Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 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("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.484000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 421.1 | ||
Root | \(-0.476925 - 1.46782i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.421 |
Dual form | 462.2.j.e.169.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −1.52029 | − | 1.10455i | −0.679893 | − | 0.493971i | 0.193429 | − | 0.981114i | \(-0.438039\pi\) |
−0.873322 | + | 0.487143i | \(0.838039\pi\) | |||||||
\(6\) | −0.809017 | − | 0.587785i | −0.330280 | − | 0.239962i | ||||
\(7\) | 0.309017 | − | 0.951057i | 0.116797 | − | 0.359466i | ||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 1.87918 | 0.594248 | ||||||||
\(11\) | −2.97414 | − | 1.46782i | −0.896736 | − | 0.442566i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.748606 | + | 0.543894i | −0.207626 | + | 0.150849i | −0.686739 | − | 0.726904i | \(-0.740958\pi\) |
0.479113 | + | 0.877753i | \(0.340958\pi\) | |||||||
\(14\) | 0.309017 | + | 0.951057i | 0.0825883 | + | 0.254181i | ||||
\(15\) | 0.580698 | − | 1.78720i | 0.149936 | − | 0.461454i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −3.66140 | − | 2.66016i | −0.888019 | − | 0.645184i | 0.0473418 | − | 0.998879i | \(-0.484925\pi\) |
−0.935361 | + | 0.353695i | \(0.884925\pi\) | |||||||
\(18\) | 0.309017 | − | 0.951057i | 0.0728360 | − | 0.224166i | ||||
\(19\) | −0.858891 | − | 2.64339i | −0.197043 | − | 0.606436i | −0.999947 | − | 0.0103274i | \(-0.996713\pi\) |
0.802904 | − | 0.596109i | \(-0.203287\pi\) | |||||||
\(20\) | −1.52029 | + | 1.10455i | −0.339947 | + | 0.246986i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 3.26889 | − | 0.560659i | 0.696930 | − | 0.119533i | ||||
\(23\) | −4.11525 | −0.858088 | −0.429044 | − | 0.903284i | \(-0.641149\pi\) | ||||
−0.429044 | + | 0.903284i | \(0.641149\pi\) | |||||||
\(24\) | −0.809017 | + | 0.587785i | −0.165140 | + | 0.119981i | ||||
\(25\) | −0.453850 | − | 1.39681i | −0.0907700 | − | 0.279361i | ||||
\(26\) | 0.285942 | − | 0.880039i | 0.0560779 | − | 0.172590i | ||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | −0.809017 | − | 0.587785i | −0.152890 | − | 0.111081i | ||||
\(29\) | 1.44131 | − | 4.43590i | 0.267645 | − | 0.823726i | −0.723427 | − | 0.690401i | \(-0.757434\pi\) |
0.991072 | − | 0.133326i | \(-0.0425657\pi\) | |||||||
\(30\) | 0.580698 | + | 1.78720i | 0.106020 | + | 0.326297i | ||||
\(31\) | −0.635083 | + | 0.461415i | −0.114064 | + | 0.0828726i | −0.643355 | − | 0.765568i | \(-0.722458\pi\) |
0.529291 | + | 0.848441i | \(0.322458\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.476925 | − | 3.28216i | 0.0830220 | − | 0.571350i | ||||
\(34\) | 4.52573 | 0.776157 | ||||||||
\(35\) | −1.52029 | + | 1.10455i | −0.256975 | + | 0.186704i | ||||
\(36\) | 0.309017 | + | 0.951057i | 0.0515028 | + | 0.158509i | ||||
\(37\) | 0.344630 | − | 1.06066i | 0.0566568 | − | 0.174372i | −0.918723 | − | 0.394902i | \(-0.870779\pi\) |
0.975380 | + | 0.220530i | \(0.0707787\pi\) | |||||||
\(38\) | 2.24861 | + | 1.63371i | 0.364772 | + | 0.265022i | ||||
\(39\) | −0.748606 | − | 0.543894i | −0.119873 | − | 0.0870928i | ||||
\(40\) | 0.580698 | − | 1.78720i | 0.0918164 | − | 0.282582i | ||||
\(41\) | 0.146556 | + | 0.451054i | 0.0228882 | + | 0.0704427i | 0.961848 | − | 0.273584i | \(-0.0882090\pi\) |
−0.938960 | + | 0.344026i | \(0.888209\pi\) | |||||||
\(42\) | −0.809017 | + | 0.587785i | −0.124834 | + | 0.0906972i | ||||
\(43\) | 11.0065 | 1.67847 | 0.839236 | − | 0.543767i | \(-0.183003\pi\) | ||||
0.839236 | + | 0.543767i | \(0.183003\pi\) | |||||||
\(44\) | −2.31504 | + | 2.37499i | −0.349006 | + | 0.358043i | ||||
\(45\) | 1.87918 | 0.280131 | ||||||||
\(46\) | 3.32930 | − | 2.41888i | 0.490879 | − | 0.356645i | ||||
\(47\) | −0.574186 | − | 1.76716i | −0.0837536 | − | 0.257767i | 0.900406 | − | 0.435050i | \(-0.143269\pi\) |
−0.984160 | + | 0.177283i | \(0.943269\pi\) | |||||||
\(48\) | 0.309017 | − | 0.951057i | 0.0446028 | − | 0.137273i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 1.18820 | + | 0.863274i | 0.168036 | + | 0.122085i | ||||
\(51\) | 1.39853 | − | 4.30423i | 0.195833 | − | 0.602713i | ||||
\(52\) | 0.285942 | + | 0.880039i | 0.0396530 | + | 0.122039i | ||||
\(53\) | −3.70848 | + | 2.69437i | −0.509399 | + | 0.370100i | −0.812596 | − | 0.582828i | \(-0.801946\pi\) |
0.303196 | + | 0.952928i | \(0.401946\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.90025 | + | 5.51661i | 0.391070 | + | 0.743859i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 2.24861 | − | 1.63371i | 0.297835 | − | 0.216390i | ||||
\(58\) | 1.44131 | + | 4.43590i | 0.189254 | + | 0.582463i | ||||
\(59\) | −0.458940 | + | 1.41247i | −0.0597489 | + | 0.183888i | −0.976476 | − | 0.215625i | \(-0.930821\pi\) |
0.916727 | + | 0.399514i | \(0.130821\pi\) | |||||||
\(60\) | −1.52029 | − | 1.10455i | −0.196268 | − | 0.142597i | ||||
\(61\) | −11.5626 | − | 8.40071i | −1.48044 | − | 1.07560i | −0.977415 | − | 0.211327i | \(-0.932222\pi\) |
−0.503022 | − | 0.864274i | \(-0.667778\pi\) | |||||||
\(62\) | 0.242580 | − | 0.746585i | 0.0308077 | − | 0.0948164i | ||||
\(63\) | 0.309017 | + | 0.951057i | 0.0389325 | + | 0.119822i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 1.73886 | 0.215679 | ||||||||
\(66\) | 1.54336 | + | 2.93565i | 0.189975 | + | 0.361353i | ||||
\(67\) | 0.676236 | 0.0826153 | 0.0413077 | − | 0.999146i | \(-0.486848\pi\) | ||||
0.0413077 | + | 0.999146i | \(0.486848\pi\) | |||||||
\(68\) | −3.66140 | + | 2.66016i | −0.444009 | + | 0.322592i | ||||
\(69\) | −1.27168 | − | 3.91383i | −0.153092 | − | 0.471170i | ||||
\(70\) | 0.580698 | − | 1.78720i | 0.0694067 | − | 0.213612i | ||||
\(71\) | 4.30172 | + | 3.12538i | 0.510520 | + | 0.370914i | 0.813021 | − | 0.582235i | \(-0.197821\pi\) |
−0.302501 | + | 0.953149i | \(0.597821\pi\) | |||||||
\(72\) | −0.809017 | − | 0.587785i | −0.0953436 | − | 0.0692712i | ||||
\(73\) | −1.08442 | + | 3.33751i | −0.126922 | + | 0.390626i | −0.994246 | − | 0.107118i | \(-0.965838\pi\) |
0.867324 | + | 0.497743i | \(0.165838\pi\) | |||||||
\(74\) | 0.344630 | + | 1.06066i | 0.0400624 | + | 0.123299i | ||||
\(75\) | 1.18820 | − | 0.863274i | 0.137201 | − | 0.0996823i | ||||
\(76\) | −2.77943 | −0.318822 | ||||||||
\(77\) | −2.31504 | + | 2.37499i | −0.263824 | + | 0.270655i | ||||
\(78\) | 0.925328 | 0.104773 | ||||||||
\(79\) | 3.23004 | − | 2.34676i | 0.363408 | − | 0.264031i | −0.391064 | − | 0.920363i | \(-0.627893\pi\) |
0.754472 | + | 0.656332i | \(0.227893\pi\) | |||||||
\(80\) | 0.580698 | + | 1.78720i | 0.0649240 | + | 0.199816i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −0.383689 | − | 0.278766i | −0.0423714 | − | 0.0307846i | ||||
\(83\) | −2.55611 | − | 1.85712i | −0.280569 | − | 0.203846i | 0.438596 | − | 0.898684i | \(-0.355476\pi\) |
−0.719166 | + | 0.694839i | \(0.755476\pi\) | |||||||
\(84\) | 0.309017 | − | 0.951057i | 0.0337165 | − | 0.103769i | ||||
\(85\) | 2.62808 | + | 8.08841i | 0.285056 | + | 0.877312i | ||||
\(86\) | −8.90443 | + | 6.46944i | −0.960189 | + | 0.697618i | ||||
\(87\) | 4.66418 | 0.500053 | ||||||||
\(88\) | 0.476925 | − | 3.28216i | 0.0508404 | − | 0.349879i | ||||
\(89\) | −13.6366 | −1.44547 | −0.722736 | − | 0.691124i | \(-0.757116\pi\) | ||||
−0.722736 | + | 0.691124i | \(0.757116\pi\) | |||||||
\(90\) | −1.52029 | + | 1.10455i | −0.160252 | + | 0.116430i | ||||
\(91\) | 0.285942 | + | 0.880039i | 0.0299749 | + | 0.0922532i | ||||
\(92\) | −1.27168 | + | 3.91383i | −0.132582 | + | 0.408045i | ||||
\(93\) | −0.635083 | − | 0.461415i | −0.0658550 | − | 0.0478465i | ||||
\(94\) | 1.50324 | + | 1.09217i | 0.155047 | + | 0.112648i | ||||
\(95\) | −1.61401 | + | 4.96741i | −0.165594 | + | 0.509645i | ||||
\(96\) | 0.309017 | + | 0.951057i | 0.0315389 | + | 0.0970668i | ||||
