Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,2,Mod(3,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.3");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.c (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.966189864457\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 27.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 121.27 |
Dual form | 121.2.c.b.9.1 |
$q$-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 \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | 0.998886 | + | 0.0471903i | \(0.0150267\pi\) |
−0.780378 | + | 0.625308i | \(0.784973\pi\) | |||||||
\(3\) | −1.61803 | − | 1.17557i | −0.934172 | − | 0.678716i | 0.0128385 | − | 0.999918i | \(-0.495913\pi\) |
−0.947011 | + | 0.321202i | \(0.895913\pi\) | |||||||
\(4\) | 0.809017 | − | 0.587785i | 0.404508 | − | 0.293893i | ||||
\(5\) | 0.309017 | − | 0.951057i | 0.138197 | − | 0.425325i | −0.857877 | − | 0.513855i | \(-0.828217\pi\) |
0.996074 | + | 0.0885298i | \(0.0282169\pi\) | |||||||
\(6\) | 0.618034 | − | 1.90211i | 0.252311 | − | 0.776534i | ||||
\(7\) | 1.61803 | − | 1.17557i | 0.611559 | − | 0.444324i | −0.238404 | − | 0.971166i | \(-0.576624\pi\) |
0.849963 | + | 0.526842i | \(0.176624\pi\) | |||||||
\(8\) | 2.42705 | + | 1.76336i | 0.858092 | + | 0.623440i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 0.309017 | + | 0.951057i | 0.0857059 | + | 0.263776i | 0.984720 | − | 0.174143i | \(-0.0557156\pi\) |
−0.899014 | + | 0.437919i | \(0.855716\pi\) | |||||||
\(14\) | 1.61803 | + | 1.17557i | 0.432438 | + | 0.314184i | ||||
\(15\) | −1.61803 | + | 1.17557i | −0.417775 | + | 0.303531i | ||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | −1.54508 | + | 4.75528i | −0.374738 | + | 1.15333i | 0.568917 | + | 0.822395i | \(0.307363\pi\) |
−0.943655 | + | 0.330930i | \(0.892637\pi\) | |||||||
\(18\) | −0.809017 | + | 0.587785i | −0.190687 | + | 0.138542i | ||||
\(19\) | −4.85410 | − | 3.52671i | −1.11361 | − | 0.809083i | −0.130379 | − | 0.991464i | \(-0.541620\pi\) |
−0.983228 | + | 0.182381i | \(0.941620\pi\) | |||||||
\(20\) | −0.309017 | − | 0.951057i | −0.0690983 | − | 0.212663i | ||||
\(21\) | −4.00000 | −0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | −1.85410 | − | 5.70634i | −0.378467 | − | 1.16480i | ||||
\(25\) | 3.23607 | + | 2.35114i | 0.647214 | + | 0.470228i | ||||
\(26\) | −0.809017 | + | 0.587785i | −0.158661 | + | 0.115274i | ||||
\(27\) | −1.23607 | + | 3.80423i | −0.237881 | + | 0.732124i | ||||
\(28\) | 0.618034 | − | 1.90211i | 0.116797 | − | 0.359466i | ||||
\(29\) | −7.28115 | + | 5.29007i | −1.35208 | + | 0.982341i | −0.353171 | + | 0.935559i | \(0.614897\pi\) |
−0.998905 | + | 0.0467821i | \(0.985103\pi\) | |||||||
\(30\) | −1.61803 | − | 1.17557i | −0.295411 | − | 0.214629i | ||||
\(31\) | −0.618034 | − | 1.90211i | −0.111002 | − | 0.341630i | 0.880090 | − | 0.474807i | \(-0.157482\pi\) |
−0.991092 | + | 0.133177i | \(0.957482\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | −0.618034 | − | 1.90211i | −0.104467 | − | 0.321516i | ||||
\(36\) | 0.809017 | + | 0.587785i | 0.134836 | + | 0.0979642i | ||||
\(37\) | 2.42705 | − | 1.76336i | 0.399005 | − | 0.289894i | −0.370131 | − | 0.928980i | \(-0.620687\pi\) |
0.769135 | + | 0.639086i | \(0.220687\pi\) | |||||||
\(38\) | 1.85410 | − | 5.70634i | 0.300775 | − | 0.925690i | ||||
\(39\) | 0.618034 | − | 1.90211i | 0.0989646 | − | 0.304582i | ||||
\(40\) | 2.42705 | − | 1.76336i | 0.383750 | − | 0.278811i | ||||
\(41\) | 4.04508 | + | 2.93893i | 0.631736 | + | 0.458983i | 0.857001 | − | 0.515314i | \(-0.172325\pi\) |
−0.225265 | + | 0.974298i | \(0.572325\pi\) | |||||||
\(42\) | −1.23607 | − | 3.80423i | −0.190729 | − | 0.587005i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0.618034 | + | 1.90211i | 0.0911241 | + | 0.280451i | ||||
\(47\) | −1.61803 | − | 1.17557i | −0.236015 | − | 0.171475i | 0.463491 | − | 0.886101i | \(-0.346597\pi\) |
−0.699506 | + | 0.714627i | \(0.746597\pi\) | |||||||
\(48\) | 1.61803 | − | 1.17557i | 0.233543 | − | 0.169679i | ||||
\(49\) | −0.927051 | + | 2.85317i | −0.132436 | + | 0.407596i | ||||
\(50\) | −1.23607 | + | 3.80423i | −0.174806 | + | 0.537999i | ||||
\(51\) | 8.09017 | − | 5.87785i | 1.13285 | − | 0.823064i | ||||
\(52\) | 0.809017 | + | 0.587785i | 0.112190 | + | 0.0815111i | ||||
\(53\) | 2.78115 | + | 8.55951i | 0.382021 | + | 1.17574i | 0.938619 | + | 0.344957i | \(0.112106\pi\) |
−0.556598 | + | 0.830782i | \(0.687894\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.00000 | 0.801784 | ||||||||
\(57\) | 3.70820 | + | 11.4127i | 0.491164 | + | 1.51165i | ||||
\(58\) | −7.28115 | − | 5.29007i | −0.956062 | − | 0.694620i | ||||
\(59\) | −6.47214 | + | 4.70228i | −0.842600 | + | 0.612185i | −0.923096 | − | 0.384570i | \(-0.874350\pi\) |
0.0804955 | + | 0.996755i | \(0.474350\pi\) | |||||||
\(60\) | −0.618034 | + | 1.90211i | −0.0797878 | + | 0.245562i | ||||
\(61\) | 1.85410 | − | 5.70634i | 0.237393 | − | 0.730622i | −0.759401 | − | 0.650622i | \(-0.774508\pi\) |
0.996795 | − | 0.0799995i | \(-0.0254919\pi\) | |||||||
\(62\) | 1.61803 | − | 1.17557i | 0.205491 | − | 0.149298i | ||||
\(63\) | 1.61803 | + | 1.17557i | 0.203853 | + | 0.148108i | ||||
\(64\) | 2.16312 | + | 6.65740i | 0.270390 | + | 0.832174i | ||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 1.54508 | + | 4.75528i | 0.187369 | + | 0.576663i | ||||
\(69\) | −3.23607 | − | 2.35114i | −0.389577 | − | 0.283044i | ||||
\(70\) | 1.61803 | − | 1.17557i | 0.193392 | − | 0.140508i | ||||
\(71\) | 3.70820 | − | 11.4127i | 0.440083 | − | 1.35444i | −0.447704 | − | 0.894182i | \(-0.647758\pi\) |
0.887787 | − | 0.460254i | \(-0.152242\pi\) | |||||||
\(72\) | −0.927051 | + | 2.85317i | −0.109254 | + | 0.336249i | ||||
\(73\) | 1.61803 | − | 1.17557i | 0.189377 | − | 0.137590i | −0.489057 | − | 0.872252i | \(-0.662659\pi\) |
0.678434 | + | 0.734662i | \(0.262659\pi\) | |||||||
\(74\) | 2.42705 | + | 1.76336i | 0.282139 | + | 0.204986i | ||||
\(75\) | −2.47214 | − | 7.60845i | −0.285458 | − | 0.878548i | ||||
\(76\) | −6.00000 | −0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | −3.09017 | − | 9.51057i | −0.347671 | − | 1.07002i | −0.960138 | − | 0.279526i | \(-0.909823\pi\) |
0.612467 | − | 0.790496i | \(-0.290177\pi\) | |||||||
\(80\) | 0.809017 | + | 0.587785i | 0.0904508 | + | 0.0657164i | ||||
\(81\) | 8.89919 | − | 6.46564i | 0.988799 | − | 0.718404i | ||||
\(82\) | −1.54508 | + | 4.75528i | −0.170626 | + | 0.525133i | ||||
\(83\) | 1.85410 | − | 5.70634i | 0.203514 | − | 0.626352i | −0.796257 | − | 0.604959i | \(-0.793190\pi\) |
0.999771 | − | 0.0213936i | \(-0.00681031\pi\) | |||||||
\(84\) | −3.23607 | + | 2.35114i | −0.353084 | + | 0.256531i | ||||
\(85\) | 4.04508 | + | 2.93893i | 0.438751 | + | 0.318771i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.0000 | 1.92980 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0.309017 | + | 0.951057i | 0.0325733 | + | 0.100250i | ||||
\(91\) | 1.61803 | + | 1.17557i | 0.169616 | + | 0.123233i | ||||
\(92\) | 1.61803 | − | 1.17557i | 0.168692 | − | 0.122562i | ||||
\(93\) | −1.23607 | + | 3.80423i | −0.128174 | + | 0.394480i | ||||
\(94\) | 0.618034 | − | 1.90211i | 0.0637453 | − | 0.196188i | ||||
\(95\) | −4.85410 | + | 3.52671i | −0.498020 | + | 0.361833i | ||||
\(96\) | −8.09017 | − | 5.87785i | −0.825700 | − | 0.599906i | ||||
\(97\) | −4.01722 | − | 12.3637i | −0.407887 | − | 1.25535i | −0.918460 | − | 0.395513i | \(-0.870567\pi\) |
0.510573 | − | 0.859834i | \(-0.329433\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −3.09017 | − | 9.51057i | −0.307483 | − | 0.946337i | −0.978739 | − | 0.205110i | \(-0.934245\pi\) |
0.671255 | − | 0.741226i | \(-0.265755\pi\) | |||||||
\(102\) | 8.09017 | + | 5.87785i | 0.801046 | + | 0.581994i | ||||
\(103\) | −6.47214 | + | 4.70228i | −0.637719 | + | 0.463330i | −0.859066 | − | 0.511865i | \(-0.828955\pi\) |
0.221347 | + | 0.975195i | \(0.428955\pi\) | |||||||
\(104\) | −0.927051 | + | 2.85317i | −0.0909048 | + | 0.279776i | ||||
\(105\) | −1.23607 | + | 3.80423i | −0.120628 | + | 0.371254i | ||||
\(106\) | −7.28115 | + | 5.29007i | −0.707208 | + | 0.513817i | ||||
\(107\) | −4.85410 | − | 3.52671i | −0.469264 | − | 0.340940i | 0.327891 | − | 0.944716i | \(-0.393662\pi\) |
−0.797154 | + | 0.603776i | \(0.793662\pi\) | |||||||
\(108\) | 1.23607 | + | 3.80423i | 0.118941 | + | 0.366062i | ||||
\(109\) | −11.0000 | −1.05361 | −0.526804 | − | 0.849987i | \(-0.676610\pi\) | ||||
−0.526804 | + | 0.849987i | \(0.676610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0.618034 | + | 1.90211i | 0.0583987 | + | 0.179733i | ||||
\(113\) | 7.28115 | + | 5.29007i | 0.684953 | + | 0.497648i | 0.874997 | − | 0.484128i | \(-0.160863\pi\) |
−0.190044 | + | 0.981776i | \(0.560863\pi\) | |||||||
\(114\) | −9.70820 | + | 7.05342i | −0.909257 | + | 0.660614i | ||||
\(115\) | 0.618034 | − | 1.90211i | 0.0576320 | − | 0.177373i | ||||
\(116\) | −2.78115 | + | 8.55951i | −0.258224 | + | 0.794730i | ||||
\(117\) | −0.809017 | + | 0.587785i | −0.0747936 | + | 0.0543408i | ||||
\(118\) | −6.47214 | − | 4.70228i | −0.595808 | − | 0.432880i | ||||
\(119\) | 3.09017 | + | 9.51057i | 0.283275 | + | 0.871832i | ||||
