.15537i | −0.168430 | − | 0.518375i | ||||
\(142\) | −6.47214 | −0.543130 | ||||||||
\(143\) | −6.09017 | + | 2.62866i | −0.509286 | + | 0.219819i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.472136 | + | 1.45309i | 0.0392088 | + | 0.120672i | ||||
\(146\) | −8.23607 | − | 5.98385i | −0.681622 | − | 0.495227i | ||||
\(147\) | 0.809017 | − | 0.587785i | 0.0667266 | − | 0.0484797i | ||||
\(148\) | 1.19098 | − | 3.66547i | 0.0978982 | − | 0.301300i | ||||
\(149\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(150\) | 3.73607 | − | 2.71441i | 0.305049 | − | 0.221631i | ||||
\(151\) | −5.85410 | − | 4.25325i | −0.476400 | − | 0.346125i | 0.323530 | − | 0.946218i | \(-0.395130\pi\) |
−0.799930 | + | 0.600093i | \(0.795130\pi\) | |||||||
\(152\) | 1.50000 | + | 4.61653i | 0.121666 | + | 0.374450i | ||||
\(153\) | 0.381966 | 0.0308801 | ||||||||
\(154\) | −1.69098 | + | 2.85317i | −0.136263 | + | 0.229915i | ||||
\(155\) | −2.85410 | −0.229247 | ||||||||
\(156\) | −0.618034 | − | 1.90211i | −0.0494823 | − | 0.152291i | ||||
\(157\) | −3.00000 | − | 2.17963i | −0.239426 | − | 0.173953i | 0.461601 | − | 0.887087i | \(-0.347275\pi\) |
−0.701028 | + | 0.713134i | \(0.747275\pi\) | |||||||
\(158\) | 11.7082 | − | 8.50651i | 0.931455 | − | 0.676741i | ||||
\(159\) | −0.145898 | + | 0.449028i | −0.0115705 | + | 0.0356102i | ||||
\(160\) | 0.190983 | − | 0.587785i | 0.0150985 | − | 0.0464685i | ||||
\(161\) | 3.92705 | − | 2.85317i | 0.309495 | − | 0.224861i | ||||
\(162\) | 0.809017 | + | 0.587785i | 0.0635624 | + | 0.0461808i | ||||
\(163\) | 3.09017 | + | 9.51057i | 0.242041 | + | 0.744925i | 0.996109 | + | 0.0881289i | \(0.0280887\pi\) |
−0.754068 | + | 0.656796i | \(0.771911\pi\) | |||||||
\(164\) | 2.61803 | 0.204434 | ||||||||
\(165\) | −1.35410 | − | 1.53884i | −0.105417 | − | 0.119799i | ||||
\(166\) | −2.76393 | −0.214523 | ||||||||
\(167\) | 3.94427 | + | 12.1392i | 0.305217 | + | 0.939361i | 0.979596 | + | 0.200976i | \(0.0644113\pi\) |
−0.674379 | + | 0.738385i | \(0.735589\pi\) | |||||||
\(168\) | −0.809017 | − | 0.587785i | −0.0624170 | − | 0.0453486i | ||||
\(169\) | 7.28115 | − | 5.29007i | 0.560089 | − | 0.406928i | ||||
\(170\) | 0.0729490 | − | 0.224514i | 0.00559493 | − | 0.0172194i | ||||
\(171\) | −1.50000 | + | 4.61653i | −0.114708 | + | 0.353035i | ||||
\(172\) | −8.09017 | + | 5.87785i | −0.616870 | + | 0.448182i | ||||
\(173\) | −15.1631 | − | 11.0167i | −1.15283 | − | 0.837580i | −0.163976 | − | 0.986464i | \(-0.552432\pi\) |
−0.988855 | + | 0.148884i | \(0.952432\pi\) | |||||||
\(174\) | −0.763932 | − | 2.35114i | −0.0579135 | − | 0.178240i | ||||
\(175\) | −4.61803 | −0.349091 | ||||||||
\(176\) | 3.23607 | + | 0.726543i | 0.243928 | + | 0.0547652i | ||||
\(177\) | 5.23607 | 0.393567 | ||||||||
\(178\) | 4.88197 | + | 15.0251i | 0.365919 | + | 1.12618i | ||||
\(179\) | 12.9721 | + | 9.42481i | 0.969583 | + | 0.704443i | 0.955356 | − | 0.295456i | \(-0.0954714\pi\) |
0.0142265 | + | 0.999899i | \(0.495471\pi\) | |||||||
\(180\) | 0.500000 | − | 0.363271i | 0.0372678 | − | 0.0270766i | ||||
\(181\) | 5.47214 | − | 16.8415i | 0.406741 | − | 1.25182i | −0.512692 | − | 0.858572i | \(-0.671352\pi\) |
0.919433 | − | 0.393247i | \(-0.128648\pi\) | |||||||
\(182\) | −0.618034 | + | 1.90211i | −0.0458117 | + | 0.140994i | ||||
\(183\) | 9.85410 | − | 7.15942i | 0.728436 | − | 0.529240i | ||||
\(184\) | −3.92705 | − | 2.85317i | −0.289506 | − | 0.210338i | ||||
\(185\) | −0.736068 | − | 2.26538i | −0.0541168 | − | 0.166554i | ||||
\(186\) | 4.61803 | 0.338611 | ||||||||
\(187\) | 1.23607 | + | 0.277515i | 0.0903902 | + | 0.0202939i | ||||
\(188\) | 6.47214 | 0.472029 | ||||||||
\(189\) | −0.309017 | − | 0.951057i | −0.0224777 | − | 0.0691792i | ||||
\(190\) | 2.42705 | + | 1.76336i | 0.176077 | + | 0.127927i | ||||
\(191\) | 11.8262 | − | 8.59226i | 0.855717 | − | 0.621714i | −0.0709997 | − | 0.997476i | \(-0.522619\pi\) |
0.926716 | + | 0.375762i | \(0.122619\pi\) | |||||||
\(192\) | −0.309017 | + | 0.951057i | −0.0223014 | + | 0.0686366i | ||||
\(193\) | 5.60739 | − | 17.2578i | 0.403629 | − | 1.24224i | −0.518406 | − | 0.855135i | \(-0.673474\pi\) |
0.922035 | − | 0.387107i | \(-0.126526\pi\) | |||||||
\(194\) | −8.23607 | + | 5.98385i | −0.591315 | + | 0.429616i | ||||
\(195\) | −1.00000 | − | 0.726543i | −0.0716115 | − | 0.0520288i | ||||
\(196\) | 0.309017 | + | 0.951057i | 0.0220726 | + | 0.0679326i | ||||
\(197\) | 20.1803 | 1.43779 | 0.718895 | − | 0.695119i | \(-0.244648\pi\) | ||||
0.718895 | + | 0.695119i | \(0.244648\pi\) | |||||||
\(198\) | 2.19098 | + | 2.48990i | 0.155706 | + | 0.176949i | ||||
\(199\) | 4.38197 | 0.310629 | 0.155315 | − | 0.987865i | \(-0.450361\pi\) | ||||
0.155315 | + | 0.987865i | \(0.450361\pi\) | |||||||
\(200\) | 1.42705 | + | 4.39201i | 0.100908 | + | 0.310562i | ||||
\(201\) | −9.85410 | − | 7.15942i | −0.695055 | − | 0.504987i | ||||
\(202\) | −9.20820 | + | 6.69015i | −0.647887 | + | 0.470717i | ||||
\(203\) | −0.763932 | + | 2.35114i | −0.0536175 | + | 0.165018i | ||||
\(204\) | −0.118034 | + | 0.363271i | −0.00826403 | + | 0.0254341i | ||||
\(205\) | 1.30902 | − | 0.951057i | 0.0914257 | − | 0.0664247i | ||||
\(206\) | 6.92705 | + | 5.03280i | 0.482631 | + | 0.350652i | ||||
\(207\) | −1.50000 | − | 4.61653i | −0.104257 | − | 0.320871i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −8.20820 | + | 13.8496i | −0.567773 | + | 0.957995i | ||||
\(210\) | −0.618034 | −0.0426484 | ||||||||
\(211\) | 6.38197 | + | 19.6417i | 0.439353 | + | 1.35219i | 0.888560 | + | 0.458761i | \(0.151707\pi\) |
−0.449207 | + | 0.893428i | \(0.648293\pi\) | |||||||
\(212\) | −0.381966 | − | 0.277515i | −0.0262335 | − | 0.0190598i | ||||
\(213\) | 5.23607 | − | 3.80423i | 0.358769 | − | 0.260661i | ||||
\(214\) | −0.354102 | + | 1.08981i | −0.0242059 | + | 0.0744981i | ||||
\(215\) | −1.90983 | + | 5.87785i | −0.130249 | + | 0.400866i | ||||
\(216\) | −0.809017 | + | 0.587785i | −0.0550466 | + | 0.0399937i | ||||
\(217\) | −3.73607 | − | 2.71441i | −0.253621 | − | 0.184266i | ||||
\(218\) | −1.28115 | − | 3.94298i | −0.0867706 | − | 0.267053i | ||||
\(219\) | 10.1803 | 0.687924 | ||||||||
\(220\) | 1.88197 | − | 0.812299i | 0.126882 | − | 0.0547652i | ||||
\(221\) | 0.763932 | 0.0513876 | ||||||||
\(222\) | 1.19098 | + | 3.66547i | 0.0799335 | + | 0.246010i | ||||
\(223\) | 3.69098 | + | 2.68166i | 0.247167 | + | 0.179577i | 0.704470 | − | 0.709734i | \(-0.251185\pi\) |
−0.457304 | + | 0.889311i | \(0.651185\pi\) | |||||||
\(224\) | 0.809017 | − | 0.587785i | 0.0540547 | − | 0.0392731i | ||||
\(225\) | −1.42705 | + | 4.39201i | −0.0951367 | + | 0.292801i | ||||
\(226\) | 3.56231 | − | 10.9637i | 0.236961 | − | 0.729291i | ||||
\(227\) | 5.85410 | − | 4.25325i | 0.388550 | − | 0.282298i | −0.376311 | − | 0.926493i | \(-0.622808\pi\) |
0.764861 | + | 0.644195i | \(0.222808\pi\) | |||||||
\(228\) | −3.92705 | − | 2.85317i | −0.260075 | − | 0.188956i | ||||
\(229\) | −1.23607 | − | 3.80423i | −0.0816817 | − | 0.251390i | 0.901873 | − | 0.432001i | \(-0.142192\pi\) |
−0.983555 | + | 0.180611i | \(0.942192\pi\) | |||||||
\(230\) | −3.00000 | −0.197814 | ||||||||
\(231\) | −0.309017 | − | 3.30220i | −0.0203318 | − | 0.217269i | ||||
\(232\) | 2.47214 | 0.162304 | ||||||||
\(233\) | 0.236068 | + | 0.726543i | 0.0154653 | + | 0.0475974i | 0.958491 | − | 0.285122i | \(-0.0920340\pi\) |
−0.943026 | + | 0.332719i | \(0.892034\pi\) | |||||||
\(234\) | 1.61803 | + | 1.17557i | 0.105774 | + | 0.0768494i | ||||
\(235\) | 3.23607 | − | 2.35114i | 0.211098 | − | 0.153372i | ||||
\(236\) | −1.61803 | + | 4.97980i | −0.105325 | + | 0.324157i | ||||
\(237\) | −4.47214 | + | 13.7638i | −0.290496 | + | 0.894056i | ||||
\(238\) | 0.309017 | − | 0.224514i | 0.0200306 | − | 0.0145531i | ||||
\(239\) | 20.8713 | + | 15.1639i | 1.35005 | + | 0.980871i | 0.999009 | + | 0.0445127i | \(0.0141735\pi\) |
0.351045 | + | 0.936359i | \(0.385826\pi\) | |||||||
\(240\) | 0.190983 | + | 0.587785i | 0.0123279 | + | 0.0379414i | ||||
\(241\) | 29.1246 | 1.87608 | 0.938041 | − | 0.346525i | \(-0.112639\pi\) | ||||
0.938041 | + | 0.346525i | \(0.112639\pi\) | |||||||
\(242\) | 5.28115 | + | 9.64932i | 0.339485 | + | 0.620282i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.76393 | + | 11.5842i | 0.240961 | + | 0.741602i | ||||
\(245\) | 0.500000 | + | 0.363271i | 0.0319438 | + | 0.0232085i | ||||
\(246\) | −2.11803 | + | 1.53884i | −0.135041 | + | 0.0981130i | ||||
