Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(461,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.461");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 461.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.461 |
Dual form | 483.2.d.a.461.3 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.618034i | − | 0.437016i | −0.975835 | − | 0.218508i | \(-0.929881\pi\) | ||
0.975835 | − | 0.218508i | \(-0.0701190\pi\) | |||||||
\(3\) | −1.61803 | − | 0.618034i | −0.934172 | − | 0.356822i | ||||
\(4\) | 1.61803 | 0.809017 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | −0.381966 | + | 1.00000i | −0.155937 | + | 0.408248i | ||||
\(7\) | 0.381966 | + | 2.61803i | 0.144370 | + | 0.989524i | ||||
\(8\) | − | 2.23607i | − | 0.790569i | ||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | 0.236068i | 0.0746512i | ||||||||
\(11\) | 2.23607i | 0.674200i | 0.941469 | + | 0.337100i | \(0.109446\pi\) | ||||
−0.941469 | + | 0.337100i | \(0.890554\pi\) | |||||||
\(12\) | −2.61803 | − | 1.00000i | −0.755761 | − | 0.288675i | ||||
\(13\) | 0.145898i | 0.0404648i | 0.999795 | + | 0.0202324i | \(0.00644062\pi\) | ||||
−0.999795 | + | 0.0202324i | \(0.993559\pi\) | |||||||
\(14\) | 1.61803 | − | 0.236068i | 0.432438 | − | 0.0630918i | ||||
\(15\) | 0.618034 | + | 0.236068i | 0.159576 | + | 0.0609525i | ||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 7.47214 | 1.81226 | 0.906130 | − | 0.423000i | \(-0.139023\pi\) | ||||
0.906130 | + | 0.423000i | \(0.139023\pi\) | |||||||
\(18\) | 1.23607 | − | 1.38197i | 0.291344 | − | 0.325733i | ||||
\(19\) | 3.47214i | 0.796563i | 0.917263 | + | 0.398281i | \(0.130393\pi\) | ||||
−0.917263 | + | 0.398281i | \(0.869607\pi\) | |||||||
\(20\) | −0.618034 | −0.138197 | ||||||||
\(21\) | 1.00000 | − | 4.47214i | 0.218218 | − | 0.975900i | ||||
\(22\) | 1.38197 | 0.294636 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | −1.38197 | + | 3.61803i | −0.282093 | + | 0.738528i | ||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | 0.0901699 | 0.0176838 | ||||||||
\(27\) | −2.38197 | − | 4.61803i | −0.458410 | − | 0.888741i | ||||
\(28\) | 0.618034 | + | 4.23607i | 0.116797 | + | 0.800542i | ||||
\(29\) | 6.23607i | 1.15801i | 0.815324 | + | 0.579004i | \(0.196559\pi\) | ||||
−0.815324 | + | 0.579004i | \(0.803441\pi\) | |||||||
\(30\) | 0.145898 | − | 0.381966i | 0.0266372 | − | 0.0697371i | ||||
\(31\) | − | 9.47214i | − | 1.70125i | −0.525776 | − | 0.850623i | \(-0.676225\pi\) | ||
0.525776 | − | 0.850623i | \(-0.323775\pi\) | |||||||
\(32\) | − | 5.61803i | − | 0.993137i | ||||||
\(33\) | 1.38197 | − | 3.61803i | 0.240569 | − | 0.629819i | ||||
\(34\) | − | 4.61803i | − | 0.791986i | ||||||
\(35\) | −0.145898 | − | 1.00000i | −0.0246613 | − | 0.169031i | ||||
\(36\) | 3.61803 | + | 3.23607i | 0.603006 | + | 0.539345i | ||||
\(37\) | 10.2361 | 1.68280 | 0.841400 | − | 0.540413i | \(-0.181732\pi\) | ||||
0.841400 | + | 0.540413i | \(0.181732\pi\) | |||||||
\(38\) | 2.14590 | 0.348111 | ||||||||
\(39\) | 0.0901699 | − | 0.236068i | 0.0144387 | − | 0.0378011i | ||||
\(40\) | 0.854102i | 0.135045i | ||||||||
\(41\) | 4.23607 | 0.661563 | 0.330781 | − | 0.943707i | \(-0.392688\pi\) | ||||
0.330781 | + | 0.943707i | \(0.392688\pi\) | |||||||
\(42\) | −2.76393 | − | 0.618034i | −0.426484 | − | 0.0953647i | ||||
\(43\) | 5.38197 | 0.820742 | 0.410371 | − | 0.911919i | \(-0.365399\pi\) | ||||
0.410371 | + | 0.911919i | \(0.365399\pi\) | |||||||
\(44\) | 3.61803i | 0.545439i | ||||||||
\(45\) | −0.854102 | − | 0.763932i | −0.127322 | − | 0.113880i | ||||
\(46\) | −0.618034 | −0.0911241 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | −3.00000 | − | 1.14590i | −0.433013 | − | 0.165396i | ||||
\(49\) | −6.70820 | + | 2.00000i | −0.958315 | + | 0.285714i | ||||
\(50\) | 3.00000i | 0.424264i | ||||||||
\(51\) | −12.0902 | − | 4.61803i | −1.69296 | − | 0.646654i | ||||
\(52\) | 0.236068i | 0.0327367i | ||||||||
\(53\) | − | 6.56231i | − | 0.901402i | −0.892675 | − | 0.450701i | \(-0.851174\pi\) | ||
0.892675 | − | 0.450701i | \(-0.148826\pi\) | |||||||
\(54\) | −2.85410 | + | 1.47214i | −0.388394 | + | 0.200332i | ||||
\(55\) | − | 0.854102i | − | 0.115167i | ||||||
\(56\) | 5.85410 | − | 0.854102i | 0.782287 | − | 0.114134i | ||||
\(57\) | 2.14590 | − | 5.61803i | 0.284231 | − | 0.744127i | ||||
\(58\) | 3.85410 | 0.506068 | ||||||||
\(59\) | −12.5623 | −1.63547 | −0.817736 | − | 0.575593i | \(-0.804771\pi\) | ||||
−0.817736 | + | 0.575593i | \(0.804771\pi\) | |||||||
\(60\) | 1.00000 | + | 0.381966i | 0.129099 | + | 0.0493116i | ||||
\(61\) | 5.85410i | 0.749541i | 0.927118 | + | 0.374770i | \(0.122278\pi\) | ||||
−0.927118 | + | 0.374770i | \(0.877722\pi\) | |||||||
\(62\) | −5.85410 | −0.743472 | ||||||||
\(63\) | −4.38197 | + | 6.61803i | −0.552076 | + | 0.833794i | ||||
\(64\) | 0.236068 | 0.0295085 | ||||||||
\(65\) | − | 0.0557281i | − | 0.00691222i | ||||||
\(66\) | −2.23607 | − | 0.854102i | −0.275241 | − | 0.105133i | ||||
\(67\) | −8.38197 | −1.02402 | −0.512010 | − | 0.858979i | \(-0.671099\pi\) | ||||
−0.512010 | + | 0.858979i | \(0.671099\pi\) | |||||||
\(68\) | 12.0902 | 1.46615 | ||||||||
\(69\) | −0.618034 | + | 1.61803i | −0.0744025 | + | 0.194788i | ||||
\(70\) | −0.618034 | + | 0.0901699i | −0.0738692 | + | 0.0107774i | ||||
\(71\) | 10.3262i | 1.22550i | 0.790277 | + | 0.612749i | \(0.209937\pi\) | ||||
−0.790277 | + | 0.612749i | \(0.790063\pi\) | |||||||
\(72\) | 4.47214 | − | 5.00000i | 0.527046 | − | 0.589256i | ||||
\(73\) | 3.76393i | 0.440535i | 0.975440 | + | 0.220267i | \(0.0706930\pi\) | ||||
−0.975440 | + | 0.220267i | \(0.929307\pi\) | |||||||
\(74\) | − | 6.32624i | − | 0.735410i | ||||||
\(75\) | 7.85410 | + | 3.00000i | 0.906914 | + | 0.346410i | ||||
\(76\) | 5.61803i | 0.644433i | ||||||||
\(77\) | −5.85410 | + | 0.854102i | −0.667137 | + | 0.0973340i | ||||
\(78\) | −0.145898 | − | 0.0557281i | −0.0165197 | − | 0.00630996i | ||||
\(79\) | −12.2361 | −1.37667 | −0.688333 | − | 0.725395i | \(-0.741657\pi\) | ||||
−0.688333 | + | 0.725395i | \(0.741657\pi\) | |||||||
\(80\) | −0.708204 | −0.0791796 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | − | 2.61803i | − | 0.289113i | ||||||
\(83\) | −2.70820 | −0.297264 | −0.148632 | − | 0.988893i | \(-0.547487\pi\) | ||||
−0.148632 | + | 0.988893i | \(0.547487\pi\) | |||||||
\(84\) | 1.61803 | − | 7.23607i | 0.176542 | − | 0.789520i | ||||
\(85\) | −2.85410 | −0.309571 | ||||||||
\(86\) | − | 3.32624i | − | 0.358677i | ||||||
\(87\) | 3.85410 | − | 10.0902i | 0.413203 | − | 1.08178i | ||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | 3.09017 | 0.327557 | 0.163779 | − | 0.986497i | \(-0.447632\pi\) | ||||
0.163779 | + | 0.986497i | \(0.447632\pi\) | |||||||
\(90\) | −0.472136 | + | 0.527864i | −0.0497675 | + | 0.0556418i | ||||
\(91\) | −0.381966 | + | 0.0557281i | −0.0400409 | + | 0.00584189i | ||||
\(92\) | − | 1.61803i | − | 0.168692i | ||||||
\(93\) | −5.85410 | + | 15.3262i | −0.607042 | + | 1.58926i | ||||
\(94\) | − | 4.94427i | − | 0.509963i | ||||||
\(95\) | − | 1.32624i | − | 0.136069i | ||||||
\(96\) | −3.47214 | + | 9.09017i | −0.354373 | + | 0.927762i | ||||
\(97\) | − | 15.9443i | − | 1.61890i | −0.587192 | − | 0.809448i | \(-0.699767\pi\) | ||
0.587192 | − | 0.809448i | \(-0.300233\pi\) | |||||||
\(98\) | 1.23607 | + | 4.14590i | 0.124862 | + | 0.418799i | ||||
\(99\) | −4.47214 | + | 5.00000i | −0.449467 | + | 0.502519i | ||||
\(100\) | −7.85410 | −0.785410 | ||||||||
\(101\) | −6.09017 | −0.605995 | −0.302997 | − | 0.952991i | \(-0.597987\pi\) | ||||
−0.302997 | + | 0.952991i | \(0.597987\pi\) | |||||||
\(102\) | −2.85410 | + | 7.47214i | −0.282598 | + | 0.739852i | ||||
\(103\) | 12.1803i | 1.20016i | 0.799938 | + | 0.600082i | \(0.204866\pi\) | ||||
−0.799938 | + | 0.600082i | \(0.795134\pi\) | |||||||
\(104\) | 0.326238 | 0.0319903 | ||||||||
\(105\) | −0.381966 | + | 1.70820i | −0.0372761 | + | 0.166704i | ||||
\(106\) | −4.05573 | −0.393927 | ||||||||
\(107\) | 9.38197i | 0.906989i | 0.891259 | + | 0.453494i | \(0.149823\pi\) | ||||
−0.891259 | + | 0.453494i | \(0.850177\pi\) | |||||||
\(108\) | −3.85410 | − | 7.47214i | −0.370861 | − | 0.719007i | ||||
\(109\) | −8.09017 | −0.774898 | −0.387449 | − | 0.921891i | \(-0.626644\pi\) | ||||
−0.387449 | + | 0.921891i | \(0.626644\pi\) | |||||||
\(110\) | −0.527864 | −0.0503299 | ||||||||
\(111\) | −16.5623 | − | 6.32624i | −1.57202 | − | 0.600460i | ||||
\(112\) | 0.708204 | + | 4.85410i | 0.0669190 | + | 0.458670i | ||||
\(113\) | − | 13.7984i | − | 1.29804i | −0.760771 | − | 0.649021i | \(-0.775179\pi\) | ||
0.760771 | − | 0.649021i | \(-0.224821\pi\) | |||||||
\(114\) | −3.47214 | − | 1.32624i | −0.325195 | − | 0.124214i | ||||
\(115\) | 0.381966i | 0.0356185i | ||||||||
\(116\) | 10.0902i | 0.936849i | ||||||||
