Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (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: | \(4.83094932229\) |
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 | 511.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.511 |
Dual form | 605.2.g.d.251.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | −0.998886 | − | 0.0471903i | \(-0.984973\pi\) |
0.780378 | − | 0.625308i | \(-0.215027\pi\) | |||||||
\(3\) | 2.42705 | + | 1.76336i | 1.40126 | + | 1.01807i | 0.994522 | + | 0.104528i | \(0.0333333\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(4\) | 0.809017 | − | 0.587785i | 0.404508 | − | 0.293893i | ||||
\(5\) | 0.309017 | − | 0.951057i | 0.138197 | − | 0.425325i | ||||
\(6\) | 0.927051 | − | 2.85317i | 0.378467 | − | 1.16480i | ||||
\(7\) | 2.42705 | − | 1.76336i | 0.917339 | − | 0.666486i | −0.0255212 | − | 0.999674i | \(-0.508125\pi\) |
0.942860 | + | 0.333188i | \(0.108125\pi\) | |||||||
\(8\) | −2.42705 | − | 1.76336i | −0.858092 | − | 0.623440i | ||||
\(9\) | 1.85410 | + | 5.70634i | 0.618034 | + | 1.90211i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.00000 | 0.866025 | ||||||||
\(13\) | 1.23607 | + | 3.80423i | 0.342824 | + | 1.05510i | 0.962739 | + | 0.270434i | \(0.0871670\pi\) |
−0.619915 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(14\) | −2.42705 | − | 1.76336i | −0.648657 | − | 0.471277i | ||||
\(15\) | 2.42705 | − | 1.76336i | 0.626662 | − | 0.455296i | ||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(18\) | 4.85410 | − | 3.52671i | 1.14412 | − | 0.831254i | ||||
\(19\) | −3.23607 | − | 2.35114i | −0.742405 | − | 0.539389i | 0.151058 | − | 0.988525i | \(-0.451732\pi\) |
−0.893463 | + | 0.449136i | \(0.851732\pi\) | |||||||
\(20\) | −0.309017 | − | 0.951057i | −0.0690983 | − | 0.212663i | ||||
\(21\) | 9.00000 | 1.96396 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.00000 | −1.66812 | −0.834058 | − | 0.551677i | \(-0.813988\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(24\) | −2.78115 | − | 8.55951i | −0.567700 | − | 1.74720i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | 3.23607 | − | 2.35114i | 0.634645 | − | 0.461097i | ||||
\(27\) | −2.78115 | + | 8.55951i | −0.535233 | + | 1.64728i | ||||
\(28\) | 0.927051 | − | 2.85317i | 0.175196 | − | 0.539198i | ||||
\(29\) | −4.85410 | + | 3.52671i | −0.901384 | + | 0.654894i | −0.938821 | − | 0.344405i | \(-0.888081\pi\) |
0.0374370 | + | 0.999299i | \(0.488081\pi\) | |||||||
\(30\) | −2.42705 | − | 1.76336i | −0.443117 | − | 0.321943i | ||||
\(31\) | −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 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.927051 | − | 2.85317i | −0.156700 | − | 0.482274i | ||||
\(36\) | 4.85410 | + | 3.52671i | 0.809017 | + | 0.587785i | ||||
\(37\) | 6.47214 | − | 4.70228i | 1.06401 | − | 0.773050i | 0.0891861 | − | 0.996015i | \(-0.471573\pi\) |
0.974827 | + | 0.222965i | \(0.0715734\pi\) | |||||||
\(38\) | −1.23607 | + | 3.80423i | −0.200517 | + | 0.617127i | ||||
\(39\) | −3.70820 | + | 11.4127i | −0.593788 | + | 1.82749i | ||||
\(40\) | −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 | \(0.572325\pi\) | |||||||
\(42\) | −2.78115 | − | 8.55951i | −0.429141 | − | 1.32076i | ||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00000 | 0.894427 | ||||||||
\(46\) | 2.47214 | + | 7.60845i | 0.364497 | + | 1.12181i | ||||
\(47\) | 2.42705 | + | 1.76336i | 0.354022 | + | 0.257212i | 0.750554 | − | 0.660809i | \(-0.229787\pi\) |
−0.396533 | + | 0.918021i | \(0.629787\pi\) | |||||||
\(48\) | −2.42705 | + | 1.76336i | −0.350315 | + | 0.254518i | ||||
\(49\) | 0.618034 | − | 1.90211i | 0.0882906 | − | 0.271730i | ||||
\(50\) | −0.309017 | + | 0.951057i | −0.0437016 | + | 0.134500i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.23607 | + | 2.35114i | 0.448762 | + | 0.326045i | ||||
\(53\) | 1.23607 | + | 3.80423i | 0.169787 | + | 0.522551i | 0.999357 | − | 0.0358519i | \(-0.0114145\pi\) |
−0.829570 | + | 0.558403i | \(0.811414\pi\) | |||||||
\(54\) | 9.00000 | 1.22474 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.00000 | −1.20268 | ||||||||
\(57\) | −3.70820 | − | 11.4127i | −0.491164 | − | 1.51165i | ||||
\(58\) | 4.85410 | + | 3.52671i | 0.637375 | + | 0.463080i | ||||
\(59\) | 1.61803 | − | 1.17557i | 0.210650 | − | 0.153046i | −0.477458 | − | 0.878655i | \(-0.658442\pi\) |
0.688108 | + | 0.725608i | \(0.258442\pi\) | |||||||
\(60\) | 0.927051 | − | 2.85317i | 0.119682 | − | 0.368343i | ||||
\(61\) | −3.39919 | + | 10.4616i | −0.435221 | + | 1.33947i | 0.457638 | + | 0.889138i | \(0.348695\pi\) |
−0.892860 | + | 0.450335i | \(0.851305\pi\) | |||||||
\(62\) | −1.61803 | + | 1.17557i | −0.205491 | + | 0.149298i | ||||
\(63\) | 14.5623 | + | 10.5801i | 1.83468 | + | 1.33297i | ||||
\(64\) | 2.16312 | + | 6.65740i | 0.270390 | + | 0.832174i | ||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.0000 | −1.58820 | −0.794101 | − | 0.607785i | \(-0.792058\pi\) | ||||
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19.4164 | − | 14.1068i | −2.33746 | − | 1.69826i | ||||
\(70\) | −2.42705 | + | 1.76336i | −0.290088 | + | 0.210761i | ||||
\(71\) | 0.618034 | − | 1.90211i | 0.0733471 | − | 0.225739i | −0.907662 | − | 0.419703i | \(-0.862134\pi\) |
0.981009 | + | 0.193963i | \(0.0621343\pi\) | |||||||
\(72\) | 5.56231 | − | 17.1190i | 0.655524 | − | 2.01750i | ||||
\(73\) | 6.47214 | − | 4.70228i | 0.757506 | − | 0.550360i | −0.140638 | − | 0.990061i | \(-0.544915\pi\) |
0.898144 | + | 0.439701i | \(0.144915\pi\) | |||||||
\(74\) | −6.47214 | − | 4.70228i | −0.752371 | − | 0.546629i | ||||
\(75\) | −0.927051 | − | 2.85317i | −0.107047 | − | 0.329456i | ||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.0000 | 1.35873 | ||||||||
\(79\) | 3.09017 | + | 9.51057i | 0.347671 | + | 1.07002i | 0.960138 | + | 0.279526i | \(0.0901773\pi\) |
−0.612467 | + | 0.790496i | \(0.709823\pi\) | |||||||
\(80\) | 0.809017 | + | 0.587785i | 0.0904508 | + | 0.0657164i | ||||
\(81\) | −7.28115 | + | 5.29007i | −0.809017 | + | 0.587785i | ||||
\(82\) | 1.54508 | − | 4.75528i | 0.170626 | − | 0.525133i | ||||
\(83\) | 1.23607 | − | 3.80423i | 0.135676 | − | 0.417568i | −0.860018 | − | 0.510263i | \(-0.829548\pi\) |
0.995695 | + | 0.0926948i | \(0.0295481\pi\) | |||||||
\(84\) | 7.28115 | − | 5.29007i | 0.794439 | − | 0.577194i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.54508 | − | 4.75528i | −0.166611 | − | 0.512775i | ||||
\(87\) | −18.0000 | −1.92980 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00000 | 0.106000 | 0.0529999 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0529999 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(90\) | −1.85410 | − | 5.70634i | −0.195440 | − | 0.601501i | ||||
\(91\) | 9.70820 | + | 7.05342i | 1.01770 | + | 0.739400i | ||||
\(92\) | −6.47214 | + | 4.70228i | −0.674767 | + | 0.490247i | ||||
\(93\) | 1.85410 | − | 5.70634i | 0.192261 | − | 0.591720i | ||||
\(94\) | 0.927051 | − | 2.85317i | 0.0956180 | − | 0.294282i | ||||
\(95\) | −3.23607 | + | 2.35114i | −0.332014 | + | 0.241222i | ||||
\(96\) | −12.1353 | − | 8.81678i | −1.23855 | − | 0.899859i | ||||
\(97\) | −2.47214 | − | 7.60845i | −0.251007 | − | 0.772521i | −0.994590 | − | 0.103877i | \(-0.966875\pi\) |
0.743583 | − | 0.668644i | \(-0.233125\pi\) | |||||||
\(98\) | −2.00000 | −0.202031 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −1.54508 | − | 4.75528i | −0.153742 | − | 0.473168i | 0.844290 | − | 0.535887i | \(-0.180023\pi\) |
−0.998031 | + | 0.0627190i | \(0.980023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.47214 | + | 4.70228i | −0.637719 | + | 0.463330i | −0.859066 | − | 0.511865i | \(-0.828955\pi\) |
0.221347 | + | 0.975195i | \(0.428955\pi\) | |||||||
\(104\) | 3.70820 | − | 11.4127i | 0.363619 | − | 1.11911i | ||||
\(105\) | 2.78115 | − | 8.55951i | 0.271413 | − | 0.835323i | ||||
\(106\) | 3.23607 | − | 2.35114i | 0.314315 | − | 0.228363i | ||||
\(107\) | −7.28115 | − | 5.29007i | −0.703896 | − | 0.511410i | 0.177303 | − | 0.984156i | \(-0.443263\pi\) |
−0.881199 | + | 0.472746i | \(0.843263\pi\) | |||||||
\(108\) | 2.78115 | + | 8.55951i | 0.267617 | + | 0.823639i | ||||
\(109\) | −9.00000 | −0.862044 | −0.431022 | − | 0.902342i | \(-0.641847\pi\) | ||||
−0.431022 | + | 0.902342i | \(0.641847\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.0000 | 2.27798 | ||||||||
\(112\) | 0.927051 | + | 2.85317i | 0.0875981 | + | 0.269599i | ||||
\(113\) | −4.85410 | − | 3.52671i | −0.456636 | − | 0.331765i | 0.335575 | − | 0.942014i | \(-0.391070\pi\) |
−0.792210 | + | 0.610249i | \(0.791070\pi\) | |||||||
\(114\) | −9.70820 | + | 7.05342i | −0.909257 | + | 0.660614i | ||||
\(115\) | −2.47214 | + | 7.60845i | −0.230528 | + | 0.709492i | ||||
\(116\) | −1.85410 | + | 5.70634i | −0.172149 | + | 0.529820i | ||||
\(117\) | −19.4164 | + | 14.1068i | −1.79505 | + | 1.30418i | ||||
