Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,2,Mod(64,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.m (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.53363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 631.1 | ||
Root | \(1.69513 + 1.23158i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.631 |
Dual form | 693.2.m.f.190.1 |
$q$-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 \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.93376 | − | 1.40496i | −1.36737 | − | 0.993455i | −0.997937 | − | 0.0641992i | \(-0.979551\pi\) |
−0.369437 | − | 0.929256i | \(-0.620449\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.14748 | + | 3.53158i | 0.573741 | + | 1.76579i | ||||
\(5\) | −2.09529 | + | 1.52232i | −0.937044 | + | 0.680802i | −0.947707 | − | 0.319141i | \(-0.896606\pi\) |
0.0106633 | + | 0.999943i | \(0.496606\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 1.26552 | − | 3.89486i | 0.447427 | − | 1.37704i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.19059 | 1.95764 | ||||||||
\(11\) | 2.19098 | − | 2.48990i | 0.660606 | − | 0.750733i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.48555 | − | 3.98549i | −1.52142 | − | 1.10537i | −0.960779 | − | 0.277315i | \(-0.910556\pi\) |
−0.560639 | − | 0.828060i | \(-0.689444\pi\) | |||||||
\(14\) | −0.738630 | + | 2.27327i | −0.197407 | + | 0.607557i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.91102 | + | 1.38844i | −0.477755 | + | 0.347109i | ||||
\(17\) | −2.54445 | + | 1.84865i | −0.617119 | + | 0.448363i | −0.851914 | − | 0.523682i | \(-0.824558\pi\) |
0.234795 | + | 0.972045i | \(0.424558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.323071 | + | 0.994311i | −0.0741176 | + | 0.228110i | −0.981252 | − | 0.192732i | \(-0.938265\pi\) |
0.907134 | + | 0.420842i | \(0.138265\pi\) | |||||||
\(20\) | −7.78051 | − | 5.65287i | −1.73978 | − | 1.26402i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.73503 | + | 1.73662i | −1.64911 | + | 0.370249i | ||||
\(23\) | 6.52707 | 1.36099 | 0.680495 | − | 0.732753i | \(-0.261765\pi\) | ||||
0.680495 | + | 0.732753i | \(0.261765\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.527713 | − | 1.62413i | 0.105543 | − | 0.324827i | ||||
\(26\) | 5.00829 | + | 15.4139i | 0.982207 | + | 3.02292i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.00415 | − | 2.18264i | 0.567730 | − | 0.412480i | ||||
\(29\) | 0.187665 | + | 0.577574i | 0.0348486 | + | 0.107253i | 0.966968 | − | 0.254899i | \(-0.0820422\pi\) |
−0.932119 | + | 0.362152i | \(0.882042\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.14906 | + | 5.19410i | 1.28401 | + | 0.932888i | 0.999666 | − | 0.0258346i | \(-0.00822431\pi\) |
0.284344 | + | 0.958722i | \(0.408224\pi\) | |||||||
\(32\) | −2.54445 | −0.449799 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.51762 | 1.28926 | ||||||||
\(35\) | 2.09529 | + | 1.52232i | 0.354169 | + | 0.257319i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.76354 | + | 8.50529i | 0.454323 | + | 1.39826i | 0.871929 | + | 0.489633i | \(0.162869\pi\) |
−0.417606 | + | 0.908628i | \(0.637131\pi\) | |||||||
\(38\) | 2.02171 | − | 1.46886i | 0.327964 | − | 0.238280i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.27759 | + | 10.0874i | 0.518233 | + | 1.59496i | ||||
\(41\) | −2.68767 | + | 8.27178i | −0.419743 | + | 1.29184i | 0.488196 | + | 0.872734i | \(0.337655\pi\) |
−0.907939 | + | 0.419102i | \(0.862345\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.48159 | 0.683437 | 0.341718 | − | 0.939802i | \(-0.388991\pi\) | ||||
0.341718 | + | 0.939802i | \(0.388991\pi\) | |||||||
\(44\) | 11.3074 | + | 4.88053i | 1.70465 | + | 0.735768i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.6218 | − | 9.17026i | −1.86098 | − | 1.35208i | ||||
\(47\) | −1.00829 | + | 3.10320i | −0.147074 | + | 0.452648i | −0.997272 | − | 0.0738155i | \(-0.976482\pi\) |
0.850198 | + | 0.526464i | \(0.176482\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | −3.30231 | + | 2.39927i | −0.467017 | + | 0.339308i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.78051 | − | 23.9460i | 1.07896 | − | 3.32071i | ||||
\(53\) | 1.53679 | + | 1.11655i | 0.211095 | + | 0.153369i | 0.688309 | − | 0.725418i | \(-0.258353\pi\) |
−0.477214 | + | 0.878787i | \(0.658353\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.800331 | + | 8.55245i | −0.107917 | + | 1.15321i | ||||
\(56\) | −4.09529 | −0.547257 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.448568 | − | 1.38055i | 0.0588999 | − | 0.181275i | ||||
\(59\) | 0.0537709 | + | 0.165490i | 0.00700037 | + | 0.0215449i | 0.954496 | − | 0.298225i | \(-0.0963945\pi\) |
−0.947495 | + | 0.319770i | \(0.896394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.58084 | + | 4.78126i | −0.842591 | + | 0.612178i | −0.923093 | − | 0.384576i | \(-0.874348\pi\) |
0.0805023 | + | 0.996754i | \(0.474348\pi\) | |||||||
\(62\) | −6.52707 | − | 20.0883i | −0.828939 | − | 2.55121i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.74238 | + | 6.35171i | 1.09280 | + | 0.793964i | ||||
\(65\) | 17.5610 | 2.17818 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.33649 | −0.896294 | −0.448147 | − | 0.893960i | \(-0.647916\pi\) | ||||
−0.448147 | + | 0.893960i | \(0.647916\pi\) | |||||||
\(68\) | −9.44836 | − | 6.86464i | −1.14578 | − | 0.832459i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.91300 | − | 5.88760i | −0.228647 | − | 0.703703i | ||||
\(71\) | 2.18995 | − | 1.59109i | 0.259899 | − | 0.188828i | −0.450203 | − | 0.892926i | \(-0.648649\pi\) |
0.710103 | + | 0.704098i | \(0.248649\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.182297 | + | 0.561053i | 0.0213363 | + | 0.0656663i | 0.961158 | − | 0.276000i | \(-0.0890089\pi\) |
−0.939821 | + | 0.341666i | \(0.889009\pi\) | |||||||
\(74\) | 6.60556 | − | 20.3298i | 0.767881 | − | 2.36330i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.88221 | −0.445320 | ||||||||
\(77\) | −3.04508 | − | 1.31433i | −0.347020 | − | 0.149782i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.93534 | + | 5.76536i | 0.892796 | + | 0.648654i | 0.936605 | − | 0.350386i | \(-0.113950\pi\) |
−0.0438097 | + | 0.999040i | \(0.513950\pi\) | |||||||
\(80\) | 1.89050 | − | 5.81836i | 0.211364 | − | 0.650513i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16.8188 | − | 12.2196i | 1.85733 | − | 1.34943i | ||||
\(83\) | 7.07548 | − | 5.14063i | 0.776634 | − | 0.564258i | −0.127333 | − | 0.991860i | \(-0.540642\pi\) |
0.903967 | + | 0.427602i | \(0.140642\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.51713 | − | 7.74692i | 0.273021 | − | 0.840272i | ||||
\(86\) | −8.66632 | − | 6.29645i | −0.934513 | − | 0.678964i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.92507 | − | 11.6846i | −0.738215 | − | 1.24558i | ||||
\(89\) | 11.6788 | 1.23795 | 0.618976 | − | 0.785410i | \(-0.287548\pi\) | ||||
0.618976 | + | 0.785410i | \(0.287548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.09529 | + | 6.44865i | −0.219646 | + | 0.676002i | ||||
\(92\) | 7.48970 | + | 23.0509i | 0.780855 | + | 2.40322i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.30966 | − | 4.58423i | 0.650791 | − | 0.472828i | ||||
\(95\) | −0.836730 | − | 2.57519i | −0.0858467 | − | 0.264209i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.58914 | − | 6.96691i | −0.973629 | − | 0.707383i | −0.0173534 | − | 0.999849i | \(-0.505524\pi\) |
−0.956276 | + | 0.292466i | \(0.905524\pi\) | |||||||
\(98\) | 2.39026 | 0.241452 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.34131 | 0.634131 | ||||||||
\(101\) | 3.00829 | + | 2.18565i | 0.299336 | + | 0.217480i | 0.727307 | − | 0.686312i | \(-0.240772\pi\) |
−0.427971 | + | 0.903792i | \(0.640772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.26418 | + | 6.96842i | 0.223096 | + | 0.686619i | 0.998479 | + | 0.0551278i | \(0.0175566\pi\) |
−0.775383 | + | 0.631491i | \(0.782443\pi\) | |||||||
\(104\) | −22.4649 | + | 16.3217i | −2.20287 | + | 1.60048i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.40309 | − | 4.31826i | −0.136280 | − | 0.419427i | ||||
\(107\) | −4.13477 | + | 12.7255i | −0.399723 | + | 1.23022i | 0.525499 | + | 0.850794i | \(0.323879\pi\) |
−0.925222 | + | 0.379427i | \(0.876121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1228 | 1.35272 | 0.676362 | − | 0.736570i | \(-0.263556\pi\) | ||||
0.676362 | + | 0.736570i | \(0.263556\pi\) | |||||||
\(110\) | 13.5635 | − | 15.4139i | 1.29323 | − | 1.46966i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.91102 | + | 1.38844i | 0.180574 | + | 0.131195i | ||||
\(113\) | 0.823071 | − | 2.53315i | 0.0774280 | − | 0.238299i | −0.904849 | − | 0.425732i | \(-0.860017\pi\) |
