Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.64000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 215.1 | ||
Root | \(1.34500 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.215 |
Dual form | 363.2.f.a.233.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | 0.998886 | + | 0.0471903i | \(0.0150267\pi\) |
−0.780378 | + | 0.625308i | \(0.784973\pi\) | |||||||
\(3\) | −1.64027 | + | 0.556338i | −0.947011 | + | 0.321202i | ||||
\(4\) | 0.809017 | − | 0.587785i | 0.404508 | − | 0.293893i | ||||
\(5\) | −2.68999 | − | 0.874032i | −1.20300 | − | 0.390879i | −0.362137 | − | 0.932125i | \(-0.617953\pi\) |
−0.840864 | + | 0.541246i | \(0.817953\pi\) | |||||||
\(6\) | −1.03598 | − | 1.38807i | −0.422937 | − | 0.566678i | ||||
\(7\) | −0.831254 | − | 1.14412i | −0.314184 | − | 0.432438i | 0.622496 | − | 0.782623i | \(-0.286119\pi\) |
−0.936680 | + | 0.350185i | \(0.886119\pi\) | |||||||
\(8\) | 2.42705 | + | 1.76336i | 0.858092 | + | 0.623440i | ||||
\(9\) | 2.38098 | − | 1.82509i | 0.793659 | − | 0.608363i | ||||
\(10\) | − | 2.82843i | − | 0.894427i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | + | 1.41421i | −0.288675 | + | 0.408248i | ||||
\(13\) | 4.03499 | − | 1.31105i | 1.11911 | − | 0.363619i | 0.309679 | − | 0.950841i | \(-0.399778\pi\) |
0.809426 | + | 0.587222i | \(0.199778\pi\) | |||||||
\(14\) | 0.831254 | − | 1.14412i | 0.222162 | − | 0.305780i | ||||
\(15\) | 4.89858 | − | 0.0628954i | 1.26481 | − | 0.0162395i | ||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 1.85410 | − | 5.70634i | 0.449686 | − | 1.38399i | −0.427576 | − | 0.903979i | \(-0.640633\pi\) |
0.877262 | − | 0.480011i | \(-0.159367\pi\) | |||||||
\(18\) | 2.47152 | + | 1.70046i | 0.582544 | + | 0.400802i | ||||
\(19\) | 2.49376 | − | 3.43237i | 0.572108 | − | 0.787439i | −0.420694 | − | 0.907202i | \(-0.638214\pi\) |
0.992802 | + | 0.119763i | \(0.0382135\pi\) | |||||||
\(20\) | −2.68999 | + | 0.874032i | −0.601501 | + | 0.195440i | ||||
\(21\) | 2.00000 | + | 1.41421i | 0.436436 | + | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −4.96204 | − | 1.54212i | −1.01287 | − | 0.314784i | ||||
\(25\) | 2.42705 | + | 1.76336i | 0.485410 | + | 0.352671i | ||||
\(26\) | 2.49376 | + | 3.43237i | 0.489067 | + | 0.673143i | ||||
\(27\) | −2.89008 | + | 4.31827i | −0.556197 | + | 0.831051i | ||||
\(28\) | −1.34500 | − | 0.437016i | −0.254181 | − | 0.0825883i | ||||
\(29\) | 1.61803 | − | 1.17557i | 0.300461 | − | 0.218298i | −0.427331 | − | 0.904095i | \(-0.640546\pi\) |
0.727793 | + | 0.685797i | \(0.240546\pi\) | |||||||
\(30\) | 1.57356 | + | 4.63939i | 0.287291 | + | 0.847032i | ||||
\(31\) | −0.618034 | − | 1.90211i | −0.111002 | − | 0.341630i | 0.880090 | − | 0.474807i | \(-0.157482\pi\) |
−0.991092 | + | 0.133177i | \(0.957482\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 1.23607 | + | 3.80423i | 0.208934 | + | 0.643032i | ||||
\(36\) | 0.853491 | − | 2.87603i | 0.142248 | − | 0.479338i | ||||
\(37\) | −6.47214 | + | 4.70228i | −1.06401 | + | 0.773050i | −0.974827 | − | 0.222965i | \(-0.928427\pi\) |
−0.0891861 | + | 0.996015i | \(0.528427\pi\) | |||||||
\(38\) | 4.03499 | + | 1.31105i | 0.654562 | + | 0.212680i | ||||
\(39\) | −5.88909 | + | 4.39529i | −0.943010 | + | 0.703810i | ||||
\(40\) | −4.98752 | − | 6.86474i | −0.788597 | − | 1.08541i | ||||
\(41\) | −4.85410 | − | 3.52671i | −0.758083 | − | 0.550780i | 0.140238 | − | 0.990118i | \(-0.455213\pi\) |
−0.898322 | + | 0.439338i | \(0.855213\pi\) | |||||||
\(42\) | −0.726963 | + | 2.33913i | −0.112173 | + | 0.360935i | ||||
\(43\) | 4.24264i | 0.646997i | 0.946229 | + | 0.323498i | \(0.104859\pi\) | ||||
−0.946229 | + | 0.323498i | \(0.895141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.00000 | + | 2.82843i | −1.19257 | + | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.66251 | + | 2.28825i | −0.242502 | + | 0.333775i | −0.912868 | − | 0.408256i | \(-0.866137\pi\) |
0.670366 | + | 0.742031i | \(0.266137\pi\) | |||||||
\(48\) | −0.0222369 | − | 1.73191i | −0.00320962 | − | 0.249979i | ||||
\(49\) | 1.54508 | − | 4.75528i | 0.220726 | − | 0.679326i | ||||
\(50\) | −0.927051 | + | 2.85317i | −0.131105 | + | 0.403499i | ||||
\(51\) | 0.133421 | + | 10.3914i | 0.0186827 | + | 1.45509i | ||||
\(52\) | 2.49376 | − | 3.43237i | 0.345823 | − | 0.475984i | ||||
\(53\) | 5.37999 | − | 1.74806i | 0.738998 | − | 0.240115i | 0.0847577 | − | 0.996402i | \(-0.472988\pi\) |
0.654241 | + | 0.756287i | \(0.272988\pi\) | |||||||
\(54\) | −5.00000 | − | 1.41421i | −0.680414 | − | 0.192450i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 4.24264i | − | 0.566947i | ||||||
\(57\) | −2.18089 | + | 7.01739i | −0.288866 | + | 0.929476i | ||||
\(58\) | 1.61803 | + | 1.17557i | 0.212458 | + | 0.154360i | ||||
\(59\) | −6.65003 | − | 9.15298i | −0.865760 | − | 1.19162i | −0.980165 | − | 0.198183i | \(-0.936496\pi\) |
0.114405 | − | 0.993434i | \(-0.463504\pi\) | |||||||
\(60\) | 3.92606 | − | 2.93019i | 0.506852 | − | 0.378286i | ||||
\(61\) | 9.41498 | + | 3.05911i | 1.20546 | + | 0.391679i | 0.841769 | − | 0.539839i | \(-0.181515\pi\) |
0.363696 | + | 0.931518i | \(0.381515\pi\) | |||||||
\(62\) | 1.61803 | − | 1.17557i | 0.205491 | − | 0.149298i | ||||
\(63\) | −4.06732 | − | 1.20702i | −0.512434 | − | 0.152070i | ||||
\(64\) | 2.16312 | + | 6.65740i | 0.270390 | + | 0.832174i | ||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | −1.85410 | − | 5.70634i | −0.224843 | − | 0.691995i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.23607 | + | 2.35114i | −0.386784 | + | 0.281015i | ||||
\(71\) | −2.68999 | − | 0.874032i | −0.319244 | − | 0.103729i | 0.145012 | − | 0.989430i | \(-0.453678\pi\) |
−0.464255 | + | 0.885701i | \(0.653678\pi\) | |||||||
\(72\) | 8.99703 | − | 0.231073i | 1.06031 | − | 0.0272323i | ||||
\(73\) | −0.831254 | − | 1.14412i | −0.0972909 | − | 0.133909i | 0.757596 | − | 0.652724i | \(-0.226374\pi\) |
−0.854887 | + | 0.518814i | \(0.826374\pi\) | |||||||
\(74\) | −6.47214 | − | 4.70228i | −0.752371 | − | 0.546629i | ||||
\(75\) | −4.96204 | − | 1.54212i | −0.572967 | − | 0.178069i | ||||
\(76\) | − | 4.24264i | − | 0.486664i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | − | 4.24264i | −0.679366 | − | 0.480384i | ||||
\(79\) | 4.03499 | − | 1.31105i | 0.453972 | − | 0.147504i | −0.0731009 | − | 0.997325i | \(-0.523290\pi\) |
0.527073 | + | 0.849820i | \(0.323290\pi\) | |||||||
\(80\) | 1.66251 | − | 2.28825i | 0.185874 | − | 0.255834i | ||||
\(81\) | 2.33810 | − | 8.69099i | 0.259789 | − | 0.965665i | ||||
\(82\) | 1.85410 | − | 5.70634i | 0.204751 | − | 0.630160i | ||||
\(83\) | −4.94427 | + | 15.2169i | −0.542704 | + | 1.67027i | 0.183682 | + | 0.982986i | \(0.441198\pi\) |
−0.726386 | + | 0.687287i | \(0.758802\pi\) | |||||||
\(84\) | 2.44929 | − | 0.0314477i | 0.267239 | − | 0.00343123i | ||||
\(85\) | −9.97505 | + | 13.7295i | −1.08195 | + | 1.48917i | ||||
\(86\) | −4.03499 | + | 1.31105i | −0.435104 | + | 0.141374i | ||||
\(87\) | −2.00000 | + | 2.82843i | −0.214423 | + | 0.303239i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −5.16213 | − | 6.73442i | −0.544136 | − | 0.709870i | ||||
\(91\) | −4.85410 | − | 3.52671i | −0.508848 | − | 0.369700i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.07196 | + | 2.77615i | 0.214852 | + | 0.287873i | ||||
\(94\) | −2.68999 | − | 0.874032i | −0.277452 | − | 0.0901495i | ||||
\(95\) | −9.70820 | + | 7.05342i | −0.996041 | + | 0.723666i | ||||
\(96\) | −8.20135 | + | 2.78169i | −0.837047 | + | 0.283905i | ||||
\(97\) | −0.618034 | − | 1.90211i | −0.0627518 | − | 0.193130i | 0.914766 | − | 0.403985i | \(-0.132375\pi\) |
−0.977517 | + | 0.210855i | \(0.932375\pi\) | |||||||
\(98\) | 5.00000 | 0.505076 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | −3.09017 | − | 9.51057i | −0.307483 | − | 0.946337i | −0.978739 | − | 0.205110i | \(-0.934245\pi\) |
0.671255 | − | 0.741226i | \(-0.265755\pi\) | |||||||
\(102\) | −9.84163 | + | 3.33803i | −0.974466 | + | 0.330514i | ||||
\(103\) | −6.47214 | + | 4.70228i | −0.637719 | + | 0.463330i | −0.859066 | − | 0.511865i | \(-0.828955\pi\) |
0.221347 | + | 0.975195i | \(0.428955\pi\) | |||||||
\(104\) | 12.1050 | + | 3.93314i | 1.18699 | + | 0.385677i | ||||
\(105\) | −4.14392 | − | 5.55229i | −0.404405 | − | 0.541848i | ||||
\(106\) | 3.32502 | + | 4.57649i | 0.322954 | + | 0.444508i | ||||
\(107\) | 12.9443 | + | 9.40456i | 1.25137 | + | 0.909174i | 0.998301 | − | 0.0582746i | \(-0.0185599\pi\) |
0.253069 | + | 0.967448i | \(0.418560\pi\) | |||||||
\(108\) | 0.200088 | + | 5.19230i | 0.0192535 | + | 0.499629i | ||||
\(109\) | 4.24264i | 0.406371i | 0.979140 | + | 0.203186i | \(0.0651295\pi\) | ||||
−0.979140 | + | 0.203186i | \(0.934871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | − | 11.3137i | 0.759326 | − | 1.07385i | ||||
\(112\) | 1.34500 | − | 0.437016i | 0.127090 | − | 0.0412941i | ||||
\(113\) | −1.66251 | + | 2.28825i | −0.156396 | + | 0.215260i | −0.880023 | − | 0.474930i | \(-0.842473\pi\) |
0.723628 | + | 0.690190i | \(0.242473\pi\) | |||||||
\(114\) | −7.34786 | + | 0.0943431i | −0.688190 | + | 0.00883604i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.618034 | − | 1.90211i | 0.0573830 | − | 0.176607i | ||||
\(117\) | 7.21444 | − | 10.4858i | 0.666975 | − | 0.969412i | ||||
\(118\) | 6.65003 | − | 9.15298i | 0.612185 | − | 0.842600i | ||||