\(247\) | −3.00000 | + | 9.23305i | −0.190885 | + | 0.587485i | ||||
\(248\) | −1.42705 | + | 4.39201i | −0.0906178 | + | 0.278893i | ||||
\(249\) | 2.23607 | − | 1.62460i | 0.141705 | − | 0.102955i | ||||
\(250\) | 4.80902 | + | 3.49396i | 0.304149 | + | 0.220977i | ||||
\(251\) | 7.56231 | + | 23.2744i | 0.477329 | + | 1.46907i | 0.842791 | + | 0.538240i | \(0.180911\pi\) |
−0.365463 | + | 0.930826i | \(0.619089\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −1.50000 | − | 16.0292i | −0.0943042 | − | 1.00775i | ||||
\(254\) | −4.94427 | −0.310231 | ||||||||
\(255\) | 0.0729490 | + | 0.224514i | 0.00456824 | + | 0.0140596i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 11.2533 | − | 8.17599i | 0.701961 | − | 0.510004i | −0.178609 | − | 0.983920i | \(-0.557160\pi\) |
0.880570 | + | 0.473916i | \(0.157160\pi\) | |||||||
\(258\) | 3.09017 | − | 9.51057i | 0.192386 | − | 0.592102i | ||||
\(259\) | 1.19098 | − | 3.66547i | 0.0740041 | − | 0.227761i | ||||
\(260\) | 1.00000 | − | 0.726543i | 0.0620174 | − | 0.0450583i | ||||
\(261\) | 2.00000 | + | 1.45309i | 0.123797 | + | 0.0899437i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.0344 | 1.05039 | 0.525194 | − | 0.850982i | \(-0.323993\pi\) | ||||
0.525194 | + | 0.850982i | \(0.323993\pi\) | |||||||
\(264\) | −3.04508 | + | 1.31433i | −0.187412 | + | 0.0808913i | ||||
\(265\) | −0.291796 | −0.0179249 | ||||||||
\(266\) | 1.50000 | + | 4.61653i | 0.0919709 | + | 0.283057i | ||||
\(267\) | −12.7812 | − | 9.28605i | −0.782194 | − | 0.568297i | ||||
\(268\) | 9.85410 | − | 7.15942i | 0.601935 | − | 0.437331i | ||||
\(269\) | 2.43769 | − | 7.50245i | 0.148629 | − | 0.457433i | −0.848831 | − | 0.528664i | \(-0.822693\pi\) |
0.997460 | + | 0.0712319i | \(0.0226930\pi\) | |||||||
\(270\) | −0.190983 | + | 0.587785i | −0.0116229 | + | 0.0357715i | ||||
\(271\) | 7.50000 | − | 5.44907i | 0.455593 | − | 0.331007i | −0.336207 | − | 0.941788i | \(-0.609144\pi\) |
0.791800 | + | 0.610781i | \(0.209144\pi\) | |||||||
\(272\) | −0.309017 | − | 0.224514i | −0.0187369 | − | 0.0136132i | ||||
\(273\) | −0.618034 | − | 1.90211i | −0.0374051 | − | 0.115121i | ||||
\(274\) | −5.23607 | −0.316322 | ||||||||
\(275\) | −7.80902 | + | 13.1760i | −0.470901 | + | 0.794545i | ||||
\(276\) | 4.85410 | 0.292183 | ||||||||
\(277\) | −5.11803 | − | 15.7517i | −0.307513 | − | 0.946427i | −0.978728 | − | 0.205164i | \(-0.934227\pi\) |
0.671215 | − | 0.741263i | \(-0.265773\pi\) | |||||||
\(278\) | −1.30902 | − | 0.951057i | −0.0785096 | − | 0.0570406i | ||||
\(279\) | −3.73607 | + | 2.71441i | −0.223673 | + | 0.162508i | ||||
\(280\) | 0.190983 | − | 0.587785i | 0.0114134 | − | 0.0351269i | ||||
\(281\) | −7.14590 | + | 21.9928i | −0.426289 | + | 1.31198i | 0.475467 | + | 0.879734i | \(0.342279\pi\) |
−0.901755 | + | 0.432247i | \(0.857721\pi\) | |||||||
\(282\) | −5.23607 | + | 3.80423i | −0.311803 | + | 0.226538i | ||||
\(283\) | −10.1180 | − | 7.35118i | −0.601455 | − | 0.436982i | 0.244940 | − | 0.969538i | \(-0.421232\pi\) |
−0.846395 | + | 0.532556i | \(0.821232\pi\) | |||||||
\(284\) | 2.00000 | + | 6.15537i | 0.118678 | + | 0.365254i | ||||
\(285\) | −3.00000 | −0.177705 | ||||||||
\(286\) | 4.38197 | + | 4.97980i | 0.259111 | + | 0.294462i | ||||
\(287\) | 2.61803 | 0.154538 | ||||||||
\(288\) | −0.309017 | − | 0.951057i | −0.0182090 | − | 0.0560415i | ||||
\(289\) | 13.6353 | + | 9.90659i | 0.802074 | + | 0.582741i | ||||
\(290\) | 1.23607 | − | 0.898056i | 0.0725844 | − | 0.0527357i | ||||
\(291\) | 3.14590 | − | 9.68208i | 0.184416 | − | 0.567573i | ||||
\(292\) | −3.14590 | + | 9.68208i | −0.184100 | + | 0.566601i | ||||
\(293\) | −15.4443 | + | 11.2209i | −0.902264 | + | 0.655533i | −0.939047 | − | 0.343790i | \(-0.888289\pi\) |
0.0367825 | + | 0.999323i | \(0.488289\pi\) | |||||||
\(294\) | −0.809017 | − | 0.587785i | −0.0471828 | − | 0.0342803i | ||||
\(295\) | 1.00000 | + | 3.07768i | 0.0582223 | + | 0.179190i | ||||
\(296\) | −3.85410 | −0.224015 | ||||||||
\(297\) | −3.23607 | − | 0.726543i | −0.187776 | − | 0.0421583i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | − | 9.23305i | −0.173494 | − | 0.533961i | ||||
\(300\) | −3.73607 | − | 2.71441i | −0.215702 | − | 0.156717i | ||||
\(301\) | −8.09017 | + | 5.87785i | −0.466310 | + | 0.338794i | ||||
\(302\) | −2.23607 | + | 6.88191i | −0.128671 | + | 0.396009i | ||||
\(303\) | 3.51722 | − | 10.8249i | 0.202059 | − | 0.621874i | ||||
\(304\) | 3.92705 | − | 2.85317i | 0.225232 | − | 0.163640i | ||||
\(305\) | 6.09017 | + | 4.42477i | 0.348722 | + | 0.253361i | ||||
\(306\) | −0.118034 | − | 0.363271i | −0.00674755 | − | 0.0207668i | ||||
\(307\) | 0.437694 | 0.0249805 | 0.0124903 | − | 0.999922i | \(-0.496024\pi\) | ||||
0.0124903 | + | 0.999922i | \(0.496024\pi\) | |||||||
\(308\) | 3.23607 | + | 0.726543i | 0.184392 | + | 0.0413986i | ||||
\(309\) | −8.56231 | −0.487093 | ||||||||
\(310\) | 0.881966 | + | 2.71441i | 0.0500923 | + | 0.154168i | ||||
\(311\) | −26.2705 | − | 19.0866i | −1.48966 | − | 1.08230i | −0.974279 | − | 0.225345i | \(-0.927649\pi\) |
−0.515385 | − | 0.856959i | \(-0.672351\pi\) | |||||||
\(312\) | −1.61803 | + | 1.17557i | −0.0916031 | + | 0.0665536i | ||||
\(313\) | 5.47214 | − | 16.8415i | 0.309303 | − | 0.951938i | −0.668733 | − | 0.743503i | \(-0.733163\pi\) |
0.978036 | − | 0.208435i | \(-0.0668370\pi\) | |||||||
\(314\) | −1.14590 | + | 3.52671i | −0.0646668 | + | 0.199024i | ||||
\(315\) | 0.500000 | − | 0.363271i | 0.0281718 | − | 0.0204680i | ||||
\(316\) | −11.7082 | − | 8.50651i | −0.658638 | − | 0.478528i | ||||
\(317\) | −4.14590 | − | 12.7598i | −0.232857 | − | 0.716660i | −0.997398 | − | 0.0720853i | \(-0.977035\pi\) |
0.764542 | − | 0.644574i | \(-0.222965\pi\) | |||||||
\(318\) | 0.472136 | 0.0264761 | ||||||||
\(319\) | 5.41641 | + | 6.15537i | 0.303261 | + | 0.344634i | ||||
\(320\) | −0.618034 | −0.0345492 | ||||||||
\(321\) | −0.354102 | − | 1.08981i | −0.0197640 | − | 0.0608275i | ||||
\(322\) | −3.92705 | − | 2.85317i | −0.218846 | − | 0.159001i | ||||
\(323\) | 1.50000 | − | 1.08981i | 0.0834622 | − | 0.0606389i | ||||
\(324\) | 0.309017 | − | 0.951057i | 0.0171676 | − | 0.0528365i | ||||
\(325\) | −2.85410 | + | 8.78402i | −0.158317 | + | 0.487250i | ||||
\(326\) | 8.09017 | − | 5.87785i | 0.448073 | − | 0.325544i | ||||
\(327\) | 3.35410 | + | 2.43690i | 0.185482 | + | 0.134761i | ||||
\(328\) | −0.809017 | − | 2.48990i | −0.0446705 | − | 0.137482i | ||||
\(329\) | 6.47214 | 0.356820 | ||||||||
\(330\) | −1.04508 | + | 1.76336i | −0.0575300 | + | 0.0970695i | ||||
\(331\) | 2.76393 | 0.151919 | 0.0759597 | − | 0.997111i | \(-0.475798\pi\) | ||||
0.0759597 | + | 0.997111i | \(0.475798\pi\) | |||||||
\(332\) | 0.854102 | + | 2.62866i | 0.0468749 | + | 0.144266i | ||||
\(333\) | −3.11803 | − | 2.26538i | −0.170867 | − | 0.124142i | ||||
\(334\) | 10.3262 | − | 7.50245i | 0.565027 | − | 0.410516i | ||||
\(335\) | 2.32624 | − | 7.15942i | 0.127096 | − | 0.391161i | ||||
\(336\) | −0.309017 | + | 0.951057i | −0.0168583 | + | 0.0518844i | ||||
\(337\) | −12.6803 | + | 9.21281i | −0.690742 | + | 0.501854i | −0.876904 | − | 0.480666i | \(-0.840395\pi\) |
0.186162 | + | 0.982519i | \(0.440395\pi\) | |||||||
\(338\) | −7.28115 | − | 5.29007i | −0.396043 | − | 0.287742i | ||||
\(339\) | 3.56231 | + | 10.9637i | 0.193478 | + | 0.595464i | ||||
\(340\) | −0.236068 | −0.0128026 | ||||||||
\(341\) | −14.0623 | + | 6.06961i | −0.761517 | + | 0.328688i | ||||
\(342\) | 4.85410 | 0.262480 | ||||||||
\(343\) | 0.309017 | + | 0.951057i | 0.0166853 | + | 0.0513522i | ||||
\(344\) | 8.09017 | + | 5.87785i | 0.436193 | + | 0.316913i | ||||
\(345\) | 2.42705 | − | 1.76336i | 0.130668 | − | 0.0949359i | ||||
\(346\) | −5.79180 | + | 17.8253i | −0.311369 | + | 0.958295i | ||||
\(347\) | 0.843459 | − | 2.59590i | 0.0452792 | − | 0.139355i | −0.925861 | − | 0.377864i | \(-0.876659\pi\) |
0.971140 | + | 0.238509i | \(0.0766586\pi\) | |||||||
\(348\) | −2.00000 | + | 1.45309i | −0.107211 | + | 0.0778935i | ||||
\(349\) | −17.1803 | − | 12.4822i | −0.919643 | − | 0.668159i | 0.0237925 | − | 0.999717i | \(-0.492426\pi\) |
−0.943435 | + | 0.331558i | \(0.892426\pi\) | |||||||
\(350\) | 1.42705 | + | 4.39201i | 0.0762791 | + | 0.234763i | ||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | −0.309017 | − | 3.30220i | −0.0164707 | − | 0.176008i | ||||
\(353\) | −11.8885 | −0.632763 | −0.316382 | − | 0.948632i | \(-0.602468\pi\) | ||||
−0.316382 | + | 0.948632i | \(0.602468\pi\) | |||||||