\(117\) | −0.291796 | + | 0.326238i | −0.0269766 | + | 0.0301607i | ||||
\(118\) | 7.76393i | 0.714728i | ||||||||
\(119\) | 2.85410 | + | 19.5623i | 0.261635 | + | 1.79327i | ||||
\(120\) | 0.527864 | − | 1.38197i | 0.0481872 | − | 0.126156i | ||||
\(121\) | 6.00000 | 0.545455 | ||||||||
\(122\) | 3.61803 | 0.327561 | ||||||||
\(123\) | −6.85410 | − | 2.61803i | −0.618014 | − | 0.236060i | ||||
\(124\) | − | 15.3262i | − | 1.37634i | ||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | 4.09017 | + | 2.70820i | 0.364381 | + | 0.241266i | ||||
\(127\) | −16.7984 | −1.49061 | −0.745307 | − | 0.666721i | \(-0.767697\pi\) | ||||
−0.745307 | + | 0.666721i | \(0.767697\pi\) | |||||||
\(128\) | − | 11.3820i | − | 1.00603i | ||||||
\(129\) | −8.70820 | − | 3.32624i | −0.766715 | − | 0.292859i | ||||
\(130\) | −0.0344419 | −0.00302075 | ||||||||
\(131\) | 5.29180 | 0.462346 | 0.231173 | − | 0.972913i | \(-0.425744\pi\) | ||||
0.231173 | + | 0.972913i | \(0.425744\pi\) | |||||||
\(132\) | 2.23607 | − | 5.85410i | 0.194625 | − | 0.509534i | ||||
\(133\) | −9.09017 | + | 1.32624i | −0.788218 | + | 0.114999i | ||||
\(134\) | 5.18034i | 0.447513i | ||||||||
\(135\) | 0.909830 | + | 1.76393i | 0.0783057 | + | 0.151815i | ||||
\(136\) | − | 16.7082i | − | 1.43272i | ||||||
\(137\) | − | 9.76393i | − | 0.834189i | −0.908863 | − | 0.417095i | \(-0.863048\pi\) | ||
0.908863 | − | 0.417095i | \(-0.136952\pi\) | |||||||
\(138\) | 1.00000 | + | 0.381966i | 0.0851257 | + | 0.0325151i | ||||
\(139\) | 12.0902i | 1.02547i | 0.858545 | + | 0.512737i | \(0.171369\pi\) | ||||
−0.858545 | + | 0.512737i | \(0.828631\pi\) | |||||||
\(140\) | −0.236068 | − | 1.61803i | −0.0199514 | − | 0.136749i | ||||
\(141\) | −12.9443 | − | 4.94427i | −1.09010 | − | 0.416383i | ||||
\(142\) | 6.38197 | 0.535563 | ||||||||
\(143\) | −0.326238 | −0.0272814 | ||||||||
\(144\) | 4.14590 | + | 3.70820i | 0.345492 | + | 0.309017i | ||||
\(145\) | − | 2.38197i | − | 0.197812i | ||||||
\(146\) | 2.32624 | 0.192521 | ||||||||
\(147\) | 12.0902 | + | 0.909830i | 0.997180 | + | 0.0750415i | ||||
\(148\) | 16.5623 | 1.36141 | ||||||||
\(149\) | 5.70820i | 0.467634i | 0.972281 | + | 0.233817i | \(0.0751217\pi\) | ||||
−0.972281 | + | 0.233817i | \(0.924878\pi\) | |||||||
\(150\) | 1.85410 | − | 4.85410i | 0.151387 | − | 0.396336i | ||||
\(151\) | 6.47214 | 0.526695 | 0.263347 | − | 0.964701i | \(-0.415173\pi\) | ||||
0.263347 | + | 0.964701i | \(0.415173\pi\) | |||||||
\(152\) | 7.76393 | 0.629738 | ||||||||
\(153\) | 16.7082 | + | 14.9443i | 1.35078 | + | 1.20817i | ||||
\(154\) | 0.527864 | + | 3.61803i | 0.0425365 | + | 0.291549i | ||||
\(155\) | 3.61803i | 0.290607i | ||||||||
\(156\) | 0.145898 | − | 0.381966i | 0.0116812 | − | 0.0305818i | ||||
\(157\) | − | 16.4721i | − | 1.31462i | −0.753620 | − | 0.657310i | \(-0.771694\pi\) | ||
0.753620 | − | 0.657310i | \(-0.228306\pi\) | |||||||
\(158\) | 7.56231i | 0.601625i | ||||||||
\(159\) | −4.05573 | + | 10.6180i | −0.321640 | + | 0.842065i | ||||
\(160\) | 2.14590i | 0.169648i | ||||||||
\(161\) | 2.61803 | − | 0.381966i | 0.206330 | − | 0.0301031i | ||||
\(162\) | 5.52786 | − | 0.618034i | 0.434310 | − | 0.0485573i | ||||
\(163\) | −7.90983 | −0.619546 | −0.309773 | − | 0.950811i | \(-0.600253\pi\) | ||||
−0.309773 | + | 0.950811i | \(0.600253\pi\) | |||||||
\(164\) | 6.85410 | 0.535215 | ||||||||
\(165\) | −0.527864 | + | 1.38197i | −0.0410942 | + | 0.107586i | ||||
\(166\) | 1.67376i | 0.129909i | ||||||||
\(167\) | −3.18034 | −0.246102 | −0.123051 | − | 0.992400i | \(-0.539268\pi\) | ||||
−0.123051 | + | 0.992400i | \(0.539268\pi\) | |||||||
\(168\) | −10.0000 | − | 2.23607i | −0.771517 | − | 0.172516i | ||||
\(169\) | 12.9787 | 0.998363 | ||||||||
\(170\) | 1.76393i | 0.135287i | ||||||||
\(171\) | −6.94427 | + | 7.76393i | −0.531042 | + | 0.593723i | ||||
\(172\) | 8.70820 | 0.663994 | ||||||||
\(173\) | −5.47214 | −0.416039 | −0.208019 | − | 0.978125i | \(-0.566702\pi\) | ||||
−0.208019 | + | 0.978125i | \(0.566702\pi\) | |||||||
\(174\) | −6.23607 | − | 2.38197i | −0.472755 | − | 0.180576i | ||||
\(175\) | −1.85410 | − | 12.7082i | −0.140157 | − | 0.960650i | ||||
\(176\) | 4.14590i | 0.312509i | ||||||||
\(177\) | 20.3262 | + | 7.76393i | 1.52781 | + | 0.583573i | ||||
\(178\) | − | 1.90983i | − | 0.143148i | ||||||
\(179\) | − | 21.3262i | − | 1.59400i | −0.603981 | − | 0.796999i | \(-0.706420\pi\) | ||
0.603981 | − | 0.796999i | \(-0.293580\pi\) | |||||||
\(180\) | −1.38197 | − | 1.23607i | −0.103006 | − | 0.0921311i | ||||
\(181\) | − | 6.70820i | − | 0.498617i | −0.968424 | − | 0.249308i | \(-0.919797\pi\) | ||
0.968424 | − | 0.249308i | \(-0.0802033\pi\) | |||||||
\(182\) | 0.0344419 | + | 0.236068i | 0.00255300 | + | 0.0174985i | ||||
\(183\) | 3.61803 | − | 9.47214i | 0.267453 | − | 0.700200i | ||||
\(184\) | −2.23607 | −0.164845 | ||||||||
\(185\) | −3.90983 | −0.287456 | ||||||||
\(186\) | 9.47214 | + | 3.61803i | 0.694531 | + | 0.265287i | ||||
\(187\) | 16.7082i | 1.22182i | ||||||||
\(188\) | 12.9443 | 0.944058 | ||||||||
\(189\) | 11.1803 | − | 8.00000i | 0.813250 | − | 0.581914i | ||||
\(190\) | −0.819660 | −0.0594644 | ||||||||
\(191\) | − | 8.29180i | − | 0.599973i | −0.953943 | − | 0.299987i | \(-0.903018\pi\) | ||
0.953943 | − | 0.299987i | \(-0.0969822\pi\) | |||||||
\(192\) | −0.381966 | − | 0.145898i | −0.0275660 | − | 0.0105293i | ||||
\(193\) | 2.29180 | 0.164967 | 0.0824835 | − | 0.996592i | \(-0.473715\pi\) | ||||
0.0824835 | + | 0.996592i | \(0.473715\pi\) | |||||||
\(194\) | −9.85410 | −0.707483 | ||||||||
\(195\) | −0.0344419 | + | 0.0901699i | −0.00246643 | + | 0.00645720i | ||||
\(196\) | −10.8541 | + | 3.23607i | −0.775293 | + | 0.231148i | ||||
\(197\) | 14.9098i | 1.06228i | 0.847284 | + | 0.531141i | \(0.178236\pi\) | ||||
−0.847284 | + | 0.531141i | \(0.821764\pi\) | |||||||
\(198\) | 3.09017 | + | 2.76393i | 0.219609 | + | 0.196424i | ||||
\(199\) | − | 12.3820i | − | 0.877734i | −0.898552 | − | 0.438867i | \(-0.855380\pi\) | ||
0.898552 | − | 0.438867i | \(-0.144620\pi\) | |||||||
\(200\) | 10.8541i | 0.767501i | ||||||||
\(201\) | 13.5623 | + | 5.18034i | 0.956611 | + | 0.365393i | ||||
\(202\) | 3.76393i | 0.264829i | ||||||||
\(203\) | −16.3262 | + | 2.38197i | −1.14588 | + | 0.167181i | ||||
\(204\) | −19.5623 | − | 7.47214i | −1.36964 | − | 0.523154i | ||||
\(205\) | −1.61803 | −0.113008 | ||||||||
\(206\) | 7.52786 | 0.524491 | ||||||||
\(207\) | 2.00000 | − | 2.23607i | 0.139010 | − | 0.155417i | ||||
\(208\) | 0.270510i | 0.0187565i | ||||||||
\(209\) | −7.76393 | −0.537042 | ||||||||
\(210\) | 1.05573 | + | 0.236068i | 0.0728522 | + | 0.0162902i | ||||
\(211\) | −3.00000 | −0.206529 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(212\) | − | 10.6180i | − | 0.729250i | ||||||
\(213\) | 6.38197 | − | 16.7082i | 0.437285 | − | 1.14483i | ||||
\(214\) | 5.79837 | 0.396369 | ||||||||
\(215\) | −2.05573 | −0.140199 | ||||||||
\(216\) | −10.3262 | + | 5.32624i | −0.702611 | + | 0.362405i | ||||
\(217\) | 24.7984 | − | 3.61803i | 1.68342 | − | 0.245608i | ||||
\(218\) | 5.00000i | 0.338643i | ||||||||
\(219\) | 2.32624 | − | 6.09017i | 0.157193 | − | 0.411536i | ||||
\(220\) | − | 1.38197i | − | 0.0931721i | ||||||
\(221\) | 1.09017i | 0.0733328i | ||||||||
\(222\) | −3.90983 | + | 10.2361i | −0.262411 | + | 0.687000i | ||||
\(223\) | − | 5.90983i | − | 0.395751i | −0.980227 | − | 0.197876i | \(-0.936596\pi\) | ||
0.980227 | − | 0.197876i | \(-0.0634043\pi\) | |||||||
\(224\) | 14.7082 | − | 2.14590i | 0.982733 | − | 0.143379i | ||||
\(225\) | −10.8541 | − | 9.70820i | −0.723607 | − | 0.647214i | ||||
\(226\) | −8.52786 | −0.567265 | ||||||||
\(227\) | −6.67376 | −0.442953 | −0.221477 | − | 0.975166i | \(-0.571088\pi\) | ||||
−0.221477 | + | 0.975166i | \(0.571088\pi\) | |||||||
\(228\) | 3.47214 | − | 9.09017i | 0.229948 | − | 0.602011i | ||||
\(229\) | 22.0902i | 1.45976i | 0.683576 | + | 0.729880i | \(0.260424\pi\) | ||||
−0.683576 | + | 0.729880i | \(0.739576\pi\) | |||||||
\(230\) | 0.236068 | 0.0155659 | ||||||||
\(231\) | 10.0000 | + | 2.23607i | 0.657952 | + | 0.147122i | ||||
\(232\) | 13.9443 | 0.915486 | ||||||||
\(233\) | − | 29.3262i | − | 1.92123i | −0.277890 | − | 0.960613i | \(-0.589635\pi\) | ||
0.277890 | − | 0.960613i | \(-0.410365\pi\) | |||||||
\(234\) | 0.201626 | + | 0.180340i | 0.0131807 | + | 0.0117892i | ||||
\(235\) | −3.05573 | −0.199334 | ||||||||
\(236\) | −20.3262 | −1.32313 | ||||||||
\(237\) | 19.7984 | + | 7.56231i | 1.28604 | + | 0.491225i | ||||
\(238\) | 12.0902 | − | 1.76393i | 0.783689 | − | 0.114339i | ||||
\(239\) | − | 21.3262i | − | 1.37948i | −0.724057 | − | 0.689740i | \(-0.757725\pi\) | ||
0.724057 | − | 0.689740i | \(-0.242275\pi\) | |||||||
\(240\) | 1.14590 | + | 0.437694i | 0.0739674 | + | 0.0282530i | ||||