\(97\) | −3.82930 | + | 2.78215i | −0.388807 | + | 0.282485i | −0.764966 | − | 0.644070i | \(-0.777244\pi\) |
0.376160 | + | 0.926555i | \(0.377244\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 3.26889 | − | 0.560659i | 0.328536 | − | 0.0563484i | ||||
\(100\) | −1.46869 | −0.146869 | ||||||||
\(101\) | 5.06365 | − | 3.67896i | 0.503852 | − | 0.366070i | −0.306634 | − | 0.951827i | \(-0.599203\pi\) |
0.810486 | + | 0.585758i | \(0.199203\pi\) | |||||||
\(102\) | 1.39853 | + | 4.30423i | 0.138475 | + | 0.426182i | ||||
\(103\) | −4.53070 | + | 13.9440i | −0.446423 | + | 1.37395i | 0.434493 | + | 0.900675i | \(0.356927\pi\) |
−0.880916 | + | 0.473273i | \(0.843073\pi\) | |||||||
\(104\) | −0.748606 | − | 0.543894i | −0.0734069 | − | 0.0533332i | ||||
\(105\) | −1.52029 | − | 1.10455i | −0.148365 | − | 0.107793i | ||||
\(106\) | 1.41651 | − | 4.35958i | 0.137584 | − | 0.423440i | ||||
\(107\) | −2.00479 | − | 6.17011i | −0.193810 | − | 0.596487i | −0.999988 | − | 0.00481381i | \(-0.998468\pi\) |
0.806178 | − | 0.591673i | \(-0.201532\pi\) | |||||||
\(108\) | −0.809017 | + | 0.587785i | −0.0778477 | + | 0.0565597i | ||||
\(109\) | −4.20197 | −0.402476 | −0.201238 | − | 0.979542i | \(-0.564496\pi\) | ||||
−0.201238 | + | 0.979542i | \(0.564496\pi\) | |||||||
\(110\) | −5.58893 | − | 2.75830i | −0.532884 | − | 0.262994i | ||||
\(111\) | 1.11525 | 0.105854 | ||||||||
\(112\) | −0.809017 | + | 0.587785i | −0.0764449 | + | 0.0555405i | ||||
\(113\) | 6.10577 | + | 18.7916i | 0.574383 | + | 1.76777i | 0.638271 | + | 0.769812i | \(0.279650\pi\) |
−0.0638881 | + | 0.997957i | \(0.520350\pi\) | |||||||
\(114\) | −0.858891 | + | 2.64339i | −0.0804425 | + | 0.247577i | ||||
\(115\) | 6.25635 | + | 4.54551i | 0.583408 | + | 0.423871i | ||||
\(116\) | −3.77340 | − | 2.74154i | −0.350352 | − | 0.254545i | ||||
\(117\) | 0.285942 | − | 0.880039i | 0.0264354 | − | 0.0813596i | ||||
\(118\) | −0.458940 | − | 1.41247i | −0.0422488 | − | 0.130029i | ||||
\(119\) | −3.66140 | + | 2.66016i | −0.335640 | + | 0.243856i | ||||
\(120\) | 1.87918 | 0.171545 | ||||||||
\(121\) | 6.69098 | + | 8.73102i | 0.608271 | + | 0.793729i | ||||
\(122\) | 14.2921 | 1.29395 | ||||||||
\(123\) | −0.383689 | + | 0.278766i | −0.0345961 | + | 0.0251355i | ||||
\(124\) | 0.242580 | + | 0.746585i | 0.0217843 | + | 0.0670453i | ||||
\(125\) | −3.75635 | + | 11.5609i | −0.335979 | + | 1.03404i | ||||
\(126\) | −0.809017 | − | 0.587785i | −0.0720730 | − | 0.0523641i | ||||
\(127\) | −0.493038 | − | 0.358213i | −0.0437500 | − | 0.0317863i | 0.565695 | − | 0.824614i | \(-0.308608\pi\) |
−0.609445 | + | 0.792828i | \(0.708608\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 3.40119 | + | 10.4678i | 0.299458 | + | 0.921637i | ||||
\(130\) | −1.40676 | + | 1.02207i | −0.123381 | + | 0.0896418i | ||||
\(131\) | 16.7829 | 1.46633 | 0.733163 | − | 0.680053i | \(-0.238043\pi\) | ||||
0.733163 | + | 0.680053i | \(0.238043\pi\) | |||||||
\(132\) | −2.97414 | − | 1.46782i | −0.258865 | − | 0.127758i | ||||
\(133\) | −2.77943 | −0.241007 | ||||||||
\(134\) | −0.547086 | + | 0.397481i | −0.0472610 | + | 0.0343372i | ||||
\(135\) | 0.580698 | + | 1.78720i | 0.0499785 | + | 0.153818i | ||||
\(136\) | 1.39853 | − | 4.30423i | 0.119923 | − | 0.369085i | ||||
\(137\) | 17.7337 | + | 12.8843i | 1.51509 | + | 1.10078i | 0.963853 | + | 0.266435i | \(0.0858459\pi\) |
0.551242 | + | 0.834345i | \(0.314154\pi\) | |||||||
\(138\) | 3.32930 | + | 2.41888i | 0.283409 | + | 0.205909i | ||||
\(139\) | −1.72849 | + | 5.31975i | −0.146609 | + | 0.451215i | −0.997214 | − | 0.0745890i | \(-0.976236\pi\) |
0.850606 | + | 0.525804i | \(0.176236\pi\) | |||||||
\(140\) | 0.580698 | + | 1.78720i | 0.0490779 | + | 0.151046i | ||||
\(141\) | 1.50324 | − | 1.09217i | 0.126595 | − | 0.0919770i | ||||
\(142\) | −5.31722 | −0.446211 | ||||||||
\(143\) | 3.02480 | − | 0.518793i | 0.252946 | − | 0.0433837i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −7.09090 | + | 5.15184i | −0.588867 | + | 0.427837i | ||||
\(146\) | −1.08442 | − | 3.33751i | −0.0897474 | − | 0.276214i | ||||
\(147\) | 0.309017 | − | 0.951057i | 0.0254873 | − | 0.0784418i | ||||
\(148\) | −0.902253 | − | 0.655525i | −0.0741647 | − | 0.0538838i | ||||
\(149\) | −17.3172 | − | 12.5817i | −1.41868 | − | 1.03073i | −0.991987 | − | 0.126337i | \(-0.959678\pi\) |
−0.426694 | − | 0.904396i | \(-0.640322\pi\) | |||||||
\(150\) | −0.453850 | + | 1.39681i | −0.0370567 | + | 0.114049i | ||||
\(151\) | −3.30357 | − | 10.1673i | −0.268841 | − | 0.827407i | −0.990784 | − | 0.135454i | \(-0.956751\pi\) |
0.721943 | − | 0.691953i | \(-0.243249\pi\) | |||||||
\(152\) | 2.24861 | − | 1.63371i | 0.182386 | − | 0.132511i | ||||
\(153\) | 4.52573 | 0.365884 | ||||||||
\(154\) | 0.476925 | − | 3.28216i | 0.0384317 | − | 0.264484i | ||||
\(155\) | 1.47517 | 0.118488 | ||||||||
\(156\) | −0.748606 | + | 0.543894i | −0.0599364 | + | 0.0435464i | ||||
\(157\) | −1.44114 | − | 4.43537i | −0.115016 | − | 0.353981i | 0.876935 | − | 0.480609i | \(-0.159585\pi\) |
−0.991950 | + | 0.126628i | \(0.959585\pi\) | |||||||
\(158\) | −1.23377 | + | 3.79714i | −0.0981532 | + | 0.302084i | ||||
\(159\) | −3.70848 | − | 2.69437i | −0.294102 | − | 0.213677i | ||||
\(160\) | −1.52029 | − | 1.10455i | −0.120189 | − | 0.0873226i | ||||
\(161\) | −1.27168 | + | 3.91383i | −0.100222 | + | 0.308453i | ||||
\(162\) | 0.309017 | + | 0.951057i | 0.0242787 | + | 0.0747221i | ||||
\(163\) | 8.37081 | − | 6.08175i | 0.655653 | − | 0.476360i | −0.209539 | − | 0.977800i | \(-0.567196\pi\) |
0.865192 | + | 0.501441i | \(0.167196\pi\) | |||||||
\(164\) | 0.474266 | 0.0370339 | ||||||||
\(165\) | −4.35038 | + | 4.46303i | −0.338676 | + | 0.347446i | ||||
\(166\) | 3.15952 | 0.245227 | ||||||||
\(167\) | 8.26159 | − | 6.00240i | 0.639301 | − | 0.464480i | −0.220309 | − | 0.975430i | \(-0.570706\pi\) |
0.859610 | + | 0.510951i | \(0.170706\pi\) | |||||||
\(168\) | 0.309017 | + | 0.951057i | 0.0238412 | + | 0.0733756i | ||||
\(169\) | −3.75263 | + | 11.5494i | −0.288664 | + | 0.888416i | ||||
\(170\) | −6.88041 | − | 4.99891i | −0.527704 | − | 0.383399i | ||||
\(171\) | 2.24861 | + | 1.63371i | 0.171955 | + | 0.124933i | ||||
\(172\) | 3.40119 | − | 10.4678i | 0.259338 | − | 0.798161i | ||||
\(173\) | −3.11056 | − | 9.57333i | −0.236492 | − | 0.727847i | −0.996920 | − | 0.0784248i | \(-0.975011\pi\) |
0.760428 | − | 0.649422i | \(-0.224989\pi\) | |||||||
\(174\) | −3.77340 | + | 2.74154i | −0.286061 | + | 0.207835i | ||||
\(175\) | −1.46869 | −0.111023 | ||||||||
\(176\) | 1.54336 | + | 2.93565i | 0.116335 | + | 0.221283i | ||||
\(177\) | −1.48516 | −0.111631 | ||||||||
\(178\) | 11.0322 | − | 8.01537i | 0.826899 | − | 0.600777i | ||||
\(179\) | −0.505748 | − | 1.55653i | −0.0378014 | − | 0.116341i | 0.930375 | − | 0.366609i | \(-0.119481\pi\) |
−0.968177 | + | 0.250268i | \(0.919481\pi\) | |||||||
\(180\) | 0.580698 | − | 1.78720i | 0.0432827 | − | 0.133210i | ||||
\(181\) | −17.3675 | − | 12.6183i | −1.29092 | − | 0.937908i | −0.291096 | − | 0.956694i | \(-0.594020\pi\) |
−0.999824 | + | 0.0187864i | \(0.994020\pi\) | |||||||
\(182\) | −0.748606 | − | 0.543894i | −0.0554904 | − | 0.0403161i | ||||
\(183\) | 4.41651 | − | 13.5926i | 0.326478 | − | 1.00480i | ||||
\(184\) | −1.27168 | − | 3.91383i | −0.0937496 | − | 0.288531i | ||||
\(185\) | −1.69549 | + | 1.23185i | −0.124655 | + | 0.0905673i | ||||
\(186\) | 0.785006 | 0.0575594 | ||||||||
\(187\) | 6.98485 | + | 13.2860i | 0.510783 | + | 0.971566i | ||||
\(188\) | −1.85810 | −0.135516 | ||||||||
\(189\) | −0.809017 | + | 0.587785i | −0.0588473 | + | 0.0427551i | ||||
\(190\) | −1.61401 | − | 4.96741i | −0.117093 | − | 0.360374i | ||||
\(191\) | 2.08979 | − | 6.43171i | 0.151212 | − | 0.465382i | −0.846546 | − | 0.532316i | \(-0.821322\pi\) |
0.997757 | + | 0.0669340i | \(0.0213217\pi\) | |||||||
\(192\) | −0.809017 | − | 0.587785i | −0.0583858 | − | 0.0424197i | ||||