\(120\) | −6.00000 | −0.547723 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | −3.09017 | − | 9.51057i | −0.278631 | − | 0.857539i | ||||
\(124\) | −1.61803 | − | 1.17557i | −0.145304 | − | 0.105569i | ||||
\(125\) | 7.28115 | − | 5.29007i | 0.651246 | − | 0.473158i | ||||
\(126\) | −0.618034 | + | 1.90211i | −0.0550588 | + | 0.169454i | ||||
\(127\) | −4.94427 | + | 15.2169i | −0.438733 | + | 1.35028i | 0.450479 | + | 0.892787i | \(0.351253\pi\) |
−0.889212 | + | 0.457495i | \(0.848747\pi\) | |||||||
\(128\) | 2.42705 | − | 1.76336i | 0.214523 | − | 0.155860i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.309017 | + | 0.951057i | 0.0271026 | + | 0.0834132i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | −1.04053 | ||||||||
\(134\) | 0.618034 | + | 1.90211i | 0.0533900 | + | 0.164318i | ||||
\(135\) | 3.23607 | + | 2.35114i | 0.278516 | + | 0.202354i | ||||
\(136\) | −12.1353 | + | 8.81678i | −1.04059 | + | 0.756033i | ||||
\(137\) | −3.09017 | + | 9.51057i | −0.264011 | + | 0.812542i | 0.727909 | + | 0.685674i | \(0.240493\pi\) |
−0.991920 | + | 0.126868i | \(0.959507\pi\) | |||||||
\(138\) | 1.23607 | − | 3.80423i | 0.105221 | − | 0.323837i | ||||
\(139\) | 1.61803 | − | 1.17557i | 0.137240 | − | 0.0997106i | −0.517047 | − | 0.855957i | \(-0.672969\pi\) |
0.654287 | + | 0.756246i | \(0.272969\pi\) | |||||||
\(140\) | −1.61803 | − | 1.17557i | −0.136749 | − | 0.0993538i | ||||
\(141\) | 1.23607 | + | 3.80423i | 0.104096 | + | 0.320374i | ||||
\(142\) | 12.0000 | 1.00702 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 2.78115 | + | 8.55951i | 0.230962 | + | 0.710829i | ||||
\(146\) | 1.61803 | + | 1.17557i | 0.133909 | + | 0.0972909i | ||||
\(147\) | 4.85410 | − | 3.52671i | 0.400360 | − | 0.290878i | ||||
\(148\) | 0.927051 | − | 2.85317i | 0.0762031 | − | 0.234529i | ||||
\(149\) | 5.25329 | − | 16.1680i | 0.430366 | − | 1.32453i | −0.467395 | − | 0.884049i | \(-0.654807\pi\) |
0.897761 | − | 0.440482i | \(-0.145193\pi\) | |||||||
\(150\) | 6.47214 | − | 4.70228i | 0.528448 | − | 0.383940i | ||||
\(151\) | 12.9443 | + | 9.40456i | 1.05339 | + | 0.765333i | 0.972854 | − | 0.231419i | \(-0.0743369\pi\) |
0.0805358 | + | 0.996752i | \(0.474337\pi\) | |||||||
\(152\) | −5.56231 | − | 17.1190i | −0.451163 | − | 1.38854i | ||||
\(153\) | −5.00000 | −0.404226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | −0.618034 | − | 1.90211i | −0.0494823 | − | 0.152291i | ||||
\(157\) | −1.61803 | − | 1.17557i | −0.129133 | − | 0.0938207i | 0.521344 | − | 0.853347i | \(-0.325431\pi\) |
−0.650477 | + | 0.759526i | \(0.725431\pi\) | |||||||
\(158\) | 8.09017 | − | 5.87785i | 0.643619 | − | 0.467617i | ||||
\(159\) | 5.56231 | − | 17.1190i | 0.441120 | − | 1.35763i | ||||
\(160\) | 1.54508 | − | 4.75528i | 0.122150 | − | 0.375938i | ||||
\(161\) | 3.23607 | − | 2.35114i | 0.255038 | − | 0.185296i | ||||
\(162\) | 8.89919 | + | 6.46564i | 0.699186 | + | 0.507988i | ||||
\(163\) | −0.618034 | − | 1.90211i | −0.0484082 | − | 0.148985i | 0.923931 | − | 0.382560i | \(-0.124958\pi\) |
−0.972339 | + | 0.233575i | \(0.924958\pi\) | |||||||
\(164\) | 5.00000 | 0.390434 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | 3.70820 | + | 11.4127i | 0.286949 | + | 0.883140i | 0.985808 | + | 0.167879i | \(0.0536919\pi\) |
−0.698858 | + | 0.715260i | \(0.746308\pi\) | |||||||
\(168\) | −9.70820 | − | 7.05342i | −0.749004 | − | 0.544183i | ||||
\(169\) | 9.70820 | − | 7.05342i | 0.746785 | − | 0.542571i | ||||
\(170\) | −1.54508 | + | 4.75528i | −0.118503 | + | 0.364714i | ||||
\(171\) | 1.85410 | − | 5.70634i | 0.141787 | − | 0.436375i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.85410 | − | 3.52671i | −0.369051 | − | 0.268131i | 0.387767 | − | 0.921758i | \(-0.373247\pi\) |
−0.756817 | + | 0.653627i | \(0.773247\pi\) | |||||||
\(174\) | 5.56231 | + | 17.1190i | 0.421677 | + | 1.29779i | ||||
\(175\) | 8.00000 | 0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000 | 1.20263 | ||||||||
\(178\) | −2.78115 | − | 8.55951i | −0.208456 | − | 0.641562i | ||||
\(179\) | −19.4164 | − | 14.1068i | −1.45125 | − | 1.05440i | −0.985537 | − | 0.169460i | \(-0.945798\pi\) |
−0.465713 | − | 0.884936i | \(-0.654202\pi\) | |||||||
\(180\) | 0.809017 | − | 0.587785i | 0.0603006 | − | 0.0438109i | ||||
\(181\) | 0.309017 | − | 0.951057i | 0.0229691 | − | 0.0706915i | −0.938915 | − | 0.344149i | \(-0.888167\pi\) |
0.961884 | + | 0.273458i | \(0.0881674\pi\) | |||||||
\(182\) | −0.618034 | + | 1.90211i | −0.0458117 | + | 0.140994i | ||||
\(183\) | −9.70820 | + | 7.05342i | −0.717651 | + | 0.521404i | ||||
\(184\) | 4.85410 | + | 3.52671i | 0.357849 | + | 0.259993i | ||||
\(185\) | −0.927051 | − | 2.85317i | −0.0681581 | − | 0.209769i | ||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | 2.47214 | + | 7.60845i | 0.179821 | + | 0.553433i | ||||
\(190\) | −4.85410 | − | 3.52671i | −0.352154 | − | 0.255855i | ||||
\(191\) | −6.47214 | + | 4.70228i | −0.468307 | + | 0.340245i | −0.796781 | − | 0.604268i | \(-0.793466\pi\) |
0.328474 | + | 0.944513i | \(0.393466\pi\) | |||||||
\(192\) | 4.32624 | − | 13.3148i | 0.312219 | − | 0.960912i | ||||
\(193\) | −1.54508 | + | 4.75528i | −0.111218 | + | 0.342293i | −0.991139 | − | 0.132826i | \(-0.957595\pi\) |
0.879922 | + | 0.475119i | \(0.157595\pi\) | |||||||
\(194\) | 10.5172 | − | 7.64121i | 0.755092 | − | 0.548607i | ||||
\(195\) | −1.61803 | − | 1.17557i | −0.115870 | − | 0.0841844i | ||||
\(196\) | 0.927051 | + | 2.85317i | 0.0662179 | + | 0.203798i | ||||
\(197\) | −11.0000 | −0.783718 | −0.391859 | − | 0.920025i | \(-0.628168\pi\) | ||||
−0.391859 | + | 0.920025i | \(0.628168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 3.70820 | + | 11.4127i | 0.262210 | + | 0.806998i | ||||
\(201\) | −3.23607 | − | 2.35114i | −0.228255 | − | 0.165837i | ||||
\(202\) | 8.09017 | − | 5.87785i | 0.569222 | − | 0.413564i | ||||
\(203\) | −5.56231 | + | 17.1190i | −0.390397 | + | 1.20152i | ||||
\(204\) | 3.09017 | − | 9.51057i | 0.216355 | − | 0.665873i | ||||
\(205\) | 4.04508 | − | 2.93893i | 0.282521 | − | 0.205264i | ||||
\(206\) | −6.47214 | − | 4.70228i | −0.450935 | − | 0.327624i | ||||
\(207\) | 0.618034 | + | 1.90211i | 0.0429563 | + | 0.132206i | ||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.00000 | −0.276026 | ||||||||
\(211\) | 3.70820 | + | 11.4127i | 0.255283 | + | 0.785681i | 0.993774 | + | 0.111417i | \(0.0355390\pi\) |
−0.738490 | + | 0.674264i | \(0.764461\pi\) | |||||||
\(212\) | 7.28115 | + | 5.29007i | 0.500072 | + | 0.363323i | ||||
\(213\) | −19.4164 | + | 14.1068i | −1.33039 | + | 0.966585i | ||||
\(214\) | 1.85410 | − | 5.70634i | 0.126744 | − | 0.390077i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.70820 | + | 7.05342i | −0.660560 | + | 0.479925i | ||||
\(217\) | −3.23607 | − | 2.35114i | −0.219679 | − | 0.159606i | ||||
\(218\) | −3.39919 | − | 10.4616i | −0.230222 | − | 0.708550i | ||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00000 | −0.336336 | ||||||||
\(222\) | −1.85410 | − | 5.70634i | −0.124439 | − | 0.382984i | ||||
\(223\) | 16.1803 | + | 11.7557i | 1.08352 | + | 0.787220i | 0.978293 | − | 0.207228i | \(-0.0664443\pi\) |
0.105223 | + | 0.994449i | \(0.466444\pi\) | |||||||
\(224\) | 8.09017 | − | 5.87785i | 0.540547 | − | 0.392731i | ||||
\(225\) | −1.23607 | + | 3.80423i | −0.0824045 | + | 0.253615i | ||||
\(226\) | −2.78115 | + | 8.55951i | −0.185000 | + | 0.569370i | ||||
\(227\) | 19.4164 | − | 14.1068i | 1.28871 | − | 0.936304i | 0.288934 | − | 0.957349i | \(-0.406699\pi\) |
0.999779 | + | 0.0210448i | \(0.00669928\pi\) | |||||||
\(228\) | 9.70820 | + | 7.05342i | 0.642942 | + | 0.467124i | ||||
\(229\) | 2.78115 | + | 8.55951i | 0.183784 | + | 0.565628i | 0.999925 | − | 0.0122238i | \(-0.00389106\pi\) |
−0.816142 | + | 0.577852i | \(0.803891\pi\) | |||||||
\(230\) | 2.00000 | 0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −27.0000 | −1.77264 | ||||||||
\(233\) | −6.48936 | − | 19.9722i | −0.425132 | − | 1.30842i | −0.902868 | − | 0.429918i | \(-0.858542\pi\) |
0.477736 | − | 0.878503i | \(-0.341458\pi\) | |||||||
\(234\) | −0.809017 | − | 0.587785i | −0.0528871 | − | 0.0384247i | ||||
\(235\) | −1.61803 | + | 1.17557i | −0.105549 | + | 0.0766858i | ||||
\(236\) | −2.47214 | + | 7.60845i | −0.160922 | + | 0.495268i | ||||
\(237\) | −6.18034 | + | 19.0211i | −0.401456 | + | 1.23556i | ||||
\(238\) | −8.09017 | + | 5.87785i | −0.524408 | + | 0.381005i | ||||
\(239\) | −4.85410 | − | 3.52671i | −0.313986 | − | 0.228124i | 0.419619 | − | 0.907700i | \(-0.362164\pi\) |
−0.733605 | + | 0.679576i | \(0.762164\pi\) | |||||||
\(240\) | −0.618034 | − | 1.90211i | −0.0398939 | − | 0.122781i | ||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0000 | −0.641500 | ||||||||
\(244\) | −1.85410 | − | 5.70634i | −0.118697 | − | 0.365311i | ||||
\(245\) | 2.42705 | + | 1.76336i | 0.155059 | + | 0.112657i | ||||
\(246\) | 8.09017 | − | 5.87785i | 0.515810 | − | 0.374758i | ||||
\(247\) | 1.85410 | − | 5.70634i | 0.117974 | − | 0.363086i | ||||
\(248\) | 1.85410 | − | 5.70634i | 0.117736 | − | 0.362353i | ||||
\(249\) | −9.70820 | + | 7.05342i | −0.615232 | + | 0.446993i | ||||
\(250\) | 7.28115 | + | 5.29007i | 0.460501 | + | 0.334573i | ||||