\(354\) | −1.61803 | − | 4.97980i | −0.0859975 | − | 0.264673i | ||||
\(355\) | 3.23607 | + | 2.35114i | 0.171753 | + | 0.124786i | ||||
\(356\) | 12.7812 | − | 9.28605i | 0.677400 | − | 0.492160i | ||||
\(357\) | −0.118034 | + | 0.363271i | −0.00624702 | + | 0.0192264i | ||||
\(358\) | 4.95492 | − | 15.2497i | 0.261875 | − | 0.805970i | ||||
\(359\) | −28.0623 | + | 20.3885i | −1.48107 | + | 1.07606i | −0.503863 | + | 0.863784i | \(0.668088\pi\) |
−0.977209 | + | 0.212278i | \(0.931912\pi\) | |||||||
\(360\) | −0.500000 | − | 0.363271i | −0.0263523 | − | 0.0191461i | ||||
\(361\) | 1.40983 | + | 4.33901i | 0.0742016 | + | 0.228369i | ||||
\(362\) | −17.7082 | −0.930723 | ||||||||
\(363\) | −9.94427 | − | 4.70228i | −0.521939 | − | 0.246806i | ||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 1.94427 | + | 5.98385i | 0.101768 | + | 0.313209i | ||||
\(366\) | −9.85410 | − | 7.15942i | −0.515082 | − | 0.374229i | ||||
\(367\) | −14.4443 | + | 10.4944i | −0.753985 | + | 0.547802i | −0.897059 | − | 0.441910i | \(-0.854301\pi\) |
0.143075 | + | 0.989712i | \(0.454301\pi\) | |||||||
\(368\) | −1.50000 | + | 4.61653i | −0.0781929 | + | 0.240653i | ||||
\(369\) | 0.809017 | − | 2.48990i | 0.0421157 | − | 0.129619i | ||||
\(370\) | −1.92705 | + | 1.40008i | −0.100183 | + | 0.0727869i | ||||
\(371\) | −0.381966 | − | 0.277515i | −0.0198307 | − | 0.0144078i | ||||
\(372\) | −1.42705 | − | 4.39201i | −0.0739891 | − | 0.227715i | ||||
\(373\) | −3.27051 | −0.169341 | −0.0846703 | − | 0.996409i | \(-0.526984\pi\) | ||||
−0.0846703 | + | 0.996409i | \(0.526984\pi\) | |||||||
\(374\) | −0.118034 | − | 1.26133i | −0.00610339 | − | 0.0652217i | ||||
\(375\) | −5.94427 | −0.306961 | ||||||||
\(376\) | −2.00000 | − | 6.15537i | −0.103142 | − | 0.317439i | ||||
\(377\) | 4.00000 | + | 2.90617i | 0.206010 | + | 0.149675i | ||||
\(378\) | −0.809017 | + | 0.587785i | −0.0416113 | + | 0.0302324i | ||||
\(379\) | 2.90983 | − | 8.95554i | 0.149468 | − | 0.460015i | −0.848091 | − | 0.529851i | \(-0.822248\pi\) |
0.997558 | + | 0.0698364i | \(0.0222477\pi\) | |||||||
\(380\) | 0.927051 | − | 2.85317i | 0.0475567 | − | 0.146365i | ||||
\(381\) | 4.00000 | − | 2.90617i | 0.204926 | − | 0.148888i | ||||
\(382\) | −11.8262 | − | 8.59226i | −0.605083 | − | 0.439619i | ||||
\(383\) | 7.38197 | + | 22.7194i | 0.377201 | + | 1.16090i | 0.941982 | + | 0.335664i | \(0.108961\pi\) |
−0.564781 | + | 0.825241i | \(0.691039\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.88197 | − | 0.812299i | 0.0959139 | − | 0.0413986i | ||||
\(386\) | −18.1459 | −0.923602 | ||||||||
\(387\) | 3.09017 | + | 9.51057i | 0.157082 | + | 0.483449i | ||||
\(388\) | 8.23607 | + | 5.98385i | 0.418123 | + | 0.303784i | ||||
\(389\) | −1.14590 | + | 0.832544i | −0.0580993 | + | 0.0422116i | −0.616456 | − | 0.787389i | \(-0.711432\pi\) |
0.558357 | + | 0.829601i | \(0.311432\pi\) | |||||||
\(390\) | −0.381966 | + | 1.17557i | −0.0193416 | + | 0.0595273i | ||||
\(391\) | −0.572949 | + | 1.76336i | −0.0289753 | + | 0.0891767i | ||||
\(392\) | 0.809017 | − | 0.587785i | 0.0408615 | − | 0.0296876i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.23607 | − | 19.1926i | −0.314169 | − | 0.966911i | ||||
\(395\) | −8.94427 | −0.450035 | ||||||||
\(396\) | 1.69098 | − | 2.85317i | 0.0849751 | − | 0.143377i | ||||
\(397\) | −25.4164 | −1.27561 | −0.637806 | − | 0.770197i | \(-0.720158\pi\) | ||||
−0.637806 | + | 0.770197i | \(0.720158\pi\) | |||||||
\(398\) | −1.35410 | − | 4.16750i | −0.0678750 | − | 0.208898i | ||||
\(399\) | −3.92705 | − | 2.85317i | −0.196598 | − | 0.142837i | ||||
\(400\) | 3.73607 | − | 2.71441i | 0.186803 | − | 0.135721i | ||||
\(401\) | 4.81966 | − | 14.8334i | 0.240682 | − | 0.740744i | −0.755634 | − | 0.654994i | \(-0.772671\pi\) |
0.996317 | − | 0.0857504i | \(-0.0273287\pi\) | |||||||
\(402\) | −3.76393 | + | 11.5842i | −0.187728 | + | 0.577767i | ||||
\(403\) | −7.47214 | + | 5.42882i | −0.372214 | + | 0.270429i | ||||
\(404\) | 9.20820 | + | 6.69015i | 0.458125 | + | 0.332847i | ||||
\(405\) | −0.190983 | − | 0.587785i | −0.00949002 | − | 0.0292073i | ||||
\(406\) | 2.47214 | 0.122690 | ||||||||
\(407\) | −8.44427 | − | 9.59632i | −0.418567 | − | 0.475672i | ||||
\(408\) | 0.381966 | 0.0189101 | ||||||||
\(409\) | 3.32624 | + | 10.2371i | 0.164472 | + | 0.506192i | 0.998997 | − | 0.0447775i | \(-0.0142579\pi\) |
−0.834525 | + | 0.550970i | \(0.814258\pi\) | |||||||
\(410\) | −1.30902 | − | 0.951057i | −0.0646477 | − | 0.0469693i | ||||
\(411\) | 4.23607 | − | 3.07768i | 0.208950 | − | 0.151811i | ||||
\(412\) | 2.64590 | − | 8.14324i | 0.130354 | − | 0.401188i | ||||
\(413\) | −1.61803 | + | 4.97980i | −0.0796182 | + | 0.245040i | ||||
\(414\) | −3.92705 | + | 2.85317i | −0.193004 | + | 0.140226i | ||||
\(415\) | 1.38197 | + | 1.00406i | 0.0678380 | + | 0.0492872i | ||||
\(416\) | −0.618034 | − | 1.90211i | −0.0303016 | − | 0.0932588i | ||||
\(417\) | 1.61803 | 0.0792355 | ||||||||
\(418\) | 15.7082 | + | 3.52671i | 0.768313 | + | 0.172497i | ||||
\(419\) | 36.9443 | 1.80485 | 0.902423 | − | 0.430851i | \(-0.141787\pi\) | ||||
0.902423 | + | 0.430851i | \(0.141787\pi\) | |||||||
\(420\) | 0.190983 | + | 0.587785i | 0.00931902 | + | 0.0286810i | ||||
\(421\) | 6.92705 | + | 5.03280i | 0.337604 | + | 0.245284i | 0.743650 | − | 0.668569i | \(-0.233093\pi\) |
−0.406046 | + | 0.913852i | \(0.633093\pi\) | |||||||
\(422\) | 16.7082 | − | 12.1392i | 0.813343 | − | 0.590928i | ||||
\(423\) | 2.00000 | − | 6.15537i | 0.0972433 | − | 0.299284i | ||||
\(424\) | −0.145898 | + | 0.449028i | −0.00708543 | + | 0.0218067i | ||||
\(425\) | 1.42705 | − | 1.03681i | 0.0692221 | − | 0.0502928i | ||||
\(426\) | −5.23607 | − | 3.80423i | −0.253688 | − | 0.184315i | ||||
\(427\) | 3.76393 | + | 11.5842i | 0.182149 | + | 0.560598i | ||||
\(428\) | 1.14590 | 0.0553891 | ||||||||
\(429\) | −6.47214 | − | 1.45309i | −0.312478 | − | 0.0701556i | ||||
\(430\) | 6.18034 | 0.298042 | ||||||||
\(431\) | −11.8435 | − | 36.4504i | −0.570479 | − | 1.75575i | −0.651081 | − | 0.759008i | \(-0.725684\pi\) |
0.0806014 | − | 0.996746i | \(-0.474316\pi\) | |||||||
\(432\) | 0.809017 | + | 0.587785i | 0.0389238 | + | 0.0282798i | ||||
\(433\) | −18.5623 | + | 13.4863i | −0.892047 | + | 0.648110i | −0.936411 | − | 0.350905i | \(-0.885874\pi\) |
0.0443636 | + | 0.999015i | \(0.485874\pi\) | |||||||
\(434\) | −1.42705 | + | 4.39201i | −0.0685006 | + | 0.210823i | ||||
\(435\) | −0.472136 | + | 1.45309i | −0.0226372 | + | 0.0696701i | ||||
\(436\) | −3.35410 | + | 2.43690i | −0.160632 | + | 0.116706i | ||||
\(437\) | −19.0623 | − | 13.8496i | −0.911874 | − | 0.662515i | ||||
\(438\) | −3.14590 | − | 9.68208i | −0.150317 | − | 0.462628i | ||||
\(439\) | 24.6180 | 1.17495 | 0.587477 | − | 0.809241i | \(-0.300121\pi\) | ||||
0.587477 | + | 0.809241i | \(0.300121\pi\) | |||||||
\(440\) | −1.35410 | − | 1.53884i | −0.0645543 | − | 0.0733614i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.236068 | − | 0.726543i | −0.0112286 | − | 0.0345581i | ||||
\(443\) | −0.927051 | − | 0.673542i | −0.0440455 | − | 0.0320009i | 0.565545 | − | 0.824718i | \(-0.308666\pi\) |
−0.609590 | + | 0.792717i | \(0.708666\pi\) | |||||||
\(444\) | 3.11803 | − | 2.26538i | 0.147975 | − | 0.107510i | ||||
\(445\) | 3.01722 | − | 9.28605i | 0.143030 | − | 0.440201i | ||||
\(446\) | 1.40983 | − | 4.33901i | 0.0667574 | − | 0.205458i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.809017 | − | 0.587785i | −0.0382225 | − | 0.0277702i | ||||
\(449\) | 7.27051 | + | 22.3763i | 0.343117 | + | 1.05600i | 0.962584 | + | 0.270982i | \(0.0873484\pi\) |
−0.619468 | + | 0.785022i | \(0.712652\pi\) | |||||||
\(450\) | 4.61803 | 0.217696 | ||||||||
\(451\) | 4.42705 | − | 7.46969i | 0.208462 | − | 0.351734i | ||||
\(452\) | −11.5279 | −0.542225 | ||||||||
\(453\) | −2.23607 | − | 6.88191i | −0.105060 | − | 0.323340i | ||||
\(454\) | −5.85410 | − | 4.25325i | −0.274747 | − | 0.199615i | ||||
\(455\) | 1.00000 | − | 0.726543i | 0.0468807 | − | 0.0340608i | ||||
\(456\) | −1.50000 | + | 4.61653i | −0.0702439 | + | 0.216189i | ||||
\(457\) | 5.67376 | − | 17.4620i | 0.265407 | − | 0.816840i | −0.726192 | − | 0.687492i | \(-0.758712\pi\) |
0.991599 | − | 0.129348i | \(-0.0412884\pi\) | |||||||
\(458\) | −3.23607 | + | 2.35114i | −0.151212 | + | 0.109862i | ||||
\(459\) | 0.309017 | + | 0.224514i | 0.0144237 | + | 0.0104794i | ||||
\(460\) | 0.927051 | + | 2.85317i | 0.0432240 | + | 0.133030i | ||||