\(193\) | −12.5857 | − | 9.14402i | −0.905936 | − | 0.658201i | 0.0340481 | − | 0.999420i | \(-0.489160\pi\) |
−0.939984 | + | 0.341219i | \(0.889160\pi\) | |||||||
\(194\) | 1.46266 | − | 4.50162i | 0.105013 | − | 0.323197i | ||||
\(195\) | 0.537336 | + | 1.65375i | 0.0384794 | + | 0.118428i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | 19.3367 | 1.37768 | 0.688842 | − | 0.724912i | \(-0.258119\pi\) | ||||
0.688842 | + | 0.724912i | \(0.258119\pi\) | |||||||
\(198\) | −2.31504 | + | 2.37499i | −0.164523 | + | 0.168783i | ||||
\(199\) | 12.1723 | 0.862871 | 0.431435 | − | 0.902144i | \(-0.358007\pi\) | ||||
0.431435 | + | 0.902144i | \(0.358007\pi\) | |||||||
\(200\) | 1.18820 | − | 0.863274i | 0.0840181 | − | 0.0610427i | ||||
\(201\) | 0.208968 | + | 0.643138i | 0.0147395 | + | 0.0453635i | ||||
\(202\) | −1.93414 | + | 5.95268i | −0.136086 | + | 0.418829i | ||||
\(203\) | −3.77340 | − | 2.74154i | −0.264841 | − | 0.192418i | ||||
\(204\) | −3.66140 | − | 2.66016i | −0.256349 | − | 0.186248i | ||||
\(205\) | 0.275405 | − | 0.847610i | 0.0192351 | − | 0.0591996i | ||||
\(206\) | −4.53070 | − | 13.9440i | −0.315668 | − | 0.971528i | ||||
\(207\) | 3.32930 | − | 2.41888i | 0.231403 | − | 0.168124i | ||||
\(208\) | 0.925328 | 0.0641599 | ||||||||
\(209\) | −1.32558 | + | 9.12252i | −0.0916923 | + | 0.631018i | ||||
\(210\) | 1.87918 | 0.129676 | ||||||||
\(211\) | 14.8910 | − | 10.8189i | 1.02514 | − | 0.744804i | 0.0578061 | − | 0.998328i | \(-0.481589\pi\) |
0.967329 | + | 0.253523i | \(0.0815895\pi\) | |||||||
\(212\) | 1.41651 | + | 4.35958i | 0.0972866 | + | 0.299417i | ||||
\(213\) | −1.64311 | + | 5.05697i | −0.112584 | + | 0.346498i | ||||
\(214\) | 5.24861 | + | 3.81334i | 0.358787 | + | 0.260674i | ||||
\(215\) | −16.7330 | − | 12.1572i | −1.14118 | − | 0.829117i | ||||
\(216\) | 0.309017 | − | 0.951057i | 0.0210259 | − | 0.0647112i | ||||
\(217\) | 0.242580 | + | 0.746585i | 0.0164674 | + | 0.0506815i | ||||
\(218\) | 3.39947 | − | 2.46986i | 0.230241 | − | 0.167280i | ||||
\(219\) | −3.50926 | −0.237134 | ||||||||
\(220\) | 6.14283 | − | 1.05358i | 0.414150 | − | 0.0710322i | ||||
\(221\) | 4.18779 | 0.281701 | ||||||||
\(222\) | −0.902253 | + | 0.655525i | −0.0605553 | + | 0.0439960i | ||||
\(223\) | −7.34291 | − | 22.5991i | −0.491717 | − | 1.51335i | −0.822011 | − | 0.569472i | \(-0.807148\pi\) |
0.330293 | − | 0.943878i | \(-0.392852\pi\) | |||||||
\(224\) | 0.309017 | − | 0.951057i | 0.0206471 | − | 0.0635451i | ||||
\(225\) | 1.18820 | + | 0.863274i | 0.0792130 | + | 0.0575516i | ||||
\(226\) | −15.9851 | − | 11.6139i | −1.06331 | − | 0.772543i | ||||
\(227\) | 5.64470 | − | 17.3726i | 0.374652 | − | 1.15306i | −0.569061 | − | 0.822295i | \(-0.692693\pi\) |
0.943713 | − | 0.330765i | \(-0.107307\pi\) | |||||||
\(228\) | −0.858891 | − | 2.64339i | −0.0568815 | − | 0.175063i | ||||
\(229\) | −21.2156 | + | 15.4140i | −1.40197 | + | 1.01859i | −0.407538 | + | 0.913188i | \(0.633612\pi\) |
−0.994430 | + | 0.105400i | \(0.966388\pi\) | |||||||
\(230\) | −7.73328 | −0.509917 | ||||||||
\(231\) | −2.97414 | − | 1.46782i | −0.195684 | − | 0.0965758i | ||||
\(232\) | 4.66418 | 0.306219 | ||||||||
\(233\) | 21.8239 | − | 15.8560i | 1.42973 | − | 1.03876i | 0.439665 | − | 0.898162i | \(-0.355097\pi\) |
0.990067 | − | 0.140598i | \(-0.0449027\pi\) | |||||||
\(234\) | 0.285942 | + | 0.880039i | 0.0186926 | + | 0.0575300i | ||||
\(235\) | −1.07900 | + | 3.32081i | −0.0703860 | + | 0.216626i | ||||
\(236\) | 1.20152 | + | 0.872955i | 0.0782123 | + | 0.0568246i | ||||
\(237\) | 3.23004 | + | 2.34676i | 0.209814 | + | 0.152439i | ||||
\(238\) | 1.39853 | − | 4.30423i | 0.0906532 | − | 0.279002i | ||||
\(239\) | −2.35036 | − | 7.23365i | −0.152032 | − | 0.467906i | 0.845816 | − | 0.533474i | \(-0.179114\pi\) |
−0.997848 | + | 0.0655685i | \(0.979114\pi\) | |||||||
\(240\) | −1.52029 | + | 1.10455i | −0.0981341 | + | 0.0712986i | ||||
\(241\) | −17.5282 | −1.12909 | −0.564546 | − | 0.825402i | \(-0.690949\pi\) | ||||
−0.564546 | + | 0.825402i | \(0.690949\pi\) | |||||||
\(242\) | −10.5451 | − | 3.13068i | −0.677864 | − | 0.201248i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.5626 | + | 8.40071i | −0.740219 | + | 0.537800i | ||||
\(245\) | 0.580698 | + | 1.78720i | 0.0370994 | + | 0.114180i | ||||
\(246\) | 0.146556 | − | 0.451054i | 0.00934408 | − | 0.0287581i | ||||
\(247\) | 2.08070 | + | 1.51172i | 0.132392 | + | 0.0961882i | ||||
\(248\) | −0.635083 | − | 0.461415i | −0.0403278 | − | 0.0292999i | ||||
\(249\) | 0.976346 | − | 3.00489i | 0.0618734 | − | 0.190427i | ||||
\(250\) | −3.75635 | − | 11.5609i | −0.237573 | − | 0.731174i | ||||
\(251\) | 11.3761 | − | 8.26523i | 0.718054 | − | 0.521697i | −0.167708 | − | 0.985837i | \(-0.553637\pi\) |
0.885762 | + | 0.464140i | \(0.153637\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 12.2393 | + | 6.04046i | 0.769479 | + | 0.379760i | ||||
\(254\) | 0.609428 | 0.0382389 | ||||||||
\(255\) | −6.88041 | + | 4.99891i | −0.430868 | + | 0.313044i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −2.65009 | + | 8.15615i | −0.165308 | + | 0.508767i | −0.999059 | − | 0.0433745i | \(-0.986189\pi\) |
0.833751 | + | 0.552141i | \(0.186189\pi\) | |||||||
\(258\) | −8.90443 | − | 6.46944i | −0.554365 | − | 0.402770i | ||||
\(259\) | −0.902253 | − | 0.655525i | −0.0560633 | − | 0.0407324i | ||||
\(260\) | 0.537336 | − | 1.65375i | 0.0333242 | − | 0.102561i | ||||
\(261\) | 1.44131 | + | 4.43590i | 0.0892150 | + | 0.274575i | ||||
\(262\) | −13.5776 | + | 9.86473i | −0.838829 | + | 0.609445i | ||||
\(263\) | 24.1884 | 1.49152 | 0.745760 | − | 0.666215i | \(-0.232087\pi\) | ||||
0.745760 | + | 0.666215i | \(0.232087\pi\) | |||||||
\(264\) | 3.26889 | − | 0.560659i | 0.201186 | − | 0.0345062i | ||||
\(265\) | 8.61403 | 0.529156 | ||||||||
\(266\) | 2.24861 | − | 1.63371i | 0.137871 | − | 0.100169i | ||||
\(267\) | −4.21393 | − | 12.9691i | −0.257888 | − | 0.793699i | ||||
\(268\) | 0.208968 | − | 0.643138i | 0.0127648 | − | 0.0392859i | ||||
\(269\) | −13.4039 | − | 9.73853i | −0.817253 | − | 0.593769i | 0.0986716 | − | 0.995120i | \(-0.468541\pi\) |
−0.915924 | + | 0.401351i | \(0.868541\pi\) | |||||||
\(270\) | −1.52029 | − | 1.10455i | −0.0925217 | − | 0.0672210i | ||||
\(271\) | −8.90924 | + | 27.4198i | −0.541198 | + | 1.66564i | 0.188665 | + | 0.982041i | \(0.439584\pi\) |
−0.729863 | + | 0.683594i | \(0.760416\pi\) | |||||||
\(272\) | 1.39853 | + | 4.30423i | 0.0847983 | + | 0.260982i | ||||
\(273\) | −0.748606 | + | 0.543894i | −0.0453077 | + | 0.0329180i | ||||
\(274\) | −21.9201 | −1.32424 | ||||||||
\(275\) | −0.700455 | + | 4.82047i | −0.0422390 | + | 0.290685i | ||||
\(276\) | −4.11525 | −0.247709 | ||||||||
\(277\) | 13.5410 | − | 9.83813i | 0.813601 | − | 0.591116i | −0.101271 | − | 0.994859i | \(-0.532291\pi\) |
0.914872 | + | 0.403743i | \(0.132291\pi\) | |||||||
\(278\) | −1.72849 | − | 5.31975i | −0.103668 | − | 0.319057i | ||||
\(279\) | 0.242580 | − | 0.746585i | 0.0145229 | − | 0.0446969i | ||||
\(280\) | −1.52029 | − | 1.10455i | −0.0908545 | − | 0.0660097i | ||||
\(281\) | 1.02783 | + | 0.746761i | 0.0613151 | + | 0.0445480i | 0.618021 | − | 0.786162i | \(-0.287935\pi\) |
−0.556706 | + | 0.830710i | \(0.687935\pi\) | |||||||
\(282\) | −0.574186 | + | 1.76716i | −0.0341923 | + | 0.105233i | ||||
\(283\) | 7.31983 | + | 22.5281i | 0.435119 | + | 1.33916i | 0.892965 | + | 0.450127i | \(0.148621\pi\) |
−0.457846 | + | 0.889032i | \(0.651379\pi\) | |||||||
\(284\) | 4.30172 | − | 3.12538i | 0.255260 | − | 0.185457i | ||||
\(285\) | −5.22304 | −0.309386 | ||||||||
\(286\) | −2.14217 | + | 2.19764i | −0.126669 | + | 0.129949i | ||||
\(287\) | 0.474266 | 0.0279950 | ||||||||
\(288\) | −0.809017 | + | 0.587785i | −0.0476718 | + | 0.0346356i | ||||
\(289\) | 1.07608 | + | 3.31184i | 0.0632989 | + | 0.194814i | ||||
\(290\) | 2.70848 | − | 8.33585i | 0.159048 | − | 0.489498i | ||||
\(291\) | −3.82930 | − | 2.78215i | −0.224478 | − | 0.163093i | ||||