\(251\) | −0.618034 | − | 1.90211i | −0.0390100 | − | 0.120060i | 0.929655 | − | 0.368431i | \(-0.120105\pi\) |
−0.968665 | + | 0.248371i | \(0.920105\pi\) | |||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.0000 | −1.00393 | ||||||||
\(255\) | −3.09017 | − | 9.51057i | −0.193514 | − | 0.595575i | ||||
\(256\) | 13.7533 | + | 9.99235i | 0.859581 | + | 0.624522i | ||||
\(257\) | −15.3713 | + | 11.1679i | −0.958837 | + | 0.696636i | −0.952880 | − | 0.303347i | \(-0.901896\pi\) |
−0.00595648 | + | 0.999982i | \(0.501896\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.85410 | − | 5.70634i | 0.115208 | − | 0.354575i | ||||
\(260\) | 0.809017 | − | 0.587785i | 0.0501731 | − | 0.0364529i | ||||
\(261\) | −7.28115 | − | 5.29007i | −0.450692 | − | 0.327447i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.0000 | −1.35658 | −0.678289 | − | 0.734795i | \(-0.737278\pi\) | ||||
−0.678289 | + | 0.734795i | \(0.737278\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | −3.70820 | − | 11.4127i | −0.227365 | − | 0.699756i | ||||
\(267\) | 14.5623 | + | 10.5801i | 0.891199 | + | 0.647494i | ||||
\(268\) | 1.61803 | − | 1.17557i | 0.0988372 | − | 0.0718094i | ||||
\(269\) | 0.309017 | − | 0.951057i | 0.0188411 | − | 0.0579869i | −0.941194 | − | 0.337867i | \(-0.890295\pi\) |
0.960035 | + | 0.279880i | \(0.0902946\pi\) | |||||||
\(270\) | −1.23607 | + | 3.80423i | −0.0752247 | + | 0.231518i | ||||
\(271\) | −16.1803 | + | 11.7557i | −0.982886 | + | 0.714108i | −0.958352 | − | 0.285591i | \(-0.907810\pi\) |
−0.0245340 | + | 0.999699i | \(0.507810\pi\) | |||||||
\(272\) | −4.04508 | − | 2.93893i | −0.245269 | − | 0.178199i | ||||
\(273\) | −1.23607 | − | 3.80423i | −0.0748102 | − | 0.230242i | ||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.00000 | −0.240772 | ||||||||
\(277\) | 0.309017 | + | 0.951057i | 0.0185670 | + | 0.0571434i | 0.959911 | − | 0.280306i | \(-0.0904359\pi\) |
−0.941344 | + | 0.337449i | \(0.890436\pi\) | |||||||
\(278\) | 1.61803 | + | 1.17557i | 0.0970432 | + | 0.0705060i | ||||
\(279\) | 1.61803 | − | 1.17557i | 0.0968692 | − | 0.0703796i | ||||
\(280\) | 1.85410 | − | 5.70634i | 0.110804 | − | 0.341019i | ||||
\(281\) | 1.85410 | − | 5.70634i | 0.110606 | − | 0.340412i | −0.880399 | − | 0.474234i | \(-0.842725\pi\) |
0.991005 | + | 0.133822i | \(0.0427251\pi\) | |||||||
\(282\) | −3.23607 | + | 2.35114i | −0.192705 | + | 0.140008i | ||||
\(283\) | −22.6525 | − | 16.4580i | −1.34655 | − | 0.978326i | −0.999176 | − | 0.0405993i | \(-0.987073\pi\) |
−0.347374 | − | 0.937727i | \(-0.612927\pi\) | |||||||
\(284\) | −3.70820 | − | 11.4127i | −0.220041 | − | 0.677218i | ||||
\(285\) | 12.0000 | 0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0000 | 0.590281 | ||||||||
\(288\) | 1.54508 | + | 4.75528i | 0.0910450 | + | 0.280208i | ||||
\(289\) | −6.47214 | − | 4.70228i | −0.380714 | − | 0.276605i | ||||
\(290\) | −7.28115 | + | 5.29007i | −0.427564 | + | 0.310643i | ||||
\(291\) | −8.03444 | + | 24.7275i | −0.470987 | + | 1.44955i | ||||
\(292\) | 0.618034 | − | 1.90211i | 0.0361677 | − | 0.111313i | ||||
\(293\) | −7.28115 | + | 5.29007i | −0.425369 | + | 0.309049i | −0.779795 | − | 0.626035i | \(-0.784677\pi\) |
0.354425 | + | 0.935084i | \(0.384677\pi\) | |||||||
\(294\) | 4.85410 | + | 3.52671i | 0.283097 | + | 0.205682i | ||||
\(295\) | 2.47214 | + | 7.60845i | 0.143933 | + | 0.442981i | ||||
\(296\) | 9.00000 | 0.523114 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.0000 | 0.984784 | ||||||||
\(299\) | 0.618034 | + | 1.90211i | 0.0357418 | + | 0.110002i | ||||
\(300\) | −6.47214 | − | 4.70228i | −0.373669 | − | 0.271486i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.94427 | + | 15.2169i | −0.284511 | + | 0.875634i | ||||
\(303\) | −6.18034 | + | 19.0211i | −0.355051 | + | 1.09274i | ||||
\(304\) | 4.85410 | − | 3.52671i | 0.278402 | − | 0.202271i | ||||
\(305\) | −4.85410 | − | 3.52671i | −0.277945 | − | 0.201939i | ||||
\(306\) | −1.54508 | − | 4.75528i | −0.0883266 | − | 0.271841i | ||||
\(307\) | −22.0000 | −1.25561 | −0.627803 | − | 0.778372i | \(-0.716046\pi\) | ||||
−0.627803 | + | 0.778372i | \(0.716046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0000 | 0.910208 | ||||||||
\(310\) | −0.618034 | − | 1.90211i | −0.0351020 | − | 0.108033i | ||||
\(311\) | −19.4164 | − | 14.1068i | −1.10100 | − | 0.799926i | −0.119780 | − | 0.992800i | \(-0.538219\pi\) |
−0.981223 | + | 0.192875i | \(0.938219\pi\) | |||||||
\(312\) | 4.85410 | − | 3.52671i | 0.274809 | − | 0.199661i | ||||
\(313\) | 7.10739 | − | 21.8743i | 0.401733 | − | 1.23641i | −0.521859 | − | 0.853032i | \(-0.674761\pi\) |
0.923592 | − | 0.383377i | \(-0.125239\pi\) | |||||||
\(314\) | 0.618034 | − | 1.90211i | 0.0348777 | − | 0.107342i | ||||
\(315\) | 1.61803 | − | 1.17557i | 0.0911659 | − | 0.0662359i | ||||
\(316\) | −8.09017 | − | 5.87785i | −0.455108 | − | 0.330655i | ||||
\(317\) | −0.618034 | − | 1.90211i | −0.0347122 | − | 0.106833i | 0.932199 | − | 0.361946i | \(-0.117887\pi\) |
−0.966911 | + | 0.255113i | \(0.917887\pi\) | |||||||
\(318\) | 18.0000 | 1.00939 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.00000 | 0.391312 | ||||||||
\(321\) | 3.70820 | + | 11.4127i | 0.206972 | + | 0.636994i | ||||
\(322\) | 3.23607 | + | 2.35114i | 0.180339 | + | 0.131024i | ||||
\(323\) | 24.2705 | − | 17.6336i | 1.35045 | − | 0.981157i | ||||
\(324\) | 3.39919 | − | 10.4616i | 0.188844 | − | 0.581201i | ||||
\(325\) | −1.23607 | + | 3.80423i | −0.0685647 | + | 0.211020i | ||||
\(326\) | 1.61803 | − | 1.17557i | 0.0896146 | − | 0.0651088i | ||||
\(327\) | 17.7984 | + | 12.9313i | 0.984252 | + | 0.715101i | ||||
\(328\) | 4.63525 | + | 14.2658i | 0.255939 | + | 0.787700i | ||||
\(329\) | −4.00000 | −0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | −1.85410 | − | 5.70634i | −0.101757 | − | 0.313176i | ||||
\(333\) | 2.42705 | + | 1.76336i | 0.133002 | + | 0.0966313i | ||||
\(334\) | −9.70820 | + | 7.05342i | −0.531209 | + | 0.385946i | ||||
\(335\) | 0.618034 | − | 1.90211i | 0.0337668 | − | 0.103924i | ||||
\(336\) | 1.23607 | − | 3.80423i | 0.0674330 | − | 0.207538i | ||||
\(337\) | 10.5172 | − | 7.64121i | 0.572910 | − | 0.416243i | −0.263251 | − | 0.964727i | \(-0.584795\pi\) |
0.836161 | + | 0.548484i | \(0.184795\pi\) | |||||||
\(338\) | 9.70820 | + | 7.05342i | 0.528057 | + | 0.383656i | ||||
\(339\) | −5.56231 | − | 17.1190i | −0.302103 | − | 0.929777i | ||||
\(340\) | 5.00000 | 0.271163 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.00000 | 0.324443 | ||||||||
\(343\) | 6.18034 | + | 19.0211i | 0.333707 | + | 1.02704i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.23607 | + | 2.35114i | −0.174224 | + | 0.126581i | ||||
\(346\) | 1.85410 | − | 5.70634i | 0.0996771 | − | 0.306775i | ||||
\(347\) | 8.65248 | − | 26.6296i | 0.464489 | − | 1.42955i | −0.395135 | − | 0.918623i | \(-0.629302\pi\) |
0.859624 | − | 0.510928i | \(-0.170698\pi\) | |||||||
\(348\) | 14.5623 | − | 10.5801i | 0.780622 | − | 0.567155i | ||||
\(349\) | 21.8435 | + | 15.8702i | 1.16925 | + | 0.849512i | 0.990919 | − | 0.134458i | \(-0.0429292\pi\) |
0.178334 | + | 0.983970i | \(0.442929\pi\) | |||||||
\(350\) | 2.47214 | + | 7.60845i | 0.132141 | + | 0.406689i | ||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00000 | −0.479022 | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239511 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(354\) | 4.94427 | + | 15.2169i | 0.262785 | + | 0.808769i | ||||
\(355\) | −9.70820 | − | 7.05342i | −0.515258 | − | 0.374357i | ||||
\(356\) | −7.28115 | + | 5.29007i | −0.385900 | + | 0.280373i | ||||
\(357\) | 6.18034 | − | 19.0211i | 0.327098 | − | 1.00670i | ||||
\(358\) | 7.41641 | − | 22.8254i | 0.391969 | − | 1.20636i | ||||
\(359\) | 1.61803 | − | 1.17557i | 0.0853966 | − | 0.0620442i | −0.544268 | − | 0.838912i | \(-0.683192\pi\) |
0.629664 | + | 0.776867i | \(0.283192\pi\) | |||||||
\(360\) | 2.42705 | + | 1.76336i | 0.127917 | + | 0.0929370i | ||||
\(361\) | 5.25329 | + | 16.1680i | 0.276489 | + | 0.850945i | ||||
\(362\) | 1.00000 | 0.0525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −0.618034 | − | 1.90211i | −0.0323494 | − | 0.0995611i | ||||
\(366\) | −9.70820 | − | 7.05342i | −0.507456 | − | 0.368688i | ||||
\(367\) | 11.3262 | − | 8.22899i | 0.591225 | − | 0.429550i | −0.251529 | − | 0.967850i | \(-0.580933\pi\) |
0.842753 | + | 0.538300i | \(0.180933\pi\) | |||||||
\(368\) | −0.618034 | + | 1.90211i | −0.0322172 | + | 0.0991545i | ||||
\(369\) | −1.54508 | + | 4.75528i | −0.0804339 | + | 0.247550i | ||||
\(370\) | 2.42705 | − | 1.76336i | 0.126176 | − | 0.0916725i | ||||
\(371\) | 14.5623 | + | 10.5801i | 0.756037 | + | 0.549293i | ||||
\(372\) | 1.23607 | + | 3.80423i | 0.0640871 | + | 0.197240i | ||||
\(373\) | 22.0000 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0000 | −0.929516 | ||||||||
\(376\) | −1.85410 | − | 5.70634i | −0.0956180 | − | 0.294282i | ||||
\(377\) | −7.28115 | − | 5.29007i | −0.374998 | − | 0.272452i | ||||
\(378\) | −6.47214 | + | 4.70228i | −0.332891 | + | 0.241859i | ||||
\(379\) | −9.88854 | + | 30.4338i | −0.507940 | + | 1.56328i | 0.287830 | + | 0.957681i | \(0.407066\pi\) |