\(241\) | − | 9.47214i | − | 0.610154i | −0.952328 | − | 0.305077i | \(-0.901318\pi\) | ||
0.952328 | − | 0.305077i | \(-0.0986822\pi\) | |||||||
\(242\) | − | 3.70820i | − | 0.238372i | ||||||
\(243\) | 3.90983 | − | 15.0902i | 0.250816 | − | 0.968035i | ||||
\(244\) | 9.47214i | 0.606391i | ||||||||
\(245\) | 2.56231 | − | 0.763932i | 0.163700 | − | 0.0488058i | ||||
\(246\) | −1.61803 | + | 4.23607i | −0.103162 | + | 0.270082i | ||||
\(247\) | −0.506578 | −0.0322328 | ||||||||
\(248\) | −21.1803 | −1.34495 | ||||||||
\(249\) | 4.38197 | + | 1.67376i | 0.277696 | + | 0.106070i | ||||
\(250\) | − | 2.32624i | − | 0.147124i | ||||||
\(251\) | −2.47214 | −0.156040 | −0.0780199 | − | 0.996952i | \(-0.524860\pi\) | ||||
−0.0780199 | + | 0.996952i | \(0.524860\pi\) | |||||||
\(252\) | −7.09017 | + | 10.7082i | −0.446639 | + | 0.674553i | ||||
\(253\) | 2.23607 | 0.140580 | ||||||||
\(254\) | 10.3820i | 0.651422i | ||||||||
\(255\) | 4.61803 | + | 1.76393i | 0.289193 | + | 0.110462i | ||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | −13.0557 | −0.814394 | −0.407197 | − | 0.913340i | \(-0.633494\pi\) | ||||
−0.407197 | + | 0.913340i | \(0.633494\pi\) | |||||||
\(258\) | −2.05573 | + | 5.38197i | −0.127984 | + | 0.335067i | ||||
\(259\) | 3.90983 | + | 26.7984i | 0.242945 | + | 1.66517i | ||||
\(260\) | − | 0.0901699i | − | 0.00559210i | ||||||
\(261\) | −12.4721 | + | 13.9443i | −0.772006 | + | 0.863129i | ||||
\(262\) | − | 3.27051i | − | 0.202053i | ||||||
\(263\) | − | 0.0557281i | − | 0.00343634i | −0.999999 | − | 0.00171817i | \(-0.999453\pi\) | ||
0.999999 | − | 0.00171817i | \(-0.000546911\pi\) | |||||||
\(264\) | −8.09017 | − | 3.09017i | −0.497916 | − | 0.190187i | ||||
\(265\) | 2.50658i | 0.153978i | ||||||||
\(266\) | 0.819660 | + | 5.61803i | 0.0502566 | + | 0.344464i | ||||
\(267\) | −5.00000 | − | 1.90983i | −0.305995 | − | 0.116880i | ||||
\(268\) | −13.5623 | −0.828450 | ||||||||
\(269\) | 4.14590 | 0.252780 | 0.126390 | − | 0.991981i | \(-0.459661\pi\) | ||||
0.126390 | + | 0.991981i | \(0.459661\pi\) | |||||||
\(270\) | 1.09017 | − | 0.562306i | 0.0663456 | − | 0.0342208i | ||||
\(271\) | − | 2.23607i | − | 0.135831i | −0.997691 | − | 0.0679157i | \(-0.978365\pi\) | ||
0.997691 | − | 0.0679157i | \(-0.0216349\pi\) | |||||||
\(272\) | 13.8541 | 0.840028 | ||||||||
\(273\) | 0.652476 | + | 0.145898i | 0.0394896 | + | 0.00883015i | ||||
\(274\) | −6.03444 | −0.364554 | ||||||||
\(275\) | − | 10.8541i | − | 0.654527i | ||||||
\(276\) | −1.00000 | + | 2.61803i | −0.0601929 | + | 0.157587i | ||||
\(277\) | 13.8541 | 0.832412 | 0.416206 | − | 0.909270i | \(-0.363359\pi\) | ||||
0.416206 | + | 0.909270i | \(0.363359\pi\) | |||||||
\(278\) | 7.47214 | 0.448149 | ||||||||
\(279\) | 18.9443 | − | 21.1803i | 1.13416 | − | 1.26803i | ||||
\(280\) | −2.23607 | + | 0.326238i | −0.133631 | + | 0.0194964i | ||||
\(281\) | − | 18.9443i | − | 1.13012i | −0.825050 | − | 0.565060i | \(-0.808853\pi\) | ||
0.825050 | − | 0.565060i | \(-0.191147\pi\) | |||||||
\(282\) | −3.05573 | + | 8.00000i | −0.181966 | + | 0.476393i | ||||
\(283\) | 15.7984i | 0.939116i | 0.882902 | + | 0.469558i | \(0.155587\pi\) | ||||
−0.882902 | + | 0.469558i | \(0.844413\pi\) | |||||||
\(284\) | 16.7082i | 0.991449i | ||||||||
\(285\) | −0.819660 | + | 2.14590i | −0.0485525 | + | 0.127112i | ||||
\(286\) | 0.201626i | 0.0119224i | ||||||||
\(287\) | 1.61803 | + | 11.0902i | 0.0955095 | + | 0.654632i | ||||
\(288\) | 11.2361 | − | 12.5623i | 0.662092 | − | 0.740241i | ||||
\(289\) | 38.8328 | 2.28428 | ||||||||
\(290\) | −1.47214 | −0.0864468 | ||||||||
\(291\) | −9.85410 | + | 25.7984i | −0.577658 | + | 1.51233i | ||||
\(292\) | 6.09017i | 0.356400i | ||||||||
\(293\) | −27.7082 | −1.61873 | −0.809365 | − | 0.587306i | \(-0.800189\pi\) | ||||
−0.809365 | + | 0.587306i | \(0.800189\pi\) | |||||||
\(294\) | 0.562306 | − | 7.47214i | 0.0327943 | − | 0.435784i | ||||
\(295\) | 4.79837 | 0.279372 | ||||||||
\(296\) | − | 22.8885i | − | 1.33037i | ||||||
\(297\) | 10.3262 | − | 5.32624i | 0.599189 | − | 0.309060i | ||||
\(298\) | 3.52786 | 0.204364 | ||||||||
\(299\) | 0.145898 | 0.00843750 | ||||||||
\(300\) | 12.7082 | + | 4.85410i | 0.733708 | + | 0.280252i | ||||
\(301\) | 2.05573 | + | 14.0902i | 0.118490 | + | 0.812144i | ||||
\(302\) | − | 4.00000i | − | 0.230174i | ||||||
\(303\) | 9.85410 | + | 3.76393i | 0.566103 | + | 0.216232i | ||||
\(304\) | 6.43769i | 0.369227i | ||||||||
\(305\) | − | 2.23607i | − | 0.128037i | ||||||
\(306\) | 9.23607 | − | 10.3262i | 0.527991 | − | 0.590312i | ||||
\(307\) | − | 12.5279i | − | 0.715003i | −0.933913 | − | 0.357501i | \(-0.883629\pi\) | ||
0.933913 | − | 0.357501i | \(-0.116371\pi\) | |||||||
\(308\) | −9.47214 | + | 1.38197i | −0.539725 | + | 0.0787448i | ||||
\(309\) | 7.52786 | − | 19.7082i | 0.428245 | − | 1.12116i | ||||
\(310\) | 2.23607 | 0.127000 | ||||||||
\(311\) | −7.67376 | −0.435139 | −0.217570 | − | 0.976045i | \(-0.569813\pi\) | ||||
−0.217570 | + | 0.976045i | \(0.569813\pi\) | |||||||
\(312\) | −0.527864 | − | 0.201626i | −0.0298844 | − | 0.0114148i | ||||
\(313\) | 12.1803i | 0.688474i | 0.938883 | + | 0.344237i | \(0.111862\pi\) | ||||
−0.938883 | + | 0.344237i | \(0.888138\pi\) | |||||||
\(314\) | −10.1803 | −0.574510 | ||||||||
\(315\) | 1.67376 | − | 2.52786i | 0.0943058 | − | 0.142429i | ||||
\(316\) | −19.7984 | −1.11375 | ||||||||
\(317\) | 1.61803i | 0.0908778i | 0.998967 | + | 0.0454389i | \(0.0144686\pi\) | ||||
−0.998967 | + | 0.0454389i | \(0.985531\pi\) | |||||||
\(318\) | 6.56231 | + | 2.50658i | 0.367996 | + | 0.140562i | ||||
\(319\) | −13.9443 | −0.780729 | ||||||||
\(320\) | −0.0901699 | −0.00504065 | ||||||||
\(321\) | 5.79837 | − | 15.1803i | 0.323634 | − | 0.847284i | ||||
\(322\) | −0.236068 | − | 1.61803i | −0.0131556 | − | 0.0901695i | ||||
\(323\) | 25.9443i | 1.44358i | ||||||||
\(324\) | 1.61803 | + | 14.4721i | 0.0898908 | + | 0.804008i | ||||
\(325\) | − | 0.708204i | − | 0.0392841i | ||||||
\(326\) | 4.88854i | 0.270751i | ||||||||
\(327\) | 13.0902 | + | 5.00000i | 0.723888 | + | 0.276501i | ||||
\(328\) | − | 9.47214i | − | 0.523011i | ||||||
\(329\) | 3.05573 | + | 20.9443i | 0.168468 | + | 1.15470i | ||||
\(330\) | 0.854102 | + | 0.326238i | 0.0470168 | + | 0.0179588i | ||||
\(331\) | −22.0689 | −1.21302 | −0.606508 | − | 0.795078i | \(-0.707430\pi\) | ||||
−0.606508 | + | 0.795078i | \(0.707430\pi\) | |||||||
\(332\) | −4.38197 | −0.240492 | ||||||||
\(333\) | 22.8885 | + | 20.4721i | 1.25428 | + | 1.12187i | ||||
\(334\) | 1.96556i | 0.107551i | ||||||||
\(335\) | 3.20163 | 0.174924 | ||||||||
\(336\) | 1.85410 | − | 8.29180i | 0.101150 | − | 0.452355i | ||||
\(337\) | 23.4508 | 1.27745 | 0.638725 | − | 0.769435i | \(-0.279462\pi\) | ||||
0.638725 | + | 0.769435i | \(0.279462\pi\) | |||||||
\(338\) | − | 8.02129i | − | 0.436300i | ||||||
\(339\) | −8.52786 | + | 22.3262i | −0.463170 | + | 1.21259i | ||||
\(340\) | −4.61803 | −0.250448 | ||||||||
\(341\) | 21.1803 | 1.14698 | ||||||||
\(342\) | 4.79837 | + | 4.29180i | 0.259466 | + | 0.232074i | ||||
\(343\) | −7.79837 | − | 16.7984i | −0.421073 | − | 0.907027i | ||||
\(344\) | − | 12.0344i | − | 0.648854i | ||||||
\(345\) | 0.236068 | − | 0.618034i | 0.0127095 | − | 0.0332738i | ||||
\(346\) | 3.38197i | 0.181816i | ||||||||
\(347\) | − | 0.819660i | − | 0.0440017i | −0.999758 | − | 0.0220008i | \(-0.992996\pi\) | ||
0.999758 | − | 0.0220008i | \(-0.00700365\pi\) | |||||||
\(348\) | 6.23607 | − | 16.3262i | 0.334288 | − | 0.875178i | ||||
\(349\) | − | 25.1459i | − | 1.34603i | −0.739629 | − | 0.673015i | \(-0.764999\pi\) | ||
0.739629 | − | 0.673015i | \(-0.235001\pi\) | |||||||
\(350\) | −7.85410 | + | 1.14590i | −0.419819 | + | 0.0612508i | ||||
\(351\) | 0.673762 | − | 0.347524i | 0.0359628 | − | 0.0185495i | ||||
\(352\) | 12.5623 | 0.669573 | ||||||||
\(353\) | −35.4721 | −1.88799 | −0.943996 | − | 0.329958i | \(-0.892965\pi\) | ||||
−0.943996 | + | 0.329958i | \(0.892965\pi\) | |||||||
\(354\) | 4.79837 | − | 12.5623i | 0.255031 | − | 0.667679i | ||||
\(355\) | − | 3.94427i | − | 0.209340i | ||||||
\(356\) | 5.00000 | 0.264999 | ||||||||
\(357\) | 7.47214 | − | 33.4164i | 0.395467 | − | 1.76858i | ||||
\(358\) | −13.1803 | −0.696603 | ||||||||
\(359\) | − | 14.0902i | − | 0.743651i | −0.928303 | − | 0.371825i | \(-0.878732\pi\) | ||
0.928303 | − | 0.371825i | \(-0.121268\pi\) | |||||||
\(360\) | −1.70820 | + | 1.90983i | −0.0900303 | + | 0.100657i | ||||
\(361\) | 6.94427 | 0.365488 | ||||||||
\(362\) | −4.14590 | −0.217904 | ||||||||
\(363\) | −9.70820 | − | 3.70820i | −0.509549 | − | 0.194630i | ||||
\(364\) | −0.618034 | + | 0.0901699i | −0.0323938 | + | 0.00472619i | ||||
\(365\) | − | 1.43769i | − | 0.0752523i | ||||||
\(366\) | −5.85410 | − | 2.23607i | −0.305999 | − | 0.116881i | ||||