\(292\) | 2.83905 | + | 2.06269i | 0.166143 | + | 0.120710i | ||||
\(293\) | 4.10856 | − | 12.6449i | 0.240025 | − | 0.738720i | −0.756390 | − | 0.654121i | \(-0.773039\pi\) |
0.996415 | − | 0.0845996i | \(-0.0269611\pi\) | |||||||
\(294\) | 0.309017 | + | 0.951057i | 0.0180222 | + | 0.0554667i | ||||
\(295\) | 2.25787 | − | 1.64044i | 0.131458 | − | 0.0955100i | ||||
\(296\) | 1.11525 | 0.0648224 | ||||||||
\(297\) | 1.54336 | + | 2.93565i | 0.0895549 | + | 0.170344i | ||||
\(298\) | 21.4053 | 1.23997 | ||||||||
\(299\) | 3.08070 | − | 2.23826i | 0.178161 | − | 0.129442i | ||||
\(300\) | −0.453850 | − | 1.39681i | −0.0262030 | − | 0.0806447i | ||||
\(301\) | 3.40119 | − | 10.4678i | 0.196041 | − | 0.603353i | ||||
\(302\) | 8.64886 | + | 6.28376i | 0.497686 | + | 0.361590i | ||||
\(303\) | 5.06365 | + | 3.67896i | 0.290899 | + | 0.211351i | ||||
\(304\) | −0.858891 | + | 2.64339i | −0.0492608 | + | 0.151609i | ||||
\(305\) | 8.29942 | + | 25.5430i | 0.475223 | + | 1.46259i | ||||
\(306\) | −3.66140 | + | 2.66016i | −0.209308 | + | 0.152071i | ||||
\(307\) | −11.9130 | −0.679912 | −0.339956 | − | 0.940441i | \(-0.610412\pi\) | ||||
−0.339956 | + | 0.940441i | \(0.610412\pi\) | |||||||
\(308\) | 1.54336 | + | 2.93565i | 0.0879412 | + | 0.167274i | ||||
\(309\) | −14.6616 | −0.834071 | ||||||||
\(310\) | −1.19343 | + | 0.867081i | −0.0677825 | + | 0.0492469i | ||||
\(311\) | −9.20339 | − | 28.3251i | −0.521877 | − | 1.60617i | −0.770411 | − | 0.637548i | \(-0.779949\pi\) |
0.248534 | − | 0.968623i | \(-0.420051\pi\) | |||||||
\(312\) | 0.285942 | − | 0.880039i | 0.0161883 | − | 0.0498224i | ||||
\(313\) | −0.497212 | − | 0.361246i | −0.0281041 | − | 0.0204188i | 0.573645 | − | 0.819104i | \(-0.305529\pi\) |
−0.601749 | + | 0.798686i | \(0.705529\pi\) | |||||||
\(314\) | 3.77295 | + | 2.74121i | 0.212920 | + | 0.154696i | ||||
\(315\) | 0.580698 | − | 1.78720i | 0.0327186 | − | 0.100698i | ||||
\(316\) | −1.23377 | − | 3.79714i | −0.0694048 | − | 0.213606i | ||||
\(317\) | 20.7646 | − | 15.0863i | 1.16625 | − | 0.847333i | 0.175698 | − | 0.984444i | \(-0.443782\pi\) |
0.990556 | + | 0.137111i | \(0.0437818\pi\) | |||||||
\(318\) | 4.58394 | 0.257054 | ||||||||
\(319\) | −10.7978 | + | 11.0774i | −0.604560 | + | 0.620215i | ||||
\(320\) | 1.87918 | 0.105049 | ||||||||
\(321\) | 5.24861 | − | 3.81334i | 0.292949 | − | 0.212840i | ||||
\(322\) | −1.27168 | − | 3.91383i | −0.0708680 | − | 0.218109i | ||||
\(323\) | −3.88711 | + | 11.9633i | −0.216285 | + | 0.665656i | ||||
\(324\) | −0.809017 | − | 0.587785i | −0.0449454 | − | 0.0326547i | ||||
\(325\) | 1.09947 | + | 0.798812i | 0.0609876 | + | 0.0443101i | ||||
\(326\) | −3.19737 | + | 9.84048i | −0.177086 | + | 0.545014i | ||||
\(327\) | −1.29848 | − | 3.99631i | −0.0718061 | − | 0.220996i | ||||
\(328\) | −0.383689 | + | 0.278766i | −0.0211857 | + | 0.0153923i | ||||
\(329\) | −1.85810 | −0.102441 | ||||||||
\(330\) | 0.896227 | − | 6.16775i | 0.0493357 | − | 0.339524i | ||||
\(331\) | 32.4433 | 1.78324 | 0.891622 | − | 0.452780i | \(-0.149568\pi\) | ||||
0.891622 | + | 0.452780i | \(0.149568\pi\) | |||||||
\(332\) | −2.55611 | + | 1.85712i | −0.140285 | + | 0.101923i | ||||
\(333\) | 0.344630 | + | 1.06066i | 0.0188856 | + | 0.0581239i | ||||
\(334\) | −3.15565 | + | 9.71209i | −0.172669 | + | 0.531422i | ||||
\(335\) | −1.02807 | − | 0.746938i | −0.0561696 | − | 0.0408096i | ||||
\(336\) | −0.809017 | − | 0.587785i | −0.0441355 | − | 0.0320663i | ||||
\(337\) | −2.55147 | + | 7.85261i | −0.138987 | + | 0.427759i | −0.996189 | − | 0.0872220i | \(-0.972201\pi\) |
0.857202 | + | 0.514981i | \(0.172201\pi\) | |||||||
\(338\) | −3.75263 | − | 11.5494i | −0.204116 | − | 0.628205i | ||||
\(339\) | −15.9851 | + | 11.6139i | −0.868193 | + | 0.630779i | ||||
\(340\) | 8.50466 | 0.461230 | ||||||||
\(341\) | 2.56610 | − | 0.440121i | 0.138962 | − | 0.0238339i | ||||
\(342\) | −2.77943 | −0.150294 | ||||||||
\(343\) | −0.809017 | + | 0.587785i | −0.0436828 | + | 0.0317374i | ||||
\(344\) | 3.40119 | + | 10.4678i | 0.183380 | + | 0.564385i | ||||
\(345\) | −2.38971 | + | 7.35479i | −0.128658 | + | 0.395968i | ||||
\(346\) | 8.14356 | + | 5.91664i | 0.437801 | + | 0.318081i | ||||
\(347\) | 1.23880 | + | 0.900039i | 0.0665021 | + | 0.0483166i | 0.620540 | − | 0.784175i | \(-0.286914\pi\) |
−0.554038 | + | 0.832492i | \(0.686914\pi\) | |||||||
\(348\) | 1.44131 | − | 4.43590i | 0.0772624 | − | 0.237789i | ||||
\(349\) | −5.55443 | − | 17.0948i | −0.297322 | − | 0.915062i | −0.982432 | − | 0.186623i | \(-0.940246\pi\) |
0.685110 | − | 0.728440i | \(-0.259754\pi\) | |||||||
\(350\) | 1.18820 | − | 0.863274i | 0.0635117 | − | 0.0461439i | ||||
\(351\) | 0.925328 | 0.0493904 | ||||||||
\(352\) | −2.97414 | − | 1.46782i | −0.158522 | − | 0.0782353i | ||||
\(353\) | −3.36131 | −0.178904 | −0.0894522 | − | 0.995991i | \(-0.528512\pi\) | ||||
−0.0894522 | + | 0.995991i | \(0.528512\pi\) | |||||||
\(354\) | 1.20152 | − | 0.872955i | 0.0638601 | − | 0.0463971i | ||||
\(355\) | −3.08770 | − | 9.50295i | −0.163878 | − | 0.504364i | ||||
\(356\) | −4.21393 | + | 12.9691i | −0.223338 | + | 0.687363i | ||||
\(357\) | −3.66140 | − | 2.66016i | −0.193782 | − | 0.140791i | ||||
\(358\) | 1.32406 | + | 0.961989i | 0.0699790 | + | 0.0508427i | ||||
\(359\) | −6.26897 | + | 19.2939i | −0.330864 | + | 1.01829i | 0.637860 | + | 0.770152i | \(0.279820\pi\) |
−0.968724 | + | 0.248142i | \(0.920180\pi\) | |||||||
\(360\) | 0.580698 | + | 1.78720i | 0.0306055 | + | 0.0941939i | ||||
\(361\) | 9.12148 | − | 6.62714i | 0.480078 | − | 0.348797i | ||||
\(362\) | 21.4675 | 1.12830 | ||||||||
\(363\) | −6.23607 | + | 9.06154i | −0.327309 | + | 0.475607i | ||||
\(364\) | 0.925328 | 0.0485004 | ||||||||
\(365\) | 5.33509 | − | 3.87617i | 0.279251 | − | 0.202888i | ||||
\(366\) | 4.41651 | + | 13.5926i | 0.230855 | + | 0.710498i | ||||
\(367\) | 1.66725 | − | 5.13127i | 0.0870297 | − | 0.267850i | −0.898065 | − | 0.439863i | \(-0.855027\pi\) |
0.985095 | + | 0.172013i | \(0.0550271\pi\) | |||||||
\(368\) | 3.32930 | + | 2.41888i | 0.173552 | + | 0.126093i | ||||
\(369\) | −0.383689 | − | 0.278766i | −0.0199741 | − | 0.0145120i | ||||
\(370\) | 0.647621 | − | 1.99317i | 0.0336682 | − | 0.103620i | ||||
\(371\) | 1.41651 | + | 4.35958i | 0.0735417 | + | 0.226338i | ||||
\(372\) | −0.635083 | + | 0.461415i | −0.0329275 | + | 0.0239232i | ||||
\(373\) | −27.5943 | −1.42878 | −0.714389 | − | 0.699749i | \(-0.753295\pi\) | ||||
−0.714389 | + | 0.699749i | \(0.753295\pi\) | |||||||
\(374\) | −13.4602 | − | 6.64298i | −0.696008 | − | 0.343500i | ||||
\(375\) | −12.1558 | −0.627724 | ||||||||
\(376\) | 1.50324 | − | 1.09217i | 0.0775236 | − | 0.0563242i | ||||
\(377\) | 1.33369 | + | 4.10466i | 0.0686883 | + | 0.211401i | ||||
\(378\) | 0.309017 | − | 0.951057i | 0.0158941 | − | 0.0489171i | ||||
\(379\) | −6.20152 | − | 4.50567i | −0.318551 | − | 0.231441i | 0.417006 | − | 0.908904i | \(-0.363079\pi\) |
−0.735557 | + | 0.677463i | \(0.763079\pi\) | |||||||
\(380\) | 4.22553 | + | 3.07003i | 0.216765 | + | 0.157489i | ||||
\(381\) | 0.188324 | − | 0.579601i | 0.00964812 | − | 0.0296938i | ||||
\(382\) | 2.08979 | + | 6.43171i | 0.106923 | + | 0.329075i | ||||
\(383\) | 4.62451 | − | 3.35990i | 0.236301 | − | 0.171683i | −0.463333 | − | 0.886185i | \(-0.653346\pi\) |
0.699634 | + | 0.714501i | \(0.253346\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 6.14283 | − | 1.05358i | 0.313068 | − | 0.0536953i | ||||
\(386\) | 15.5567 | 0.791817 | ||||||||
\(387\) | −8.90443 | + | 6.46944i | −0.452637 | + | 0.328860i | ||||
\(388\) | 1.46266 | + | 4.50162i | 0.0742555 | + | 0.228535i | ||||
\(389\) | −3.32996 | + | 10.2486i | −0.168836 | + | 0.519623i | −0.999298 | − | 0.0374512i | \(-0.988076\pi\) |
0.830463 | + | 0.557074i | \(0.188076\pi\) | |||||||
\(390\) | −1.40676 | − | 1.02207i | −0.0712343 | − | 0.0517547i | ||||