−0.795771 | + | 0.605598i | \(0.792934\pi\) | |||||||
\(380\) | −1.85410 | + | 5.70634i | −0.0951134 | + | 0.292729i | ||||
\(381\) | 25.8885 | − | 18.8091i | 1.32631 | − | 0.963621i | ||||
\(382\) | −6.47214 | − | 4.70228i | −0.331143 | − | 0.240590i | ||||
\(383\) | 6.18034 | + | 19.0211i | 0.315801 | + | 0.971934i | 0.975424 | + | 0.220338i | \(0.0707160\pi\) |
−0.659623 | + | 0.751597i | \(0.729284\pi\) | |||||||
\(384\) | −6.00000 | −0.306186 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.5172 | − | 7.64121i | −0.533931 | − | 0.387924i | ||||
\(389\) | 2.42705 | − | 1.76336i | 0.123056 | − | 0.0894057i | −0.524555 | − | 0.851377i | \(-0.675768\pi\) |
0.647611 | + | 0.761971i | \(0.275768\pi\) | |||||||
\(390\) | 0.618034 | − | 1.90211i | 0.0312954 | − | 0.0963172i | ||||
\(391\) | −3.09017 | + | 9.51057i | −0.156277 | + | 0.480970i | ||||
\(392\) | −7.28115 | + | 5.29007i | −0.367754 | + | 0.267189i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.39919 | − | 10.4616i | −0.171249 | − | 0.527049i | ||||
\(395\) | −10.0000 | −0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0000 | 0.652451 | 0.326226 | − | 0.945292i | \(-0.394223\pi\) | ||||
0.326226 | + | 0.945292i | \(0.394223\pi\) | |||||||
\(398\) | 7.41641 | + | 22.8254i | 0.371751 | + | 1.14413i | ||||
\(399\) | 19.4164 | + | 14.1068i | 0.972036 | + | 0.706226i | ||||
\(400\) | −3.23607 | + | 2.35114i | −0.161803 | + | 0.117557i | ||||
\(401\) | 7.10739 | − | 21.8743i | 0.354926 | − | 1.09235i | −0.601126 | − | 0.799154i | \(-0.705281\pi\) |
0.956052 | − | 0.293196i | \(-0.0947189\pi\) | |||||||
\(402\) | 1.23607 | − | 3.80423i | 0.0616495 | − | 0.189738i | ||||
\(403\) | 1.61803 | − | 1.17557i | 0.0806000 | − | 0.0585593i | ||||
\(404\) | −8.09017 | − | 5.87785i | −0.402501 | − | 0.292434i | ||||
\(405\) | −3.39919 | − | 10.4616i | −0.168907 | − | 0.519842i | ||||
\(406\) | −18.0000 | −0.893325 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 30.0000 | 1.48522 | ||||||||
\(409\) | −6.48936 | − | 19.9722i | −0.320878 | − | 0.987561i | −0.973267 | − | 0.229677i | \(-0.926233\pi\) |
0.652389 | − | 0.757884i | \(-0.273767\pi\) | |||||||
\(410\) | 4.04508 | + | 2.93893i | 0.199773 | + | 0.145143i | ||||
\(411\) | 16.1803 | − | 11.7557i | 0.798117 | − | 0.579866i | ||||
\(412\) | −2.47214 | + | 7.60845i | −0.121793 | + | 0.374842i | ||||
\(413\) | −4.94427 | + | 15.2169i | −0.243292 | + | 0.748775i | ||||
\(414\) | −1.61803 | + | 1.17557i | −0.0795220 | + | 0.0577761i | ||||
\(415\) | −4.85410 | − | 3.52671i | −0.238278 | − | 0.173119i | ||||
\(416\) | 1.54508 | + | 4.75528i | 0.0757540 | + | 0.233147i | ||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.00000 | 0.0977064 | 0.0488532 | − | 0.998806i | \(-0.484443\pi\) | ||||
0.0488532 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(420\) | 1.23607 | + | 3.80423i | 0.0603139 | + | 0.185627i | ||||
\(421\) | −10.5172 | − | 7.64121i | −0.512578 | − | 0.372410i | 0.301223 | − | 0.953554i | \(-0.402605\pi\) |
−0.813801 | + | 0.581144i | \(0.802605\pi\) | |||||||
\(422\) | −9.70820 | + | 7.05342i | −0.472588 | + | 0.343355i | ||||
\(423\) | 0.618034 | − | 1.90211i | 0.0300498 | − | 0.0924839i | ||||
\(424\) | −8.34346 | + | 25.6785i | −0.405194 | + | 1.24706i | ||||
\(425\) | −16.1803 | + | 11.7557i | −0.784862 | + | 0.570235i | ||||
\(426\) | −19.4164 | − | 14.1068i | −0.940728 | − | 0.683479i | ||||
\(427\) | −3.70820 | − | 11.4127i | −0.179453 | − | 0.552298i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.70820 | + | 11.4127i | 0.178618 | + | 0.549729i | 0.999780 | − | 0.0209654i | \(-0.00667397\pi\) |
−0.821162 | + | 0.570695i | \(0.806674\pi\) | |||||||
\(432\) | −3.23607 | − | 2.35114i | −0.155695 | − | 0.113119i | ||||
\(433\) | −15.3713 | + | 11.1679i | −0.738699 | + | 0.536696i | −0.892303 | − | 0.451436i | \(-0.850912\pi\) |
0.153605 | + | 0.988132i | \(0.450912\pi\) | |||||||
\(434\) | 1.23607 | − | 3.80423i | 0.0593332 | − | 0.182609i | ||||
\(435\) | 5.56231 | − | 17.1190i | 0.266692 | − | 0.820794i | ||||
\(436\) | −8.89919 | + | 6.46564i | −0.426194 | + | 0.309648i | ||||
\(437\) | −9.70820 | − | 7.05342i | −0.464406 | − | 0.337411i | ||||
\(438\) | −1.23607 | − | 3.80423i | −0.0590616 | − | 0.181773i | ||||
\(439\) | 22.0000 | 1.05000 | 0.525001 | − | 0.851101i | \(-0.324065\pi\) | ||||
0.525001 | + | 0.851101i | \(0.324065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −1.54508 | − | 4.75528i | −0.0734922 | − | 0.226186i | ||||
\(443\) | 16.1803 | + | 11.7557i | 0.768751 | + | 0.558530i | 0.901582 | − | 0.432608i | \(-0.142407\pi\) |
−0.132831 | + | 0.991139i | \(0.542407\pi\) | |||||||
\(444\) | −4.85410 | + | 3.52671i | −0.230365 | + | 0.167370i | ||||
\(445\) | −2.78115 | + | 8.55951i | −0.131839 | + | 0.405760i | ||||
\(446\) | −6.18034 | + | 19.0211i | −0.292648 | + | 0.900677i | ||||
\(447\) | −27.5066 | + | 19.9847i | −1.30102 | + | 0.945244i | ||||
\(448\) | 11.3262 | + | 8.22899i | 0.535114 | + | 0.388783i | ||||
\(449\) | −4.01722 | − | 12.3637i | −0.189584 | − | 0.583481i | 0.810413 | − | 0.585859i | \(-0.199243\pi\) |
−0.999997 | + | 0.00237857i | \(0.999243\pi\) | |||||||
\(450\) | −4.00000 | −0.188562 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.00000 | 0.423324 | ||||||||
\(453\) | −9.88854 | − | 30.4338i | −0.464604 | − | 1.42991i | ||||
\(454\) | 19.4164 | + | 14.1068i | 0.911257 | + | 0.662067i | ||||
\(455\) | 1.61803 | − | 1.17557i | 0.0758546 | − | 0.0551116i | ||||
\(456\) | −11.1246 | + | 34.2380i | −0.520958 | + | 1.60334i | ||||
\(457\) | 12.0517 | − | 37.0912i | 0.563753 | − | 1.73505i | −0.107875 | − | 0.994165i | \(-0.534405\pi\) |
0.671628 | − | 0.740889i | \(-0.265595\pi\) | |||||||
\(458\) | −7.28115 | + | 5.29007i | −0.340226 | + | 0.247189i | ||||
\(459\) | −16.1803 | − | 11.7557i | −0.755234 | − | 0.548709i | ||||
\(460\) | −0.618034 | − | 1.90211i | −0.0288160 | − | 0.0886865i | ||||
\(461\) | 33.0000 | 1.53696 | 0.768482 | − | 0.639872i | \(-0.221013\pi\) | ||||
0.768482 | + | 0.639872i | \(0.221013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | −2.78115 | − | 8.55951i | −0.129112 | − | 0.397365i | ||||
\(465\) | 3.23607 | + | 2.35114i | 0.150069 | + | 0.109032i | ||||
\(466\) | 16.9894 | − | 12.3435i | 0.787017 | − | 0.571801i | ||||
\(467\) | 3.70820 | − | 11.4127i | 0.171595 | − | 0.528116i | −0.827866 | − | 0.560925i | \(-0.810445\pi\) |
0.999462 | + | 0.0328096i | \(0.0104455\pi\) | |||||||
\(468\) | −0.309017 | + | 0.951057i | −0.0142843 | + | 0.0439626i | ||||
\(469\) | 3.23607 | − | 2.35114i | 0.149428 | − | 0.108566i | ||||
\(470\) | −1.61803 | − | 1.17557i | −0.0746343 | − | 0.0542250i | ||||
\(471\) | 1.23607 | + | 3.80423i | 0.0569550 | + | 0.175289i | ||||
\(472\) | −24.0000 | −1.10469 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −20.0000 | −0.918630 | ||||||||
\(475\) | −7.41641 | − | 22.8254i | −0.340288 | − | 1.04730i | ||||
\(476\) | 8.09017 | + | 5.87785i | 0.370812 | + | 0.269411i | ||||
\(477\) | −7.28115 | + | 5.29007i | −0.333381 | + | 0.242216i | ||||
\(478\) | 1.85410 | − | 5.70634i | 0.0848047 | − | 0.261002i | ||||
\(479\) | −4.94427 | + | 15.2169i | −0.225910 | + | 0.695278i | 0.772288 | + | 0.635272i | \(0.219112\pi\) |
−0.998198 | + | 0.0600061i | \(0.980888\pi\) | |||||||
\(480\) | −8.09017 | + | 5.87785i | −0.369264 | + | 0.268286i | ||||
\(481\) | 2.42705 | + | 1.76336i | 0.110664 | + | 0.0804021i | ||||
\(482\) | 6.79837 | + | 20.9232i | 0.309657 | + | 0.953028i | ||||
\(483\) | −8.00000 | −0.364013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0000 | −0.590300 | ||||||||
\(486\) | −3.09017 | − | 9.51057i | −0.140173 | − | 0.431408i | ||||
\(487\) | −1.61803 | − | 1.17557i | −0.0733201 | − | 0.0532702i | 0.550521 | − | 0.834821i | \(-0.314429\pi\) |
−0.623842 | + | 0.781551i | \(0.714429\pi\) | |||||||
\(488\) | 14.5623 | − | 10.5801i | 0.659205 | − | 0.478940i | ||||
\(489\) | −1.23607 | + | 3.80423i | −0.0558969 | + | 0.172033i | ||||
\(490\) | −0.927051 | + | 2.85317i | −0.0418799 | + | 0.128893i | ||||
\(491\) | 1.61803 | − | 1.17557i | 0.0730209 | − | 0.0530528i | −0.550676 | − | 0.834719i | \(-0.685630\pi\) |
0.623697 | + | 0.781666i | \(0.285630\pi\) | |||||||
\(492\) | −8.09017 | − | 5.87785i | −0.364733 | − | 0.264994i | ||||
\(493\) | −13.9058 | − | 42.7975i | −0.626284 | − | 1.92750i | ||||
\(494\) | 6.00000 | 0.269953 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −7.41641 | − | 22.8254i | −0.332671 | − | 1.02386i | ||||
\(498\) | −9.70820 | − | 7.05342i | −0.435035 | − | 0.316071i | ||||
\(499\) | −6.47214 | + | 4.70228i | −0.289733 | + | 0.210503i | −0.723151 | − | 0.690690i | \(-0.757307\pi\) |
0.433419 | + | 0.901193i | \(0.357307\pi\) | |||||||
\(500\) | 2.78115 | − | 8.55951i | 0.124377 | − | 0.382793i | ||||
\(501\) | 7.41641 | − | 22.8254i | 0.331341 | − | 1.01976i | ||||
\(502\) | 1.61803 | − | 1.17557i | 0.0722164 | − | 0.0524683i | ||||
\(503\) | 30.7426 | + | 22.3358i | 1.37075 | + | 0.995906i | 0.997678 | + | 0.0681020i | \(0.0216943\pi\) |
0.373068 | + | 0.927804i | \(0.378306\pi\) | |||||||
\(504\) | 1.85410 | + | 5.70634i | 0.0825883 | + | 0.254181i | ||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.0000 | −1.06588 | ||||||||