\(367\) | − | 11.2705i | − | 0.588316i | −0.955757 | − | 0.294158i | \(-0.904961\pi\) | ||
0.955757 | − | 0.294158i | \(-0.0950392\pi\) | |||||||
\(368\) | − | 1.85410i | − | 0.0966517i | ||||||
\(369\) | 9.47214 | + | 8.47214i | 0.493100 | + | 0.441042i | ||||
\(370\) | 2.41641i | 0.125623i | ||||||||
\(371\) | 17.1803 | − | 2.50658i | 0.891959 | − | 0.130135i | ||||
\(372\) | −9.47214 | + | 24.7984i | −0.491107 | + | 1.28574i | ||||
\(373\) | −1.00000 | −0.0517780 | −0.0258890 | − | 0.999665i | \(-0.508242\pi\) | ||||
−0.0258890 | + | 0.999665i | \(0.508242\pi\) | |||||||
\(374\) | 10.3262 | 0.533957 | ||||||||
\(375\) | −6.09017 | − | 2.32624i | −0.314495 | − | 0.120126i | ||||
\(376\) | − | 17.8885i | − | 0.922531i | ||||||
\(377\) | −0.909830 | −0.0468586 | ||||||||
\(378\) | −4.94427 | − | 6.90983i | −0.254306 | − | 0.355403i | ||||
\(379\) | 15.5279 | 0.797613 | 0.398806 | − | 0.917035i | \(-0.369425\pi\) | ||||
0.398806 | + | 0.917035i | \(0.369425\pi\) | |||||||
\(380\) | − | 2.14590i | − | 0.110082i | ||||||
\(381\) | 27.1803 | + | 10.3820i | 1.39249 | + | 0.531884i | ||||
\(382\) | −5.12461 | −0.262198 | ||||||||
\(383\) | −3.76393 | −0.192328 | −0.0961640 | − | 0.995366i | \(-0.530657\pi\) | ||||
−0.0961640 | + | 0.995366i | \(0.530657\pi\) | |||||||
\(384\) | −7.03444 | + | 18.4164i | −0.358975 | + | 0.939808i | ||||
\(385\) | 2.23607 | − | 0.326238i | 0.113961 | − | 0.0166266i | ||||
\(386\) | − | 1.41641i | − | 0.0720933i | ||||||
\(387\) | 12.0344 | + | 10.7639i | 0.611745 | + | 0.547161i | ||||
\(388\) | − | 25.7984i | − | 1.30971i | ||||||
\(389\) | − | 19.2918i | − | 0.978133i | −0.872247 | − | 0.489066i | \(-0.837338\pi\) | ||
0.872247 | − | 0.489066i | \(-0.162662\pi\) | |||||||
\(390\) | 0.0557281 | + | 0.0212862i | 0.00282190 | + | 0.00107787i | ||||
\(391\) | − | 7.47214i | − | 0.377882i | ||||||
\(392\) | 4.47214 | + | 15.0000i | 0.225877 | + | 0.757614i | ||||
\(393\) | −8.56231 | − | 3.27051i | −0.431911 | − | 0.164975i | ||||
\(394\) | 9.21478 | 0.464234 | ||||||||
\(395\) | 4.67376 | 0.235162 | ||||||||
\(396\) | −7.23607 | + | 8.09017i | −0.363626 | + | 0.406546i | ||||
\(397\) | 10.7639i | 0.540226i | 0.962829 | + | 0.270113i | \(0.0870611\pi\) | ||||
−0.962829 | + | 0.270113i | \(0.912939\pi\) | |||||||
\(398\) | −7.65248 | −0.383584 | ||||||||
\(399\) | 15.5279 | + | 3.47214i | 0.777366 | + | 0.173824i | ||||
\(400\) | −9.00000 | −0.450000 | ||||||||
\(401\) | 18.4164i | 0.919672i | 0.888004 | + | 0.459836i | \(0.152092\pi\) | ||||
−0.888004 | + | 0.459836i | \(0.847908\pi\) | |||||||
\(402\) | 3.20163 | − | 8.38197i | 0.159683 | − | 0.418054i | ||||
\(403\) | 1.38197 | 0.0688406 | ||||||||
\(404\) | −9.85410 | −0.490260 | ||||||||
\(405\) | −0.381966 | − | 3.41641i | −0.0189800 | − | 0.169763i | ||||
\(406\) | 1.47214 | + | 10.0902i | 0.0730609 | + | 0.500767i | ||||
\(407\) | 22.8885i | 1.13454i | ||||||||
\(408\) | −10.3262 | + | 27.0344i | −0.511225 | + | 1.33840i | ||||
\(409\) | 24.5279i | 1.21282i | 0.795150 | + | 0.606412i | \(0.207392\pi\) | ||||
−0.795150 | + | 0.606412i | \(0.792608\pi\) | |||||||
\(410\) | 1.00000i | 0.0493865i | ||||||||
\(411\) | −6.03444 | + | 15.7984i | −0.297657 | + | 0.779276i | ||||
\(412\) | 19.7082i | 0.970954i | ||||||||
\(413\) | −4.79837 | − | 32.8885i | −0.236113 | − | 1.61834i | ||||
\(414\) | −1.38197 | − | 1.23607i | −0.0679199 | − | 0.0607494i | ||||
\(415\) | 1.03444 | 0.0507788 | ||||||||
\(416\) | 0.819660 | 0.0401871 | ||||||||
\(417\) | 7.47214 | − | 19.5623i | 0.365912 | − | 0.957970i | ||||
\(418\) | 4.79837i | 0.234696i | ||||||||
\(419\) | −0.201626 | −0.00985008 | −0.00492504 | − | 0.999988i | \(-0.501568\pi\) | ||||
−0.00492504 | + | 0.999988i | \(0.501568\pi\) | |||||||
\(420\) | −0.618034 | + | 2.76393i | −0.0301570 | + | 0.134866i | ||||
\(421\) | −20.6869 | −1.00822 | −0.504109 | − | 0.863640i | \(-0.668179\pi\) | ||||
−0.504109 | + | 0.863640i | \(0.668179\pi\) | |||||||
\(422\) | 1.85410i | 0.0902563i | ||||||||
\(423\) | 17.8885 | + | 16.0000i | 0.869771 | + | 0.777947i | ||||
\(424\) | −14.6738 | −0.712621 | ||||||||
\(425\) | −36.2705 | −1.75938 | ||||||||
\(426\) | −10.3262 | − | 3.94427i | −0.500308 | − | 0.191101i | ||||
\(427\) | −15.3262 | + | 2.23607i | −0.741689 | + | 0.108211i | ||||
\(428\) | 15.1803i | 0.733769i | ||||||||
\(429\) | 0.527864 | + | 0.201626i | 0.0254855 | + | 0.00973460i | ||||
\(430\) | 1.27051i | 0.0612694i | ||||||||
\(431\) | 33.0902i | 1.59390i | 0.604047 | + | 0.796949i | \(0.293554\pi\) | ||||
−0.604047 | + | 0.796949i | \(0.706446\pi\) | |||||||
\(432\) | −4.41641 | − | 8.56231i | −0.212485 | − | 0.411954i | ||||
\(433\) | 10.4721i | 0.503259i | 0.967824 | + | 0.251629i | \(0.0809664\pi\) | ||||
−0.967824 | + | 0.251629i | \(0.919034\pi\) | |||||||
\(434\) | −2.23607 | − | 15.3262i | −0.107335 | − | 0.735683i | ||||
\(435\) | −1.47214 | + | 3.85410i | −0.0705835 | + | 0.184790i | ||||
\(436\) | −13.0902 | −0.626905 | ||||||||
\(437\) | 3.47214 | 0.166095 | ||||||||
\(438\) | −3.76393 | − | 1.43769i | −0.179848 | − | 0.0686957i | ||||
\(439\) | − | 16.5279i | − | 0.788832i | −0.918932 | − | 0.394416i | \(-0.870947\pi\) | ||
0.918932 | − | 0.394416i | \(-0.129053\pi\) | |||||||
\(440\) | −1.90983 | −0.0910476 | ||||||||
\(441\) | −19.0000 | − | 8.94427i | −0.904762 | − | 0.425918i | ||||
\(442\) | 0.673762 | 0.0320476 | ||||||||
\(443\) | − | 0.180340i | − | 0.00856821i | −0.999991 | − | 0.00428410i | \(-0.998636\pi\) | ||
0.999991 | − | 0.00428410i | \(-0.00136368\pi\) | |||||||
\(444\) | −26.7984 | − | 10.2361i | −1.27179 | − | 0.485782i | ||||
\(445\) | −1.18034 | −0.0559535 | ||||||||
\(446\) | −3.65248 | −0.172950 | ||||||||
\(447\) | 3.52786 | − | 9.23607i | 0.166862 | − | 0.436851i | ||||
\(448\) | 0.0901699 | + | 0.618034i | 0.00426013 | + | 0.0291994i | ||||
\(449\) | 22.0902i | 1.04250i | 0.853404 | + | 0.521250i | \(0.174534\pi\) | ||||
−0.853404 | + | 0.521250i | \(0.825466\pi\) | |||||||
\(450\) | −6.00000 | + | 6.70820i | −0.282843 | + | 0.316228i | ||||
\(451\) | 9.47214i | 0.446025i | ||||||||
\(452\) | − | 22.3262i | − | 1.05014i | ||||||
\(453\) | −10.4721 | − | 4.00000i | −0.492024 | − | 0.187936i | ||||
\(454\) | 4.12461i | 0.193578i | ||||||||
\(455\) | 0.145898 | − | 0.0212862i | 0.00683981 | − | 0.000997914i | ||||
\(456\) | −12.5623 | − | 4.79837i | −0.588284 | − | 0.224704i | ||||
\(457\) | −4.56231 | −0.213416 | −0.106708 | − | 0.994290i | \(-0.534031\pi\) | ||||
−0.106708 | + | 0.994290i | \(0.534031\pi\) | |||||||
\(458\) | 13.6525 | 0.637938 | ||||||||
\(459\) | −17.7984 | − | 34.5066i | −0.830757 | − | 1.61063i | ||||
\(460\) | 0.618034i | 0.0288160i | ||||||||
\(461\) | −35.6869 | −1.66211 | −0.831053 | − | 0.556194i | \(-0.812261\pi\) | ||||
−0.831053 | + | 0.556194i | \(0.812261\pi\) | |||||||
\(462\) | 1.38197 | − | 6.18034i | 0.0642949 | − | 0.287535i | ||||
\(463\) | −25.4721 | −1.18379 | −0.591895 | − | 0.806015i | \(-0.701620\pi\) | ||||
−0.591895 | + | 0.806015i | \(0.701620\pi\) | |||||||
\(464\) | 11.5623i | 0.536767i | ||||||||
\(465\) | 2.23607 | − | 5.85410i | 0.103695 | − | 0.271477i | ||||
\(466\) | −18.1246 | −0.839606 | ||||||||
\(467\) | 19.8328 | 0.917753 | 0.458877 | − | 0.888500i | \(-0.348252\pi\) | ||||
0.458877 | + | 0.888500i | \(0.348252\pi\) | |||||||
\(468\) | −0.472136 | + | 0.527864i | −0.0218245 | + | 0.0244005i | ||||
\(469\) | −3.20163 | − | 21.9443i | −0.147837 | − | 1.01329i | ||||
\(470\) | 1.88854i | 0.0871120i | ||||||||
\(471\) | −10.1803 | + | 26.6525i | −0.469085 | + | 1.22808i | ||||
\(472\) | 28.0902i | 1.29295i | ||||||||
\(473\) | 12.0344i | 0.553344i | ||||||||
\(474\) | 4.67376 | − | 12.2361i | 0.214673 | − | 0.562021i | ||||
\(475\) | − | 16.8541i | − | 0.773319i | ||||||
\(476\) | 4.61803 | + | 31.6525i | 0.211667 | + | 1.45079i | ||||
\(477\) | 13.1246 | − | 14.6738i | 0.600935 | − | 0.671865i | ||||
\(478\) | −13.1803 | −0.602855 | ||||||||
\(479\) | −5.65248 | −0.258268 | −0.129134 | − | 0.991627i | \(-0.541220\pi\) | ||||
−0.129134 | + | 0.991627i | \(0.541220\pi\) | |||||||
\(480\) | 1.32624 | − | 3.47214i | 0.0605342 | − | 0.158481i | ||||
\(481\) | 1.49342i | 0.0680942i | ||||||||
\(482\) | −5.85410 | −0.266647 | ||||||||
\(483\) | −4.47214 | − | 1.00000i | −0.203489 | − | 0.0455016i | ||||
\(484\) | 9.70820 | 0.441282 | ||||||||
\(485\) | 6.09017i | 0.276540i | ||||||||
\(486\) | −9.32624 | − | 2.41641i | −0.423047 | − | 0.109610i | ||||
\(487\) | 1.29180 | 0.0585369 | 0.0292684 | − | 0.999572i | \(-0.490682\pi\) | ||||
0.0292684 | + | 0.999572i | \(0.490682\pi\) | |||||||
\(488\) | 13.0902 | 0.592564 | ||||||||
\(489\) | 12.7984 | + | 4.88854i | 0.578762 | + | 0.221068i | ||||
\(490\) | −0.472136 | − | 1.58359i | −0.0213289 | − | 0.0715394i | ||||
\(491\) | 33.0902i | 1.49334i | 0.665196 | + | 0.746669i | \(0.268348\pi\) | ||||