\(391\) | 15.0675 | + | 10.9472i | 0.761999 | + | 0.553624i | ||||
\(392\) | 0.309017 | − | 0.951057i | 0.0156077 | − | 0.0480356i | ||||
\(393\) | 5.18619 | + | 15.9615i | 0.261609 | + | 0.805149i | ||||
\(394\) | −15.6437 | + | 11.3658i | −0.788120 | + | 0.572603i | ||||
\(395\) | −7.50272 | −0.377503 | ||||||||
\(396\) | 0.476925 | − | 3.28216i | 0.0239664 | − | 0.164935i | ||||
\(397\) | 18.7092 | 0.938987 | 0.469493 | − | 0.882936i | \(-0.344437\pi\) | ||||
0.469493 | + | 0.882936i | \(0.344437\pi\) | |||||||
\(398\) | −9.84759 | + | 7.15469i | −0.493615 | + | 0.358632i | ||||
\(399\) | −0.858891 | − | 2.64339i | −0.0429983 | − | 0.132335i | ||||
\(400\) | −0.453850 | + | 1.39681i | −0.0226925 | + | 0.0698404i | ||||
\(401\) | −0.0994701 | − | 0.0722692i | −0.00496730 | − | 0.00360895i | 0.585299 | − | 0.810818i | \(-0.300977\pi\) |
−0.590266 | + | 0.807209i | \(0.700977\pi\) | |||||||
\(402\) | −0.547086 | − | 0.397481i | −0.0272862 | − | 0.0198246i | ||||
\(403\) | 0.224466 | − | 0.690836i | 0.0111815 | − | 0.0344130i | ||||
\(404\) | −1.93414 | − | 5.95268i | −0.0962271 | − | 0.296157i | ||||
\(405\) | −1.52029 | + | 1.10455i | −0.0755437 | + | 0.0548857i | ||||
\(406\) | 4.66418 | 0.231480 | ||||||||
\(407\) | −2.58184 | + | 2.64870i | −0.127977 | + | 0.131291i | ||||
\(408\) | 4.52573 | 0.224057 | ||||||||
\(409\) | −11.8550 | + | 8.61316i | −0.586192 | + | 0.425894i | −0.840951 | − | 0.541111i | \(-0.818004\pi\) |
0.254759 | + | 0.967005i | \(0.418004\pi\) | |||||||
\(410\) | 0.275405 | + | 0.847610i | 0.0136013 | + | 0.0418605i | ||||
\(411\) | −6.77368 | + | 20.8472i | −0.334121 | + | 1.02832i | ||||
\(412\) | 11.8615 | + | 8.61789i | 0.584375 | + | 0.424573i | ||||
\(413\) | 1.20152 | + | 0.872955i | 0.0591229 | + | 0.0429553i | ||||
\(414\) | −1.27168 | + | 3.91383i | −0.0624997 | + | 0.192354i | ||||
\(415\) | 1.83473 | + | 5.64671i | 0.0900633 | + | 0.277186i | ||||
\(416\) | −0.748606 | + | 0.543894i | −0.0367034 | + | 0.0266666i | ||||
\(417\) | −5.59351 | −0.273916 | ||||||||
\(418\) | −4.28967 | − | 8.15943i | −0.209814 | − | 0.399091i | ||||
\(419\) | −6.44949 | −0.315078 | −0.157539 | − | 0.987513i | \(-0.550356\pi\) | ||||
−0.157539 | + | 0.987513i | \(0.550356\pi\) | |||||||
\(420\) | −1.52029 | + | 1.10455i | −0.0741824 | + | 0.0538967i | ||||
\(421\) | −7.96927 | − | 24.5269i | −0.388398 | − | 1.19537i | −0.933985 | − | 0.357313i | \(-0.883693\pi\) |
0.545586 | − | 0.838055i | \(-0.316307\pi\) | |||||||
\(422\) | −5.68784 | + | 17.5054i | −0.276880 | + | 0.852148i | ||||
\(423\) | 1.50324 | + | 1.09217i | 0.0730899 | + | 0.0531029i | ||||
\(424\) | −3.70848 | − | 2.69437i | −0.180100 | − | 0.130850i | ||||
\(425\) | −2.05401 | + | 6.32158i | −0.0996339 | + | 0.306642i | ||||
\(426\) | −1.64311 | − | 5.05697i | −0.0796089 | − | 0.245011i | ||||
\(427\) | −11.5626 | + | 8.40071i | −0.559553 | + | 0.406539i | ||||
\(428\) | −6.48763 | −0.313592 | ||||||||
\(429\) | 1.42812 | + | 2.71644i | 0.0689501 | + | 0.131151i | ||||
\(430\) | 20.6831 | 0.997429 | ||||||||
\(431\) | −19.2466 | + | 13.9835i | −0.927075 | + | 0.673559i | −0.945275 | − | 0.326275i | \(-0.894206\pi\) |
0.0182002 | + | 0.999834i | \(0.494206\pi\) | |||||||
\(432\) | 0.309017 | + | 0.951057i | 0.0148676 | + | 0.0457577i | ||||
\(433\) | 7.93826 | − | 24.4314i | 0.381488 | − | 1.17410i | −0.557507 | − | 0.830172i | \(-0.688242\pi\) |
0.938996 | − | 0.343929i | \(-0.111758\pi\) | |||||||
\(434\) | −0.635083 | − | 0.461415i | −0.0304850 | − | 0.0221486i | ||||
\(435\) | −7.09090 | − | 5.15184i | −0.339983 | − | 0.247012i | ||||
\(436\) | −1.29848 | + | 3.99631i | −0.0621859 | + | 0.191389i | ||||
\(437\) | 3.53455 | + | 10.8782i | 0.169080 | + | 0.520376i | ||||
\(438\) | 2.83905 | − | 2.06269i | 0.135655 | − | 0.0985593i | ||||
\(439\) | 31.8712 | 1.52113 | 0.760565 | − | 0.649262i | \(-0.224922\pi\) | ||||
0.760565 | + | 0.649262i | \(0.224922\pi\) | |||||||
\(440\) | −4.35038 | + | 4.46303i | −0.207396 | + | 0.212767i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −3.38799 | + | 2.46152i | −0.161150 | + | 0.117083i | ||||
\(443\) | 4.04349 | + | 12.4446i | 0.192112 | + | 0.591260i | 0.999998 | + | 0.00192142i | \(0.000611607\pi\) |
−0.807886 | + | 0.589339i | \(0.799388\pi\) | |||||||
\(444\) | 0.344630 | − | 1.06066i | 0.0163554 | − | 0.0503368i | ||||
\(445\) | 20.7315 | + | 15.0623i | 0.982767 | + | 0.714022i | ||||
\(446\) | 19.2240 | + | 13.9670i | 0.910282 | + | 0.661358i | ||||
\(447\) | 6.61459 | − | 20.3576i | 0.312859 | − | 0.962882i | ||||
\(448\) | 0.309017 | + | 0.951057i | 0.0145997 | + | 0.0449332i | ||||
\(449\) | −28.7467 | + | 20.8857i | −1.35664 | + | 0.985656i | −0.357989 | + | 0.933726i | \(0.616538\pi\) |
−0.998651 | + | 0.0519307i | \(0.983462\pi\) | |||||||
\(450\) | −1.46869 | −0.0692347 | ||||||||
\(451\) | 0.226189 | − | 1.55661i | 0.0106508 | − | 0.0732981i | ||||
\(452\) | 19.7587 | 0.929371 | ||||||||
\(453\) | 8.64886 | − | 6.28376i | 0.406359 | − | 0.295237i | ||||
\(454\) | 5.64470 | + | 17.3726i | 0.264919 | + | 0.815337i | ||||
\(455\) | 0.537336 | − | 1.65375i | 0.0251907 | − | 0.0775290i | ||||
\(456\) | 2.24861 | + | 1.63371i | 0.105301 | + | 0.0765054i | ||||
\(457\) | −12.9573 | − | 9.41403i | −0.606117 | − | 0.440370i | 0.241928 | − | 0.970294i | \(-0.422220\pi\) |
−0.848045 | + | 0.529925i | \(0.822220\pi\) | |||||||
\(458\) | 8.10364 | − | 24.9405i | 0.378658 | − | 1.16539i | ||||
\(459\) | 1.39853 | + | 4.30423i | 0.0652777 | + | 0.200904i | ||||
\(460\) | 6.25635 | − | 4.54551i | 0.291704 | − | 0.211935i | ||||
\(461\) | −4.43314 | −0.206472 | −0.103236 | − | 0.994657i | \(-0.532920\pi\) | ||||
−0.103236 | + | 0.994657i | \(0.532920\pi\) | |||||||
\(462\) | 3.26889 | − | 0.560659i | 0.152083 | − | 0.0260842i | ||||
\(463\) | −24.2555 | −1.12725 | −0.563624 | − | 0.826031i | \(-0.690593\pi\) | ||||
−0.563624 | + | 0.826031i | \(0.690593\pi\) | |||||||
\(464\) | −3.77340 | + | 2.74154i | −0.175176 | + | 0.127273i | ||||
\(465\) | 0.455851 | + | 1.40297i | 0.0211396 | + | 0.0650610i | ||||
\(466\) | −8.33599 | + | 25.6555i | −0.386157 | + | 1.18847i | ||||
\(467\) | 6.12054 | + | 4.44684i | 0.283225 | + | 0.205775i | 0.720323 | − | 0.693639i | \(-0.243994\pi\) |
−0.437098 | + | 0.899414i | \(0.643994\pi\) | |||||||
\(468\) | −0.748606 | − | 0.543894i | −0.0346043 | − | 0.0251415i | ||||
\(469\) | 0.208968 | − | 0.643138i | 0.00964926 | − | 0.0296974i | ||||
\(470\) | −1.07900 | − | 3.32081i | −0.0497704 | − | 0.153178i | ||||
\(471\) | 3.77295 | − | 2.74121i | 0.173849 | − | 0.126308i | ||||
\(472\) | −1.48516 | −0.0683600 | ||||||||
\(473\) | −32.7348 | − | 16.1556i | −1.50515 | − | 0.742834i | ||||
\(474\) | −3.99255 | −0.183384 | ||||||||
\(475\) | −3.30250 | + | 2.39941i | −0.151529 | + | 0.110092i | ||||
\(476\) | 1.39853 | + | 4.30423i | 0.0641015 | + | 0.197284i | ||||
\(477\) | 1.41651 | − | 4.35958i | 0.0648577 | − | 0.199612i | ||||
\(478\) | 6.15331 | + | 4.47064i | 0.281446 | + | 0.204482i | ||||
\(479\) | −14.3237 | − | 10.4068i | −0.654466 | − | 0.475498i | 0.210323 | − | 0.977632i | \(-0.432548\pi\) |
−0.864790 | + | 0.502134i | \(0.832548\pi\) | |||||||
\(480\) | 0.580698 | − | 1.78720i | 0.0265051 | − | 0.0815744i | ||||
\(481\) | 0.318896 | + | 0.981460i | 0.0145404 | + | 0.0447507i | ||||
\(482\) | 14.1806 | − | 10.3028i | 0.645909 | − | 0.469281i | ||||
\(483\) | −4.11525 | −0.187250 | ||||||||
\(484\) | 10.3713 | − | 3.66547i | 0.471424 | − | 0.166612i | ||||
\(485\) | 8.89468 | 0.403886 | ||||||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | −8.04047 | − | 24.7460i | −0.364348 | − | 1.12135i | −0.950388 | − | 0.311067i | \(-0.899314\pi\) |
0.586040 | − | 0.810282i | \(-0.300686\pi\) | |||||||
\(488\) | 4.41651 | − | 13.5926i | 0.199926 | − | 0.615310i | ||||
\(489\) | 8.37081 | + | 6.08175i | 0.378541 | + | 0.275026i | ||||
\(490\) | −1.52029 | − | 1.10455i | −0.0686796 | − | 0.0498986i | ||||
