Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.1 | ||
Root | \(2.52809 - 1.83676i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.148 |
Dual form | 847.2.f.t.372.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.656626 | − | 2.02089i | −0.464304 | − | 1.42898i | −0.859855 | − | 0.510538i | \(-0.829446\pi\) |
0.395551 | − | 0.918444i | \(-0.370554\pi\) | |||||||
\(3\) | 2.52809 | + | 1.83676i | 1.45959 | + | 1.06045i | 0.983469 | + | 0.181075i | \(0.0579578\pi\) |
0.476122 | + | 0.879379i | \(0.342042\pi\) | |||||||
\(4\) | −2.03479 | + | 1.47836i | −1.01739 | + | 0.739181i | ||||
\(5\) | 0.149831 | − | 0.461131i | 0.0670063 | − | 0.206224i | −0.911947 | − | 0.410307i | \(-0.865421\pi\) |
0.978954 | + | 0.204083i | \(0.0654214\pi\) | |||||||
\(6\) | 2.05188 | − | 6.31504i | 0.837677 | − | 2.57810i | ||||
\(7\) | −0.809017 | + | 0.587785i | −0.305780 | + | 0.222162i | ||||
\(8\) | 0.885558 | + | 0.643395i | 0.313092 | + | 0.227475i | ||||
\(9\) | 2.09047 | + | 6.43381i | 0.696824 | + | 2.14460i | ||||
\(10\) | −1.03028 | −0.325802 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −7.85952 | −2.26885 | ||||||||
\(13\) | 1.73351 | + | 5.33519i | 0.480788 | + | 1.47971i | 0.837989 | + | 0.545687i | \(0.183731\pi\) |
−0.357201 | + | 0.934028i | \(0.616269\pi\) | |||||||
\(14\) | 1.71907 | + | 1.24898i | 0.459440 | + | 0.333803i | ||||
\(15\) | 1.22577 | − | 0.890576i | 0.316493 | − | 0.229946i | ||||
\(16\) | −0.835692 | + | 2.57200i | −0.208923 | + | 0.642999i | ||||
\(17\) | 1.73351 | − | 5.33519i | 0.420437 | − | 1.29397i | −0.486859 | − | 0.873481i | \(-0.661857\pi\) |
0.907296 | − | 0.420492i | \(-0.138143\pi\) | |||||||
\(18\) | 11.6293 | − | 8.44921i | 2.74106 | − | 1.99150i | ||||
\(19\) | 4.27165 | + | 3.10353i | 0.979983 | + | 0.711999i | 0.957705 | − | 0.287752i | \(-0.0929080\pi\) |
0.0222783 | + | 0.999752i | \(0.492908\pi\) | |||||||
\(20\) | 0.376845 | + | 1.15981i | 0.0842650 | + | 0.259341i | ||||
\(21\) | −3.12489 | −0.681906 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.48486 | 0.518130 | 0.259065 | − | 0.965860i | \(-0.416586\pi\) | ||||
0.259065 | + | 0.965860i | \(0.416586\pi\) | |||||||
\(24\) | 1.05700 | + | 3.25312i | 0.215760 | + | 0.664040i | ||||
\(25\) | 3.85489 | + | 2.80074i | 0.770978 | + | 0.560149i | ||||
\(26\) | 9.64354 | − | 7.00644i | 1.89125 | − | 1.37408i | ||||
\(27\) | −3.63556 | + | 11.1891i | −0.699663 | + | 2.15334i | ||||
\(28\) | 0.777220 | − | 2.39204i | 0.146881 | − | 0.452053i | ||||
\(29\) | −4.27165 | + | 3.10353i | −0.793225 | + | 0.576312i | −0.908919 | − | 0.416973i | \(-0.863091\pi\) |
0.115694 | + | 0.993285i | \(0.463091\pi\) | |||||||
\(30\) | −2.60463 | − | 1.89237i | −0.475537 | − | 0.345498i | ||||
\(31\) | −2.20171 | − | 6.77617i | −0.395439 | − | 1.21704i | −0.928619 | − | 0.371034i | \(-0.879003\pi\) |
0.533180 | − | 0.846002i | \(-0.320997\pi\) | |||||||
\(32\) | 7.93567 | 1.40284 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.9201 | −2.04428 | ||||||||
\(35\) | 0.149831 | + | 0.461131i | 0.0253260 | + | 0.0779454i | ||||
\(36\) | −13.7652 | − | 10.0010i | −2.29419 | − | 1.66683i | ||||
\(37\) | 0.190193 | − | 0.138183i | 0.0312675 | − | 0.0227172i | −0.572042 | − | 0.820225i | \(-0.693848\pi\) |
0.603309 | + | 0.797507i | \(0.293848\pi\) | |||||||
\(38\) | 3.46701 | − | 10.6704i | 0.562424 | − | 1.73096i | ||||
\(39\) | −5.41701 | + | 16.6718i | −0.867416 | + | 2.66963i | ||||
\(40\) | 0.429373 | − | 0.311958i | 0.0678899 | − | 0.0493249i | ||||
\(41\) | −1.93375 | − | 1.40496i | −0.302002 | − | 0.219417i | 0.426455 | − | 0.904509i | \(-0.359762\pi\) |
−0.728457 | + | 0.685092i | \(0.759762\pi\) | |||||||
\(42\) | 2.05188 | + | 6.31504i | 0.316612 | + | 0.974431i | ||||
\(43\) | 1.03028 | 0.157116 | 0.0785578 | − | 0.996910i | \(-0.474968\pi\) | ||||
0.0785578 | + | 0.996910i | \(0.474968\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.28005 | 0.488961 | ||||||||
\(46\) | −1.63162 | − | 5.02162i | −0.240570 | − | 0.740398i | ||||
\(47\) | 1.30231 | + | 0.946186i | 0.189962 | + | 0.138015i | 0.678701 | − | 0.734414i | \(-0.262543\pi\) |
−0.488739 | + | 0.872430i | \(0.662543\pi\) | |||||||
\(48\) | −6.83684 | + | 4.96726i | −0.986814 | + | 0.716962i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 3.12876 | − | 9.62934i | 0.442474 | − | 1.36179i | ||||
\(51\) | 14.1819 | − | 10.3038i | 1.98587 | − | 1.44282i | ||||
\(52\) | −11.4147 | − | 8.29323i | −1.58293 | − | 1.15006i | ||||
\(53\) | −0.936407 | − | 2.88196i | −0.128625 | − | 0.395868i | 0.865919 | − | 0.500185i | \(-0.166735\pi\) |
−0.994544 | + | 0.104316i | \(0.966735\pi\) | |||||||
\(54\) | 24.9991 | 3.40194 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.09461 | −0.146273 | ||||||||
\(57\) | 5.09864 | + | 15.6920i | 0.675331 | + | 2.07846i | ||||
\(58\) | 9.07676 | + | 6.59465i | 1.19184 | + | 0.865920i | ||||
\(59\) | −2.52809 | + | 1.83676i | −0.329129 | + | 0.239126i | −0.740061 | − | 0.672540i | \(-0.765203\pi\) |
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(60\) | −1.17760 | + | 3.62427i | −0.152027 | + | 0.467891i | ||||
\(61\) | −0.738629 | + | 2.27327i | −0.0945717 | + | 0.291062i | −0.987142 | − | 0.159847i | \(-0.948900\pi\) |
0.892570 | + | 0.450909i | \(0.148900\pi\) | |||||||
\(62\) | −12.2482 | + | 8.89881i | −1.55552 | + | 1.13015i | ||||
\(63\) | −5.47293 | − | 3.97631i | −0.689524 | − | 0.500968i | ||||
\(64\) | −3.53938 | − | 10.8931i | −0.442422 | − | 1.36164i | ||||
\(65\) | 2.71995 | 0.337369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0147 | 1.22349 | 0.611744 | − | 0.791056i | \(-0.290468\pi\) | ||||
0.611744 | + | 0.791056i | \(0.290468\pi\) | |||||||
\(68\) | 4.36001 | + | 13.4187i | 0.528729 | + | 1.62726i | ||||
\(69\) | 6.28194 | + | 4.56410i | 0.756257 | + | 0.549453i | ||||
\(70\) | 0.833511 | − | 0.605581i | 0.0996236 | − | 0.0723808i | ||||
\(71\) | 3.73145 | − | 11.4842i | 0.442842 | − | 1.36293i | −0.441991 | − | 0.897019i | \(-0.645728\pi\) |
0.884833 | − | 0.465908i | \(-0.154272\pi\) | |||||||
\(72\) | −2.28825 | + | 7.04251i | −0.269673 | + | 0.829968i | ||||
\(73\) | −1.93375 | + | 1.40496i | −0.226329 | + | 0.164438i | −0.695171 | − | 0.718844i | \(-0.744671\pi\) |
0.468842 | + | 0.883282i | \(0.344671\pi\) | |||||||
\(74\) | −0.404138 | − | 0.293623i | −0.0469801 | − | 0.0341330i | ||||
\(75\) | 4.60120 | + | 14.1610i | 0.531301 | + | 1.63518i | ||||
\(76\) | −13.2800 | −1.52333 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 37.2489 | 4.21760 | ||||||||
\(79\) | 2.79051 | + | 8.58830i | 0.313957 | + | 0.966260i | 0.976182 | + | 0.216954i | \(0.0696123\pi\) |
−0.662225 | + | 0.749305i | \(0.730388\pi\) | |||||||
\(80\) | 1.06082 | + | 0.770727i | 0.118603 | + | 0.0861699i | ||||
\(81\) | −13.3239 | + | 9.68039i | −1.48044 | + | 1.07560i | ||||
\(82\) | −1.56950 | + | 4.83043i | −0.173322 | + | 0.533432i | ||||
\(83\) | −0.994879 | + | 3.06192i | −0.109202 | + | 0.336090i | −0.990694 | − | 0.136110i | \(-0.956540\pi\) |
0.881492 | + | 0.472200i | \(0.156540\pi\) | |||||||
\(84\) | 6.35848 | − | 4.61971i | 0.693767 | − | 0.504052i | ||||
\(85\) | −2.20049 | − | 1.59875i | −0.238676 | − | 0.173409i | ||||
\(86\) | −0.676506 | − | 2.08207i | −0.0729495 | − | 0.224515i | ||||
\(87\) | −16.4995 | −1.76894 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.26537 | −0.134129 | −0.0670643 | − | 0.997749i | \(-0.521363\pi\) | ||||
−0.0670643 | + | 0.997749i | \(0.521363\pi\) | |||||||
\(90\) | −2.15376 | − | 6.62860i | −0.227027 | − | 0.698716i | ||||
\(91\) | −4.53838 | − | 3.29733i | −0.475752 | − | 0.345654i | ||||
\(92\) | −5.05617 | + | 3.67352i | −0.527142 | + | 0.382991i | ||||
\(93\) | 6.88009 | − | 21.1748i | 0.713432 | − | 2.19572i | ||||
\(94\) | 1.05700 | − | 3.25312i | 0.109021 | − | 0.335533i | ||||
\(95\) | 2.07116 | − | 1.50479i | 0.212496 | − | 0.154388i | ||||
\(96\) | 20.0620 | + | 14.5759i | 2.04757 | + | 1.48765i | ||||
\(97\) | −2.71786 | − | 8.36472i | −0.275957 | − | 0.849308i | −0.988965 | − | 0.148152i | \(-0.952667\pi\) |
0.713008 | − | 0.701156i | \(-0.247333\pi\) | |||||||
\(98\) | −2.12489 | −0.214646 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.9844 | −1.19844 | ||||||||
\(101\) | −4.00188 | − | 12.3165i | −0.398202 | − | 1.22554i | −0.926440 | − | 0.376443i | \(-0.877147\pi\) |
0.528238 | − | 0.849096i | \(-0.322853\pi\) | |||||||
\(102\) | −30.1350 | − | 21.8943i | −2.98381 | − | 2.16786i | ||||
\(103\) | −9.84561 | + | 7.15325i | −0.970117 | + | 0.704831i | −0.955478 | − | 0.295062i | \(-0.904660\pi\) |
−0.0146385 | + | 0.999893i | \(0.504660\pi\) | |||||||
\(104\) | −1.89751 | + | 5.83995i | −0.186066 | + | 0.572654i | ||||
\(105\) | −0.468203 | + | 1.44098i | −0.0456920 | + | 0.140625i | ||||
\(106\) | −5.20925 | + | 3.78474i | −0.505967 | + | 0.367607i | ||||
\(107\) | −8.54330 | − | 6.20707i | −0.825912 | − | 0.600060i | 0.0924881 | − | 0.995714i | \(-0.470518\pi\) |
−0.918400 | + | 0.395654i | \(0.870518\pi\) | |||||||
\(108\) | −9.14393 | − | 28.1421i | −0.879875 | − | 2.70798i | ||||
\(109\) | −7.34060 | −0.703102 | −0.351551 | − | 0.936169i | \(-0.614346\pi\) | ||||
−0.351551 | + | 0.936169i | \(0.614346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.734633 | 0.0697283 | ||||||||
\(112\) | −0.835692 | − | 2.57200i | −0.0789655 | − | 0.243031i | ||||
\(113\) | −11.1360 | − | 8.09081i | −1.04759 | − | 0.761119i | −0.0758381 | − | 0.997120i | \(-0.524163\pi\) |
−0.971753 | + | 0.236001i | \(0.924163\pi\) | |||||||
\(114\) | 28.3638 | − | 20.6075i | 2.65652 | − | 1.93007i | ||||
\(115\) | 0.372308 | − | 1.14585i | 0.0347179 | − | 0.106851i | ||||