0.982277 | + | 0.187433i | \(0.0600167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.6761 | + | 9.93630i | −1.27531 | + | 0.926564i | ||||
\(116\) | −1.82441 | + | 1.32551i | −0.169392 | + | 0.123071i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.128526 | − | 0.395563i | 0.0118318 | − | 0.0364145i | ||||
\(119\) | 2.54445 | + | 1.84865i | 0.233249 | + | 0.169465i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.39919 | − | 10.9106i | −0.127199 | − | 0.991877i | ||||
\(122\) | 19.4432 | 1.76031 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.1400 | + | 31.2077i | −0.910597 | + | 2.80253i | ||||
\(125\) | −2.63492 | − | 8.10944i | −0.235674 | − | 0.725331i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.38410 | − | 6.09140i | 0.743968 | − | 0.540525i | −0.149983 | − | 0.988689i | \(-0.547922\pi\) |
0.893951 | + | 0.448164i | \(0.147922\pi\) | |||||||
\(128\) | −6.40921 | − | 19.7255i | −0.566500 | − | 1.74351i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −33.9588 | − | 24.6725i | −2.97838 | − | 2.16392i | ||||
\(131\) | 11.6441 | 1.01735 | 0.508674 | − | 0.860959i | \(-0.330136\pi\) | ||||
0.508674 | + | 0.860959i | \(0.330136\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.04548 | 0.0906546 | ||||||||
\(134\) | 14.1870 | + | 10.3075i | 1.22557 | + | 0.890428i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.98018 | + | 12.2497i | 0.341298 | + | 1.05041i | ||||
\(137\) | −12.5313 | + | 9.10450i | −1.07062 | + | 0.777850i | −0.976023 | − | 0.217665i | \(-0.930156\pi\) |
−0.0945956 | + | 0.995516i | \(0.530156\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.79789 | − | 5.53332i | −0.152495 | − | 0.469330i | 0.845404 | − | 0.534128i | \(-0.179360\pi\) |
−0.997898 | + | 0.0647974i | \(0.979360\pi\) | |||||||
\(140\) | −2.97189 | + | 9.14654i | −0.251171 | + | 0.773024i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.47025 | −0.542971 | ||||||||
\(143\) | −21.9422 | + | 4.92633i | −1.83490 | + | 0.411961i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.27247 | − | 0.924501i | −0.105673 | − | 0.0767757i | ||||
\(146\) | 0.435737 | − | 1.34106i | 0.0360618 | − | 0.110987i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −26.8661 | + | 19.5193i | −2.20838 | + | 1.60448i | ||||
\(149\) | −11.6614 | + | 8.47254i | −0.955343 | + | 0.694097i | −0.952064 | − | 0.305897i | \(-0.901044\pi\) |
−0.00327837 | + | 0.999995i | \(0.501044\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.86547 | + | 21.1297i | −0.558704 | + | 1.71951i | 0.127252 | + | 0.991870i | \(0.459384\pi\) |
−0.685956 | + | 0.727643i | \(0.740616\pi\) | |||||||
\(152\) | 3.46385 | + | 2.51663i | 0.280955 | + | 0.204126i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.04188 | + | 6.81981i | 0.325704 | + | 0.549556i | ||||
\(155\) | −22.8865 | −1.83829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.02566 | + | 9.31203i | −0.241474 | + | 0.743181i | 0.754722 | + | 0.656045i | \(0.227772\pi\) |
−0.996196 | + | 0.0871366i | \(0.972228\pi\) | |||||||
\(158\) | −7.24494 | − | 22.2976i | −0.576377 | − | 1.77390i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.33136 | − | 3.87346i | 0.421481 | − | 0.306224i | ||||
\(161\) | −2.01698 | − | 6.20762i | −0.158960 | − | 0.489229i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.19351 | − | 6.67948i | −0.720091 | − | 0.523177i | 0.166322 | − | 0.986071i | \(-0.446811\pi\) |
−0.886413 | + | 0.462895i | \(0.846811\pi\) | |||||||
\(164\) | −32.2965 | −2.52194 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.9046 | −1.62251 | ||||||||
\(167\) | −4.11700 | − | 2.99118i | −0.318583 | − | 0.231464i | 0.416988 | − | 0.908912i | \(-0.363086\pi\) |
−0.735571 | + | 0.677448i | \(0.763086\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1899 | + | 31.3614i | 0.783842 | + | 2.41242i | ||||
\(170\) | −15.7516 | + | 11.4442i | −1.20809 | + | 0.877731i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.14255 | + | 15.8271i | 0.392115 | + | 1.20681i | ||||
\(173\) | −2.40250 | + | 7.39415i | −0.182659 | + | 0.562167i | −0.999900 | − | 0.0141291i | \(-0.995502\pi\) |
0.817241 | + | 0.576296i | \(0.195502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.70772 | −0.129091 | ||||||||
\(176\) | −0.729944 | + | 7.80028i | −0.0550216 | + | 0.587968i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.5840 | − | 16.4082i | −1.69274 | − | 1.22985i | ||||
\(179\) | 1.89919 | − | 5.84510i | 0.141952 | − | 0.436883i | −0.854655 | − | 0.519197i | \(-0.826231\pi\) |
0.996606 | + | 0.0823141i | \(0.0262311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.48988 | − | 5.44172i | 0.556719 | − | 0.404480i | −0.273538 | − | 0.961861i | \(-0.588194\pi\) |
0.830257 | + | 0.557381i | \(0.188194\pi\) | |||||||
\(182\) | 13.1119 | − | 9.52634i | 0.971917 | − | 0.706139i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.26011 | − | 25.4220i | 0.608944 | − | 1.87414i | ||||
\(185\) | −18.7382 | − | 13.6141i | −1.37766 | − | 1.00093i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.971892 | + | 10.3858i | −0.0710718 | + | 0.759483i | ||||
\(188\) | −12.1162 | −0.883665 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.00000 | + | 6.15537i | −0.145095 | + | 0.446557i | ||||
\(191\) | 4.52322 | + | 13.9210i | 0.327289 | + | 1.00729i | 0.970397 | + | 0.241515i | \(0.0776444\pi\) |
−0.643108 | + | 0.765775i | \(0.722356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3256 | − | 9.68161i | 0.959198 | − | 0.696898i | 0.00623334 | − | 0.999981i | \(-0.498016\pi\) |
0.952964 | + | 0.303083i | \(0.0980159\pi\) | |||||||
\(194\) | 8.75485 | + | 26.9447i | 0.628562 | + | 1.93451i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00415 | − | 2.18264i | −0.214582 | − | 0.155903i | ||||
\(197\) | 6.81654 | 0.485658 | 0.242829 | − | 0.970069i | \(-0.421925\pi\) | ||||
0.242829 | + | 0.970069i | \(0.421925\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5561 | 1.10275 | 0.551373 | − | 0.834259i | \(-0.314104\pi\) | ||||
0.551373 | + | 0.834259i | \(0.314104\pi\) | |||||||
\(200\) | −5.65794 | − | 4.11073i | −0.400077 | − | 0.290673i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.74656 | − | 8.45304i | −0.193247 | − | 0.594754i | ||||
\(203\) | 0.491314 | − | 0.356961i | 0.0344835 | − | 0.0250537i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.96085 | − | 21.4233i | −0.486167 | − | 1.49627i | ||||
\(206\) | 5.41196 | − | 16.6563i | 0.377069 | − | 1.16050i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.0166 | 1.11055 | ||||||||
\(209\) | 1.76789 | + | 2.98293i | 0.122287 | + | 0.206334i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.26582 | − | 0.919672i | −0.0871427 | − | 0.0633129i | 0.543361 | − | 0.839499i | \(-0.317152\pi\) |
−0.630504 | + | 0.776186i | \(0.717152\pi\) | |||||||
\(212\) | −2.17974 | + | 6.70853i | −0.149705 | + | 0.460744i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.8744 | − | 18.7989i | 1.76874 | − | 1.28506i | ||||
\(215\) | −9.39026 | + | 6.82242i | −0.640410 | + | 0.465285i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.73070 | − | 8.40423i | 0.185372 | − | 0.570516i | ||||
\(218\) | −27.3102 | − | 19.8420i | −1.84968 | − | 1.34387i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −31.1221 | + | 6.98734i | −2.09825 | + | 0.471086i | ||||
\(221\) | 21.3254 | 1.43450 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.27910 | − | 3.93667i | 0.0856550 | − | 0.263619i | −0.899051 | − | 0.437844i | \(-0.855742\pi\) |
0.984706 | + | 0.174225i | \(0.0557421\pi\) | |||||||
\(224\) | 0.786277 | + | 2.41991i | 0.0525353 | + | 0.161687i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.15059 | + | 3.74212i | −0.342612 | + | 0.248922i | ||||
\(227\) | 1.72358 | + | 5.30462i | 0.114398 | + | 0.352080i | 0.991821 | − | 0.127637i | \(-0.0407393\pi\) |
−0.877423 | + | 0.479717i | \(0.840739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.637851 | + | 0.463426i | 0.0421504 | + | 0.0306241i | 0.608661 | − | 0.793430i | \(-0.291707\pi\) |
−0.566511 | + | 0.824054i | \(0.691707\pi\) | |||||||
\(230\) | 40.4064 | 2.66432 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.48706 | 0.163284 | ||||||||
\(233\) | 22.4151 | + | 16.2855i | 1.46846 | + | 1.06690i | 0.981055 | + | 0.193727i | \(0.0620578\pi\) |
0.487409 | + | 0.873174i | \(0.337942\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.61140 | − | 8.03706i | −0.170349 | − | 0.524280i | ||||
\(236\) | −0.522740 | + | 0.379793i | −0.0340275 | + | 0.0247224i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.32307 | − | 7.14968i | −0.150582 | − | 0.463445i | ||||