\(491\) | 10.9992 | − | 33.8521i | 0.496388 | − | 1.52772i | −0.318396 | − | 0.947958i | \(-0.603144\pi\) |
0.814783 | − | 0.579766i | \(-0.196856\pi\) | |||||||
\(492\) | 0.146556 | + | 0.451054i | 0.00660726 | + | 0.0203351i | ||||
\(493\) | −17.0774 | + | 12.4075i | −0.769128 | + | 0.558805i | ||||
\(494\) | −2.57188 | −0.115715 | ||||||||
\(495\) | −5.58893 | − | 2.75830i | −0.251204 | − | 0.123977i | ||||
\(496\) | 0.785006 | 0.0352478 | ||||||||
\(497\) | 4.30172 | − | 3.12538i | 0.192958 | − | 0.140193i | ||||
\(498\) | 0.976346 | + | 3.00489i | 0.0437511 | + | 0.134652i | ||||
\(499\) | −4.54496 | + | 13.9879i | −0.203460 | + | 0.626186i | 0.796313 | + | 0.604885i | \(0.206781\pi\) |
−0.999773 | + | 0.0213012i | \(0.993219\pi\) | |||||||
\(500\) | 9.83426 | + | 7.14501i | 0.439802 | + | 0.319535i | ||||
\(501\) | 8.26159 | + | 6.00240i | 0.369101 | + | 0.268167i | ||||
\(502\) | −4.34529 | + | 13.3734i | −0.193940 | + | 0.596885i | ||||
\(503\) | 13.2446 | + | 40.7626i | 0.590546 | + | 1.81751i | 0.575753 | + | 0.817623i | \(0.304709\pi\) |
0.0147926 | + | 0.999891i | \(0.495291\pi\) | |||||||
\(504\) | −0.809017 | + | 0.587785i | −0.0360365 | + | 0.0261820i | ||||
\(505\) | −11.7618 | −0.523393 | ||||||||
\(506\) | −13.4523 | + | 2.30725i | −0.598028 | + | 0.102570i | ||||
\(507\) | −12.1438 | −0.539324 | ||||||||
\(508\) | −0.493038 | + | 0.358213i | −0.0218750 | + | 0.0158931i | ||||
\(509\) | −8.08783 | − | 24.8918i | −0.358487 | − | 1.10331i | −0.953960 | − | 0.299934i | \(-0.903035\pi\) |
0.595473 | − | 0.803375i | \(-0.296965\pi\) | |||||||
\(510\) | 2.62808 | − | 8.08841i | 0.116374 | − | 0.358161i | ||||
\(511\) | 2.83905 | + | 2.06269i | 0.125592 | + | 0.0912482i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | −0.858891 | + | 2.64339i | −0.0379210 | + | 0.116709i | ||||
\(514\) | −2.65009 | − | 8.15615i | −0.116891 | − | 0.359752i | ||||
\(515\) | 22.2899 | − | 16.1946i | 0.982210 | − | 0.713617i | ||||
\(516\) | 11.0065 | 0.484533 | ||||||||
\(517\) | −0.886176 | + | 6.09859i | −0.0389740 | + | 0.268216i | ||||
\(518\) | 1.11525 | 0.0490011 | ||||||||
\(519\) | 8.14356 | − | 5.91664i | 0.357463 | − | 0.259712i | ||||
\(520\) | 0.537336 | + | 1.65375i | 0.0235637 | + | 0.0725217i | ||||
\(521\) | 0.887886 | − | 2.73263i | 0.0388990 | − | 0.119719i | −0.929721 | − | 0.368264i | \(-0.879952\pi\) |
0.968620 | + | 0.248545i | \(0.0799524\pi\) | |||||||
\(522\) | −3.77340 | − | 2.74154i | −0.165157 | − | 0.119994i | ||||
\(523\) | 18.1287 | + | 13.1713i | 0.792712 | + | 0.575939i | 0.908767 | − | 0.417304i | \(-0.137025\pi\) |
−0.116055 | + | 0.993243i | \(0.537025\pi\) | |||||||
\(524\) | 5.18619 | − | 15.9615i | 0.226560 | − | 0.697280i | ||||
\(525\) | −0.453850 | − | 1.39681i | −0.0198076 | − | 0.0609617i | ||||
\(526\) | −19.5688 | + | 14.2176i | −0.853241 | + | 0.619916i | ||||
\(527\) | 3.55273 | 0.154759 | ||||||||
\(528\) | −2.31504 | + | 2.37499i | −0.100749 | + | 0.103358i | ||||
\(529\) | −6.06475 | −0.263685 | ||||||||
\(530\) | −6.96890 | + | 5.06320i | −0.302710 | + | 0.219931i | ||||
\(531\) | −0.458940 | − | 1.41247i | −0.0199163 | − | 0.0612960i | ||||
\(532\) | −0.858891 | + | 2.64339i | −0.0372377 | + | 0.114606i | ||||
\(533\) | −0.355038 | − | 0.257950i | −0.0153784 | − | 0.0111731i | ||||
\(534\) | 11.0322 | + | 8.01537i | 0.477410 | + | 0.346859i | ||||
\(535\) | −3.76736 | + | 11.5947i | −0.162877 | + | 0.501284i | ||||
\(536\) | 0.208968 | + | 0.643138i | 0.00902606 | + | 0.0277793i | ||||
\(537\) | 1.32406 | − | 0.961989i | 0.0571376 | − | 0.0415129i | ||||
\(538\) | 16.5682 | 0.714305 | ||||||||
\(539\) | 1.54336 | + | 2.93565i | 0.0664773 | + | 0.126447i | ||||
\(540\) | 1.87918 | 0.0808669 | ||||||||
\(541\) | 23.1086 | − | 16.7894i | 0.993515 | − | 0.721831i | 0.0328269 | − | 0.999461i | \(-0.489549\pi\) |
0.960688 | + | 0.277630i | \(0.0895490\pi\) | |||||||
\(542\) | −8.90924 | − | 27.4198i | −0.382685 | − | 1.17778i | ||||
\(543\) | 6.63381 | − | 20.4168i | 0.284684 | − | 0.876167i | ||||
\(544\) | −3.66140 | − | 2.66016i | −0.156981 | − | 0.114053i | ||||
\(545\) | 6.38820 | + | 4.64130i | 0.273640 | + | 0.198811i | ||||
\(546\) | 0.285942 | − | 0.880039i | 0.0122372 | − | 0.0376622i | ||||
\(547\) | −6.80194 | − | 20.9342i | −0.290830 | − | 0.895082i | −0.984590 | − | 0.174877i | \(-0.944047\pi\) |
0.693760 | − | 0.720206i | \(-0.255953\pi\) | |||||||
\(548\) | 17.7337 | − | 12.8843i | 0.757547 | − | 0.550390i | ||||
\(549\) | 14.2921 | 0.609974 | ||||||||
\(550\) | −2.26672 | − | 4.31156i | −0.0966533 | − | 0.183845i | ||||
\(551\) | −12.9638 | −0.552275 | ||||||||
\(552\) | 3.32930 | − | 2.41888i | 0.141705 | − | 0.102954i | ||||
\(553\) | −1.23377 | − | 3.79714i | −0.0524651 | − | 0.161471i | ||||
\(554\) | −5.17221 | + | 15.9184i | −0.219746 | + | 0.676309i | ||||
\(555\) | −1.69549 | − | 1.23185i | −0.0719697 | − | 0.0522891i | ||||
\(556\) | 4.52525 | + | 3.28779i | 0.191913 | + | 0.139433i | ||||
\(557\) | −9.27072 | + | 28.5323i | −0.392813 | + | 1.20895i | 0.537838 | + | 0.843048i | \(0.319241\pi\) |
−0.930652 | + | 0.365907i | \(0.880759\pi\) | |||||||
\(558\) | 0.242580 | + | 0.746585i | 0.0102692 | + | 0.0316055i | ||||
\(559\) | −8.23951 | + | 5.98636i | −0.348494 | + | 0.253196i | ||||
\(560\) | 1.87918 | 0.0794098 | ||||||||
\(561\) | −10.4773 | + | 10.7486i | −0.442351 | + | 0.453805i | ||||
\(562\) | −1.27046 | −0.0535913 | ||||||||
\(563\) | −11.0797 | + | 8.04991i | −0.466956 | + | 0.339263i | −0.796254 | − | 0.604963i | \(-0.793188\pi\) |
0.329298 | + | 0.944226i | \(0.393188\pi\) | |||||||
\(564\) | −0.574186 | − | 1.76716i | −0.0241776 | − | 0.0744110i | ||||
\(565\) | 11.4738 | − | 35.3128i | 0.482708 | − | 1.48562i | ||||
\(566\) | −19.1636 | − | 13.9231i | −0.805505 | − | 0.585234i | ||||
\(567\) | −0.809017 | − | 0.587785i | −0.0339755 | − | 0.0246847i | ||||
\(568\) | −1.64311 | + | 5.05697i | −0.0689434 | + | 0.212186i | ||||
\(569\) | −4.79962 | − | 14.7717i | −0.201211 | − | 0.619263i | −0.999848 | − | 0.0174499i | \(-0.994445\pi\) |
0.798637 | − | 0.601813i | \(-0.205555\pi\) | |||||||
\(570\) | 4.22553 | − | 3.07003i | 0.176988 | − | 0.128589i | ||||
\(571\) | 0.403940 | 0.0169044 | 0.00845218 | − | 0.999964i | \(-0.497310\pi\) | ||||
0.00845218 | + | 0.999964i | \(0.497310\pi\) | |||||||
\(572\) | 0.441312 | − | 3.03707i | 0.0184522 | − | 0.126986i | ||||
\(573\) | 6.76270 | 0.282516 | ||||||||
\(574\) | −0.383689 | + | 0.278766i | −0.0160149 | + | 0.0116355i | ||||
\(575\) | 1.86770 | + | 5.74820i | 0.0778887 | + | 0.239717i | ||||
\(576\) | 0.309017 | − | 0.951057i | 0.0128757 | − | 0.0396274i | ||||
\(577\) | 14.6103 | + | 10.6150i | 0.608235 | + | 0.441909i | 0.848792 | − | 0.528726i | \(-0.177330\pi\) |
−0.240557 | + | 0.970635i | \(0.577330\pi\) | |||||||
\(578\) | −2.81722 | − | 2.04683i | −0.117181 | − | 0.0851368i | ||||
\(579\) | 4.80729 | − | 14.7953i | 0.199784 | − | 0.614873i | ||||
\(580\) | 2.70848 | + | 8.33585i | 0.112464 | + | 0.346127i | ||||
\(581\) | −2.55611 | + | 1.85712i | −0.106045 | + | 0.0770464i | ||||
\(582\) | 4.73328 | 0.196201 | ||||||||
\(583\) | 14.9844 | − | 2.57003i | 0.620590 | − | 0.106440i | ||||
\(584\) | −3.50926 | −0.145214 | ||||||||
\(585\) | −1.40676 | + | 1.02207i | −0.0581625 | + | 0.0422576i | ||||
\(586\) | 4.10856 | + | 12.6449i | 0.169723 | + | 0.522354i | ||||
\(587\) | −0.361493 | + | 1.11256i | −0.0149204 | + | 0.0459203i | −0.958240 | − | 0.285967i | \(-0.907685\pi\) |
0.943319 | + | 0.331887i | \(0.107685\pi\) | |||||||
\(588\) | −0.809017 | − | 0.587785i | −0.0333633 | − | 0.0242399i | ||||
\(589\) | 1.76517 | + | 1.28247i | 0.0727325 | + | 0.0528433i | ||||
\(590\) | −0.862430 | + | 2.65429i | −0.0355057 | + | 0.109275i | ||||
\(591\) | 5.97537 | + | 18.3903i | 0.245794 | + | 0.756476i | ||||
\(592\) | −0.902253 | + | 0.655525i | −0.0370824 | + | 0.0269419i | ||||
\(593\) | 20.2877 | 0.833117 | 0.416558 | − | 0.909109i | \(-0.363236\pi\) | ||||