\(119\) | −8.06998 | + | 2.62210i | −0.739774 | + | 0.240367i | ||||
\(120\) | 12.0000 | + | 8.48528i | 1.09545 | + | 0.774597i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.89949i | 0.896258i | ||||||||
\(123\) | 9.92408 | + | 3.08424i | 0.894825 | + | 0.278097i | ||||
\(124\) | −1.61803 | − | 1.17557i | −0.145304 | − | 0.105569i | ||||
\(125\) | 3.32502 | + | 4.57649i | 0.297398 | + | 0.409334i | ||||
\(126\) | −0.108929 | − | 4.24124i | −0.00970417 | − | 0.377840i | ||||
\(127\) | 9.41498 | + | 3.05911i | 0.835444 | + | 0.271452i | 0.695337 | − | 0.718684i | \(-0.255255\pi\) |
0.140107 | + | 0.990136i | \(0.455255\pi\) | |||||||
\(128\) | 2.42705 | − | 1.76336i | 0.214523 | − | 0.155860i | ||||
\(129\) | −2.36034 | − | 6.95908i | −0.207816 | − | 0.612713i | ||||
\(130\) | −3.70820 | − | 11.4127i | −0.325231 | − | 1.00096i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | −0.520266 | ||||||||
\(134\) | 0.618034 | + | 1.90211i | 0.0533900 | + | 0.164318i | ||||
\(135\) | 11.5486 | − | 9.09009i | 0.993946 | − | 0.782350i | ||||
\(136\) | 14.5623 | − | 10.5801i | 1.24871 | − | 0.907239i | ||||
\(137\) | −2.68999 | − | 0.874032i | −0.229822 | − | 0.0746736i | 0.191842 | − | 0.981426i | \(-0.438554\pi\) |
−0.421664 | + | 0.906752i | \(0.638554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.831254 | − | 1.14412i | −0.0705060 | − | 0.0970432i | 0.772308 | − | 0.635249i | \(-0.219102\pi\) |
−0.842814 | + | 0.538206i | \(0.819102\pi\) | |||||||
\(140\) | 3.23607 | + | 2.35114i | 0.273498 | + | 0.198708i | ||||
\(141\) | 1.45393 | − | 4.67826i | 0.122443 | − | 0.393980i | ||||
\(142\) | − | 2.82843i | − | 0.237356i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | + | 2.82843i | 0.0833333 | + | 0.235702i | ||||
\(145\) | −5.37999 | + | 1.74806i | −0.446784 | + | 0.145169i | ||||
\(146\) | 0.831254 | − | 1.14412i | 0.0687951 | − | 0.0946883i | ||||
\(147\) | 0.111184 | + | 8.65954i | 0.00917034 | + | 0.714227i | ||||
\(148\) | −2.47214 | + | 7.60845i | −0.203208 | + | 0.625411i | ||||
\(149\) | 1.85410 | − | 5.70634i | 0.151894 | − | 0.467482i | −0.845939 | − | 0.533280i | \(-0.820959\pi\) |
0.997833 | + | 0.0657982i | \(0.0209593\pi\) | |||||||
\(150\) | −0.0667106 | − | 5.19572i | −0.00544690 | − | 0.424229i | ||||
\(151\) | 2.49376 | − | 3.43237i | 0.202939 | − | 0.279322i | −0.695401 | − | 0.718622i | \(-0.744773\pi\) |
0.898341 | + | 0.439300i | \(0.144773\pi\) | |||||||
\(152\) | 12.1050 | − | 3.93314i | 0.981843 | − | 0.319020i | ||||
\(153\) | −6.00000 | − | 16.9706i | −0.485071 | − | 1.37199i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.65685i | 0.454369i | ||||||||
\(156\) | −2.18089 | + | 7.01739i | −0.174611 | + | 0.561841i | ||||
\(157\) | 16.1803 | + | 11.7557i | 1.29133 | + | 0.938207i | 0.999831 | − | 0.0183633i | \(-0.00584556\pi\) |
0.291500 | + | 0.956571i | \(0.405846\pi\) | |||||||
\(158\) | 2.49376 | + | 3.43237i | 0.198393 | + | 0.273065i | ||||
\(159\) | −7.85212 | + | 5.86039i | −0.622714 | + | 0.464759i | ||||
\(160\) | −13.4500 | − | 4.37016i | −1.06331 | − | 0.345492i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.98813 | − | 0.461994i | 0.706175 | − | 0.0362977i | ||||
\(163\) | 6.18034 | + | 19.0211i | 0.484082 | + | 1.48985i | 0.833307 | + | 0.552811i | \(0.186445\pi\) |
−0.349225 | + | 0.937039i | \(0.613555\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.0000 | −1.24184 | ||||||||
\(167\) | 3.70820 | + | 11.4127i | 0.286949 | + | 0.883140i | 0.985808 | + | 0.167879i | \(0.0536919\pi\) |
−0.698858 | + | 0.715260i | \(0.746308\pi\) | |||||||
\(168\) | 2.36034 | + | 6.95908i | 0.182104 | + | 0.536905i | ||||
\(169\) | 4.04508 | − | 2.93893i | 0.311160 | − | 0.226071i | ||||
\(170\) | −16.1400 | − | 5.24419i | −1.23788 | − | 0.402211i | ||||
\(171\) | −0.326787 | − | 12.7237i | −0.0249900 | − | 0.973008i | ||||
\(172\) | 2.49376 | + | 3.43237i | 0.190148 | + | 0.261716i | ||||
\(173\) | −4.85410 | − | 3.52671i | −0.369051 | − | 0.268131i | 0.387767 | − | 0.921758i | \(-0.373247\pi\) |
−0.756817 | + | 0.653627i | \(0.773247\pi\) | |||||||
\(174\) | −3.30803 | − | 1.02808i | −0.250781 | − | 0.0779386i | ||||
\(175\) | − | 4.24264i | − | 0.320713i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000 | + | 11.3137i | 1.20263 | + | 0.850390i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.66251 | + | 2.28825i | −0.124262 | + | 0.171032i | −0.866615 | − | 0.498977i | \(-0.833709\pi\) |
0.742354 | + | 0.670008i | \(0.233709\pi\) | |||||||
\(180\) | −4.80963 | + | 6.99053i | −0.358489 | + | 0.521043i | ||||
\(181\) | −3.09017 | + | 9.51057i | −0.229691 | + | 0.706915i | 0.768091 | + | 0.640341i | \(0.221207\pi\) |
−0.997781 | + | 0.0665740i | \(0.978793\pi\) | |||||||
\(182\) | 1.85410 | − | 5.70634i | 0.137435 | − | 0.422982i | ||||
\(183\) | −17.1450 | + | 0.220134i | −1.26740 | + | 0.0162728i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.5200 | − | 6.99226i | 1.58218 | − | 0.514081i | ||||
\(186\) | −2.00000 | + | 2.82843i | −0.146647 | + | 0.207390i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.82843i | 0.206284i | ||||||||
\(189\) | 7.34302 | − | 0.282967i | 0.534126 | − | 0.0205828i | ||||
\(190\) | −9.70820 | − | 7.05342i | −0.704307 | − | 0.511709i | ||||
\(191\) | 11.6376 | + | 16.0177i | 0.842064 | + | 1.15900i | 0.985556 | + | 0.169350i | \(0.0541668\pi\) |
−0.143492 | + | 0.989651i | \(0.545833\pi\) | |||||||
\(192\) | −7.25186 | − | 9.71651i | −0.523358 | − | 0.701229i | ||||
\(193\) | −20.1750 | − | 6.55524i | −1.45223 | − | 0.471857i | −0.526540 | − | 0.850151i | \(-0.676511\pi\) |
−0.925685 | + | 0.378294i | \(0.876511\pi\) | |||||||
\(194\) | 1.61803 | − | 1.17557i | 0.116168 | − | 0.0844010i | ||||
\(195\) | 19.6833 | − | 6.67605i | 1.40955 | − | 0.478082i | ||||
\(196\) | −1.54508 | − | 4.75528i | −0.110363 | − | 0.339663i | ||||
\(197\) | 22.0000 | 1.56744 | 0.783718 | − | 0.621117i | \(-0.213321\pi\) | ||||
0.783718 | + | 0.621117i | \(0.213321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 2.78115 | + | 8.55951i | 0.196657 | + | 0.605249i | ||||
\(201\) | −3.28054 | + | 1.11268i | −0.231392 | + | 0.0784821i | ||||
\(202\) | 8.09017 | − | 5.87785i | 0.569222 | − | 0.413564i | ||||
\(203\) | −2.68999 | − | 0.874032i | −0.188801 | − | 0.0613450i | ||||
\(204\) | 6.21588 | + | 8.32844i | 0.435199 | + | 0.583107i | ||||
\(205\) | 9.97505 | + | 13.7295i | 0.696687 | + | 0.958908i | ||||
\(206\) | −6.47214 | − | 4.70228i | −0.450935 | − | 0.327624i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.24264i | 0.294174i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.00000 | − | 5.65685i | 0.276026 | − | 0.390360i | ||||
\(211\) | −25.5549 | + | 8.30330i | −1.75927 | + | 0.571623i | −0.997125 | − | 0.0757773i | \(-0.975856\pi\) |
−0.762150 | + | 0.647400i | \(0.775856\pi\) | |||||||
\(212\) | 3.32502 | − | 4.57649i | 0.228363 | − | 0.314315i | ||||
\(213\) | 4.89858 | − | 0.0628954i | 0.335645 | − | 0.00430952i | ||||
\(214\) | −4.94427 | + | 15.2169i | −0.337983 | + | 1.04021i | ||||
\(215\) | 3.70820 | − | 11.4127i | 0.252897 | − | 0.778338i | ||||
\(216\) | −14.6290 | + | 5.38441i | −0.995378 | + | 0.366363i | ||||
\(217\) | −1.66251 | + | 2.28825i | −0.112858 | + | 0.155336i | ||||
\(218\) | −4.03499 | + | 1.31105i | −0.273284 | + | 0.0887954i | ||||
\(219\) | 2.00000 | + | 1.41421i | 0.135147 | + | 0.0955637i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 25.4558i | − | 1.71235i | ||||||
\(222\) | 13.2321 | + | 4.11232i | 0.888081 | + | 0.276001i | ||||
\(223\) | −19.4164 | − | 14.1068i | −1.30022 | − | 0.944664i | −0.300261 | − | 0.953857i | \(-0.597074\pi\) |
−0.999958 | + | 0.00919277i | \(0.997074\pi\) | |||||||
\(224\) | −4.15627 | − | 5.72061i | −0.277702 | − | 0.382225i | ||||
\(225\) | 8.99703 | − | 0.231073i | 0.599802 | − | 0.0154049i | ||||
\(226\) | −2.68999 | − | 0.874032i | −0.178936 | − | 0.0581397i | ||||
\(227\) | 19.4164 | − | 14.1068i | 1.28871 | − | 0.936304i | 0.288934 | − | 0.957349i | \(-0.406699\pi\) |
0.999779 | + | 0.0210448i | \(0.00669928\pi\) | |||||||
\(228\) | 2.36034 | + | 6.95908i | 0.156317 | + | 0.460876i | ||||
\(229\) | −7.41641 | − | 22.8254i | −0.490090 | − | 1.50834i | −0.824471 | − | 0.565904i | \(-0.808527\pi\) |
0.334381 | − | 0.942438i | \(-0.391473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | −3.09017 | − | 9.51057i | −0.202444 | − | 0.623058i | −0.999809 | − | 0.0195604i | \(-0.993773\pi\) |
0.797365 | − | 0.603497i | \(-0.206227\pi\) | |||||||
\(234\) | 12.2020 | + | 3.62105i | 0.797667 | + | 0.236716i | ||||
\(235\) | 6.47214 | − | 4.70228i | 0.422196 | − | 0.306743i | ||||
\(236\) | −10.7600 | − | 3.49613i | −0.700415 | − | 0.227579i | ||||
\(237\) | −5.88909 | + | 4.39529i | −0.382538 | + | 0.285505i | ||||
\(238\) | −4.98752 | − | 6.86474i | −0.323293 | − | 0.444975i | ||||
\(239\) | 12.9443 | + | 9.40456i | 0.837295 | + | 0.608331i | 0.921614 | − | 0.388108i | \(-0.126871\pi\) |
−0.0843185 | + | 0.996439i | \(0.526871\pi\) | |||||||
\(240\) | −1.45393 | + | 4.67826i | −0.0938505 | + | 0.301980i | ||||
\(241\) | 4.24264i | 0.273293i | 0.990620 | + | 0.136646i | \(0.0436324\pi\) | ||||
−0.990620 | + | 0.136646i | \(0.956368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 9.41498 | − | 3.05911i | 0.602732 | − | 0.195840i | ||||
\(245\) | −8.31254 | + | 11.4412i | −0.531069 | + | 0.730953i | ||||
\(246\) | 0.133421 | + | 10.3914i | 0.00850663 | + | 0.662535i | ||||