\(118\) | −1.61803 | − | 1.17557i | −0.148952 | − | 0.108220i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −9.00000 | −0.821584 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 11.0000 | 0.995893 | ||||||||
\(123\) | 4.63525 | + | 14.2658i | 0.417947 | + | 1.28631i | ||||
\(124\) | −1.61803 | − | 1.17557i | −0.145304 | − | 0.105569i | ||||
\(125\) | −0.809017 | + | 0.587785i | −0.0723607 | + | 0.0525731i | ||||
\(126\) | 5.56231 | − | 17.1190i | 0.495530 | − | 1.52508i | ||||
\(127\) | 3.39919 | − | 10.4616i | 0.301629 | − | 0.928319i | −0.679285 | − | 0.733875i | \(-0.737710\pi\) |
0.980914 | − | 0.194444i | \(-0.0622902\pi\) | |||||||
\(128\) | −2.42705 | + | 1.76336i | −0.214523 | + | 0.155860i | ||||
\(129\) | 12.1353 | + | 8.81678i | 1.06845 | + | 0.776274i | ||||
\(130\) | −1.23607 | − | 3.80423i | −0.108410 | − | 0.333653i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | −1.04053 | ||||||||
\(134\) | 4.01722 | + | 12.3637i | 0.347035 | + | 1.06806i | ||||
\(135\) | 7.28115 | + | 5.29007i | 0.626662 | + | 0.455296i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(138\) | −7.41641 | + | 22.8254i | −0.631327 | + | 1.94302i | ||||
\(139\) | 14.5623 | − | 10.5801i | 1.23516 | − | 0.897395i | 0.237893 | − | 0.971291i | \(-0.423543\pi\) |
0.997266 | + | 0.0738961i | \(0.0235433\pi\) | |||||||
\(140\) | −2.42705 | − | 1.76336i | −0.205123 | − | 0.149031i | ||||
\(141\) | 2.78115 | + | 8.55951i | 0.234215 | + | 0.720841i | ||||
\(142\) | −2.00000 | −0.167836 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.00000 | −0.500000 | ||||||||
\(145\) | 1.85410 | + | 5.70634i | 0.153975 | + | 0.473886i | ||||
\(146\) | −6.47214 | − | 4.70228i | −0.535638 | − | 0.389164i | ||||
\(147\) | 4.85410 | − | 3.52671i | 0.400360 | − | 0.290878i | ||||
\(148\) | 2.47214 | − | 7.60845i | 0.203208 | − | 0.625411i | ||||
\(149\) | −5.25329 | + | 16.1680i | −0.430366 | + | 1.32453i | 0.467395 | + | 0.884049i | \(0.345193\pi\) |
−0.897761 | + | 0.440482i | \(0.854807\pi\) | |||||||
\(150\) | −2.42705 | + | 1.76336i | −0.198168 | + | 0.143977i | ||||
\(151\) | 11.3262 | + | 8.22899i | 0.921716 | + | 0.669666i | 0.943951 | − | 0.330087i | \(-0.107078\pi\) |
−0.0222344 | + | 0.999753i | \(0.507078\pi\) | |||||||
\(152\) | 3.70820 | + | 11.4127i | 0.300775 | + | 0.925690i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 3.70820 | + | 11.4127i | 0.296894 | + | 0.913746i | ||||
\(157\) | 6.47214 | + | 4.70228i | 0.516533 | + | 0.375283i | 0.815296 | − | 0.579044i | \(-0.196574\pi\) |
−0.298763 | + | 0.954327i | \(0.596574\pi\) | |||||||
\(158\) | 8.09017 | − | 5.87785i | 0.643619 | − | 0.467617i | ||||
\(159\) | −3.70820 | + | 11.4127i | −0.294080 | + | 0.905084i | ||||
\(160\) | −1.54508 | + | 4.75528i | −0.122150 | + | 0.375938i | ||||
\(161\) | −19.4164 | + | 14.1068i | −1.53023 | + | 1.11178i | ||||
\(162\) | 7.28115 | + | 5.29007i | 0.572061 | + | 0.415627i | ||||
\(163\) | −5.25329 | − | 16.1680i | −0.411469 | − | 1.26637i | −0.915371 | − | 0.402611i | \(-0.868103\pi\) |
0.503902 | − | 0.863761i | \(-0.331897\pi\) | |||||||
\(164\) | 5.00000 | 0.390434 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | −2.16312 | − | 6.65740i | −0.167387 | − | 0.515165i | 0.831817 | − | 0.555050i | \(-0.187301\pi\) |
−0.999204 | + | 0.0398851i | \(0.987301\pi\) | |||||||
\(168\) | −21.8435 | − | 15.8702i | −1.68526 | − | 1.22441i | ||||
\(169\) | −2.42705 | + | 1.76336i | −0.186696 | + | 0.135643i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.41641 | − | 22.8254i | 0.567147 | − | 1.74550i | ||||
\(172\) | 4.04508 | − | 2.93893i | 0.308435 | − | 0.224091i | ||||
\(173\) | −19.4164 | − | 14.1068i | −1.47620 | − | 1.07252i | −0.978756 | − | 0.205029i | \(-0.934271\pi\) |
−0.497446 | − | 0.867495i | \(-0.665729\pi\) | |||||||
\(174\) | 5.56231 | + | 17.1190i | 0.421677 | + | 1.29779i | ||||
\(175\) | −3.00000 | −0.226779 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | −0.309017 | − | 0.951057i | −0.0231618 | − | 0.0712847i | ||||
\(179\) | 21.0344 | + | 15.2824i | 1.57219 | + | 1.14226i | 0.925023 | + | 0.379912i | \(0.124046\pi\) |
0.647165 | + | 0.762350i | \(0.275954\pi\) | |||||||
\(180\) | 4.85410 | − | 3.52671i | 0.361803 | − | 0.262866i | ||||
\(181\) | −5.87132 | + | 18.0701i | −0.436412 | + | 1.34314i | 0.455221 | + | 0.890379i | \(0.349560\pi\) |
−0.891633 | + | 0.452759i | \(0.850440\pi\) | |||||||
\(182\) | 3.70820 | − | 11.4127i | 0.274870 | − | 0.845964i | ||||
\(183\) | −26.6976 | + | 19.3969i | −1.97354 | + | 1.43386i | ||||
\(184\) | 19.4164 | + | 14.1068i | 1.43140 | + | 1.03997i | ||||
\(185\) | −2.47214 | − | 7.60845i | −0.181755 | − | 0.559385i | ||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | 8.34346 | + | 25.6785i | 0.606897 | + | 1.86784i | ||||
\(190\) | 3.23607 | + | 2.35114i | 0.234769 | + | 0.170570i | ||||
\(191\) | −6.47214 | + | 4.70228i | −0.468307 | + | 0.340245i | −0.796781 | − | 0.604268i | \(-0.793466\pi\) |
0.328474 | + | 0.944513i | \(0.393466\pi\) | |||||||
\(192\) | −6.48936 | + | 19.9722i | −0.468329 | + | 1.44137i | ||||
\(193\) | −3.09017 | + | 9.51057i | −0.222435 | + | 0.684585i | 0.776107 | + | 0.630602i | \(0.217192\pi\) |
−0.998542 | + | 0.0539836i | \(0.982808\pi\) | |||||||
\(194\) | −6.47214 | + | 4.70228i | −0.464672 | + | 0.337604i | ||||
\(195\) | 9.70820 | + | 7.05342i | 0.695219 | + | 0.505106i | ||||
\(196\) | −0.618034 | − | 1.90211i | −0.0441453 | − | 0.135865i | ||||
\(197\) | −14.0000 | −0.997459 | −0.498729 | − | 0.866758i | \(-0.666200\pi\) | ||||
−0.498729 | + | 0.866758i | \(0.666200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.00000 | −0.425329 | −0.212664 | − | 0.977125i | \(-0.568214\pi\) | ||||
−0.212664 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(200\) | 0.927051 | + | 2.85317i | 0.0655524 | + | 0.201750i | ||||
\(201\) | −31.5517 | − | 22.9236i | −2.22548 | − | 1.61691i | ||||
\(202\) | −4.04508 | + | 2.93893i | −0.284611 | + | 0.206782i | ||||
\(203\) | −5.56231 | + | 17.1190i | −0.390397 | + | 1.20152i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.04508 | − | 2.93893i | 0.282521 | − | 0.205264i | ||||
\(206\) | 6.47214 | + | 4.70228i | 0.450935 | + | 0.327624i | ||||
\(207\) | −14.8328 | − | 45.6507i | −1.03095 | − | 3.17294i | ||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −9.00000 | −0.621059 | ||||||||
\(211\) | −6.79837 | − | 20.9232i | −0.468019 | − | 1.44042i | −0.855145 | − | 0.518389i | \(-0.826532\pi\) |
0.387126 | − | 0.922027i | \(-0.373468\pi\) | |||||||
\(212\) | 3.23607 | + | 2.35114i | 0.222254 | + | 0.161477i | ||||
\(213\) | 4.85410 | − | 3.52671i | 0.332598 | − | 0.241646i | ||||
\(214\) | −2.78115 | + | 8.55951i | −0.190116 | + | 0.585116i | ||||
\(215\) | 1.54508 | − | 4.75528i | 0.105374 | − | 0.324308i | ||||
\(216\) | 21.8435 | − | 15.8702i | 1.48626 | − | 1.07983i | ||||
\(217\) | −4.85410 | − | 3.52671i | −0.329518 | − | 0.239409i | ||||
\(218\) | 2.78115 | + | 8.55951i | 0.188363 | + | 0.579723i | ||||
\(219\) | 24.0000 | 1.62177 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.41641 | − | 22.8254i | −0.497757 | − | 1.53194i | ||||
\(223\) | −4.04508 | − | 2.93893i | −0.270879 | − | 0.196805i | 0.444050 | − | 0.896002i | \(-0.353541\pi\) |
−0.714929 | + | 0.699197i | \(0.753541\pi\) | |||||||
\(224\) | −12.1353 | + | 8.81678i | −0.810821 | + | 0.589096i | ||||
\(225\) | 1.85410 | − | 5.70634i | 0.123607 | − | 0.380423i | ||||
\(226\) | −1.85410 | + | 5.70634i | −0.123333 | + | 0.379580i | ||||
\(227\) | 0.809017 | − | 0.587785i | 0.0536963 | − | 0.0390127i | −0.560613 | − | 0.828078i | \(-0.689435\pi\) |
0.614310 | + | 0.789065i | \(0.289435\pi\) | |||||||
\(228\) | −9.70820 | − | 7.05342i | −0.642942 | − | 0.467124i | ||||
\(229\) | −0.309017 | − | 0.951057i | −0.0204204 | − | 0.0628476i | 0.940327 | − | 0.340272i | \(-0.110519\pi\) |
−0.960747 | + | 0.277424i | \(0.910519\pi\) | |||||||
\(230\) | 8.00000 | 0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.0000 | 1.18176 | ||||||||
\(233\) | −7.41641 | − | 22.8254i | −0.485865 | − | 1.49534i | −0.830724 | − | 0.556684i | \(-0.812073\pi\) |
0.344859 | − | 0.938654i | \(-0.387927\pi\) | |||||||
\(234\) | 19.4164 | + | 14.1068i | 1.26929 | + | 0.922193i | ||||
\(235\) | 2.42705 | − | 1.76336i | 0.158323 | − | 0.115029i | ||||
\(236\) | 0.618034 | − | 1.90211i | 0.0402306 | − | 0.123817i | ||||
\(237\) | −9.27051 | + | 28.5317i | −0.602184 | + | 1.85333i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.23607 | − | 2.35114i | −0.209324 | − | 0.152083i | 0.478184 | − | 0.878260i | \(-0.341295\pi\) |
−0.687508 | + | 0.726177i | \(0.741295\pi\) | |||||||
\(240\) | 0.927051 | + | 2.85317i | 0.0598409 | + | 0.184171i | ||||
\(241\) | 23.0000 | 1.48156 | 0.740780 | − | 0.671748i | \(-0.234456\pi\) | ||||
0.740780 | + | 0.671748i | \(0.234456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.39919 | + | 10.4616i | 0.217611 | + | 0.669737i | ||||