\(116\) | 4.10376 | − | 12.6301i | 0.381025 | − | 1.17267i | ||||
\(117\) | −30.7017 | + | 22.3061i | −2.83838 | + | 2.06220i | ||||
\(118\) | 5.37189 | + | 3.90291i | 0.494523 | + | 0.359292i | ||||
\(119\) | 1.73351 | + | 5.33519i | 0.158910 | + | 0.489076i | ||||
\(120\) | 1.65848 | 0.151398 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.07901 | 0.459832 | ||||||||
\(123\) | −2.30813 | − | 7.10369i | −0.208117 | − | 0.640518i | ||||
\(124\) | 14.4976 | + | 10.5332i | 1.30193 | + | 0.945905i | ||||
\(125\) | 3.83040 | − | 2.78295i | 0.342601 | − | 0.248914i | ||||
\(126\) | −4.44201 | + | 13.6711i | −0.395726 | + | 1.21792i | ||||
\(127\) | 0.791113 | − | 2.43479i | 0.0701999 | − | 0.216053i | −0.909802 | − | 0.415044i | \(-0.863766\pi\) |
0.980001 | + | 0.198991i | \(0.0637663\pi\) | |||||||
\(128\) | −6.84946 | + | 4.97643i | −0.605413 | + | 0.439858i | ||||
\(129\) | 2.60463 | + | 1.89237i | 0.229325 | + | 0.166614i | ||||
\(130\) | −1.78599 | − | 5.49672i | −0.156642 | − | 0.482094i | ||||
\(131\) | −2.71995 | −0.237643 | −0.118822 | − | 0.992916i | \(-0.537912\pi\) | ||||
−0.118822 | + | 0.992916i | \(0.537912\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.28005 | −0.457838 | ||||||||
\(134\) | −6.57590 | − | 20.2385i | −0.568071 | − | 1.74834i | ||||
\(135\) | 4.61492 | + | 3.35294i | 0.397189 | + | 0.288575i | ||||
\(136\) | 4.96775 | − | 3.60928i | 0.425981 | − | 0.309494i | ||||
\(137\) | −2.99881 | + | 9.22939i | −0.256206 | + | 0.788520i | 0.737384 | + | 0.675474i | \(0.236061\pi\) |
−0.993590 | + | 0.113046i | \(0.963939\pi\) | |||||||
\(138\) | 5.09864 | − | 15.6920i | 0.434025 | − | 1.33579i | ||||
\(139\) | 15.9530 | − | 11.5906i | 1.35312 | − | 0.983098i | 0.354269 | − | 0.935143i | \(-0.384730\pi\) |
0.998850 | − | 0.0479549i | \(-0.0152704\pi\) | |||||||
\(140\) | −0.986592 | − | 0.716801i | −0.0833822 | − | 0.0605807i | ||||
\(141\) | 1.55444 | + | 4.78408i | 0.130908 | + | 0.402892i | ||||
\(142\) | −25.6585 | −2.15321 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −18.2947 | −1.52456 | ||||||||
\(145\) | 0.791113 | + | 2.43479i | 0.0656983 | + | 0.202199i | ||||
\(146\) | 4.10901 | + | 2.98537i | 0.340064 | + | 0.247071i | ||||
\(147\) | 2.52809 | − | 1.83676i | 0.208513 | − | 0.151494i | ||||
\(148\) | −0.182718 | + | 0.562347i | −0.0150193 | + | 0.0462246i | ||||
\(149\) | 3.26325 | − | 10.0432i | 0.267336 | − | 0.822775i | −0.723810 | − | 0.689999i | \(-0.757611\pi\) |
0.991146 | − | 0.132776i | \(-0.0423890\pi\) | |||||||
\(150\) | 25.5966 | − | 18.5970i | 2.08995 | − | 1.51844i | ||||
\(151\) | −12.5149 | − | 9.09261i | −1.01845 | − | 0.739946i | −0.0524839 | − | 0.998622i | \(-0.516714\pi\) |
−0.965964 | + | 0.258676i | \(0.916714\pi\) | |||||||
\(152\) | 1.78599 | + | 5.49672i | 0.144863 | + | 0.445842i | ||||
\(153\) | 37.9494 | 3.06803 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.45459 | −0.277479 | ||||||||
\(156\) | −13.6245 | − | 41.9320i | −1.09084 | − | 3.35725i | ||||
\(157\) | −7.36651 | − | 5.35208i | −0.587912 | − | 0.427143i | 0.253656 | − | 0.967294i | \(-0.418367\pi\) |
−0.841568 | + | 0.540152i | \(0.818367\pi\) | |||||||
\(158\) | 15.5237 | − | 11.2786i | 1.23500 | − | 0.897277i | ||||
\(159\) | 2.92616 | − | 9.00581i | 0.232060 | − | 0.714207i | ||||
\(160\) | 1.18901 | − | 3.65938i | 0.0939991 | − | 0.289300i | ||||
\(161\) | −2.01030 | + | 1.46057i | −0.158433 | + | 0.115109i | ||||
\(162\) | 28.3118 | + | 20.5697i | 2.22438 | + | 1.61611i | ||||
\(163\) | −4.10376 | − | 12.6301i | −0.321431 | − | 0.989264i | −0.973026 | − | 0.230696i | \(-0.925900\pi\) |
0.651594 | − | 0.758567i | \(-0.274100\pi\) | |||||||
\(164\) | 6.01182 | 0.469444 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.84106 | 0.530969 | ||||||||
\(167\) | 3.10888 | + | 9.56815i | 0.240572 | + | 0.740406i | 0.996333 | + | 0.0855581i | \(0.0272673\pi\) |
−0.755761 | + | 0.654848i | \(0.772733\pi\) | |||||||
\(168\) | −2.76727 | − | 2.01054i | −0.213499 | − | 0.155116i | ||||
\(169\) | −14.9419 | + | 10.8560i | −1.14938 | + | 0.835074i | ||||
\(170\) | −1.78599 | + | 5.49672i | −0.136979 | + | 0.421579i | ||||
\(171\) | −11.0378 | + | 33.9708i | −0.844081 | + | 2.59781i | ||||
\(172\) | −2.09639 | + | 1.52312i | −0.159849 | + | 0.116137i | ||||
\(173\) | 6.60954 | + | 4.80211i | 0.502514 | + | 0.365098i | 0.809976 | − | 0.586462i | \(-0.199480\pi\) |
−0.307462 | + | 0.951560i | \(0.599480\pi\) | |||||||
\(174\) | 10.8340 | + | 33.3437i | 0.821325 | + | 2.52778i | ||||
\(175\) | −4.76491 | −0.360193 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.76491 | −0.733975 | ||||||||
\(178\) | 0.830873 | + | 2.55716i | 0.0622765 | + | 0.191667i | ||||
\(179\) | 9.92215 | + | 7.20886i | 0.741616 | + | 0.538816i | 0.893217 | − | 0.449626i | \(-0.148443\pi\) |
−0.151601 | + | 0.988442i | \(0.548443\pi\) | |||||||
\(180\) | −6.67420 | + | 4.84909i | −0.497466 | + | 0.361430i | ||||
\(181\) | −2.17701 | + | 6.70015i | −0.161816 | + | 0.498018i | −0.998788 | − | 0.0492280i | \(-0.984324\pi\) |
0.836972 | + | 0.547246i | \(0.184324\pi\) | |||||||
\(182\) | −3.68350 | + | 11.3367i | −0.273040 | + | 0.840329i | ||||
\(183\) | −6.04276 | + | 4.39032i | −0.446694 | + | 0.324542i | ||||
\(184\) | 2.20049 | + | 1.59875i | 0.162222 | + | 0.117861i | ||||
\(185\) | −0.0352238 | − | 0.108408i | −0.00258971 | − | 0.00797030i | ||||
\(186\) | −47.3094 | −3.46889 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.04874 | −0.295284 | ||||||||
\(189\) | −3.63556 | − | 11.1891i | −0.264448 | − | 0.813887i | ||||
\(190\) | −4.40098 | − | 3.19750i | −0.319280 | − | 0.231971i | ||||
\(191\) | −15.2056 | + | 11.0475i | −1.10024 | + | 0.799371i | −0.981099 | − | 0.193506i | \(-0.938014\pi\) |
−0.119141 | + | 0.992877i | \(0.538014\pi\) | |||||||
\(192\) | 11.0602 | − | 34.0396i | 0.798198 | − | 2.45660i | ||||
\(193\) | 5.09864 | − | 15.6920i | 0.367008 | − | 1.12953i | −0.581706 | − | 0.813399i | \(-0.697615\pi\) |
0.948714 | − | 0.316136i | \(-0.102385\pi\) | |||||||
\(194\) | −15.1195 | + | 10.9850i | −1.08552 | + | 0.788675i | ||||
\(195\) | 6.87627 | + | 4.99591i | 0.492420 | + | 0.357764i | ||||
\(196\) | 0.777220 | + | 2.39204i | 0.0555157 | + | 0.170860i | ||||
\(197\) | 24.4995 | 1.74552 | 0.872760 | − | 0.488149i | \(-0.162328\pi\) | ||||
0.872760 | + | 0.488149i | \(0.162328\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.3893 | −1.09092 | −0.545461 | − | 0.838136i | \(-0.683645\pi\) | ||||
−0.545461 | + | 0.838136i | \(0.683645\pi\) | |||||||
\(200\) | 1.61174 | + | 4.96044i | 0.113968 | + | 0.350756i | ||||
\(201\) | 25.3180 | + | 18.3946i | 1.78579 | + | 1.29745i | ||||
\(202\) | −22.2625 | + | 16.1747i | −1.56639 | + | 1.13805i | ||||
\(203\) | 1.63162 | − | 5.02162i | 0.114518 | − | 0.352449i | ||||
\(204\) | −13.6245 | + | 41.9320i | −0.953908 | + | 2.93583i | ||||
\(205\) | −0.937604 | + | 0.681209i | −0.0654851 | + | 0.0475777i | ||||
\(206\) | 20.9208 | + | 15.1998i | 1.45762 | + | 1.05902i | ||||
\(207\) | 5.19453 | + | 15.9871i | 0.361045 | + | 1.11118i | ||||
\(208\) | −15.1708 | −1.05190 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.21949 | 0.222166 | ||||||||
\(211\) | −4.46189 | − | 13.7323i | −0.307169 | − | 0.945370i | −0.978859 | − | 0.204537i | \(-0.934431\pi\) |
0.671689 | − | 0.740833i | \(-0.265569\pi\) | |||||||
\(212\) | 6.16597 | + | 4.47984i | 0.423481 | + | 0.307677i | ||||
\(213\) | 30.5272 | − | 22.1793i | 2.09169 | − | 1.51970i | ||||
\(214\) | −6.93403 | + | 21.3407i | −0.474000 | + | 1.45882i | ||||
\(215\) | 0.154367 | − | 0.475092i | 0.0105277 | − | 0.0324010i | ||||
\(216\) | −10.4185 | + | 7.56949i | −0.708889 | + | 0.515038i | ||||
\(217\) | 5.76415 | + | 4.18790i | 0.391296 | + | 0.284293i | ||||
\(218\) | 4.82003 | + | 14.8345i | 0.326453 | + | 1.00472i | ||||
\(219\) | −7.46927 | −0.504726 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.4693 | 2.11685 | ||||||||
\(222\) | −0.482379 | − | 1.48461i | −0.0323751 | − | 0.0996404i | ||||
\(223\) | −13.9584 | − | 10.1414i | −0.934725 | − | 0.679117i | 0.0124203 | − | 0.999923i | \(-0.496046\pi\) |
−0.947145 | + | 0.320806i | \(0.896046\pi\) | |||||||
\(224\) | −6.42009 | + | 4.66447i | −0.428960 | + | 0.311658i | ||||
\(225\) | −9.96091 | + | 30.6565i | −0.664061 | + | 2.04377i | ||||
\(226\) | −9.03839 | + | 27.8173i | −0.601225 | + | 1.85038i | ||||
\(227\) | −8.67262 | + | 6.30103i | −0.575622 | + | 0.418214i | −0.837143 | − | 0.546984i | \(-0.815776\pi\) |
0.261521 | + | 0.965198i | \(0.415776\pi\) | |||||||
\(228\) | −33.5731 | − | 24.3923i | −2.22343 | − | 1.61542i | ||||
\(229\) | 1.68556 | + | 5.18762i | 0.111385 | + | 0.342808i | 0.991176 | − | 0.132553i | \(-0.0423175\pi\) |
−0.879791 | + | 0.475361i | \(0.842318\pi\) | |||||||
\(230\) | −2.56009 | −0.168808 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.77959 | −0.379449 | ||||||||
\(233\) | 9.20240 | + | 28.3221i | 0.602869 | + | 1.85544i | 0.510823 | + | 0.859686i | \(0.329341\pi\) |
0.0920461 | + | 0.995755i | \(0.470659\pi\) | |||||||
\(234\) | 65.2377 | + | 47.3979i | 4.26472 | + | 3.09850i | ||||
\(235\) | 0.631442 | − | 0.458769i | 0.0411907 | − | 0.0299268i | ||||
\(236\) | 2.42872 | − | 7.47485i | 0.158097 | − | 0.486571i | ||||
\(237\) | −8.72002 | + | 26.8375i | −0.566426 | + | 1.74328i | ||||
\(238\) | 9.64354 | − | 7.00644i | 0.625098 | − | 0.454160i | ||||
\(239\) | −2.07116 | − | 1.50479i | −0.133972 | − | 0.0973365i | 0.518781 | − | 0.854907i | \(-0.326386\pi\) |
−0.652753 | + | 0.757571i | \(0.726386\pi\) | |||||||
\(240\) | 1.26619 | + | 3.89693i | 0.0817321 | + | 0.251546i | ||||