\(247\) | 5.56231 | − | 17.1190i | 0.353921 | − | 1.08926i | ||||
\(248\) | 1.85410 | − | 5.70634i | 0.117736 | − | 0.362353i | ||||
\(249\) | −0.355790 | − | 27.7105i | −0.0225473 | − | 1.75608i | ||||
\(250\) | −3.32502 | + | 4.57649i | −0.210292 | + | 0.289443i | ||||
\(251\) | −24.2099 | + | 7.86629i | −1.52812 | + | 0.496516i | −0.948069 | − | 0.318065i | \(-0.896967\pi\) |
−0.580050 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(252\) | −4.00000 | + | 1.41421i | −0.251976 | + | 0.0890871i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 9.89949i | 0.621150i | ||||||||
\(255\) | 8.72356 | − | 28.0695i | 0.546290 | − | 1.75778i | ||||
\(256\) | 13.7533 | + | 9.99235i | 0.859581 | + | 0.624522i | ||||
\(257\) | −6.65003 | − | 9.15298i | −0.414818 | − | 0.570947i | 0.549568 | − | 0.835449i | \(-0.314792\pi\) |
−0.964385 | + | 0.264502i | \(0.914792\pi\) | |||||||
\(258\) | 5.88909 | − | 4.39529i | 0.366639 | − | 0.273639i | ||||
\(259\) | 10.7600 | + | 3.49613i | 0.668592 | + | 0.217239i | ||||
\(260\) | −9.70820 | + | 7.05342i | −0.602077 | + | 0.437435i | ||||
\(261\) | 1.70698 | − | 5.75206i | 0.105660 | − | 0.356044i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0000 | −0.982872 | ||||||||
\(266\) | −1.85410 | − | 5.70634i | −0.113682 | − | 0.349878i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.61803 | − | 1.17557i | 0.0988372 | − | 0.0718094i | ||||
\(269\) | 26.8999 | + | 8.74032i | 1.64012 | + | 0.532907i | 0.976565 | − | 0.215222i | \(-0.0690476\pi\) |
0.663553 | + | 0.748129i | \(0.269048\pi\) | |||||||
\(270\) | 12.2139 | + | 8.17439i | 0.743314 | + | 0.497477i | ||||
\(271\) | 17.4563 | + | 24.0266i | 1.06040 | + | 1.45951i | 0.879434 | + | 0.476021i | \(0.157921\pi\) |
0.180963 | + | 0.983490i | \(0.442079\pi\) | |||||||
\(272\) | 4.85410 | + | 3.52671i | 0.294323 | + | 0.213838i | ||||
\(273\) | 9.92408 | + | 3.08424i | 0.600633 | + | 0.186667i | ||||
\(274\) | − | 2.82843i | − | 0.170872i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.03499 | − | 1.31105i | 0.242439 | − | 0.0787732i | −0.185277 | − | 0.982686i | \(-0.559318\pi\) |
0.427716 | + | 0.903913i | \(0.359318\pi\) | |||||||
\(278\) | 0.831254 | − | 1.14412i | 0.0498553 | − | 0.0686199i | ||||
\(279\) | −4.94305 | − | 3.40092i | −0.295933 | − | 0.203608i | ||||
\(280\) | −3.70820 | + | 11.4127i | −0.221608 | + | 0.682038i | ||||
\(281\) | 1.85410 | − | 5.70634i | 0.110606 | − | 0.340412i | −0.880399 | − | 0.474234i | \(-0.842725\pi\) |
0.991005 | + | 0.133822i | \(0.0427251\pi\) | |||||||
\(282\) | 4.89858 | − | 0.0628954i | 0.291706 | − | 0.00374537i | ||||
\(283\) | −15.7938 | + | 21.7383i | −0.938845 | + | 1.29221i | 0.0174623 | + | 0.999848i | \(0.494441\pi\) |
−0.956308 | + | 0.292362i | \(0.905559\pi\) | |||||||
\(284\) | −2.68999 | + | 0.874032i | −0.159622 | + | 0.0518643i | ||||
\(285\) | 12.0000 | − | 16.9706i | 0.710819 | − | 1.00525i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.48528i | 0.500870i | ||||||||
\(288\) | 11.9049 | − | 9.12544i | 0.701502 | − | 0.537722i | ||||
\(289\) | −15.3713 | − | 11.1679i | −0.904195 | − | 0.656936i | ||||
\(290\) | −3.32502 | − | 4.57649i | −0.195252 | − | 0.268741i | ||||
\(291\) | 2.07196 | + | 2.77615i | 0.121460 | + | 0.162741i | ||||
\(292\) | −1.34500 | − | 0.437016i | −0.0787100 | − | 0.0255744i | ||||
\(293\) | 1.61803 | − | 1.17557i | 0.0945266 | − | 0.0686776i | −0.539518 | − | 0.841974i | \(-0.681394\pi\) |
0.634045 | + | 0.773296i | \(0.281394\pi\) | |||||||
\(294\) | −8.20135 | + | 2.78169i | −0.478313 | + | 0.162231i | ||||
\(295\) | 9.88854 | + | 30.4338i | 0.575733 | + | 1.77192i | ||||
\(296\) | −24.0000 | −1.39497 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.92081 | + | 1.66901i | −0.284103 | + | 0.0963605i | ||||
\(301\) | 4.85410 | − | 3.52671i | 0.279786 | − | 0.203276i | ||||
\(302\) | 4.03499 | + | 1.31105i | 0.232188 | + | 0.0754423i | ||||
\(303\) | 10.3598 | + | 13.8807i | 0.595155 | + | 0.797427i | ||||
\(304\) | 2.49376 | + | 3.43237i | 0.143027 | + | 0.196860i | ||||
\(305\) | −22.6525 | − | 16.4580i | −1.29708 | − | 0.942382i | ||||
\(306\) | 14.2859 | − | 10.9505i | 0.816668 | − | 0.626000i | ||||
\(307\) | 4.24264i | 0.242140i | 0.992644 | + | 0.121070i | \(0.0386326\pi\) | ||||
−0.992644 | + | 0.121070i | \(0.961367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | − | 11.3137i | 0.455104 | − | 0.643614i | ||||
\(310\) | −5.37999 | + | 1.74806i | −0.305563 | + | 0.0992834i | ||||
\(311\) | 16.6251 | − | 22.8825i | 0.942722 | − | 1.29755i | −0.0119638 | − | 0.999928i | \(-0.503808\pi\) |
0.954685 | − | 0.297617i | \(-0.0961917\pi\) | |||||||
\(312\) | −22.0436 | + | 0.283029i | −1.24797 | + | 0.0160234i | ||||
\(313\) | 3.70820 | − | 11.4127i | 0.209600 | − | 0.645083i | −0.789893 | − | 0.613245i | \(-0.789864\pi\) |
0.999493 | − | 0.0318380i | \(-0.0101361\pi\) | |||||||
\(314\) | −6.18034 | + | 19.0211i | −0.348777 | + | 1.07342i | ||||
\(315\) | 9.88610 | + | 6.80184i | 0.557019 | + | 0.383240i | ||||
\(316\) | 2.49376 | − | 3.43237i | 0.140285 | − | 0.193086i | ||||
\(317\) | −24.2099 | + | 7.86629i | −1.35977 | + | 0.441815i | −0.895965 | − | 0.444125i | \(-0.853515\pi\) |
−0.463801 | + | 0.885939i | \(0.653515\pi\) | |||||||
\(318\) | −8.00000 | − | 5.65685i | −0.448618 | − | 0.317221i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 19.7990i | − | 1.10680i | ||||||
\(321\) | −26.4642 | − | 8.22465i | −1.47709 | − | 0.459055i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.9626 | − | 20.5942i | −0.832540 | − | 1.14589i | ||||
\(324\) | −3.21687 | − | 8.40546i | −0.178715 | − | 0.466970i | ||||
\(325\) | 12.1050 | + | 3.93314i | 0.671463 | + | 0.218172i | ||||
\(326\) | −16.1803 | + | 11.7557i | −0.896146 | + | 0.651088i | ||||
\(327\) | −2.36034 | − | 6.95908i | −0.130527 | − | 0.384838i | ||||
\(328\) | −5.56231 | − | 17.1190i | −0.307127 | − | 0.945240i | ||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | 4.94427 | + | 15.2169i | 0.271352 | + | 0.835136i | ||||
\(333\) | −6.82793 | + | 23.0082i | −0.374168 | + | 1.26084i | ||||
\(334\) | −9.70820 | + | 7.05342i | −0.531209 | + | 0.385946i | ||||
\(335\) | −5.37999 | − | 1.74806i | −0.293940 | − | 0.0955069i | ||||
\(336\) | −1.96303 | + | 1.46510i | −0.107092 | + | 0.0799276i | ||||
\(337\) | −19.1188 | − | 26.3148i | −1.04147 | − | 1.43346i | −0.895977 | − | 0.444100i | \(-0.853523\pi\) |
−0.145493 | − | 0.989359i | \(-0.546477\pi\) | |||||||
\(338\) | 4.04508 | + | 2.93893i | 0.220024 | + | 0.159857i | ||||
\(339\) | 1.45393 | − | 4.67826i | 0.0789664 | − | 0.254088i | ||||
\(340\) | 16.9706i | 0.920358i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.0000 | − | 4.24264i | 0.648886 | − | 0.229416i | ||||
\(343\) | −16.1400 | + | 5.24419i | −0.871476 | + | 0.283160i | ||||
\(344\) | −7.48128 | + | 10.2971i | −0.403364 | + | 0.555183i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.85410 | − | 5.70634i | 0.0996771 | − | 0.306775i | ||||
\(347\) | −4.94427 | + | 15.2169i | −0.265422 | + | 0.816886i | 0.726173 | + | 0.687512i | \(0.241297\pi\) |
−0.991596 | + | 0.129375i | \(0.958703\pi\) | |||||||
\(348\) | 0.0444738 | + | 3.46382i | 0.00238404 | + | 0.185680i | ||||
\(349\) | 2.49376 | − | 3.43237i | 0.133488 | − | 0.183730i | −0.737040 | − | 0.675849i | \(-0.763777\pi\) |
0.870528 | + | 0.492118i | \(0.163777\pi\) | |||||||
\(350\) | 4.03499 | − | 1.31105i | 0.215679 | − | 0.0700785i | ||||
\(351\) | −6.00000 | + | 21.2132i | −0.320256 | + | 1.13228i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | −5.81570 | + | 18.7130i | −0.309101 | + | 0.994586i | ||||
\(355\) | 6.47214 | + | 4.70228i | 0.343505 | + | 0.249571i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.7782 | − | 8.79058i | 0.623368 | − | 0.465247i | ||||
\(358\) | −2.68999 | − | 0.874032i | −0.142171 | − | 0.0461940i | ||||
\(359\) | −16.1803 | + | 11.7557i | −0.853966 | + | 0.620442i | −0.926237 | − | 0.376943i | \(-0.876975\pi\) |
0.0722709 | + | 0.997385i | \(0.476975\pi\) | |||||||
\(360\) | −24.4039 | − | 7.24211i | −1.28620 | − | 0.381693i | ||||
\(361\) | 0.309017 | + | 0.951057i | 0.0162641 | + | 0.0500556i | ||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.00000 | −0.314485 | ||||||||
\(365\) | 1.23607 | + | 3.80423i | 0.0646988 | + | 0.199122i | ||||
\(366\) | −5.50746 | − | 16.2379i | −0.287880 | − | 0.848766i | ||||
\(367\) | −6.47214 | + | 4.70228i | −0.337843 | + | 0.245457i | −0.743751 | − | 0.668457i | \(-0.766955\pi\) |
0.405908 | + | 0.913914i | \(0.366955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.9941 | + | 0.462147i | −0.936734 | + | 0.0240584i | ||||
\(370\) | 13.3001 | + | 18.3060i | 0.691437 | + | 0.951682i | ||||
\(371\) | −6.47214 | − | 4.70228i | −0.336017 | − | 0.244130i | ||||
\(372\) | 3.30803 | + | 1.02808i | 0.171513 | + | 0.0533035i | ||||
\(373\) | 4.24264i | 0.219676i | 0.993950 | + | 0.109838i | \(0.0350331\pi\) | ||||
−0.993950 | + | 0.109838i | \(0.964967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.00000 | − | 5.65685i | −0.413118 | − | 0.292119i | ||||
\(376\) | −8.06998 | + | 2.62210i | −0.416178 | + | 0.135224i | ||||
\(377\) | 4.98752 | − | 6.86474i | 0.256871 | − | 0.353552i | ||||
\(378\) | 2.53824 | + | 6.89618i | 0.130553 | + | 0.354701i | ||||
\(379\) | 3.70820 | − | 11.4127i | 0.190478 | − | 0.586230i | −0.809522 | − | 0.587090i | \(-0.800274\pi\) |