\(239\) | 2.65174 | − | 8.16123i | 0.171527 | − | 0.527906i | −0.827931 | − | 0.560830i | \(-0.810482\pi\) |
0.999458 | + | 0.0329243i | \(0.0104820\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6392 | −1.26507 | −0.632535 | − | 0.774531i | \(-0.717986\pi\) | ||||
−0.632535 | + | 0.774531i | \(0.717986\pi\) | |||||||
\(242\) | −12.6233 | + | 23.0644i | −0.811457 | + | 1.48263i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.4368 | − | 17.7544i | −1.56441 | − | 1.13661i | ||||
\(245\) | 0.800331 | − | 2.46317i | 0.0511313 | − | 0.157366i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.73503 | − | 4.16675i | 0.364911 | − | 0.265124i | ||||
\(248\) | 29.2775 | − | 21.2714i | 1.85912 | − | 1.35073i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.29813 | + | 19.3837i | −0.398329 | + | 1.22593i | ||||
\(251\) | −24.1522 | − | 17.5476i | −1.52448 | − | 1.10760i | −0.959213 | − | 0.282685i | \(-0.908775\pi\) |
−0.565263 | − | 0.824911i | \(-0.691225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.3007 | − | 16.2518i | 0.899078 | − | 1.02174i | ||||
\(254\) | −24.7710 | −1.55427 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.64108 | + | 26.5945i | −0.540067 | + | 1.66216i | ||||
\(257\) | −0.876598 | − | 2.69789i | −0.0546807 | − | 0.168290i | 0.919987 | − | 0.391950i | \(-0.128199\pi\) |
−0.974667 | + | 0.223660i | \(0.928199\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.23503 | − | 5.25656i | 0.449563 | − | 0.326627i | ||||
\(260\) | 20.1510 | + | 62.0183i | 1.24971 | + | 3.84621i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −22.5168 | − | 16.3594i | −1.39109 | − | 1.01069i | ||||
\(263\) | −10.2373 | −0.631262 | −0.315631 | − | 0.948882i | \(-0.602216\pi\) | ||||
−0.315631 | + | 0.948882i | \(0.602216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.91978 | −0.302219 | ||||||||
\(266\) | −2.02171 | − | 1.46886i | −0.123959 | − | 0.0900613i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.41848 | − | 25.9094i | −0.514241 | − | 1.58267i | ||||
\(269\) | 8.12925 | − | 5.90624i | 0.495649 | − | 0.360110i | −0.311704 | − | 0.950179i | \(-0.600900\pi\) |
0.807353 | + | 0.590069i | \(0.200900\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.773878 | − | 2.38175i | −0.0470098 | − | 0.144681i | 0.924796 | − | 0.380462i | \(-0.124235\pi\) |
−0.971806 | + | 0.235781i | \(0.924235\pi\) | |||||||
\(272\) | 2.29575 | − | 7.06560i | 0.139200 | − | 0.428415i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 37.0239 | 2.23670 | ||||||||
\(275\) | −2.88772 | − | 4.87240i | −0.174136 | − | 0.293817i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0631 | + | 8.76435i | 0.724801 | + | 0.526599i | 0.887915 | − | 0.460008i | \(-0.152154\pi\) |
−0.163113 | + | 0.986607i | \(0.552154\pi\) | |||||||
\(278\) | −4.29741 | + | 13.2261i | −0.257741 | + | 0.793247i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.58084 | − | 6.23435i | 0.512804 | − | 0.372574i | ||||
\(281\) | 1.65586 | − | 1.20305i | 0.0987805 | − | 0.0717682i | −0.537299 | − | 0.843392i | \(-0.680555\pi\) |
0.636079 | + | 0.771624i | \(0.280555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.27563 | − | 16.2367i | 0.313604 | − | 0.965174i | −0.662721 | − | 0.748866i | \(-0.730599\pi\) |
0.976325 | − | 0.216307i | \(-0.0694014\pi\) | |||||||
\(284\) | 8.13200 | + | 5.90824i | 0.482545 | + | 0.350590i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 49.3522 | + | 21.3015i | 2.91826 | + | 1.25959i | ||||
\(287\) | 8.69747 | 0.513395 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.19658 | + | 6.76039i | −0.129211 | + | 0.397670i | ||||
\(290\) | 1.16176 | + | 3.57552i | 0.0682208 | + | 0.209962i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.77222 | + | 1.28760i | −0.103712 | + | 0.0753508i | ||||
\(293\) | 8.26173 | + | 25.4270i | 0.482655 | + | 1.48546i | 0.835348 | + | 0.549721i | \(0.185266\pi\) |
−0.352693 | + | 0.935739i | \(0.614734\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.364594 | − | 0.264893i | −0.0212275 | − | 0.0154227i | ||||
\(296\) | 36.6242 | 2.12874 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 34.4540 | 1.99587 | ||||||||
\(299\) | −35.8046 | − | 26.0136i | −2.07063 | − | 1.50440i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.38489 | − | 4.26225i | −0.0798237 | − | 0.245672i | ||||
\(302\) | 42.9625 | − | 31.2141i | 2.47222 | − | 1.79617i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.763142 | − | 2.34871i | −0.0437692 | − | 0.134708i | ||||
\(305\) | 6.51019 | − | 20.0363i | 0.372772 | − | 1.14728i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.3329 | −0.932166 | −0.466083 | − | 0.884741i | \(-0.654335\pi\) | ||||
−0.466083 | + | 0.884741i | \(0.654335\pi\) | |||||||
\(308\) | 1.14748 | − | 12.2621i | 0.0653838 | − | 0.698700i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 44.2569 | + | 32.1545i | 2.51362 | + | 1.82625i | ||||
\(311\) | −8.05494 | + | 24.7906i | −0.456754 | + | 1.40574i | 0.412310 | + | 0.911043i | \(0.364722\pi\) |
−0.869064 | + | 0.494700i | \(0.835278\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.3831 | − | 12.6295i | 0.982549 | − | 0.713864i | 0.0242721 | − | 0.999705i | \(-0.492273\pi\) |
0.958277 | + | 0.285842i | \(0.0922732\pi\) | |||||||
\(314\) | 18.9339 | − | 13.7563i | 1.06850 | − | 0.776313i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.2552 | + | 34.6400i | −0.633155 | + | 1.94865i | ||||
\(317\) | −20.0804 | − | 14.5893i | −1.12783 | − | 0.819417i | −0.142453 | − | 0.989802i | \(-0.545499\pi\) |
−0.985378 | + | 0.170385i | \(0.945499\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.84927 | + | 0.798188i | 0.103539 | + | 0.0446900i | ||||
\(320\) | −27.9872 | −1.56453 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.82109 | + | 14.8378i | −0.268669 | + | 0.826878i | ||||
\(323\) | −1.01609 | − | 3.12721i | −0.0565370 | − | 0.174003i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.36776 | + | 6.80608i | −0.519630 | + | 0.377533i | ||||
\(326\) | 8.39365 | + | 25.8330i | 0.464881 | + | 1.43076i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 28.8161 | + | 20.9361i | 1.59110 | + | 1.15600i | ||||
\(329\) | 3.26290 | 0.179889 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.6351 | −1.73882 | −0.869411 | − | 0.494089i | \(-0.835502\pi\) | ||||
−0.869411 | + | 0.494089i | \(0.835502\pi\) | |||||||
\(332\) | 26.2736 | + | 19.0889i | 1.44195 | + | 1.04764i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.75881 | + | 11.5684i | 0.205673 | + | 0.632996i | ||||
\(335\) | 15.3721 | − | 11.1685i | 0.839867 | − | 0.610199i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1381 | − | 31.2018i | −0.552256 | − | 1.69967i | −0.703081 | − | 0.711110i | \(-0.748193\pi\) |
0.150825 | − | 0.988560i | \(-0.451807\pi\) | |||||||
\(338\) | 24.3566 | − | 74.9619i | 1.32482 | − | 4.07739i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 30.2473 | 1.64039 | ||||||||
\(341\) | 28.5963 | − | 6.42026i | 1.54857 | − | 0.347677i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 5.67153 | − | 17.4552i | 0.305788 | − | 0.941119i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.0343 | − | 10.9231i | 0.808251 | − | 0.587228i | ||||
\(347\) | 11.3979 | − | 8.28107i | 0.611872 | − | 0.444551i | −0.238201 | − | 0.971216i | \(-0.576558\pi\) |
0.850073 | + | 0.526665i | \(0.176558\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.87264 | + | 21.1518i | −0.367884 | + | 1.13223i | 0.580271 | + | 0.814423i | \(0.302947\pi\) |
−0.948155 | + | 0.317807i | \(0.897053\pi\) | |||||||
\(350\) | 3.30231 | + | 2.39927i | 0.176516 | + | 0.128246i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.57484 | + | 6.33541i | −0.297140 | + | 0.337679i | ||||
\(353\) | −15.2345 | −0.810850 | −0.405425 | − | 0.914128i | \(-0.632876\pi\) | ||||
−0.405425 | + | 0.914128i | \(0.632876\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.16644 | + | 6.66761i | −0.114983 | + | 0.353880i | ||||
\(356\) | 13.4012 | + | 41.2447i | 0.710264 | + | 2.18597i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.8847 | + | 8.63473i | −0.628125 | + | 0.456360i | ||||
\(359\) | −4.77379 | − | 14.6922i | −0.251951 | − | 0.775425i | −0.994415 | − | 0.105539i | \(-0.966343\pi\) |
0.742464 | − | 0.669886i | \(-0.233657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4870 | + | 10.5255i | 0.762476 | + | 0.553971i | ||||
\(362\) | −22.1290 | −1.16308 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −25.1783 | −1.31970 | ||||||||
\(365\) | −1.23607 | − | 0.898056i | −0.0646988 | − | 0.0470064i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.75723 | + | 26.9520i | 0.457124 | + | 1.40688i | 0.868624 | + | 0.495472i | \(0.165005\pi\) |