\(241\) | 27.3893 | 1.76430 | 0.882151 | − | 0.470966i | \(-0.156095\pi\) | ||||
0.882151 | + | 0.470966i | \(0.156095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1698 | −1.03730 | ||||||||
\(244\) | −1.85775 | − | 5.71758i | −0.118930 | − | 0.366030i | ||||
\(245\) | −0.392262 | − | 0.284995i | −0.0250607 | − | 0.0182076i | ||||
\(246\) | −12.8402 | + | 9.32894i | −0.818660 | + | 0.594791i | ||||
\(247\) | −9.15300 | + | 28.1700i | −0.582391 | + | 1.79242i | ||||
\(248\) | 2.41001 | − | 7.41726i | 0.153036 | − | 0.470996i | ||||
\(249\) | −8.13916 | + | 5.91344i | −0.515798 | + | 0.374749i | ||||
\(250\) | −8.13916 | − | 5.91344i | −0.514766 | − | 0.373999i | ||||
\(251\) | 3.04222 | + | 9.36300i | 0.192023 | + | 0.590987i | 0.999998 | + | 0.00177049i | \(0.000563565\pi\) |
−0.807975 | + | 0.589217i | \(0.799436\pi\) | |||||||
\(252\) | 17.0147 | 1.07182 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.43991 | −0.341330 | ||||||||
\(255\) | −2.62650 | − | 8.08354i | −0.164478 | − | 0.506211i | ||||
\(256\) | −3.97810 | − | 2.89026i | −0.248631 | − | 0.180641i | ||||
\(257\) | 18.2025 | − | 13.2249i | 1.13544 | − | 0.824947i | 0.148964 | − | 0.988843i | \(-0.452406\pi\) |
0.986478 | + | 0.163896i | \(0.0524062\pi\) | |||||||
\(258\) | 2.11400 | − | 6.50623i | 0.131612 | − | 0.405060i | ||||
\(259\) | −0.0726471 | + | 0.223585i | −0.00451407 | + | 0.0138929i | ||||
\(260\) | −5.53453 | + | 4.02107i | −0.343237 | + | 0.249376i | ||||
\(261\) | −28.8973 | − | 20.9951i | −1.78870 | − | 1.29957i | ||||
\(262\) | 1.78599 | + | 5.49672i | 0.110339 | + | 0.339588i | ||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.46927 | −0.0902563 | ||||||||
\(266\) | 3.46701 | + | 10.6704i | 0.212576 | + | 0.654243i | ||||
\(267\) | −3.19896 | − | 2.32418i | −0.195773 | − | 0.142237i | ||||
\(268\) | −20.3778 | + | 14.8053i | −1.24477 | + | 0.904378i | ||||
\(269\) | 2.84898 | − | 8.76826i | 0.173705 | − | 0.534610i | −0.825867 | − | 0.563866i | \(-0.809314\pi\) |
0.999572 | + | 0.0292553i | \(0.00931359\pi\) | |||||||
\(270\) | 3.74563 | − | 11.5279i | 0.227952 | − | 0.701563i | ||||
\(271\) | −8.54330 | + | 6.20707i | −0.518968 | + | 0.377052i | −0.816215 | − | 0.577748i | \(-0.803932\pi\) |
0.297247 | + | 0.954801i | \(0.403932\pi\) | |||||||
\(272\) | 12.2734 | + | 8.91715i | 0.744184 | + | 0.540682i | ||||
\(273\) | −5.41701 | − | 16.6718i | −0.327852 | − | 1.00903i | ||||
\(274\) | 20.6206 | 1.24574 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −19.5298 | −1.17556 | ||||||||
\(277\) | −5.73538 | − | 17.6517i | −0.344606 | − | 1.06059i | −0.961794 | − | 0.273773i | \(-0.911728\pi\) |
0.617189 | − | 0.786815i | \(-0.288272\pi\) | |||||||
\(278\) | −33.8984 | − | 24.6286i | −2.03309 | − | 1.47713i | ||||
\(279\) | 38.9940 | − | 28.3308i | 2.33451 | − | 1.69612i | ||||
\(280\) | −0.164006 | + | 0.504758i | −0.00980123 | + | 0.0301651i | ||||
\(281\) | 7.92891 | − | 24.4027i | 0.472999 | − | 1.45574i | −0.375638 | − | 0.926766i | \(-0.622577\pi\) |
0.848637 | − | 0.528975i | \(-0.177423\pi\) | |||||||
\(282\) | 8.64739 | − | 6.28270i | 0.514945 | − | 0.374129i | ||||
\(283\) | −24.4963 | − | 17.7976i | −1.45616 | − | 1.05796i | −0.984344 | − | 0.176260i | \(-0.943600\pi\) |
−0.471812 | − | 0.881699i | \(-0.656400\pi\) | |||||||
\(284\) | 9.38512 | + | 28.8844i | 0.556904 | + | 1.71397i | ||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.39025 | 0.141092 | ||||||||
\(288\) | 16.5893 | + | 51.0566i | 0.977533 | + | 3.00854i | ||||
\(289\) | −11.7059 | − | 8.50482i | −0.688581 | − | 0.500284i | ||||
\(290\) | 4.40098 | − | 3.19750i | 0.258434 | − | 0.187763i | ||||
\(291\) | 8.49301 | − | 26.1388i | 0.497869 | − | 1.53228i | ||||
\(292\) | 1.85775 | − | 5.71758i | 0.108717 | − | 0.334596i | ||||
\(293\) | −2.46722 | + | 1.79254i | −0.144137 | + | 0.104721i | −0.657517 | − | 0.753440i | \(-0.728393\pi\) |
0.513380 | + | 0.858161i | \(0.328393\pi\) | |||||||
\(294\) | −5.37189 | − | 3.90291i | −0.313295 | − | 0.227622i | ||||
\(295\) | 0.468203 | + | 1.44098i | 0.0272599 | + | 0.0838972i | ||||
\(296\) | 0.257333 | 0.0149572 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.4390 | −1.29986 | ||||||||
\(299\) | 4.30753 | + | 13.2572i | 0.249111 | + | 0.766684i | ||||
\(300\) | −30.2976 | − | 22.0125i | −1.74923 | − | 1.27089i | ||||
\(301\) | −0.833511 | + | 0.605581i | −0.0480428 | + | 0.0349051i | ||||
\(302\) | −10.1575 | + | 31.2616i | −0.584499 | + | 1.79890i | ||||
\(303\) | 12.5054 | − | 38.4877i | 0.718417 | − | 2.21106i | ||||
\(304\) | −11.5521 | + | 8.39306i | −0.662556 | + | 0.481375i | ||||
\(305\) | 0.937604 | + | 0.681209i | 0.0536871 | + | 0.0390059i | ||||
\(306\) | −24.9186 | − | 76.6915i | −1.42450 | − | 4.38416i | ||||
\(307\) | 3.71904 | 0.212257 | 0.106128 | − | 0.994352i | \(-0.466155\pi\) | ||||
0.106128 | + | 0.994352i | \(0.466155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −38.0294 | −2.16341 | ||||||||
\(310\) | 2.26837 | + | 6.98132i | 0.128835 | + | 0.396513i | ||||
\(311\) | −3.37347 | − | 2.45097i | −0.191292 | − | 0.138982i | 0.488017 | − | 0.872834i | \(-0.337720\pi\) |
−0.679309 | + | 0.733852i | \(0.737720\pi\) | |||||||
\(312\) | −15.5237 | + | 11.2786i | −0.878854 | + | 0.638525i | ||||
\(313\) | −3.61685 | + | 11.1315i | −0.204436 | + | 0.629190i | 0.795300 | + | 0.606216i | \(0.207313\pi\) |
−0.999736 | + | 0.0229737i | \(0.992687\pi\) | |||||||
\(314\) | −5.97891 | + | 18.4012i | −0.337409 | + | 1.03844i | ||||
\(315\) | −2.65361 | + | 1.92796i | −0.149514 | + | 0.108628i | ||||
\(316\) | −18.3747 | − | 13.3500i | −1.03366 | − | 0.750997i | ||||
\(317\) | −0.690681 | − | 2.12570i | −0.0387925 | − | 0.119391i | 0.929785 | − | 0.368103i | \(-0.119993\pi\) |
−0.968577 | + | 0.248712i | \(0.919993\pi\) | |||||||
\(318\) | −20.1211 | −1.12834 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −5.55345 | −0.310447 | ||||||||
\(321\) | −10.1973 | − | 31.3840i | −0.569157 | − | 1.75168i | ||||
\(322\) | 4.27165 | + | 3.10353i | 0.238050 | + | 0.172953i | ||||
\(323\) | 23.9629 | − | 17.4100i | 1.33333 | − | 0.968721i | ||||
\(324\) | 12.8002 | − | 39.3951i | 0.711125 | − | 2.18862i | ||||
\(325\) | −8.26000 | + | 25.4217i | −0.458183 | + | 1.41014i | ||||
\(326\) | −22.8293 | + | 16.5865i | −1.26440 | + | 0.918639i | ||||
\(327\) | −18.5577 | − | 13.4829i | −1.02624 | − | 0.745608i | ||||
\(328\) | −0.808510 | − | 2.48834i | −0.0446425 | − | 0.137395i | ||||
\(329\) | −1.60975 | −0.0887482 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.3250 | 1.22709 | 0.613547 | − | 0.789659i | \(-0.289742\pi\) | ||||
0.613547 | + | 0.789659i | \(0.289742\pi\) | |||||||
\(332\) | −2.50226 | − | 7.70116i | −0.137329 | − | 0.422656i | ||||
\(333\) | 1.28664 | + | 0.934796i | 0.0705072 | + | 0.0512265i | ||||
\(334\) | 17.2948 | − | 12.5654i | 0.946328 | − | 0.687548i | ||||
\(335\) | 1.50051 | − | 4.61808i | 0.0819814 | − | 0.252313i | ||||
\(336\) | 2.61144 | − | 8.03719i | 0.142466 | − | 0.438465i | ||||
\(337\) | 10.7438 | − | 7.80582i | 0.585251 | − | 0.425210i | −0.255362 | − | 0.966845i | \(-0.582195\pi\) |
0.840613 | + | 0.541636i | \(0.182195\pi\) | |||||||
\(338\) | 31.7499 | + | 23.0677i | 1.72697 | + | 1.25472i | ||||
\(339\) | −13.2920 | − | 40.9085i | −0.721921 | − | 2.22185i | ||||
\(340\) | 6.84106 | 0.371008 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 75.8989 | 4.10414 | ||||||||
\(343\) | 0.309017 | + | 0.951057i | 0.0166853 | + | 0.0513522i | ||||
\(344\) | 0.912369 | + | 0.662875i | 0.0491916 | + | 0.0357398i | ||||
\(345\) | 3.04588 | − | 2.21296i | 0.163984 | − | 0.119142i | ||||
\(346\) | 5.36453 | − | 16.5103i | 0.288399 | − | 0.887600i | ||||
\(347\) | −5.57138 | + | 17.1469i | −0.299087 | + | 0.920496i | 0.682731 | + | 0.730670i | \(0.260792\pi\) |
−0.981818 | + | 0.189826i | \(0.939208\pi\) | |||||||
\(348\) | 33.5731 | − | 24.3923i | 1.79971 | − | 1.30756i | ||||
\(349\) | 17.7575 | + | 12.9016i | 0.950535 | + | 0.690604i | 0.950933 | − | 0.309396i | \(-0.100127\pi\) |
−0.000398242 | 1.00000i | \(0.500127\pi\) | ||||||||
\(350\) | 3.12876 | + | 9.62934i | 0.167239 | + | 0.514710i | ||||
\(351\) | −65.9982 | −3.52272 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8557 | 1.00359 | 0.501795 | − | 0.864987i | \(-0.332673\pi\) | ||||
0.501795 | + | 0.864987i | \(0.332673\pi\) | |||||||
\(354\) | 6.41189 | + | 19.7338i | 0.340788 | + | 1.04884i | ||||
\(355\) | −4.73665 | − | 3.44138i | −0.251395 | − | 0.182649i | ||||
\(356\) | 2.57476 | − | 1.87067i | 0.136462 | − | 0.0991453i | ||||
\(357\) | −5.41701 | + | 16.6718i | −0.286699 | + | 0.882368i | ||||
\(358\) | 8.05315 | − | 24.7851i | 0.425622 | − | 1.30993i | ||||
\(359\) | −1.23765 | + | 0.899204i | −0.0653206 | + | 0.0474582i | −0.619966 | − | 0.784628i | \(-0.712854\pi\) |
0.554646 | + | 0.832087i | \(0.312854\pi\) | |||||||
\(360\) | 2.90467 | + | 2.11037i | 0.153090 | + | 0.111226i | ||||
\(361\) | 2.74373 | + | 8.44433i | 0.144407 | + | 0.444439i | ||||
\(362\) | 14.9697 | 0.786791 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.1093 | 0.739528 | ||||||||
\(365\) | 0.358133 | + | 1.10222i | 0.0187455 | + | 0.0576928i | ||||
\(366\) | 12.8402 | + | 9.32894i | 0.671167 | + | 0.487631i | ||||
\(367\) | −11.8559 | + | 8.61382i | −0.618873 | + | 0.449638i | −0.852528 | − | 0.522682i | \(-0.824932\pi\) |
0.233655 | + | 0.972320i | \(0.424932\pi\) | |||||||
\(368\) | −2.07658 | + | 6.39106i | −0.108249 | + | 0.333157i | ||||
\(369\) | 4.99676 | − | 15.3784i | 0.260121 | − | 0.800569i | ||||
\(370\) | −0.195951 | + | 0.142367i | −0.0101870 | + | 0.00740129i | ||||