0.416558 | + | 0.909109i | \(0.363236\pi\) | |||||||
\(594\) | −2.97414 | − | 1.46782i | −0.122030 | − | 0.0602256i | ||||
\(595\) | 8.50466 | 0.348657 | ||||||||
\(596\) | −17.3172 | + | 12.5817i | −0.709341 | + | 0.515366i | ||||
\(597\) | 3.76144 | + | 11.5765i | 0.153946 | + | 0.473796i | ||||
\(598\) | −1.17672 | + | 3.62158i | −0.0481197 | + | 0.148097i | ||||
\(599\) | −5.44110 | − | 3.95319i | −0.222317 | − | 0.161523i | 0.471052 | − | 0.882106i | \(-0.343874\pi\) |
−0.693369 | + | 0.720582i | \(0.743874\pi\) | |||||||
\(600\) | 1.18820 | + | 0.863274i | 0.0485079 | + | 0.0352430i | ||||
\(601\) | 10.9414 | − | 33.6741i | 0.446308 | − | 1.37360i | −0.434734 | − | 0.900559i | \(-0.643158\pi\) |
0.881043 | − | 0.473037i | \(-0.156842\pi\) | |||||||
\(602\) | 3.40119 | + | 10.4678i | 0.138622 | + | 0.426635i | ||||
\(603\) | −0.547086 | + | 0.397481i | −0.0222791 | + | 0.0161867i | ||||
\(604\) | −10.6906 | −0.434993 | ||||||||
\(605\) | −0.528336 | − | 20.6642i | −0.0214799 | − | 0.840119i | ||||
\(606\) | −6.25901 | −0.254255 | ||||||||
\(607\) | −21.6961 | + | 15.7632i | −0.880618 | + | 0.639807i | −0.933415 | − | 0.358799i | \(-0.883186\pi\) |
0.0527968 | + | 0.998605i | \(0.483186\pi\) | |||||||
\(608\) | −0.858891 | − | 2.64339i | −0.0348326 | − | 0.107204i | ||||
\(609\) | 1.44131 | − | 4.43590i | 0.0584049 | − | 0.179752i | ||||
\(610\) | −21.7282 | − | 15.7864i | −0.879747 | − | 0.639174i | ||||
\(611\) | 1.39099 | + | 1.01061i | 0.0562734 | + | 0.0408850i | ||||
\(612\) | 1.39853 | − | 4.30423i | 0.0565322 | − | 0.173988i | ||||
\(613\) | −9.20392 | − | 28.3268i | −0.371743 | − | 1.14411i | −0.945650 | − | 0.325187i | \(-0.894573\pi\) |
0.573907 | − | 0.818920i | \(-0.305427\pi\) | |||||||
\(614\) | 9.63783 | − | 7.00230i | 0.388951 | − | 0.282590i | ||||
\(615\) | 0.891230 | 0.0359379 | ||||||||
\(616\) | −2.97414 | − | 1.46782i | −0.119831 | − | 0.0591403i | ||||
\(617\) | −21.7810 | −0.876870 | −0.438435 | − | 0.898763i | \(-0.644467\pi\) | ||||
−0.438435 | + | 0.898763i | \(0.644467\pi\) | |||||||
\(618\) | 11.8615 | − | 8.61789i | 0.477140 | − | 0.346663i | ||||
\(619\) | −10.0918 | − | 31.0594i | −0.405624 | − | 1.24838i | −0.920373 | − | 0.391042i | \(-0.872115\pi\) |
0.514749 | − | 0.857341i | \(-0.327885\pi\) | |||||||
\(620\) | 0.455851 | − | 1.40297i | 0.0183074 | − | 0.0563445i | ||||
\(621\) | 3.32930 | + | 2.41888i | 0.133600 | + | 0.0970663i | ||||
\(622\) | 24.0948 | + | 17.5059i | 0.966113 | + | 0.701922i | ||||
\(623\) | −4.21393 | + | 12.9691i | −0.168828 | + | 0.519598i | ||||
\(624\) | 0.285942 | + | 0.880039i | 0.0114468 | + | 0.0352298i | ||||
\(625\) | 12.5394 | − | 9.11038i | 0.501574 | − | 0.364415i | ||||
\(626\) | 0.614588 | 0.0245639 | ||||||||
\(627\) | −9.08566 | + | 1.55831i | −0.362846 | + | 0.0622330i | ||||
\(628\) | −4.66363 | −0.186099 | ||||||||
\(629\) | −4.08336 | + | 2.96673i | −0.162814 | + | 0.118291i | ||||
\(630\) | 0.580698 | + | 1.78720i | 0.0231356 | + | 0.0712039i | ||||
\(631\) | 1.84535 | − | 5.67939i | 0.0734620 | − | 0.226093i | −0.907583 | − | 0.419873i | \(-0.862075\pi\) |
0.981045 | + | 0.193780i | \(0.0620747\pi\) | |||||||
\(632\) | 3.23004 | + | 2.34676i | 0.128484 | + | 0.0933492i | ||||
\(633\) | 14.8910 | + | 10.8189i | 0.591862 | + | 0.430013i | ||||
\(634\) | −7.93135 | + | 24.4102i | −0.314994 | + | 0.969453i | ||||
\(635\) | 0.353894 | + | 1.08917i | 0.0140438 | + | 0.0432225i | ||||
\(636\) | −3.70848 | + | 2.69437i | −0.147051 | + | 0.106839i | ||||
\(637\) | 0.925328 | 0.0366628 | ||||||||
\(638\) | 2.22447 | − | 15.3086i | 0.0880675 | − | 0.606072i | ||||
\(639\) | −5.31722 | −0.210346 | ||||||||
\(640\) | −1.52029 | + | 1.10455i | −0.0600946 | + | 0.0436613i | ||||
\(641\) | 13.1962 | + | 40.6138i | 0.521219 | + | 1.60415i | 0.771673 | + | 0.636020i | \(0.219420\pi\) |
−0.250453 | + | 0.968129i | \(0.580580\pi\) | |||||||
\(642\) | −2.00479 | + | 6.17011i | −0.0791227 | + | 0.243515i | ||||
\(643\) | 13.6064 | + | 9.88563i | 0.536584 | + | 0.389851i | 0.822815 | − | 0.568310i | \(-0.192402\pi\) |
−0.286231 | + | 0.958161i | \(0.592402\pi\) | |||||||
\(644\) | 3.32930 | + | 2.41888i | 0.131193 | + | 0.0953173i | ||||
\(645\) | 6.39144 | − | 19.6708i | 0.251663 | − | 0.774538i | ||||
\(646\) | −3.88711 | − | 11.9633i | −0.152936 | − | 0.470690i | ||||
\(647\) | 11.4531 | − | 8.32115i | 0.450267 | − | 0.327138i | −0.339434 | − | 0.940630i | \(-0.610236\pi\) |
0.789701 | + | 0.613492i | \(0.210236\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 3.43821 | − | 3.52724i | 0.134962 | − | 0.138456i | ||||
\(650\) | −1.35902 | −0.0533051 | ||||||||
\(651\) | −0.635083 | + | 0.461415i | −0.0248909 | + | 0.0180843i | ||||
\(652\) | −3.19737 | − | 9.84048i | −0.125219 | − | 0.385383i | ||||
\(653\) | 9.21659 | − | 28.3657i | 0.360673 | − | 1.11004i | −0.591974 | − | 0.805957i | \(-0.701651\pi\) |
0.952647 | − | 0.304080i | \(-0.0983490\pi\) | |||||||
\(654\) | 3.39947 | + | 2.46986i | 0.132930 | + | 0.0965790i | ||||
\(655\) | −25.5148 | − | 18.5376i | −0.996945 | − | 0.724323i | ||||
\(656\) | 0.146556 | − | 0.451054i | 0.00572206 | − | 0.0176107i | ||||
\(657\) | −1.08442 | − | 3.33751i | −0.0423073 | − | 0.130209i | ||||
\(658\) | 1.50324 | − | 1.09217i | 0.0586023 | − | 0.0425771i | ||||
\(659\) | −37.3447 | −1.45474 | −0.727371 | − | 0.686244i | \(-0.759258\pi\) | ||||
−0.727371 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(660\) | 2.90025 | + | 5.51661i | 0.112892 | + | 0.214734i | ||||
\(661\) | −16.1887 | −0.629667 | −0.314833 | − | 0.949147i | \(-0.601949\pi\) | ||||
−0.314833 | + | 0.949147i | \(0.601949\pi\) | |||||||
\(662\) | −26.2472 | + | 19.0697i | −1.02013 | + | 0.741164i | ||||
\(663\) | 1.29410 | + | 3.98282i | 0.0502586 | + | 0.154680i | ||||
\(664\) | 0.976346 | − | 3.00489i | 0.0378896 | − | 0.116612i | ||||
\(665\) | 4.22553 | + | 3.07003i | 0.163859 | + | 0.119051i | ||||
\(666\) | −0.902253 | − | 0.655525i | −0.0349616 | − | 0.0254011i | ||||
\(667\) | −5.93135 | + | 18.2548i | −0.229663 | + | 0.706830i | ||||
\(668\) | −3.15565 | − | 9.71209i | −0.122096 | − | 0.375772i | ||||
\(669\) | 19.2240 | − | 13.9670i | 0.743242 | − | 0.539997i | ||||
\(670\) | 1.27077 | 0.0490940 | ||||||||
\(671\) | 22.0579 | + | 41.9567i | 0.851537 | + | 1.61972i | ||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 10.4650 | − | 7.60326i | 0.403396 | − | 0.293084i | −0.367527 | − | 0.930013i | \(-0.619795\pi\) |
0.770923 | + | 0.636929i | \(0.219795\pi\) | |||||||
\(674\) | −2.55147 | − | 7.85261i | −0.0982789 | − | 0.302471i | ||||
\(675\) | −0.453850 | + | 1.39681i | −0.0174687 | + | 0.0537631i | ||||
\(676\) | 9.82451 | + | 7.13793i | 0.377866 | + | 0.274536i | ||||
\(677\) | −25.0430 | − | 18.1948i | −0.962483 | − | 0.699284i | −0.00875653 | − | 0.999962i | \(-0.502787\pi\) |
−0.953726 | + | 0.300677i | \(0.902787\pi\) | |||||||
\(678\) | 6.10577 | − | 18.7916i | 0.234491 | − | 0.721689i | ||||
\(679\) | 1.46266 | + | 4.50162i | 0.0561319 | + | 0.172756i | ||||
\(680\) | −6.88041 | + | 4.99891i | −0.263852 | + | 0.191700i | ||||
\(681\) | 18.2666 | 0.699979 | ||||||||
\(682\) | −1.81732 | + | 1.86438i | −0.0695889 | + | 0.0713908i | ||||
\(683\) | −46.0524 | −1.76215 | −0.881073 | − | 0.472980i | \(-0.843178\pi\) | ||||
−0.881073 | + | 0.472980i | \(0.843178\pi\) | |||||||
\(684\) | 2.24861 | − | 1.63371i | 0.0859776 | − | 0.0624664i | ||||
\(685\) | −12.7290 | − | 39.1757i | −0.486348 | − | 1.49683i | ||||
\(686\) | 0.309017 | − | 0.951057i | 0.0117983 | − | 0.0363115i | ||||
\(687\) | −21.2156 | − | 15.4140i | −0.809426 | − | 0.588083i | ||||
\(688\) | −8.90443 | − | 6.46944i | −0.339478 | − | 0.246645i | ||||
\(689\) | 1.31074 | − | 4.03404i | 0.0499352 | − | 0.153685i | ||||
\(690\) | −2.38971 | − | 7.35479i | −0.0909749 | − | 0.279992i | ||||
\(691\) | 29.3220 | − | 21.3037i | 1.11546 | − | 0.810432i | 0.131948 | − | 0.991257i | \(-0.457877\pi\) |