−0.665196 | + | 0.746669i | \(0.731652\pi\) | |||||||
\(492\) | −11.0902 | − | 4.23607i | −0.499983 | − | 0.190977i | ||||
\(493\) | 46.5967i | 2.09861i | ||||||||
\(494\) | 0.313082i | 0.0140862i | ||||||||
\(495\) | 1.70820 | − | 1.90983i | 0.0767781 | − | 0.0858405i | ||||
\(496\) | − | 17.5623i | − | 0.788571i | ||||||
\(497\) | −27.0344 | + | 3.94427i | −1.21266 | + | 0.176925i | ||||
\(498\) | 1.03444 | − | 2.70820i | 0.0463544 | − | 0.121358i | ||||
\(499\) | 2.56231 | 0.114705 | 0.0573523 | − | 0.998354i | \(-0.481734\pi\) | ||||
0.0573523 | + | 0.998354i | \(0.481734\pi\) | |||||||
\(500\) | 6.09017 | 0.272361 | ||||||||
\(501\) | 5.14590 | + | 1.96556i | 0.229902 | + | 0.0878147i | ||||
\(502\) | 1.52786i | 0.0681919i | ||||||||
\(503\) | 42.7426 | 1.90580 | 0.952900 | − | 0.303284i | \(-0.0980831\pi\) | ||||
0.952900 | + | 0.303284i | \(0.0980831\pi\) | |||||||
\(504\) | 14.7984 | + | 9.79837i | 0.659172 | + | 0.436454i | ||||
\(505\) | 2.32624 | 0.103516 | ||||||||
\(506\) | − | 1.38197i | − | 0.0614359i | ||||||
\(507\) | −21.0000 | − | 8.02129i | −0.932643 | − | 0.356238i | ||||
\(508\) | −27.1803 | −1.20593 | ||||||||
\(509\) | −20.0000 | −0.886484 | −0.443242 | − | 0.896402i | \(-0.646172\pi\) | ||||
−0.443242 | + | 0.896402i | \(0.646172\pi\) | |||||||
\(510\) | 1.09017 | − | 2.85410i | 0.0482735 | − | 0.126382i | ||||
\(511\) | −9.85410 | + | 1.43769i | −0.435920 | + | 0.0635998i | ||||
\(512\) | − | 18.7082i | − | 0.826794i | ||||||
\(513\) | 16.0344 | − | 8.27051i | 0.707938 | − | 0.365152i | ||||
\(514\) | 8.06888i | 0.355903i | ||||||||
\(515\) | − | 4.65248i | − | 0.205013i | ||||||
\(516\) | −14.0902 | − | 5.38197i | −0.620285 | − | 0.236928i | ||||
\(517\) | 17.8885i | 0.786737i | ||||||||
\(518\) | 16.5623 | − | 2.41641i | 0.727706 | − | 0.106171i | ||||
\(519\) | 8.85410 | + | 3.38197i | 0.388652 | + | 0.148452i | ||||
\(520\) | −0.124612 | −0.00546459 | ||||||||
\(521\) | 27.5279 | 1.20602 | 0.603009 | − | 0.797735i | \(-0.293968\pi\) | ||||
0.603009 | + | 0.797735i | \(0.293968\pi\) | |||||||
\(522\) | 8.61803 | + | 7.70820i | 0.377201 | + | 0.337379i | ||||
\(523\) | − | 23.5967i | − | 1.03181i | −0.856645 | − | 0.515907i | \(-0.827455\pi\) | ||
0.856645 | − | 0.515907i | \(-0.172545\pi\) | |||||||
\(524\) | 8.56231 | 0.374046 | ||||||||
\(525\) | −4.85410 | + | 21.7082i | −0.211850 | + | 0.947424i | ||||
\(526\) | −0.0344419 | −0.00150174 | ||||||||
\(527\) | − | 70.7771i | − | 3.08310i | ||||||
\(528\) | 2.56231 | − | 6.70820i | 0.111510 | − | 0.291937i | ||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 1.54915 | 0.0672908 | ||||||||
\(531\) | −28.0902 | − | 25.1246i | −1.21901 | − | 1.09032i | ||||
\(532\) | −14.7082 | + | 2.14590i | −0.637682 | + | 0.0930365i | ||||
\(533\) | 0.618034i | 0.0267700i | ||||||||
\(534\) | −1.18034 | + | 3.09017i | −0.0510783 | + | 0.133725i | ||||
\(535\) | − | 3.58359i | − | 0.154932i | ||||||
\(536\) | 18.7426i | 0.809559i | ||||||||
\(537\) | −13.1803 | + | 34.5066i | −0.568774 | + | 1.48907i | ||||
\(538\) | − | 2.56231i | − | 0.110469i | ||||||
\(539\) | −4.47214 | − | 15.0000i | −0.192629 | − | 0.646096i | ||||
\(540\) | 1.47214 | + | 2.85410i | 0.0633506 | + | 0.122821i | ||||
\(541\) | −20.7639 | −0.892711 | −0.446356 | − | 0.894856i | \(-0.647278\pi\) | ||||
−0.446356 | + | 0.894856i | \(0.647278\pi\) | |||||||
\(542\) | −1.38197 | −0.0593605 | ||||||||
\(543\) | −4.14590 | + | 10.8541i | −0.177918 | + | 0.465794i | ||||
\(544\) | − | 41.9787i | − | 1.79982i | ||||||
\(545\) | 3.09017 | 0.132368 | ||||||||
\(546\) | 0.0901699 | − | 0.403252i | 0.00385892 | − | 0.0172576i | ||||
\(547\) | 31.2148 | 1.33465 | 0.667324 | − | 0.744768i | \(-0.267440\pi\) | ||||
0.667324 | + | 0.744768i | \(0.267440\pi\) | |||||||
\(548\) | − | 15.7984i | − | 0.674873i | ||||||
\(549\) | −11.7082 | + | 13.0902i | −0.499694 | + | 0.558675i | ||||
\(550\) | −6.70820 | −0.286039 | ||||||||
\(551\) | −21.6525 | −0.922426 | ||||||||
\(552\) | 3.61803 | + | 1.38197i | 0.153994 | + | 0.0588204i | ||||
\(553\) | −4.67376 | − | 32.0344i | −0.198749 | − | 1.36224i | ||||
\(554\) | − | 8.56231i | − | 0.363778i | ||||||
\(555\) | 6.32624 | + | 2.41641i | 0.268534 | + | 0.102571i | ||||
\(556\) | 19.5623i | 0.829627i | ||||||||
\(557\) | − | 26.0689i | − | 1.10457i | −0.833654 | − | 0.552287i | \(-0.813755\pi\) | ||
0.833654 | − | 0.552287i | \(-0.186245\pi\) | |||||||
\(558\) | −13.0902 | − | 11.7082i | −0.554151 | − | 0.495648i | ||||
\(559\) | 0.785218i | 0.0332112i | ||||||||
\(560\) | −0.270510 | − | 1.85410i | −0.0114311 | − | 0.0783501i | ||||
\(561\) | 10.3262 | − | 27.0344i | 0.435974 | − | 1.14140i | ||||
\(562\) | −11.7082 | −0.493881 | ||||||||
\(563\) | 18.1459 | 0.764758 | 0.382379 | − | 0.924005i | \(-0.375105\pi\) | ||||
0.382379 | + | 0.924005i | \(0.375105\pi\) | |||||||
\(564\) | −20.9443 | − | 8.00000i | −0.881913 | − | 0.336861i | ||||
\(565\) | 5.27051i | 0.221732i | ||||||||
\(566\) | 9.76393 | 0.410409 | ||||||||
\(567\) | −23.0344 | + | 6.03444i | −0.967356 | + | 0.253423i | ||||
\(568\) | 23.0902 | 0.968842 | ||||||||
\(569\) | 13.5967i | 0.570005i | 0.958527 | + | 0.285003i | \(0.0919945\pi\) | ||||
−0.958527 | + | 0.285003i | \(0.908006\pi\) | |||||||
\(570\) | 1.32624 | + | 0.506578i | 0.0555500 | + | 0.0212182i | ||||
\(571\) | 10.4164 | 0.435913 | 0.217957 | − | 0.975958i | \(-0.430061\pi\) | ||||
0.217957 | + | 0.975958i | \(0.430061\pi\) | |||||||
\(572\) | −0.527864 | −0.0220711 | ||||||||
\(573\) | −5.12461 | + | 13.4164i | −0.214084 | + | 0.560478i | ||||
\(574\) | 6.85410 | − | 1.00000i | 0.286085 | − | 0.0417392i | ||||
\(575\) | 4.85410i | 0.202430i | ||||||||
\(576\) | 0.527864 | + | 0.472136i | 0.0219943 | + | 0.0196723i | ||||
\(577\) | 29.3050i | 1.21998i | 0.792409 | + | 0.609991i | \(0.208827\pi\) | ||||
−0.792409 | + | 0.609991i | \(0.791173\pi\) | |||||||
\(578\) | − | 24.0000i | − | 0.998268i | ||||||
\(579\) | −3.70820 | − | 1.41641i | −0.154108 | − | 0.0588639i | ||||
\(580\) | − | 3.85410i | − | 0.160033i | ||||||
\(581\) | −1.03444 | − | 7.09017i | −0.0429159 | − | 0.294150i | ||||
\(582\) | 15.9443 | + | 6.09017i | 0.660911 | + | 0.252446i | ||||
\(583\) | 14.6738 | 0.607725 | ||||||||
\(584\) | 8.41641 | 0.348273 | ||||||||
\(585\) | 0.111456 | − | 0.124612i | 0.00460815 | − | 0.00515206i | ||||
\(586\) | 17.1246i | 0.707411i | ||||||||
\(587\) | −2.32624 | −0.0960141 | −0.0480071 | − | 0.998847i | \(-0.515287\pi\) | ||||
−0.0480071 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(588\) | 19.5623 | + | 1.47214i | 0.806736 | + | 0.0607099i | ||||
\(589\) | 32.8885 | 1.35515 | ||||||||
\(590\) | − | 2.96556i | − | 0.122090i | ||||||
\(591\) | 9.21478 | − | 24.1246i | 0.379045 | − | 0.992354i | ||||
\(592\) | 18.9787 | 0.780020 | ||||||||
\(593\) | 9.12461 | 0.374703 | 0.187351 | − | 0.982293i | \(-0.440010\pi\) | ||||
0.187351 | + | 0.982293i | \(0.440010\pi\) | |||||||
\(594\) | −3.29180 | − | 6.38197i | −0.135064 | − | 0.261855i | ||||
\(595\) | −1.09017 | − | 7.47214i | −0.0446926 | − | 0.306328i | ||||
\(596\) | 9.23607i | 0.378324i | ||||||||
\(597\) | −7.65248 | + | 20.0344i | −0.313195 | + | 0.819955i | ||||
\(598\) | − | 0.0901699i | − | 0.00368732i | ||||||
\(599\) | 9.85410i | 0.402628i | 0.979527 | + | 0.201314i | \(0.0645211\pi\) | ||||
−0.979527 | + | 0.201314i | \(0.935479\pi\) | |||||||
\(600\) | 6.70820 | − | 17.5623i | 0.273861 | − | 0.716978i | ||||
\(601\) | 25.3262i | 1.03308i | 0.856263 | + | 0.516539i | \(0.172780\pi\) | ||||
−0.856263 | + | 0.516539i | \(0.827220\pi\) | |||||||
\(602\) | 8.70820 | − | 1.27051i | 0.354920 | − | 0.0517821i | ||||
\(603\) | −18.7426 | − | 16.7639i | −0.763260 | − | 0.682680i | ||||
\(604\) | 10.4721 | 0.426105 | ||||||||
\(605\) | −2.29180 | −0.0931748 | ||||||||
\(606\) | 2.32624 | − | 6.09017i | 0.0944970 | − | 0.247396i | ||||
\(607\) | − | 14.4377i | − | 0.586008i | −0.956111 | − | 0.293004i | \(-0.905345\pi\) | ||
0.956111 | − | 0.293004i | \(-0.0946549\pi\) | |||||||
\(608\) | 19.5066 | 0.791096 | ||||||||
\(609\) | 27.8885 | + | 6.23607i | 1.13010 | + | 0.252698i | ||||
\(610\) | −1.38197 | −0.0559542 | ||||||||
\(611\) | 1.16718i | 0.0472192i | ||||||||
\(612\) | 27.0344 | + | 24.1803i | 1.09280 | + | 0.977432i | ||||
\(613\) | 3.47214 | 0.140238 | 0.0701191 | − | 0.997539i | \(-0.477662\pi\) | ||||
0.0701191 | + | 0.997539i | \(0.477662\pi\) | |||||||
\(614\) | −7.74265 | −0.312468 | ||||||||
\(615\) | 2.61803 | + | 1.00000i | 0.105569 | + | 0.0403239i | ||||
\(616\) | 1.90983 | + | 13.0902i | 0.0769492 | + | 0.527418i | ||||
\(617\) | 21.0902i | 0.849058i | 0.905414 | + | 0.424529i | \(0.139560\pi\) | ||||
−0.905414 | + | 0.424529i | \(0.860440\pi\) | |||||||
\(618\) | −12.1803 | − | 4.65248i | −0.489965 | − | 0.187150i | ||||