\(371\) | 2.45154 | + | 1.78115i | 0.127278 | + | 0.0924728i | ||||
\(372\) | 17.3044 | + | 53.2574i | 0.897191 | + | 2.76127i | ||||
\(373\) | 10.0606 | 0.520916 | 0.260458 | − | 0.965485i | \(-0.416127\pi\) | ||||
0.260458 | + | 0.965485i | \(0.416127\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.7952 | 0.764020 | ||||||||
\(376\) | 0.544502 | + | 1.67580i | 0.0280805 | + | 0.0864230i | ||||
\(377\) | −23.9629 | − | 17.4100i | −1.23415 | − | 0.896663i | ||||
\(378\) | −20.2247 | + | 14.6941i | −1.04025 | + | 0.755783i | ||||
\(379\) | −5.52942 | + | 17.0178i | −0.284027 | + | 0.874146i | 0.702661 | + | 0.711524i | \(0.251995\pi\) |
−0.986689 | + | 0.162621i | \(0.948005\pi\) | |||||||
\(380\) | −1.98976 | + | 6.12384i | −0.102072 | + | 0.314147i | ||||
\(381\) | 6.47214 | − | 4.70228i | 0.331578 | − | 0.240905i | ||||
\(382\) | 32.3102 | + | 23.4747i | 1.65313 | + | 1.20107i | ||||
\(383\) | −5.86052 | − | 18.0368i | −0.299458 | − | 0.921638i | −0.981687 | − | 0.190499i | \(-0.938989\pi\) |
0.682229 | − | 0.731139i | \(-0.261011\pi\) | |||||||
\(384\) | −26.4565 | −1.35010 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −35.0596 | −1.78449 | ||||||||
\(387\) | 2.15376 | + | 6.62860i | 0.109482 | + | 0.336951i | ||||
\(388\) | 17.8963 | + | 13.0025i | 0.908549 | + | 0.660100i | ||||
\(389\) | −27.7205 | + | 20.1401i | −1.40549 | + | 1.02115i | −0.411527 | + | 0.911398i | \(0.635004\pi\) |
−0.993959 | + | 0.109748i | \(0.964996\pi\) | |||||||
\(390\) | 5.58102 | − | 17.1766i | 0.282606 | − | 0.869771i | ||||
\(391\) | 4.30753 | − | 13.2572i | 0.217841 | − | 0.670446i | ||||
\(392\) | 0.885558 | − | 0.643395i | 0.0447274 | − | 0.0324964i | ||||
\(393\) | −6.87627 | − | 4.99591i | −0.346862 | − | 0.252010i | ||||
\(394\) | −16.0870 | − | 49.5108i | −0.810453 | − | 2.49432i | ||||
\(395\) | 4.37844 | 0.220303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2791 | 0.817026 | 0.408513 | − | 0.912752i | \(-0.366047\pi\) | ||||
0.408513 | + | 0.912752i | \(0.366047\pi\) | |||||||
\(398\) | 10.1050 | + | 31.1001i | 0.506520 | + | 1.55891i | ||||
\(399\) | −13.3484 | − | 9.69819i | −0.668256 | − | 0.485517i | ||||
\(400\) | −10.4250 | + | 7.57421i | −0.521250 | + | 0.378710i | ||||
\(401\) | 8.94250 | − | 27.5222i | 0.446567 | − | 1.37439i | −0.434189 | − | 0.900822i | \(-0.642965\pi\) |
0.880756 | − | 0.473570i | \(-0.157035\pi\) | |||||||
\(402\) | 20.5489 | − | 63.2431i | 1.02489 | − | 3.15428i | ||||
\(403\) | 32.3354 | − | 23.4931i | 1.61074 | − | 1.17027i | ||||
\(404\) | 26.3512 | + | 19.1453i | 1.31102 | + | 0.952514i | ||||
\(405\) | 2.46760 | + | 7.59449i | 0.122616 | + | 0.377373i | ||||
\(406\) | −11.2195 | −0.556814 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 19.1883 | 0.949963 | ||||||||
\(409\) | 4.79299 | + | 14.7513i | 0.236998 | + | 0.729405i | 0.996850 | + | 0.0793090i | \(0.0252714\pi\) |
−0.759852 | + | 0.650096i | \(0.774729\pi\) | |||||||
\(410\) | 1.99230 | + | 1.44749i | 0.0983928 | + | 0.0714865i | ||||
\(411\) | −24.5334 | + | 17.8246i | −1.21015 | + | 0.879222i | ||||
\(412\) | 9.45865 | − | 29.1107i | 0.465994 | − | 1.43418i | ||||
\(413\) | 0.965643 | − | 2.97194i | 0.0475162 | − | 0.146240i | ||||
\(414\) | 28.8973 | − | 20.9951i | 1.42023 | − | 1.03185i | ||||
\(415\) | 1.26288 | + | 0.917539i | 0.0619925 | + | 0.0450402i | ||||
\(416\) | 13.7565 | + | 42.3383i | 0.674470 | + | 2.07580i | ||||
\(417\) | 61.6197 | 3.01753 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.9503 | −0.632666 | −0.316333 | − | 0.948648i | \(-0.602452\pi\) | ||||
−0.316333 | + | 0.948648i | \(0.602452\pi\) | |||||||
\(420\) | −1.17760 | − | 3.62427i | −0.0574608 | − | 0.176846i | ||||
\(421\) | 13.8268 | + | 10.0457i | 0.673876 | + | 0.489599i | 0.871320 | − | 0.490715i | \(-0.163264\pi\) |
−0.197445 | + | 0.980314i | \(0.563264\pi\) | |||||||
\(422\) | −24.8216 | + | 18.0340i | −1.20830 | + | 0.877879i | ||||
\(423\) | −3.36513 | + | 10.3568i | −0.163618 | + | 0.503565i | ||||
\(424\) | 1.02500 | − | 3.15462i | 0.0497784 | − | 0.153202i | ||||
\(425\) | 21.6250 | − | 15.7115i | 1.04897 | − | 0.762118i | ||||
\(426\) | −64.8668 | − | 47.1285i | −3.14281 | − | 2.28338i | ||||
\(427\) | −0.738629 | − | 2.27327i | −0.0357447 | − | 0.110011i | ||||
\(428\) | 26.5601 | 1.28383 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.06147 | −0.0511886 | ||||||||
\(431\) | 5.97891 | + | 18.4012i | 0.287994 | + | 0.886354i | 0.985485 | + | 0.169761i | \(0.0542996\pi\) |
−0.697491 | + | 0.716593i | \(0.745700\pi\) | |||||||
\(432\) | −25.7401 | − | 18.7013i | −1.23842 | − | 0.899766i | ||||
\(433\) | −12.8031 | + | 9.30197i | −0.615276 | + | 0.447024i | −0.851268 | − | 0.524731i | \(-0.824166\pi\) |
0.235992 | + | 0.971755i | \(0.424166\pi\) | |||||||
\(434\) | 4.67838 | − | 14.3986i | 0.224570 | − | 0.691154i | ||||
\(435\) | −2.47214 | + | 7.60845i | −0.118530 | + | 0.364797i | ||||
\(436\) | 14.9366 | − | 10.8521i | 0.715332 | − | 0.519719i | ||||
\(437\) | 10.6145 | + | 7.71185i | 0.507758 | + | 0.368908i | ||||
\(438\) | 4.90451 | + | 15.0945i | 0.234347 | + | 0.721245i | ||||
\(439\) | −11.0596 | −0.527848 | −0.263924 | − | 0.964544i | \(-0.585017\pi\) | ||||
−0.263924 | + | 0.964544i | \(0.585017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.76491 | 0.322139 | ||||||||
\(442\) | −20.6635 | − | 63.5958i | −0.982864 | − | 3.02494i | ||||
\(443\) | 28.0757 | + | 20.3982i | 1.33392 | + | 0.969146i | 0.999644 | + | 0.0266694i | \(0.00849013\pi\) |
0.334271 | + | 0.942477i | \(0.391510\pi\) | |||||||
\(444\) | −1.49482 | + | 1.08605i | −0.0709412 | + | 0.0515418i | ||||
\(445\) | −0.189591 | + | 0.583500i | −0.00898746 | + | 0.0276606i | ||||
\(446\) | −11.3291 | + | 34.8675i | −0.536450 | + | 1.65102i | ||||
\(447\) | 26.6968 | − | 19.3964i | 1.26272 | − | 0.917417i | ||||
\(448\) | 9.26621 | + | 6.73230i | 0.437787 | + | 0.318071i | ||||
\(449\) | −11.2154 | − | 34.5175i | −0.529288 | − | 1.62898i | −0.755678 | − | 0.654943i | \(-0.772693\pi\) |
0.226390 | − | 0.974037i | \(-0.427307\pi\) | |||||||
\(450\) | 68.4939 | 3.22883 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 34.6206 | 1.62842 | ||||||||
\(453\) | −14.9378 | − | 45.9738i | −0.701838 | − | 2.16004i | ||||
\(454\) | 18.4283 | + | 13.3890i | 0.864885 | + | 0.628375i | ||||
\(455\) | −2.20049 | + | 1.59875i | −0.103160 | + | 0.0749505i | ||||
\(456\) | −5.58102 | + | 17.1766i | −0.261355 | + | 0.804368i | ||||
\(457\) | −0.636746 | + | 1.95970i | −0.0297857 | + | 0.0916710i | −0.964844 | − | 0.262822i | \(-0.915347\pi\) |
0.935059 | + | 0.354493i | \(0.115347\pi\) | |||||||
\(458\) | 9.37681 | − | 6.81265i | 0.438149 | − | 0.318334i | ||||
\(459\) | 53.3936 | + | 38.7927i | 2.49220 | + | 1.81069i | ||||
\(460\) | 0.936407 | + | 2.88196i | 0.0436602 | + | 0.134372i | ||||
\(461\) | −7.17076 | −0.333975 | −0.166988 | − | 0.985959i | \(-0.553404\pi\) | ||||
−0.166988 | + | 0.985959i | \(0.553404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.45459 | 0.160548 | 0.0802741 | − | 0.996773i | \(-0.474420\pi\) | ||||
0.0802741 | + | 0.996773i | \(0.474420\pi\) | |||||||
\(464\) | −4.41249 | − | 13.5803i | −0.204845 | − | 0.630448i | ||||
\(465\) | −8.73349 | − | 6.34525i | −0.405006 | − | 0.294254i | ||||
\(466\) | 51.1932 | − | 37.1940i | 2.37148 | − | 1.72298i | ||||
\(467\) | −4.17042 | + | 12.8352i | −0.192984 | + | 0.593944i | 0.807010 | + | 0.590537i | \(0.201084\pi\) |
−0.999994 | + | 0.00340617i | \(0.998916\pi\) | |||||||
\(468\) | 29.4951 | − | 90.7765i | 1.36341 | − | 4.19614i | ||||
\(469\) | −8.10205 | + | 5.88648i | −0.374118 | + | 0.271812i | ||||
\(470\) | −1.34174 | − | 0.974833i | −0.0618899 | − | 0.0449657i | ||||
\(471\) | −8.79267 | − | 27.0610i | −0.405145 | − | 1.24691i | ||||
\(472\) | −3.42053 | −0.157443 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 59.9612 | 2.75411 | ||||||||
\(475\) | 7.77454 | + | 23.9276i | 0.356720 | + | 1.09787i | ||||
\(476\) | −11.4147 | − | 8.29323i | −0.523190 | − | 0.380120i | ||||
\(477\) | 16.5845 | − | 12.0493i | 0.759351 | − | 0.551701i | ||||
\(478\) | −1.68102 | + | 5.17366i | −0.0768882 | + | 0.236638i | ||||
\(479\) | 10.8340 | − | 33.3437i | 0.495019 | − | 1.52351i | −0.321908 | − | 0.946771i | \(-0.604324\pi\) |
0.816927 | − | 0.576741i | \(-0.195676\pi\) | |||||||
\(480\) | 9.72732 | − | 7.06731i | 0.443989 | − | 0.322577i | ||||
\(481\) | 1.06693 | + | 0.775172i | 0.0486480 | + | 0.0353448i | ||||
\(482\) | −17.9845 | − | 55.3507i | −0.819173 | − | 2.52116i | ||||
\(483\) | −7.76491 | −0.353316 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.26445 | −0.193639 | ||||||||
\(486\) | 10.6175 | + | 32.6774i | 0.481621 | + | 1.48228i | ||||
\(487\) | −24.0000 | − | 17.4370i | −1.08754 | − | 0.790146i | −0.108560 | − | 0.994090i | \(-0.534624\pi\) |
−0.978983 | + | 0.203944i | \(0.934624\pi\) | |||||||
\(488\) | −2.11671 | + | 1.53788i | −0.0958188 | + | 0.0696164i | ||||
\(489\) | 12.8238 | − | 39.4675i | 0.579911 | − | 1.78478i | ||||
\(490\) | −0.318373 | + | 0.979851i | −0.0143826 | + | 0.0442651i | ||||
\(491\) | −20.6541 | + | 15.0061i | −0.932105 | + | 0.677214i | −0.946507 | − | 0.322683i | \(-0.895415\pi\) |
0.0144027 | + | 0.999896i | \(0.495415\pi\) | |||||||
\(492\) | 15.1984 | + | 11.0423i | 0.685196 | + | 0.497824i | ||||
\(493\) | 9.15300 | + | 28.1700i | 0.412230 | + | 1.26871i | ||||
\(494\) | 62.9385 | 2.83174 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.2682 | 0.865169 | ||||||||
\(497\) | 3.73145 | + | 11.4842i | 0.167378 | + | 0.515138i | ||||
\(498\) | 17.2948 | + | 12.5654i | 0.774998 | + | 0.563069i | ||||