−0.411500 | + | 0.911410i | \(0.634995\pi\) | |||||||
\(368\) | −12.4734 | + | 9.06243i | −0.650219 | + | 0.472412i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.1079 | + | 52.6528i | 0.889398 | + | 2.73729i | ||||
\(371\) | 0.587003 | − | 1.80661i | 0.0304757 | − | 0.0937945i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.01940 | −0.0527828 | −0.0263914 | − | 0.999652i | \(-0.508402\pi\) | ||||
−0.0263914 | + | 0.999652i | \(0.508402\pi\) | |||||||
\(374\) | 16.4710 | − | 18.7181i | 0.851694 | − | 0.967890i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.8105 | + | 7.85430i | 0.557510 | + | 0.405054i | ||||
\(377\) | 1.27247 | − | 3.91625i | 0.0655354 | − | 0.201697i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.20632 | − | 5.23569i | 0.370164 | − | 0.268940i | −0.387115 | − | 0.922031i | \(-0.626528\pi\) |
0.757279 | + | 0.653092i | \(0.226528\pi\) | |||||||
\(380\) | 8.13437 | − | 5.90997i | 0.417284 | − | 0.303175i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.8117 | − | 33.2748i | 0.553172 | − | 1.70249i | ||||
\(383\) | 7.93470 | + | 5.76490i | 0.405444 | + | 0.294573i | 0.771755 | − | 0.635920i | \(-0.219379\pi\) |
−0.366311 | + | 0.930493i | \(0.619379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.38118 | − | 1.88169i | 0.427144 | − | 0.0958999i | ||||
\(386\) | −39.3707 | −2.00392 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.6009 | − | 41.8593i | 0.690481 | − | 2.12508i | ||||
\(389\) | −7.46028 | − | 22.9604i | −0.378251 | − | 1.16414i | −0.941259 | − | 0.337686i | \(-0.890356\pi\) |
0.563007 | − | 0.826452i | \(-0.309644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.6078 | + | 12.0663i | −0.839892 | + | 0.610217i | ||||
\(392\) | 1.26552 | + | 3.89486i | 0.0639182 | + | 0.196720i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.1815 | − | 9.57694i | −0.664076 | − | 0.482480i | ||||
\(395\) | −25.4036 | −1.27819 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.6730 | 1.03755 | 0.518773 | − | 0.854912i | \(-0.326389\pi\) | ||||
0.518773 | + | 0.854912i | \(0.326389\pi\) | |||||||
\(398\) | −30.0818 | − | 21.8557i | −1.50786 | − | 1.09553i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.24654 | + | 3.83645i | 0.0623268 | + | 0.191822i | ||||
\(401\) | −20.4007 | + | 14.8220i | −1.01876 | + | 0.740173i | −0.966029 | − | 0.258435i | \(-0.916793\pi\) |
−0.0527328 | + | 0.998609i | \(0.516793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.5155 | − | 56.9850i | −0.922325 | − | 2.83862i | ||||
\(404\) | −4.26685 | + | 13.1320i | −0.212284 | + | 0.653343i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.45160 | −0.0720416 | ||||||||
\(407\) | 27.2322 | + | 11.7540i | 1.34985 | + | 0.582625i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.21625 | − | 5.96946i | −0.406267 | − | 0.295171i | 0.365822 | − | 0.930685i | \(-0.380788\pi\) |
−0.772089 | + | 0.635514i | \(0.780788\pi\) | |||||||
\(410\) | −16.6382 | + | 51.2072i | −0.821704 | + | 2.52894i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.0115 | + | 15.9923i | −1.08443 | + | 0.787882i | ||||
\(413\) | 0.140774 | − | 0.102278i | 0.00692704 | − | 0.00503279i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.99951 | + | 21.5423i | −0.343593 | + | 1.05747i | ||||
\(416\) | 13.9577 | + | 10.1409i | 0.684332 | + | 0.497196i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.772223 | − | 8.25208i | 0.0377707 | − | 0.403622i | ||||
\(419\) | 28.3684 | 1.38589 | 0.692943 | − | 0.720993i | \(-0.256314\pi\) | ||||
0.692943 | + | 0.720993i | \(0.256314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.55479 | + | 26.3289i | −0.416935 | + | 1.28319i | 0.493574 | + | 0.869704i | \(0.335690\pi\) |
−0.910509 | + | 0.413490i | \(0.864310\pi\) | |||||||
\(422\) | 1.15569 | + | 3.55685i | 0.0562581 | + | 0.173145i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.29362 | − | 4.57259i | 0.305645 | − | 0.222064i | ||||
\(425\) | 1.65971 | + | 5.10808i | 0.0805080 | + | 0.247778i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.58084 | + | 4.78126i | 0.318469 | + | 0.231382i | ||||
\(428\) | −49.6858 | −2.40165 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 27.7437 | 1.33792 | ||||||||
\(431\) | 5.91592 | + | 4.29817i | 0.284960 | + | 0.207035i | 0.721078 | − | 0.692854i | \(-0.243647\pi\) |
−0.436118 | + | 0.899889i | \(0.643647\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.25461 | − | 10.0167i | −0.156406 | − | 0.481369i | 0.841894 | − | 0.539643i | \(-0.181441\pi\) |
−0.998301 | + | 0.0582730i | \(0.981441\pi\) | |||||||
\(434\) | −17.0881 | + | 12.4152i | −0.820255 | + | 0.595950i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.2057 | + | 49.8760i | 0.776112 | + | 2.38863i | ||||
\(437\) | −2.10871 | + | 6.48994i | −0.100873 | + | 0.310456i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.574098 | −0.0274002 | −0.0137001 | − | 0.999906i | \(-0.504361\pi\) | ||||
−0.0137001 | + | 0.999906i | \(0.504361\pi\) | |||||||
\(440\) | 32.2977 | + | 13.9404i | 1.53973 | + | 0.664584i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −41.2383 | − | 29.9614i | −1.96150 | − | 1.42512i | ||||
\(443\) | 5.62774 | − | 17.3204i | 0.267382 | − | 0.822917i | −0.723753 | − | 0.690059i | \(-0.757585\pi\) |
0.991135 | − | 0.132858i | \(-0.0424154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.4706 | + | 17.7789i | −1.16002 | + | 0.842801i | ||||
\(446\) | −8.00433 | + | 5.81549i | −0.379016 | + | 0.275371i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.33929 | − | 10.2773i | 0.157767 | − | 0.485556i | ||||
\(449\) | 3.58700 | + | 2.60611i | 0.169281 | + | 0.122990i | 0.669200 | − | 0.743082i | \(-0.266637\pi\) |
−0.499919 | + | 0.866072i | \(0.666637\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.7073 | + | 24.8153i | 0.692538 | + | 1.16851i | ||||
\(452\) | 9.89050 | 0.465210 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.11979 | − | 12.6794i | 0.193351 | − | 0.595074i | ||||
\(455\) | −5.42666 | − | 16.7015i | −0.254406 | − | 0.782980i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.4174 | − | 11.9280i | 0.767976 | − | 0.557967i | −0.133371 | − | 0.991066i | \(-0.542580\pi\) |
0.901346 | + | 0.433099i | \(0.142580\pi\) | |||||||
\(458\) | −0.582356 | − | 1.79231i | −0.0272117 | − | 0.0837491i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −50.7840 | − | 36.8967i | −2.36782 | − | 1.72032i | ||||
\(461\) | 4.85723 | 0.226224 | 0.113112 | − | 0.993582i | \(-0.463918\pi\) | ||||
0.113112 | + | 0.993582i | \(0.463918\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.5168 | −0.907024 | −0.453512 | − | 0.891250i | \(-0.649829\pi\) | ||||
−0.453512 | + | 0.891250i | \(0.649829\pi\) | |||||||
\(464\) | −1.16056 | − | 0.843194i | −0.0538775 | − | 0.0391443i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.4649 | − | 62.9846i | −0.948020 | − | 2.91771i | ||||
\(467\) | −2.22175 | + | 1.61420i | −0.102810 | + | 0.0746961i | −0.638003 | − | 0.770034i | \(-0.720239\pi\) |
0.535192 | + | 0.844730i | \(0.320239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.26710 | + | 6.97741i | 0.104685 | + | 0.322187i | ||||
\(470\) | −6.24191 | + | 19.2106i | −0.287918 | + | 0.886120i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.712607 | 0.0328004 | ||||||||
\(473\) | 9.81910 | − | 11.1587i | 0.451483 | − | 0.513078i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.44440 | + | 1.04942i | 0.0662738 | + | 0.0481508i | ||||
\(476\) | −3.60895 | + | 11.1072i | −0.165416 | + | 0.509098i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.5940 | + | 12.0563i | −0.758992 | + | 0.551440i | ||||
\(479\) | −14.5827 | + | 10.5950i | −0.666302 | + | 0.484097i | −0.868785 | − | 0.495189i | \(-0.835099\pi\) |
0.202483 | + | 0.979286i | \(0.435099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.7382 | − | 57.6703i | 0.854388 | − | 2.62954i | ||||
\(482\) | 37.9774 | + | 27.5922i | 1.72982 | + | 1.25679i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 36.9263 | − | 17.4611i | 1.67847 | − | 0.793687i | ||||
\(485\) | 30.6979 | 1.39392 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.82668 | + | 11.7773i | −0.173404 | + | 0.533681i | −0.999557 | − | 0.0297639i | \(-0.990524\pi\) |
0.826153 | + | 0.563445i | \(0.190524\pi\) | |||||||
\(488\) | 10.2942 | + | 31.6822i | 0.465995 | + | 1.43419i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.00829 | + | 3.63874i | −0.226252 | + | 0.164381i | ||||
\(491\) | −5.13486 | − | 15.8035i | −0.231733 | − | 0.713201i | −0.997538 | − | 0.0701280i | \(-0.977659\pi\) |