\(619\) | − | 6.97871i | − | 0.280498i | −0.990116 | − | 0.140249i | \(-0.955210\pi\) | ||
0.990116 | − | 0.140249i | \(-0.0447903\pi\) | |||||||
\(620\) | 5.85410i | 0.235106i | ||||||||
\(621\) | −4.61803 | + | 2.38197i | −0.185315 | + | 0.0955850i | ||||
\(622\) | 4.74265i | 0.190163i | ||||||||
\(623\) | 1.18034 | + | 8.09017i | 0.0472893 | + | 0.324126i | ||||
\(624\) | 0.167184 | − | 0.437694i | 0.00669273 | − | 0.0175218i | ||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 7.52786 | 0.300874 | ||||||||
\(627\) | 12.5623 | + | 4.79837i | 0.501690 | + | 0.191629i | ||||
\(628\) | − | 26.6525i | − | 1.06355i | ||||||
\(629\) | 76.4853 | 3.04967 | ||||||||
\(630\) | −1.56231 | − | 1.03444i | −0.0622438 | − | 0.0412131i | ||||
\(631\) | −29.1803 | −1.16165 | −0.580825 | − | 0.814028i | \(-0.697270\pi\) | ||||
−0.580825 | + | 0.814028i | \(0.697270\pi\) | |||||||
\(632\) | 27.3607i | 1.08835i | ||||||||
\(633\) | 4.85410 | + | 1.85410i | 0.192933 | + | 0.0736939i | ||||
\(634\) | 1.00000 | 0.0397151 | ||||||||
\(635\) | 6.41641 | 0.254627 | ||||||||
\(636\) | −6.56231 | + | 17.1803i | −0.260212 | + | 0.681245i | ||||
\(637\) | −0.291796 | − | 0.978714i | −0.0115614 | − | 0.0387781i | ||||
\(638\) | 8.61803i | 0.341191i | ||||||||
\(639\) | −20.6525 | + | 23.0902i | −0.816999 | + | 0.913433i | ||||
\(640\) | 4.34752i | 0.171851i | ||||||||
\(641\) | − | 27.5623i | − | 1.08865i | −0.838876 | − | 0.544323i | \(-0.816787\pi\) | ||
0.838876 | − | 0.544323i | \(-0.183213\pi\) | |||||||
\(642\) | −9.38197 | − | 3.58359i | −0.370277 | − | 0.141433i | ||||
\(643\) | − | 18.7984i | − | 0.741335i | −0.928766 | − | 0.370668i | \(-0.879129\pi\) | ||
0.928766 | − | 0.370668i | \(-0.120871\pi\) | |||||||
\(644\) | 4.23607 | − | 0.618034i | 0.166924 | − | 0.0243540i | ||||
\(645\) | 3.32624 | + | 1.27051i | 0.130970 | + | 0.0500263i | ||||
\(646\) | 16.0344 | 0.630867 | ||||||||
\(647\) | −4.96556 | −0.195216 | −0.0976081 | − | 0.995225i | \(-0.531119\pi\) | ||||
−0.0976081 | + | 0.995225i | \(0.531119\pi\) | |||||||
\(648\) | 20.0000 | − | 2.23607i | 0.785674 | − | 0.0878410i | ||||
\(649\) | − | 28.0902i | − | 1.10264i | ||||||
\(650\) | −0.437694 | −0.0171678 | ||||||||
\(651\) | −42.3607 | − | 9.47214i | −1.66025 | − | 0.371242i | ||||
\(652\) | −12.7984 | −0.501223 | ||||||||
\(653\) | − | 35.5066i | − | 1.38948i | −0.719261 | − | 0.694740i | \(-0.755519\pi\) | ||
0.719261 | − | 0.694740i | \(-0.244481\pi\) | |||||||
\(654\) | 3.09017 | − | 8.09017i | 0.120835 | − | 0.316351i | ||||
\(655\) | −2.02129 | −0.0789782 | ||||||||
\(656\) | 7.85410 | 0.306651 | ||||||||
\(657\) | −7.52786 | + | 8.41641i | −0.293690 | + | 0.328355i | ||||
\(658\) | 12.9443 | − | 1.88854i | 0.504620 | − | 0.0736231i | ||||
\(659\) | 22.4164i | 0.873219i | 0.899651 | + | 0.436610i | \(0.143821\pi\) | ||||
−0.899651 | + | 0.436610i | \(0.856179\pi\) | |||||||
\(660\) | −0.854102 | + | 2.23607i | −0.0332459 | + | 0.0870388i | ||||
\(661\) | − | 33.9443i | − | 1.32028i | −0.751143 | − | 0.660140i | \(-0.770497\pi\) | ||
0.751143 | − | 0.660140i | \(-0.229503\pi\) | |||||||
\(662\) | 13.6393i | 0.530107i | ||||||||
\(663\) | 0.673762 | − | 1.76393i | 0.0261668 | − | 0.0685054i | ||||
\(664\) | 6.05573i | 0.235008i | ||||||||
\(665\) | 3.47214 | − | 0.506578i | 0.134644 | − | 0.0196442i | ||||
\(666\) | 12.6525 | − | 14.1459i | 0.490273 | − | 0.548142i | ||||
\(667\) | 6.23607 | 0.241462 | ||||||||
\(668\) | −5.14590 | −0.199101 | ||||||||
\(669\) | −3.65248 | + | 9.56231i | −0.141213 | + | 0.369700i | ||||
\(670\) | − | 1.97871i | − | 0.0764444i | ||||||
\(671\) | −13.0902 | −0.505340 | ||||||||
\(672\) | −25.1246 | − | 5.61803i | −0.969203 | − | 0.216720i | ||||
\(673\) | 1.76393 | 0.0679946 | 0.0339973 | − | 0.999422i | \(-0.489176\pi\) | ||||
0.0339973 | + | 0.999422i | \(0.489176\pi\) | |||||||
\(674\) | − | 14.4934i | − | 0.558266i | ||||||
\(675\) | 11.5623 | + | 22.4164i | 0.445033 | + | 0.862808i | ||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | 24.5066 | 0.941864 | 0.470932 | − | 0.882169i | \(-0.343918\pi\) | ||||
0.470932 | + | 0.882169i | \(0.343918\pi\) | |||||||
\(678\) | 13.7984 | + | 5.27051i | 0.529923 | + | 0.202413i | ||||
\(679\) | 41.7426 | − | 6.09017i | 1.60194 | − | 0.233719i | ||||
\(680\) | 6.38197i | 0.244737i | ||||||||
\(681\) | 10.7984 | + | 4.12461i | 0.413795 | + | 0.158055i | ||||
\(682\) | − | 13.0902i | − | 0.501249i | ||||||
\(683\) | 20.5967i | 0.788113i | 0.919086 | + | 0.394056i | \(0.128929\pi\) | ||||
−0.919086 | + | 0.394056i | \(0.871071\pi\) | |||||||
\(684\) | −11.2361 | + | 12.5623i | −0.429622 | + | 0.480332i | ||||
\(685\) | 3.72949i | 0.142496i | ||||||||
\(686\) | −10.3820 | + | 4.81966i | −0.396385 | + | 0.184015i | ||||
\(687\) | 13.6525 | − | 35.7426i | 0.520874 | − | 1.36367i | ||||
\(688\) | 9.97871 | 0.380435 | ||||||||
\(689\) | 0.957428 | 0.0364751 | ||||||||
\(690\) | −0.381966 | − | 0.145898i | −0.0145412 | − | 0.00555424i | ||||
\(691\) | − | 3.09017i | − | 0.117556i | −0.998271 | − | 0.0587778i | \(-0.981280\pi\) | ||
0.998271 | − | 0.0587778i | \(-0.0187203\pi\) | |||||||
\(692\) | −8.85410 | −0.336582 | ||||||||
\(693\) | −14.7984 | − | 9.79837i | −0.562144 | − | 0.372209i | ||||
\(694\) | −0.506578 | −0.0192294 | ||||||||
\(695\) | − | 4.61803i | − | 0.175172i | ||||||
\(696\) | −22.5623 | − | 8.61803i | −0.855222 | − | 0.326666i | ||||
\(697\) | 31.6525 | 1.19892 | ||||||||
\(698\) | −15.5410 | −0.588236 | ||||||||
\(699\) | −18.1246 | + | 47.4508i | −0.685536 | + | 1.79476i | ||||
\(700\) | −3.00000 | − | 20.5623i | −0.113389 | − | 0.777182i | ||||
\(701\) | 46.6312i | 1.76124i | 0.473827 | + | 0.880618i | \(0.342872\pi\) | ||||
−0.473827 | + | 0.880618i | \(0.657128\pi\) | |||||||
\(702\) | −0.214782 | − | 0.416408i | −0.00810641 | − | 0.0157163i | ||||
\(703\) | 35.5410i | 1.34045i | ||||||||
\(704\) | 0.527864i | 0.0198946i | ||||||||
\(705\) | 4.94427 | + | 1.88854i | 0.186212 | + | 0.0711267i | ||||
\(706\) | 21.9230i | 0.825082i | ||||||||
\(707\) | −2.32624 | − | 15.9443i | −0.0874872 | − | 0.599646i | ||||
\(708\) | 32.8885 | + | 12.5623i | 1.23603 | + | 0.472120i | ||||
\(709\) | 12.4377 | 0.467107 | 0.233554 | − | 0.972344i | \(-0.424965\pi\) | ||||
0.233554 | + | 0.972344i | \(0.424965\pi\) | |||||||
\(710\) | −2.43769 | −0.0914850 | ||||||||
\(711\) | −27.3607 | − | 24.4721i | −1.02611 | − | 0.917777i | ||||
\(712\) | − | 6.90983i | − | 0.258957i | ||||||
\(713\) | −9.47214 | −0.354734 | ||||||||
\(714\) | −20.6525 | − | 4.61803i | −0.772899 | − | 0.172826i | ||||
\(715\) | 0.124612 | 0.00466022 | ||||||||
\(716\) | − | 34.5066i | − | 1.28957i | ||||||
\(717\) | −13.1803 | + | 34.5066i | −0.492229 | + | 1.28867i | ||||
\(718\) | −8.70820 | −0.324987 | ||||||||
\(719\) | 22.2361 | 0.829265 | 0.414633 | − | 0.909989i | \(-0.363910\pi\) | ||||
0.414633 | + | 0.909989i | \(0.363910\pi\) | |||||||
\(720\) | −1.58359 | − | 1.41641i | −0.0590170 | − | 0.0527864i | ||||
\(721\) | −31.8885 | + | 4.65248i | −1.18759 | + | 0.173267i | ||||
\(722\) | − | 4.29180i | − | 0.159724i | ||||||
\(723\) | −5.85410 | + | 15.3262i | −0.217716 | + | 0.569989i | ||||
\(724\) | − | 10.8541i | − | 0.403390i | ||||||
\(725\) | − | 30.2705i | − | 1.12422i | ||||||
\(726\) | −2.29180 | + | 6.00000i | −0.0850565 | + | 0.222681i | ||||
\(727\) | − | 11.4721i | − | 0.425478i | −0.977109 | − | 0.212739i | \(-0.931762\pi\) | ||
0.977109 | − | 0.212739i | \(-0.0682384\pi\) | |||||||
\(728\) | 0.124612 | + | 0.854102i | 0.00461842 | + | 0.0316551i | ||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | −0.888544 | −0.0328865 | ||||||||
\(731\) | 40.2148 | 1.48740 | ||||||||
\(732\) | 5.85410 | − | 15.3262i | 0.216374 | − | 0.566474i | ||||
\(733\) | − | 6.36068i | − | 0.234937i | −0.993077 | − | 0.117469i | \(-0.962522\pi\) | ||
0.993077 | − | 0.117469i | \(-0.0374779\pi\) | |||||||
\(734\) | −6.96556 | −0.257103 | ||||||||
\(735\) | −4.61803 | − | 0.347524i | −0.170339 | − | 0.0128186i | ||||
\(736\) | −5.61803 | −0.207083 | ||||||||
\(737\) | − | 18.7426i | − | 0.690394i | ||||||
\(738\) | 5.23607 | − | 5.85410i | 0.192742 | − | 0.215492i | ||||
\(739\) | −1.58359 | −0.0582534 | −0.0291267 | − | 0.999576i | \(-0.509273\pi\) | ||||
−0.0291267 | + | 0.999576i | \(0.509273\pi\) | |||||||
\(740\) | −6.32624 | −0.232557 | ||||||||
\(741\) | 0.819660 | + | 0.313082i | 0.0301110 | + | 0.0115014i | ||||
\(742\) | −1.54915 | − | 10.6180i | −0.0568711 | − | 0.389800i | ||||
\(743\) | 5.14590i | 0.188785i | 0.995535 | + | 0.0943923i | \(0.0300908\pi\) | ||||
−0.995535 | + | 0.0943923i | \(0.969909\pi\) | |||||||
\(744\) | 34.2705 | + | 13.0902i | 1.25642 | + | 0.479909i | ||||
\(745\) | − | 2.18034i | − | 0.0798815i | ||||||
\(746\) | 0.618034i | 0.0226278i | ||||||||
\(747\) | −6.05573 | − | 5.41641i | −0.221568 | − | 0.198176i | ||||