\(245\) | −1.61803 | − | 1.17557i | −0.103372 | − | 0.0751044i | ||||
\(246\) | 12.1353 | − | 8.81678i | 0.773716 | − | 0.562137i | ||||
\(247\) | 4.94427 | − | 15.2169i | 0.314596 | − | 0.968228i | ||||
\(248\) | −1.85410 | + | 5.70634i | −0.117736 | + | 0.362353i | ||||
\(249\) | 9.70820 | − | 7.05342i | 0.615232 | − | 0.446993i | ||||
\(250\) | 0.809017 | + | 0.587785i | 0.0511667 | + | 0.0371748i | ||||
\(251\) | 5.56231 | + | 17.1190i | 0.351090 | + | 1.08054i | 0.958242 | + | 0.285958i | \(0.0923116\pi\) |
−0.607153 | + | 0.794585i | \(0.707688\pi\) | |||||||
\(252\) | 18.0000 | 1.13389 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −11.0000 | −0.690201 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.7533 | + | 9.99235i | 0.859581 | + | 0.624522i | ||||
\(257\) | 4.85410 | − | 3.52671i | 0.302791 | − | 0.219990i | −0.426006 | − | 0.904720i | \(-0.640080\pi\) |
0.728797 | + | 0.684730i | \(0.240080\pi\) | |||||||
\(258\) | 4.63525 | − | 14.2658i | 0.288578 | − | 0.888153i | ||||
\(259\) | 7.41641 | − | 22.8254i | 0.460833 | − | 1.41830i | ||||
\(260\) | 3.23607 | − | 2.35114i | 0.200692 | − | 0.145812i | ||||
\(261\) | −29.1246 | − | 21.1603i | −1.80277 | − | 1.30979i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | 0.739952 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 3.70820 | + | 11.4127i | 0.227365 | + | 0.699756i | ||||
\(267\) | 2.42705 | + | 1.76336i | 0.148533 | + | 0.107916i | ||||
\(268\) | −10.5172 | + | 7.64121i | −0.642442 | + | 0.466761i | ||||
\(269\) | 6.48936 | − | 19.9722i | 0.395663 | − | 1.21773i | −0.532781 | − | 0.846253i | \(-0.678853\pi\) |
0.928444 | − | 0.371472i | \(-0.121147\pi\) | |||||||
\(270\) | 2.78115 | − | 8.55951i | 0.169256 | − | 0.520915i | ||||
\(271\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.1246 | + | 34.2380i | 0.673292 | + | 2.07218i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −24.0000 | −1.44463 | ||||||||
\(277\) | 4.32624 | + | 13.3148i | 0.259938 | + | 0.800008i | 0.992816 | + | 0.119648i | \(0.0381766\pi\) |
−0.732878 | + | 0.680360i | \(0.761823\pi\) | |||||||
\(278\) | −14.5623 | − | 10.5801i | −0.873389 | − | 0.634554i | ||||
\(279\) | 9.70820 | − | 7.05342i | 0.581215 | − | 0.422277i | ||||
\(280\) | −2.78115 | + | 8.55951i | −0.166206 | + | 0.511528i | ||||
\(281\) | −1.85410 | + | 5.70634i | −0.110606 | + | 0.340412i | −0.991005 | − | 0.133822i | \(-0.957275\pi\) |
0.880399 | + | 0.474234i | \(0.157275\pi\) | |||||||
\(282\) | 7.28115 | − | 5.29007i | 0.433586 | − | 0.315019i | ||||
\(283\) | 10.5172 | + | 7.64121i | 0.625184 | + | 0.454223i | 0.854728 | − | 0.519075i | \(-0.173724\pi\) |
−0.229545 | + | 0.973298i | \(0.573724\pi\) | |||||||
\(284\) | −0.618034 | − | 1.90211i | −0.0366736 | − | 0.112870i | ||||
\(285\) | −12.0000 | −0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.0000 | 0.885422 | ||||||||
\(288\) | −9.27051 | − | 28.5317i | −0.546270 | − | 1.68125i | ||||
\(289\) | 13.7533 | + | 9.99235i | 0.809017 | + | 0.587785i | ||||
\(290\) | 4.85410 | − | 3.52671i | 0.285043 | − | 0.207096i | ||||
\(291\) | 7.41641 | − | 22.8254i | 0.434758 | − | 1.33805i | ||||
\(292\) | 2.47214 | − | 7.60845i | 0.144671 | − | 0.445251i | ||||
\(293\) | 27.5066 | − | 19.9847i | 1.60695 | − | 1.16752i | 0.734798 | − | 0.678286i | \(-0.237277\pi\) |
0.872153 | − | 0.489233i | \(-0.162723\pi\) | |||||||
\(294\) | −4.85410 | − | 3.52671i | −0.283097 | − | 0.205682i | ||||
\(295\) | −0.618034 | − | 1.90211i | −0.0359833 | − | 0.110745i | ||||
\(296\) | −24.0000 | −1.39497 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.0000 | 0.984784 | ||||||||
\(299\) | −9.88854 | − | 30.4338i | −0.571869 | − | 1.76003i | ||||
\(300\) | −2.42705 | − | 1.76336i | −0.140126 | − | 0.101807i | ||||
\(301\) | 12.1353 | − | 8.81678i | 0.699464 | − | 0.508191i | ||||
\(302\) | 4.32624 | − | 13.3148i | 0.248947 | − | 0.766180i | ||||
\(303\) | 4.63525 | − | 14.2658i | 0.266288 | − | 0.819552i | ||||
\(304\) | 3.23607 | − | 2.35114i | 0.185601 | − | 0.134847i | ||||
\(305\) | 8.89919 | + | 6.46564i | 0.509566 | + | 0.370221i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.00000 | −0.456584 | −0.228292 | − | 0.973593i | \(-0.573314\pi\) | ||||
−0.228292 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.0000 | −1.36531 | ||||||||
\(310\) | 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 | \(0.938219\pi\) | |||||||
\(312\) | 29.1246 | − | 21.1603i | 1.64886 | − | 1.19796i | ||||
\(313\) | 2.47214 | − | 7.60845i | 0.139733 | − | 0.430055i | −0.856563 | − | 0.516043i | \(-0.827405\pi\) |
0.996296 | + | 0.0859876i | \(0.0274046\pi\) | |||||||
\(314\) | 2.47214 | − | 7.60845i | 0.139511 | − | 0.429370i | ||||
\(315\) | 14.5623 | − | 10.5801i | 0.820493 | − | 0.596123i | ||||
\(316\) | 8.09017 | + | 5.87785i | 0.455108 | + | 0.330655i | ||||
\(317\) | 5.56231 | + | 17.1190i | 0.312410 | + | 0.961500i | 0.976807 | + | 0.214120i | \(0.0686884\pi\) |
−0.664397 | + | 0.747380i | \(0.731312\pi\) | |||||||
\(318\) | 12.0000 | 0.672927 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.00000 | 0.391312 | ||||||||
\(321\) | −8.34346 | − | 25.6785i | −0.465686 | − | 1.43324i | ||||
\(322\) | 19.4164 | + | 14.1068i | 1.08203 | + | 0.786144i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.78115 | + | 8.55951i | −0.154508 | + | 0.475528i | ||||
\(325\) | 1.23607 | − | 3.80423i | 0.0685647 | − | 0.211020i | ||||
\(326\) | −13.7533 | + | 9.99235i | −0.761724 | + | 0.553425i | ||||
\(327\) | −21.8435 | − | 15.8702i | −1.20795 | − | 0.877624i | ||||
\(328\) | −4.63525 | − | 14.2658i | −0.255939 | − | 0.787700i | ||||
\(329\) | 9.00000 | 0.496186 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | −1.23607 | − | 3.80423i | −0.0678380 | − | 0.208784i | ||||
\(333\) | 38.8328 | + | 28.2137i | 2.12803 | + | 1.54610i | ||||
\(334\) | −5.66312 | + | 4.11450i | −0.309872 | + | 0.225135i | ||||
\(335\) | −4.01722 | + | 12.3637i | −0.219484 | + | 0.675503i | ||||
\(336\) | −2.78115 | + | 8.55951i | −0.151724 | + | 0.466959i | ||||
\(337\) | 9.70820 | − | 7.05342i | 0.528840 | − | 0.384224i | −0.291084 | − | 0.956698i | \(-0.594016\pi\) |
0.819924 | + | 0.572473i | \(0.194016\pi\) | |||||||
\(338\) | 2.42705 | + | 1.76336i | 0.132014 | + | 0.0959139i | ||||
\(339\) | −5.56231 | − | 17.1190i | −0.302103 | − | 0.929777i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −24.0000 | −1.29777 | ||||||||
\(343\) | 4.63525 | + | 14.2658i | 0.250280 | + | 0.770283i | ||||
\(344\) | −12.1353 | − | 8.81678i | −0.654289 | − | 0.475369i | ||||
\(345\) | −19.4164 | + | 14.1068i | −1.04534 | + | 0.759487i | ||||
\(346\) | −7.41641 | + | 22.8254i | −0.398709 | + | 1.22710i | ||||
\(347\) | 2.16312 | − | 6.65740i | 0.116122 | − | 0.357388i | −0.876057 | − | 0.482207i | \(-0.839835\pi\) |
0.992179 | + | 0.124820i | \(0.0398352\pi\) | |||||||
\(348\) | −14.5623 | + | 10.5801i | −0.780622 | + | 0.567155i | ||||
\(349\) | −17.7984 | − | 12.9313i | −0.952725 | − | 0.692195i | −0.00127528 | − | 0.999999i | \(-0.500406\pi\) |
−0.951450 | + | 0.307804i | \(0.900406\pi\) | |||||||
\(350\) | 0.927051 | + | 2.85317i | 0.0495530 | + | 0.152508i | ||||
\(351\) | −36.0000 | −1.92154 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | −1.85410 | − | 5.70634i | −0.0985444 | − | 0.303289i | ||||
\(355\) | −1.61803 | − | 1.17557i | −0.0858763 | − | 0.0623928i | ||||
\(356\) | 0.809017 | − | 0.587785i | 0.0428778 | − | 0.0311526i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.03444 | − | 24.7275i | 0.424633 | − | 1.30689i | ||||
\(359\) | 22.6525 | − | 16.4580i | 1.19555 | − | 0.868619i | 0.201712 | − | 0.979445i | \(-0.435349\pi\) |
0.993840 | + | 0.110826i | \(0.0353495\pi\) | |||||||
\(360\) | −14.5623 | − | 10.5801i | −0.767501 | − | 0.557622i | ||||
\(361\) | −0.927051 | − | 2.85317i | −0.0487922 | − | 0.150167i | ||||
\(362\) | 19.0000 | 0.998618 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0000 | 0.628971 | ||||||||
\(365\) | −2.47214 | − | 7.60845i | −0.129398 | − | 0.398245i | ||||
\(366\) | 26.6976 | + | 19.3969i | 1.39550 | + | 1.01389i | ||||
\(367\) | −0.809017 | + | 0.587785i | −0.0422303 | + | 0.0306821i | −0.608700 | − | 0.793400i | \(-0.708309\pi\) |
0.566470 | + | 0.824082i | \(0.308309\pi\) | |||||||
\(368\) | 2.47214 | − | 7.60845i | 0.128869 | − | 0.396618i | ||||
\(369\) | −9.27051 | + | 28.5317i | −0.482603 | + | 1.48530i | ||||
\(370\) | −6.47214 | + | 4.70228i | −0.336470 | + | 0.244460i | ||||
\(371\) | 9.70820 | + | 7.05342i | 0.504025 | + | 0.366195i | ||||
\(372\) | −1.85410 | − | 5.70634i | −0.0961307 | − | 0.295860i | ||||
\(373\) | 18.0000 | 0.932005 | 0.466002 | − | 0.884783i | \(-0.345694\pi\) | ||||
0.466002 | + | 0.884783i | \(0.345694\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.00000 | −0.154919 | ||||||||
\(376\) | −2.78115 | − | 8.55951i | −0.143427 | − | 0.441423i | ||||