0.765805 | − | 0.643073i | \(-0.222341\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.54524 | − | 1.12268i | −0.0695939 | − | 0.0505629i | ||||
\(494\) | −16.9443 | −0.762359 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.8737 | −0.937255 | ||||||||
\(497\) | −2.18995 | − | 1.59109i | −0.0982326 | − | 0.0713702i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.29931 | − | 19.3873i | −0.281996 | − | 0.867894i | −0.987283 | − | 0.158972i | \(-0.949182\pi\) |
0.705287 | − | 0.708922i | \(-0.250818\pi\) | |||||||
\(500\) | 25.6157 | − | 18.6109i | 1.14557 | − | 0.832303i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.0509 | + | 67.8657i | 0.984180 | + | 3.02900i | ||||
\(503\) | −2.06474 | + | 6.35462i | −0.0920622 | + | 0.283338i | −0.986477 | − | 0.163900i | \(-0.947593\pi\) |
0.894415 | + | 0.447239i | \(0.147593\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.63051 | −0.428552 | ||||||||
\(506\) | −50.4871 | + | 11.3351i | −2.24443 | + | 0.503905i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 31.1329 | + | 22.6194i | 1.38130 | + | 1.00357i | ||||
\(509\) | 5.65853 | − | 17.4152i | 0.250810 | − | 0.771914i | −0.743816 | − | 0.668384i | \(-0.766986\pi\) |
0.994626 | − | 0.103530i | \(-0.0330138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.477260 | − | 0.346750i | 0.0211127 | − | 0.0153393i | ||||
\(512\) | 20.5148 | − | 14.9049i | 0.906637 | − | 0.658710i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.09529 | + | 6.44865i | −0.0924195 | + | 0.284438i | ||||
\(515\) | −15.3523 | − | 11.1541i | −0.676502 | − | 0.491508i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.51750 | + | 9.30960i | 0.242660 | + | 0.409436i | ||||
\(518\) | −21.3761 | −0.939210 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 22.2238 | − | 68.3977i | 0.974576 | − | 2.99944i | ||||
\(521\) | 0.181507 | + | 0.558621i | 0.00795197 | + | 0.0244736i | 0.954954 | − | 0.296755i | \(-0.0959043\pi\) |
−0.947002 | + | 0.321228i | \(0.895904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.1458 | + | 16.8164i | −1.01210 | + | 0.735331i | −0.964648 | − | 0.263543i | \(-0.915109\pi\) |
−0.0474487 | + | 0.998874i | \(0.515109\pi\) | |||||||
\(524\) | 13.3614 | + | 41.1220i | 0.583694 | + | 1.79642i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.7966 | + | 14.3830i | 0.863171 | + | 0.627130i | ||||
\(527\) | −27.7925 | −1.21066 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.6027 | 0.852291 | ||||||||
\(530\) | 9.51366 | + | 6.91208i | 0.413247 | + | 0.300241i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.19967 | + | 3.69220i | 0.0520122 | + | 0.160077i | ||||
\(533\) | 47.7104 | − | 34.6636i | 2.06657 | − | 1.50145i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.7087 | − | 32.9581i | −0.462979 | − | 1.42490i | ||||
\(536\) | −9.28444 | + | 28.5746i | −0.401027 | + | 1.23423i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.0180 | −1.03549 | ||||||||
\(539\) | −0.309017 | + | 3.30220i | −0.0133103 | + | 0.142236i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.99897 | − | 3.63196i | −0.214922 | − | 0.156150i | 0.475116 | − | 0.879923i | \(-0.342406\pi\) |
−0.690038 | + | 0.723773i | \(0.742406\pi\) | |||||||
\(542\) | −1.84977 | + | 5.69300i | −0.0794543 | + | 0.244535i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.47420 | − | 4.70378i | 0.277579 | − | 0.201673i | ||||
\(545\) | −29.5915 | + | 21.4995i | −1.26756 | + | 0.920937i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.87099 | + | 5.75830i | −0.0799976 | + | 0.246207i | −0.983054 | − | 0.183314i | \(-0.941318\pi\) |
0.903057 | + | 0.429521i | \(0.141318\pi\) | |||||||
\(548\) | −46.5327 | − | 33.8080i | −1.98778 | − | 1.44421i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.26137 | + | 13.4792i | −0.0537850 | + | 0.574754i | ||||
\(551\) | −0.634918 | −0.0270484 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.03103 | − | 9.32855i | 0.128893 | − | 0.396690i | ||||
\(554\) | −11.0136 | − | 33.8963i | −0.467922 | − | 1.44011i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.4784 | − | 12.6988i | 0.741248 | − | 0.538548i | ||||
\(557\) | 1.85039 | + | 5.69491i | 0.0784035 | + | 0.241301i | 0.982574 | − | 0.185870i | \(-0.0595103\pi\) |
−0.904171 | + | 0.427171i | \(0.859510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.5840 | − | 17.8613i | −1.03979 | − | 0.755454i | ||||
\(560\) | −6.11779 | −0.258524 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.89228 | −0.206368 | ||||||||
\(563\) | 29.2653 | + | 21.2625i | 1.23338 | + | 0.896106i | 0.997139 | − | 0.0755874i | \(-0.0240832\pi\) |
0.236245 | + | 0.971694i | \(0.424083\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.13169 | + | 6.56068i | 0.0896810 | + | 0.276010i | ||||
\(566\) | −33.0137 | + | 23.9859i | −1.38767 | + | 1.00820i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.42566 | − | 10.5431i | −0.143737 | − | 0.442378i | ||||
\(569\) | −10.3428 | + | 31.8319i | −0.433594 | + | 1.33446i | 0.460927 | + | 0.887438i | \(0.347517\pi\) |
−0.894521 | + | 0.447026i | \(0.852483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.96371 | −0.207725 | −0.103862 | − | 0.994592i | \(-0.533120\pi\) | ||||
−0.103862 | + | 0.994592i | \(0.533120\pi\) | |||||||
\(572\) | −42.5760 | − | 71.8379i | −1.78019 | − | 3.00369i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.8188 | − | 12.2196i | −0.702003 | − | 0.510035i | ||||
\(575\) | 3.44442 | − | 10.6008i | 0.143642 | − | 0.442086i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.80923 | + | 7.12682i | −0.408364 | + | 0.296694i | −0.772939 | − | 0.634480i | \(-0.781214\pi\) |
0.364575 | + | 0.931174i | \(0.381214\pi\) | |||||||
\(578\) | 13.7457 | − | 9.98686i | 0.571747 | − | 0.415398i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.80482 | − | 5.55467i | 0.0749412 | − | 0.230645i | ||||
\(581\) | −7.07548 | − | 5.14063i | −0.293540 | − | 0.213269i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.14718 | − | 1.38013i | 0.254590 | − | 0.0571590i | ||||
\(584\) | 2.41592 | 0.0999715 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.7477 | − | 60.7770i | 0.815768 | − | 2.51068i | ||||
\(587\) | 1.48194 | + | 4.56094i | 0.0611661 | + | 0.188250i | 0.976970 | − | 0.213375i | \(-0.0684456\pi\) |
−0.915804 | + | 0.401625i | \(0.868446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.47420 | + | 5.43033i | −0.307969 | + | 0.223753i | ||||
\(590\) | 0.332873 | + | 1.02448i | 0.0137042 | + | 0.0421771i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.0902 | − | 12.4168i | −0.702404 | − | 0.510326i | ||||
\(593\) | −15.3387 | −0.629886 | −0.314943 | − | 0.949111i | \(-0.601985\pi\) | ||||
−0.314943 | + | 0.949111i | \(0.601985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.14560 | −0.333937 | ||||||||
\(596\) | −43.3028 | − | 31.4613i | −1.77375 | − | 1.28871i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.6895 | + | 100.608i | 1.33677 | + | 4.11416i | ||||
\(599\) | −37.3303 | + | 27.1220i | −1.52527 | + | 1.10818i | −0.566478 | + | 0.824077i | \(0.691694\pi\) |
−0.958795 | + | 0.284099i | \(0.908306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.65222 | + | 29.7065i | 0.393722 | + | 1.21175i | 0.929952 | + | 0.367681i | \(0.119848\pi\) |
−0.536230 | + | 0.844072i | \(0.680152\pi\) | |||||||
\(602\) | −3.31024 | + | 10.1879i | −0.134915 | + | 0.415227i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −82.4994 | −3.35685 | ||||||||
\(605\) | 19.5412 | + | 20.7310i | 0.794463 | + | 0.842835i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.9173 | + | 8.65845i | 0.483710 | + | 0.351436i | 0.802760 | − | 0.596302i | \(-0.203364\pi\) |
−0.319051 | + | 0.947738i | \(0.603364\pi\) | |||||||
\(608\) | 0.822037 | − | 2.52997i | 0.0333380 | − | 0.102604i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −40.7393 | + | 29.5988i | −1.64949 | + | 1.19842i | ||||
\(611\) | 17.8988 | − | 13.0042i | 0.724108 | − | 0.526095i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.53268 | + | 26.2609i | −0.344632 | + | 1.06067i | 0.617149 | + | 0.786846i | \(0.288287\pi\) |
−0.961781 | + | 0.273821i | \(0.911713\pi\) | |||||||
\(614\) | 31.5838 | + | 22.9470i | 1.27462 | + | 0.926065i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.97272 | + | 10.1969i | −0.361521 | + | 0.410843i | ||||
\(617\) | −3.29610 | −0.132696 | −0.0663479 | − | 0.997797i | \(-0.521135\pi\) | ||||
−0.0663479 | + | 0.997797i | \(0.521135\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.11467 | + | 3.43059i | −0.0448022 | + | 0.137887i | −0.970955 | − | 0.239261i | \(-0.923095\pi\) |