\(508\) | 4.94427 | + | 15.2169i | 0.219367 | + | 0.675141i | ||||
\(509\) | 33.9787 | + | 24.6870i | 1.50608 | + | 1.09423i | 0.967880 | + | 0.251414i | \(0.0808957\pi\) |
0.538200 | + | 0.842817i | \(0.319104\pi\) | |||||||
\(510\) | 8.09017 | − | 5.87785i | 0.358239 | − | 0.260276i | ||||
\(511\) | 1.23607 | − | 3.80423i | 0.0546804 | − | 0.168289i | ||||
\(512\) | −3.39919 | + | 10.4616i | −0.150224 | + | 0.462343i | ||||
\(513\) | 19.4164 | − | 14.1068i | 0.857255 | − | 0.622832i | ||||
\(514\) | −15.3713 | − | 11.1679i | −0.678000 | − | 0.492596i | ||||
\(515\) | 2.47214 | + | 7.60845i | 0.108935 | + | 0.335268i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.00000 | 0.263625 | ||||||||
\(519\) | 3.70820 | + | 11.4127i | 0.162772 | + | 0.500961i | ||||
\(520\) | 2.42705 | + | 1.76336i | 0.106433 | + | 0.0773283i | ||||
\(521\) | −24.2705 | + | 17.6336i | −1.06331 | + | 0.772540i | −0.974698 | − | 0.223526i | \(-0.928243\pi\) |
−0.0886124 | + | 0.996066i | \(0.528243\pi\) | |||||||
\(522\) | 2.78115 | − | 8.55951i | 0.121728 | − | 0.374640i | ||||
\(523\) | −4.94427 | + | 15.2169i | −0.216198 | + | 0.665389i | 0.782868 | + | 0.622187i | \(0.213756\pi\) |
−0.999066 | + | 0.0432015i | \(0.986244\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.9443 | − | 9.40456i | −0.564934 | − | 0.410449i | ||||
\(526\) | −6.79837 | − | 20.9232i | −0.296423 | − | 0.912297i | ||||
\(527\) | 10.0000 | 0.435607 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 2.78115 | + | 8.55951i | 0.120806 | + | 0.371801i | ||||
\(531\) | −6.47214 | − | 4.70228i | −0.280867 | − | 0.204062i | ||||
\(532\) | −9.70820 | + | 7.05342i | −0.420904 | + | 0.305805i | ||||
\(533\) | −1.54508 | + | 4.75528i | −0.0669251 | + | 0.205974i | ||||
\(534\) | −5.56231 | + | 17.1190i | −0.240705 | + | 0.740812i | ||||
\(535\) | −4.85410 | + | 3.52671i | −0.209861 | + | 0.152473i | ||||
\(536\) | 4.85410 | + | 3.52671i | 0.209665 | + | 0.152331i | ||||
\(537\) | 14.8328 | + | 45.6507i | 0.640083 | + | 1.96997i | ||||
\(538\) | 1.00000 | 0.0431131 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | 10.5066 | + | 32.3359i | 0.451713 | + | 1.39023i | 0.874951 | + | 0.484211i | \(0.160893\pi\) |
−0.423238 | + | 0.906019i | \(0.639107\pi\) | |||||||
\(542\) | −16.1803 | − | 11.7557i | −0.695005 | − | 0.504951i | ||||
\(543\) | −1.61803 | + | 1.17557i | −0.0694365 | + | 0.0504486i | ||||
\(544\) | −7.72542 | + | 23.7764i | −0.331225 | + | 1.01941i | ||||
\(545\) | −3.39919 | + | 10.4616i | −0.145605 | + | 0.448127i | ||||
\(546\) | 3.23607 | − | 2.35114i | 0.138491 | − | 0.100620i | ||||
\(547\) | 12.9443 | + | 9.40456i | 0.553457 | + | 0.402110i | 0.829058 | − | 0.559162i | \(-0.188877\pi\) |
−0.275601 | + | 0.961272i | \(0.588877\pi\) | |||||||
\(548\) | 3.09017 | + | 9.51057i | 0.132006 | + | 0.406271i | ||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.0000 | 2.30048 | ||||||||
\(552\) | −3.70820 | − | 11.4127i | −0.157832 | − | 0.485756i | ||||
\(553\) | −16.1803 | − | 11.7557i | −0.688058 | − | 0.499903i | ||||
\(554\) | −0.809017 | + | 0.587785i | −0.0343718 | + | 0.0249726i | ||||
\(555\) | −1.85410 | + | 5.70634i | −0.0787022 | + | 0.242221i | ||||
\(556\) | 0.618034 | − | 1.90211i | 0.0262105 | − | 0.0806676i | ||||
\(557\) | 1.61803 | − | 1.17557i | 0.0685583 | − | 0.0498105i | −0.552978 | − | 0.833196i | \(-0.686509\pi\) |
0.621537 | + | 0.783385i | \(0.286509\pi\) | |||||||
\(558\) | 1.61803 | + | 1.17557i | 0.0684968 | + | 0.0497659i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 10.5066 | + | 32.3359i | 0.442799 | + | 1.36280i | 0.884879 | + | 0.465821i | \(0.154241\pi\) |
−0.442080 | + | 0.896976i | \(0.645759\pi\) | |||||||
\(564\) | 3.23607 | + | 2.35114i | 0.136263 | + | 0.0990009i | ||||
\(565\) | 7.28115 | − | 5.29007i | 0.306320 | − | 0.222555i | ||||
\(566\) | 8.65248 | − | 26.6296i | 0.363691 | − | 1.11932i | ||||
\(567\) | 6.79837 | − | 20.9232i | 0.285505 | − | 0.878694i | ||||
\(568\) | 29.1246 | − | 21.1603i | 1.22204 | − | 0.887865i | ||||
\(569\) | −4.85410 | − | 3.52671i | −0.203495 | − | 0.147847i | 0.481371 | − | 0.876517i | \(-0.340139\pi\) |
−0.684865 | + | 0.728670i | \(0.740139\pi\) | |||||||
\(570\) | 3.70820 | + | 11.4127i | 0.155320 | + | 0.478024i | ||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | 3.09017 | + | 9.51057i | 0.128981 | + | 0.396963i | ||||
\(575\) | 6.47214 | + | 4.70228i | 0.269907 | + | 0.196099i | ||||
\(576\) | −5.66312 | + | 4.11450i | −0.235963 | + | 0.171437i | ||||
\(577\) | −6.48936 | + | 19.9722i | −0.270155 | + | 0.831453i | 0.720305 | + | 0.693657i | \(0.244002\pi\) |
−0.990461 | + | 0.137796i | \(0.955998\pi\) | |||||||
\(578\) | 2.47214 | − | 7.60845i | 0.102827 | − | 0.316470i | ||||
\(579\) | 8.09017 | − | 5.87785i | 0.336216 | − | 0.244275i | ||||
\(580\) | 7.28115 | + | 5.29007i | 0.302333 | + | 0.219658i | ||||
\(581\) | −3.70820 | − | 11.4127i | −0.153842 | − | 0.473478i | ||||
\(582\) | −26.0000 | −1.07773 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0.309017 | + | 0.951057i | 0.0127763 | + | 0.0393213i | ||||
\(586\) | −7.28115 | − | 5.29007i | −0.300782 | − | 0.218531i | ||||
\(587\) | 11.3262 | − | 8.22899i | 0.467484 | − | 0.339647i | −0.328976 | − | 0.944338i | \(-0.606704\pi\) |
0.796460 | + | 0.604691i | \(0.206704\pi\) | |||||||
\(588\) | 1.85410 | − | 5.70634i | 0.0764619 | − | 0.235325i | ||||
\(589\) | −3.70820 | + | 11.4127i | −0.152794 | + | 0.470251i | ||||
\(590\) | −6.47214 | + | 4.70228i | −0.266454 | + | 0.193590i | ||||
\(591\) | 17.7984 | + | 12.9313i | 0.732127 | + | 0.531922i | ||||
\(592\) | 0.927051 | + | 2.85317i | 0.0381016 | + | 0.117265i | ||||
\(593\) | 11.0000 | 0.451716 | 0.225858 | − | 0.974160i | \(-0.427481\pi\) | ||||
0.225858 | + | 0.974160i | \(0.427481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | 0.409960 | ||||||||
\(596\) | −5.25329 | − | 16.1680i | −0.215183 | − | 0.662265i | ||||
\(597\) | −38.8328 | − | 28.2137i | −1.58932 | − | 1.15471i | ||||
\(598\) | −1.61803 | + | 1.17557i | −0.0661663 | + | 0.0480727i | ||||
\(599\) | 10.5066 | − | 32.3359i | 0.429287 | − | 1.32121i | −0.469542 | − | 0.882910i | \(-0.655581\pi\) |
0.898829 | − | 0.438300i | \(-0.144419\pi\) | |||||||
\(600\) | 7.41641 | − | 22.8254i | 0.302774 | − | 0.931841i | ||||
\(601\) | 10.5172 | − | 7.64121i | 0.429006 | − | 0.311691i | −0.352245 | − | 0.935908i | \(-0.614582\pi\) |
0.781251 | + | 0.624216i | \(0.214582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.618034 | + | 1.90211i | 0.0251683 | + | 0.0774600i | ||||
\(604\) | 16.0000 | 0.651031 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.0000 | −0.812444 | ||||||||
\(607\) | −3.09017 | − | 9.51057i | −0.125426 | − | 0.386022i | 0.868552 | − | 0.495597i | \(-0.165051\pi\) |
−0.993978 | + | 0.109576i | \(0.965051\pi\) | |||||||
\(608\) | −24.2705 | − | 17.6336i | −0.984299 | − | 0.715135i | ||||
\(609\) | 29.1246 | − | 21.1603i | 1.18019 | − | 0.857457i | ||||
\(610\) | 1.85410 | − | 5.70634i | 0.0750704 | − | 0.231043i | ||||
\(611\) | 0.618034 | − | 1.90211i | 0.0250030 | − | 0.0769513i | ||||
\(612\) | −4.04508 | + | 2.93893i | −0.163513 | + | 0.118799i | ||||
\(613\) | −13.7533 | − | 9.99235i | −0.555490 | − | 0.403587i | 0.274315 | − | 0.961640i | \(-0.411549\pi\) |
−0.829806 | + | 0.558053i | \(0.811549\pi\) | |||||||
\(614\) | −6.79837 | − | 20.9232i | −0.274360 | − | 0.844393i | ||||
\(615\) | −10.0000 | −0.403239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00000 | −0.362326 | −0.181163 | − | 0.983453i | \(-0.557986\pi\) | ||||
−0.181163 | + | 0.983453i | \(0.557986\pi\) | |||||||
\(618\) | 4.94427 | + | 15.2169i | 0.198888 | + | 0.612114i | ||||
\(619\) | −1.61803 | − | 1.17557i | −0.0650343 | − | 0.0472502i | 0.554793 | − | 0.831988i | \(-0.312797\pi\) |
−0.619827 | + | 0.784738i | \(0.712797\pi\) | |||||||
\(620\) | −1.61803 | + | 1.17557i | −0.0649818 | + | 0.0472120i | ||||
\(621\) | −2.47214 | + | 7.60845i | −0.0992034 | + | 0.305317i | ||||
\(622\) | 7.41641 | − | 22.8254i | 0.297371 | − | 0.915213i | ||||
\(623\) | −14.5623 | + | 10.5801i | −0.583426 | + | 0.423884i | ||||
\(624\) | 1.61803 | + | 1.17557i | 0.0647732 | + | 0.0470605i | ||||
\(625\) | 3.39919 | + | 10.4616i | 0.135967 | + | 0.418465i | ||||
\(626\) | 23.0000 | 0.919265 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | 4.63525 | + | 14.2658i | 0.184820 | + | 0.568817i | ||||
\(630\) | 1.61803 | + | 1.17557i | 0.0644640 | + | 0.0468358i | ||||
\(631\) | 11.3262 | − | 8.22899i | 0.450890 | − | 0.327591i | −0.339057 | − | 0.940766i | \(-0.610108\pi\) |
0.789947 | + | 0.613175i | \(0.210108\pi\) | |||||||
\(632\) | 9.27051 | − | 28.5317i | 0.368761 | − | 1.13493i | ||||
\(633\) | 7.41641 | − | 22.8254i | 0.294776 | − | 0.907226i | ||||
\(634\) | 1.61803 | − | 1.17557i | 0.0642603 | − | 0.0466879i | ||||
\(635\) | 12.9443 | + | 9.40456i | 0.513678 | + | 0.373209i | ||||
\(636\) | −5.56231 | − | 17.1190i | −0.220560 | − | 0.678813i | ||||
\(637\) | −3.00000 | −0.118864 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | −0.927051 | − | 2.85317i | −0.0366449 | − | 0.112781i | ||||
\(641\) | 7.28115 | + | 5.29007i | 0.287588 | + | 0.208945i | 0.722220 | − | 0.691663i | \(-0.243122\pi\) |