\(377\) | −19.4164 | − | 14.1068i | −0.999996 | − | 0.726540i | ||||
\(378\) | 21.8435 | − | 15.8702i | 1.12351 | − | 0.816275i | ||||
\(379\) | −6.79837 | + | 20.9232i | −0.349209 | + | 1.07475i | 0.610083 | + | 0.792338i | \(0.291136\pi\) |
−0.959292 | + | 0.282417i | \(0.908864\pi\) | |||||||
\(380\) | −1.23607 | + | 3.80423i | −0.0634089 | + | 0.195153i | ||||
\(381\) | 26.6976 | − | 19.3969i | 1.36776 | − | 0.993734i | ||||
\(382\) | 6.47214 | + | 4.70228i | 0.331143 | + | 0.240590i | ||||
\(383\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(384\) | −9.00000 | −0.459279 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | 9.27051 | + | 28.5317i | 0.471246 | + | 1.45035i | ||||
\(388\) | −6.47214 | − | 4.70228i | −0.328573 | − | 0.238722i | ||||
\(389\) | 2.42705 | − | 1.76336i | 0.123056 | − | 0.0894057i | −0.524555 | − | 0.851377i | \(-0.675768\pi\) |
0.647611 | + | 0.761971i | \(0.275768\pi\) | |||||||
\(390\) | 3.70820 | − | 11.4127i | 0.187772 | − | 0.577903i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.85410 | + | 3.52671i | −0.245169 | + | 0.178126i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.32624 | + | 13.3148i | 0.217953 | + | 0.670789i | ||||
\(395\) | 10.0000 | 0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.0000 | −0.602263 | −0.301131 | − | 0.953583i | \(-0.597364\pi\) | ||||
−0.301131 | + | 0.953583i | \(0.597364\pi\) | |||||||
\(398\) | 1.85410 | + | 5.70634i | 0.0929377 | + | 0.286033i | ||||
\(399\) | −29.1246 | − | 21.1603i | −1.45805 | − | 1.05934i | ||||
\(400\) | 0.809017 | − | 0.587785i | 0.0404508 | − | 0.0293893i | ||||
\(401\) | −11.4336 | + | 35.1891i | −0.570968 | + | 1.75726i | 0.0785467 | + | 0.996910i | \(0.474972\pi\) |
−0.649515 | + | 0.760349i | \(0.725028\pi\) | |||||||
\(402\) | −12.0517 | + | 37.0912i | −0.601082 | + | 1.84994i | ||||
\(403\) | 6.47214 | − | 4.70228i | 0.322400 | − | 0.234237i | ||||
\(404\) | −4.04508 | − | 2.93893i | −0.201250 | − | 0.146217i | ||||
\(405\) | 2.78115 | + | 8.55951i | 0.138197 | + | 0.425325i | ||||
\(406\) | 18.0000 | 0.893325 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.48936 | + | 19.9722i | 0.320878 | + | 0.987561i | 0.973267 | + | 0.229677i | \(0.0737669\pi\) |
−0.652389 | + | 0.757884i | \(0.726233\pi\) | |||||||
\(410\) | −4.04508 | − | 2.93893i | −0.199773 | − | 0.145143i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.47214 | + | 7.60845i | −0.121793 | + | 0.374842i | ||||
\(413\) | 1.85410 | − | 5.70634i | 0.0912344 | − | 0.280791i | ||||
\(414\) | −38.8328 | + | 28.2137i | −1.90853 | + | 1.38663i | ||||
\(415\) | −3.23607 | − | 2.35114i | −0.158852 | − | 0.115413i | ||||
\(416\) | −6.18034 | − | 19.0211i | −0.303016 | − | 0.932588i | ||||
\(417\) | 54.0000 | 2.64439 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.0000 | 1.56330 | 0.781651 | − | 0.623716i | \(-0.214378\pi\) | ||||
0.781651 | + | 0.623716i | \(0.214378\pi\) | |||||||
\(420\) | −2.78115 | − | 8.55951i | −0.135706 | − | 0.417661i | ||||
\(421\) | −2.42705 | − | 1.76336i | −0.118287 | − | 0.0859407i | 0.527069 | − | 0.849823i | \(-0.323291\pi\) |
−0.645356 | + | 0.763882i | \(0.723291\pi\) | |||||||
\(422\) | −17.7984 | + | 12.9313i | −0.866411 | + | 0.629485i | ||||
\(423\) | −5.56231 | + | 17.1190i | −0.270449 | + | 0.832355i | ||||
\(424\) | 3.70820 | − | 11.4127i | 0.180086 | − | 0.554249i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.85410 | − | 3.52671i | −0.235182 | − | 0.170870i | ||||
\(427\) | 10.1976 | + | 31.3849i | 0.493495 | + | 1.51882i | ||||
\(428\) | −9.00000 | −0.435031 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.00000 | −0.241121 | ||||||||
\(431\) | 5.56231 | + | 17.1190i | 0.267927 | + | 0.824594i | 0.991005 | + | 0.133827i | \(0.0427268\pi\) |
−0.723078 | + | 0.690767i | \(0.757273\pi\) | |||||||
\(432\) | −7.28115 | − | 5.29007i | −0.350315 | − | 0.254518i | ||||
\(433\) | −11.3262 | + | 8.22899i | −0.544304 | + | 0.395460i | −0.825681 | − | 0.564137i | \(-0.809209\pi\) |
0.281377 | + | 0.959597i | \(0.409209\pi\) | |||||||
\(434\) | −1.85410 | + | 5.70634i | −0.0889997 | + | 0.273913i | ||||
\(435\) | −5.56231 | + | 17.1190i | −0.266692 | + | 0.820794i | ||||
\(436\) | −7.28115 | + | 5.29007i | −0.348704 | + | 0.253348i | ||||
\(437\) | 25.8885 | + | 18.8091i | 1.23842 | + | 0.899763i | ||||
\(438\) | −7.41641 | − | 22.8254i | −0.354370 | − | 1.09064i | ||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.2254 | + | 14.6946i | 0.960939 | + | 0.698163i | 0.953369 | − | 0.301808i | \(-0.0975903\pi\) |
0.00757032 | + | 0.999971i | \(0.497590\pi\) | |||||||
\(444\) | 19.4164 | − | 14.1068i | 0.921462 | − | 0.669481i | ||||
\(445\) | 0.309017 | − | 0.951057i | 0.0146488 | − | 0.0450844i | ||||
\(446\) | −1.54508 | + | 4.75528i | −0.0731619 | + | 0.225169i | ||||
\(447\) | −41.2599 | + | 29.9770i | −1.95152 | + | 1.41787i | ||||
\(448\) | 16.9894 | + | 12.3435i | 0.802672 | + | 0.583175i | ||||
\(449\) | −4.01722 | − | 12.3637i | −0.189584 | − | 0.583481i | 0.810413 | − | 0.585859i | \(-0.199243\pi\) |
−0.999997 | + | 0.00237857i | \(0.999243\pi\) | |||||||
\(450\) | −6.00000 | −0.282843 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 12.9787 | + | 39.9444i | 0.609793 | + | 1.87675i | ||||
\(454\) | −0.809017 | − | 0.587785i | −0.0379690 | − | 0.0275861i | ||||
\(455\) | 9.70820 | − | 7.05342i | 0.455128 | − | 0.330670i | ||||
\(456\) | −11.1246 | + | 34.2380i | −0.520958 | + | 1.60334i | ||||
\(457\) | 8.03444 | − | 24.7275i | 0.375835 | − | 1.15670i | −0.567078 | − | 0.823664i | \(-0.691926\pi\) |
0.942913 | − | 0.333038i | \(-0.108074\pi\) | |||||||
\(458\) | −0.809017 | + | 0.587785i | −0.0378029 | + | 0.0274654i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.47214 | + | 7.60845i | 0.115264 | + | 0.354746i | ||||
\(461\) | 7.00000 | 0.326023 | 0.163011 | − | 0.986624i | \(-0.447879\pi\) | ||||
0.163011 | + | 0.986624i | \(0.447879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0000 | −0.697109 | −0.348555 | − | 0.937288i | \(-0.613327\pi\) | ||||
−0.348555 | + | 0.937288i | \(0.613327\pi\) | |||||||
\(464\) | −1.85410 | − | 5.70634i | −0.0860745 | − | 0.264910i | ||||
\(465\) | −4.85410 | − | 3.52671i | −0.225104 | − | 0.163547i | ||||
\(466\) | −19.4164 | + | 14.1068i | −0.899448 | + | 0.653487i | ||||
\(467\) | 8.34346 | − | 25.6785i | 0.386089 | − | 1.18826i | −0.549598 | − | 0.835429i | \(-0.685219\pi\) |
0.935687 | − | 0.352831i | \(-0.114781\pi\) | |||||||
\(468\) | −7.41641 | + | 22.8254i | −0.342824 | + | 1.05510i | ||||
\(469\) | −31.5517 | + | 22.9236i | −1.45692 | + | 1.05851i | ||||
\(470\) | −2.42705 | − | 1.76336i | −0.111952 | − | 0.0813375i | ||||
\(471\) | 7.41641 | + | 22.8254i | 0.341730 | + | 1.05174i | ||||
\(472\) | −6.00000 | −0.276172 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 30.0000 | 1.37795 | ||||||||
\(475\) | 1.23607 | + | 3.80423i | 0.0567147 | + | 0.174550i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.4164 | + | 14.1068i | −0.889016 | + | 0.645908i | ||||
\(478\) | −1.23607 | + | 3.80423i | −0.0565364 | + | 0.174001i | ||||
\(479\) | 1.85410 | − | 5.70634i | 0.0847161 | − | 0.260729i | −0.899721 | − | 0.436465i | \(-0.856230\pi\) |
0.984437 | + | 0.175736i | \(0.0562303\pi\) | |||||||
\(480\) | −12.1353 | + | 8.81678i | −0.553896 | + | 0.402429i | ||||
\(481\) | 25.8885 | + | 18.8091i | 1.18042 | + | 0.857622i | ||||
\(482\) | −7.10739 | − | 21.8743i | −0.323733 | − | 0.996347i | ||||
\(483\) | −72.0000 | −3.27611 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.00000 | −0.363261 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.47214 | + | 4.70228i | 0.293280 | + | 0.213081i | 0.724689 | − | 0.689076i | \(-0.241983\pi\) |
−0.431409 | + | 0.902157i | \(0.641983\pi\) | |||||||
\(488\) | 26.6976 | − | 19.3969i | 1.20854 | − | 0.878057i | ||||
\(489\) | 15.7599 | − | 48.5039i | 0.712686 | − | 2.19342i | ||||
\(490\) | −0.618034 | + | 1.90211i | −0.0279199 | + | 0.0859287i | ||||
\(491\) | −17.7984 | + | 12.9313i | −0.803229 | + | 0.583580i | −0.911860 | − | 0.410502i | \(-0.865354\pi\) |
0.108630 | + | 0.994082i | \(0.465354\pi\) | |||||||
\(492\) | 12.1353 | + | 8.81678i | 0.547100 | + | 0.397491i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −16.0000 | −0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −1.85410 | − | 5.70634i | −0.0831678 | − | 0.255964i | ||||
\(498\) | −9.70820 | − | 7.05342i | −0.435035 | − | 0.316071i | ||||
\(499\) | 33.9787 | − | 24.6870i | 1.52110 | − | 1.10514i | 0.560155 | − | 0.828388i | \(-0.310742\pi\) |
0.960941 | − | 0.276753i | \(-0.0892585\pi\) | |||||||
\(500\) | −0.309017 | + | 0.951057i | −0.0138197 | + | 0.0425325i | ||||
\(501\) | 6.48936 | − | 19.9722i | 0.289923 | − | 0.892292i | ||||
\(502\) | 14.5623 | − | 10.5801i | 0.649948 | − | 0.472215i | ||||
\(503\) | −10.5172 | − | 7.64121i | −0.468940 | − | 0.340705i | 0.328088 | − | 0.944647i | \(-0.393596\pi\) |