\(499\) | 20.7581 | − | 15.0817i | 0.929262 | − | 0.675149i | −0.0165497 | − | 0.999863i | \(-0.505268\pi\) |
0.945812 | + | 0.324714i | \(0.105268\pi\) | |||||||
\(500\) | −3.67985 | + | 11.3254i | −0.164568 | + | 0.506488i | ||||
\(501\) | −9.71490 | + | 29.8994i | −0.434030 | + | 1.33581i | ||||
\(502\) | 16.9240 | − | 12.2960i | 0.755353 | − | 0.548796i | ||||
\(503\) | −2.07116 | − | 1.50479i | −0.0923484 | − | 0.0670951i | 0.540653 | − | 0.841246i | \(-0.318177\pi\) |
−0.633001 | + | 0.774151i | \(0.718177\pi\) | |||||||
\(504\) | −2.28825 | − | 7.04251i | −0.101927 | − | 0.313698i | ||||
\(505\) | −6.27913 | −0.279418 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −57.7143 | −2.56318 | ||||||||
\(508\) | 1.98976 | + | 6.12384i | 0.0882812 | + | 0.271702i | ||||
\(509\) | −10.8850 | − | 7.90841i | −0.482469 | − | 0.350534i | 0.319812 | − | 0.947481i | \(-0.396380\pi\) |
−0.802281 | + | 0.596947i | \(0.796380\pi\) | |||||||
\(510\) | −14.6113 | + | 10.6157i | −0.646999 | + | 0.470072i | ||||
\(511\) | 0.738629 | − | 2.27327i | 0.0326750 | − | 0.100563i | ||||
\(512\) | −8.46129 | + | 26.0412i | −0.373940 | + | 1.15087i | ||||
\(513\) | −50.2555 | + | 36.5128i | −2.21884 | + | 1.61208i | ||||
\(514\) | −38.6783 | − | 28.1014i | −1.70602 | − | 1.23950i | ||||
\(515\) | 1.82341 | + | 5.61189i | 0.0803492 | + | 0.247290i | ||||
\(516\) | −8.09747 | −0.356471 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.499542 | 0.0219486 | ||||||||
\(519\) | 7.88915 | + | 24.2803i | 0.346295 | + | 1.06579i | ||||
\(520\) | 2.40867 | + | 1.75000i | 0.105627 | + | 0.0767428i | ||||
\(521\) | 26.0773 | − | 18.9462i | 1.14247 | − | 0.830050i | 0.155004 | − | 0.987914i | \(-0.450461\pi\) |
0.987461 | + | 0.157864i | \(0.0504608\pi\) | |||||||
\(522\) | −23.4540 | + | 72.1841i | −1.02656 | + | 3.15941i | ||||
\(523\) | −9.99351 | + | 30.7569i | −0.436986 | + | 1.34490i | 0.454052 | + | 0.890975i | \(0.349978\pi\) |
−0.891038 | + | 0.453929i | \(0.850022\pi\) | |||||||
\(524\) | 5.53453 | − | 4.02107i | 0.241777 | − | 0.175661i | ||||
\(525\) | −12.0461 | − | 8.75200i | −0.525735 | − | 0.381969i | ||||
\(526\) | 10.5060 | + | 32.3342i | 0.458084 | + | 1.40984i | ||||
\(527\) | −39.9688 | −1.74107 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8255 | −0.731542 | ||||||||
\(530\) | 0.964758 | + | 2.96922i | 0.0419064 | + | 0.128975i | ||||
\(531\) | −17.1023 | − | 12.4255i | −0.742175 | − | 0.539222i | ||||
\(532\) | 10.7438 | − | 7.80582i | 0.465802 | − | 0.338425i | ||||
\(533\) | 4.14352 | − | 12.7524i | 0.179476 | − | 0.552370i | ||||
\(534\) | −2.59638 | + | 7.99084i | −0.112356 | + | 0.345798i | ||||
\(535\) | −4.14232 | + | 3.00957i | −0.179088 | + | 0.130115i | ||||
\(536\) | 8.86858 | + | 6.44340i | 0.383064 | + | 0.278312i | ||||
\(537\) | 11.8431 | + | 36.4492i | 0.511067 | + | 1.57290i | ||||
\(538\) | −19.5904 | −0.844601 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −14.3472 | −0.617407 | ||||||||
\(541\) | −7.26204 | − | 22.3503i | −0.312220 | − | 0.960913i | −0.976884 | − | 0.213771i | \(-0.931425\pi\) |
0.664664 | − | 0.747142i | \(-0.268575\pi\) | |||||||
\(542\) | 18.1535 | + | 13.1893i | 0.779761 | + | 0.566529i | ||||
\(543\) | −17.8103 | + | 12.9399i | −0.764311 | + | 0.555304i | ||||
\(544\) | 13.7565 | − | 42.3383i | 0.589807 | − | 1.81524i | ||||
\(545\) | −1.09985 | + | 3.38498i | −0.0471122 | + | 0.144997i | ||||
\(546\) | −30.1350 | + | 21.8943i | −1.28966 | + | 0.936991i | ||||
\(547\) | 3.33404 | + | 2.42232i | 0.142553 | + | 0.103571i | 0.656776 | − | 0.754085i | \(-0.271920\pi\) |
−0.514223 | + | 0.857657i | \(0.671920\pi\) | |||||||
\(548\) | −7.54242 | − | 23.2132i | −0.322196 | − | 0.991619i | ||||
\(549\) | −16.1698 | −0.690112 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.8789 | −1.18768 | ||||||||
\(552\) | 2.62650 | + | 8.08354i | 0.111791 | + | 0.344059i | ||||
\(553\) | −7.30565 | − | 5.30786i | −0.310668 | − | 0.225713i | ||||
\(554\) | −31.9061 | + | 23.1811i | −1.35556 | + | 0.984871i | ||||
\(555\) | 0.110070 | − | 0.338762i | 0.00467223 | − | 0.0143796i | ||||
\(556\) | −15.3260 | + | 47.1687i | −0.649969 | + | 2.00040i | ||||
\(557\) | 11.2773 | − | 8.19340i | 0.477832 | − | 0.347166i | −0.322653 | − | 0.946517i | \(-0.604575\pi\) |
0.800486 | + | 0.599352i | \(0.204575\pi\) | |||||||
\(558\) | −82.8577 | − | 60.1997i | −3.50765 | − | 2.54845i | ||||
\(559\) | 1.78599 | + | 5.49672i | 0.0755394 | + | 0.232486i | ||||
\(560\) | −1.31124 | −0.0554100 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −54.5213 | −2.29984 | ||||||||
\(563\) | 0.840512 | + | 2.58683i | 0.0354233 | + | 0.109022i | 0.967205 | − | 0.253998i | \(-0.0817457\pi\) |
−0.931781 | + | 0.363020i | \(0.881746\pi\) | |||||||
\(564\) | −10.2356 | − | 7.43656i | −0.430995 | − | 0.313136i | ||||
\(565\) | −5.39944 | + | 3.92293i | −0.227156 | + | 0.165039i | ||||
\(566\) | −19.8821 | + | 61.1907i | −0.835705 | + | 2.57204i | ||||
\(567\) | 5.08928 | − | 15.6632i | 0.213730 | − | 0.657793i | ||||
\(568\) | 10.6933 | − | 7.76915i | 0.448681 | − | 0.325986i | ||||
\(569\) | 22.4252 | + | 16.2928i | 0.940112 | + | 0.683031i | 0.948448 | − | 0.316934i | \(-0.102653\pi\) |
−0.00833555 | + | 0.999965i | \(0.502653\pi\) | |||||||
\(570\) | −5.25301 | − | 16.1671i | −0.220024 | − | 0.677165i | ||||
\(571\) | 38.1193 | 1.59524 | 0.797621 | − | 0.603159i | \(-0.206092\pi\) | ||||
0.797621 | + | 0.603159i | \(0.206092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −58.7328 | −2.45360 | ||||||||
\(574\) | −1.56950 | − | 4.83043i | −0.0655097 | − | 0.201618i | ||||
\(575\) | 9.57888 | + | 6.95946i | 0.399467 | + | 0.290230i | ||||
\(576\) | 62.6851 | − | 45.5434i | 2.61188 | − | 1.89764i | ||||
\(577\) | 7.17068 | − | 22.0691i | 0.298519 | − | 0.918748i | −0.683497 | − | 0.729953i | \(-0.739542\pi\) |
0.982017 | − | 0.188795i | \(-0.0604582\pi\) | |||||||
\(578\) | −9.50089 | + | 29.2407i | −0.395185 | + | 1.21625i | ||||
\(579\) | 41.7123 | − | 30.3057i | 1.73350 | − | 1.25946i | ||||
\(580\) | −5.20925 | − | 3.78474i | −0.216302 | − | 0.157153i | ||||
\(581\) | −0.994879 | − | 3.06192i | −0.0412745 | − | 0.127030i | ||||
\(582\) | −58.4002 | −2.42077 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.61639 | −0.108267 | ||||||||
\(585\) | 5.68599 | + | 17.4997i | 0.235087 | + | 0.723522i | ||||
\(586\) | 5.24256 | + | 3.80894i | 0.216568 | + | 0.157346i | ||||
\(587\) | 8.93936 | − | 6.49482i | 0.368967 | − | 0.268070i | −0.387816 | − | 0.921737i | \(-0.626770\pi\) |
0.756782 | + | 0.653667i | \(0.226770\pi\) | |||||||
\(588\) | −2.42872 | + | 7.47485i | −0.100159 | + | 0.308257i | ||||
\(589\) | 11.6251 | − | 35.7785i | 0.479005 | − | 1.47423i | ||||
\(590\) | 2.60463 | − | 1.89237i | 0.107231 | − | 0.0779077i | ||||
\(591\) | 61.9369 | + | 44.9998i | 2.54775 | + | 1.85105i | ||||
\(592\) | 0.196464 | + | 0.604653i | 0.00807461 | + | 0.0248511i | ||||
\(593\) | −36.3884 | −1.49429 | −0.747147 | − | 0.664659i | \(-0.768577\pi\) | ||||
−0.747147 | + | 0.664659i | \(0.768577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.71995 | 0.111507 | ||||||||
\(596\) | 8.20752 | + | 25.2602i | 0.336193 | + | 1.03470i | ||||
\(597\) | −38.9056 | − | 28.2665i | −1.59230 | − | 1.15687i | ||||
\(598\) | 23.9629 | − | 17.4100i | 0.979914 | − | 0.711949i | ||||
\(599\) | 9.16498 | − | 28.2069i | 0.374471 | − | 1.15250i | −0.569364 | − | 0.822085i | \(-0.692811\pi\) |
0.943835 | − | 0.330417i | \(-0.107189\pi\) | |||||||
\(600\) | −5.03652 | + | 15.5008i | −0.205615 | + | 0.632818i | ||||
\(601\) | −1.12548 | + | 0.817709i | −0.0459093 | + | 0.0333550i | −0.610503 | − | 0.792014i | \(-0.709033\pi\) |
0.564594 | + | 0.825369i | \(0.309033\pi\) | |||||||
\(602\) | 1.77112 | + | 1.28679i | 0.0721853 | + | 0.0524457i | ||||
\(603\) | 20.9354 | + | 64.4326i | 0.852556 | + | 2.62390i | ||||
\(604\) | 38.9073 | 1.58312 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −85.9906 | −3.49313 | ||||||||
\(607\) | 9.56053 | + | 29.4243i | 0.388050 | + | 1.19430i | 0.934243 | + | 0.356636i | \(0.116076\pi\) |
−0.546193 | + | 0.837659i | \(0.683924\pi\) | |||||||
\(608\) | 33.8984 | + | 24.6286i | 1.37476 | + | 0.998822i | ||||
\(609\) | 13.3484 | − | 9.69819i | 0.540905 | − | 0.392990i | ||||
\(610\) | 0.760991 | − | 2.34209i | 0.0308116 | − | 0.0948285i | ||||
\(611\) | −2.79051 | + | 8.58830i | −0.112892 | + | 0.347446i | ||||
\(612\) | −77.2191 | + | 56.1030i | −3.12140 | + | 2.26783i | ||||
\(613\) | −6.60146 | − | 4.79624i | −0.266631 | − | 0.193719i | 0.446434 | − | 0.894816i | \(-0.352694\pi\) |
−0.713065 | + | 0.701098i | \(0.752694\pi\) | |||||||
\(614\) | −2.44201 | − | 7.51575i | −0.0985517 | − | 0.303311i | ||||
\(615\) | −3.62156 | −0.146036 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.5298 | −1.10831 | −0.554154 | − | 0.832414i | \(-0.686958\pi\) | ||||
−0.554154 | + | 0.832414i | \(0.686958\pi\) | |||||||
\(618\) | 24.9711 | + | 76.8530i | 1.00448 | + | 3.09148i | ||||
\(619\) | −16.1589 | − | 11.7401i | −0.649481 | − | 0.471876i | 0.213613 | − | 0.976918i | \(-0.431477\pi\) |
−0.863094 | + | 0.505043i | \(0.831477\pi\) | |||||||
\(620\) | 7.02935 | − | 5.10713i | 0.282306 | − | 0.205107i | ||||
\(621\) | −9.03386 | + | 27.8034i | −0.362516 | + | 1.11571i | ||||
\(622\) | −2.73802 | + | 8.42677i | −0.109785 | + | 0.337883i | ||||
\(623\) | 1.02370 | − | 0.743764i | 0.0410138 | − | 0.0297983i | ||||
\(624\) | −38.3530 | − | 27.8651i | −1.53535 | − | 1.11550i | ||||
\(625\) | 6.65280 | + | 20.4752i | 0.266112 | + | 0.819008i | ||||
\(626\) | 24.8704 | 0.994022 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.9016 | 0.913874 | ||||||||