\(461\) | 21.0557 | 0.980663 | 0.490332 | − | 0.871536i | \(-0.336876\pi\) | ||||
0.490332 | + | 0.871536i | \(0.336876\pi\) | |||||||
\(462\) | −3.04508 | + | 1.31433i | −0.141670 | + | 0.0611481i | ||||
\(463\) | −38.5410 | −1.79115 | −0.895577 | − | 0.444907i | \(-0.853237\pi\) | ||||
−0.895577 | + | 0.444907i | \(0.853237\pi\) | |||||||
\(464\) | −0.763932 | − | 2.35114i | −0.0354647 | − | 0.109149i | ||||
\(465\) | −2.30902 | − | 1.67760i | −0.107078 | − | 0.0777968i | ||||
\(466\) | 0.618034 | − | 0.449028i | 0.0286299 | − | 0.0208008i | ||||
\(467\) | 8.61803 | − | 26.5236i | 0.398795 | − | 1.22736i | −0.527171 | − | 0.849759i | \(-0.676747\pi\) |
0.925966 | − | 0.377606i | \(-0.123253\pi\) | |||||||
\(468\) | 0.618034 | − | 1.90211i | 0.0285686 | − | 0.0879252i | ||||
\(469\) | 9.85410 | − | 7.15942i | 0.455020 | − | 0.330591i | ||||
\(470\) | −3.23607 | − | 2.35114i | −0.149269 | − | 0.108450i | ||||
\(471\) | −1.14590 | − | 3.52671i | −0.0528002 | − | 0.162502i | ||||
\(472\) | 5.23607 | 0.241010 | ||||||||
\(473\) | 3.09017 | + | 33.0220i | 0.142086 | + | 1.51835i | ||||
\(474\) | 14.4721 | 0.664727 | ||||||||
\(475\) | 6.92705 | + | 21.3193i | 0.317835 | + | 0.978195i | ||||
\(476\) | −0.309017 | − | 0.224514i | −0.0141638 | − | 0.0102906i | ||||
\(477\) | −0.381966 | + | 0.277515i | −0.0174890 | + | 0.0127065i | ||||
\(478\) | 7.97214 | − | 24.5357i | 0.364637 | − | 1.12224i | ||||
\(479\) | −5.70820 | + | 17.5680i | −0.260814 | + | 0.802704i | 0.731814 | + | 0.681505i | \(0.238674\pi\) |
−0.992628 | + | 0.121200i | \(0.961326\pi\) | |||||||
\(480\) | 0.500000 | − | 0.363271i | 0.0228218 | − | 0.0165810i | ||||
\(481\) | −6.23607 | − | 4.53077i | −0.284340 | − | 0.206585i | ||||
\(482\) | −9.00000 | − | 27.6992i | −0.409939 | − | 1.26166i | ||||
\(483\) | 4.85410 | 0.220869 | ||||||||
\(484\) | 7.54508 | − | 8.00448i | 0.342958 | − | 0.363840i | ||||
\(485\) | 6.29180 | 0.285696 | ||||||||
\(486\) | 0.309017 | + | 0.951057i | 0.0140173 | + | 0.0431408i | ||||
\(487\) | 1.90983 | + | 1.38757i | 0.0865427 | + | 0.0628769i | 0.630215 | − | 0.776420i | \(-0.282967\pi\) |
−0.543673 | + | 0.839297i | \(0.682967\pi\) | |||||||
\(488\) | 9.85410 | − | 7.15942i | 0.446074 | − | 0.324092i | ||||
\(489\) | −3.09017 | + | 9.51057i | −0.139742 | + | 0.430083i | ||||
\(490\) | 0.190983 | − | 0.587785i | 0.00862773 | − | 0.0265534i | ||||
\(491\) | −5.07295 | + | 3.68571i | −0.228939 | + | 0.166334i | −0.696341 | − | 0.717711i | \(-0.745190\pi\) |
0.467402 | + | 0.884045i | \(0.345190\pi\) | |||||||
\(492\) | 2.11803 | + | 1.53884i | 0.0954883 | + | 0.0693763i | ||||
\(493\) | −0.291796 | − | 0.898056i | −0.0131418 | − | 0.0404464i | ||||
\(494\) | 9.70820 | 0.436793 | ||||||||
\(495\) | −0.190983 | − | 2.04087i | −0.00858405 | − | 0.0917303i | ||||
\(496\) | 4.61803 | 0.207356 | ||||||||
\(497\) | 2.00000 | + | 6.15537i | 0.0897123 | + | 0.276106i | ||||
\(498\) | −2.23607 | − | 1.62460i | −0.100201 | − | 0.0728000i | ||||
\(499\) | −22.2705 | + | 16.1805i | −0.996965 | + | 0.724337i | −0.961435 | − | 0.275031i | \(-0.911312\pi\) |
−0.0355296 | + | 0.999369i | \(0.511312\pi\) | |||||||
\(500\) | 1.83688 | − | 5.65334i | 0.0821478 | − | 0.252825i | ||||
\(501\) | −3.94427 | + | 12.1392i | −0.176217 | + | 0.542340i | ||||
\(502\) | 19.7984 | − | 14.3844i | 0.883645 | − | 0.642005i | ||||
\(503\) | −16.3262 | − | 11.8617i | −0.727951 | − | 0.528887i | 0.160964 | − | 0.986960i | \(-0.448540\pi\) |
−0.888915 | + | 0.458073i | \(0.848540\pi\) | |||||||
\(504\) | −0.309017 | − | 0.951057i | −0.0137647 | − | 0.0423634i | ||||
\(505\) | 7.03444 | 0.313029 | ||||||||
\(506\) | −14.7812 | + | 6.37988i | −0.657102 | + | 0.283620i | ||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 1.52786 | + | 4.70228i | 0.0677880 | + | 0.208630i | ||||
\(509\) | 11.7361 | + | 8.52675i | 0.520192 | + | 0.377942i | 0.816676 | − | 0.577096i | \(-0.195814\pi\) |
−0.296484 | + | 0.955038i | \(0.595814\pi\) | |||||||
\(510\) | 0.190983 | − | 0.138757i | 0.00845687 | − | 0.00614428i | ||||
\(511\) | −3.14590 | + | 9.68208i | −0.139166 | + | 0.428310i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | −3.92705 | + | 2.85317i | −0.173384 | + | 0.125971i | ||||
\(514\) | −11.2533 | − | 8.17599i | −0.496361 | − | 0.360628i | ||||
\(515\) | −1.63525 | − | 5.03280i | −0.0720579 | − | 0.221772i | ||||
\(516\) | −10.0000 | −0.440225 | ||||||||
\(517\) | 10.9443 | − | 18.4661i | 0.481329 | − | 0.812138i | ||||
\(518\) | −3.85410 | −0.169340 | ||||||||
\(519\) | −5.79180 | − | 17.8253i | −0.254232 | − | 0.782445i | ||||
\(520\) | −1.00000 | − | 0.726543i | −0.0438529 | − | 0.0318610i | ||||
\(521\) | −16.0623 | + | 11.6699i | −0.703702 | + | 0.511270i | −0.881136 | − | 0.472863i | \(-0.843221\pi\) |
0.177434 | + | 0.984133i | \(0.443221\pi\) | |||||||
\(522\) | 0.763932 | − | 2.35114i | 0.0334364 | − | 0.102907i | ||||
\(523\) | 4.91641 | − | 15.1311i | 0.214980 | − | 0.661639i | −0.784176 | − | 0.620539i | \(-0.786914\pi\) |
0.999155 | − | 0.0410998i | \(-0.0130862\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.73607 | − | 2.71441i | −0.163055 | − | 0.118467i | ||||
\(526\) | −5.26393 | − | 16.2007i | −0.229518 | − | 0.706385i | ||||
\(527\) | 1.76393 | 0.0768381 | ||||||||
\(528\) | 2.19098 | + | 2.48990i | 0.0953503 | + | 0.108359i | ||||
\(529\) | 0.562306 | 0.0244481 | ||||||||
\(530\) | 0.0901699 | + | 0.277515i | 0.00391673 | + | 0.0120545i | ||||
\(531\) | 4.23607 | + | 3.07768i | 0.183830 | + | 0.133560i | ||||
\(532\) | 3.92705 | − | 2.85317i | 0.170259 | − | 0.123701i | ||||
\(533\) | 1.61803 | − | 4.97980i | 0.0700848 | − | 0.215699i | ||||
\(534\) | −4.88197 | + | 15.0251i | −0.211263 | + | 0.650202i | ||||
\(535\) | 0.572949 | − | 0.416272i | 0.0247707 | − | 0.0179970i | ||||
\(536\) | −9.85410 | − | 7.15942i | −0.425632 | − | 0.309240i | ||||
\(537\) | 4.95492 | + | 15.2497i | 0.213820 | + | 0.658071i | ||||
\(538\) | −7.88854 | −0.340099 | ||||||||
\(539\) | 3.23607 | + | 0.726543i | 0.139387 | + | 0.0312944i | ||||
\(540\) | 0.618034 | 0.0265959 | ||||||||
\(541\) | 2.13525 | + | 6.57164i | 0.0918018 | + | 0.282537i | 0.986407 | − | 0.164321i | \(-0.0525431\pi\) |
−0.894605 | + | 0.446857i | \(0.852543\pi\) | |||||||
\(542\) | −7.50000 | − | 5.44907i | −0.322153 | − | 0.234058i | ||||
\(543\) | 14.3262 | − | 10.4086i | 0.614798 | − | 0.446677i | ||||
\(544\) | −0.118034 | + | 0.363271i | −0.00506067 | + | 0.0155751i | ||||
\(545\) | −0.791796 | + | 2.43690i | −0.0339168 | + | 0.104385i | ||||
\(546\) | −1.61803 | + | 1.17557i | −0.0692455 | + | 0.0503098i | ||||
\(547\) | −11.5623 | − | 8.40051i | −0.494369 | − | 0.359180i | 0.312493 | − | 0.949920i | \(-0.398836\pi\) |
−0.806862 | + | 0.590740i | \(0.798836\pi\) | |||||||
\(548\) | 1.61803 | + | 4.97980i | 0.0691190 | + | 0.212726i | ||||
\(549\) | 12.1803 | 0.519844 | ||||||||
\(550\) | 14.9443 | + | 3.35520i | 0.637226 | + | 0.143066i | ||||
\(551\) | 12.0000 | 0.511217 | ||||||||
\(552\) | −1.50000 | − | 4.61653i | −0.0638442 | − | 0.196492i | ||||
\(553\) | −11.7082 | − | 8.50651i | −0.497883 | − | 0.361734i | ||||
\(554\) | −13.3992 | + | 9.73508i | −0.569277 | + | 0.413604i | ||||
\(555\) | 0.736068 | − | 2.26538i | 0.0312443 | − | 0.0961602i | ||||
\(556\) | −0.500000 | + | 1.53884i | −0.0212047 | + | 0.0652614i | ||||
\(557\) | −9.61803 | + | 6.98791i | −0.407529 | + | 0.296087i | −0.772601 | − | 0.634892i | \(-0.781045\pi\) |
0.365072 | + | 0.930979i | \(0.381045\pi\) | |||||||
\(558\) | 3.73607 | + | 2.71441i | 0.158160 | + | 0.114910i | ||||
\(559\) | 6.18034 | + | 19.0211i | 0.261401 | + | 0.804508i | ||||
\(560\) | −0.618034 | −0.0261167 | ||||||||
\(561\) | 0.836881 | + | 0.951057i | 0.0353331 | + | 0.0401536i | ||||
\(562\) | 23.1246 | 0.975453 | ||||||||
\(563\) | −11.9787 | − | 36.8667i | −0.504843 | − | 1.55375i | −0.801035 | − | 0.598617i | \(-0.795717\pi\) |
0.296192 | − | 0.955128i | \(-0.404283\pi\) | |||||||
\(564\) | 5.23607 | + | 3.80423i | 0.220478 | + | 0.160187i | ||||
\(565\) | −5.76393 | + | 4.18774i | −0.242490 | + | 0.176180i | ||||
\(566\) | −3.86475 | + | 11.8945i | −0.162447 | + | 0.499962i | ||||
\(567\) | 0.309017 | − | 0.951057i | 0.0129775 | − | 0.0399406i | ||||
\(568\) | 5.23607 | − | 3.80423i | 0.219701 | − | 0.159622i | ||||
\(569\) | 26.2705 | + | 19.0866i | 1.10132 | + | 0.800154i | 0.981274 | − | 0.192615i | \(-0.0616969\pi\) |
0.120043 | + | 0.992769i | \(0.461697\pi\) | |||||||
\(570\) | 0.927051 | + | 2.85317i | 0.0388299 | + | 0.119506i | ||||