−0.434632 | + | 0.900608i | \(0.643122\pi\) | |||||||
\(642\) | −9.70820 | + | 7.05342i | −0.383152 | + | 0.278376i | ||||
\(643\) | −3.09017 | + | 9.51057i | −0.121864 | + | 0.375060i | −0.993317 | − | 0.115420i | \(-0.963179\pi\) |
0.871452 | + | 0.490480i | \(0.163179\pi\) | |||||||
\(644\) | 1.23607 | − | 3.80423i | 0.0487079 | − | 0.149908i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.2705 | + | 17.6336i | 0.954910 | + | 0.693783i | ||||
\(647\) | 6.18034 | + | 19.0211i | 0.242974 | + | 0.747798i | 0.995963 | + | 0.0897645i | \(0.0286114\pi\) |
−0.752989 | + | 0.658033i | \(0.771389\pi\) | |||||||
\(648\) | 33.0000 | 1.29636 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | −0.156893 | ||||||||
\(651\) | 2.47214 | + | 7.60845i | 0.0968906 | + | 0.298199i | ||||
\(652\) | −1.61803 | − | 1.17557i | −0.0633671 | − | 0.0460389i | ||||
\(653\) | 11.3262 | − | 8.22899i | 0.443230 | − | 0.322025i | −0.343687 | − | 0.939084i | \(-0.611676\pi\) |
0.786917 | + | 0.617059i | \(0.211676\pi\) | |||||||
\(654\) | −6.79837 | + | 20.9232i | −0.265837 | + | 0.818164i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.04508 | + | 2.93893i | −0.157934 | + | 0.114746i | ||||
\(657\) | 1.61803 | + | 1.17557i | 0.0631255 | + | 0.0458634i | ||||
\(658\) | −1.23607 | − | 3.80423i | −0.0481869 | − | 0.148304i | ||||
\(659\) | 22.0000 | 0.856998 | 0.428499 | − | 0.903542i | \(-0.359042\pi\) | ||||
0.428499 | + | 0.903542i | \(0.359042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0000 | 0.505641 | 0.252821 | − | 0.967513i | \(-0.418642\pi\) | ||||
0.252821 | + | 0.967513i | \(0.418642\pi\) | |||||||
\(662\) | −6.18034 | − | 19.0211i | −0.240206 | − | 0.739277i | ||||
\(663\) | 8.09017 | + | 5.87785i | 0.314196 | + | 0.228277i | ||||
\(664\) | 14.5623 | − | 10.5801i | 0.565127 | − | 0.410589i | ||||
\(665\) | −3.70820 | + | 11.4127i | −0.143798 | + | 0.442565i | ||||
\(666\) | −0.927051 | + | 2.85317i | −0.0359225 | + | 0.110558i | ||||
\(667\) | −14.5623 | + | 10.5801i | −0.563855 | + | 0.409664i | ||||
\(668\) | 9.70820 | + | 7.05342i | 0.375622 | + | 0.272905i | ||||
\(669\) | −12.3607 | − | 38.0423i | −0.477891 | − | 1.47080i | ||||
\(670\) | 2.00000 | 0.0772667 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −20.0000 | −0.771517 | ||||||||
\(673\) | −3.09017 | − | 9.51057i | −0.119117 | − | 0.366605i | 0.873666 | − | 0.486526i | \(-0.161736\pi\) |
−0.992784 | + | 0.119920i | \(0.961736\pi\) | |||||||
\(674\) | 10.5172 | + | 7.64121i | 0.405108 | + | 0.294328i | ||||
\(675\) | −12.9443 | + | 9.40456i | −0.498225 | + | 0.361982i | ||||
\(676\) | 3.70820 | − | 11.4127i | 0.142623 | − | 0.438949i | ||||
\(677\) | −8.34346 | + | 25.6785i | −0.320665 | + | 0.986906i | 0.652694 | + | 0.757621i | \(0.273639\pi\) |
−0.973359 | + | 0.229285i | \(0.926361\pi\) | |||||||
\(678\) | 14.5623 | − | 10.5801i | 0.559262 | − | 0.406328i | ||||
\(679\) | −21.0344 | − | 15.2824i | −0.807228 | − | 0.586485i | ||||
\(680\) | 4.63525 | + | 14.2658i | 0.177754 | + | 0.547070i | ||||
\(681\) | −48.0000 | −1.83936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.00000 | 0.0765279 | 0.0382639 | − | 0.999268i | \(-0.487817\pi\) | ||||
0.0382639 | + | 0.999268i | \(0.487817\pi\) | |||||||
\(684\) | −1.85410 | − | 5.70634i | −0.0708934 | − | 0.218187i | ||||
\(685\) | 8.09017 | + | 5.87785i | 0.309110 | + | 0.224581i | ||||
\(686\) | −16.1803 | + | 11.7557i | −0.617768 | + | 0.448835i | ||||
\(687\) | 5.56231 | − | 17.1190i | 0.212215 | − | 0.653131i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.28115 | + | 5.29007i | −0.277390 | + | 0.201536i | ||||
\(690\) | −3.23607 | − | 2.35114i | −0.123195 | − | 0.0895064i | ||||
\(691\) | 6.18034 | + | 19.0211i | 0.235111 | + | 0.723598i | 0.997107 | + | 0.0760155i | \(0.0242198\pi\) |
−0.761995 | + | 0.647582i | \(0.775780\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | −0.618034 | − | 1.90211i | −0.0234434 | − | 0.0721513i | ||||
\(696\) | 43.6869 | + | 31.7404i | 1.65595 | + | 1.20312i | ||||
\(697\) | −20.2254 | + | 14.6946i | −0.766093 | + | 0.556599i | ||||
\(698\) | −8.34346 | + | 25.6785i | −0.315805 | + | 0.971947i | ||||
\(699\) | −12.9787 | + | 39.9444i | −0.490900 | + | 1.51083i | ||||
\(700\) | 6.47214 | − | 4.70228i | 0.244624 | − | 0.177730i | ||||
\(701\) | −13.7533 | − | 9.99235i | −0.519455 | − | 0.377406i | 0.296944 | − | 0.954895i | \(-0.404033\pi\) |
−0.816398 | + | 0.577489i | \(0.804033\pi\) | |||||||
\(702\) | −1.23607 | − | 3.80423i | −0.0466524 | − | 0.143581i | ||||
\(703\) | −18.0000 | −0.678883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | −2.78115 | − | 8.55951i | −0.104670 | − | 0.322141i | ||||
\(707\) | −16.1803 | − | 11.7557i | −0.608524 | − | 0.442119i | ||||
\(708\) | 12.9443 | − | 9.40456i | 0.486476 | − | 0.353445i | ||||
\(709\) | −3.09017 | + | 9.51057i | −0.116054 | + | 0.357177i | −0.992165 | − | 0.124932i | \(-0.960129\pi\) |
0.876112 | + | 0.482108i | \(0.160129\pi\) | |||||||
\(710\) | 3.70820 | − | 11.4127i | 0.139166 | − | 0.428310i | ||||
\(711\) | 8.09017 | − | 5.87785i | 0.303405 | − | 0.220437i | ||||
\(712\) | −21.8435 | − | 15.8702i | −0.818618 | − | 0.594761i | ||||
\(713\) | −1.23607 | − | 3.80423i | −0.0462911 | − | 0.142469i | ||||
\(714\) | 20.0000 | 0.748481 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.0000 | −0.896922 | ||||||||
\(717\) | 3.70820 | + | 11.4127i | 0.138485 | + | 0.426214i | ||||
\(718\) | 1.61803 | + | 1.17557i | 0.0603845 | + | 0.0438719i | ||||
\(719\) | −24.2705 | + | 17.6336i | −0.905137 | + | 0.657621i | −0.939780 | − | 0.341779i | \(-0.888971\pi\) |
0.0346431 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(720\) | −0.309017 | + | 0.951057i | −0.0115164 | + | 0.0354438i | ||||
\(721\) | −4.94427 | + | 15.2169i | −0.184134 | + | 0.566707i | ||||
\(722\) | −13.7533 | + | 9.99235i | −0.511844 | + | 0.371877i | ||||
\(723\) | −35.5967 | − | 25.8626i | −1.32386 | − | 0.961839i | ||||
\(724\) | −0.309017 | − | 0.951057i | −0.0114845 | − | 0.0353457i | ||||
\(725\) | −36.0000 | −1.33701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0000 | −1.55769 | −0.778847 | − | 0.627214i | \(-0.784195\pi\) | ||||
−0.778847 | + | 0.627214i | \(0.784195\pi\) | |||||||
\(728\) | 1.85410 | + | 5.70634i | 0.0687176 | + | 0.211491i | ||||
\(729\) | −10.5172 | − | 7.64121i | −0.389527 | − | 0.283008i | ||||
\(730\) | 1.61803 | − | 1.17557i | 0.0598861 | − | 0.0435098i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.70820 | + | 11.4127i | −0.137059 | + | 0.421825i | ||||
\(733\) | −7.28115 | + | 5.29007i | −0.268936 | + | 0.195393i | −0.714077 | − | 0.700067i | \(-0.753153\pi\) |
0.445141 | + | 0.895460i | \(0.353153\pi\) | |||||||
\(734\) | 11.3262 | + | 8.22899i | 0.418059 | + | 0.303738i | ||||
\(735\) | −1.85410 | − | 5.70634i | −0.0683896 | − | 0.210481i | ||||
\(736\) | 10.0000 | 0.368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.00000 | −0.184053 | ||||||||
\(739\) | −3.09017 | − | 9.51057i | −0.113674 | − | 0.349852i | 0.877994 | − | 0.478671i | \(-0.158881\pi\) |
−0.991668 | + | 0.128819i | \(0.958881\pi\) | |||||||
\(740\) | −2.42705 | − | 1.76336i | −0.0892202 | − | 0.0648222i | ||||
\(741\) | −9.70820 | + | 7.05342i | −0.356640 | + | 0.259114i | ||||
\(742\) | −5.56231 | + | 17.1190i | −0.204199 | + | 0.628459i | ||||
\(743\) | −11.7426 | + | 36.1401i | −0.430796 | + | 1.32585i | 0.466538 | + | 0.884501i | \(0.345501\pi\) |
−0.897334 | + | 0.441352i | \(0.854499\pi\) | |||||||
\(744\) | −9.70820 | + | 7.05342i | −0.355920 | + | 0.258591i | ||||
\(745\) | −13.7533 | − | 9.99235i | −0.503882 | − | 0.366091i | ||||
\(746\) | 6.79837 | + | 20.9232i | 0.248906 | + | 0.766054i | ||||
\(747\) | 6.00000 | 0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | −5.56231 | − | 17.1190i | −0.203107 | − | 0.625098i | ||||
\(751\) | 16.1803 | + | 11.7557i | 0.590429 | + | 0.428972i | 0.842469 | − | 0.538745i | \(-0.181101\pi\) |
−0.252040 | + | 0.967717i | \(0.581101\pi\) | |||||||
\(752\) | 1.61803 | − | 1.17557i | 0.0590036 | − | 0.0428686i | ||||
\(753\) | −1.23607 | + | 3.80423i | −0.0450448 | + | 0.138634i | ||||
\(754\) | 2.78115 | − | 8.55951i | 0.101284 | − | 0.311719i | ||||
\(755\) | 12.9443 | − | 9.40456i | 0.471090 | − | 0.342267i | ||||
\(756\) | 6.47214 | + | 4.70228i | 0.235389 | + | 0.171020i | ||||
\(757\) | 16.3779 | + | 50.4060i | 0.595265 | + | 1.83204i | 0.553403 | + | 0.832914i | \(0.313329\pi\) |
0.0418620 | + | 0.999123i | \(0.486671\pi\) | |||||||
\(758\) | −32.0000 | −1.16229 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.0000 | −0.652929 | ||||||||
\(761\) | −6.48936 | − | 19.9722i | −0.235239 | − | 0.723991i | −0.997090 | − | 0.0762384i | \(-0.975709\pi\) |
0.761851 | − | 0.647753i | \(-0.224291\pi\) | |||||||
\(762\) | 25.8885 | + | 18.8091i | 0.937843 | + | 0.681383i | ||||
\(763\) | −17.7984 | + | 12.9313i | −0.644344 | + | 0.468144i | ||||
\(764\) | −2.47214 | + | 7.60845i | −0.0894387 | + | 0.275264i | ||||
\(765\) | −1.54508 | + | 4.75528i | −0.0558627 | + | 0.171928i | ||||
\(766\) | −16.1803 | + | 11.7557i | −0.584619 | + | 0.424751i | ||||
\(767\) | −6.47214 | − | 4.70228i | −0.233695 | − | 0.169790i | ||||