1.00000 | 0.000859657i | \(0.000273637\pi\) | ||||||||
\(380\) | −3.70820 | + | 11.4127i | −0.190227 | + | 0.585458i | ||||
\(381\) | −17.1450 | + | 0.220134i | −0.878366 | + | 0.0112778i | ||||
\(382\) | −11.6376 | + | 16.0177i | −0.595429 | + | 0.819538i | ||||
\(383\) | 5.37999 | − | 1.74806i | 0.274905 | − | 0.0893219i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.443225 | + | 0.896410i | \(0.353834\pi\) | |||||||
\(384\) | −3.00000 | + | 4.24264i | −0.153093 | + | 0.216506i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 21.2132i | − | 1.07972i | ||||||
\(387\) | 7.74320 | + | 10.1016i | 0.393609 | + | 0.513495i | ||||
\(388\) | −1.61803 | − | 1.17557i | −0.0821432 | − | 0.0596806i | ||||
\(389\) | 11.6376 | + | 16.0177i | 0.590047 | + | 0.812131i | 0.994752 | − | 0.102317i | \(-0.0326256\pi\) |
−0.404704 | + | 0.914448i | \(0.632626\pi\) | |||||||
\(390\) | 12.4318 | + | 16.6569i | 0.629507 | + | 0.843453i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 12.1353 | − | 8.81678i | 0.612923 | − | 0.445315i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.79837 | + | 20.9232i | 0.342497 | + | 1.05410i | ||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0.618034 | + | 1.90211i | 0.0309792 | + | 0.0953443i | ||||
\(399\) | 9.84163 | − | 3.33803i | 0.492698 | − | 0.167110i | ||||
\(400\) | −2.42705 | + | 1.76336i | −0.121353 | + | 0.0881678i | ||||
\(401\) | −2.68999 | − | 0.874032i | −0.134332 | − | 0.0436471i | 0.241079 | − | 0.970505i | \(-0.422499\pi\) |
−0.375411 | + | 0.926858i | \(0.622499\pi\) | |||||||
\(402\) | −2.07196 | − | 2.77615i | −0.103340 | − | 0.138462i | ||||
\(403\) | −4.98752 | − | 6.86474i | −0.248446 | − | 0.341957i | ||||
\(404\) | −8.09017 | − | 5.87785i | −0.402501 | − | 0.292434i | ||||
\(405\) | −13.8857 | + | 21.3351i | −0.689985 | + | 1.06015i | ||||
\(406\) | − | 2.82843i | − | 0.140372i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.0000 | + | 25.4558i | −0.891133 | + | 1.26025i | ||||
\(409\) | 4.03499 | − | 1.31105i | 0.199517 | − | 0.0648272i | −0.207554 | − | 0.978224i | \(-0.566550\pi\) |
0.407071 | + | 0.913396i | \(0.366550\pi\) | |||||||
\(410\) | −9.97505 | + | 13.7295i | −0.492632 | + | 0.678050i | ||||
\(411\) | 4.89858 | − | 0.0628954i | 0.241629 | − | 0.00310240i | ||||
\(412\) | −2.47214 | + | 7.60845i | −0.121793 | + | 0.374842i | ||||
\(413\) | −4.94427 | + | 15.2169i | −0.243292 | + | 0.748775i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.6001 | − | 36.6119i | 1.30575 | − | 1.79721i | ||||
\(416\) | 20.1750 | − | 6.55524i | 0.989159 | − | 0.321397i | ||||
\(417\) | 2.00000 | + | 1.41421i | 0.0979404 | + | 0.0692543i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1127i | 1.51995i | 0.649950 | + | 0.759977i | \(0.274790\pi\) | ||||
−0.649950 | + | 0.759977i | \(0.725210\pi\) | |||||||
\(420\) | −6.61606 | − | 2.05616i | −0.322830 | − | 0.100330i | ||||
\(421\) | 16.1803 | + | 11.7557i | 0.788582 | + | 0.572938i | 0.907542 | − | 0.419961i | \(-0.137956\pi\) |
−0.118961 | + | 0.992899i | \(0.537956\pi\) | |||||||
\(422\) | −15.7938 | − | 21.7383i | −0.768831 | − | 1.05821i | ||||
\(423\) | 0.217858 | + | 8.48248i | 0.0105926 | + | 0.412432i | ||||
\(424\) | 16.1400 | + | 5.24419i | 0.783826 | + | 0.254680i | ||||
\(425\) | 14.5623 | − | 10.5801i | 0.706376 | − | 0.513212i | ||||
\(426\) | 1.57356 | + | 4.63939i | 0.0762392 | + | 0.224779i | ||||
\(427\) | −4.32624 | − | 13.3148i | −0.209361 | − | 0.644348i | ||||
\(428\) | 16.0000 | 0.773389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | 0.578691 | ||||||||
\(431\) | −9.88854 | − | 30.4338i | −0.476314 | − | 1.46594i | −0.844177 | − | 0.536065i | \(-0.819910\pi\) |
0.367862 | − | 0.929880i | \(-0.380090\pi\) | |||||||
\(432\) | −3.21383 | − | 4.08305i | −0.154626 | − | 0.196446i | ||||
\(433\) | −24.2705 | + | 17.6336i | −1.16637 | + | 0.847415i | −0.990569 | − | 0.137012i | \(-0.956250\pi\) |
−0.175797 | + | 0.984426i | \(0.556250\pi\) | |||||||
\(434\) | −2.68999 | − | 0.874032i | −0.129124 | − | 0.0419549i | ||||
\(435\) | 7.85212 | − | 5.86039i | 0.376481 | − | 0.280984i | ||||
\(436\) | 2.49376 | + | 3.43237i | 0.119430 | + | 0.164381i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.726963 | + | 2.33913i | −0.0347356 | + | 0.111768i | ||||
\(439\) | − | 26.8701i | − | 1.28244i | −0.767358 | − | 0.641219i | \(-0.778429\pi\) | ||
0.767358 | − | 0.641219i | \(-0.221571\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | − | 14.1421i | −0.238095 | − | 0.673435i | ||||
\(442\) | 24.2099 | − | 7.86629i | 1.15155 | − | 0.374161i | ||||
\(443\) | 16.6251 | − | 22.8825i | 0.789881 | − | 1.08718i | −0.204242 | − | 0.978921i | \(-0.565473\pi\) |
0.994123 | − | 0.108258i | \(-0.0345272\pi\) | |||||||
\(444\) | −0.177895 | − | 13.8553i | −0.00844253 | − | 0.657542i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.41641 | − | 22.8254i | 0.351177 | − | 1.08081i | ||||
\(447\) | 0.133421 | + | 10.3914i | 0.00631061 | + | 0.491499i | ||||
\(448\) | 5.81878 | − | 8.00886i | 0.274911 | − | 0.378383i | ||||
\(449\) | 5.37999 | − | 1.74806i | 0.253897 | − | 0.0824962i | −0.179303 | − | 0.983794i | \(-0.557384\pi\) |
0.433200 | + | 0.901298i | \(0.357384\pi\) | |||||||
\(450\) | 3.00000 | + | 8.48528i | 0.141421 | + | 0.400000i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.82843i | 0.133038i | ||||||||
\(453\) | −2.18089 | + | 7.01739i | −0.102467 | + | 0.329706i | ||||
\(454\) | 19.4164 | + | 14.1068i | 0.911257 | + | 0.662067i | ||||
\(455\) | 9.97505 | + | 13.7295i | 0.467637 | + | 0.643648i | ||||
\(456\) | −17.6673 | + | 13.1859i | −0.827346 | + | 0.617485i | ||||
\(457\) | 9.41498 | + | 3.05911i | 0.440414 | + | 0.143099i | 0.520827 | − | 0.853662i | \(-0.325624\pi\) |
−0.0804125 | + | 0.996762i | \(0.525624\pi\) | |||||||
\(458\) | 19.4164 | − | 14.1068i | 0.907269 | − | 0.659170i | ||||
\(459\) | 19.2830 | + | 24.4983i | 0.900053 | + | 1.14348i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0000 | 1.02464 | 0.512321 | − | 0.858794i | \(-0.328786\pi\) | ||||
0.512321 | + | 0.858794i | \(0.328786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(464\) | 0.618034 | + | 1.90211i | 0.0286915 | + | 0.0883034i | ||||
\(465\) | −3.14712 | − | 9.27877i | −0.145944 | − | 0.430293i | ||||
\(466\) | 8.09017 | − | 5.87785i | 0.374770 | − | 0.272286i | ||||
\(467\) | 26.8999 | + | 8.74032i | 1.24478 | + | 0.404454i | 0.856048 | − | 0.516897i | \(-0.172913\pi\) |
0.388733 | + | 0.921350i | \(0.372913\pi\) | |||||||
\(468\) | −0.326787 | − | 12.7237i | −0.0151057 | − | 0.588154i | ||||
\(469\) | −1.66251 | − | 2.28825i | −0.0767675 | − | 0.105661i | ||||
\(470\) | 6.47214 | + | 4.70228i | 0.298537 | + | 0.216900i | ||||
\(471\) | −33.0803 | − | 10.2808i | −1.52426 | − | 0.473715i | ||||
\(472\) | − | 33.9411i | − | 1.56227i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.00000 | − | 4.24264i | −0.275589 | − | 0.194871i | ||||
\(475\) | 12.1050 | − | 3.93314i | 0.555414 | − | 0.180465i | ||||
\(476\) | −4.98752 | + | 6.86474i | −0.228603 | + | 0.314645i | ||||
\(477\) | 9.61926 | − | 13.9811i | 0.440435 | − | 0.640149i | ||||
\(478\) | −4.94427 | + | 15.2169i | −0.226146 | + | 0.696005i | ||||
\(479\) | 8.65248 | − | 26.6296i | 0.395342 | − | 1.21674i | −0.533353 | − | 0.845893i | \(-0.679068\pi\) |
0.928695 | − | 0.370844i | \(-0.120932\pi\) | |||||||
\(480\) | 24.4929 | − | 0.314477i | 1.11794 | − | 0.0143538i | ||||
\(481\) | −19.9501 | + | 27.4589i | −0.909646 | + | 1.25202i | ||||
\(482\) | −4.03499 | + | 1.31105i | −0.183789 | + | 0.0597166i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.65685i | 0.256865i | ||||||||
\(486\) | −14.4860 | + | 5.75823i | −0.657096 | + | 0.261199i | ||||
\(487\) | −1.61803 | − | 1.17557i | −0.0733201 | − | 0.0532702i | 0.550521 | − | 0.834821i | \(-0.314429\pi\) |
−0.623842 | + | 0.781551i | \(0.714429\pi\) | |||||||
\(488\) | 17.4563 | + | 24.0266i | 0.790211 | + | 1.08763i | ||||
\(489\) | −20.7196 | − | 27.7615i | −0.936973 | − | 1.25542i | ||||
\(490\) | −13.4500 | − | 4.37016i | −0.607608 | − | 0.197424i | ||||
\(491\) | −16.1803 | + | 11.7557i | −0.730209 | + | 0.530528i | −0.889629 | − | 0.456683i | \(-0.849037\pi\) |
0.159421 | + | 0.987211i | \(0.449037\pi\) | |||||||
\(492\) | 9.84163 | − | 3.33803i | 0.443695 | − | 0.150490i | ||||
\(493\) | −3.70820 | − | 11.4127i | −0.167009 | − | 0.514001i | ||||
\(494\) | 18.0000 | 0.809858 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 1.23607 | + | 3.80423i | 0.0554452 | + | 0.170643i | ||||
\(498\) | 26.2443 | − | 8.90140i | 1.17604 | − | 0.398881i | ||||
\(499\) | 11.3262 | − | 8.22899i | 0.507032 | − | 0.368380i | −0.304664 | − | 0.952460i | \(-0.598544\pi\) |
0.811697 | + | 0.584079i | \(0.198544\pi\) | |||||||
\(500\) | 5.37999 | + | 1.74806i | 0.240600 | + | 0.0781758i | ||||
\(501\) | −12.4318 | − | 16.6569i | −0.555410 | − | 0.744174i | ||||
\(502\) | −14.9626 | − | 20.5942i | −0.667812 | − | 0.919165i | ||||
\(503\) | 12.9443 | + | 9.40456i | 0.577157 | + | 0.419329i | 0.837698 | − | 0.546134i | \(-0.183901\pi\) |
−0.260541 | + | 0.965463i | \(0.583901\pi\) | |||||||
\(504\) | −7.74320 | − | 10.1016i | −0.344909 | − | 0.449962i | ||||
\(505\) | 28.2843i | 1.25863i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | + | 7.07107i | −0.222058 | + | 0.314037i | ||||