\(629\) | −0.407532 | − | 1.25426i | −0.0162494 | − | 0.0500104i | ||||
\(630\) | 5.63863 | + | 4.09670i | 0.224648 | + | 0.163216i | ||||
\(631\) | 13.9427 | − | 10.1300i | 0.555052 | − | 0.403269i | −0.274593 | − | 0.961561i | \(-0.588543\pi\) |
0.829645 | + | 0.558292i | \(0.188543\pi\) | |||||||
\(632\) | −3.05452 | + | 9.40084i | −0.121502 | + | 0.373945i | ||||
\(633\) | 13.9429 | − | 42.9118i | 0.554181 | − | 1.70559i | ||||
\(634\) | −3.84227 | + | 2.79158i | −0.152596 | + | 0.110868i | ||||
\(635\) | −1.00423 | − | 0.729613i | −0.0398515 | − | 0.0289538i | ||||
\(636\) | 7.35971 | + | 22.6508i | 0.291831 | + | 0.898165i | ||||
\(637\) | 5.60975 | 0.222266 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 81.6878 | 3.23152 | ||||||||
\(640\) | 1.26853 | + | 3.90412i | 0.0501429 | + | 0.154324i | ||||
\(641\) | 35.9324 | + | 26.1064i | 1.41925 | + | 1.03114i | 0.991896 | + | 0.127056i | \(0.0405527\pi\) |
0.427350 | + | 0.904086i | \(0.359447\pi\) | |||||||
\(642\) | −56.7277 | + | 41.2151i | −2.23886 | + | 1.62663i | ||||
\(643\) | −6.96326 | + | 21.4307i | −0.274604 | + | 0.845145i | 0.714719 | + | 0.699411i | \(0.246554\pi\) |
−0.989324 | + | 0.145734i | \(0.953446\pi\) | |||||||
\(644\) | 1.93129 | − | 5.94389i | 0.0761033 | − | 0.234222i | ||||
\(645\) | 1.26288 | − | 0.917539i | 0.0497260 | − | 0.0361281i | ||||
\(646\) | −50.9183 | − | 36.9943i | −2.00336 | − | 1.45552i | ||||
\(647\) | −5.80204 | − | 17.8569i | −0.228102 | − | 0.702025i | −0.997962 | − | 0.0638126i | \(-0.979674\pi\) |
0.769860 | − | 0.638213i | \(-0.220326\pi\) | |||||||
\(648\) | −18.0274 | −0.708184 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 56.7980 | 2.22780 | ||||||||
\(651\) | 6.88009 | + | 21.1748i | 0.269652 | + | 0.829904i | ||||
\(652\) | 27.0221 | + | 19.6327i | 1.05827 | + | 0.768876i | ||||
\(653\) | −25.5751 | + | 18.5814i | −1.00083 | + | 0.727147i | −0.962267 | − | 0.272109i | \(-0.912279\pi\) |
−0.0385660 | + | 0.999256i | \(0.512279\pi\) | |||||||
\(654\) | −15.0620 | + | 46.3562i | −0.588972 | + | 1.81267i | ||||
\(655\) | −0.407532 | + | 1.25426i | −0.0159236 | + | 0.0490078i | ||||
\(656\) | 5.22956 | − | 3.79950i | 0.204180 | − | 0.148346i | ||||
\(657\) | −13.0817 | − | 9.50439i | −0.510365 | − | 0.370802i | ||||
\(658\) | 1.05700 | + | 3.25312i | 0.0412062 | + | 0.126820i | ||||
\(659\) | 19.8477 | 0.773157 | 0.386578 | − | 0.922257i | \(-0.373657\pi\) | ||||
0.386578 | + | 0.922257i | \(0.373657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.4234 | 1.22223 | 0.611114 | − | 0.791542i | \(-0.290722\pi\) | ||||
0.611114 | + | 0.791542i | \(0.290722\pi\) | |||||||
\(662\) | −14.6592 | − | 45.1163i | −0.569745 | − | 1.75349i | ||||
\(663\) | 79.5570 | + | 57.8015i | 3.08974 | + | 2.24483i | ||||
\(664\) | −2.85105 | + | 2.07141i | −0.110642 | + | 0.0803862i | ||||
\(665\) | −0.791113 | + | 2.43479i | −0.0306780 | + | 0.0944173i | ||||
\(666\) | 1.04428 | − | 3.21396i | 0.0404649 | − | 0.124538i | ||||
\(667\) | −10.6145 | + | 7.71185i | −0.410993 | + | 0.298604i | ||||
\(668\) | −20.4711 | − | 14.8731i | −0.792051 | − | 0.575459i | ||||
\(669\) | −16.6608 | − | 51.2766i | −0.644142 | − | 1.98247i | ||||
\(670\) | −10.3179 | −0.398615 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −24.7980 | −0.956606 | ||||||||
\(673\) | −5.93915 | − | 18.2788i | −0.228937 | − | 0.704597i | −0.997868 | − | 0.0652647i | \(-0.979211\pi\) |
0.768931 | − | 0.639332i | \(-0.220789\pi\) | |||||||
\(674\) | −22.8293 | − | 16.5865i | −0.879352 | − | 0.638887i | ||||
\(675\) | −45.3525 | + | 32.9505i | −1.74562 | + | 1.26826i | ||||
\(676\) | 14.3547 | − | 44.1792i | 0.552103 | − | 1.69920i | ||||
\(677\) | 7.95127 | − | 24.4715i | 0.305592 | − | 0.940516i | −0.673863 | − | 0.738856i | \(-0.735366\pi\) |
0.979456 | − | 0.201660i | \(-0.0646336\pi\) | |||||||
\(678\) | −73.9436 | + | 53.7232i | −2.83979 | + | 2.06323i | ||||
\(679\) | 7.11545 | + | 5.16968i | 0.273066 | + | 0.198394i | ||||
\(680\) | −0.920032 | − | 2.83157i | −0.0352816 | − | 0.108586i | ||||
\(681\) | −33.4986 | −1.28367 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.0596 | −0.423185 | −0.211593 | − | 0.977358i | \(-0.567865\pi\) | ||||
−0.211593 | + | 0.977358i | \(0.567865\pi\) | |||||||
\(684\) | −27.7616 | − | 85.4413i | −1.06149 | − | 3.26693i | ||||
\(685\) | 3.80665 | + | 2.76569i | 0.145444 | + | 0.105672i | ||||
\(686\) | 1.71907 | − | 1.24898i | 0.0656343 | − | 0.0476861i | ||||
\(687\) | −5.26718 | + | 16.2107i | −0.200955 | + | 0.618477i | ||||
\(688\) | −0.860994 | + | 2.64987i | −0.0328251 | + | 0.101025i | ||||
\(689\) | 13.7525 | − | 9.99181i | 0.523930 | − | 0.380658i | ||||
\(690\) | −6.47214 | − | 4.70228i | −0.246390 | − | 0.179013i | ||||
\(691\) | 13.9137 | + | 42.8219i | 0.529301 | + | 1.62902i | 0.755651 | + | 0.654975i | \(0.227321\pi\) |
−0.226350 | + | 0.974046i | \(0.572679\pi\) | |||||||
\(692\) | −20.5483 | −0.781128 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.3103 | 1.45424 | ||||||||
\(695\) | −2.95451 | − | 9.09306i | −0.112071 | − | 0.344919i | ||||
\(696\) | −14.6113 | − | 10.6157i | −0.553840 | − | 0.402388i | ||||
\(697\) | −10.8479 | + | 7.88144i | −0.410893 | + | 0.298531i | ||||
\(698\) | 14.4126 | − | 44.3573i | 0.545523 | − | 1.67895i | ||||
\(699\) | −28.7564 | + | 88.5032i | −1.08767 | + | 3.34750i | ||||
\(700\) | 9.69559 | − | 7.04426i | 0.366459 | − | 0.266248i | ||||
\(701\) | −37.8447 | − | 27.4958i | −1.42938 | − | 1.03850i | −0.990132 | − | 0.140135i | \(-0.955246\pi\) |
−0.439244 | − | 0.898368i | \(-0.644754\pi\) | |||||||
\(702\) | 43.3361 | + | 133.375i | 1.63562 | + | 5.03391i | ||||
\(703\) | 1.24129 | 0.0468162 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.43899 | 0.0918577 | ||||||||
\(706\) | −12.3812 | − | 38.1053i | −0.465971 | − | 1.43411i | ||||
\(707\) | 10.4771 | + | 7.61202i | 0.394030 | + | 0.286280i | ||||
\(708\) | 19.8695 | − | 14.4361i | 0.746743 | − | 0.542540i | ||||
\(709\) | −2.82573 | + | 8.69671i | −0.106123 | + | 0.326612i | −0.989992 | − | 0.141121i | \(-0.954929\pi\) |
0.883870 | + | 0.467733i | \(0.154929\pi\) | |||||||
\(710\) | −3.84443 | + | 11.8319i | −0.144279 | + | 0.444044i | ||||
\(711\) | −49.4220 | + | 35.9072i | −1.85347 | + | 1.34663i | ||||
\(712\) | −1.12056 | − | 0.814131i | −0.0419946 | − | 0.0305109i | ||||
\(713\) | −5.47095 | − | 16.8378i | −0.204889 | − | 0.630582i | ||||
\(714\) | 37.2489 | 1.39400 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −30.8468 | −1.15280 | ||||||||
\(717\) | −2.47214 | − | 7.60845i | −0.0923236 | − | 0.284143i | ||||
\(718\) | 2.62986 | + | 1.91071i | 0.0981456 | + | 0.0713069i | ||||
\(719\) | 24.6471 | − | 17.9072i | 0.919182 | − | 0.667824i | −0.0241386 | − | 0.999709i | \(-0.507684\pi\) |
0.943320 | + | 0.331884i | \(0.107684\pi\) | |||||||
\(720\) | −2.74111 | + | 8.43627i | −0.102155 | + | 0.314401i | ||||
\(721\) | 3.76069 | − | 11.5742i | 0.140055 | − | 0.431046i | ||||
\(722\) | 15.2634 | − | 11.0895i | 0.568046 | − | 0.412710i | ||||
\(723\) | 69.2426 | + | 50.3077i | 2.57516 | + | 1.87096i | ||||
\(724\) | −5.47548 | − | 16.8518i | −0.203495 | − | 0.626292i | ||||
\(725\) | −25.1589 | −0.934380 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.12580 | −0.227193 | −0.113597 | − | 0.993527i | \(-0.536237\pi\) | ||||
−0.113597 | + | 0.993527i | \(0.536237\pi\) | |||||||
\(728\) | −1.89751 | − | 5.83995i | −0.0703265 | − | 0.216443i | ||||
\(729\) | −0.906992 | − | 0.658969i | −0.0335923 | − | 0.0244062i | ||||
\(730\) | 1.99230 | − | 1.44749i | 0.0737384 | − | 0.0535741i | ||||
\(731\) | 1.78599 | − | 5.49672i | 0.0660573 | − | 0.203303i | ||||
\(732\) | 5.80527 | − | 17.8668i | 0.214569 | − | 0.660375i | ||||
\(733\) | 34.0358 | − | 24.7284i | 1.25714 | − | 0.913366i | 0.258526 | − | 0.966004i | \(-0.416763\pi\) |
0.998614 | + | 0.0526384i | \(0.0167631\pi\) | |||||||
\(734\) | 25.1924 | + | 18.3034i | 0.929870 | + | 0.675590i | ||||
\(735\) | −0.468203 | − | 1.44098i | −0.0172699 | − | 0.0531514i | ||||
\(736\) | 19.7190 | 0.726853 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −34.3591 | −1.26477 | ||||||||
\(739\) | −8.92379 | − | 27.4646i | −0.328267 | − | 1.01030i | −0.969944 | − | 0.243327i | \(-0.921761\pi\) |
0.641678 | − | 0.766974i | \(-0.278239\pi\) | |||||||
\(740\) | 0.231939 | + | 0.168514i | 0.00852625 | + | 0.00619468i | ||||
\(741\) | −74.8812 | + | 54.4044i | −2.75083 | + | 1.99859i | ||||
\(742\) | 1.98976 | − | 6.12384i | 0.0730463 | − | 0.224813i | ||||
\(743\) | −4.53674 | + | 13.9626i | −0.166437 | + | 0.512240i | −0.999139 | − | 0.0414808i | \(-0.986792\pi\) |
0.832702 | + | 0.553721i | \(0.186792\pi\) | |||||||
\(744\) | 19.7165 | − | 14.3248i | 0.722840 | − | 0.525174i | ||||
\(745\) | −4.14232 | − | 3.00957i | −0.151763 | − | 0.110262i | ||||
\(746\) | −6.60602 | − | 20.3312i | −0.241863 | − | 0.744379i | ||||
\(747\) | −21.7796 | −0.796873 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5601 | 0.385857 | ||||||||
\(750\) | −9.71490 | − | 29.8994i | −0.354738 | − | 1.09177i | ||||
\(751\) | 5.34434 | + | 3.88289i | 0.195018 | + | 0.141689i | 0.681009 | − | 0.732275i | \(-0.261541\pi\) |
−0.485991 | + | 0.873964i | \(0.661541\pi\) | |||||||
\(752\) | −3.52192 | + | 2.55882i | −0.128431 | + | 0.0933107i | ||||
\(753\) | −9.50660 | + | 29.2583i | −0.346440 | + | 1.06623i | ||||
\(754\) | −19.4491 | + | 59.8581i | −0.708294 | + | 2.17990i | ||||
\(755\) | −6.06800 | + | 4.40866i | −0.220837 | + | 0.160448i | ||||
\(756\) | 23.9391 | + | 17.3928i | 0.870657 | + | 0.632569i | ||||