−0.797028 | + | 0.603942i | \(0.793596\pi\) | |||||||
\(504\) | −16.6869 | − | 51.3571i | −0.743294 | − | 2.28762i | ||||
\(505\) | −5.00000 | −0.222497 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | −3.39919 | − | 10.4616i | −0.150815 | − | 0.464159i | ||||
\(509\) | −18.6074 | − | 13.5191i | −0.824758 | − | 0.599222i | 0.0933133 | − | 0.995637i | \(-0.470254\pi\) |
−0.918071 | + | 0.396415i | \(0.870254\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.41641 | − | 22.8254i | 0.328083 | − | 1.00973i | ||||
\(512\) | 3.39919 | − | 10.4616i | 0.150224 | − | 0.462343i | ||||
\(513\) | 29.1246 | − | 21.1603i | 1.28588 | − | 0.934249i | ||||
\(514\) | −4.85410 | − | 3.52671i | −0.214105 | − | 0.155557i | ||||
\(515\) | 2.47214 | + | 7.60845i | 0.108935 | + | 0.335268i | ||||
\(516\) | 15.0000 | 0.660338 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −24.0000 | −1.05450 | ||||||||
\(519\) | −22.2492 | − | 68.4761i | −0.976633 | − | 3.00577i | ||||
\(520\) | −9.70820 | − | 7.05342i | −0.425733 | − | 0.309313i | ||||
\(521\) | −12.1353 | + | 8.81678i | −0.531655 | + | 0.386270i | −0.820977 | − | 0.570962i | \(-0.806570\pi\) |
0.289321 | + | 0.957232i | \(0.406570\pi\) | |||||||
\(522\) | −11.1246 | + | 34.2380i | −0.486911 | + | 1.49856i | ||||
\(523\) | −1.23607 | + | 3.80423i | −0.0540495 | + | 0.166347i | −0.974437 | − | 0.224659i | \(-0.927873\pi\) |
0.920388 | + | 0.391007i | \(0.127873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.28115 | − | 5.29007i | −0.317776 | − | 0.230877i | ||||
\(526\) | −3.70820 | − | 11.4127i | −0.161685 | − | 0.497616i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | −1.23607 | − | 3.80423i | −0.0536914 | − | 0.165245i | ||||
\(531\) | 9.70820 | + | 7.05342i | 0.421300 | + | 0.306092i | ||||
\(532\) | −9.70820 | + | 7.05342i | −0.420904 | + | 0.305805i | ||||
\(533\) | −6.18034 | + | 19.0211i | −0.267700 | + | 0.823897i | ||||
\(534\) | 0.927051 | − | 2.85317i | 0.0401174 | − | 0.123469i | ||||
\(535\) | −7.28115 | + | 5.29007i | −0.314792 | + | 0.228710i | ||||
\(536\) | 31.5517 | + | 22.9236i | 1.36282 | + | 0.990150i | ||||
\(537\) | 24.1033 | + | 74.1824i | 1.04014 | + | 3.20121i | ||||
\(538\) | −21.0000 | −0.905374 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.00000 | 0.387298 | ||||||||
\(541\) | 9.57953 | + | 29.4828i | 0.411856 | + | 1.26756i | 0.915033 | + | 0.403379i | \(0.132164\pi\) |
−0.503177 | + | 0.864183i | \(0.667836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −46.1140 | + | 33.5038i | −1.97894 | + | 1.43778i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.78115 | + | 8.55951i | −0.119132 | + | 0.366649i | ||||
\(546\) | 29.1246 | − | 21.1603i | 1.24642 | − | 0.905576i | ||||
\(547\) | −29.1246 | − | 21.1603i | −1.24528 | − | 0.904748i | −0.247340 | − | 0.968929i | \(-0.579557\pi\) |
−0.997938 | + | 0.0641809i | \(0.979557\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −66.0000 | −2.81681 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | 22.2492 | + | 68.4761i | 0.946990 | + | 2.91454i | ||||
\(553\) | 24.2705 | + | 17.6336i | 1.03209 | + | 0.749855i | ||||
\(554\) | 11.3262 | − | 8.22899i | 0.481206 | − | 0.349616i | ||||
\(555\) | 7.41641 | − | 22.8254i | 0.314809 | − | 0.968882i | ||||
\(556\) | 5.56231 | − | 17.1190i | 0.235894 | − | 0.726008i | ||||
\(557\) | 22.6525 | − | 16.4580i | 0.959816 | − | 0.697347i | 0.00670815 | − | 0.999978i | \(-0.497865\pi\) |
0.953108 | + | 0.302630i | \(0.0978647\pi\) | |||||||
\(558\) | −9.70820 | − | 7.05342i | −0.410981 | − | 0.298595i | ||||
\(559\) | 6.18034 | + | 19.0211i | 0.261401 | + | 0.804508i | ||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 6.48936 | + | 19.9722i | 0.273494 | + | 0.841727i | 0.989614 | + | 0.143750i | \(0.0459162\pi\) |
−0.716120 | + | 0.697977i | \(0.754084\pi\) | |||||||
\(564\) | 7.28115 | + | 5.29007i | 0.306592 | + | 0.222752i | ||||
\(565\) | −4.85410 | + | 3.52671i | −0.204214 | + | 0.148370i | ||||
\(566\) | 4.01722 | − | 12.3637i | 0.168856 | − | 0.519687i | ||||
\(567\) | −8.34346 | + | 25.6785i | −0.350392 | + | 1.07840i | ||||
\(568\) | −4.85410 | + | 3.52671i | −0.203674 | + | 0.147978i | ||||
\(569\) | 8.89919 | + | 6.46564i | 0.373073 | + | 0.271054i | 0.758484 | − | 0.651691i | \(-0.225940\pi\) |
−0.385411 | + | 0.922745i | \(0.625940\pi\) | |||||||
\(570\) | 3.70820 | + | 11.4127i | 0.155320 | + | 0.478024i | ||||
\(571\) | −18.0000 | −0.753277 | −0.376638 | − | 0.926360i | \(-0.622920\pi\) | ||||
−0.376638 | + | 0.926360i | \(0.622920\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | −4.63525 | − | 14.2658i | −0.193472 | − | 0.595445i | ||||
\(575\) | 6.47214 | + | 4.70228i | 0.269907 | + | 0.196099i | ||||
\(576\) | −33.9787 | + | 24.6870i | −1.41578 | + | 1.02862i | ||||
\(577\) | 4.32624 | − | 13.3148i | 0.180104 | − | 0.554302i | −0.819726 | − | 0.572756i | \(-0.805874\pi\) |
0.999830 | + | 0.0184538i | \(0.00587434\pi\) | |||||||
\(578\) | 5.25329 | − | 16.1680i | 0.218508 | − | 0.672499i | ||||
\(579\) | −24.2705 | + | 17.6336i | −1.00865 | + | 0.732826i | ||||
\(580\) | 4.85410 | + | 3.52671i | 0.201556 | + | 0.146439i | ||||
\(581\) | −3.70820 | − | 11.4127i | −0.153842 | − | 0.473478i | ||||
\(582\) | −24.0000 | −0.994832 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −24.0000 | −0.993127 | ||||||||
\(585\) | 7.41641 | + | 22.8254i | 0.306631 | + | 0.943712i | ||||
\(586\) | −27.5066 | − | 19.9847i | −1.13629 | − | 0.825560i | ||||
\(587\) | −16.9894 | + | 12.3435i | −0.701226 | + | 0.509470i | −0.880331 | − | 0.474360i | \(-0.842680\pi\) |
0.179105 | + | 0.983830i | \(0.442680\pi\) | |||||||
\(588\) | 1.85410 | − | 5.70634i | 0.0764619 | − | 0.235325i | ||||
\(589\) | −2.47214 | + | 7.60845i | −0.101863 | + | 0.313501i | ||||
\(590\) | −1.61803 | + | 1.17557i | −0.0666134 | + | 0.0483975i | ||||
\(591\) | −33.9787 | − | 24.6870i | −1.39770 | − | 1.01549i | ||||
\(592\) | 2.47214 | + | 7.60845i | 0.101604 | + | 0.312705i | ||||
\(593\) | 44.0000 | 1.80686 | 0.903432 | − | 0.428732i | \(-0.141040\pi\) | ||||
0.903432 | + | 0.428732i | \(0.141040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.25329 | + | 16.1680i | 0.215183 | + | 0.662265i | ||||
\(597\) | −14.5623 | − | 10.5801i | −0.595996 | − | 0.433016i | ||||
\(598\) | −25.8885 | + | 18.8091i | −1.05866 | + | 0.769162i | ||||
\(599\) | 7.41641 | − | 22.8254i | 0.303026 | − | 0.932619i | −0.677380 | − | 0.735633i | \(-0.736885\pi\) |
0.980406 | − | 0.196986i | \(-0.0631152\pi\) | |||||||
\(600\) | −2.78115 | + | 8.55951i | −0.113540 | + | 0.349440i | ||||
\(601\) | 1.61803 | − | 1.17557i | 0.0660010 | − | 0.0479525i | −0.554296 | − | 0.832320i | \(-0.687012\pi\) |
0.620297 | + | 0.784367i | \(0.287012\pi\) | |||||||
\(602\) | −12.1353 | − | 8.81678i | −0.494596 | − | 0.359345i | ||||
\(603\) | −24.1033 | − | 74.1824i | −0.981563 | − | 3.02094i | ||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.0000 | −0.609333 | ||||||||
\(607\) | −12.3607 | − | 38.0423i | −0.501705 | − | 1.54409i | −0.806241 | − | 0.591587i | \(-0.798502\pi\) |
0.304537 | − | 0.952501i | \(-0.401498\pi\) | |||||||
\(608\) | 16.1803 | + | 11.7557i | 0.656199 | + | 0.476757i | ||||
\(609\) | −43.6869 | + | 31.7404i | −1.77028 | + | 1.28619i | ||||
\(610\) | 3.39919 | − | 10.4616i | 0.137629 | − | 0.423579i | ||||
\(611\) | −3.70820 | + | 11.4127i | −0.150018 | + | 0.461708i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.7984 | + | 12.9313i | 0.718870 | + | 0.522289i | 0.886023 | − | 0.463642i | \(-0.153457\pi\) |
−0.167153 | + | 0.985931i | \(0.553457\pi\) | |||||||
\(614\) | 2.47214 | + | 7.60845i | 0.0997673 | + | 0.307052i | ||||
\(615\) | 15.0000 | 0.604858 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.0000 | 1.04672 | 0.523360 | − | 0.852111i | \(-0.324678\pi\) | ||||
0.523360 | + | 0.852111i | \(0.324678\pi\) | |||||||
\(618\) | 7.41641 | + | 22.8254i | 0.298332 | + | 0.918170i | ||||
\(619\) | 6.47214 | + | 4.70228i | 0.260137 | + | 0.189001i | 0.710207 | − | 0.703992i | \(-0.248601\pi\) |
−0.450070 | + | 0.892993i | \(0.648601\pi\) | |||||||
\(620\) | −1.61803 | + | 1.17557i | −0.0649818 | + | 0.0472120i | ||||
\(621\) | 22.2492 | − | 68.4761i | 0.892831 | − | 2.74785i | ||||
\(622\) | −7.41641 | + | 22.8254i | −0.297371 | + | 0.915213i | ||||
\(623\) | 2.42705 | − | 1.76336i | 0.0972377 | − | 0.0706474i | ||||
\(624\) | −9.70820 | − | 7.05342i | −0.388639 | − | 0.282363i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | −8.00000 | −0.319744 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.00000 | 0.319235 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −14.5623 | − | 10.5801i | −0.580176 | − | 0.421523i | ||||
\(631\) | 35.5967 | − | 25.8626i | 1.41708 | − | 1.02957i | 0.424840 | − | 0.905269i | \(-0.360330\pi\) |
0.992244 | − | 0.124303i | \(-0.0396696\pi\) | |||||||