\(508\) | 9.41498 | − | 3.05911i | 0.417722 | − | 0.135726i | ||||
\(509\) | −19.9501 | + | 27.4589i | −0.884272 | + | 1.21710i | 0.0909469 | + | 0.995856i | \(0.471011\pi\) |
−0.975219 | + | 0.221241i | \(0.928989\pi\) | |||||||
\(510\) | 29.3915 | − | 0.377372i | 1.30148 | − | 0.0167103i | ||||
\(511\) | −0.618034 | + | 1.90211i | −0.0273402 | + | 0.0841445i | ||||
\(512\) | −3.39919 | + | 10.4616i | −0.150224 | + | 0.462343i | ||||
\(513\) | 7.61471 | + | 20.6886i | 0.336197 | + | 0.913422i | ||||
\(514\) | 6.65003 | − | 9.15298i | 0.293320 | − | 0.403721i | ||||
\(515\) | 21.5200 | − | 6.99226i | 0.948282 | − | 0.308116i | ||||
\(516\) | −6.00000 | − | 4.24264i | −0.264135 | − | 0.186772i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.3137i | 0.497096i | ||||||||
\(519\) | 9.92408 | + | 3.08424i | 0.435619 | + | 0.135383i | ||||
\(520\) | −29.1246 | − | 21.1603i | −1.27720 | − | 0.927939i | ||||
\(521\) | 11.6376 | + | 16.0177i | 0.509851 | + | 0.701749i | 0.983894 | − | 0.178752i | \(-0.0572061\pi\) |
−0.474044 | + | 0.880501i | \(0.657206\pi\) | |||||||
\(522\) | 5.99802 | − | 0.154049i | 0.262526 | − | 0.00674254i | ||||
\(523\) | −20.1750 | − | 6.55524i | −0.882189 | − | 0.286641i | −0.167323 | − | 0.985902i | \(-0.553512\pi\) |
−0.714866 | + | 0.699261i | \(0.753512\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.36034 | + | 6.95908i | 0.103014 | + | 0.303719i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | −4.94427 | − | 15.2169i | −0.214765 | − | 0.660980i | ||||
\(531\) | −32.5386 | − | 9.65615i | −1.41205 | − | 0.419041i | ||||
\(532\) | −4.85410 | + | 3.52671i | −0.210452 | + | 0.152902i | ||||
\(533\) | −24.2099 | − | 7.86629i | −1.04865 | − | 0.340727i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.6001 | − | 36.6119i | −1.15002 | − | 1.58287i | ||||
\(536\) | 4.85410 | + | 3.52671i | 0.209665 | + | 0.152331i | ||||
\(537\) | 1.45393 | − | 4.67826i | 0.0627415 | − | 0.201882i | ||||
\(538\) | 28.2843i | 1.21942i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.00000 | − | 14.1421i | 0.172133 | − | 0.608581i | ||||
\(541\) | 33.6249 | − | 10.9254i | 1.44565 | − | 0.469720i | 0.521995 | − | 0.852949i | \(-0.325188\pi\) |
0.923653 | + | 0.383229i | \(0.125188\pi\) | |||||||
\(542\) | −17.4563 | + | 24.0266i | −0.749814 | + | 1.03203i | ||||
\(543\) | −0.222369 | − | 17.3191i | −0.00954276 | − | 0.743233i | ||||
\(544\) | 9.27051 | − | 28.5317i | 0.397470 | − | 1.22329i | ||||
\(545\) | 3.70820 | − | 11.4127i | 0.158842 | − | 0.488865i | ||||
\(546\) | 0.133421 | + | 10.3914i | 0.00570990 | + | 0.444713i | ||||
\(547\) | 20.7813 | − | 28.6031i | 0.888546 | − | 1.22298i | −0.0854335 | − | 0.996344i | \(-0.527228\pi\) |
0.973980 | − | 0.226635i | \(-0.0727725\pi\) | |||||||
\(548\) | −2.68999 | + | 0.874032i | −0.114911 | + | 0.0373368i | ||||
\(549\) | 28.0000 | − | 9.89949i | 1.19501 | − | 0.422500i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.48528i | − | 0.361485i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.85410 | − | 3.52671i | −0.206417 | − | 0.149971i | ||||
\(554\) | 2.49376 | + | 3.43237i | 0.105950 | + | 0.145827i | ||||
\(555\) | −31.4085 | + | 23.4416i | −1.33322 | + | 0.995038i | ||||
\(556\) | −1.34500 | − | 0.437016i | −0.0570406 | − | 0.0185336i | ||||
\(557\) | 1.61803 | − | 1.17557i | 0.0685583 | − | 0.0498105i | −0.552978 | − | 0.833196i | \(-0.686509\pi\) |
0.621537 | + | 0.783385i | \(0.286509\pi\) | |||||||
\(558\) | 1.70698 | − | 5.75206i | 0.0722623 | − | 0.243504i | ||||
\(559\) | 5.56231 | + | 17.1190i | 0.235260 | + | 0.724057i | ||||
\(560\) | −4.00000 | −0.169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 3.70820 | + | 11.4127i | 0.156282 | + | 0.480987i | 0.998289 | − | 0.0584805i | \(-0.0186256\pi\) |
−0.842006 | + | 0.539468i | \(0.818626\pi\) | |||||||
\(564\) | −1.57356 | − | 4.63939i | −0.0662588 | − | 0.195353i | ||||
\(565\) | 6.47214 | − | 4.70228i | 0.272285 | − | 0.197826i | ||||
\(566\) | −25.5549 | − | 8.30330i | −1.07415 | − | 0.349014i | ||||
\(567\) | −11.8871 | + | 4.54934i | −0.499212 | + | 0.191054i | ||||
\(568\) | −4.98752 | − | 6.86474i | −0.209272 | − | 0.288038i | ||||
\(569\) | 30.7426 | + | 22.3358i | 1.28880 | + | 0.936367i | 0.999780 | − | 0.0209564i | \(-0.00667113\pi\) |
0.289018 | + | 0.957324i | \(0.406671\pi\) | |||||||
\(570\) | 19.8482 | + | 6.16849i | 0.831348 | + | 0.258369i | ||||
\(571\) | − | 26.8701i | − | 1.12448i | −0.826975 | − | 0.562238i | \(-0.809940\pi\) | ||
0.826975 | − | 0.562238i | \(-0.190060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.0000 | − | 19.7990i | −1.16972 | − | 0.827115i | ||||
\(574\) | −8.06998 | + | 2.62210i | −0.336835 | + | 0.109444i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 17.3007 | + | 11.9032i | 0.720861 | + | 0.495968i | ||||
\(577\) | −9.88854 | + | 30.4338i | −0.411665 | + | 1.26698i | 0.503534 | + | 0.863975i | \(0.332033\pi\) |
−0.915200 | + | 0.403001i | \(0.867967\pi\) | |||||||
\(578\) | 5.87132 | − | 18.0701i | 0.244215 | − | 0.751616i | ||||
\(579\) | 36.7393 | − | 0.471715i | 1.52683 | − | 0.0196038i | ||||
\(580\) | −3.32502 | + | 4.57649i | −0.138064 | + | 0.190028i | ||||
\(581\) | 21.5200 | − | 6.99226i | 0.892798 | − | 0.290088i | ||||
\(582\) | −2.00000 | + | 2.82843i | −0.0829027 | + | 0.117242i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 4.24264i | − | 0.175562i | ||||||
\(585\) | −28.5717 | + | 21.9011i | −1.18130 | + | 0.905498i | ||||
\(586\) | 1.61803 | + | 1.17557i | 0.0668404 | + | 0.0485624i | ||||
\(587\) | −6.65003 | − | 9.15298i | −0.274476 | − | 0.377784i | 0.649418 | − | 0.760431i | \(-0.275012\pi\) |
−0.923894 | + | 0.382647i | \(0.875012\pi\) | |||||||
\(588\) | 5.17990 | + | 6.94036i | 0.213615 | + | 0.286216i | ||||
\(589\) | −8.06998 | − | 2.62210i | −0.332518 | − | 0.108042i | ||||
\(590\) | −25.8885 | + | 18.8091i | −1.06581 | + | 0.774360i | ||||
\(591\) | −36.0860 | + | 12.2394i | −1.48438 | + | 0.503463i | ||||
\(592\) | −2.47214 | − | 7.60845i | −0.101604 | − | 0.312705i | ||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | 0.983904 | ||||||||
\(596\) | −1.85410 | − | 5.70634i | −0.0759470 | − | 0.233741i | ||||
\(597\) | −3.28054 | + | 1.11268i | −0.134264 | + | 0.0455388i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.2799 | − | 10.4884i | −1.31892 | − | 0.428544i | −0.436798 | − | 0.899560i | \(-0.643887\pi\) |
−0.882125 | + | 0.471016i | \(0.843887\pi\) | |||||||
\(600\) | −9.32382 | − | 12.4927i | −0.380643 | − | 0.510010i | ||||
\(601\) | 17.4563 | + | 24.0266i | 0.712059 | + | 0.980065i | 0.999750 | + | 0.0223415i | \(0.00711213\pi\) |
−0.287692 | + | 0.957723i | \(0.592888\pi\) | |||||||
\(602\) | 4.85410 | + | 3.52671i | 0.197838 | + | 0.143738i | ||||
\(603\) | 4.76195 | − | 3.65018i | 0.193922 | − | 0.148647i | ||||
\(604\) | − | 4.24264i | − | 0.172631i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.0000 | + | 14.1421i | −0.406222 | + | 0.574485i | ||||
\(607\) | 4.03499 | − | 1.31105i | 0.163775 | − | 0.0532138i | −0.225982 | − | 0.974132i | \(-0.572559\pi\) |
0.389757 | + | 0.920918i | \(0.372559\pi\) | |||||||
\(608\) | 12.4688 | − | 17.1618i | 0.505677 | − | 0.696005i | ||||
\(609\) | 4.89858 | − | 0.0628954i | 0.198500 | − | 0.00254865i | ||||
\(610\) | 8.65248 | − | 26.6296i | 0.350329 | − | 1.07820i | ||||
\(611\) | −3.70820 | + | 11.4127i | −0.150018 | + | 0.461708i | ||||
\(612\) | −14.8291 | − | 10.2028i | −0.599433 | − | 0.412422i | ||||
\(613\) | 2.49376 | − | 3.43237i | 0.100722 | − | 0.138632i | −0.755681 | − | 0.654940i | \(-0.772694\pi\) |
0.856403 | + | 0.516308i | \(0.172694\pi\) | |||||||
\(614\) | −4.03499 | + | 1.31105i | −0.162839 | + | 0.0529096i | ||||
\(615\) | −24.0000 | − | 16.9706i | −0.967773 | − | 0.684319i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1127i | 1.25255i | 0.779602 | + | 0.626275i | \(0.215421\pi\) | ||||
−0.779602 | + | 0.626275i | \(0.784579\pi\) | |||||||
\(618\) | 13.2321 | + | 4.11232i | 0.532274 | + | 0.165422i | ||||
\(619\) | 16.1803 | + | 11.7557i | 0.650343 | + | 0.472502i | 0.863388 | − | 0.504541i | \(-0.168338\pi\) |
−0.213045 | + | 0.977042i | \(0.568338\pi\) | |||||||
\(620\) | 3.32502 | + | 4.57649i | 0.133536 | + | 0.183796i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.8999 | + | 8.74032i | 1.07859 | + | 0.350455i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.36034 | − | 6.95908i | −0.0944892 | − | 0.278586i | ||||
\(625\) | −9.57953 | − | 29.4828i | −0.383181 | − | 1.17931i | ||||
\(626\) | 12.0000 | 0.479616 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.0000 | 0.798087 | ||||||||
\(629\) | 14.8328 | + | 45.6507i | 0.591423 | + | 1.82021i | ||||
\(630\) | −3.41396 | + | 11.5041i | −0.136016 | + | 0.458335i | ||||
\(631\) | 11.3262 | − | 8.22899i | 0.450890 | − | 0.327591i | −0.339057 | − | 0.940766i | \(-0.610108\pi\) |
0.789947 | + | 0.613175i | \(0.210108\pi\) | |||||||
\(632\) | 12.1050 | + | 3.93314i | 0.481510 | + | 0.156452i | ||||
\(633\) | 37.2976 | − | 27.8368i | 1.48245 | − | 1.10642i | ||||
\(634\) | −14.9626 | − | 20.5942i | −0.594240 | − | 0.817901i | ||||
\(635\) | −22.6525 | − | 16.4580i | −0.898936 | − | 0.653115i | ||||
\(636\) | −2.90785 | + | 9.35652i | −0.115304 | + | 0.371010i | ||||
\(637\) | − | 21.2132i | − | 0.840498i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | + | 2.82843i | −0.316475 | + | 0.111891i | ||||