\(757\) | 0.772401 | + | 2.37721i | 0.0280734 | + | 0.0864010i | 0.964112 | − | 0.265498i | \(-0.0855362\pi\) |
−0.936038 | + | 0.351899i | \(0.885536\pi\) | |||||||
\(758\) | 38.0218 | 1.38101 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.80230 | 0.101650 | ||||||||
\(761\) | −3.72326 | − | 11.4590i | −0.134968 | − | 0.415390i | 0.860617 | − | 0.509253i | \(-0.170078\pi\) |
−0.995585 | + | 0.0938635i | \(0.970078\pi\) | |||||||
\(762\) | −13.7525 | − | 9.99181i | −0.498202 | − | 0.361965i | ||||
\(763\) | 5.93867 | − | 4.31470i | 0.214994 | − | 0.156202i | ||||
\(764\) | 14.6080 | − | 44.9588i | 0.528499 | − | 1.62655i | ||||
\(765\) | 5.68599 | − | 17.4997i | 0.205577 | − | 0.632702i | ||||
\(766\) | −32.6022 | + | 23.6869i | −1.17796 | + | 0.855841i | ||||
\(767\) | −14.1819 | − | 10.3038i | −0.512079 | − | 0.372048i | ||||
\(768\) | −4.74826 | − | 14.6137i | −0.171338 | − | 0.527325i | ||||
\(769\) | 0.489560 | 0.0176540 | 0.00882699 | − | 0.999961i | \(-0.497190\pi\) | ||||
0.00882699 | + | 0.999961i | \(0.497190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 70.3085 | 2.53210 | ||||||||
\(772\) | 12.8238 | + | 39.4675i | 0.461538 | + | 1.42047i | ||||
\(773\) | 37.7958 | + | 27.4602i | 1.35942 | + | 0.987676i | 0.998482 | + | 0.0550854i | \(0.0175431\pi\) |
0.360937 | + | 0.932590i | \(0.382457\pi\) | |||||||
\(774\) | 11.9814 | − | 8.70502i | 0.430664 | − | 0.312895i | ||||
\(775\) | 10.4910 | − | 32.2878i | 0.376846 | − | 1.15981i | ||||
\(776\) | 2.97500 | − | 9.15610i | 0.106796 | − | 0.328685i | ||||
\(777\) | −0.594330 | + | 0.431806i | −0.0213215 | + | 0.0154910i | ||||
\(778\) | 58.9029 | + | 42.7955i | 2.11177 | + | 1.53429i | ||||
\(779\) | −3.89999 | − | 12.0029i | −0.139732 | − | 0.430050i | ||||
\(780\) | −21.3775 | −0.765438 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −29.6197 | −1.05920 | ||||||||
\(783\) | −19.1959 | − | 59.0789i | −0.686006 | − | 2.11131i | ||||
\(784\) | 2.18787 | + | 1.58958i | 0.0781382 | + | 0.0567707i | ||||
\(785\) | −3.57174 | + | 2.59502i | −0.127481 | + | 0.0926203i | ||||
\(786\) | −5.58102 | + | 17.1766i | −0.199068 | + | 0.612669i | ||||
\(787\) | −2.57710 | + | 7.93151i | −0.0918638 | + | 0.282728i | −0.986424 | − | 0.164220i | \(-0.947489\pi\) |
0.894560 | + | 0.446948i | \(0.147489\pi\) | |||||||
\(788\) | −49.8514 | + | 36.2192i | −1.77588 | + | 1.29025i | ||||
\(789\) | −40.4494 | − | 29.3882i | −1.44004 | − | 1.04625i | ||||
\(790\) | −2.87499 | − | 8.84832i | −0.102288 | − | 0.314809i | ||||
\(791\) | 13.7649 | 0.489424 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.4087 | −0.476157 | ||||||||
\(794\) | −10.6893 | − | 32.8983i | −0.379349 | − | 1.16752i | ||||
\(795\) | −3.71443 | − | 2.69869i | −0.131737 | − | 0.0957127i | ||||
\(796\) | 31.3141 | − | 22.7510i | 1.10990 | − | 0.806388i | ||||
\(797\) | −9.73871 | + | 29.9727i | −0.344963 | + | 1.06169i | 0.616641 | + | 0.787245i | \(0.288493\pi\) |
−0.961604 | + | 0.274442i | \(0.911507\pi\) | |||||||
\(798\) | −10.8340 | + | 33.3437i | −0.383520 | + | 1.18035i | ||||
\(799\) | 7.30565 | − | 5.30786i | 0.258455 | − | 0.187779i | ||||
\(800\) | 30.5911 | + | 22.2258i | 1.08156 | + | 0.785799i | ||||
\(801\) | −2.64521 | − | 8.14113i | −0.0934641 | − | 0.287653i | ||||
\(802\) | −61.4911 | −2.17132 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −78.7106 | −2.77591 | ||||||||
\(805\) | 0.372308 | + | 1.14585i | 0.0131221 | + | 0.0403858i | ||||
\(806\) | −68.7091 | − | 49.9201i | −2.42018 | − | 1.75836i | ||||
\(807\) | 23.3077 | − | 16.9340i | 0.820469 | − | 0.596106i | ||||
\(808\) | 4.38049 | − | 13.4818i | 0.154105 | − | 0.474287i | ||||
\(809\) | 4.78991 | − | 14.7418i | 0.168404 | − | 0.518295i | −0.830867 | − | 0.556471i | \(-0.812155\pi\) |
0.999271 | + | 0.0381767i | \(0.0121550\pi\) | |||||||
\(810\) | 13.7273 | − | 9.97348i | 0.482329 | − | 0.350432i | ||||
\(811\) | 39.1076 | + | 28.4134i | 1.37325 | + | 0.997728i | 0.997475 | + | 0.0710186i | \(0.0226250\pi\) |
0.375779 | + | 0.926709i | \(0.377375\pi\) | |||||||
\(812\) | 4.10376 | + | 12.6301i | 0.144014 | + | 0.443229i | ||||
\(813\) | −32.9991 | −1.15733 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.43899 | −0.225548 | ||||||||
\(816\) | 14.6495 | + | 45.0866i | 0.512836 | + | 1.57835i | ||||
\(817\) | 4.40098 | + | 3.19750i | 0.153971 | + | 0.111866i | ||||
\(818\) | 26.6635 | − | 19.3722i | 0.932268 | − | 0.677332i | ||||
\(819\) | 11.7270 | − | 36.0921i | 0.409775 | − | 1.26116i | ||||
\(820\) | 0.900754 | − | 2.77224i | 0.0314557 | − | 0.0968107i | ||||
\(821\) | 8.54330 | − | 6.20707i | 0.298163 | − | 0.216628i | −0.428638 | − | 0.903476i | \(-0.641006\pi\) |
0.726801 | + | 0.686848i | \(0.241006\pi\) | |||||||
\(822\) | 52.1308 | + | 37.8752i | 1.81827 | + | 1.32105i | ||||
\(823\) | 5.97147 | + | 18.3783i | 0.208152 | + | 0.640627i | 0.999569 | + | 0.0293503i | \(0.00934383\pi\) |
−0.791417 | + | 0.611277i | \(0.790656\pi\) | |||||||
\(824\) | −13.3212 | −0.464067 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.64002 | −0.231036 | ||||||||
\(827\) | −0.164006 | − | 0.504758i | −0.00570305 | − | 0.0175522i | 0.948165 | − | 0.317780i | \(-0.102937\pi\) |
−0.953868 | + | 0.300228i | \(0.902937\pi\) | |||||||
\(828\) | −34.2045 | − | 24.8510i | −1.18869 | − | 0.863634i | ||||
\(829\) | 38.1819 | − | 27.7408i | 1.32611 | − | 0.963477i | 0.326278 | − | 0.945274i | \(-0.394206\pi\) |
0.999834 | − | 0.0182029i | \(-0.00579448\pi\) | |||||||
\(830\) | 1.02500 | − | 3.15462i | 0.0355783 | − | 0.109499i | ||||
\(831\) | 17.9224 | − | 55.1595i | 0.621722 | − | 1.91346i | ||||
\(832\) | 51.9811 | − | 37.7665i | 1.80212 | − | 1.30932i | ||||
\(833\) | −4.53838 | − | 3.29733i | −0.157246 | − | 0.114246i | ||||
\(834\) | −40.4611 | − | 124.526i | −1.40105 | − | 4.31200i | ||||
\(835\) | 4.87798 | 0.168809 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 83.8236 | 2.89737 | ||||||||
\(838\) | 8.50353 | + | 26.1712i | 0.293750 | + | 0.904068i | ||||
\(839\) | 30.6646 | + | 22.2792i | 1.05866 | + | 0.769162i | 0.973840 | − | 0.227235i | \(-0.0729684\pi\) |
0.0848203 | + | 0.996396i | \(0.472968\pi\) | |||||||
\(840\) | −1.34174 | + | 0.974833i | −0.0462945 | + | 0.0336349i | ||||
\(841\) | −0.346440 | + | 1.06623i | −0.0119462 | + | 0.0367667i | ||||
\(842\) | 11.2223 | − | 34.5386i | 0.386745 | − | 1.19028i | ||||
\(843\) | 64.8668 | − | 47.1285i | 2.23413 | − | 1.62319i | ||||
\(844\) | 29.3803 | + | 21.3460i | 1.01131 | + | 0.734761i | ||||
\(845\) | 2.76726 | + | 8.51675i | 0.0951967 | + | 0.292985i | ||||
\(846\) | 23.1396 | 0.795555 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.19495 | 0.281416 | ||||||||
\(849\) | −29.2388 | − | 89.9878i | −1.00347 | − | 3.08837i | ||||
\(850\) | −45.9506 | − | 33.3851i | −1.57609 | − | 1.14510i | ||||
\(851\) | 0.472603 | − | 0.343366i | 0.0162006 | − | 0.0117704i | ||||
\(852\) | −29.3274 | + | 90.2605i | −1.00474 | + | 3.09227i | ||||
\(853\) | −1.93727 | + | 5.96231i | −0.0663310 | + | 0.204146i | −0.978729 | − | 0.205159i | \(-0.934229\pi\) |
0.912398 | + | 0.409305i | \(0.134229\pi\) | |||||||
\(854\) | −4.10901 | + | 2.98537i | −0.140607 | + | 0.102157i | ||||
\(855\) | 14.0112 | + | 10.1797i | 0.479173 | + | 0.348140i | ||||
\(856\) | −3.57198 | − | 10.9934i | −0.122088 | − | 0.375748i | ||||
\(857\) | 36.9503 | 1.26220 | 0.631100 | − | 0.775702i | \(-0.282604\pi\) | ||||
0.631100 | + | 0.775702i | \(0.282604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.90447 | 0.303817 | 0.151908 | − | 0.988395i | \(-0.451458\pi\) | ||||
0.151908 | + | 0.988395i | \(0.451458\pi\) | |||||||
\(860\) | 0.388254 | + | 1.19492i | 0.0132394 | + | 0.0407465i | ||||
\(861\) | 6.04276 | + | 4.39032i | 0.205937 | + | 0.149622i | ||||
\(862\) | 33.2608 | − | 24.1654i | 1.13287 | − | 0.823077i | ||||
\(863\) | −13.0156 | + | 40.0578i | −0.443055 | + | 1.36358i | 0.441547 | + | 0.897238i | \(0.354430\pi\) |
−0.884603 | + | 0.466346i | \(0.845570\pi\) | |||||||
\(864\) | −28.8506 | + | 88.7929i | −0.981516 | + | 3.02080i | ||||
\(865\) | 3.20471 | − | 2.32836i | 0.108964 | − | 0.0791667i | ||||
\(866\) | 27.2051 | + | 19.7656i | 0.924465 | + | 0.671663i | ||||
\(867\) | −13.9721 | − | 43.0018i | −0.474519 | − | 1.46042i | ||||
\(868\) | −17.9201 | −0.608247 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 16.9991 | 0.576323 | ||||||||
\(871\) | 17.3605 | + | 53.4302i | 0.588239 | + | 1.81041i | ||||
\(872\) | −6.50052 | − | 4.72291i | −0.220135 | − | 0.159938i | ||||
\(873\) | 48.1354 | − | 34.9724i | 1.62914 | − | 1.18364i | ||||
\(874\) | 8.61505 | − | 26.5144i | 0.291408 | − | 0.896863i | ||||
\(875\) | −1.46308 | + | 4.50290i | −0.0494612 | + | 0.152226i | ||||
\(876\) | 15.1984 | − | 11.0423i | 0.513506 | − | 0.373084i | ||||
\(877\) | −19.6912 | − | 14.3065i | −0.664925 | − | 0.483096i | 0.203397 | − | 0.979096i | \(-0.434802\pi\) |
−0.868323 | + | 0.496000i | \(0.834802\pi\) | |||||||
\(878\) | 7.26204 | + | 22.3503i | 0.245082 | + | 0.754285i | ||||
\(879\) | −9.52982 | −0.321433 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.64380 | 0.190145 | 0.0950723 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950723 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(882\) | −4.44201 | − | 13.6711i | −0.149570 | − | 0.460330i | ||||
\(883\) | −12.2815 | − | 8.92302i | −0.413305 | − | 0.300283i | 0.361634 | − | 0.932320i | \(-0.382219\pi\) |
−0.774938 | + | 0.632037i | \(0.782219\pi\) | |||||||
\(884\) | −64.0333 | + | 46.5229i | −2.15367 | + | 1.56474i | ||||
\(885\) | −1.46308 | + | 4.50290i | −0.0491810 | + | 0.151363i | ||||
\(886\) | 22.7872 | − | 70.1317i | 0.765550 | − | 2.35612i | ||||