0.926153 | + | 0.377147i | \(0.123095\pi\) | |||||||
\(620\) | −26.2618 | − | 80.8255i | −1.05470 | − | 3.24603i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 50.4060 | − | 36.6221i | 2.02110 | − | 1.46841i | ||||
\(623\) | −3.60895 | − | 11.1072i | −0.144590 | − | 0.445001i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7739 | + | 17.9993i | 0.990958 | + | 0.719973i | ||||
\(626\) | −51.3586 | −2.05270 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.3581 | −1.45085 | ||||||||
\(629\) | −22.7550 | − | 16.5324i | −0.907300 | − | 0.659192i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.3409 | − | 41.0591i | −0.531093 | − | 1.63454i | −0.751942 | − | 0.659229i | \(-0.770883\pi\) |
0.220849 | − | 0.975308i | \(-0.429117\pi\) | |||||||
\(632\) | 32.4976 | − | 23.6109i | 1.29268 | − | 0.939189i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.3334 | + | 56.4244i | 0.728112 | + | 2.24090i | ||||
\(635\) | −8.29408 | + | 25.5266i | −0.329141 | + | 1.01299i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.78051 | 0.268654 | ||||||||
\(638\) | −2.45463 | − | 4.14165i | −0.0971796 | − | 0.163970i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 43.4578 | + | 31.5739i | 1.71782 | + | 1.24807i | ||||
\(641\) | −7.71648 | + | 23.7489i | −0.304783 | + | 0.938025i | 0.674975 | + | 0.737840i | \(0.264154\pi\) |
−0.979758 | + | 0.200185i | \(0.935846\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.58786 | − | 4.78636i | 0.259800 | − | 0.188756i | −0.450259 | − | 0.892898i | \(-0.648668\pi\) |
0.710059 | + | 0.704142i | \(0.248668\pi\) | |||||||
\(644\) | 19.6083 | − | 14.2462i | 0.772674 | − | 0.561381i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.42872 | + | 7.47485i | −0.0955569 | + | 0.294094i | ||||
\(647\) | 32.2628 | + | 23.4403i | 1.26838 | + | 0.921534i | 0.999137 | − | 0.0415375i | \(-0.0132256\pi\) |
0.269246 | + | 0.963072i | \(0.413226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.529864 | + | 0.228701i | 0.0207990 | + | 0.00897731i | ||||
\(650\) | 27.6772 | 1.08559 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0398 | − | 40.1322i | 0.510676 | − | 1.57170i | ||||
\(653\) | −0.505763 | − | 1.55658i | −0.0197920 | − | 0.0609136i | 0.940673 | − | 0.339315i | \(-0.110195\pi\) |
−0.960465 | + | 0.278402i | \(0.910195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.3978 | + | 17.7260i | −0.953299 | + | 0.692612i | ||||
\(656\) | −6.34867 | − | 19.5392i | −0.247874 | − | 0.762877i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.30966 | − | 4.58423i | −0.245976 | − | 0.178712i | ||||
\(659\) | 7.63149 | 0.297281 | 0.148640 | − | 0.988891i | \(-0.452510\pi\) | ||||
0.148640 | + | 0.988891i | \(0.452510\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.4402 | 0.795031 | 0.397516 | − | 0.917595i | \(-0.369872\pi\) | ||||
0.397516 | + | 0.917595i | \(0.369872\pi\) | |||||||
\(662\) | 61.1746 | + | 44.4460i | 2.37762 | + | 1.72744i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.0679 | − | 34.0635i | −0.429518 | − | 1.32192i | ||||
\(665\) | −2.19059 | + | 1.59156i | −0.0849474 | + | 0.0617179i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.22491 | + | 3.76987i | 0.0474285 | + | 0.145970i | ||||
\(668\) | 5.83941 | − | 17.9719i | 0.225934 | − | 0.695352i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −45.4172 | −1.75462 | ||||||||
\(671\) | −2.51366 | + | 26.8613i | −0.0970387 | + | 1.03697i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.4612 | + | 14.1394i | 0.750176 | + | 0.545035i | 0.895881 | − | 0.444293i | \(-0.146545\pi\) |
−0.145705 | + | 0.989328i | \(0.546545\pi\) | |||||||
\(674\) | −24.2326 | + | 74.5803i | −0.933405 | + | 2.87273i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −99.0628 | + | 71.9733i | −3.81011 | + | 2.76821i | ||||
\(677\) | −6.50994 | + | 4.72974i | −0.250197 | + | 0.181779i | −0.705814 | − | 0.708397i | \(-0.749419\pi\) |
0.455617 | + | 0.890176i | \(0.349419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.66272 | + | 11.2727i | −0.140562 | + | 0.432607i | ||||
\(680\) | −26.9877 | − | 19.6077i | −1.03493 | − | 0.751921i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −64.3185 | − | 27.7613i | −2.46288 | − | 1.06304i | ||||
\(683\) | 19.2894 | 0.738089 | 0.369045 | − | 0.929412i | \(-0.379685\pi\) | ||||
0.369045 | + | 0.929412i | \(0.379685\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.3967 | − | 38.1532i | 0.473655 | − | 1.45776i | ||||
\(686\) | −0.738630 | − | 2.27327i | −0.0282010 | − | 0.0867938i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.56441 | + | 6.22241i | −0.326515 | + | 0.237227i | ||||
\(689\) | −3.98018 | − | 12.2497i | −0.151633 | − | 0.466678i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.7744 | + | 18.7262i | 0.980505 | + | 0.712379i | 0.957821 | − | 0.287364i | \(-0.0927789\pi\) |
0.0226837 | + | 0.999743i | \(0.492779\pi\) | |||||||
\(692\) | −28.8699 | −1.09747 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −33.6753 | −1.27830 | ||||||||
\(695\) | 12.1906 | + | 8.85698i | 0.462415 | + | 0.335964i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.45300 | − | 26.0157i | −0.320180 | − | 0.985413i | ||||
\(698\) | 43.0074 | − | 31.2467i | 1.62786 | − | 1.18271i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.95957 | − | 6.03094i | −0.0740649 | − | 0.227948i | ||||
\(701\) | 10.8378 | − | 33.3555i | 0.409340 | − | 1.25982i | −0.507877 | − | 0.861430i | \(-0.669570\pi\) |
0.917217 | − | 0.398389i | \(-0.130430\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.34972 | −0.352631 | ||||||||
\(704\) | 34.9695 | − | 7.85115i | 1.31796 | − | 0.295901i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.4598 | + | 21.4038i | 1.10873 | + | 0.805543i | ||||
\(707\) | 1.14906 | − | 3.53646i | 0.0432150 | − | 0.133002i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2499 | − | 8.17356i | 0.422500 | − | 0.306965i | −0.356143 | − | 0.934432i | \(-0.615908\pi\) |
0.778643 | + | 0.627467i | \(0.215908\pi\) | |||||||
\(710\) | 13.5571 | − | 9.84979i | 0.508788 | − | 0.369656i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.7797 | − | 45.4873i | 0.553894 | − | 1.70471i | ||||
\(713\) | 46.6625 | + | 33.9023i | 1.74752 | + | 1.26965i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.4759 | − | 43.7252i | 1.43892 | − | 1.63523i | ||||
\(716\) | 22.8217 | 0.852888 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.4106 | + | 35.1181i | −0.425839 | + | 1.31060i | ||||
\(719\) | 12.6402 | + | 38.9026i | 0.471401 | + | 1.45082i | 0.850751 | + | 0.525570i | \(0.176148\pi\) |
−0.379350 | + | 0.925253i | \(0.623852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.92769 | − | 4.30672i | 0.220759 | − | 0.160391i | ||||
\(722\) | −13.2266 | − | 40.7074i | −0.492244 | − | 1.51497i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 27.8124 | + | 20.2069i | 1.03364 | + | 0.750983i | ||||
\(725\) | 1.03709 | 0.0385166 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.5963 | −1.06058 | −0.530288 | − | 0.847817i | \(-0.677916\pi\) | ||||
−0.530288 | + | 0.847817i | \(0.677916\pi\) | |||||||
\(728\) | 22.4649 | + | 16.3217i | 0.832606 | + | 0.604924i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.12853 | + | 3.47325i | 0.0417686 | + | 0.128551i | ||||
\(731\) | −11.4032 | + | 8.28489i | −0.421762 | + | 0.306428i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.74381 | + | 14.6000i | 0.175217 | + | 0.539262i | 0.999643 | − | 0.0267073i | \(-0.00850221\pi\) |
−0.824427 | + | 0.565969i | \(0.808502\pi\) | |||||||
\(734\) | 20.9320 | − | 64.4221i | 0.772615 | − | 2.37786i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.6078 | −0.612171 | ||||||||
\(737\) | −16.0741 | + | 18.2671i | −0.592098 | + | 0.672877i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.9639 | − | 18.1374i | −0.918313 | − | 0.667194i | 0.0247903 | − | 0.999693i | \(-0.492108\pi\) |
−0.943104 | + | 0.332499i | \(0.892108\pi\) | |||||||
\(740\) | 26.5776 | − | 81.7975i | 0.977012 | − | 3.00693i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.67333 | + | 2.66883i | −0.134852 | + | 0.0979759i | ||||
\(743\) | −34.3881 | + | 24.9845i | −1.26158 | + | 0.916591i | −0.998834 | − | 0.0482747i | \(-0.984628\pi\) |
−0.262745 | + | 0.964865i | \(0.584628\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.5362 | − | 35.5049i | 0.422655 | − | 1.30080i | ||||
\(746\) | 1.97128 | + | 1.43222i | 0.0721738 | + | 0.0524373i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −37.7934 | + | 8.48516i | −1.38187 | + | 0.310248i | ||||
\(749\) | 13.3804 | 0.488909 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.51443 | − | 20.0494i | 0.237715 | − | 0.731611i | −0.759035 | − | 0.651050i | \(-0.774329\pi\) |