\(748\) | 27.0344i | 0.988477i | ||||||||
\(749\) | −24.5623 | + | 3.58359i | −0.897487 | + | 0.130942i | ||||
\(750\) | −1.43769 | + | 3.76393i | −0.0524972 | + | 0.137439i | ||||
\(751\) | 14.9656 | 0.546101 | 0.273050 | − | 0.962000i | \(-0.411967\pi\) | ||||
0.273050 | + | 0.962000i | \(0.411967\pi\) | |||||||
\(752\) | 14.8328 | 0.540897 | ||||||||
\(753\) | 4.00000 | + | 1.52786i | 0.145768 | + | 0.0556785i | ||||
\(754\) | 0.562306i | 0.0204780i | ||||||||
\(755\) | −2.47214 | −0.0899702 | ||||||||
\(756\) | 18.0902 | − | 12.9443i | 0.657933 | − | 0.470779i | ||||
\(757\) | −17.0000 | −0.617876 | −0.308938 | − | 0.951082i | \(-0.599973\pi\) | ||||
−0.308938 | + | 0.951082i | \(0.599973\pi\) | |||||||
\(758\) | − | 9.59675i | − | 0.348570i | ||||||
\(759\) | −3.61803 | − | 1.38197i | −0.131326 | − | 0.0501622i | ||||
\(760\) | −2.96556 | −0.107572 | ||||||||
\(761\) | 22.0000 | 0.797499 | 0.398750 | − | 0.917060i | \(-0.369444\pi\) | ||||
0.398750 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(762\) | 6.41641 | − | 16.7984i | 0.232442 | − | 0.608541i | ||||
\(763\) | −3.09017 | − | 21.1803i | −0.111872 | − | 0.766780i | ||||
\(764\) | − | 13.4164i | − | 0.485389i | ||||||
\(765\) | −6.38197 | − | 5.70820i | −0.230740 | − | 0.206381i | ||||
\(766\) | 2.32624i | 0.0840504i | ||||||||
\(767\) | − | 1.83282i | − | 0.0661791i | ||||||
\(768\) | 10.6180 | + | 4.05573i | 0.383145 | + | 0.146348i | ||||
\(769\) | 0.180340i | 0.00650322i | 0.999995 | + | 0.00325161i | \(0.00103502\pi\) | ||||
−0.999995 | + | 0.00325161i | \(0.998965\pi\) | |||||||
\(770\) | −0.201626 | − | 1.38197i | −0.00726610 | − | 0.0498026i | ||||
\(771\) | 21.1246 | + | 8.06888i | 0.760784 | + | 0.290594i | ||||
\(772\) | 3.70820 | 0.133461 | ||||||||
\(773\) | −12.7082 | −0.457082 | −0.228541 | − | 0.973534i | \(-0.573396\pi\) | ||||
−0.228541 | + | 0.973534i | \(0.573396\pi\) | |||||||
\(774\) | 6.65248 | − | 7.43769i | 0.239118 | − | 0.267342i | ||||
\(775\) | 45.9787i | 1.65160i | ||||||||
\(776\) | −35.6525 | −1.27985 | ||||||||
\(777\) | 10.2361 | − | 45.7771i | 0.367217 | − | 1.64224i | ||||
\(778\) | −11.9230 | −0.427460 | ||||||||
\(779\) | 14.7082i | 0.526976i | ||||||||
\(780\) | −0.0557281 | + | 0.145898i | −0.00199539 | + | 0.00522399i | ||||
\(781\) | −23.0902 | −0.826231 | ||||||||
\(782\) | −4.61803 | −0.165141 | ||||||||
\(783\) | 28.7984 | − | 14.8541i | 1.02917 | − | 0.530842i | ||||
\(784\) | −12.4377 | + | 3.70820i | −0.444203 | + | 0.132436i | ||||
\(785\) | 6.29180i | 0.224564i | ||||||||
\(786\) | −2.02129 | + | 5.29180i | −0.0720969 | + | 0.188752i | ||||
\(787\) | 19.5066i | 0.695334i | 0.937618 | + | 0.347667i | \(0.113026\pi\) | ||||
−0.937618 | + | 0.347667i | \(0.886974\pi\) | |||||||
\(788\) | 24.1246i | 0.859404i | ||||||||
\(789\) | −0.0344419 | + | 0.0901699i | −0.00122616 | + | 0.00321014i | ||||
\(790\) | − | 2.88854i | − | 0.102770i | ||||||
\(791\) | 36.1246 | − | 5.27051i | 1.28444 | − | 0.187398i | ||||
\(792\) | 11.1803 | + | 10.0000i | 0.397276 | + | 0.355335i | ||||
\(793\) | −0.854102 | −0.0303301 | ||||||||
\(794\) | 6.65248 | 0.236088 | ||||||||
\(795\) | 1.54915 | − | 4.05573i | 0.0549427 | − | 0.143842i | ||||
\(796\) | − | 20.0344i | − | 0.710102i | ||||||
\(797\) | −40.5410 | −1.43604 | −0.718018 | − | 0.696024i | \(-0.754951\pi\) | ||||
−0.718018 | + | 0.696024i | \(0.754951\pi\) | |||||||
\(798\) | 2.14590 | − | 9.59675i | 0.0759640 | − | 0.339721i | ||||
\(799\) | 59.7771 | 2.11476 | ||||||||
\(800\) | 27.2705i | 0.964158i | ||||||||
\(801\) | 6.90983 | + | 6.18034i | 0.244147 | + | 0.218372i | ||||
\(802\) | 11.3820 | 0.401911 | ||||||||
\(803\) | −8.41641 | −0.297009 | ||||||||
\(804\) | 21.9443 | + | 8.38197i | 0.773915 | + | 0.295609i | ||||
\(805\) | −1.00000 | + | 0.145898i | −0.0352454 | + | 0.00514223i | ||||
\(806\) | − | 0.854102i | − | 0.0300845i | ||||||
\(807\) | −6.70820 | − | 2.56231i | −0.236140 | − | 0.0901974i | ||||
\(808\) | 13.6180i | 0.479081i | ||||||||
\(809\) | 6.03444i | 0.212160i | 0.994358 | + | 0.106080i | \(0.0338299\pi\) | ||||
−0.994358 | + | 0.106080i | \(0.966170\pi\) | |||||||
\(810\) | −2.11146 | + | 0.236068i | −0.0741890 | + | 0.00829458i | ||||
\(811\) | − | 9.06888i | − | 0.318452i | −0.987242 | − | 0.159226i | \(-0.949100\pi\) | ||
0.987242 | − | 0.159226i | \(-0.0508998\pi\) | |||||||
\(812\) | −26.4164 | + | 3.85410i | −0.927034 | + | 0.135252i | ||||
\(813\) | −1.38197 | + | 3.61803i | −0.0484677 | + | 0.126890i | ||||
\(814\) | 14.1459 | 0.495813 | ||||||||
\(815\) | 3.02129 | 0.105831 | ||||||||
\(816\) | −22.4164 | − | 8.56231i | −0.784731 | − | 0.299741i | ||||
\(817\) | 18.6869i | 0.653772i | ||||||||
\(818\) | 15.1591 | 0.530024 | ||||||||
\(819\) | −0.965558 | − | 0.639320i | −0.0337393 | − | 0.0223397i | ||||
\(820\) | −2.61803 | −0.0914257 | ||||||||
\(821\) | 3.81966i | 0.133307i | 0.997776 | + | 0.0666535i | \(0.0212322\pi\) | ||||
−0.997776 | + | 0.0666535i | \(0.978768\pi\) | |||||||
\(822\) | 9.76393 | + | 3.72949i | 0.340556 | + | 0.130081i | ||||
\(823\) | −8.56231 | −0.298463 | −0.149232 | − | 0.988802i | \(-0.547680\pi\) | ||||
−0.149232 | + | 0.988802i | \(0.547680\pi\) | |||||||
\(824\) | 27.2361 | 0.948813 | ||||||||
\(825\) | −6.70820 | + | 17.5623i | −0.233550 | + | 0.611441i | ||||
\(826\) | −20.3262 | + | 2.96556i | −0.707240 | + | 0.103185i | ||||
\(827\) | − | 25.2148i | − | 0.876804i | −0.898779 | − | 0.438402i | \(-0.855545\pi\) | ||
0.898779 | − | 0.438402i | \(-0.144455\pi\) | |||||||
\(828\) | 3.23607 | − | 3.61803i | 0.112461 | − | 0.125735i | ||||
\(829\) | − | 1.00000i | − | 0.0347314i | −0.999849 | − | 0.0173657i | \(-0.994472\pi\) | ||
0.999849 | − | 0.0173657i | \(-0.00552796\pi\) | |||||||
\(830\) | − | 0.639320i | − | 0.0221911i | ||||||
\(831\) | −22.4164 | − | 8.56231i | −0.777617 | − | 0.297023i | ||||
\(832\) | 0.0344419i | 0.00119406i | ||||||||
\(833\) | −50.1246 | + | 14.9443i | −1.73671 | + | 0.517788i | ||||
\(834\) | −12.0902 | − | 4.61803i | −0.418648 | − | 0.159909i | ||||
\(835\) | 1.21478 | 0.0420393 | ||||||||
\(836\) | −12.5623 | −0.434476 | ||||||||
\(837\) | −43.7426 | + | 22.5623i | −1.51197 | + | 0.779867i | ||||
\(838\) | 0.124612i | 0.00430464i | ||||||||
\(839\) | 4.14590 | 0.143132 | 0.0715661 | − | 0.997436i | \(-0.477200\pi\) | ||||
0.0715661 | + | 0.997436i | \(0.477200\pi\) | |||||||
\(840\) | 3.81966 | + | 0.854102i | 0.131791 | + | 0.0294693i | ||||
\(841\) | −9.88854 | −0.340984 | ||||||||
\(842\) | 12.7852i | 0.440608i | ||||||||
\(843\) | −11.7082 | + | 30.6525i | −0.403252 | + | 1.05573i | ||||
\(844\) | −4.85410 | −0.167085 | ||||||||
\(845\) | −4.95743 | −0.170541 | ||||||||
\(846\) | 9.88854 | − | 11.0557i | 0.339975 | − | 0.380104i | ||||
\(847\) | 2.29180 | + | 15.7082i | 0.0787470 | + | 0.539740i | ||||
\(848\) | − | 12.1672i | − | 0.417823i | ||||||
\(849\) | 9.76393 | − | 25.5623i | 0.335097 | − | 0.877296i | ||||
\(850\) | 22.4164i | 0.768876i | ||||||||
\(851\) | − | 10.2361i | − | 0.350888i | ||||||
\(852\) | 10.3262 | − | 27.0344i | 0.353771 | − | 0.926185i | ||||
\(853\) | 36.6525i | 1.25496i | 0.778634 | + | 0.627478i | \(0.215913\pi\) | ||||
−0.778634 | + | 0.627478i | \(0.784087\pi\) | |||||||
\(854\) | 1.38197 | + | 9.47214i | 0.0472899 | + | 0.324130i | ||||
\(855\) | 2.65248 | − | 2.96556i | 0.0907128 | − | 0.101420i | ||||
\(856\) | 20.9787 | 0.717038 | ||||||||
\(857\) | −17.5279 | −0.598740 | −0.299370 | − | 0.954137i | \(-0.596777\pi\) | ||||
−0.299370 | + | 0.954137i | \(0.596777\pi\) | |||||||
\(858\) | 0.124612 | − | 0.326238i | 0.00425418 | − | 0.0111376i | ||||
\(859\) | 29.5279i | 1.00748i | 0.863856 | + | 0.503739i | \(0.168043\pi\) | ||||
−0.863856 | + | 0.503739i | \(0.831957\pi\) | |||||||
\(860\) | −3.32624 | −0.113424 | ||||||||
\(861\) | 4.23607 | − | 18.9443i | 0.144365 | − | 0.645619i | ||||
\(862\) | 20.4508 | 0.696559 | ||||||||
\(863\) | 28.3607i | 0.965409i | 0.875783 | + | 0.482704i | \(0.160345\pi\) | ||||
−0.875783 | + | 0.482704i | \(0.839655\pi\) | |||||||
\(864\) | −25.9443 | + | 13.3820i | −0.882642 | + | 0.455264i | ||||
\(865\) | 2.09017 | 0.0710679 | ||||||||
\(866\) | 6.47214 | 0.219932 | ||||||||
\(867\) | −62.8328 | − | 24.0000i | −2.13391 | − | 0.815083i | ||||
\(868\) | 40.1246 | − | 5.85410i | 1.36192 | − | 0.198701i | ||||
\(869\) | − | 27.3607i | − | 0.928147i | ||||||
\(870\) | 2.38197 | + | 0.909830i | 0.0807562 | + | 0.0308461i | ||||
\(871\) | − | 1.22291i | − | 0.0414368i | ||||||
\(872\) | 18.0902i | 0.612610i | ||||||||
\(873\) | 31.8885 | − | 35.6525i | 1.07926 | − | 1.20665i | ||||
\(874\) | − | 2.14590i | − | 0.0725861i | ||||||
\(875\) | 1.43769 | + | 9.85410i | 0.0486029 | + | 0.333129i | ||||
\(876\) | 3.76393 | − | 9.85410i | 0.127171 | − | 0.332939i | ||||
\(877\) | −3.70820 | −0.125217 | −0.0626086 | − | 0.998038i | \(-0.519942\pi\) | ||||