\(571\) | −43.1246 | −1.80471 | −0.902354 | − | 0.430995i | \(-0.858163\pi\) | ||||
−0.902354 | + | 0.430995i | \(0.858163\pi\) | |||||||
\(572\) | 3.38197 | − | 5.70634i | 0.141407 | − | 0.238594i | ||||
\(573\) | 14.6180 | 0.610677 | ||||||||
\(574\) | −0.809017 | − | 2.48990i | −0.0337677 | − | 0.103926i | ||||
\(575\) | −18.1353 | − | 13.1760i | −0.756292 | − | 0.549479i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | −8.43769 | + | 25.9686i | −0.351266 | + | 1.08108i | 0.606877 | + | 0.794795i | \(0.292422\pi\) |
−0.958143 | + | 0.286289i | \(0.907578\pi\) | |||||||
\(578\) | 5.20820 | − | 16.0292i | 0.216633 | − | 0.666727i | ||||
\(579\) | 14.6803 | − | 10.6659i | 0.610094 | − | 0.443259i | ||||
\(580\) | −1.23607 | − | 0.898056i | −0.0513249 | − | 0.0372897i | ||||
\(581\) | 0.854102 | + | 2.62866i | 0.0354341 | + | 0.109055i | ||||
\(582\) | −10.1803 | −0.421989 | ||||||||
\(583\) | −1.43769 | + | 0.620541i | −0.0595432 | + | 0.0257002i | ||||
\(584\) | 10.1803 | 0.421265 | ||||||||
\(585\) | −0.381966 | − | 1.17557i | −0.0157924 | − | 0.0486039i | ||||
\(586\) | 15.4443 | + | 11.2209i | 0.637997 | + | 0.463532i | ||||
\(587\) | −15.7984 | + | 11.4782i | −0.652069 | + | 0.473756i | −0.863975 | − | 0.503534i | \(-0.832033\pi\) |
0.211907 | + | 0.977290i | \(0.432033\pi\) | |||||||
\(588\) | −0.309017 | + | 0.951057i | −0.0127436 | + | 0.0392209i | ||||
\(589\) | −6.92705 | + | 21.3193i | −0.285424 | + | 0.878445i | ||||
\(590\) | 2.61803 | − | 1.90211i | 0.107783 | − | 0.0783088i | ||||
\(591\) | 16.3262 | + | 11.8617i | 0.671572 | + | 0.487925i | ||||
\(592\) | 1.19098 | + | 3.66547i | 0.0489491 | + | 0.150650i | ||||
\(593\) | −8.50658 | −0.349323 | −0.174662 | − | 0.984629i | \(-0.555883\pi\) | ||||
−0.174662 | + | 0.984629i | \(0.555883\pi\) | |||||||
\(594\) | 0.309017 | + | 3.30220i | 0.0126791 | + | 0.135491i | ||||
\(595\) | −0.236068 | −0.00967784 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.54508 | + | 2.57565i | 0.145091 | + | 0.105415i | ||||
\(598\) | −7.85410 | + | 5.70634i | −0.321178 | + | 0.233350i | ||||
\(599\) | 1.26393 | − | 3.88998i | 0.0516429 | − | 0.158940i | −0.921909 | − | 0.387406i | \(-0.873371\pi\) |
0.973552 | + | 0.228466i | \(0.0733710\pi\) | |||||||
\(600\) | −1.42705 | + | 4.39201i | −0.0582591 | + | 0.179303i | ||||
\(601\) | 26.5623 | − | 19.2986i | 1.08350 | − | 0.787208i | 0.105209 | − | 0.994450i | \(-0.466449\pi\) |
0.978290 | + | 0.207242i | \(0.0664487\pi\) | |||||||
\(602\) | 8.09017 | + | 5.87785i | 0.329731 | + | 0.239563i | ||||
\(603\) | −3.76393 | − | 11.5842i | −0.153279 | − | 0.471745i | ||||
\(604\) | 7.23607 | 0.294431 | ||||||||
\(605\) | 0.864745 | − | 6.74315i | 0.0351569 | − | 0.274148i | ||||
\(606\) | −11.3820 | −0.462361 | ||||||||
\(607\) | 7.40983 | + | 22.8051i | 0.300756 | + | 0.925631i | 0.981227 | + | 0.192856i | \(0.0617751\pi\) |
−0.680471 | + | 0.732775i | \(0.738225\pi\) | |||||||
\(608\) | −3.92705 | − | 2.85317i | −0.159263 | − | 0.115711i | ||||
\(609\) | −2.00000 | + | 1.45309i | −0.0810441 | + | 0.0588820i | ||||
\(610\) | 2.32624 | − | 7.15942i | 0.0941866 | − | 0.289877i | ||||
\(611\) | 4.00000 | − | 12.3107i | 0.161823 | − | 0.498039i | ||||
\(612\) | −0.309017 | + | 0.224514i | −0.0124913 | + | 0.00907544i | ||||
\(613\) | −14.7812 | − | 10.7391i | −0.597005 | − | 0.433750i | 0.247809 | − | 0.968809i | \(-0.420289\pi\) |
−0.844815 | + | 0.535059i | \(0.820289\pi\) | |||||||
\(614\) | −0.135255 | − | 0.416272i | −0.00545844 | − | 0.0167994i | ||||
\(615\) | 1.61803 | 0.0652454 | ||||||||
\(616\) | −0.309017 | − | 3.30220i | −0.0124506 | − | 0.133049i | ||||
\(617\) | 44.7214 | 1.80041 | 0.900207 | − | 0.435462i | \(-0.143415\pi\) | ||||
0.900207 | + | 0.435462i | \(0.143415\pi\) | |||||||
\(618\) | 2.64590 | + | 8.14324i | 0.106434 | + | 0.327569i | ||||
\(619\) | −6.59017 | − | 4.78804i | −0.264881 | − | 0.192448i | 0.447415 | − | 0.894326i | \(-0.352345\pi\) |
−0.712296 | + | 0.701879i | \(0.752345\pi\) | |||||||
\(620\) | 2.30902 | − | 1.67760i | 0.0927324 | − | 0.0673740i | ||||
\(621\) | 1.50000 | − | 4.61653i | 0.0601929 | − | 0.185255i | ||||
\(622\) | −10.0344 | + | 30.8828i | −0.402344 | + | 1.23829i | ||||
\(623\) | 12.7812 | − | 9.28605i | 0.512066 | − | 0.372038i | ||||
\(624\) | 1.61803 | + | 1.17557i | 0.0647732 | + | 0.0470605i | ||||
\(625\) | 6.00000 | + | 18.4661i | 0.240000 | + | 0.738644i | ||||
\(626\) | −17.7082 | −0.707762 | ||||||||
\(627\) | −14.7812 | + | 6.37988i | −0.590302 | + | 0.254788i | ||||
\(628\) | 3.70820 | 0.147973 | ||||||||
\(629\) | 0.454915 | + | 1.40008i | 0.0181387 | + | 0.0558250i | ||||
\(630\) | −0.500000 | − | 0.363271i | −0.0199205 | − | 0.0144731i | ||||
\(631\) | −39.2705 | + | 28.5317i | −1.56333 | + | 1.13583i | −0.630126 | + | 0.776493i | \(0.716997\pi\) |
−0.933208 | + | 0.359336i | \(0.883003\pi\) | |||||||
\(632\) | −4.47214 | + | 13.7638i | −0.177892 | + | 0.547495i | ||||
\(633\) | −6.38197 | + | 19.6417i | −0.253660 | + | 0.780686i | ||||
\(634\) | −10.8541 | + | 7.88597i | −0.431071 | + | 0.313192i | ||||
\(635\) | 2.47214 | + | 1.79611i | 0.0981037 | + | 0.0712765i | ||||
\(636\) | −0.145898 | − | 0.449028i | −0.00578523 | − | 0.0178051i | ||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 4.18034 | − | 7.05342i | 0.165501 | − | 0.279248i | ||||
\(639\) | 6.47214 | 0.256034 | ||||||||
\(640\) | 0.190983 | + | 0.587785i | 0.00754927 | + | 0.0232343i | ||||
\(641\) | 28.4164 | + | 20.6457i | 1.12238 | + | 0.815457i | 0.984568 | − | 0.175001i | \(-0.0559929\pi\) |
0.137812 | + | 0.990458i | \(0.455993\pi\) | |||||||
\(642\) | −0.927051 | + | 0.673542i | −0.0365878 | + | 0.0265826i | ||||
\(643\) | 10.8607 | − | 33.4257i | 0.428303 | − | 1.31818i | −0.471492 | − | 0.881870i | \(-0.656284\pi\) |
0.899795 | − | 0.436312i | \(-0.143716\pi\) | |||||||
\(644\) | −1.50000 | + | 4.61653i | −0.0591083 | + | 0.181917i | ||||
\(645\) | −5.00000 | + | 3.63271i | −0.196875 | + | 0.143038i | ||||
\(646\) | −1.50000 | − | 1.08981i | −0.0590167 | − | 0.0428782i | ||||
\(647\) | −11.0557 | − | 34.0260i | −0.434646 | − | 1.33770i | −0.893449 | − | 0.449164i | \(-0.851722\pi\) |
0.458804 | − | 0.888538i | \(-0.348278\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 11.4721 | + | 13.0373i | 0.450321 | + | 0.511758i | ||||
\(650\) | 9.23607 | 0.362268 | ||||||||
\(651\) | −1.42705 | − | 4.39201i | −0.0559305 | − | 0.172136i | ||||
\(652\) | −8.09017 | − | 5.87785i | −0.316836 | − | 0.230194i | ||||
\(653\) | −17.1803 | + | 12.4822i | −0.672319 | + | 0.488468i | −0.870801 | − | 0.491636i | \(-0.836399\pi\) |
0.198482 | + | 0.980105i | \(0.436399\pi\) | |||||||
\(654\) | 1.28115 | − | 3.94298i | 0.0500970 | − | 0.154183i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.11803 | + | 1.53884i | −0.0826953 | + | 0.0600817i | ||||
\(657\) | 8.23607 | + | 5.98385i | 0.321320 | + | 0.233452i | ||||
\(658\) | −2.00000 | − | 6.15537i | −0.0779681 | − | 0.239961i | ||||
\(659\) | −23.0902 | −0.899465 | −0.449733 | − | 0.893163i | \(-0.648481\pi\) | ||||
−0.449733 | + | 0.893163i | \(0.648481\pi\) | |||||||
\(660\) | 2.00000 | + | 0.449028i | 0.0778499 | + | 0.0174784i | ||||
\(661\) | 0.360680 | 0.0140288 | 0.00701441 | − | 0.999975i | \(-0.497767\pi\) | ||||
0.00701441 | + | 0.999975i | \(0.497767\pi\) | |||||||
\(662\) | −0.854102 | − | 2.62866i | −0.0331956 | − | 0.102166i | ||||
\(663\) | 0.618034 | + | 0.449028i | 0.0240025 | + | 0.0174388i | ||||
\(664\) | 2.23607 | − | 1.62460i | 0.0867763 | − | 0.0630466i | ||||
\(665\) | 0.927051 | − | 2.85317i | 0.0359495 | − | 0.110641i | ||||
\(666\) | −1.19098 | + | 3.66547i | −0.0461497 | + | 0.142034i | ||||
\(667\) | −9.70820 | + | 7.05342i | −0.375903 | + | 0.273110i | ||||
\(668\) | −10.3262 | − | 7.50245i | −0.399534 | − | 0.290279i | ||||
\(669\) | 1.40983 | + | 4.33901i | 0.0545072 | + | 0.167756i | ||||
\(670\) | −7.52786 | −0.290827 | ||||||||
\(671\) | 39.4164 | + | 8.84953i | 1.52165 | + | 0.341633i | ||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 0.798374 | + | 2.45714i | 0.0307751 | + | 0.0947159i | 0.965264 | − | 0.261276i | \(-0.0841432\pi\) |
−0.934489 | + | 0.355992i | \(0.884143\pi\) | |||||||
\(674\) | 12.6803 | + | 9.21281i | 0.488428 | + | 0.354864i | ||||
\(675\) | −3.73607 | + | 2.71441i | −0.143801 | + | 0.104478i | ||||
\(676\) | −2.78115 | + | 8.55951i | −0.106967 | + | 0.329212i | ||||