0.996750 | − | 0.0805613i | \(-0.0256713\pi\) | |||||||
\(752\) | −2.38173 | − | 7.33022i | −0.0868529 | − | 0.267306i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.96281 | + | 5.78532i | −0.289988 | + | 0.210689i | ||||
\(755\) | −17.7810 | − | 54.7244i | −0.647119 | − | 1.99163i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.5741 | − | 25.1196i | −1.25662 | − | 0.912986i | −0.258031 | − | 0.966137i | \(-0.583074\pi\) |
−0.998587 | + | 0.0531506i | \(0.983074\pi\) | |||||||
\(758\) | −21.2912 | −0.773331 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.0889 | −0.402236 | ||||||||
\(761\) | −11.3231 | − | 8.22669i | −0.410461 | − | 0.298217i | 0.363327 | − | 0.931662i | \(-0.381641\pi\) |
−0.773788 | + | 0.633444i | \(0.781641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.36420 | − | 13.4316i | −0.157995 | − | 0.486257i | ||||
\(764\) | −43.9730 | + | 31.9482i | −1.59089 | + | 1.15585i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.24436 | − | 22.2958i | −0.261749 | − | 0.805582i | ||||
\(767\) | 0.364594 | − | 1.12211i | 0.0131647 | − | 0.0405169i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.8142 | 0.858761 | 0.429380 | − | 0.903124i | \(-0.358732\pi\) | ||||
0.429380 | + | 0.903124i | \(0.358732\pi\) | |||||||
\(770\) | −18.8509 | − | 8.13646i | −0.679338 | − | 0.293218i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 49.4823 | + | 35.9510i | 1.78091 | + | 1.29391i | ||||
\(773\) | 13.2976 | − | 40.9259i | 0.478283 | − | 1.47200i | −0.363196 | − | 0.931713i | \(-0.618314\pi\) |
0.841479 | − | 0.540291i | \(-0.181686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.2086 | − | 8.87005i | 0.438545 | − | 0.318621i | ||||
\(776\) | −39.2703 | + | 28.5316i | −1.40972 | + | 1.02422i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.8320 | + | 54.8812i | −0.639308 | + | 1.96759i | ||||
\(779\) | −7.35641 | − | 5.34475i | −0.263571 | − | 0.191495i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.836486 | − | 8.93880i | 0.0299318 | − | 0.319856i | ||||
\(782\) | 49.0680 | 1.75467 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.729944 | − | 2.24654i | 0.0260694 | − | 0.0802335i | ||||
\(785\) | −7.83624 | − | 24.1175i | −0.279687 | − | 0.860790i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.3636 | + | 18.4278i | −0.904116 | + | 0.656878i | −0.939520 | − | 0.342495i | \(-0.888728\pi\) |
0.0354042 | + | 0.999373i | \(0.488728\pi\) | |||||||
\(788\) | 7.82185 | + | 24.0732i | 0.278642 | + | 0.857571i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 49.1244 | + | 35.6910i | 1.74777 | + | 1.26983i | ||||
\(791\) | −2.66351 | −0.0947037 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.1552 | 1.95862 | ||||||||
\(794\) | −39.9765 | − | 29.0447i | −1.41871 | − | 1.03076i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.8504 | + | 54.9378i | 0.632690 | + | 1.94722i | ||||
\(797\) | −5.62839 | + | 4.08927i | −0.199368 | + | 0.144849i | −0.682990 | − | 0.730428i | \(-0.739321\pi\) |
0.483622 | + | 0.875277i | \(0.339321\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.17118 | − | 9.75990i | −0.112188 | − | 0.345280i | ||||
\(800\) | −1.34274 | + | 4.13252i | −0.0474729 | + | 0.146107i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 60.2742 | 2.12836 | ||||||||
\(803\) | 1.79637 | + | 0.775356i | 0.0633927 | + | 0.0273617i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.6761 | + | 9.93630i | 0.482021 | + | 0.350208i | ||||
\(806\) | −44.2569 | + | 136.209i | −1.55888 | + | 4.79775i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.3198 | − | 8.95088i | 0.433410 | − | 0.314891i | ||||
\(809\) | 40.2788 | − | 29.2642i | 1.41613 | − | 1.02888i | 0.423730 | − | 0.905789i | \(-0.360721\pi\) |
0.992396 | − | 0.123087i | \(-0.0392793\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.46897 | + | 4.52102i | −0.0515825 | + | 0.158755i | −0.973529 | − | 0.228562i | \(-0.926598\pi\) |
0.921947 | + | 0.387316i | \(0.126598\pi\) | |||||||
\(812\) | 1.82441 | + | 1.32551i | 0.0640243 | + | 0.0465163i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −36.1465 | − | 60.9895i | −1.26694 | − | 2.13768i | ||||
\(815\) | 29.4314 | 1.03094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.44787 | + | 4.45610i | −0.0506547 | + | 0.155899i | ||||
\(818\) | 7.50141 | + | 23.0870i | 0.262281 | + | 0.807217i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 67.6708 | − | 49.1657i | 2.36317 | − | 1.71694i | ||||
\(821\) | −5.46804 | − | 16.8289i | −0.190836 | − | 0.587332i | 0.809164 | − | 0.587583i | \(-0.199920\pi\) |
−1.00000 | 0.000250536i | \(0.999920\pi\) | ||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.7605 | + | 15.0834i | 0.723667 | + | 0.525775i | 0.887554 | − | 0.460704i | \(-0.152403\pi\) |
−0.163887 | + | 0.986479i | \(0.552403\pi\) | |||||||
\(824\) | 30.0063 | 1.04532 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.415920 | −0.0144717 | ||||||||
\(827\) | 33.4044 | + | 24.2697i | 1.16158 | + | 0.843940i | 0.989977 | − | 0.141226i | \(-0.0451044\pi\) |
0.171606 | + | 0.985166i | \(0.445104\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.89845 | + | 21.2312i | 0.239593 | + | 0.737391i | 0.996479 | + | 0.0838443i | \(0.0267198\pi\) |
−0.756886 | + | 0.653547i | \(0.773280\pi\) | |||||||
\(830\) | 43.8014 | − | 31.8236i | 1.52037 | − | 1.10461i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.6421 | − | 69.6853i | −0.784974 | − | 2.41590i | ||||
\(833\) | 0.971892 | − | 2.99118i | 0.0336741 | − | 0.103638i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.1799 | 0.456108 | ||||||||
\(836\) | −8.50586 | + | 9.66631i | −0.294181 | + | 0.334316i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −54.8576 | − | 39.8564i | −1.89502 | − | 1.37682i | ||||
\(839\) | 0.983838 | − | 3.02794i | 0.0339659 | − | 0.104536i | −0.932636 | − | 0.360818i | \(-0.882498\pi\) |
0.966602 | + | 0.256282i | \(0.0824975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.1631 | − | 16.8290i | 0.798728 | − | 0.580310i | ||||
\(842\) | 53.5339 | − | 38.8947i | 1.84490 | − | 1.34040i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.79540 | − | 5.52566i | 0.0618001 | − | 0.190201i | ||||
\(845\) | −69.0931 | − | 50.1991i | −2.37687 | − | 1.72690i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.94427 | + | 4.70228i | −0.341689 | + | 0.161572i | ||||
\(848\) | −4.48710 | −0.154087 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.96714 | − | 12.2096i | 0.136072 | − | 0.418786i | ||||
\(851\) | 18.0378 | + | 55.5147i | 0.618328 | + | 1.90302i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.85527 | − | 4.25410i | 0.200481 | − | 0.145658i | −0.483016 | − | 0.875612i | \(-0.660459\pi\) |
0.683496 | + | 0.729954i | \(0.260459\pi\) | |||||||
\(854\) | −6.00829 | − | 18.4916i | −0.205599 | − | 0.632770i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44.3314 | + | 32.2086i | 1.51522 | + | 1.10087i | ||||
\(857\) | −9.16216 | −0.312973 | −0.156487 | − | 0.987680i | \(-0.550017\pi\) | ||||
−0.156487 | + | 0.987680i | \(0.550017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.2015 | −0.621028 | −0.310514 | − | 0.950569i | \(-0.600501\pi\) | ||||
−0.310514 | + | 0.950569i | \(0.600501\pi\) | |||||||
\(860\) | −34.8691 | − | 25.3339i | −1.18903 | − | 0.863878i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.40122 | − | 16.6232i | −0.183966 | − | 0.566190i | ||||
\(863\) | 15.6086 | − | 11.3403i | 0.531322 | − | 0.386028i | −0.289530 | − | 0.957169i | \(-0.593499\pi\) |
0.820852 | + | 0.571141i | \(0.193499\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.22231 | − | 19.1503i | −0.211565 | − | 0.651130i | ||||
\(866\) | −7.77935 | + | 23.9424i | −0.264353 | + | 0.813595i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.8137 | 1.11377 | ||||||||
\(869\) | 31.7414 | − | 7.12638i | 1.07675 | − | 0.241746i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.2447 | + | 29.2395i | 1.36364 | + | 0.990741i | ||||
\(872\) | 17.8727 | − | 55.0064i | 0.605245 | − | 1.86275i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.1958 | − | 9.58733i | 0.446355 | − | 0.324296i | ||||
\(875\) | −6.89830 | + | 5.01191i | −0.233205 | + | 0.169434i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.25066 | − | 3.84914i | 0.0422318 | − | 0.129976i | −0.927718 | − | 0.373283i | \(-0.878232\pi\) |
0.969949 | + | 0.243307i | \(0.0782321\pi\) | |||||||
\(878\) | 1.11017 | + | 0.806584i | 0.0374663 | + | 0.0272209i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.3451 | − | 17.4551i | −0.348733 | − | 0.588411i | ||||