\(768\) | −10.5066 | − | 32.3359i | −0.379123 | − | 1.16682i | ||||
\(769\) | 11.0000 | 0.396670 | 0.198335 | − | 0.980134i | \(-0.436447\pi\) | ||||
0.198335 | + | 0.980134i | \(0.436447\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.0000 | 1.36854 | ||||||||
\(772\) | 1.54508 | + | 4.75528i | 0.0556088 | + | 0.171146i | ||||
\(773\) | 33.9787 | + | 24.6870i | 1.22213 | + | 0.887929i | 0.996275 | − | 0.0862321i | \(-0.0274827\pi\) |
0.225854 | + | 0.974161i | \(0.427483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.47214 | − | 7.60845i | 0.0888017 | − | 0.273304i | ||||
\(776\) | 12.0517 | − | 37.0912i | 0.432629 | − | 1.33150i | ||||
\(777\) | −9.70820 | + | 7.05342i | −0.348280 | + | 0.253040i | ||||
\(778\) | 2.42705 | + | 1.76336i | 0.0870140 | + | 0.0632194i | ||||
\(779\) | −9.27051 | − | 28.5317i | −0.332150 | − | 1.02225i | ||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −10.0000 | −0.357599 | ||||||||
\(783\) | −11.1246 | − | 34.2380i | −0.397561 | − | 1.22357i | ||||
\(784\) | −2.42705 | − | 1.76336i | −0.0866804 | − | 0.0629770i | ||||
\(785\) | −1.61803 | + | 1.17557i | −0.0577501 | + | 0.0419579i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.65248 | − | 26.6296i | 0.308427 | − | 0.949242i | −0.669948 | − | 0.742408i | \(-0.733684\pi\) |
0.978376 | − | 0.206835i | \(-0.0663162\pi\) | |||||||
\(788\) | −8.89919 | + | 6.46564i | −0.317020 | + | 0.230329i | ||||
\(789\) | 35.5967 | + | 25.8626i | 1.26728 | + | 0.920731i | ||||
\(790\) | −3.09017 | − | 9.51057i | −0.109943 | − | 0.338371i | ||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | 0.213066 | ||||||||
\(794\) | 4.01722 | + | 12.3637i | 0.142566 | + | 0.438773i | ||||
\(795\) | −14.5623 | − | 10.5801i | −0.516472 | − | 0.375239i | ||||
\(796\) | 19.4164 | − | 14.1068i | 0.688196 | − | 0.500004i | ||||
\(797\) | −3.09017 | + | 9.51057i | −0.109459 | + | 0.336882i | −0.990751 | − | 0.135691i | \(-0.956675\pi\) |
0.881292 | + | 0.472573i | \(0.156675\pi\) | |||||||
\(798\) | −7.41641 | + | 22.8254i | −0.262538 | + | 0.808009i | ||||
\(799\) | 8.09017 | − | 5.87785i | 0.286210 | − | 0.207943i | ||||
\(800\) | 16.1803 | + | 11.7557i | 0.572061 | + | 0.415627i | ||||
\(801\) | −2.78115 | − | 8.55951i | −0.0982672 | − | 0.302435i | ||||
\(802\) | 23.0000 | 0.812158 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | −1.23607 | − | 3.80423i | −0.0435657 | − | 0.134081i | ||||
\(806\) | 1.61803 | + | 1.17557i | 0.0569928 | + | 0.0414077i | ||||
\(807\) | −1.61803 | + | 1.17557i | −0.0569575 | + | 0.0413820i | ||||
\(808\) | 9.27051 | − | 28.5317i | 0.326135 | − | 1.00374i | ||||
\(809\) | 1.85410 | − | 5.70634i | 0.0651868 | − | 0.200624i | −0.913158 | − | 0.407605i | \(-0.866364\pi\) |
0.978345 | + | 0.206981i | \(0.0663639\pi\) | |||||||
\(810\) | 8.89919 | − | 6.46564i | 0.312686 | − | 0.227179i | ||||
\(811\) | −22.6525 | − | 16.4580i | −0.795436 | − | 0.577918i | 0.114136 | − | 0.993465i | \(-0.463590\pi\) |
−0.909572 | + | 0.415547i | \(0.863590\pi\) | |||||||
\(812\) | 5.56231 | + | 17.1190i | 0.195199 | + | 0.600760i | ||||
\(813\) | 40.0000 | 1.40286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | −0.0700569 | ||||||||
\(816\) | 3.09017 | + | 9.51057i | 0.108178 | + | 0.332936i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 16.9894 | − | 12.3435i | 0.594019 | − | 0.431580i | ||||
\(819\) | −0.618034 | + | 1.90211i | −0.0215959 | + | 0.0664652i | ||||
\(820\) | 1.54508 | − | 4.75528i | 0.0539567 | − | 0.166062i | ||||
\(821\) | 1.61803 | − | 1.17557i | 0.0564698 | − | 0.0410277i | −0.559192 | − | 0.829038i | \(-0.688889\pi\) |
0.615662 | + | 0.788010i | \(0.288889\pi\) | |||||||
\(822\) | 16.1803 | + | 11.7557i | 0.564354 | + | 0.410027i | ||||
\(823\) | −7.41641 | − | 22.8254i | −0.258520 | − | 0.795642i | −0.993116 | − | 0.117137i | \(-0.962628\pi\) |
0.734596 | − | 0.678505i | \(-0.237372\pi\) | |||||||
\(824\) | −24.0000 | −0.836080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.0000 | −0.556711 | ||||||||
\(827\) | −3.09017 | − | 9.51057i | −0.107456 | − | 0.330715i | 0.882843 | − | 0.469668i | \(-0.155626\pi\) |
−0.990299 | + | 0.138953i | \(0.955626\pi\) | |||||||
\(828\) | 1.61803 | + | 1.17557i | 0.0562306 | + | 0.0408539i | ||||
\(829\) | 38.0238 | − | 27.6259i | 1.32062 | − | 0.959487i | 0.320697 | − | 0.947182i | \(-0.396083\pi\) |
0.999924 | − | 0.0123055i | \(-0.00391706\pi\) | |||||||
\(830\) | 1.85410 | − | 5.70634i | 0.0643568 | − | 0.198070i | ||||
\(831\) | 0.618034 | − | 1.90211i | 0.0214394 | − | 0.0659836i | ||||
\(832\) | −5.66312 | + | 4.11450i | −0.196333 | + | 0.142645i | ||||
\(833\) | −12.1353 | − | 8.81678i | −0.420462 | − | 0.305483i | ||||
\(834\) | −1.23607 | − | 3.80423i | −0.0428015 | − | 0.131730i | ||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 0.618034 | + | 1.90211i | 0.0213496 | + | 0.0657074i | ||||
\(839\) | −37.2148 | − | 27.0381i | −1.28480 | − | 0.933460i | −0.285110 | − | 0.958495i | \(-0.592030\pi\) |
−0.999687 | + | 0.0250351i | \(0.992030\pi\) | |||||||
\(840\) | −9.70820 | + | 7.05342i | −0.334965 | + | 0.243366i | ||||
\(841\) | 16.0689 | − | 49.4549i | 0.554099 | − | 1.70534i | ||||
\(842\) | 4.01722 | − | 12.3637i | 0.138443 | − | 0.426082i | ||||
\(843\) | −9.70820 | + | 7.05342i | −0.334368 | + | 0.242933i | ||||
\(844\) | 9.70820 | + | 7.05342i | 0.334170 | + | 0.242789i | ||||
\(845\) | −3.70820 | − | 11.4127i | −0.127566 | − | 0.392608i | ||||
\(846\) | 2.00000 | 0.0687614 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.00000 | −0.309061 | ||||||||
\(849\) | 17.3050 | + | 53.2592i | 0.593904 | + | 1.82785i | ||||
\(850\) | −16.1803 | − | 11.7557i | −0.554981 | − | 0.403217i | ||||
\(851\) | 4.85410 | − | 3.52671i | 0.166396 | − | 0.120894i | ||||
\(852\) | −7.41641 | + | 22.8254i | −0.254082 | + | 0.781984i | ||||
\(853\) | 5.25329 | − | 16.1680i | 0.179869 | − | 0.553580i | −0.819953 | − | 0.572431i | \(-0.806001\pi\) |
0.999822 | + | 0.0188502i | \(0.00600057\pi\) | |||||||
\(854\) | 9.70820 | − | 7.05342i | 0.332208 | − | 0.241363i | ||||
\(855\) | −4.85410 | − | 3.52671i | −0.166007 | − | 0.120611i | ||||
\(856\) | −5.56231 | − | 17.1190i | −0.190116 | − | 0.585116i | ||||
\(857\) | −22.0000 | −0.751506 | −0.375753 | − | 0.926720i | \(-0.622616\pi\) | ||||
−0.375753 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0000 | 0.818869 | 0.409435 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409435 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.1803 | − | 11.7557i | −0.551425 | − | 0.400633i | ||||
\(862\) | −9.70820 | + | 7.05342i | −0.330663 | + | 0.240241i | ||||
\(863\) | −16.6869 | + | 51.3571i | −0.568029 | + | 1.74821i | 0.0907454 | + | 0.995874i | \(0.471075\pi\) |
−0.658775 | + | 0.752340i | \(0.728925\pi\) | |||||||
\(864\) | −6.18034 | + | 19.0211i | −0.210259 | + | 0.647112i | ||||
\(865\) | −4.85410 | + | 3.52671i | −0.165044 | + | 0.119912i | ||||
\(866\) | −15.3713 | − | 11.1679i | −0.522339 | − | 0.379501i | ||||
\(867\) | 4.94427 | + | 15.2169i | 0.167916 | + | 0.516793i | ||||
\(868\) | −4.00000 | −0.135769 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.0000 | 0.610257 | ||||||||
\(871\) | 0.618034 | + | 1.90211i | 0.0209413 | + | 0.0644506i | ||||
\(872\) | −26.6976 | − | 19.3969i | −0.904093 | − | 0.656862i | ||||
\(873\) | 10.5172 | − | 7.64121i | 0.355954 | − | 0.258616i | ||||
\(874\) | 3.70820 | − | 11.4127i | 0.125432 | − | 0.386040i | ||||
\(875\) | 5.56231 | − | 17.1190i | 0.188040 | − | 0.578728i | ||||
\(876\) | −3.23607 | + | 2.35114i | −0.109337 | + | 0.0794377i | ||||
\(877\) | 21.8435 | + | 15.8702i | 0.737601 | + | 0.535899i | 0.891959 | − | 0.452116i | \(-0.149331\pi\) |
−0.154358 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(878\) | 6.79837 | + | 20.9232i | 0.229434 | + | 0.706125i | ||||
\(879\) | 18.0000 | 0.607125 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.0000 | 1.17918 | 0.589590 | − | 0.807703i | \(-0.299289\pi\) | ||||
0.589590 | + | 0.807703i | \(0.299289\pi\) | |||||||
\(882\) | −0.927051 | − | 2.85317i | −0.0312154 | − | 0.0960712i | ||||
\(883\) | 16.1803 | + | 11.7557i | 0.544512 | + | 0.395611i | 0.825758 | − | 0.564025i | \(-0.190748\pi\) |
−0.281246 | + | 0.959636i | \(0.590748\pi\) | |||||||
\(884\) | −4.04508 | + | 2.93893i | −0.136051 | + | 0.0988468i | ||||
\(885\) | 4.94427 | − | 15.2169i | 0.166200 | − | 0.511511i | ||||
\(886\) | −6.18034 | + | 19.0211i | −0.207633 | + | 0.639027i | ||||
\(887\) | 37.2148 | − | 27.0381i | 1.24955 | − | 0.907851i | 0.251354 | − | 0.967895i | \(-0.419124\pi\) |
0.998196 | + | 0.0600439i | \(0.0191241\pi\) | |||||||
\(888\) | −14.5623 | − | 10.5801i | −0.488679 | − | 0.355046i | ||||
\(889\) | 9.88854 | + | 30.4338i | 0.331651 | + | 1.02072i | ||||
\(890\) | −9.00000 | −0.301681 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.0000 | 0.669650 | ||||||||
\(893\) | 3.70820 | + | 11.4127i | 0.124090 | + | 0.381911i | ||||
\(894\) | −27.5066 | − | 19.9847i | −0.919958 | − | 0.668388i | ||||
\(895\) | −19.4164 | + | 14.1068i | −0.649019 | + | 0.471540i | ||||
\(896\) | 1.85410 | − | 5.70634i | 0.0619412 | − | 0.190635i | ||||
\(897\) | 1.23607 | − | 3.80423i | 0.0412711 | − | 0.127019i | ||||