\(677\) | 4.90983 | − | 15.1109i | 0.188700 | − | 0.580759i | −0.811292 | − | 0.584641i | \(-0.801236\pi\) |
0.999992 | + | 0.00388147i | \(0.00123551\pi\) | |||||||
\(678\) | 9.32624 | − | 6.77591i | 0.358172 | − | 0.260227i | ||||
\(679\) | 8.23607 | + | 5.98385i | 0.316071 | + | 0.229639i | ||||
\(680\) | 0.0729490 | + | 0.224514i | 0.00279747 | + | 0.00860972i | ||||
\(681\) | 7.23607 | 0.277287 | ||||||||
\(682\) | 10.1180 | + | 11.4984i | 0.387440 | + | 0.440298i | ||||
\(683\) | −19.3820 | −0.741630 | −0.370815 | − | 0.928707i | \(-0.620922\pi\) | ||||
−0.370815 | + | 0.928707i | \(0.620922\pi\) | |||||||
\(684\) | −1.50000 | − | 4.61653i | −0.0573539 | − | 0.176517i | ||||
\(685\) | 2.61803 | + | 1.90211i | 0.100030 | + | 0.0726760i | ||||
\(686\) | 0.809017 | − | 0.587785i | 0.0308884 | − | 0.0224417i | ||||
\(687\) | 1.23607 | − | 3.80423i | 0.0471589 | − | 0.145140i | ||||
\(688\) | 3.09017 | − | 9.51057i | 0.117812 | − | 0.362587i | ||||
\(689\) | −0.763932 | + | 0.555029i | −0.0291035 | + | 0.0211449i | ||||
\(690\) | −2.42705 | − | 1.76336i | −0.0923963 | − | 0.0671298i | ||||
\(691\) | 5.08359 | + | 15.6457i | 0.193389 | + | 0.595190i | 0.999992 | + | 0.00409598i | \(0.00130379\pi\) |
−0.806603 | + | 0.591094i | \(0.798696\pi\) | |||||||
\(692\) | 18.7426 | 0.712488 | ||||||||
\(693\) | 1.69098 | − | 2.85317i | 0.0642351 | − | 0.108383i | ||||
\(694\) | −2.72949 | −0.103610 | ||||||||
\(695\) | 0.309017 | + | 0.951057i | 0.0117217 | + | 0.0360756i | ||||
\(696\) | 2.00000 | + | 1.45309i | 0.0758098 | + | 0.0550790i | ||||
\(697\) | −0.809017 | + | 0.587785i | −0.0306437 | + | 0.0222640i | ||||
\(698\) | −6.56231 | + | 20.1967i | −0.248387 | + | 0.764456i | ||||
\(699\) | −0.236068 | + | 0.726543i | −0.00892891 | + | 0.0274804i | ||||
\(700\) | 3.73607 | − | 2.71441i | 0.141210 | − | 0.102595i | ||||
\(701\) | −8.00000 | − | 5.81234i | −0.302156 | − | 0.219529i | 0.426368 | − | 0.904550i | \(-0.359793\pi\) |
−0.728523 | + | 0.685021i | \(0.759793\pi\) | |||||||
\(702\) | 0.618034 | + | 1.90211i | 0.0233262 | + | 0.0717906i | ||||
\(703\) | −18.7082 | −0.705593 | ||||||||
\(704\) | −3.04508 | + | 1.31433i | −0.114766 | + | 0.0495356i | ||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | 3.67376 | + | 11.3067i | 0.138264 | + | 0.425532i | ||||
\(707\) | 9.20820 | + | 6.69015i | 0.346310 | + | 0.251609i | ||||
\(708\) | −4.23607 | + | 3.07768i | −0.159201 | + | 0.115666i | ||||
\(709\) | −12.1353 | + | 37.3485i | −0.455749 | + | 1.40265i | 0.414504 | + | 0.910047i | \(0.363955\pi\) |
−0.870254 | + | 0.492604i | \(0.836045\pi\) | |||||||
\(710\) | 1.23607 | − | 3.80423i | 0.0463888 | − | 0.142770i | ||||
\(711\) | −11.7082 | + | 8.50651i | −0.439092 | + | 0.319019i | ||||
\(712\) | −12.7812 | − | 9.28605i | −0.478994 | − | 0.348009i | ||||
\(713\) | −6.92705 | − | 21.3193i | −0.259420 | − | 0.798413i | ||||
\(714\) | 0.381966 | 0.0142947 | ||||||||
\(715\) | −0.381966 | − | 4.08174i | −0.0142847 | − | 0.152648i | ||||
\(716\) | −16.0344 | −0.599235 | ||||||||
\(717\) | 7.97214 | + | 24.5357i | 0.297725 | + | 0.916303i | ||||
\(718\) | 28.0623 | + | 20.3885i | 1.04728 | + | 0.760891i | ||||
\(719\) | 37.4164 | − | 27.1846i | 1.39540 | − | 1.01381i | 0.400148 | − | 0.916451i | \(-0.368959\pi\) |
0.995249 | − | 0.0973643i | \(-0.0310412\pi\) | |||||||
\(720\) | −0.190983 | + | 0.587785i | −0.00711752 | + | 0.0219055i | ||||
\(721\) | 2.64590 | − | 8.14324i | 0.0985384 | − | 0.303270i | ||||
\(722\) | 3.69098 | − | 2.68166i | 0.137364 | − | 0.0998009i | ||||
\(723\) | 23.5623 | + | 17.1190i | 0.876292 | + | 0.636663i | ||||
\(724\) | 5.47214 | + | 16.8415i | 0.203370 | + | 0.625910i | ||||
\(725\) | 11.4164 | 0.423995 | ||||||||
\(726\) | −1.39919 | + | 10.9106i | −0.0519287 | + | 0.404932i | ||||
\(727\) | 25.6869 | 0.952675 | 0.476338 | − | 0.879263i | \(-0.341964\pi\) | ||||
0.476338 | + | 0.879263i | \(0.341964\pi\) | |||||||
\(728\) | −0.618034 | − | 1.90211i | −0.0229059 | − | 0.0704970i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 5.09017 | − | 3.69822i | 0.188396 | − | 0.136877i | ||||
\(731\) | 1.18034 | − | 3.63271i | 0.0436564 | − | 0.134361i | ||||
\(732\) | −3.76393 | + | 11.5842i | −0.139119 | + | 0.428164i | ||||
\(733\) | −26.1246 | + | 18.9806i | −0.964935 | + | 0.701066i | −0.954292 | − | 0.298877i | \(-0.903388\pi\) |
−0.0106430 | + | 0.999943i | \(0.503388\pi\) | |||||||
\(734\) | 14.4443 | + | 10.4944i | 0.533148 | + | 0.387355i | ||||
\(735\) | 0.190983 | + | 0.587785i | 0.00704451 | + | 0.0216808i | ||||
\(736\) | 4.85410 | 0.178925 | ||||||||
\(737\) | −3.76393 | − | 40.2219i | −0.138646 | − | 1.48159i | ||||
\(738\) | −2.61803 | −0.0963712 | ||||||||
\(739\) | −10.2361 | − | 31.5034i | −0.376540 | − | 1.15887i | −0.942434 | − | 0.334393i | \(-0.891469\pi\) |
0.565894 | − | 0.824478i | \(-0.308531\pi\) | |||||||
\(740\) | 1.92705 | + | 1.40008i | 0.0708398 | + | 0.0514681i | ||||
\(741\) | −7.85410 | + | 5.70634i | −0.288528 | + | 0.209628i | ||||
\(742\) | −0.145898 | + | 0.449028i | −0.00535609 | + | 0.0164843i | ||||
\(743\) | 1.28115 | − | 3.94298i | 0.0470009 | − | 0.144654i | −0.924802 | − | 0.380449i | \(-0.875769\pi\) |
0.971803 | + | 0.235795i | \(0.0757694\pi\) | |||||||
\(744\) | −3.73607 | + | 2.71441i | −0.136971 | + | 0.0995152i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.01064 | + | 3.11044i | 0.0370023 | + | 0.113881i | ||||
\(747\) | 2.76393 | 0.101127 | ||||||||
\(748\) | −1.16312 | + | 0.502029i | −0.0425278 | + | 0.0183560i | ||||
\(749\) | 1.14590 | 0.0418702 | ||||||||
\(750\) | 1.83688 | + | 5.65334i | 0.0670734 | + | 0.206431i | ||||
\(751\) | 31.6525 | + | 22.9969i | 1.15502 | + | 0.839168i | 0.989140 | − | 0.146979i | \(-0.0469550\pi\) |
0.165876 | + | 0.986147i | \(0.446955\pi\) | |||||||
\(752\) | −5.23607 | + | 3.80423i | −0.190940 | + | 0.138726i | ||||
\(753\) | −7.56231 | + | 23.2744i | −0.275586 | + | 0.848166i | ||||
\(754\) | 1.52786 | − | 4.70228i | 0.0556415 | − | 0.171247i | ||||
\(755\) | 3.61803 | − | 2.62866i | 0.131674 | − | 0.0956666i | ||||
\(756\) | 0.809017 | + | 0.587785i | 0.0294237 | + | 0.0213775i | ||||
\(757\) | −6.40983 | − | 19.7274i | −0.232969 | − | 0.717006i | −0.997384 | − | 0.0722811i | \(-0.976972\pi\) |
0.764415 | − | 0.644724i | \(-0.223028\pi\) | |||||||
\(758\) | −9.41641 | −0.342019 | ||||||||
\(759\) | 8.20820 | − | 13.8496i | 0.297939 | − | 0.502708i | ||||
\(760\) | −3.00000 | −0.108821 | ||||||||
\(761\) | −14.3262 | − | 44.0916i | −0.519326 | − | 1.59832i | −0.775271 | − | 0.631629i | \(-0.782387\pi\) |
0.255945 | − | 0.966691i | \(-0.417613\pi\) | |||||||
\(762\) | −4.00000 | − | 2.90617i | −0.144905 | − | 0.105279i | ||||
\(763\) | −3.35410 | + | 2.43690i | −0.121427 | + | 0.0882216i | ||||
\(764\) | −4.51722 | + | 13.9026i | −0.163427 | + | 0.502978i | ||||
\(765\) | −0.0729490 | + | 0.224514i | −0.00263748 | + | 0.00811732i | ||||
\(766\) | 19.3262 | − | 14.0413i | 0.698285 | − | 0.507334i | ||||
\(767\) | 8.47214 | + | 6.15537i | 0.305911 | + | 0.222257i | ||||
\(768\) | −0.309017 | − | 0.951057i | −0.0111507 | − | 0.0343183i | ||||
\(769\) | −1.34752 | −0.0485930 | −0.0242965 | − | 0.999705i | \(-0.507735\pi\) | ||||
−0.0242965 | + | 0.999705i | \(0.507735\pi\) | |||||||
\(770\) | −1.35410 | − | 1.53884i | −0.0487984 | − | 0.0554560i | ||||
\(771\) | 13.9098 | 0.500950 | ||||||||
\(772\) | 5.60739 | + | 17.2578i | 0.201814 | + | 0.621121i | ||||
\(773\) | −18.5623 | − | 13.4863i | −0.667640 | − | 0.485069i | 0.201595 | − | 0.979469i | \(-0.435388\pi\) |
−0.869234 | + | 0.494400i | \(0.835388\pi\) | |||||||
\(774\) | 8.09017 | − | 5.87785i | 0.290795 | − | 0.211275i | ||||
\(775\) | −6.59017 | + | 20.2825i | −0.236726 | + | 0.728567i | ||||
\(776\) | 3.14590 | − | 9.68208i | 0.112931 | − | 0.347566i | ||||
\(777\) | 3.11803 | − | 2.26538i | 0.111859 | − | 0.0812702i | ||||
\(778\) | 1.14590 | + | 0.832544i | 0.0410824 | + | 0.0298481i | ||||
\(779\) | −3.92705 | − | 12.0862i | −0.140701 | − | 0.433034i | ||||
\(780\) | 1.23607 | 0.0442583 | ||||||||
\(781\) | 20.9443 | + | 4.70228i | 0.749445 | + | 0.168261i | ||||
\(782\) | 1.85410 | 0.0663026 | ||||||||
\(783\) | 0.763932 | + | 2.35114i | 0.0273007 | + | 0.0840229i | ||||
\(784\) | −0.809017 | − | 0.587785i | −0.0288935 | − | 0.0209923i | ||||
\(785\) | 1.85410 | − | 1.34708i | 0.0661757 | − | 0.0480795i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.10081 | − | 21.8541i | 0.253117 | − | 0.779013i | −0.741078 | − | 0.671419i | \(-0.765685\pi\) |