\(881\) | −6.68797 | −0.225324 | −0.112662 | − | 0.993633i | \(-0.535938\pi\) | ||||
−0.112662 | + | 0.993633i | \(0.535938\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.571764 | + | 1.75971i | −0.0192414 | + | 0.0592189i | −0.960216 | − | 0.279258i | \(-0.909912\pi\) |
0.940975 | + | 0.338477i | \(0.109912\pi\) | |||||||
\(884\) | 24.4706 | + | 75.3126i | 0.823034 | + | 2.53304i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.2171 | + | 25.5867i | −1.18314 | + | 0.859603i | ||||
\(887\) | −4.35733 | − | 13.4105i | −0.146305 | − | 0.450280i | 0.850872 | − | 0.525373i | \(-0.176074\pi\) |
−0.997176 | + | 0.0750938i | \(0.976074\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.38410 | − | 6.09140i | −0.281194 | − | 0.204299i | ||||
\(890\) | 72.2987 | 2.42346 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.3704 | 0.514640 | ||||||||
\(893\) | −2.75980 | − | 2.00511i | −0.0923530 | − | 0.0670984i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.91875 | + | 15.1384i | 0.164416 | + | 0.506020i | ||||
\(896\) | −16.7795 | + | 12.1910i | −0.560565 | + | 0.407274i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.27492 | − | 10.0792i | −0.109286 | − | 0.336346i | ||||
\(899\) | −1.65835 | + | 5.10387i | −0.0553090 | + | 0.170224i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.97439 | −0.199036 | ||||||||
\(902\) | 6.42421 | − | 68.6500i | 0.213903 | − | 2.28579i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.82465 | − | 6.41149i | −0.293504 | − | 0.213243i | ||||
\(905\) | −7.40947 | + | 22.8040i | −0.246299 | + | 0.758031i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.62569 | − | 1.18113i | 0.0539800 | − | 0.0392188i | −0.560468 | − | 0.828176i | \(-0.689379\pi\) |
0.614448 | + | 0.788957i | \(0.289379\pi\) | |||||||
\(908\) | −16.7559 | + | 12.1739i | −0.556066 | + | 0.404005i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.9711 | + | 39.9209i | −0.429988 | + | 1.32337i | ||||
\(911\) | 33.6157 | + | 24.4232i | 1.11374 | + | 0.809177i | 0.983248 | − | 0.182273i | \(-0.0583454\pi\) |
0.130489 | + | 0.991450i | \(0.458345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.70259 | − | 28.8803i | 0.0894427 | − | 0.955797i | ||||
\(914\) | −48.5057 | −1.60442 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.904706 | + | 2.78440i | −0.0298923 | + | 0.0919991i | ||||
\(917\) | −3.59822 | − | 11.0742i | −0.118824 | − | 0.365701i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.3471 | + | 20.5954i | −0.935085 | + | 0.679379i | −0.947233 | − | 0.320547i | \(-0.896133\pi\) |
0.0121473 | + | 0.999926i | \(0.496133\pi\) | |||||||
\(920\) | 21.3931 | + | 65.8411i | 0.705309 | + | 2.17072i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.39270 | − | 6.82420i | −0.309332 | − | 0.224743i | ||||
\(923\) | −18.3543 | −0.604141 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.2721 | 0.502143 | ||||||||
\(926\) | 37.7408 | + | 27.4203i | 1.24024 | + | 0.901087i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.477504 | − | 1.46961i | −0.0156748 | − | 0.0482422i | ||||
\(929\) | −1.24832 | + | 0.906954i | −0.0409559 | + | 0.0297562i | −0.608075 | − | 0.793880i | \(-0.708058\pi\) |
0.567119 | + | 0.823636i | \(0.308058\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.323071 | − | 0.994311i | −0.0105882 | − | 0.0325872i | ||||
\(932\) | −31.7928 | + | 97.8483i | −1.04141 | + | 3.20513i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.56421 | 0.214788 | ||||||||
\(935\) | −13.7741 | − | 23.2408i | −0.450460 | − | 0.760054i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.3581 | + | 24.9626i | 1.12243 | + | 0.815494i | 0.984576 | − | 0.174959i | \(-0.0559792\pi\) |
0.137855 | + | 0.990452i | \(0.455979\pi\) | |||||||
\(938\) | 5.41895 | − | 16.6778i | 0.176935 | − | 0.544550i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.3870 | − | 18.4448i | 0.828033 | − | 0.601601i | ||||
\(941\) | 3.89751 | − | 2.83171i | 0.127055 | − | 0.0923111i | −0.522443 | − | 0.852674i | \(-0.674979\pi\) |
0.649498 | + | 0.760363i | \(0.274979\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.5426 | + | 53.9905i | −0.571265 | + | 1.75817i | ||||
\(944\) | −0.332529 | − | 0.241597i | −0.0108229 | − | 0.00786330i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.6653 | + | 7.78284i | −1.12707 | + | 0.253042i | ||||
\(947\) | −18.0449 | −0.586379 | −0.293189 | − | 0.956054i | \(-0.594717\pi\) | ||||
−0.293189 | + | 0.956054i | \(0.594717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.23607 | − | 3.80423i | 0.0401245 | − | 0.123490i | ||||
\(950\) | −1.31874 | − | 4.05866i | −0.0427855 | − | 0.131680i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.4203 | − | 7.57076i | 0.337722 | − | 0.245370i | ||||
\(953\) | 11.5977 | + | 35.6940i | 0.375686 | + | 1.15624i | 0.943015 | + | 0.332750i | \(0.107977\pi\) |
−0.567329 | + | 0.823491i | \(0.692023\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.6697 | − | 22.2829i | −0.992449 | − | 0.721057i | ||||
\(956\) | 31.8649 | 1.03058 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 43.0850 | 1.39201 | ||||||||
\(959\) | 12.5313 | + | 9.10450i | 0.404656 | + | 0.294000i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5509 | + | 44.7832i | 0.469385 | + | 1.44462i | ||||
\(962\) | −117.259 | + | 85.1940i | −3.78060 | + | 2.74676i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.5356 | − | 69.3574i | −0.725823 | − | 2.23385i | ||||
\(965\) | −13.1825 | + | 40.5717i | −0.424361 | + | 1.30605i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.06636 | 0.0342919 | 0.0171460 | − | 0.999853i | \(-0.494542\pi\) | ||||
0.0171460 | + | 0.999853i | \(0.494542\pi\) | |||||||
\(968\) | −44.2661 | − | 8.35796i | −1.42277 | − | 0.268635i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −59.3624 | − | 43.1293i | −1.90601 | − | 1.38480i | ||||
\(971\) | 14.1398 | − | 43.5180i | 0.453769 | − | 1.39656i | −0.418805 | − | 0.908076i | \(-0.637551\pi\) |
0.872574 | − | 0.488481i | \(-0.162449\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.70693 | + | 3.41978i | −0.150897 | + | 0.109633i | ||||
\(974\) | 23.9465 | − | 17.3982i | 0.767296 | − | 0.557473i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.93764 | − | 18.2742i | 0.190059 | − | 0.584942i | ||||
\(977\) | −27.6930 | − | 20.1201i | −0.885976 | − | 0.643700i | 0.0488494 | − | 0.998806i | \(-0.484445\pi\) |
−0.934826 | + | 0.355107i | \(0.884445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.5881 | − | 29.0791i | 0.817799 | − | 0.929371i | ||||
\(980\) | 9.61724 | 0.307212 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.2736 | + | 37.7744i | −0.391667 | + | 1.20543i | ||||
\(983\) | 9.06625 | + | 27.9031i | 0.289169 | + | 0.889969i | 0.985118 | + | 0.171879i | \(0.0549837\pi\) |
−0.695950 | + | 0.718091i | \(0.745016\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.2826 | + | 10.3770i | −0.455083 | + | 0.330637i | ||||
\(986\) | 1.41080 | + | 4.34198i | 0.0449289 | + | 0.138277i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.2961 | + | 15.4725i | 0.677518 | + | 0.492246i | ||||
\(989\) | 29.2517 | 0.930150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0194 | 0.604171 | 0.302086 | − | 0.953281i | \(-0.402317\pi\) | ||||
0.302086 | + | 0.953281i | \(0.402317\pi\) | |||||||
\(992\) | −18.1904 | − | 13.2161i | −0.577546 | − | 0.419612i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.99942 | + | 6.15357i | 0.0634176 | + | 0.195179i | ||||
\(995\) | −32.5947 | + | 23.6814i | −1.03332 | + | 0.750752i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.36942 | − | 4.21463i | −0.0433699 | − | 0.133479i | 0.927027 | − | 0.374995i | \(-0.122355\pi\) |
−0.970397 | + | 0.241516i | \(0.922355\pi\) | |||||||
\(998\) | −15.0570 | + | 46.3406i | −0.476620 | + | 1.46689i | ||||
\(999\) | 0 | 0 |
(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 | 693.2.m.f.631.1 | 8 | ||
3.2 | odd | 2 | 231.2.j.f.169.2 | ✓ | 8 | ||
11.3 | even | 5 | inner | 693.2.m.f.190.1 | 8 | ||
11.5 | even | 5 | 7623.2.a.ci.1.4 | 4 | |||
11.6 | odd | 10 | 7623.2.a.cl.1.1 | 4 | |||
33.5 | odd | 10 | 2541.2.a.bn.1.1 | 4 | |||
33.14 | odd | 10 | 231.2.j.f.190.2 | yes | 8 | ||
33.17 | even | 10 | 2541.2.a.bm.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.f.169.2 | ✓ | 8 | 3.2 | odd | 2 | ||
231.2.j.f.190.2 | yes | 8 | 33.14 | odd | 10 | ||
693.2.m.f.190.1 | 8 | 11.3 | even | 5 | inner | ||
693.2.m.f.631.1 | 8 | 1.1 | even | 1 | trivial | ||
2541.2.a.bm.1.4 | 4 | 33.17 | even | 10 | |||
2541.2.a.bn.1.1 | 4 | 33.5 | odd | 10 | |||
7623.2.a.ci.1.4 | 4 | 11.5 | even | 5 | |||
7623.2.a.cl.1.1 | 4 | 11.6 | odd | 10 |