\(898\) | 10.5172 | − | 7.64121i | 0.350964 | − | 0.254990i | ||||
\(899\) | 14.5623 | + | 10.5801i | 0.485680 | + | 0.352867i | ||||
\(900\) | 1.23607 | + | 3.80423i | 0.0412023 | + | 0.126808i | ||||
\(901\) | −45.0000 | −1.49917 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.34346 | + | 25.6785i | 0.277499 | + | 0.854055i | ||||
\(905\) | −0.809017 | − | 0.587785i | −0.0268926 | − | 0.0195386i | ||||
\(906\) | 25.8885 | − | 18.8091i | 0.860089 | − | 0.624891i | ||||
\(907\) | 3.70820 | − | 11.4127i | 0.123129 | − | 0.378952i | −0.870427 | − | 0.492298i | \(-0.836157\pi\) |
0.993556 | + | 0.113346i | \(0.0361570\pi\) | |||||||
\(908\) | 7.41641 | − | 22.8254i | 0.246122 | − | 0.757486i | ||||
\(909\) | 8.09017 | − | 5.87785i | 0.268334 | − | 0.194956i | ||||
\(910\) | 1.61803 | + | 1.17557i | 0.0536373 | + | 0.0389698i | ||||
\(911\) | −7.41641 | − | 22.8254i | −0.245717 | − | 0.756238i | −0.995518 | − | 0.0945746i | \(-0.969851\pi\) |
0.749801 | − | 0.661663i | \(-0.230149\pi\) | |||||||
\(912\) | −12.0000 | −0.397360 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 39.0000 | 1.29001 | ||||||||
\(915\) | 3.70820 | + | 11.4127i | 0.122589 | + | 0.377292i | ||||
\(916\) | 7.28115 | + | 5.29007i | 0.240576 | + | 0.174789i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.18034 | − | 19.0211i | 0.203982 | − | 0.627791i | ||||
\(919\) | 8.65248 | − | 26.6296i | 0.285419 | − | 0.878429i | −0.700854 | − | 0.713305i | \(-0.747198\pi\) |
0.986273 | − | 0.165124i | \(-0.0528025\pi\) | |||||||
\(920\) | 4.85410 | − | 3.52671i | 0.160035 | − | 0.116272i | ||||
\(921\) | 35.5967 | + | 25.8626i | 1.17295 | + | 0.852200i | ||||
\(922\) | 10.1976 | + | 31.3849i | 0.335839 | + | 1.03361i | ||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0000 | 0.394558 | ||||||||
\(926\) | −6.18034 | − | 19.0211i | −0.203099 | − | 0.625073i | ||||
\(927\) | −6.47214 | − | 4.70228i | −0.212573 | − | 0.154443i | ||||
\(928\) | −36.4058 | + | 26.4503i | −1.19508 | + | 0.868275i | ||||
\(929\) | −6.48936 | + | 19.9722i | −0.212909 | + | 0.655266i | 0.786387 | + | 0.617735i | \(0.211949\pi\) |
−0.999295 | + | 0.0375315i | \(0.988051\pi\) | |||||||
\(930\) | −1.23607 | + | 3.80423i | −0.0405323 | + | 0.124745i | ||||
\(931\) | 14.5623 | − | 10.5801i | 0.477260 | − | 0.346750i | ||||
\(932\) | −16.9894 | − | 12.3435i | −0.556505 | − | 0.404324i | ||||
\(933\) | 14.8328 | + | 45.6507i | 0.485605 | + | 1.49454i | ||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.00000 | −0.0980581 | ||||||||
\(937\) | 7.10739 | + | 21.8743i | 0.232188 | + | 0.714602i | 0.997482 | + | 0.0709209i | \(0.0225938\pi\) |
−0.765294 | + | 0.643681i | \(0.777406\pi\) | |||||||
\(938\) | 3.23607 | + | 2.35114i | 0.105661 | + | 0.0767675i | ||||
\(939\) | −37.2148 | + | 27.0381i | −1.21446 | + | 0.882356i | ||||
\(940\) | −0.618034 | + | 1.90211i | −0.0201580 | + | 0.0620401i | ||||
\(941\) | −8.34346 | + | 25.6785i | −0.271989 | + | 0.837096i | 0.718011 | + | 0.696031i | \(0.245053\pi\) |
−0.990000 | + | 0.141065i | \(0.954947\pi\) | |||||||
\(942\) | −3.23607 | + | 2.35114i | −0.105437 | + | 0.0766043i | ||||
\(943\) | 8.09017 | + | 5.87785i | 0.263452 | + | 0.191409i | ||||
\(944\) | −2.47214 | − | 7.60845i | −0.0804612 | − | 0.247634i | ||||
\(945\) | 8.00000 | 0.260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.0000 | −1.36482 | −0.682408 | − | 0.730971i | \(-0.739067\pi\) | ||||
−0.682408 | + | 0.730971i | \(0.739067\pi\) | |||||||
\(948\) | 6.18034 | + | 19.0211i | 0.200728 | + | 0.617778i | ||||
\(949\) | 1.61803 | + | 1.17557i | 0.0525236 | + | 0.0381606i | ||||
\(950\) | 19.4164 | − | 14.1068i | 0.629951 | − | 0.457687i | ||||
\(951\) | −1.23607 | + | 3.80423i | −0.0400823 | + | 0.123360i | ||||
\(952\) | −9.27051 | + | 28.5317i | −0.300459 | + | 0.924718i | ||||
\(953\) | −25.0795 | + | 18.2213i | −0.812406 | + | 0.590247i | −0.914527 | − | 0.404525i | \(-0.867437\pi\) |
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(954\) | −7.28115 | − | 5.29007i | −0.235736 | − | 0.171272i | ||||
\(955\) | 2.47214 | + | 7.60845i | 0.0799964 | + | 0.246204i | ||||
\(956\) | −6.00000 | −0.194054 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.0000 | −0.516937 | ||||||||
\(959\) | 6.18034 | + | 19.0211i | 0.199574 | + | 0.614224i | ||||
\(960\) | −11.3262 | − | 8.22899i | −0.365553 | − | 0.265590i | ||||
\(961\) | 21.8435 | − | 15.8702i | 0.704628 | − | 0.511942i | ||||
\(962\) | −0.927051 | + | 2.85317i | −0.0298893 | + | 0.0919899i | ||||
\(963\) | 1.85410 | − | 5.70634i | 0.0597476 | − | 0.183884i | ||||
\(964\) | 17.7984 | − | 12.9313i | 0.573247 | − | 0.416488i | ||||
\(965\) | 4.04508 | + | 2.93893i | 0.130216 | + | 0.0946074i | ||||
\(966\) | −2.47214 | − | 7.60845i | −0.0795397 | − | 0.244798i | ||||
\(967\) | 22.0000 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −60.0000 | −1.92748 | ||||||||
\(970\) | −4.01722 | − | 12.3637i | −0.128985 | − | 0.396976i | ||||
\(971\) | −1.61803 | − | 1.17557i | −0.0519252 | − | 0.0377259i | 0.561520 | − | 0.827463i | \(-0.310217\pi\) |
−0.613445 | + | 0.789737i | \(0.710217\pi\) | |||||||
\(972\) | −8.09017 | + | 5.87785i | −0.259492 | + | 0.188532i | ||||
\(973\) | 1.23607 | − | 3.80423i | 0.0396265 | − | 0.121958i | ||||
\(974\) | 0.618034 | − | 1.90211i | 0.0198031 | − | 0.0609476i | ||||
\(975\) | 6.47214 | − | 4.70228i | 0.207274 | − | 0.150594i | ||||
\(976\) | 4.85410 | + | 3.52671i | 0.155376 | + | 0.112887i | ||||
\(977\) | −17.6140 | − | 54.2102i | −0.563521 | − | 1.73434i | −0.672306 | − | 0.740273i | \(-0.734696\pi\) |
0.108785 | − | 0.994065i | \(-0.465304\pi\) | |||||||
\(978\) | −4.00000 | −0.127906 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | −3.39919 | − | 10.4616i | −0.108528 | − | 0.334014i | ||||
\(982\) | 1.61803 | + | 1.17557i | 0.0516335 | + | 0.0375140i | ||||
\(983\) | 29.1246 | − | 21.1603i | 0.928931 | − | 0.674908i | −0.0168000 | − | 0.999859i | \(-0.505348\pi\) |
0.945731 | + | 0.324951i | \(0.105348\pi\) | |||||||
\(984\) | 9.27051 | − | 28.5317i | 0.295533 | − | 0.909557i | ||||
\(985\) | −3.39919 | + | 10.4616i | −0.108307 | + | 0.333335i | ||||
\(986\) | 36.4058 | − | 26.4503i | 1.15940 | − | 0.842350i | ||||
\(987\) | 6.47214 | + | 4.70228i | 0.206010 | + | 0.149675i | ||||
\(988\) | −1.85410 | − | 5.70634i | −0.0589868 | − | 0.181543i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0000 | −0.635321 | −0.317660 | − | 0.948205i | \(-0.602897\pi\) | ||||
−0.317660 | + | 0.948205i | \(0.602897\pi\) | |||||||
\(992\) | −3.09017 | − | 9.51057i | −0.0981130 | − | 0.301961i | ||||
\(993\) | 32.3607 | + | 23.5114i | 1.02694 | + | 0.746112i | ||||
\(994\) | 19.4164 | − | 14.1068i | 0.615851 | − | 0.447442i | ||||
\(995\) | 7.41641 | − | 22.8254i | 0.235116 | − | 0.723612i | ||||
\(996\) | −3.70820 | + | 11.4127i | −0.117499 | + | 0.361625i | ||||
\(997\) | −42.8779 | + | 31.1526i | −1.35796 | + | 0.986613i | −0.359385 | + | 0.933189i | \(0.617013\pi\) |
−0.998572 | + | 0.0534239i | \(0.982987\pi\) | |||||||
\(998\) | −6.47214 | − | 4.70228i | −0.204872 | − | 0.148848i | ||||
\(999\) | 3.70820 | + | 11.4127i | 0.117322 | + | 0.361081i |
(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 | 121.2.c.b.27.1 | 4 | ||
11.2 | odd | 10 | 121.2.c.d.9.1 | 4 | |||
11.3 | even | 5 | 121.2.a.c.1.1 | yes | 1 | ||
11.4 | even | 5 | inner | 121.2.c.b.3.1 | 4 | ||
11.5 | even | 5 | inner | 121.2.c.b.81.1 | 4 | ||
11.6 | odd | 10 | 121.2.c.d.81.1 | 4 | |||
11.7 | odd | 10 | 121.2.c.d.3.1 | 4 | |||
11.8 | odd | 10 | 121.2.a.a.1.1 | ✓ | 1 | ||
11.9 | even | 5 | inner | 121.2.c.b.9.1 | 4 | ||
11.10 | odd | 2 | 121.2.c.d.27.1 | 4 | |||
33.8 | even | 10 | 1089.2.a.i.1.1 | 1 | |||
33.14 | odd | 10 | 1089.2.a.c.1.1 | 1 | |||
44.3 | odd | 10 | 1936.2.a.b.1.1 | 1 | |||
44.19 | even | 10 | 1936.2.a.a.1.1 | 1 | |||
55.14 | even | 10 | 3025.2.a.b.1.1 | 1 | |||
55.19 | odd | 10 | 3025.2.a.e.1.1 | 1 | |||
77.41 | even | 10 | 5929.2.a.a.1.1 | 1 | |||
77.69 | odd | 10 | 5929.2.a.g.1.1 | 1 | |||
88.3 | odd | 10 | 7744.2.a.bf.1.1 | 1 | |||
88.19 | even | 10 | 7744.2.a.be.1.1 | 1 | |||
88.69 | even | 10 | 7744.2.a.c.1.1 | 1 | |||
88.85 | odd | 10 | 7744.2.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
121.2.a.a.1.1 | ✓ | 1 | 11.8 | odd | 10 | ||
121.2.a.c.1.1 | yes | 1 | 11.3 | even | 5 | ||
121.2.c.b.3.1 | 4 | 11.4 | even | 5 | inner | ||
121.2.c.b.9.1 | 4 | 11.9 | even | 5 | inner | ||
121.2.c.b.27.1 | 4 | 1.1 | even | 1 | trivial | ||
121.2.c.b.81.1 | 4 | 11.5 | even | 5 | inner | ||
121.2.c.d.3.1 | 4 | 11.7 | odd | 10 | |||
121.2.c.d.9.1 | 4 | 11.2 | odd | 10 | |||
121.2.c.d.27.1 | 4 | 11.10 | odd | 2 | |||
121.2.c.d.81.1 | 4 | 11.6 | odd | 10 | |||
1089.2.a.c.1.1 | 1 | 33.14 | odd | 10 | |||
1089.2.a.i.1.1 | 1 | 33.8 | even | 10 | |||
1936.2.a.a.1.1 | 1 | 44.19 | even | 10 | |||
1936.2.a.b.1.1 | 1 | 44.3 | odd | 10 | |||
3025.2.a.b.1.1 | 1 | 55.14 | even | 10 | |||
3025.2.a.e.1.1 | 1 | 55.19 | odd | 10 | |||
5929.2.a.a.1.1 | 1 | 77.41 | even | 10 | |||
5929.2.a.g.1.1 | 1 | 77.69 | odd | 10 | |||
7744.2.a.c.1.1 | 1 | 88.69 | even | 10 | |||
7744.2.a.f.1.1 | 1 | 88.85 | odd | 10 | |||
7744.2.a.be.1.1 | 1 | 88.19 | even | 10 | |||
7744.2.a.bf.1.1 | 1 | 88.3 | odd | 10 |