0.994195 | − | 0.107594i | \(-0.0343147\pi\) | |||||||
\(788\) | −16.3262 | + | 11.8617i | −0.581598 | + | 0.422556i | ||||
\(789\) | 13.7812 | + | 10.0126i | 0.490622 | + | 0.356458i | ||||
\(790\) | 2.76393 | + | 8.50651i | 0.0983363 | + | 0.302648i | ||||
\(791\) | −11.5279 | −0.409884 | ||||||||
\(792\) | −3.23607 | − | 0.726543i | −0.114989 | − | 0.0258166i | ||||
\(793\) | 24.3607 | 0.865073 | ||||||||
\(794\) | 7.85410 | + | 24.1724i | 0.278732 | + | 0.857848i | ||||
\(795\) | −0.236068 | − | 0.171513i | −0.00837247 | − | 0.00608295i | ||||
\(796\) | −3.54508 | + | 2.57565i | −0.125652 | + | 0.0912917i | ||||
\(797\) | −1.92047 | + | 5.91061i | −0.0680267 | + | 0.209365i | −0.979291 | − | 0.202457i | \(-0.935107\pi\) |
0.911264 | + | 0.411822i | \(0.135107\pi\) | |||||||
\(798\) | −1.50000 | + | 4.61653i | −0.0530994 | + | 0.163423i | ||||
\(799\) | −2.00000 | + | 1.45309i | −0.0707549 | + | 0.0514065i | ||||
\(800\) | −3.73607 | − | 2.71441i | −0.132090 | − | 0.0959690i | ||||
\(801\) | −4.88197 | − | 15.0251i | −0.172496 | − | 0.530887i | ||||
\(802\) | −15.5967 | −0.550740 | ||||||||
\(803\) | 22.3050 | + | 25.3480i | 0.787125 | + | 0.894512i | ||||
\(804\) | 12.1803 | 0.429567 | ||||||||
\(805\) | 0.927051 | + | 2.85317i | 0.0326743 | + | 0.100561i | ||||
\(806\) | 7.47214 | + | 5.42882i | 0.263195 | + | 0.191222i | ||||
\(807\) | 6.38197 | − | 4.63677i | 0.224656 | − | 0.163222i | ||||
\(808\) | 3.51722 | − | 10.8249i | 0.123735 | − | 0.380818i | ||||
\(809\) | −13.0902 | + | 40.2874i | −0.460226 | + | 1.41643i | 0.404663 | + | 0.914466i | \(0.367389\pi\) |
−0.864889 | + | 0.501964i | \(0.832611\pi\) | |||||||
\(810\) | −0.500000 | + | 0.363271i | −0.0175682 | + | 0.0127641i | ||||
\(811\) | 10.4721 | + | 7.60845i | 0.367726 | + | 0.267169i | 0.756268 | − | 0.654263i | \(-0.227021\pi\) |
−0.388541 | + | 0.921431i | \(0.627021\pi\) | |||||||
\(812\) | −0.763932 | − | 2.35114i | −0.0268088 | − | 0.0825089i | ||||
\(813\) | 9.27051 | 0.325131 | ||||||||
\(814\) | −6.51722 | + | 10.9964i | −0.228428 | + | 0.385424i | ||||
\(815\) | −6.18034 | −0.216488 | ||||||||
\(816\) | −0.118034 | − | 0.363271i | −0.00413202 | − | 0.0127170i | ||||
\(817\) | 39.2705 | + | 28.5317i | 1.37390 | + | 0.998198i | ||||
\(818\) | 8.70820 | − | 6.32688i | 0.304475 | − | 0.221214i | ||||
\(819\) | 0.618034 | − | 1.90211i | 0.0215959 | − | 0.0664652i | ||||
\(820\) | −0.500000 | + | 1.53884i | −0.0174608 | + | 0.0537387i | ||||
\(821\) | 5.23607 | − | 3.80423i | 0.182740 | − | 0.132768i | −0.492655 | − | 0.870225i | \(-0.663973\pi\) |
0.675395 | + | 0.737457i | \(0.263973\pi\) | |||||||
\(822\) | −4.23607 | − | 3.07768i | −0.147750 | − | 0.107347i | ||||
\(823\) | 15.2918 | + | 47.0633i | 0.533039 | + | 1.64052i | 0.747850 | + | 0.663868i | \(0.231086\pi\) |
−0.214811 | + | 0.976656i | \(0.568914\pi\) | |||||||
\(824\) | −8.56231 | −0.298282 | ||||||||
\(825\) | −14.0623 | + | 6.06961i | −0.489587 | + | 0.211317i | ||||
\(826\) | 5.23607 | 0.182186 | ||||||||
\(827\) | −6.06231 | − | 18.6579i | −0.210807 | − | 0.648797i | −0.999425 | − | 0.0339136i | \(-0.989203\pi\) |
0.788618 | − | 0.614884i | \(-0.210797\pi\) | |||||||
\(828\) | 3.92705 | + | 2.85317i | 0.136474 | + | 0.0991545i | ||||
\(829\) | −3.14590 | + | 2.28563i | −0.109262 | + | 0.0793832i | −0.641074 | − | 0.767479i | \(-0.721511\pi\) |
0.531813 | + | 0.846862i | \(0.321511\pi\) | |||||||
\(830\) | 0.527864 | − | 1.62460i | 0.0183224 | − | 0.0563906i | ||||
\(831\) | 5.11803 | − | 15.7517i | 0.177543 | − | 0.546420i | ||||
\(832\) | −1.61803 | + | 1.17557i | −0.0560952 | + | 0.0407556i | ||||
\(833\) | −0.309017 | − | 0.224514i | −0.0107068 | − | 0.00777895i | ||||
\(834\) | −0.500000 | − | 1.53884i | −0.0173136 | − | 0.0532857i | ||||
\(835\) | −7.88854 | −0.272994 | ||||||||
\(836\) | −1.50000 | − | 16.0292i | −0.0518786 | − | 0.554382i | ||||
\(837\) | −4.61803 | −0.159623 | ||||||||
\(838\) | −11.4164 | − | 35.1361i | −0.394373 | − | 1.21376i | ||||
\(839\) | −35.2705 | − | 25.6255i | −1.21767 | − | 0.884691i | −0.221768 | − | 0.975099i | \(-0.571183\pi\) |
−0.995905 | + | 0.0904080i | \(0.971183\pi\) | |||||||
\(840\) | 0.500000 | − | 0.363271i | 0.0172516 | − | 0.0125340i | ||||
\(841\) | −7.07295 | + | 21.7683i | −0.243895 | + | 0.750631i | ||||
\(842\) | 2.64590 | − | 8.14324i | 0.0911837 | − | 0.280634i | ||||
\(843\) | −18.7082 | + | 13.5923i | −0.644345 | + | 0.468144i | ||||
\(844\) | −16.7082 | − | 12.1392i | −0.575120 | − | 0.417849i | ||||
\(845\) | 1.71885 | + | 5.29007i | 0.0591301 | + | 0.181984i | ||||
\(846\) | −6.47214 | −0.222517 | ||||||||
\(847\) | 7.54508 | − | 8.00448i | 0.259252 | − | 0.275037i | ||||
\(848\) | 0.472136 | 0.0162132 | ||||||||
\(849\) | −3.86475 | − | 11.8945i | −0.132638 | − | 0.408217i | ||||
\(850\) | −1.42705 | − | 1.03681i | −0.0489474 | − | 0.0355624i | ||||
\(851\) | 15.1353 | − | 10.9964i | 0.518830 | − | 0.376952i | ||||
\(852\) | −2.00000 | + | 6.15537i | −0.0685189 | + | 0.210879i | ||||
\(853\) | 13.5836 | − | 41.8060i | 0.465093 | − | 1.43141i | −0.393772 | − | 0.919208i | \(-0.628830\pi\) |
0.858865 | − | 0.512202i | \(-0.171170\pi\) | |||||||
\(854\) | 9.85410 | − | 7.15942i | 0.337200 | − | 0.244990i | ||||
\(855\) | −2.42705 | − | 1.76336i | −0.0830034 | − | 0.0603055i | ||||
\(856\) | −0.354102 | − | 1.08981i | −0.0121030 | − | 0.0372491i | ||||
\(857\) | 28.2492 | 0.964975 | 0.482488 | − | 0.875903i | \(-0.339733\pi\) | ||||
0.482488 | + | 0.875903i | \(0.339733\pi\) | |||||||
\(858\) | 0.618034 | + | 6.60440i | 0.0210993 | + | 0.225470i | ||||
\(859\) | −43.4164 | −1.48135 | −0.740674 | − | 0.671864i | \(-0.765494\pi\) | ||||
−0.740674 | + | 0.671864i | \(0.765494\pi\) | |||||||
\(860\) | −1.90983 | − | 5.87785i | −0.0651247 | − | 0.200433i | ||||
\(861\) | 2.11803 | + | 1.53884i | 0.0721824 | + | 0.0524436i | ||||
\(862\) | −31.0066 | + | 22.5276i | −1.05609 | + | 0.767293i | ||||
\(863\) | 13.5729 | − | 41.7732i | 0.462029 | − | 1.42198i | −0.400653 | − | 0.916230i | \(-0.631217\pi\) |
0.862681 | − | 0.505748i | \(-0.168783\pi\) | |||||||
\(864\) | 0.309017 | − | 0.951057i | 0.0105130 | − | 0.0323556i | ||||
\(865\) | 9.37132 | − | 6.80866i | 0.318635 | − | 0.231502i | ||||
\(866\) | 18.5623 | + | 13.4863i | 0.630773 | + | 0.458283i | ||||
\(867\) | 5.20820 | + | 16.0292i | 0.176880 | + | 0.544380i | ||||
\(868\) | 4.61803 | 0.156746 | ||||||||
\(869\) | −44.0689 | + | 19.0211i | −1.49493 | + | 0.645248i | ||||
\(870\) | 1.52786 | 0.0517994 | ||||||||
\(871\) | −7.52786 | − | 23.1684i | −0.255072 | − | 0.785031i | ||||
\(872\) | 3.35410 | + | 2.43690i | 0.113584 | + | 0.0825238i | ||||
\(873\) | 8.23607 | − | 5.98385i | 0.278749 | − | 0.202523i | ||||
\(874\) | −7.28115 | + | 22.4091i | −0.246289 | + | 0.757999i | ||||
\(875\) | 1.83688 | − | 5.65334i | 0.0620979 | − | 0.191118i | ||||
\(876\) | −8.23607 | + | 5.98385i | −0.278271 | + | 0.202176i | ||||
\(877\) | −9.32624 | − | 6.77591i | −0.314925 | − | 0.228806i | 0.419082 | − | 0.907948i | \(-0.362352\pi\) |
−0.734007 | + | 0.679142i | \(0.762352\pi\) | |||||||
\(878\) | −7.60739 | − | 23.4131i | −0.256737 | − | 0.790155i | ||||
\(879\) | −19.0902 | −0.643895 | ||||||||
\(880\) | −1.04508 | + | 1.76336i | −0.0352298 | + | 0.0594427i | ||||
\(881\) | 34.8541 | 1.17426 | 0.587132 | − | 0.809491i | \(-0.300257\pi\) | ||||
0.587132 | + | 0.809491i | \(0.300257\pi\) | |||||||
\(882\) | −0.309017 | − | 0.951057i | −0.0104051 | − | 0.0320237i | ||||
\(883\) | −44.3607 | − | 32.2299i | −1.49286 | − | 1.08462i | −0.973121 | − | 0.230296i | \(-0.926031\pi\) |
−0.519735 | − | 0.854328i | \(-0.673969\pi\) | |||||||
\(884\) | −0.618034 | + | 0.449028i | −0.0207867 | + | 0.0151024i | ||||
\(885\) | −1.00000 | + | 3.07768i | −0.0336146 | + | 0.103455i | ||||
\(886\) | −0.354102 | + | 1.08981i | −0.0118963 | + | 0.0366130i | ||||
\(887\) | 1.00000 | − | 0.726543i | 0.0335767 | − | 0.0243949i | −0.570870 | − | 0.821040i | \(-0.693394\pi\) |
0.604447 | + | 0.796645i | \(0.293394\pi\) | |||||||
\(888\) | −3.11803 | − | 2.26538i | −0.104634 | − | 0.0760213i | ||||
\(889\) | 1.52786 | + | 4.70228i | 0.0512429 | + | 0.157709i | ||||
\(890\) | −9.76393 | −0.327288 | ||||||||
\(891\) | −2.19098 | − | 2.48990i | −0.0734007 | − | 0.0834147i | ||||
\(892\) | −4.56231 | −0.152757 | ||||||||
\(893\) | −9.70820 | − | 29.8788i | −0.324873 | − | 0.999855i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.01722 | + | 5.82485i | −0.267986 | + | 0.194703i | ||||