\(640\) | −8.06998 | + | 2.62210i | −0.318994 | + | 0.103647i | ||||
\(641\) | 16.6251 | − | 22.8825i | 0.656651 | − | 0.903803i | −0.342714 | − | 0.939440i | \(-0.611346\pi\) |
0.999365 | + | 0.0356372i | \(0.0113461\pi\) | |||||||
\(642\) | −0.355790 | − | 27.7105i | −0.0140419 | − | 1.09365i | ||||
\(643\) | 3.70820 | − | 11.4127i | 0.146237 | − | 0.450072i | −0.850931 | − | 0.525278i | \(-0.823961\pi\) |
0.997168 | + | 0.0752058i | \(0.0239614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.266843 | + | 20.7829i | 0.0105069 | + | 0.818326i | ||||
\(646\) | 14.9626 | − | 20.5942i | 0.588694 | − | 0.810268i | ||||
\(647\) | 5.37999 | − | 1.74806i | 0.211509 | − | 0.0687235i | −0.201346 | − | 0.979520i | \(-0.564532\pi\) |
0.412855 | + | 0.910797i | \(0.364532\pi\) | |||||||
\(648\) | 21.0000 | − | 16.9706i | 0.824958 | − | 0.666667i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 12.7279i | 0.499230i | ||||||||
\(651\) | 1.45393 | − | 4.67826i | 0.0569839 | − | 0.183355i | ||||
\(652\) | 16.1803 | + | 11.7557i | 0.633671 | + | 0.460389i | ||||
\(653\) | −6.65003 | − | 9.15298i | −0.260236 | − | 0.358184i | 0.658827 | − | 0.752294i | \(-0.271053\pi\) |
−0.919063 | + | 0.394110i | \(0.871053\pi\) | |||||||
\(654\) | 5.88909 | − | 4.39529i | 0.230282 | − | 0.171869i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.85410 | − | 3.52671i | 0.189521 | − | 0.137695i | ||||
\(657\) | −4.06732 | − | 1.20702i | −0.158681 | − | 0.0470903i | ||||
\(658\) | 1.23607 | + | 3.80423i | 0.0481869 | + | 0.148304i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0000 | −0.777910 | −0.388955 | − | 0.921257i | \(-0.627164\pi\) | ||||
−0.388955 | + | 0.921257i | \(0.627164\pi\) | |||||||
\(662\) | −6.18034 | − | 19.0211i | −0.240206 | − | 0.739277i | ||||
\(663\) | 14.1620 | + | 41.7545i | 0.550008 | + | 1.62161i | ||||
\(664\) | −38.8328 | + | 28.2137i | −1.50701 | + | 1.09490i | ||||
\(665\) | 16.1400 | + | 5.24419i | 0.625881 | + | 0.203361i | ||||
\(666\) | −23.9921 | + | 0.616196i | −0.929675 | + | 0.0238771i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 9.70820 | + | 7.05342i | 0.375622 | + | 0.272905i | ||||
\(669\) | 39.6963 | + | 12.3370i | 1.53475 | + | 0.476975i | ||||
\(670\) | − | 5.65685i | − | 0.218543i | ||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 10.0000 | + | 7.07107i | 0.385758 | + | 0.272772i | ||||
\(673\) | 4.03499 | − | 1.31105i | 0.155537 | − | 0.0505372i | −0.230213 | − | 0.973140i | \(-0.573942\pi\) |
0.385751 | + | 0.922603i | \(0.373942\pi\) | |||||||
\(674\) | 19.1188 | − | 26.3148i | 0.736430 | − | 1.01361i | ||||
\(675\) | −14.6290 | + | 5.38441i | −0.563071 | + | 0.207246i | ||||
\(676\) | 1.54508 | − | 4.75528i | 0.0594263 | − | 0.182895i | ||||
\(677\) | −11.7426 | + | 36.1401i | −0.451307 | + | 1.38898i | 0.424111 | + | 0.905610i | \(0.360587\pi\) |
−0.875417 | + | 0.483368i | \(0.839413\pi\) | |||||||
\(678\) | 4.89858 | − | 0.0628954i | 0.188129 | − | 0.00241548i | ||||
\(679\) | −1.66251 | + | 2.28825i | −0.0638012 | + | 0.0878148i | ||||
\(680\) | −48.4199 | + | 15.7326i | −1.85682 | + | 0.603317i | ||||
\(681\) | −24.0000 | + | 33.9411i | −0.919682 | + | 1.30063i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 31.1127i | − | 1.19049i | −0.803543 | − | 0.595247i | \(-0.797054\pi\) | ||
0.803543 | − | 0.595247i | \(-0.202946\pi\) | |||||||
\(684\) | −7.74320 | − | 10.1016i | −0.296068 | − | 0.386245i | ||||
\(685\) | 6.47214 | + | 4.70228i | 0.247288 | + | 0.179665i | ||||
\(686\) | −9.97505 | − | 13.7295i | −0.380849 | − | 0.524194i | ||||
\(687\) | 24.8635 | + | 33.3137i | 0.948602 | + | 1.27100i | ||||
\(688\) | −4.03499 | − | 1.31105i | −0.153833 | − | 0.0499832i | ||||
\(689\) | 19.4164 | − | 14.1068i | 0.739706 | − | 0.537428i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.18034 | + | 19.0211i | 0.235111 | + | 0.723598i | 0.997107 | + | 0.0760155i | \(0.0242198\pi\) |
−0.761995 | + | 0.647582i | \(0.775780\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | 1.23607 | + | 3.80423i | 0.0468867 | + | 0.144303i | ||||
\(696\) | −9.84163 | + | 3.33803i | −0.373046 | + | 0.126528i | ||||
\(697\) | −29.1246 | + | 21.1603i | −1.10317 | + | 0.801502i | ||||
\(698\) | 4.03499 | + | 1.31105i | 0.152727 | + | 0.0496239i | ||||
\(699\) | 10.3598 | + | 13.8807i | 0.391844 | + | 0.525017i | ||||
\(700\) | −2.49376 | − | 3.43237i | −0.0942553 | − | 0.129731i | ||||
\(701\) | −4.85410 | − | 3.52671i | −0.183337 | − | 0.133202i | 0.492331 | − | 0.870408i | \(-0.336145\pi\) |
−0.675668 | + | 0.737206i | \(0.736145\pi\) | |||||||
\(702\) | −22.0291 | + | 0.848901i | −0.831433 | + | 0.0320397i | ||||
\(703\) | 33.9411i | 1.28011i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | + | 11.3137i | −0.301297 | + | 0.426099i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.31254 | + | 11.4412i | −0.312625 | + | 0.430292i | ||||
\(708\) | 19.5943 | − | 0.251582i | 0.736399 | − | 0.00945502i | ||||
\(709\) | −9.88854 | + | 30.4338i | −0.371372 | + | 1.14297i | 0.574522 | + | 0.818489i | \(0.305188\pi\) |
−0.945894 | + | 0.324476i | \(0.894812\pi\) | |||||||
\(710\) | −2.47214 | + | 7.60845i | −0.0927776 | + | 0.285540i | ||||
\(711\) | 7.21444 | − | 10.4858i | 0.270563 | − | 0.393248i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 12.0000 | + | 8.48528i | 0.449089 | + | 0.317554i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.82843i | 0.105703i | ||||||||
\(717\) | −26.4642 | − | 8.22465i | −0.988325 | − | 0.307155i | ||||
\(718\) | −16.1803 | − | 11.7557i | −0.603845 | − | 0.438719i | ||||
\(719\) | 11.6376 | + | 16.0177i | 0.434008 | + | 0.597360i | 0.968867 | − | 0.247581i | \(-0.0796355\pi\) |
−0.534860 | + | 0.844941i | \(0.679636\pi\) | |||||||
\(720\) | −0.217858 | − | 8.48248i | −0.00811909 | − | 0.316124i | ||||
\(721\) | 10.7600 | + | 3.49613i | 0.400722 | + | 0.130203i | ||||
\(722\) | −0.809017 | + | 0.587785i | −0.0301085 | + | 0.0218751i | ||||
\(723\) | −2.36034 | − | 6.95908i | −0.0877820 | − | 0.258811i | ||||
\(724\) | 3.09017 | + | 9.51057i | 0.114845 | + | 0.353457i | ||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | 0.0741759 | 0.0370879 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370879 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(728\) | −5.56231 | − | 17.1190i | −0.206153 | − | 0.634473i | ||||
\(729\) | −10.2949 | − | 24.9603i | −0.381291 | − | 0.924455i | ||||
\(730\) | −3.23607 | + | 2.35114i | −0.119772 | + | 0.0870196i | ||||
\(731\) | 24.2099 | + | 7.86629i | 0.895437 | + | 0.290945i | ||||
\(732\) | −13.7412 | + | 10.2557i | −0.507890 | + | 0.379061i | ||||
\(733\) | −0.831254 | − | 1.14412i | −0.0307031 | − | 0.0422591i | 0.793389 | − | 0.608714i | \(-0.208314\pi\) |
−0.824093 | + | 0.566455i | \(0.808314\pi\) | |||||||
\(734\) | −6.47214 | − | 4.70228i | −0.238891 | − | 0.173564i | ||||
\(735\) | 7.26963 | − | 23.3913i | 0.268144 | − | 0.862801i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.00000 | − | 16.9706i | −0.220863 | − | 0.624695i | ||||
\(739\) | 4.03499 | − | 1.31105i | 0.148430 | − | 0.0482277i | −0.233860 | − | 0.972270i | \(-0.575136\pi\) |
0.382289 | + | 0.924043i | \(0.375136\pi\) | |||||||
\(740\) | 13.3001 | − | 18.3060i | 0.488920 | − | 0.672941i | ||||
\(741\) | 0.400264 | + | 31.1743i | 0.0147041 | + | 1.14522i | ||||
\(742\) | 2.47214 | − | 7.60845i | 0.0907550 | − | 0.279315i | ||||
\(743\) | −4.94427 | + | 15.2169i | −0.181388 | + | 0.558254i | −0.999867 | − | 0.0162814i | \(-0.994817\pi\) |
0.818480 | + | 0.574535i | \(0.194817\pi\) | |||||||
\(744\) | 0.133421 | + | 10.3914i | 0.00489146 | + | 0.380969i | ||||
\(745\) | −9.97505 | + | 13.7295i | −0.365457 | + | 0.503009i | ||||
\(746\) | −4.03499 | + | 1.31105i | −0.147732 | + | 0.0480009i | ||||
\(747\) | 16.0000 | + | 45.2548i | 0.585409 | + | 1.65579i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 22.6274i | − | 0.826788i | ||||||
\(750\) | 2.90785 | − | 9.35652i | 0.106180 | − | 0.341652i | ||||
\(751\) | −1.61803 | − | 1.17557i | −0.0590429 | − | 0.0428972i | 0.557872 | − | 0.829927i | \(-0.311618\pi\) |
−0.616915 | + | 0.787030i | \(0.711618\pi\) | |||||||
\(752\) | −1.66251 | − | 2.28825i | −0.0606254 | − | 0.0834437i | ||||
\(753\) | 35.3346 | − | 26.3717i | 1.28766 | − | 0.961040i | ||||
\(754\) | 8.06998 | + | 2.62210i | 0.293891 | + | 0.0954911i | ||||
\(755\) | −9.70820 | + | 7.05342i | −0.353318 | + | 0.256700i | ||||
\(756\) | 5.77430 | − | 4.54504i | 0.210009 | − | 0.165302i | ||||
\(757\) | 6.18034 | + | 19.0211i | 0.224628 | + | 0.691335i | 0.998329 | + | 0.0577836i | \(0.0184034\pi\) |
−0.773701 | + | 0.633551i | \(0.781597\pi\) | |||||||
\(758\) | 12.0000 | 0.435860 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −36.0000 | −1.30586 | ||||||||
\(761\) | −3.09017 | − | 9.51057i | −0.112019 | − | 0.344758i | 0.879295 | − | 0.476278i | \(-0.158014\pi\) |
−0.991314 | + | 0.131520i | \(0.958014\pi\) | |||||||
\(762\) | −5.50746 | − | 16.2379i | −0.199514 | − | 0.588235i | ||||
\(763\) | 4.85410 | − | 3.52671i | 0.175730 | − | 0.127676i | ||||
\(764\) | 18.8300 | + | 6.11822i | 0.681244 | + | 0.221350i | ||||
\(765\) | 1.30715 | + | 50.8949i | 0.0472601 | + | 1.84011i | ||||
\(766\) | 3.32502 | + | 4.57649i | 0.120138 | + | 0.165355i | ||||
\(767\) | −38.8328 | − | 28.2137i | −1.40217 | − | 1.01874i | ||||
\(768\) | −28.1182 | − | 8.73869i | −1.01463 | − | 0.315330i | ||||