\(887\) | −21.6958 | + | 15.7629i | −0.728472 | + | 0.529266i | −0.889080 | − | 0.457752i | \(-0.848655\pi\) |
0.160608 | + | 0.987018i | \(0.448655\pi\) | |||||||
\(888\) | 0.650560 | + | 0.472659i | 0.0218314 | + | 0.0158614i | ||||
\(889\) | 0.791113 | + | 2.43479i | 0.0265331 | + | 0.0816604i | ||||
\(890\) | 1.30368 | 0.0436994 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 43.3951 | 1.45297 | ||||||||
\(893\) | 2.62650 | + | 8.08354i | 0.0878926 | + | 0.270506i | ||||
\(894\) | −56.7277 | − | 41.2151i | −1.89726 | − | 1.37844i | ||||
\(895\) | 4.81087 | − | 3.49530i | 0.160810 | − | 0.116835i | ||||
\(896\) | 2.61626 | − | 8.05203i | 0.0874032 | − | 0.268999i | ||||
\(897\) | −13.4605 | + | 41.4272i | −0.449434 | + | 1.38322i | ||||
\(898\) | −62.3915 | + | 45.3301i | −2.08203 | + | 1.51269i | ||||
\(899\) | 30.4350 | + | 22.1123i | 1.01506 | + | 0.737487i | ||||
\(900\) | −25.0531 | − | 77.1054i | −0.835102 | − | 2.57018i | ||||
\(901\) | −16.9991 | −0.566322 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.21949 | −0.107138 | ||||||||
\(904\) | −4.65602 | − | 14.3298i | −0.154857 | − | 0.476601i | ||||
\(905\) | 2.76347 | + | 2.00778i | 0.0918607 | + | 0.0667407i | ||||
\(906\) | −83.0992 | + | 60.3751i | −2.76079 | + | 2.00583i | ||||
\(907\) | 9.91866 | − | 30.5265i | 0.329344 | − | 1.01362i | −0.640098 | − | 0.768294i | \(-0.721106\pi\) |
0.969441 | − | 0.245323i | \(-0.0788939\pi\) | |||||||
\(908\) | 8.33177 | − | 25.6425i | 0.276499 | − | 0.850978i | ||||
\(909\) | 70.8763 | − | 51.4946i | 2.35082 | − | 1.70797i | ||||
\(910\) | 4.67579 | + | 3.39716i | 0.155001 | + | 0.112615i | ||||
\(911\) | 3.75760 | + | 11.5647i | 0.124495 | + | 0.383156i | 0.993809 | − | 0.111105i | \(-0.0354389\pi\) |
−0.869314 | + | 0.494261i | \(0.835439\pi\) | |||||||
\(912\) | −44.6206 | −1.47754 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 4.37844 | 0.144826 | ||||||||
\(915\) | 1.11912 | + | 3.44431i | 0.0369971 | + | 0.113865i | ||||
\(916\) | −11.0989 | − | 8.06385i | −0.366719 | − | 0.266437i | ||||
\(917\) | 2.20049 | − | 1.59875i | 0.0726665 | − | 0.0527953i | ||||
\(918\) | 43.3361 | − | 133.375i | 1.43030 | − | 4.40202i | ||||
\(919\) | −12.3607 | + | 38.0423i | −0.407741 | + | 1.25490i | 0.510843 | + | 0.859674i | \(0.329333\pi\) |
−0.918585 | + | 0.395225i | \(0.870667\pi\) | |||||||
\(920\) | 1.06693 | − | 0.775172i | 0.0351757 | − | 0.0255567i | ||||
\(921\) | 9.40204 | + | 6.83098i | 0.309808 | + | 0.225089i | ||||
\(922\) | 4.70850 | + | 14.4913i | 0.155066 | + | 0.477245i | ||||
\(923\) | 67.7390 | 2.22966 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12019 | 0.0368315 | ||||||||
\(926\) | −2.26837 | − | 6.98132i | −0.0745433 | − | 0.229421i | ||||
\(927\) | −66.6046 | − | 48.3911i | −2.18758 | − | 1.58937i | ||||
\(928\) | −33.8984 | + | 24.6286i | −1.11277 | + | 0.808474i | ||||
\(929\) | −6.60658 | + | 20.3330i | −0.216755 | + | 0.667103i | 0.782269 | + | 0.622940i | \(0.214062\pi\) |
−0.999024 | + | 0.0441629i | \(0.985938\pi\) | |||||||
\(930\) | −7.08840 | + | 21.8158i | −0.232438 | + | 0.715370i | ||||
\(931\) | 4.27165 | − | 3.10353i | 0.139998 | − | 0.101714i | ||||
\(932\) | −60.5952 | − | 44.0250i | −1.98486 | − | 1.44209i | ||||
\(933\) | −4.02658 | − | 12.3925i | −0.131824 | − | 0.405713i | ||||
\(934\) | 28.6769 | 0.938338 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −41.5398 | −1.35777 | ||||||||
\(937\) | −9.73726 | − | 29.9682i | −0.318102 | − | 0.979019i | −0.974459 | − | 0.224567i | \(-0.927903\pi\) |
0.656356 | − | 0.754451i | \(-0.272097\pi\) | |||||||
\(938\) | 17.2159 | + | 12.5081i | 0.562120 | + | 0.408404i | ||||
\(939\) | −29.5896 | + | 21.4981i | −0.965621 | + | 0.701564i | ||||
\(940\) | −0.606625 | + | 1.86700i | −0.0197859 | + | 0.0608948i | ||||
\(941\) | 13.2043 | − | 40.6386i | 0.430447 | − | 1.32478i | −0.467234 | − | 0.884134i | \(-0.654749\pi\) |
0.897681 | − | 0.440646i | \(-0.145251\pi\) | |||||||
\(942\) | −48.9138 | + | 35.5380i | −1.59370 | + | 1.15789i | ||||
\(943\) | −4.80511 | − | 3.49112i | −0.156476 | − | 0.113687i | ||||
\(944\) | −2.61144 | − | 8.03719i | −0.0849952 | − | 0.261588i | ||||
\(945\) | −5.70436 | −0.185563 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.29473 | 0.107064 | 0.0535321 | − | 0.998566i | \(-0.482952\pi\) | ||||
0.0535321 | + | 0.998566i | \(0.482952\pi\) | |||||||
\(948\) | −21.9321 | − | 67.4999i | −0.712320 | − | 2.19230i | ||||
\(949\) | −10.8479 | − | 7.88144i | −0.352137 | − | 0.255842i | ||||
\(950\) | 43.2499 | − | 31.4229i | 1.40321 | − | 1.01949i | ||||
\(951\) | 2.15830 | − | 6.64256i | 0.0699877 | − | 0.215400i | ||||
\(952\) | −1.89751 | + | 5.83995i | −0.0614988 | + | 0.189274i | ||||
\(953\) | −31.2937 | + | 22.7362i | −1.01370 | + | 0.736499i | −0.964983 | − | 0.262313i | \(-0.915515\pi\) |
−0.0487212 | + | 0.998812i | \(0.515515\pi\) | |||||||
\(954\) | −35.2401 | − | 25.6034i | −1.14094 | − | 0.828942i | ||||
\(955\) | 2.81609 | + | 8.66704i | 0.0911266 | + | 0.280459i | ||||
\(956\) | 6.43899 | 0.208252 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −74.4977 | −2.40691 | ||||||||
\(959\) | −2.99881 | − | 9.22939i | −0.0968367 | − | 0.298033i | ||||
\(960\) | −14.0396 | − | 10.2004i | −0.453126 | − | 0.329215i | ||||
\(961\) | −15.9894 | + | 11.6170i | −0.515787 | + | 0.374741i | ||||
\(962\) | 0.865959 | − | 2.66515i | 0.0279196 | − | 0.0859278i | ||||
\(963\) | 22.0756 | − | 67.9416i | 0.711376 | − | 2.18939i | ||||
\(964\) | −55.7315 | + | 40.4913i | −1.79499 | + | 1.30414i | ||||
\(965\) | −6.47214 | − | 4.70228i | −0.208345 | − | 0.151372i | ||||
\(966\) | 5.09864 | + | 15.6920i | 0.164046 | + | 0.504882i | ||||
\(967\) | −3.34816 | −0.107670 | −0.0538348 | − | 0.998550i | \(-0.517144\pi\) | ||||
−0.0538348 | + | 0.998550i | \(0.517144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 92.5583 | 2.97340 | ||||||||
\(970\) | 2.80015 | + | 8.61797i | 0.0899073 | + | 0.276706i | ||||
\(971\) | −47.5002 | − | 34.5109i | −1.52435 | − | 1.10751i | −0.959277 | − | 0.282468i | \(-0.908847\pi\) |
−0.565076 | − | 0.825039i | \(-0.691153\pi\) | |||||||
\(972\) | 32.9022 | − | 23.9049i | 1.05534 | − | 0.766749i | ||||
\(973\) | −6.09352 | + | 18.7539i | −0.195349 | + | 0.601223i | ||||
\(974\) | −19.4792 | + | 59.9508i | −0.624154 | + | 1.92095i | ||||
\(975\) | −67.5756 | + | 49.0965i | −2.16415 | + | 1.57235i | ||||
\(976\) | −5.22956 | − | 3.79950i | −0.167394 | − | 0.121619i | ||||
\(977\) | 4.25359 | + | 13.0912i | 0.136084 | + | 0.418825i | 0.995757 | − | 0.0920204i | \(-0.0293325\pi\) |
−0.859673 | + | 0.510845i | \(0.829333\pi\) | |||||||
\(978\) | −88.1798 | −2.81968 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.21949 | 0.0389553 | ||||||||
\(981\) | −15.3453 | − | 47.2280i | −0.489938 | − | 1.50787i | ||||
\(982\) | 43.8875 | + | 31.8861i | 1.40051 | + | 1.01753i | ||||
\(983\) | −40.6239 | + | 29.5150i | −1.29570 | + | 0.941382i | −0.999904 | − | 0.0138693i | \(-0.995585\pi\) |
−0.295797 | + | 0.955251i | \(0.595585\pi\) | |||||||
\(984\) | 2.52650 | − | 7.77577i | 0.0805419 | − | 0.247882i | ||||
\(985\) | 3.67078 | − | 11.2975i | 0.116961 | − | 0.359968i | ||||
\(986\) | 50.9183 | − | 36.9943i | 1.62157 | − | 1.17814i | ||||
\(987\) | −4.06958 | − | 2.95672i | −0.129536 | − | 0.0941135i | ||||
\(988\) | −23.0211 | − | 70.8515i | −0.732397 | − | 2.25409i | ||||
\(989\) | 2.56009 | 0.0814062 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.65940 | −0.148011 | −0.0740054 | − | 0.997258i | \(-0.523578\pi\) | ||||
−0.0740054 | + | 0.997258i | \(0.523578\pi\) | |||||||
\(992\) | −17.4720 | − | 53.7734i | −0.554738 | − | 1.70731i | ||||
\(993\) | 56.4395 | + | 41.0057i | 1.79105 | + | 1.30128i | ||||
\(994\) | 20.7581 | − | 15.0817i | 0.658409 | − | 0.478362i | ||||
\(995\) | −2.30579 | + | 7.09650i | −0.0730986 | + | 0.224974i | ||||
\(996\) | 7.81927 | − | 24.0652i | 0.247763 | − | 0.762536i | ||||
\(997\) | −2.74203 | + | 1.99220i | −0.0868410 | + | 0.0630937i | −0.630359 | − | 0.776304i | \(-0.717092\pi\) |
0.543518 | + | 0.839398i | \(0.317092\pi\) | |||||||
\(998\) | −44.1087 | − | 32.0468i | −1.39624 | − | 1.01442i | ||||
\(999\) | 0.854687 | + | 2.63046i | 0.0270411 | + | 0.0832240i |
(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 | 847.2.f.t.148.1 | 12 | ||
11.2 | odd | 10 | 847.2.f.u.372.3 | 12 | |||
11.3 | even | 5 | 847.2.a.j.1.1 | yes | 3 | ||
11.4 | even | 5 | inner | 847.2.f.t.729.3 | 12 | ||
11.5 | even | 5 | inner | 847.2.f.t.323.3 | 12 | ||
11.6 | odd | 10 | 847.2.f.u.323.1 | 12 | |||
11.7 | odd | 10 | 847.2.f.u.729.1 | 12 | |||
11.8 | odd | 10 | 847.2.a.i.1.3 | ✓ | 3 | ||
11.9 | even | 5 | inner | 847.2.f.t.372.1 | 12 | ||
11.10 | odd | 2 | 847.2.f.u.148.3 | 12 | |||
33.8 | even | 10 | 7623.2.a.ce.1.1 | 3 | |||
33.14 | odd | 10 | 7623.2.a.bz.1.3 | 3 | |||
77.41 | even | 10 | 5929.2.a.t.1.3 | 3 | |||
77.69 | odd | 10 | 5929.2.a.y.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.3 | ✓ | 3 | 11.8 | odd | 10 | ||
847.2.a.j.1.1 | yes | 3 | 11.3 | even | 5 | ||
847.2.f.t.148.1 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.t.323.3 | 12 | 11.5 | even | 5 | inner | ||
847.2.f.t.372.1 | 12 | 11.9 | even | 5 | inner | ||
847.2.f.t.729.3 | 12 | 11.4 | even | 5 | inner | ||
847.2.f.u.148.3 | 12 | 11.10 | odd | 2 | |||
847.2.f.u.323.1 | 12 | 11.6 | odd | 10 | |||
847.2.f.u.372.3 | 12 | 11.2 | odd | 10 | |||
847.2.f.u.729.1 | 12 | 11.7 | odd | 10 | |||
5929.2.a.t.1.3 | 3 | 77.41 | even | 10 | |||
5929.2.a.y.1.1 | 3 | 77.69 | odd | 10 | |||
7623.2.a.bz.1.3 | 3 | 33.14 | odd | 10 | |||
7623.2.a.ce.1.1 | 3 | 33.8 | even | 10 |