\(896\) | −0.309017 | + | 0.951057i | −0.0103235 | + | 0.0317726i | ||||
\(897\) | 3.00000 | − | 9.23305i | 0.100167 | − | 0.308283i | ||||
\(898\) | 19.0344 | − | 13.8293i | 0.635188 | − | 0.461491i | ||||
\(899\) | 9.23607 | + | 6.71040i | 0.308040 | + | 0.223804i | ||||
\(900\) | −1.42705 | − | 4.39201i | −0.0475684 | − | 0.146400i | ||||
\(901\) | 0.180340 | 0.00600799 | ||||||||
\(902\) | −8.47214 | − | 1.90211i | −0.282091 | − | 0.0633334i | ||||
\(903\) | −10.0000 | −0.332779 | ||||||||
\(904\) | 3.56231 | + | 10.9637i | 0.118481 | + | 0.364646i | ||||
\(905\) | 8.85410 | + | 6.43288i | 0.294320 | + | 0.213836i | ||||
\(906\) | −5.85410 | + | 4.25325i | −0.194490 | + | 0.141305i | ||||
\(907\) | 9.61803 | − | 29.6013i | 0.319362 | − | 0.982894i | −0.654560 | − | 0.756010i | \(-0.727146\pi\) |
0.973922 | − | 0.226884i | \(-0.0728538\pi\) | |||||||
\(908\) | −2.23607 | + | 6.88191i | −0.0742065 | + | 0.228384i | ||||
\(909\) | 9.20820 | − | 6.69015i | 0.305417 | − | 0.221898i | ||||
\(910\) | −1.00000 | − | 0.726543i | −0.0331497 | − | 0.0240847i | ||||
\(911\) | −15.2361 | − | 46.8918i | −0.504793 | − | 1.55359i | −0.801118 | − | 0.598507i | \(-0.795761\pi\) |
0.296324 | − | 0.955087i | \(-0.404239\pi\) | |||||||
\(912\) | 4.85410 | 0.160735 | ||||||||
\(913\) | 8.94427 | + | 2.00811i | 0.296012 | + | 0.0664589i | ||||
\(914\) | −18.3607 | −0.607317 | ||||||||
\(915\) | 2.32624 | + | 7.15942i | 0.0769031 | + | 0.236683i | ||||
\(916\) | 3.23607 | + | 2.35114i | 0.106923 | + | 0.0776839i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.118034 | − | 0.363271i | 0.00389570 | − | 0.0119897i | ||||
\(919\) | 17.9443 | − | 55.2268i | 0.591927 | − | 1.82176i | 0.0224626 | − | 0.999748i | \(-0.492849\pi\) |
0.569464 | − | 0.822016i | \(-0.307151\pi\) | |||||||
\(920\) | 2.42705 | − | 1.76336i | 0.0800175 | − | 0.0581361i | ||||
\(921\) | 0.354102 | + | 0.257270i | 0.0116681 | + | 0.00847734i | ||||
\(922\) | −6.50658 | − | 20.0252i | −0.214283 | − | 0.659494i | ||||
\(923\) | 12.9443 | 0.426066 | ||||||||
\(924\) | 2.19098 | + | 2.48990i | 0.0720780 | + | 0.0819116i | ||||
\(925\) | −17.7984 | −0.585207 | ||||||||
\(926\) | 11.9098 | + | 36.6547i | 0.391381 | + | 1.20455i | ||||
\(927\) | −6.92705 | − | 5.03280i | −0.227514 | − | 0.165299i | ||||
\(928\) | −2.00000 | + | 1.45309i | −0.0656532 | + | 0.0476999i | ||||
\(929\) | −3.35410 | + | 10.3229i | −0.110045 | + | 0.338682i | −0.990881 | − | 0.134738i | \(-0.956981\pi\) |
0.880837 | + | 0.473420i | \(0.156981\pi\) | |||||||
\(930\) | −0.881966 | + | 2.71441i | −0.0289208 | + | 0.0890091i | ||||
\(931\) | 3.92705 | − | 2.85317i | 0.128704 | − | 0.0935089i | ||||
\(932\) | −0.618034 | − | 0.449028i | −0.0202444 | − | 0.0147084i | ||||
\(933\) | −10.0344 | − | 30.8828i | −0.328513 | − | 1.01106i | ||||
\(934\) | −27.8885 | −0.912541 | ||||||||
\(935\) | −0.399187 | + | 0.673542i | −0.0130548 | + | 0.0220272i | ||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | 1.43769 | + | 4.42477i | 0.0469674 | + | 0.144551i | 0.971790 | − | 0.235848i | \(-0.0757867\pi\) |
−0.924823 | + | 0.380399i | \(0.875787\pi\) | |||||||
\(938\) | −9.85410 | − | 7.15942i | −0.321748 | − | 0.233763i | ||||
\(939\) | 14.3262 | − | 10.4086i | 0.467519 | − | 0.339673i | ||||
\(940\) | −1.23607 | + | 3.80423i | −0.0403161 | + | 0.124080i | ||||
\(941\) | −6.15248 | + | 18.9354i | −0.200565 | + | 0.617276i | 0.799301 | + | 0.600930i | \(0.205203\pi\) |
−0.999866 | + | 0.0163452i | \(0.994797\pi\) | |||||||
\(942\) | −3.00000 | + | 2.17963i | −0.0977453 | + | 0.0710161i | ||||
\(943\) | 10.2812 | + | 7.46969i | 0.334800 | + | 0.243247i | ||||
\(944\) | −1.61803 | − | 4.97980i | −0.0526625 | − | 0.162079i | ||||
\(945\) | 0.618034 | 0.0201046 | ||||||||
\(946\) | 30.4508 | − | 13.1433i | 0.990043 | − | 0.427325i | ||||
\(947\) | 33.9230 | 1.10235 | 0.551174 | − | 0.834390i | \(-0.314180\pi\) | ||||
0.551174 | + | 0.834390i | \(0.314180\pi\) | |||||||
\(948\) | −4.47214 | − | 13.7638i | −0.145248 | − | 0.447028i | ||||
\(949\) | 16.4721 | + | 11.9677i | 0.534708 | + | 0.388488i | ||||
\(950\) | 18.1353 | − | 13.1760i | 0.588385 | − | 0.427487i | ||||
\(951\) | 4.14590 | − | 12.7598i | 0.134440 | − | 0.413764i | ||||
\(952\) | −0.118034 | + | 0.363271i | −0.00382550 | + | 0.0117737i | ||||
\(953\) | 9.70820 | − | 7.05342i | 0.314480 | − | 0.228483i | −0.419337 | − | 0.907831i | \(-0.637737\pi\) |
0.733816 | + | 0.679348i | \(0.237737\pi\) | |||||||
\(954\) | 0.381966 | + | 0.277515i | 0.0123666 | + | 0.00898487i | ||||
\(955\) | 2.79180 | + | 8.59226i | 0.0903404 | + | 0.278039i | ||||
\(956\) | −25.7984 | −0.834379 | ||||||||
\(957\) | 0.763932 | + | 8.16348i | 0.0246944 | + | 0.263888i | ||||
\(958\) | 18.4721 | 0.596808 | ||||||||
\(959\) | 1.61803 | + | 4.97980i | 0.0522490 | + | 0.160806i | ||||
\(960\) | −0.500000 | − | 0.363271i | −0.0161374 | − | 0.0117245i | ||||
\(961\) | 7.82624 | − | 5.68609i | 0.252459 | − | 0.183422i | ||||
\(962\) | −2.38197 | + | 7.33094i | −0.0767977 | + | 0.236359i | ||||
\(963\) | 0.354102 | − | 1.08981i | 0.0114108 | − | 0.0351188i | ||||
\(964\) | −23.5623 | + | 17.1190i | −0.758891 | + | 0.551366i | ||||
\(965\) | 9.07295 | + | 6.59188i | 0.292069 | + | 0.212200i | ||||
\(966\) | −1.50000 | − | 4.61653i | −0.0482617 | − | 0.148534i | ||||
\(967\) | −30.0000 | −0.964735 | −0.482367 | − | 0.875969i | \(-0.660223\pi\) | ||||
−0.482367 | + | 0.875969i | \(0.660223\pi\) | |||||||
\(968\) | −9.94427 | − | 4.70228i | −0.319621 | − | 0.151137i | ||||
\(969\) | 1.85410 | 0.0595623 | ||||||||
\(970\) | −1.94427 | − | 5.98385i | −0.0624268 | − | 0.192130i | ||||
\(971\) | −14.0344 | − | 10.1966i | −0.450387 | − | 0.327225i | 0.339362 | − | 0.940656i | \(-0.389789\pi\) |
−0.789748 | + | 0.613431i | \(0.789789\pi\) | |||||||
\(972\) | 0.809017 | − | 0.587785i | 0.0259492 | − | 0.0188532i | ||||
\(973\) | −0.500000 | + | 1.53884i | −0.0160293 | + | 0.0493330i | ||||
\(974\) | 0.729490 | − | 2.24514i | 0.0233744 | − | 0.0719389i | ||||
\(975\) | −7.47214 | + | 5.42882i | −0.239300 | + | 0.173862i | ||||
\(976\) | −9.85410 | − | 7.15942i | −0.315422 | − | 0.229168i | ||||
\(977\) | −3.70820 | − | 11.4127i | −0.118636 | − | 0.365124i | 0.874052 | − | 0.485832i | \(-0.161483\pi\) |
−0.992688 | + | 0.120708i | \(0.961483\pi\) | |||||||
\(978\) | 10.0000 | 0.319765 | ||||||||
\(979\) | −4.88197 | − | 52.1694i | −0.156028 | − | 1.66734i | ||||
\(980\) | −0.618034 | −0.0197424 | ||||||||
\(981\) | 1.28115 | + | 3.94298i | 0.0409041 | + | 0.125890i | ||||
\(982\) | 5.07295 | + | 3.68571i | 0.161884 | + | 0.117616i | ||||
\(983\) | −40.7426 | + | 29.6013i | −1.29949 | + | 0.944134i | −0.999950 | − | 0.00995062i | \(-0.996833\pi\) |
−0.299538 | + | 0.954084i | \(0.596833\pi\) | |||||||
\(984\) | 0.809017 | − | 2.48990i | 0.0257905 | − | 0.0793751i | ||||
\(985\) | −3.85410 | + | 11.8617i | −0.122802 | + | 0.377945i | ||||
\(986\) | −0.763932 | + | 0.555029i | −0.0243286 | + | 0.0176757i | ||||
\(987\) | 5.23607 | + | 3.80423i | 0.166666 | + | 0.121090i | ||||
\(988\) | −3.00000 | − | 9.23305i | −0.0954427 | − | 0.293742i | ||||
\(989\) | −48.5410 | −1.54351 | ||||||||
\(990\) | −1.88197 | + | 0.812299i | −0.0598128 | + | 0.0258166i | ||||
\(991\) | −1.59675 | −0.0507224 | −0.0253612 | − | 0.999678i | \(-0.508074\pi\) | ||||
−0.0253612 | + | 0.999678i | \(0.508074\pi\) | |||||||
\(992\) | −1.42705 | − | 4.39201i | −0.0453089 | − | 0.139446i | ||||
\(993\) | 2.23607 | + | 1.62460i | 0.0709595 | + | 0.0515551i | ||||
\(994\) | 5.23607 | − | 3.80423i | 0.166078 | − | 0.120663i | ||||
\(995\) | −0.836881 | + | 2.57565i | −0.0265309 | + | 0.0816538i | ||||
\(996\) | −0.854102 | + | 2.62866i | −0.0270633 | + | 0.0832921i | ||||
\(997\) | 46.9787 | − | 34.1320i | 1.48783 | − | 1.08097i | 0.512904 | − | 0.858446i | \(-0.328570\pi\) |
0.974927 | − | 0.222526i | \(-0.0714304\pi\) | |||||||
\(998\) | 22.2705 | + | 16.1805i | 0.704961 | + | 0.512184i | ||||
\(999\) | −1.19098 | − | 3.66547i | −0.0376810 | − | 0.115970i |
(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 | 462.2.j.d.379.1 | yes | 4 | |
11.3 | even | 5 | 5082.2.a.bf.1.1 | 2 | |||
11.8 | odd | 10 | 5082.2.a.bp.1.1 | 2 | |||
11.9 | even | 5 | inner | 462.2.j.d.295.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.d.295.1 | ✓ | 4 | 11.9 | even | 5 | inner | |
462.2.j.d.379.1 | yes | 4 | 1.1 | even | 1 | trivial | |
5082.2.a.bf.1.1 | 2 | 11.3 | even | 5 | |||
5082.2.a.bp.1.1 | 2 | 11.8 | odd | 10 |