\(769\) | 35.3553i | 1.27495i | 0.770473 | + | 0.637473i | \(0.220020\pi\) | ||||
−0.770473 | + | 0.637473i | \(0.779980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0000 | + | 11.3137i | 0.576226 | + | 0.407453i | ||||
\(772\) | −20.1750 | + | 6.55524i | −0.726113 | + | 0.235928i | ||||
\(773\) | −19.9501 | + | 27.4589i | −0.717555 | + | 0.987630i | 0.282047 | + | 0.959401i | \(0.408987\pi\) |
−0.999601 | + | 0.0282290i | \(0.991013\pi\) | |||||||
\(774\) | −7.21444 | + | 10.4858i | −0.259318 | + | 0.376904i | ||||
\(775\) | 1.85410 | − | 5.70634i | 0.0666013 | − | 0.204978i | ||||
\(776\) | 1.85410 | − | 5.70634i | 0.0665584 | − | 0.204846i | ||||
\(777\) | −19.5943 | + | 0.251582i | −0.702942 | + | 0.00902544i | ||||
\(778\) | −11.6376 | + | 16.0177i | −0.417227 | + | 0.574263i | ||||
\(779\) | −24.2099 | + | 7.86629i | −0.867411 | + | 0.281839i | ||||
\(780\) | 12.0000 | − | 16.9706i | 0.429669 | − | 0.607644i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.400176 | + | 10.3846i | 0.0143011 | + | 0.371115i | ||||
\(784\) | 4.04508 | + | 2.93893i | 0.144467 | + | 0.104962i | ||||
\(785\) | −33.2502 | − | 45.7649i | −1.18675 | − | 1.63342i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.1750 | − | 6.55524i | −0.719159 | − | 0.233669i | −0.0735007 | − | 0.997295i | \(-0.523417\pi\) |
−0.645659 | + | 0.763626i | \(0.723417\pi\) | |||||||
\(788\) | 17.7984 | − | 12.9313i | 0.634041 | − | 0.460658i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.70820 | − | 11.4127i | −0.131932 | − | 0.406045i | ||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.0000 | 1.49146 | ||||||||
\(794\) | 0.618034 | + | 1.90211i | 0.0219332 | + | 0.0675035i | ||||
\(795\) | 26.2443 | − | 8.90140i | 0.930791 | − | 0.315700i | ||||
\(796\) | 1.61803 | − | 1.17557i | 0.0573497 | − | 0.0416670i | ||||
\(797\) | −2.68999 | − | 0.874032i | −0.0952845 | − | 0.0309598i | 0.260987 | − | 0.965342i | \(-0.415952\pi\) |
−0.356271 | + | 0.934383i | \(0.615952\pi\) | |||||||
\(798\) | 6.21588 | + | 8.32844i | 0.220040 | + | 0.294823i | ||||
\(799\) | 9.97505 | + | 13.7295i | 0.352892 | + | 0.485714i | ||||
\(800\) | 12.1353 | + | 8.81678i | 0.429046 | + | 0.311720i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 2.82843i | − | 0.0998752i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.00000 | + | 2.82843i | −0.0705346 | + | 0.0997509i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.98752 | − | 6.86474i | 0.175678 | − | 0.241800i | ||||
\(807\) | −48.9858 | + | 0.628954i | −1.72438 | + | 0.0221402i | ||||
\(808\) | 9.27051 | − | 28.5317i | 0.326135 | − | 1.00374i | ||||
\(809\) | 15.4508 | − | 47.5528i | 0.543223 | − | 1.67187i | −0.181955 | − | 0.983307i | \(-0.558243\pi\) |
0.725178 | − | 0.688561i | \(-0.241757\pi\) | |||||||
\(810\) | −24.5818 | − | 6.61316i | −0.863717 | − | 0.232363i | ||||
\(811\) | −15.7938 | + | 21.7383i | −0.554596 | + | 0.763336i | −0.990627 | − | 0.136596i | \(-0.956384\pi\) |
0.436031 | + | 0.899932i | \(0.356384\pi\) | |||||||
\(812\) | −2.68999 | + | 0.874032i | −0.0944003 | + | 0.0306725i | ||||
\(813\) | −42.0000 | − | 29.6985i | −1.47300 | − | 1.04157i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 56.5685i | − | 1.98151i | ||||||
\(816\) | −9.92408 | − | 3.08424i | −0.347412 | − | 0.107970i | ||||
\(817\) | 14.5623 | + | 10.5801i | 0.509471 | + | 0.370152i | ||||
\(818\) | 2.49376 | + | 3.43237i | 0.0871923 | + | 0.120010i | ||||
\(819\) | −17.9941 | + | 0.462147i | −0.628764 | + | 0.0161487i | ||||
\(820\) | 16.1400 | + | 5.24419i | 0.563632 | + | 0.183135i | ||||
\(821\) | −33.9787 | + | 24.6870i | −1.18587 | + | 0.861582i | −0.992821 | − | 0.119609i | \(-0.961836\pi\) |
−0.193044 | + | 0.981190i | \(0.561836\pi\) | |||||||
\(822\) | 1.57356 | + | 4.63939i | 0.0548842 | + | 0.161817i | ||||
\(823\) | −7.41641 | − | 22.8254i | −0.258520 | − | 0.795642i | −0.993116 | − | 0.117137i | \(-0.962628\pi\) |
0.734596 | − | 0.678505i | \(-0.237372\pi\) | |||||||
\(824\) | −24.0000 | −0.836080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.0000 | −0.556711 | ||||||||
\(827\) | 3.70820 | + | 11.4127i | 0.128947 | + | 0.396858i | 0.994600 | − | 0.103787i | \(-0.0330962\pi\) |
−0.865653 | + | 0.500645i | \(0.833096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3262 | − | 8.22899i | 0.393377 | − | 0.285805i | −0.373461 | − | 0.927646i | \(-0.621829\pi\) |
0.766838 | + | 0.641841i | \(0.221829\pi\) | |||||||
\(830\) | 43.0399 | + | 13.9845i | 1.49394 | + | 0.485410i | ||||
\(831\) | −5.88909 | + | 4.39529i | −0.204290 | + | 0.152471i | ||||
\(832\) | 17.4563 | + | 24.0266i | 0.605189 | + | 0.832972i | ||||
\(833\) | −24.2705 | − | 17.6336i | −0.840923 | − | 0.610967i | ||||
\(834\) | −0.726963 | + | 2.33913i | −0.0251727 | + | 0.0809974i | ||||
\(835\) | − | 33.9411i | − | 1.17458i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0000 | + | 2.82843i | 0.345651 | + | 0.0977647i | ||||
\(838\) | −29.5899 | + | 9.61435i | −1.02217 | + | 0.332122i | ||||
\(839\) | −19.9501 | + | 27.4589i | −0.688754 | + | 0.947988i | −0.999997 | − | 0.00234204i | \(-0.999255\pi\) |
0.311244 | + | 0.950330i | \(0.399255\pi\) | |||||||
\(840\) | −0.266843 | − | 20.7829i | −0.00920694 | − | 0.717078i | ||||
\(841\) | −7.72542 | + | 23.7764i | −0.266394 | + | 0.819876i | ||||
\(842\) | −6.18034 | + | 19.0211i | −0.212989 | + | 0.655511i | ||||
\(843\) | 0.133421 | + | 10.3914i | 0.00459527 | + | 0.357900i | ||||
\(844\) | −15.7938 | + | 21.7383i | −0.543646 | + | 0.748264i | ||||
\(845\) | −13.4500 | + | 4.37016i | −0.462693 | + | 0.150338i | ||||
\(846\) | −8.00000 | + | 2.82843i | −0.275046 | + | 0.0972433i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.65685i | 0.194257i | ||||||||
\(849\) | 13.8123 | − | 44.4435i | 0.474037 | − | 1.52530i | ||||
\(850\) | 14.5623 | + | 10.5801i | 0.499483 | + | 0.362896i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 3.92606 | − | 2.93019i | 0.134505 | − | 0.100387i | ||||
\(853\) | 39.0049 | + | 12.6735i | 1.33550 | + | 0.433931i | 0.887791 | − | 0.460247i | \(-0.152239\pi\) |
0.447712 | + | 0.894178i | \(0.352239\pi\) | |||||||
\(854\) | 11.3262 | − | 8.22899i | 0.387576 | − | 0.281590i | ||||
\(855\) | −10.2419 | + | 34.5124i | −0.350265 | + | 1.18030i | ||||
\(856\) | 14.8328 | + | 45.6507i | 0.506975 | + | 1.56031i | ||||
\(857\) | −22.0000 | −0.751506 | −0.375753 | − | 0.926720i | \(-0.622616\pi\) | ||||
−0.375753 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0000 | −0.682391 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(860\) | −3.70820 | − | 11.4127i | −0.126449 | − | 0.389169i | ||||
\(861\) | −4.72068 | − | 13.9182i | −0.160880 | − | 0.474330i | ||||
\(862\) | 25.8885 | − | 18.8091i | 0.881767 | − | 0.640641i | ||||
\(863\) | −32.2799 | − | 10.4884i | −1.09882 | − | 0.357029i | −0.297173 | − | 0.954824i | \(-0.596044\pi\) |
−0.801649 | + | 0.597795i | \(0.796044\pi\) | |||||||
\(864\) | −14.4504 | + | 21.5913i | −0.491613 | + | 0.734552i | ||||
\(865\) | 9.97505 | + | 13.7295i | 0.339162 | + | 0.466816i | ||||
\(866\) | −24.2705 | − | 17.6336i | −0.824745 | − | 0.599213i | ||||
\(867\) | 31.4263 | + | 9.76677i | 1.06729 | + | 0.331697i | ||||
\(868\) | 2.82843i | 0.0960031i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 8.00000 | + | 5.65685i | 0.271225 | + | 0.191785i | ||||
\(871\) | 8.06998 | − | 2.62210i | 0.273441 | − | 0.0888463i | ||||
\(872\) | −7.48128 | + | 10.2971i | −0.253348 | + | 0.348704i | ||||
\(873\) | −4.94305 | − | 3.40092i | −0.167297 | − | 0.115104i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.47214 | − | 7.60845i | 0.0835734 | − | 0.257213i | ||||
\(876\) | 2.44929 | − | 0.0314477i | 0.0827538 | − | 0.00106252i | ||||
\(877\) | 20.7813 | − | 28.6031i | 0.701736 | − | 0.965857i | −0.298199 | − | 0.954504i | \(-0.596386\pi\) |
0.999936 | − | 0.0113534i | \(-0.00361399\pi\) | |||||||
\(878\) | 25.5549 | − | 8.30330i | 0.862438 | − | 0.280223i | ||||
\(879\) | −2.00000 | + | 2.82843i | −0.0674583 | + | 0.0954005i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1127i | 1.04821i | 0.851653 | + | 0.524107i | \(0.175601\pi\) | ||||
−0.851653 | + | 0.524107i | \(0.824399\pi\) | |||||||
\(882\) | 11.9049 | − | 9.12544i | 0.400858 | − | 0.307270i | ||||
\(883\) | −37.2148 | − | 27.0381i | −1.25238 | − | 0.909905i | −0.254020 | − | 0.967199i | \(-0.581753\pi\) |
−0.998357 | + | 0.0572938i | \(0.981753\pi\) | |||||||
\(884\) | −14.9626 | − | 20.5942i | −0.503246 | − | 0.692658i | ||||
\(885\) | −33.1514 | − | 44.4183i | −1.11437 | − | 1.49311i | ||||
\(886\) | 26.8999 | + | 8.74032i | 0.903721 | + | 0.293637i | ||||
\(887\) | 19.4164 | − | 14.1068i | 0.651939 | − | 0.473662i | −0.211992 | − | 0.977271i | \(-0.567995\pi\) |
0.863931 | + | 0.503610i | \(0.167995\pi\) | |||||||
\(888\) | 39.3665 | − | 13.3521i | 1.32105 | − | 0.448067i | ||||
\(889\) | −4.32624 | − | 13.3148i | −0.145097 | − | 0.446564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.0000 | −0.803579 | ||||||||
\(893\) | 3.70820 | + | 11.4127i | 0.124090 | + | 0.381911i | ||||
\(894\) | −9.84163 | + | 3.33803i | −0.329153 | + | 0.111640i | ||||
\(895\) | 6.47214 | − | 4.70228i | 0.216340 | − | 0.157180i | ||||
\(896\) | −4.03499 | − | 1.31105i | −0.134800 | − | 0.0437990i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.32502 | + | 4.57649i | 0.110957 | + | 0.152719i | ||||