−0.0626086 | + | 0.998038i | \(0.519942\pi\) | |||||||
\(878\) | −10.2148 | −0.344732 | ||||||||
\(879\) | 44.8328 | + | 17.1246i | 1.51217 | + | 0.577599i | ||||
\(880\) | − | 1.58359i | − | 0.0533829i | ||||||
\(881\) | 9.88854 | 0.333154 | 0.166577 | − | 0.986028i | \(-0.446729\pi\) | ||||
0.166577 | + | 0.986028i | \(0.446729\pi\) | |||||||
\(882\) | −5.52786 | + | 11.7426i | −0.186133 | + | 0.395395i | ||||
\(883\) | −13.1591 | −0.442837 | −0.221419 | − | 0.975179i | \(-0.571069\pi\) | ||||
−0.221419 | + | 0.975179i | \(0.571069\pi\) | |||||||
\(884\) | 1.76393i | 0.0593275i | ||||||||
\(885\) | −7.76393 | − | 2.96556i | −0.260982 | − | 0.0996861i | ||||
\(886\) | −0.111456 | −0.00374444 | ||||||||
\(887\) | 31.0902 | 1.04391 | 0.521953 | − | 0.852974i | \(-0.325204\pi\) | ||||
0.521953 | + | 0.852974i | \(0.325204\pi\) | |||||||
\(888\) | −14.1459 | + | 37.0344i | −0.474705 | + | 1.24279i | ||||
\(889\) | −6.41641 | − | 43.9787i | −0.215199 | − | 1.47500i | ||||
\(890\) | 0.729490i | 0.0244526i | ||||||||
\(891\) | −20.0000 | + | 2.23607i | −0.670025 | + | 0.0749111i | ||||
\(892\) | − | 9.56231i | − | 0.320170i | ||||||
\(893\) | 27.7771i | 0.929525i | ||||||||
\(894\) | −5.70820 | − | 2.18034i | −0.190911 | − | 0.0729215i | ||||
\(895\) | 8.14590i | 0.272287i | ||||||||
\(896\) | 29.7984 | − | 4.34752i | 0.995494 | − | 0.145241i | ||||
\(897\) | −0.236068 | − | 0.0901699i | −0.00788208 | − | 0.00301069i | ||||
\(898\) | 13.6525 | 0.455589 | ||||||||
\(899\) | 59.0689 | 1.97006 | ||||||||
\(900\) | −17.5623 | − | 15.7082i | −0.585410 | − | 0.523607i | ||||
\(901\) | − | 49.0344i | − | 1.63357i | ||||||
\(902\) | 5.85410 | 0.194920 | ||||||||
\(903\) | 5.38197 | − | 24.0689i | 0.179101 | − | 0.800962i | ||||
\(904\) | −30.8541 | −1.02619 | ||||||||
\(905\) | 2.56231i | 0.0851739i | ||||||||
\(906\) | −2.47214 | + | 6.47214i | −0.0821312 | + | 0.215022i | ||||
\(907\) | 25.0344 | 0.831255 | 0.415627 | − | 0.909535i | \(-0.363562\pi\) | ||||
0.415627 | + | 0.909535i | \(0.363562\pi\) | |||||||
\(908\) | −10.7984 | −0.358357 | ||||||||
\(909\) | −13.6180 | − | 12.1803i | −0.451682 | − | 0.403996i | ||||
\(910\) | −0.0131556 | − | 0.0901699i | −0.000436104 | − | 0.00298910i | ||||
\(911\) | − | 25.1246i | − | 0.832416i | −0.909270 | − | 0.416208i | \(-0.863359\pi\) | ||
0.909270 | − | 0.416208i | \(-0.136641\pi\) | |||||||
\(912\) | 3.97871 | − | 10.4164i | 0.131748 | − | 0.344922i | ||||
\(913\) | − | 6.05573i | − | 0.200415i | ||||||
\(914\) | 2.81966i | 0.0932661i | ||||||||
\(915\) | −1.38197 | + | 3.61803i | −0.0456864 | + | 0.119609i | ||||
\(916\) | 35.7426i | 1.18097i | ||||||||
\(917\) | 2.02129 | + | 13.8541i | 0.0667488 | + | 0.457503i | ||||
\(918\) | −21.3262 | + | 11.0000i | −0.703871 | + | 0.363054i | ||||
\(919\) | −45.6525 | −1.50594 | −0.752968 | − | 0.658057i | \(-0.771379\pi\) | ||||
−0.752968 | + | 0.658057i | \(0.771379\pi\) | |||||||
\(920\) | 0.854102 | 0.0281589 | ||||||||
\(921\) | −7.74265 | + | 20.2705i | −0.255129 | + | 0.667936i | ||||
\(922\) | 22.0557i | 0.726367i | ||||||||
\(923\) | −1.50658 | −0.0495896 | ||||||||
\(924\) | 16.1803 | + | 3.61803i | 0.532294 | + | 0.119025i | ||||
\(925\) | −49.6869 | −1.63370 | ||||||||
\(926\) | 15.7426i | 0.517335i | ||||||||
\(927\) | −24.3607 | + | 27.2361i | −0.800110 | + | 0.894550i | ||||
\(928\) | 35.0344 | 1.15006 | ||||||||
\(929\) | 39.3951 | 1.29251 | 0.646256 | − | 0.763121i | \(-0.276334\pi\) | ||||
0.646256 | + | 0.763121i | \(0.276334\pi\) | |||||||
\(930\) | −3.61803 | − | 1.38197i | −0.118640 | − | 0.0453165i | ||||
\(931\) | −6.94427 | − | 23.2918i | −0.227589 | − | 0.763358i | ||||
\(932\) | − | 47.4508i | − | 1.55430i | ||||||
\(933\) | 12.4164 | + | 4.74265i | 0.406495 | + | 0.155267i | ||||
\(934\) | − | 12.2574i | − | 0.401073i | ||||||
\(935\) | − | 6.38197i | − | 0.208713i | ||||||
\(936\) | 0.729490 | + | 0.652476i | 0.0238441 | + | 0.0213268i | ||||
\(937\) | − | 25.2918i | − | 0.826247i | −0.910675 | − | 0.413123i | \(-0.864438\pi\) | ||
0.910675 | − | 0.413123i | \(-0.135562\pi\) | |||||||
\(938\) | −13.5623 | + | 1.97871i | −0.442825 | + | 0.0646073i | ||||
\(939\) | 7.52786 | − | 19.7082i | 0.245663 | − | 0.643153i | ||||
\(940\) | −4.94427 | −0.161264 | ||||||||
\(941\) | 17.5279 | 0.571392 | 0.285696 | − | 0.958320i | \(-0.407775\pi\) | ||||
0.285696 | + | 0.958320i | \(0.407775\pi\) | |||||||
\(942\) | 16.4721 | + | 6.29180i | 0.536691 | + | 0.204998i | ||||
\(943\) | − | 4.23607i | − | 0.137945i | ||||||
\(944\) | −23.2918 | −0.758083 | ||||||||
\(945\) | −4.27051 | + | 3.05573i | −0.138920 | + | 0.0994028i | ||||
\(946\) | 7.43769 | 0.241820 | ||||||||
\(947\) | − | 48.8328i | − | 1.58685i | −0.608666 | − | 0.793427i | \(-0.708295\pi\) | ||
0.608666 | − | 0.793427i | \(-0.291705\pi\) | |||||||
\(948\) | 32.0344 | + | 12.2361i | 1.04043 | + | 0.397409i | ||||
\(949\) | −0.549150 | −0.0178262 | ||||||||
\(950\) | −10.4164 | −0.337953 | ||||||||
\(951\) | 1.00000 | − | 2.61803i | 0.0324272 | − | 0.0848956i | ||||
\(952\) | 43.7426 | − | 6.38197i | 1.41771 | − | 0.206841i | ||||
\(953\) | − | 26.0344i | − | 0.843338i | −0.906750 | − | 0.421669i | \(-0.861444\pi\) | ||
0.906750 | − | 0.421669i | \(-0.138556\pi\) | |||||||
\(954\) | −9.06888 | − | 8.11146i | −0.293616 | − | 0.262618i | ||||
\(955\) | 3.16718i | 0.102488i | ||||||||
\(956\) | − | 34.5066i | − | 1.11602i | ||||||
\(957\) | 22.5623 | + | 8.61803i | 0.729336 | + | 0.278581i | ||||
\(958\) | 3.49342i | 0.112867i | ||||||||
\(959\) | 25.5623 | − | 3.72949i | 0.825450 | − | 0.120432i | ||||
\(960\) | 0.145898 | + | 0.0557281i | 0.00470884 | + | 0.00179862i | ||||
\(961\) | −58.7214 | −1.89424 | ||||||||
\(962\) | 0.922986 | 0.0297583 | ||||||||
\(963\) | −18.7639 | + | 20.9787i | −0.604659 | + | 0.676030i | ||||
\(964\) | − | 15.3262i | − | 0.493625i | ||||||
\(965\) | −0.875388 | −0.0281797 | ||||||||
\(966\) | −0.618034 | + | 2.76393i | −0.0198849 | + | 0.0889281i | ||||
\(967\) | −19.8885 | −0.639572 | −0.319786 | − | 0.947490i | \(-0.603611\pi\) | ||||
−0.319786 | + | 0.947490i | \(0.603611\pi\) | |||||||
\(968\) | − | 13.4164i | − | 0.431220i | ||||||
\(969\) | 16.0344 | − | 41.9787i | 0.515100 | − | 1.34855i | ||||
\(970\) | 3.76393 | 0.120853 | ||||||||
\(971\) | 35.7426 | 1.14704 | 0.573518 | − | 0.819193i | \(-0.305578\pi\) | ||||
0.573518 | + | 0.819193i | \(0.305578\pi\) | |||||||
\(972\) | 6.32624 | − | 24.4164i | 0.202914 | − | 0.783157i | ||||
\(973\) | −31.6525 | + | 4.61803i | −1.01473 | + | 0.148047i | ||||
\(974\) | − | 0.798374i | − | 0.0255815i | ||||||
\(975\) | −0.437694 | + | 1.14590i | −0.0140174 | + | 0.0366981i | ||||
\(976\) | 10.8541i | 0.347431i | ||||||||
\(977\) | 38.9787i | 1.24704i | 0.781808 | + | 0.623520i | \(0.214298\pi\) | ||||
−0.781808 | + | 0.623520i | \(0.785702\pi\) | |||||||
\(978\) | 3.02129 | − | 7.90983i | 0.0966101 | − | 0.252928i | ||||
\(979\) | 6.90983i | 0.220839i | ||||||||
\(980\) | 4.14590 | − | 1.23607i | 0.132436 | − | 0.0394847i | ||||
\(981\) | −18.0902 | − | 16.1803i | −0.577575 | − | 0.516598i | ||||
\(982\) | 20.4508 | 0.652613 | ||||||||
\(983\) | 25.1803 | 0.803128 | 0.401564 | − | 0.915831i | \(-0.368467\pi\) | ||||
0.401564 | + | 0.915831i | \(0.368467\pi\) | |||||||
\(984\) | −5.85410 | + | 15.3262i | −0.186622 | + | 0.488583i | ||||
\(985\) | − | 5.69505i | − | 0.181459i | ||||||
\(986\) | 28.7984 | 0.917127 | ||||||||
\(987\) | 8.00000 | − | 35.7771i | 0.254643 | − | 1.13880i | ||||
\(988\) | −0.819660 | −0.0260769 | ||||||||
\(989\) | − | 5.38197i | − | 0.171137i | ||||||
\(990\) | −1.18034 | − | 1.05573i | −0.0375137 | − | 0.0335532i | ||||
\(991\) | 26.7984 | 0.851278 | 0.425639 | − | 0.904893i | \(-0.360049\pi\) | ||||
0.425639 | + | 0.904893i | \(0.360049\pi\) | |||||||
\(992\) | −53.2148 | −1.68957 | ||||||||
\(993\) | 35.7082 | + | 13.6393i | 1.13317 | + | 0.432831i | ||||
\(994\) | 2.43769 | + | 16.7082i | 0.0773190 | + | 0.529952i | ||||
\(995\) | 4.72949i | 0.149935i | ||||||||
\(996\) | 7.09017 | + | 2.70820i | 0.224661 | + | 0.0858127i | ||||
\(997\) | − | 35.9443i | − | 1.13837i | −0.822211 | − | 0.569183i | \(-0.807259\pi\) | ||
0.822211 | − | 0.569183i | \(-0.192741\pi\) | |||||||
\(998\) | − | 1.58359i | − | 0.0501277i | ||||||
\(999\) | −24.3820 | − | 47.2705i | −0.771411 | − | 1.49557i |
(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 | 483.2.d.a.461.2 | ✓ | 4 | |
3.2 | odd | 2 | 483.2.d.b.461.3 | yes | 4 | ||
7.6 | odd | 2 | 483.2.d.b.461.2 | yes | 4 | ||
21.20 | even | 2 | inner | 483.2.d.a.461.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.d.a.461.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
483.2.d.a.461.3 | yes | 4 | 21.20 | even | 2 | inner | |
483.2.d.b.461.2 | yes | 4 | 7.6 | odd | 2 | ||
483.2.d.b.461.3 | yes | 4 | 3.2 | odd | 2 |