\(632\) | 9.27051 | − | 28.5317i | 0.368761 | − | 1.13493i | ||||
\(633\) | 20.3951 | − | 62.7697i | 0.810633 | − | 2.49487i | ||||
\(634\) | 14.5623 | − | 10.5801i | 0.578343 | − | 0.420191i | ||||
\(635\) | −8.89919 | − | 6.46564i | −0.353153 | − | 0.256581i | ||||
\(636\) | 3.70820 | + | 11.4127i | 0.147040 | + | 0.452542i | ||||
\(637\) | 8.00000 | 0.316972 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0.927051 | + | 2.85317i | 0.0366449 | + | 0.112781i | ||||
\(641\) | 11.3262 | + | 8.22899i | 0.447360 | + | 0.325026i | 0.788552 | − | 0.614968i | \(-0.210831\pi\) |
−0.341193 | + | 0.939993i | \(0.610831\pi\) | |||||||
\(642\) | −21.8435 | + | 15.8702i | −0.862093 | + | 0.626347i | ||||
\(643\) | 10.8156 | − | 33.2870i | 0.426525 | − | 1.31271i | −0.475001 | − | 0.879985i | \(-0.657552\pi\) |
0.901526 | − | 0.432725i | \(-0.142448\pi\) | |||||||
\(644\) | −7.41641 | + | 22.8254i | −0.292247 | + | 0.899445i | ||||
\(645\) | 12.1353 | − | 8.81678i | 0.477825 | − | 0.347160i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.72542 | − | 23.7764i | −0.303718 | − | 0.934747i | −0.980153 | − | 0.198245i | \(-0.936476\pi\) |
0.676435 | − | 0.736503i | \(-0.263524\pi\) | |||||||
\(648\) | 27.0000 | 1.06066 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | −0.156893 | ||||||||
\(651\) | −5.56231 | − | 17.1190i | −0.218004 | − | 0.670947i | ||||
\(652\) | −13.7533 | − | 9.99235i | −0.538620 | − | 0.391331i | ||||
\(653\) | 27.5066 | − | 19.9847i | 1.07642 | − | 0.782062i | 0.0993611 | − | 0.995051i | \(-0.468320\pi\) |
0.977054 | + | 0.212990i | \(0.0683201\pi\) | |||||||
\(654\) | −8.34346 | + | 25.6785i | −0.326255 | + | 1.00411i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.04508 | + | 2.93893i | −0.157934 | + | 0.114746i | ||||
\(657\) | 38.8328 | + | 28.2137i | 1.51501 | + | 1.10072i | ||||
\(658\) | −2.78115 | − | 8.55951i | −0.108421 | − | 0.333684i | ||||
\(659\) | −42.0000 | −1.63609 | −0.818044 | − | 0.575156i | \(-0.804941\pi\) | ||||
−0.818044 | + | 0.575156i | \(0.804941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.0000 | −1.43913 | −0.719567 | − | 0.694423i | \(-0.755660\pi\) | ||||
−0.719567 | + | 0.694423i | \(0.755660\pi\) | |||||||
\(662\) | 6.18034 | + | 19.0211i | 0.240206 | + | 0.739277i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.70820 | + | 7.05342i | −0.376751 | + | 0.273726i | ||||
\(665\) | −3.70820 | + | 11.4127i | −0.143798 | + | 0.442565i | ||||
\(666\) | 14.8328 | − | 45.6507i | 0.574760 | − | 1.76893i | ||||
\(667\) | 38.8328 | − | 28.2137i | 1.50361 | − | 1.09244i | ||||
\(668\) | −5.66312 | − | 4.11450i | −0.219113 | − | 0.159195i | ||||
\(669\) | −4.63525 | − | 14.2658i | −0.179209 | − | 0.551550i | ||||
\(670\) | 13.0000 | 0.502234 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −45.0000 | −1.73591 | ||||||||
\(673\) | −3.09017 | − | 9.51057i | −0.119117 | − | 0.366605i | 0.873666 | − | 0.486526i | \(-0.161736\pi\) |
−0.992784 | + | 0.119920i | \(0.961736\pi\) | |||||||
\(674\) | −9.70820 | − | 7.05342i | −0.373946 | − | 0.271688i | ||||
\(675\) | 7.28115 | − | 5.29007i | 0.280252 | − | 0.203615i | ||||
\(676\) | −0.927051 | + | 2.85317i | −0.0356558 | + | 0.109737i | ||||
\(677\) | −8.65248 | + | 26.6296i | −0.332542 | + | 1.02346i | 0.635379 | + | 0.772201i | \(0.280844\pi\) |
−0.967920 | + | 0.251257i | \(0.919156\pi\) | |||||||
\(678\) | −14.5623 | + | 10.5801i | −0.559262 | + | 0.406328i | ||||
\(679\) | −19.4164 | − | 14.1068i | −0.745133 | − | 0.541371i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.0000 | 1.79841 | 0.899203 | − | 0.437533i | \(-0.144148\pi\) | ||||
0.899203 | + | 0.437533i | \(0.144148\pi\) | |||||||
\(684\) | −7.41641 | − | 22.8254i | −0.283573 | − | 0.872749i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.1353 | − | 8.81678i | 0.463326 | − | 0.336626i | ||||
\(687\) | 0.927051 | − | 2.85317i | 0.0353692 | − | 0.108855i | ||||
\(688\) | −1.54508 | + | 4.75528i | −0.0589058 | + | 0.181293i | ||||
\(689\) | −12.9443 | + | 9.40456i | −0.493137 | + | 0.358285i | ||||
\(690\) | 19.4164 | + | 14.1068i | 0.739170 | + | 0.537038i | ||||
\(691\) | −12.3607 | − | 38.0423i | −0.470222 | − | 1.44720i | −0.852294 | − | 0.523063i | \(-0.824789\pi\) |
0.382072 | − | 0.924133i | \(-0.375211\pi\) | |||||||
\(692\) | −24.0000 | −0.912343 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.00000 | −0.265716 | ||||||||
\(695\) | −5.56231 | − | 17.1190i | −0.210990 | − | 0.649361i | ||||
\(696\) | 43.6869 | + | 31.7404i | 1.65595 | + | 1.20312i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −6.79837 | + | 20.9232i | −0.257322 | + | 0.791956i | ||||
\(699\) | 22.2492 | − | 68.4761i | 0.841543 | − | 2.59000i | ||||
\(700\) | −2.42705 | + | 1.76336i | −0.0917339 | + | 0.0666486i | ||||
\(701\) | −30.7426 | − | 22.3358i | −1.16113 | − | 0.843613i | −0.171213 | − | 0.985234i | \(-0.554769\pi\) |
−0.989921 | + | 0.141621i | \(0.954769\pi\) | |||||||
\(702\) | 11.1246 | + | 34.2380i | 0.419871 | + | 1.29223i | ||||
\(703\) | −32.0000 | −1.20690 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.00000 | 0.338960 | ||||||||
\(706\) | −1.85410 | − | 5.70634i | −0.0697800 | − | 0.214761i | ||||
\(707\) | −12.1353 | − | 8.81678i | −0.456393 | − | 0.331589i | ||||
\(708\) | 4.85410 | − | 3.52671i | 0.182428 | − | 0.132542i | ||||
\(709\) | −7.72542 | + | 23.7764i | −0.290134 | + | 0.892942i | 0.694678 | + | 0.719321i | \(0.255547\pi\) |
−0.984813 | + | 0.173621i | \(0.944453\pi\) | |||||||
\(710\) | −0.618034 | + | 1.90211i | −0.0231944 | + | 0.0713850i | ||||
\(711\) | −48.5410 | + | 35.2671i | −1.82043 | + | 1.32262i | ||||
\(712\) | −2.42705 | − | 1.76336i | −0.0909576 | − | 0.0660846i | ||||
\(713\) | 4.94427 | + | 15.2169i | 0.185164 | + | 0.569878i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.0000 | 0.971666 | ||||||||
\(717\) | −3.70820 | − | 11.4127i | −0.138485 | − | 0.426214i | ||||
\(718\) | −22.6525 | − | 16.4580i | −0.845383 | − | 0.614207i | ||||
\(719\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(720\) | −1.85410 | + | 5.70634i | −0.0690983 | + | 0.212663i | ||||
\(721\) | −7.41641 | + | 22.8254i | −0.276201 | + | 0.850061i | ||||
\(722\) | −2.42705 | + | 1.76336i | −0.0903255 | + | 0.0656253i | ||||
\(723\) | 55.8222 | + | 40.5572i | 2.07605 | + | 1.50834i | ||||
\(724\) | 5.87132 | + | 18.0701i | 0.218206 | + | 0.671569i | ||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.0000 | −0.630495 | −0.315248 | − | 0.949009i | \(-0.602088\pi\) | ||||
−0.315248 | + | 0.949009i | \(0.602088\pi\) | |||||||
\(728\) | −11.1246 | − | 34.2380i | −0.412306 | − | 1.26895i | ||||
\(729\) | 21.8435 | + | 15.8702i | 0.809017 | + | 0.587785i | ||||
\(730\) | −6.47214 | + | 4.70228i | −0.239544 | + | 0.174039i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −10.1976 | + | 31.3849i | −0.376913 | + | 1.16002i | ||||
\(733\) | −29.1246 | + | 21.1603i | −1.07574 | + | 0.781572i | −0.976936 | − | 0.213534i | \(-0.931502\pi\) |
−0.0988065 | + | 0.995107i | \(0.531502\pi\) | |||||||
\(734\) | 0.809017 | + | 0.587785i | 0.0298614 | + | 0.0216955i | ||||
\(735\) | −1.85410 | − | 5.70634i | −0.0683896 | − | 0.210481i | ||||
\(736\) | 40.0000 | 1.47442 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 30.0000 | 1.10432 | ||||||||
\(739\) | −3.09017 | − | 9.51057i | −0.113674 | − | 0.349852i | 0.877994 | − | 0.478671i | \(-0.158881\pi\) |
−0.991668 | + | 0.128819i | \(0.958881\pi\) | |||||||
\(740\) | −6.47214 | − | 4.70228i | −0.237920 | − | 0.172859i | ||||
\(741\) | 38.8328 | − | 28.2137i | 1.42656 | − | 1.03646i | ||||
\(742\) | 3.70820 | − | 11.4127i | 0.136132 | − | 0.418973i | ||||
\(743\) | −2.16312 | + | 6.65740i | −0.0793571 | + | 0.244236i | −0.982862 | − | 0.184341i | \(-0.940985\pi\) |
0.903505 | + | 0.428577i | \(0.140985\pi\) | |||||||
\(744\) | −14.5623 | + | 10.5801i | −0.533880 | + | 0.387887i | ||||
\(745\) | 13.7533 | + | 9.99235i | 0.503882 | + | 0.366091i | ||||
\(746\) | −5.56231 | − | 17.1190i | −0.203650 | − | 0.626772i | ||||
\(747\) | 24.0000 | 0.878114 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.0000 | −0.986559 | ||||||||
\(750\) | 0.927051 | + | 2.85317i | 0.0338511 | + | 0.104183i | ||||
\(751\) | −8.09017 | − | 5.87785i | −0.295214 | − | 0.214486i | 0.430312 | − | 0.902680i | \(-0.358404\pi\) |
−0.725526 | + | 0.688194i | \(0.758404\pi\) | |||||||
\(752\) | −2.42705 | + | 1.76336i | −0.0885054 | + | 0.0643030i | ||||
\(753\) | −16.6869 | + | 51.3571i | −0.608105 | + | 1.87156i | ||||
\(754\) | −7.41641 | + | 22.8254i | −0.270090 | + | 0.831250i | ||||
\(755\) | 11.3262 | − | 8.22899i | 0.412204 | − | 0.299484i | ||||
\(756\) | 21.8435 | + | 15.8702i | 0.794439 | + | 0.577194i | ||||
\(757\) | −3.70820 | − | 11.4127i | −0.134777 | − | 0.414801i | 0.860778 | − | 0.508980i | \(-0.169977\pi\) |
−0.995555 | + | 0.0941792i | \(0.969977\pi\) | |||||||