\(899\) | −3.23607 | − | 2.35114i | −0.107929 | − | 0.0784149i | ||||
\(900\) | 7.14293 | − | 5.47527i | 0.238098 | − | 0.182509i | ||||
\(901\) | − | 33.9411i | − | 1.13074i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00000 | + | 8.48528i | −0.199667 | + | 0.282372i | ||||
\(904\) | −8.06998 | + | 2.62210i | −0.268404 | + | 0.0872096i | ||||
\(905\) | 16.6251 | − | 22.8825i | 0.552636 | − | 0.760639i | ||||
\(906\) | −7.34786 | + | 0.0943431i | −0.244116 | + | 0.00313434i | ||||
\(907\) | 3.70820 | − | 11.4127i | 0.123129 | − | 0.378952i | −0.870427 | − | 0.492298i | \(-0.836157\pi\) |
0.993556 | + | 0.113346i | \(0.0361570\pi\) | |||||||
\(908\) | 7.41641 | − | 22.8254i | 0.246122 | − | 0.757486i | ||||
\(909\) | −24.7152 | − | 17.0046i | −0.819753 | − | 0.564007i | ||||
\(910\) | −9.97505 | + | 13.7295i | −0.330670 | + | 0.455128i | ||||
\(911\) | 34.9699 | − | 11.3624i | 1.15861 | − | 0.376454i | 0.334227 | − | 0.942493i | \(-0.391525\pi\) |
0.824378 | + | 0.566039i | \(0.191525\pi\) | |||||||
\(912\) | −6.00000 | − | 4.24264i | −0.198680 | − | 0.140488i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.89949i | 0.327446i | ||||||||
\(915\) | 46.3124 | + | 14.3931i | 1.53104 | + | 0.475822i | ||||
\(916\) | −19.4164 | − | 14.1068i | −0.641536 | − | 0.466103i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −17.3405 | + | 25.9096i | −0.572322 | + | 0.855144i | ||||
\(919\) | −20.1750 | − | 6.55524i | −0.665510 | − | 0.216237i | −0.0432697 | − | 0.999063i | \(-0.513777\pi\) |
−0.622241 | + | 0.782826i | \(0.713777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.36034 | − | 6.95908i | −0.0777759 | − | 0.229309i | ||||
\(922\) | 6.79837 | + | 20.9232i | 0.223893 | + | 0.689070i | ||||
\(923\) | −12.0000 | −0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0000 | −0.789115 | ||||||||
\(926\) | 7.41641 | + | 22.8254i | 0.243718 | + | 0.750088i | ||||
\(927\) | −6.82793 | + | 23.0082i | −0.224259 | + | 0.755690i | ||||
\(928\) | 8.09017 | − | 5.87785i | 0.265573 | − | 0.192950i | ||||
\(929\) | −2.68999 | − | 0.874032i | −0.0882558 | − | 0.0286761i | 0.264556 | − | 0.964370i | \(-0.414775\pi\) |
−0.352812 | + | 0.935694i | \(0.614775\pi\) | |||||||
\(930\) | 7.85212 | − | 5.86039i | 0.257481 | − | 0.192170i | ||||
\(931\) | −12.4688 | − | 17.1618i | −0.408649 | − | 0.562457i | ||||
\(932\) | −8.09017 | − | 5.87785i | −0.265002 | − | 0.192535i | ||||
\(933\) | −14.5393 | + | 46.7826i | −0.475994 | + | 1.53159i | ||||
\(934\) | 28.2843i | 0.925490i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 36.0000 | − | 12.7279i | 1.17670 | − | 0.416025i | ||||
\(937\) | 33.6249 | − | 10.9254i | 1.09848 | − | 0.356917i | 0.296962 | − | 0.954889i | \(-0.404027\pi\) |
0.801517 | + | 0.597972i | \(0.204027\pi\) | |||||||
\(938\) | 1.66251 | − | 2.28825i | 0.0542828 | − | 0.0747139i | ||||
\(939\) | 0.266843 | + | 20.7829i | 0.00870808 | + | 0.678224i | ||||
\(940\) | 2.47214 | − | 7.60845i | 0.0806322 | − | 0.248160i | ||||
\(941\) | −11.7426 | + | 36.1401i | −0.382799 | + | 1.17814i | 0.555265 | + | 0.831674i | \(0.312617\pi\) |
−0.938064 | + | 0.346462i | \(0.887383\pi\) | |||||||
\(942\) | −0.444738 | − | 34.6382i | −0.0144903 | − | 1.12857i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 10.7600 | − | 3.49613i | 0.350207 | − | 0.113789i | ||||
\(945\) | −20.0000 | − | 5.65685i | −0.650600 | − | 0.184017i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 31.1127i | − | 1.01103i | −0.862819 | − | 0.505513i | \(-0.831303\pi\) | ||
0.862819 | − | 0.505513i | \(-0.168697\pi\) | |||||||
\(948\) | −2.18089 | + | 7.01739i | −0.0708320 | + | 0.227914i | ||||
\(949\) | −4.85410 | − | 3.52671i | −0.157571 | − | 0.114482i | ||||
\(950\) | 7.48128 | + | 10.2971i | 0.242725 | + | 0.334082i | ||||
\(951\) | 35.3346 | − | 26.3717i | 1.14580 | − | 0.855162i | ||||
\(952\) | −24.2099 | − | 7.86629i | −0.784649 | − | 0.254948i | ||||
\(953\) | 1.61803 | − | 1.17557i | 0.0524133 | − | 0.0380805i | −0.561270 | − | 0.827633i | \(-0.689687\pi\) |
0.613683 | + | 0.789552i | \(0.289687\pi\) | |||||||
\(954\) | 16.2693 | + | 4.82807i | 0.526738 | + | 0.156315i | ||||
\(955\) | −17.3050 | − | 53.2592i | −0.559975 | − | 1.72343i | ||||
\(956\) | 16.0000 | 0.517477 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.0000 | 0.904639 | ||||||||
\(959\) | 1.23607 | + | 3.80423i | 0.0399147 | + | 0.122845i | ||||
\(960\) | 11.0149 | + | 32.4757i | 0.355505 | + | 1.04815i | ||||
\(961\) | 21.8435 | − | 15.8702i | 0.704628 | − | 0.511942i | ||||
\(962\) | −32.2799 | − | 10.4884i | −1.04075 | − | 0.338159i | ||||
\(963\) | 47.9842 | − | 1.23239i | 1.54627 | − | 0.0397133i | ||||
\(964\) | 2.49376 | + | 3.43237i | 0.0803187 | + | 0.110549i | ||||
\(965\) | 48.5410 | + | 35.2671i | 1.56259 | + | 1.13529i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.24264i | 0.136434i | 0.997671 | + | 0.0682171i | \(0.0217310\pi\) | ||||
−0.997671 | + | 0.0682171i | \(0.978269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.0000 | + | 25.4558i | 1.15649 | + | 0.817760i | ||||
\(970\) | −5.37999 | + | 1.74806i | −0.172741 | + | 0.0561270i | ||||
\(971\) | −19.9501 | + | 27.4589i | −0.640229 | + | 0.881200i | −0.998628 | − | 0.0523690i | \(-0.983323\pi\) |
0.358399 | + | 0.933569i | \(0.383323\pi\) | |||||||
\(972\) | 9.95281 | + | 11.9976i | 0.319237 | + | 0.384822i | ||||
\(973\) | −0.618034 | + | 1.90211i | −0.0198133 | + | 0.0609789i | ||||
\(974\) | 0.618034 | − | 1.90211i | 0.0198031 | − | 0.0609476i | ||||
\(975\) | −22.0436 | + | 0.283029i | −0.705960 | + | 0.00906419i | ||||
\(976\) | −5.81878 | + | 8.00886i | −0.186255 | + | 0.256357i | ||||
\(977\) | −24.2099 | + | 7.86629i | −0.774545 | + | 0.251665i | −0.669509 | − | 0.742804i | \(-0.733496\pi\) |
−0.105035 | + | 0.994468i | \(0.533496\pi\) | |||||||
\(978\) | 20.0000 | − | 28.2843i | 0.639529 | − | 0.904431i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.1421i | 0.451754i | ||||||||
\(981\) | 7.74320 | + | 10.1016i | 0.247221 | + | 0.322520i | ||||
\(982\) | −16.1803 | − | 11.7557i | −0.516335 | − | 0.375140i | ||||
\(983\) | −6.65003 | − | 9.15298i | −0.212103 | − | 0.291935i | 0.689688 | − | 0.724106i | \(-0.257748\pi\) |
−0.901791 | + | 0.432171i | \(0.857748\pi\) | |||||||
\(984\) | 18.6476 | + | 24.9853i | 0.594465 | + | 0.796502i | ||||
\(985\) | −59.1799 | − | 19.2287i | −1.88563 | − | 0.612677i | ||||
\(986\) | 9.70820 | − | 7.05342i | 0.309172 | − | 0.224627i | ||||
\(987\) | −6.56108 | + | 2.22535i | −0.208842 | + | 0.0708337i | ||||
\(988\) | −5.56231 | − | 17.1190i | −0.176961 | − | 0.544628i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.0000 | −1.33417 | −0.667087 | − | 0.744980i | \(-0.732459\pi\) | ||||
−0.667087 | + | 0.744980i | \(0.732459\pi\) | |||||||
\(992\) | −3.09017 | − | 9.51057i | −0.0981130 | − | 0.301961i | ||||
\(993\) | 32.8054 | − | 11.1268i | 1.04105 | − | 0.353097i | ||||
\(994\) | −3.23607 | + | 2.35114i | −0.102642 | + | 0.0745737i | ||||
\(995\) | −5.37999 | − | 1.74806i | −0.170557 | − | 0.0554174i | ||||
\(996\) | −16.5757 | − | 22.2092i | −0.525221 | − | 0.703724i | ||||
\(997\) | 17.4563 | + | 24.0266i | 0.552848 | + | 0.760929i | 0.990395 | − | 0.138266i | \(-0.0441528\pi\) |
−0.437548 | + | 0.899195i | \(0.644153\pi\) | |||||||
\(998\) | 11.3262 | + | 8.22899i | 0.358526 | + | 0.260484i | ||||
\(999\) | −1.60070 | − | 41.5384i | −0.0506440 | − | 1.31422i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 363.2.f.a.215.1 | 8 | ||
3.2 | odd | 2 | 363.2.f.f.215.2 | 8 | |||
11.2 | odd | 10 | 363.2.f.f.233.2 | 8 | |||
11.3 | even | 5 | 363.2.d.b.362.1 | yes | 2 | ||
11.4 | even | 5 | inner | 363.2.f.a.239.2 | 8 | ||
11.5 | even | 5 | inner | 363.2.f.a.161.1 | 8 | ||
11.6 | odd | 10 | 363.2.f.f.161.1 | 8 | |||
11.7 | odd | 10 | 363.2.f.f.239.2 | 8 | |||
11.8 | odd | 10 | 363.2.d.a.362.1 | ✓ | 2 | ||
11.9 | even | 5 | inner | 363.2.f.a.233.2 | 8 | ||
11.10 | odd | 2 | 363.2.f.f.215.1 | 8 | |||
33.2 | even | 10 | inner | 363.2.f.a.233.1 | 8 | ||
33.5 | odd | 10 | 363.2.f.f.161.2 | 8 | |||
33.8 | even | 10 | 363.2.d.b.362.2 | yes | 2 | ||
33.14 | odd | 10 | 363.2.d.a.362.2 | yes | 2 | ||
33.17 | even | 10 | inner | 363.2.f.a.161.2 | 8 | ||
33.20 | odd | 10 | 363.2.f.f.233.1 | 8 | |||
33.26 | odd | 10 | 363.2.f.f.239.1 | 8 | |||
33.29 | even | 10 | inner | 363.2.f.a.239.1 | 8 | ||
33.32 | even | 2 | inner | 363.2.f.a.215.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.a.362.1 | ✓ | 2 | 11.8 | odd | 10 | ||
363.2.d.a.362.2 | yes | 2 | 33.14 | odd | 10 | ||
363.2.d.b.362.1 | yes | 2 | 11.3 | even | 5 | ||
363.2.d.b.362.2 | yes | 2 | 33.8 | even | 10 | ||
363.2.f.a.161.1 | 8 | 11.5 | even | 5 | inner | ||
363.2.f.a.161.2 | 8 | 33.17 | even | 10 | inner | ||
363.2.f.a.215.1 | 8 | 1.1 | even | 1 | trivial | ||
363.2.f.a.215.2 | 8 | 33.32 | even | 2 | inner | ||
363.2.f.a.233.1 | 8 | 33.2 | even | 10 | inner | ||
363.2.f.a.233.2 | 8 | 11.9 | even | 5 | inner | ||
363.2.f.a.239.1 | 8 | 33.29 | even | 10 | inner | ||
363.2.f.a.239.2 | 8 | 11.4 | even | 5 | inner | ||
363.2.f.f.161.1 | 8 | 11.6 | odd | 10 | |||
363.2.f.f.161.2 | 8 | 33.5 | odd | 10 | |||
363.2.f.f.215.1 | 8 | 11.10 | odd | 2 | |||
363.2.f.f.215.2 | 8 | 3.2 | odd | 2 | |||
363.2.f.f.233.1 | 8 | 33.20 | odd | 10 | |||
363.2.f.f.233.2 | 8 | 11.2 | odd | 10 | |||
363.2.f.f.239.1 | 8 | 33.26 | odd | 10 | |||
363.2.f.f.239.2 | 8 | 11.7 | odd | 10 |