\(758\) | 22.0000 | 0.799076 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | 8.03444 | + | 24.7275i | 0.291248 | + | 0.896370i | 0.984456 | + | 0.175632i | \(0.0561969\pi\) |
−0.693208 | + | 0.720738i | \(0.743803\pi\) | |||||||
\(762\) | −26.6976 | − | 19.3969i | −0.967151 | − | 0.702676i | ||||
\(763\) | −21.8435 | + | 15.8702i | −0.790786 | + | 0.574540i | ||||
\(764\) | −2.47214 | + | 7.60845i | −0.0894387 | + | 0.275264i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.47214 | + | 4.70228i | 0.233695 | + | 0.169790i | ||||
\(768\) | 15.7599 | + | 48.5039i | 0.568685 | + | 1.75023i | ||||
\(769\) | −26.0000 | −0.937584 | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||||
−0.468792 | + | 0.883309i | \(0.655311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 3.09017 | + | 9.51057i | 0.111218 | + | 0.342293i | ||||
\(773\) | 17.7984 | + | 12.9313i | 0.640163 | + | 0.465106i | 0.859906 | − | 0.510452i | \(-0.170522\pi\) |
−0.219743 | + | 0.975558i | \(0.570522\pi\) | |||||||
\(774\) | 24.2705 | − | 17.6336i | 0.872385 | − | 0.633825i | ||||
\(775\) | −0.618034 | + | 1.90211i | −0.0222004 | + | 0.0683259i | ||||
\(776\) | −7.41641 | + | 22.8254i | −0.266234 | + | 0.819383i | ||||
\(777\) | 58.2492 | − | 42.3205i | 2.08968 | − | 1.51824i | ||||
\(778\) | −2.42705 | − | 1.76336i | −0.0870140 | − | 0.0632194i | ||||
\(779\) | −6.18034 | − | 19.0211i | −0.221434 | − | 0.681503i | ||||
\(780\) | 12.0000 | 0.429669 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.6869 | − | 51.3571i | −0.596342 | − | 1.83535i | ||||
\(784\) | 1.61803 | + | 1.17557i | 0.0577869 | + | 0.0419847i | ||||
\(785\) | 6.47214 | − | 4.70228i | 0.231000 | − | 0.167832i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.2877 | + | 40.8954i | −0.473656 | + | 1.45776i | 0.374105 | + | 0.927386i | \(0.377950\pi\) |
−0.847761 | + | 0.530378i | \(0.822050\pi\) | |||||||
\(788\) | −11.3262 | + | 8.22899i | −0.403481 | + | 0.293146i | ||||
\(789\) | 29.1246 | + | 21.1603i | 1.03686 | + | 0.753326i | ||||
\(790\) | −3.09017 | − | 9.51057i | −0.109943 | − | 0.338371i | ||||
\(791\) | −18.0000 | −0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.0000 | −1.56249 | ||||||||
\(794\) | 3.70820 | + | 11.4127i | 0.131599 | + | 0.405021i | ||||
\(795\) | 9.70820 | + | 7.05342i | 0.344315 | + | 0.250159i | ||||
\(796\) | −4.85410 | + | 3.52671i | −0.172049 | + | 0.125001i | ||||
\(797\) | −15.4508 | + | 47.5528i | −0.547297 | + | 1.68441i | 0.168167 | + | 0.985758i | \(0.446215\pi\) |
−0.715465 | + | 0.698649i | \(0.753785\pi\) | |||||||
\(798\) | −11.1246 | + | 34.2380i | −0.393807 | + | 1.21201i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.04508 | + | 2.93893i | 0.143015 | + | 0.103907i | ||||
\(801\) | 1.85410 | + | 5.70634i | 0.0655115 | + | 0.201624i | ||||
\(802\) | 37.0000 | 1.30652 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −39.0000 | −1.37542 | ||||||||
\(805\) | 7.41641 | + | 22.8254i | 0.261394 | + | 0.804488i | ||||
\(806\) | −6.47214 | − | 4.70228i | −0.227971 | − | 0.165631i | ||||
\(807\) | 50.9681 | − | 37.0305i | 1.79416 | − | 1.30353i | ||||
\(808\) | −4.63525 | + | 14.2658i | −0.163068 | + | 0.501871i | ||||
\(809\) | 16.6869 | − | 51.3571i | 0.586681 | − | 1.80562i | −0.00573251 | − | 0.999984i | \(-0.501825\pi\) |
0.592413 | − | 0.805634i | \(-0.298175\pi\) | |||||||
\(810\) | 7.28115 | − | 5.29007i | 0.255834 | − | 0.185874i | ||||
\(811\) | −33.9787 | − | 24.6870i | −1.19315 | − | 0.866877i | −0.199560 | − | 0.979886i | \(-0.563951\pi\) |
−0.993594 | + | 0.113008i | \(0.963951\pi\) | |||||||
\(812\) | 5.56231 | + | 17.1190i | 0.195199 | + | 0.600760i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.0000 | −0.595484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1803 | − | 11.7557i | −0.566078 | − | 0.411280i | ||||
\(818\) | 16.9894 | − | 12.3435i | 0.594019 | − | 0.431580i | ||||
\(819\) | −22.2492 | + | 68.4761i | −0.777451 | + | 2.39275i | ||||
\(820\) | 1.54508 | − | 4.75528i | 0.0539567 | − | 0.166062i | ||||
\(821\) | 2.42705 | − | 1.76336i | 0.0847047 | − | 0.0615415i | −0.544627 | − | 0.838678i | \(-0.683329\pi\) |
0.629332 | + | 0.777137i | \(0.283329\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.7599 | + | 48.5039i | 0.549354 | + | 1.69074i | 0.710405 | + | 0.703793i | \(0.248512\pi\) |
−0.161051 | + | 0.986946i | \(0.551488\pi\) | |||||||
\(824\) | 24.0000 | 0.836080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | −0.208767 | ||||||||
\(827\) | 13.9058 | + | 42.7975i | 0.483551 | + | 1.48822i | 0.834069 | + | 0.551660i | \(0.186006\pi\) |
−0.350518 | + | 0.936556i | \(0.613994\pi\) | |||||||
\(828\) | −38.8328 | − | 28.2137i | −1.34953 | − | 0.980494i | ||||
\(829\) | −10.5172 | + | 7.64121i | −0.365278 | + | 0.265390i | −0.755250 | − | 0.655437i | \(-0.772485\pi\) |
0.389972 | + | 0.920827i | \(0.372485\pi\) | |||||||
\(830\) | −1.23607 | + | 3.80423i | −0.0429045 | + | 0.132047i | ||||
\(831\) | −12.9787 | + | 39.9444i | −0.450227 | + | 1.38565i | ||||
\(832\) | −22.6525 | + | 16.4580i | −0.785333 | + | 0.570578i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.6869 | − | 51.3571i | −0.577821 | − | 1.77835i | ||||
\(835\) | −7.00000 | −0.242245 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.0000 | 0.622171 | ||||||||
\(838\) | −9.88854 | − | 30.4338i | −0.341594 | − | 1.05132i | ||||
\(839\) | 11.3262 | + | 8.22899i | 0.391025 | + | 0.284096i | 0.765875 | − | 0.642989i | \(-0.222306\pi\) |
−0.374850 | + | 0.927085i | \(0.622306\pi\) | |||||||
\(840\) | −21.8435 | + | 15.8702i | −0.753671 | + | 0.547574i | ||||
\(841\) | 2.16312 | − | 6.65740i | 0.0745903 | − | 0.229565i | ||||
\(842\) | −0.927051 | + | 2.85317i | −0.0319483 | + | 0.0983267i | ||||
\(843\) | −14.5623 | + | 10.5801i | −0.501552 | + | 0.364399i | ||||
\(844\) | −17.7984 | − | 12.9313i | −0.612645 | − | 0.445113i | ||||
\(845\) | 0.927051 | + | 2.85317i | 0.0318915 | + | 0.0981520i | ||||
\(846\) | 18.0000 | 0.618853 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.00000 | −0.137361 | ||||||||
\(849\) | 12.0517 | + | 37.0912i | 0.413612 | + | 1.27297i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51.7771 | + | 37.6183i | −1.77490 | + | 1.28954i | ||||
\(852\) | 1.85410 | − | 5.70634i | 0.0635205 | − | 0.195496i | ||||
\(853\) | −9.88854 | + | 30.4338i | −0.338577 | + | 1.04203i | 0.626356 | + | 0.779537i | \(0.284546\pi\) |
−0.964933 | + | 0.262496i | \(0.915454\pi\) | |||||||
\(854\) | 26.6976 | − | 19.3969i | 0.913572 | − | 0.663749i | ||||
\(855\) | −19.4164 | − | 14.1068i | −0.664027 | − | 0.482444i | ||||
\(856\) | 8.34346 | + | 25.6785i | 0.285174 | + | 0.877674i | ||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | 0.136478 | 0.0682391 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682391 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(860\) | −1.54508 | − | 4.75528i | −0.0526870 | − | 0.162154i | ||||
\(861\) | 36.4058 | + | 26.4503i | 1.24071 | + | 0.901425i | ||||
\(862\) | 14.5623 | − | 10.5801i | 0.495994 | − | 0.360361i | ||||
\(863\) | 9.57953 | − | 29.4828i | 0.326091 | − | 1.00360i | −0.644855 | − | 0.764305i | \(-0.723082\pi\) |
0.970946 | − | 0.239300i | \(-0.0769178\pi\) | |||||||
\(864\) | 13.9058 | − | 42.7975i | 0.473084 | − | 1.45600i | ||||
\(865\) | −19.4164 | + | 14.1068i | −0.660178 | + | 0.479647i | ||||
\(866\) | 11.3262 | + | 8.22899i | 0.384881 | + | 0.279633i | ||||
\(867\) | 15.7599 | + | 48.5039i | 0.535233 | + | 1.64728i | ||||
\(868\) | −6.00000 | −0.203653 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.0000 | 0.610257 | ||||||||
\(871\) | −16.0689 | − | 49.4549i | −0.544473 | − | 1.67572i | ||||
\(872\) | 21.8435 | + | 15.8702i | 0.739713 | + | 0.537433i | ||||
\(873\) | 38.8328 | − | 28.2137i | 1.31429 | − | 0.954889i | ||||
\(874\) | 9.88854 | − | 30.4338i | 0.334485 | − | 1.02944i | ||||
\(875\) | −0.927051 | + | 2.85317i | −0.0313400 | + | 0.0964547i | ||||
\(876\) | 19.4164 | − | 14.1068i | 0.656020 | − | 0.476626i | ||||
\(877\) | −17.7984 | − | 12.9313i | −0.601008 | − | 0.436658i | 0.245228 | − | 0.969465i | \(-0.421137\pi\) |
−0.846237 | + | 0.532807i | \(0.821137\pi\) | |||||||
\(878\) | −2.47214 | − | 7.60845i | −0.0834305 | − | 0.256773i | ||||
\(879\) | 102.000 | 3.44037 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | −3.70820 | − | 11.4127i | −0.124862 | − | 0.384285i | ||||
\(883\) | −16.1803 | − | 11.7557i | −0.544512 | − | 0.395611i | 0.281246 | − | 0.959636i | \(-0.409252\pi\) |
−0.825758 | + | 0.564025i | \(0.809252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.85410 | − | 5.70634i | 0.0623250 | − | 0.191816i | ||||
\(886\) | 7.72542 | − | 23.7764i | 0.259541 | − | 0.798784i | ||||
\(887\) | −0.809017 | + | 0.587785i | −0.0271641 | + | 0.0197359i | −0.601284 | − | 0.799035i | \(-0.705344\pi\) |
0.574120 | + | 0.818771i | \(0.305344\pi\) | |||||||
\(888\) | −58.2492 | − | 42.3205i | −1.95472 | − | 1.42018i | ||||
\(889\) | −10.1976 | − | 31.3849i | −0.342015 | − | 1.05261i | ||||
\(890\) | −1.00000 | −0.0335201 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.00000 | −0.167412 | ||||||||
\(893\) | −3.70820 | − | 11.4127i | −0.124090 | − | 0.381911i | ||||
\(894\) | 41.2599 | + | 29.9770i | 1.37994 | + | 1.00258i | ||||
\(895\) | 21.0344 | − | 15.2824i | 0.703104 | − | 0.510835i | ||||
\(896\) | −2.78115 | + | 8.55951i | −0.0929118 | + | 0.285953i | ||||
\(897\) | 29.6656 | − | 91.3014i | 0.990507 | − | 3.04847i | ||||
\(898\) | −10.5172 | + | 7.64121i | −0.350964 | + | 0.254990i | ||||
\(899\) | 9.70820 | + | 7.05342i | 0.323787 | + | 0.235245i | ||||
\(900\) | −1.85410 | − | 5.70634i | −0.0618034 | − | 0.190211i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 45.0000 | 1.49751 | ||||||||
\(904\) | 5.56231 | + | 17.1190i | 0.185000 | + | 0.569370i | ||||
\(905\) | 15.3713 | + | 11.1679i | 0.510960 | + | 0.371234i | ||||
\(906\) | 33.9787 | − | 24.6870i | 1.12887 | − | 0.820170i | ||||
\(907\) | −13.2877 | + | 40.8954i | −0.441212 | + | 1.35791i | 0.445373 | + | 0.895345i | \(0.353071\pi\) |
−0.886585 | + | 0.462565i | \(0.846929\pi\) | |||||||
\(908\) | 0.309017 | − | 0.951057i | 0.0102551 | − | 0.0315619i | ||||
\(909\) | 24.2705 | − | 17.6336i | 0.805002 | − | 0.584868i | ||||
\(910\) | −9.70820 | − | 7.05342i | −0.321824 | − | 0.233819i | ||||
\(911\) | −10.5066 | − | 32.3359i | −0.348098 | − | 1.07134i | −0.959904 | − | 0.280329i | \(-0.909557\pi\) |
0.611806 | − | 0.791008i | \(-0.290443\pi\) | |||||||
\(912\) | 12.0000 | 0.397360 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −26.0000 | −0.860004 | ||||||||
\(915\) | 10.1976 | + | 31.3849i | 0.337121 | + | 1.03755i | ||||
\(916\) | −0.809017 | − | 0.587785i | −0.0267307 | − | 0.0194210i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.70820 | − | 11.4127i | 0.122322 | − | 0.376470i | −0.871081 | − | 0.491139i | \(-0.836581\pi\) |
0.993404 | + | 0.114669i | \(0.0365808\pi\) | |||||||
\(920\) | 19.4164 | − | 14.1068i | 0.640140 | − | 0.465089i | ||||
\(921\) | −19.4164 | − | 14.1068i | −0.639792 | − | 0.464836i | ||||
\(922\) | −2.16312 | − | 6.65740i | −0.0712385 | − | 0.219250i | ||||
\(923\) | 8.00000 | 0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.00000 | −0.263038 | ||||||||
\(926\) | 4.63525 | + | 14.2658i | 0.152324 | + | 0.468805i | ||||
\(927\) | −38.8328 | − | 28.2137i | −1.27544 | − | 0.926659i | ||||
\(928\) | 24.2705 | − | 17.6336i | 0.796719 | − | 0.578850i | ||||
\(929\) | −8.03444 | + | 24.7275i | −0.263601 | + | 0.811282i | 0.728411 | + | 0.685141i | \(0.240259\pi\) |
−0.992012 | + | 0.126141i | \(0.959741\pi\) | |||||||
\(930\) | −1.85410 | + | 5.70634i | −0.0607984 | + | 0.187118i | ||||
\(931\) | −6.47214 | + | 4.70228i | −0.212116 | + | 0.154111i | ||||
\(932\) | −19.4164 | − | 14.1068i | −0.636006 | − | 0.462085i | ||||
\(933\) | −22.2492 | − | 68.4761i | −0.728407 | − | 2.24181i | ||||
\(934\) | −27.0000 | −0.883467 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 72.0000 | 2.35339 | ||||||||
\(937\) | −5.56231 | − | 17.1190i | −0.181713 | − | 0.559254i | 0.818164 | − | 0.574985i | \(-0.194992\pi\) |
−0.999876 | + | 0.0157315i | \(0.994992\pi\) | |||||||
\(938\) | 31.5517 | + | 22.9236i | 1.03020 | + | 0.748483i | ||||
\(939\) | 19.4164 | − | 14.1068i | 0.633631 | − | 0.460360i | ||||
\(940\) | 0.927051 | − | 2.85317i | 0.0302371 | − | 0.0930601i | ||||
\(941\) | −4.01722 | + | 12.3637i | −0.130958 | + | 0.403046i | −0.994939 | − | 0.100477i | \(-0.967963\pi\) |
0.863982 | + | 0.503523i | \(0.167963\pi\) | |||||||
\(942\) | 19.4164 | − | 14.1068i | 0.632621 | − | 0.459626i | ||||
\(943\) | −32.3607 | − | 23.5114i | −1.05381 | − | 0.765637i | ||||
\(944\) | 0.618034 | + | 1.90211i | 0.0201153 | + | 0.0619085i | ||||
\(945\) | 27.0000 | 0.878310 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 9.27051 | + | 28.5317i | 0.301092 | + | 0.926666i | ||||
\(949\) | 25.8885 | + | 18.8091i | 0.840378 | + | 0.610570i | ||||
\(950\) | 3.23607 | − | 2.35114i | 0.104992 | − | 0.0762811i | ||||
\(951\) | −16.6869 | + | 51.3571i | −0.541110 | + | 1.66537i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.1246 | − | 21.1603i | 0.943439 | − | 0.685448i | −0.00580723 | − | 0.999983i | \(-0.501849\pi\) |
0.949246 | + | 0.314535i | \(0.101849\pi\) | |||||||
\(954\) | 19.4164 | + | 14.1068i | 0.628629 | + | 0.456726i | ||||
\(955\) | 2.47214 | + | 7.60845i | 0.0799964 | + | 0.246204i | ||||
\(956\) | −4.00000 | −0.129369 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.00000 | −0.193851 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 16.9894 | + | 12.3435i | 0.548329 | + | 0.398384i | ||||
\(961\) | 21.8435 | − | 15.8702i | 0.704628 | − | 0.511942i | ||||
\(962\) | 9.88854 | − | 30.4338i | 0.318819 | − | 0.981225i | ||||
\(963\) | 16.6869 | − | 51.3571i | 0.537728 | − | 1.65496i | ||||
\(964\) | 18.6074 | − | 13.5191i | 0.599304 | − | 0.435420i | ||||
\(965\) | 8.09017 | + | 5.87785i | 0.260432 | + | 0.189215i | ||||
\(966\) | 22.2492 | + | 68.4761i | 0.715857 | + | 2.20318i | ||||
\(967\) | −32.0000 | −1.02905 | −0.514525 | − | 0.857475i | \(-0.672032\pi\) | ||||
−0.514525 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.47214 | + | 7.60845i | 0.0793755 | + | 0.244293i | ||||
\(971\) | −9.70820 | − | 7.05342i | −0.311551 | − | 0.226355i | 0.421011 | − | 0.907056i | \(-0.361675\pi\) |
−0.732562 | + | 0.680701i | \(0.761675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6869 | − | 51.3571i | 0.534958 | − | 1.64643i | ||||
\(974\) | 2.47214 | − | 7.60845i | 0.0792123 | − | 0.243791i | ||||
\(975\) | 9.70820 | − | 7.05342i | 0.310911 | − | 0.225890i | ||||
\(976\) | −8.89919 | − | 6.46564i | −0.284856 | − | 0.206960i | ||||
\(977\) | 8.65248 | + | 26.6296i | 0.276817 | + | 0.851956i | 0.988733 | + | 0.149691i | \(0.0478278\pi\) |
−0.711916 | + | 0.702265i | \(0.752172\pi\) | |||||||
\(978\) | −51.0000 | −1.63080 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | −16.6869 | − | 51.3571i | −0.532772 | − | 1.63970i | ||||
\(982\) | 17.7984 | + | 12.9313i | 0.567969 | + | 0.412654i | ||||
\(983\) | 49.3500 | − | 35.8549i | 1.57402 | − | 1.14359i | 0.650850 | − | 0.759207i | \(-0.274413\pi\) |
0.923172 | − | 0.384387i | \(-0.125587\pi\) | |||||||
\(984\) | 13.9058 | − | 42.7975i | 0.443300 | − | 1.36434i | ||||
\(985\) | −4.32624 | + | 13.3148i | −0.137845 | + | 0.424245i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.8435 | + | 15.8702i | 0.695285 | + | 0.505154i | ||||
\(988\) | −4.94427 | − | 15.2169i | −0.157298 | − | 0.484114i | ||||
\(989\) | −40.0000 | −1.27193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 3.09017 | + | 9.51057i | 0.0981130 | + | 0.301961i | ||||
\(993\) | −48.5410 | − | 35.2671i | −1.54040 | − | 1.11917i | ||||
\(994\) | −4.85410 | + | 3.52671i | −0.153963 | + | 0.111860i | ||||
\(995\) | −1.85410 | + | 5.70634i | −0.0587790 | + | 0.180903i | ||||
\(996\) | 3.70820 | − | 11.4127i | 0.117499 | − | 0.361625i | ||||
\(997\) | −42.0689 | + | 30.5648i | −1.33233 | + | 0.967998i | −0.332646 | + | 0.943052i | \(0.607941\pi\) |
−0.999689 | + | 0.0249463i | \(0.992059\pi\) | |||||||
\(998\) | −33.9787 | − | 24.6870i | −1.07558 | − | 0.781453i | ||||
\(999\) | 22.2492 | + | 68.4761i | 0.703934 | + | 2.16649i |
(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 | 605.2.g.d.511.1 | 4 | ||
11.2 | odd | 10 | 605.2.g.b.251.1 | 4 | |||
11.3 | even | 5 | 605.2.a.a.1.1 | ✓ | 1 | ||
11.4 | even | 5 | inner | 605.2.g.d.366.1 | 4 | ||
11.5 | even | 5 | inner | 605.2.g.d.81.1 | 4 | ||
11.6 | odd | 10 | 605.2.g.b.81.1 | 4 | |||
11.7 | odd | 10 | 605.2.g.b.366.1 | 4 | |||
11.8 | odd | 10 | 605.2.a.c.1.1 | yes | 1 | ||
11.9 | even | 5 | inner | 605.2.g.d.251.1 | 4 | ||
11.10 | odd | 2 | 605.2.g.b.511.1 | 4 | |||
33.8 | even | 10 | 5445.2.a.d.1.1 | 1 | |||
33.14 | odd | 10 | 5445.2.a.h.1.1 | 1 | |||
44.3 | odd | 10 | 9680.2.a.bf.1.1 | 1 | |||
44.19 | even | 10 | 9680.2.a.be.1.1 | 1 | |||
55.14 | even | 10 | 3025.2.a.g.1.1 | 1 | |||
55.19 | odd | 10 | 3025.2.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.a.1.1 | ✓ | 1 | 11.3 | even | 5 | ||
605.2.a.c.1.1 | yes | 1 | 11.8 | odd | 10 | ||
605.2.g.b.81.1 | 4 | 11.6 | odd | 10 | |||
605.2.g.b.251.1 | 4 | 11.2 | odd | 10 | |||
605.2.g.b.366.1 | 4 | 11.7 | odd | 10 | |||
605.2.g.b.511.1 | 4 | 11.10 | odd | 2 | |||
605.2.g.d.81.1 | 4 | 11.5 | even | 5 | inner | ||
605.2.g.d.251.1 | 4 | 11.9 | even | 5 | inner | ||
605.2.g.d.366.1 | 4 | 11.4 | even | 5 | inner | ||
605.2.g.d.511.1 | 4 | 1.1 | even | 1 | trivial | ||
3025.2.a.c.1.1 | 1 | 55.19 | odd | 10 | |||
3025.2.a.g.1.1 | 1 | 55.14 | even | 10 | |||
5445.2.a.d.1.1 | 1 | 33.8 | even | 10 | |||
5445.2.a.h.1.1 | 1 | 33.14 | odd | 10 | |||
9680.2.a.be.1.1 | 1 | 44.19 | even | 10 | |||
9680.2.a.bf.1.1 | 1 | 44.3 | odd | 10 |