0.983515 | + | 0.180825i | \(0.0578768\pi\) | |||||||
\(692\) | −10.0660 | −0.382652 | ||||||||
\(693\) | 0.476925 | − | 3.28216i | 0.0181169 | − | 0.124679i | ||||
\(694\) | −1.53124 | −0.0581250 | ||||||||
\(695\) | 8.50375 | − | 6.17833i | 0.322565 | − | 0.234358i | ||||
\(696\) | 1.44131 | + | 4.43590i | 0.0546328 | + | 0.168142i | ||||
\(697\) | 0.663274 | − | 2.04135i | 0.0251233 | − | 0.0773216i | ||||
\(698\) | 14.5417 | + | 10.5652i | 0.550411 | + | 0.399897i | ||||
\(699\) | 21.8239 | + | 15.8560i | 0.825456 | + | 0.599729i | ||||
\(700\) | −0.453850 | + | 1.39681i | −0.0171539 | + | 0.0527943i | ||||
\(701\) | 5.47700 | + | 16.8565i | 0.206864 | + | 0.636661i | 0.999632 | + | 0.0271374i | \(0.00863915\pi\) |
−0.792768 | + | 0.609523i | \(0.791361\pi\) | |||||||
\(702\) | −0.748606 | + | 0.543894i | −0.0282543 | + | 0.0205280i | ||||
\(703\) | −3.09975 | −0.116909 | ||||||||
\(704\) | 3.26889 | − | 0.560659i | 0.123201 | − | 0.0211306i | ||||
\(705\) | −3.49171 | −0.131505 | ||||||||
\(706\) | 2.71936 | − | 1.97573i | 0.102344 | − | 0.0743575i | ||||
\(707\) | −1.93414 | − | 5.95268i | −0.0727409 | − | 0.223873i | ||||
\(708\) | −0.458940 | + | 1.41247i | −0.0172480 | + | 0.0530839i | ||||
\(709\) | 9.18489 | + | 6.67321i | 0.344946 | + | 0.250618i | 0.746746 | − | 0.665110i | \(-0.231615\pi\) |
−0.401800 | + | 0.915727i | \(0.631615\pi\) | |||||||
\(710\) | 8.08369 | + | 5.87315i | 0.303376 | + | 0.220415i | ||||
\(711\) | −1.23377 | + | 3.79714i | −0.0462699 | + | 0.142404i | ||||
\(712\) | −4.21393 | − | 12.9691i | −0.157924 | − | 0.486039i | ||||
\(713\) | 2.61352 | − | 1.89884i | 0.0978772 | − | 0.0711120i | ||||
\(714\) | 4.52573 | 0.169371 | ||||||||
\(715\) | −5.17160 | − | 2.55234i | −0.193407 | − | 0.0954519i | ||||
\(716\) | −1.63663 | −0.0611639 | ||||||||
\(717\) | 6.15331 | − | 4.47064i | 0.229800 | − | 0.166959i | ||||
\(718\) | −6.26897 | − | 19.2939i | −0.233956 | − | 0.720042i | ||||
\(719\) | −5.52218 | + | 16.9955i | −0.205943 | + | 0.633826i | 0.793731 | + | 0.608269i | \(0.208136\pi\) |
−0.999673 | + | 0.0255570i | \(0.991864\pi\) | |||||||
\(720\) | −1.52029 | − | 1.10455i | −0.0566578 | − | 0.0411643i | ||||
\(721\) | 11.8615 | + | 8.61789i | 0.441746 | + | 0.320947i | ||||
\(722\) | −3.48410 | + | 10.7229i | −0.129665 | + | 0.399067i | ||||
\(723\) | −5.41651 | − | 16.6703i | −0.201442 | − | 0.619976i | ||||
\(724\) | −17.3675 | + | 12.6183i | −0.645460 | + | 0.468954i | ||||
\(725\) | −6.85024 | −0.254412 | ||||||||
\(726\) | −0.281153 | − | 10.9964i | −0.0104346 | − | 0.408115i | ||||
\(727\) | 2.31474 | 0.0858490 | 0.0429245 | − | 0.999078i | \(-0.486333\pi\) | ||||
0.0429245 | + | 0.999078i | \(0.486333\pi\) | |||||||
\(728\) | −0.748606 | + | 0.543894i | −0.0277452 | + | 0.0201581i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −2.03782 | + | 6.27177i | −0.0754232 | + | 0.232129i | ||||
\(731\) | −40.2991 | − | 29.2790i | −1.49051 | − | 1.08292i | ||||
\(732\) | −11.5626 | − | 8.40071i | −0.427365 | − | 0.310499i | ||||
\(733\) | −6.09213 | + | 18.7496i | −0.225018 | + | 0.692534i | 0.773272 | + | 0.634075i | \(0.218619\pi\) |
−0.998290 | + | 0.0584593i | \(0.981381\pi\) | |||||||
\(734\) | 1.66725 | + | 5.13127i | 0.0615393 | + | 0.189399i | ||||
\(735\) | −1.52029 | + | 1.10455i | −0.0560766 | + | 0.0407421i | ||||
\(736\) | −4.11525 | −0.151690 | ||||||||
\(737\) | −2.01122 | − | 0.992595i | −0.0740841 | − | 0.0365627i | ||||
\(738\) | 0.474266 | 0.0174580 | ||||||||
\(739\) | −25.3919 | + | 18.4483i | −0.934056 | + | 0.678631i | −0.946982 | − | 0.321285i | \(-0.895885\pi\) |
0.0129268 | + | 0.999916i | \(0.495885\pi\) | |||||||
\(740\) | 0.647621 | + | 1.99317i | 0.0238070 | + | 0.0732705i | ||||
\(741\) | −0.794756 | + | 2.44601i | −0.0291961 | + | 0.0898563i | ||||
\(742\) | −3.70848 | − | 2.69437i | −0.136143 | − | 0.0989134i | ||||
\(743\) | 7.25656 | + | 5.27220i | 0.266217 | + | 0.193418i | 0.712884 | − | 0.701282i | \(-0.247389\pi\) |
−0.446666 | + | 0.894701i | \(0.647389\pi\) | |||||||
\(744\) | 0.242580 | − | 0.746585i | 0.00889342 | − | 0.0273711i | ||||
\(745\) | 12.4300 | + | 38.2556i | 0.455400 | + | 1.40158i | ||||
\(746\) | 22.3242 | − | 16.2195i | 0.817348 | − | 0.593838i | ||||
\(747\) | 3.15952 | 0.115601 | ||||||||
\(748\) | 14.7941 | − | 2.53739i | 0.540927 | − | 0.0927763i | ||||
\(749\) | −6.48763 | −0.237053 | ||||||||
\(750\) | 9.83426 | − | 7.14501i | 0.359097 | − | 0.260899i | ||||
\(751\) | 3.72495 | + | 11.4642i | 0.135925 | + | 0.418336i | 0.995733 | − | 0.0922830i | \(-0.0294165\pi\) |
−0.859807 | + | 0.510619i | \(0.829416\pi\) | |||||||
\(752\) | −0.574186 | + | 1.76716i | −0.0209384 | + | 0.0644418i | ||||
\(753\) | 11.3761 | + | 8.26523i | 0.414569 | + | 0.301202i | ||||
\(754\) | −3.49164 | − | 2.53682i | −0.127158 | − | 0.0923856i | ||||
\(755\) | −6.20800 | + | 19.1062i | −0.225932 | + | 0.695347i | ||||
\(756\) | 0.309017 | + | 0.951057i | 0.0112388 | + | 0.0345896i | ||||
\(757\) | 3.56307 | − | 2.58872i | 0.129502 | − | 0.0940887i | −0.521149 | − | 0.853466i | \(-0.674496\pi\) |
0.650651 | + | 0.759377i | \(0.274496\pi\) | |||||||
\(758\) | 7.66550 | 0.278424 | ||||||||
\(759\) | −1.96266 | + | 13.5069i | −0.0712402 | + | 0.490269i | ||||
\(760\) | −5.22304 | −0.189460 | ||||||||
\(761\) | 10.1558 | − | 7.37864i | 0.368148 | − | 0.267475i | −0.388294 | − | 0.921535i | \(-0.626936\pi\) |
0.756443 | + | 0.654060i | \(0.226936\pi\) | |||||||
\(762\) | 0.188324 | + | 0.579601i | 0.00682225 | + | 0.0209967i | ||||
\(763\) | −1.29848 | + | 3.99631i | −0.0470081 | + | 0.144676i | ||||
\(764\) | −5.47114 | − | 3.97502i | −0.197939 | − | 0.143811i | ||||
\(765\) | −6.88041 | − | 4.99891i | −0.248762 | − | 0.180736i | ||||
\(766\) | −1.76641 | + | 5.43644i | −0.0638228 | + | 0.196426i | ||||
\(767\) | −0.424670 | − | 1.30700i | −0.0153339 | − | 0.0471930i | ||||
\(768\) | −0.809017 | + | 0.587785i | −0.0291929 | + | 0.0212099i | ||||
\(769\) | −37.9619 | −1.36894 | −0.684471 | − | 0.729041i | \(-0.739967\pi\) | ||||
−0.684471 | + | 0.729041i | \(0.739967\pi\) | |||||||
\(770\) | −4.35038 | + | 4.46303i | −0.156777 | + | 0.160836i | ||||
\(771\) | −8.57589 | −0.308853 | ||||||||
\(772\) | −12.5857 | + | 9.14402i | −0.452968 | + | 0.329100i | ||||
\(773\) | 12.8817 | + | 39.6456i | 0.463321 | + | 1.42595i | 0.861082 | + | 0.508466i | \(0.169787\pi\) |
−0.397761 | + | 0.917489i | \(0.630213\pi\) | |||||||
\(774\) | 3.40119 | − | 10.4678i | 0.122253 | − | 0.376257i | ||||
\(775\) | 0.932740 | + | 0.677675i | 0.0335050 | + | 0.0243428i | ||||
\(776\) | −3.82930 | − | 2.78215i | −0.137464 | − | 0.0998734i | ||||
\(777\) | 0.344630 | − | 1.06066i | 0.0123635 | − | 0.0380510i | ||||
\(778\) | −3.32996 | − | 10.2486i | −0.119385 | − | 0.367429i | ||||
\(779\) | 1.06644 | − | 0.774812i | 0.0382091 | − | 0.0277605i | ||||
\(780\) | 1.73886 | 0.0622610 | ||||||||
\(781\) | −8.20639 | − | 15.6095i | −0.293648 | − | 0.558551i | ||||
\(782\) | −18.6245 | −0.666011 | ||||||||
\(783\) | −3.77340 | + | 2.74154i | −0.134850 | + | 0.0979746i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | −2.70816 | + | 8.33486i | −0.0966583 | + | 0.297484i | ||||
\(786\) | −13.5776 | − | 9.86473i | −0.484298 | − | 0.351863i | ||||
\(787\) | −4.37209 | − | 3.17651i | −0.155848 | − | 0.113230i | 0.507128 | − | 0.861871i | \(-0.330707\pi\) |
−0.662976 | + | 0.748640i | \(0.730707\pi\) | |||||||
\(788\) | 5.97537 | − | 18.3903i | 0.212864 | − | 0.655128i | ||||
\(789\) | 7.47462 | + | 23.0045i | 0.266104 | + | 0.818983i | ||||
\(790\) | 6.06982 | − | 4.40999i | 0.215955 | − | 0.156900i | ||||
\(791\) | 19.7587 | 0.702538 | ||||||||
\(792\) | 1.54336 | + | 2.93565i | 0.0548410 | + | 0.104314i | ||||
\(793\) | 13.2249 | 0.469631 | ||||||||
\(794\) | −15.1360 | + | 10.9970i | −0.537158 | + | 0.390268i | ||||
\(795\) | 2.66188 | + | 8.19243i | 0.0944072 | + | 0.290556i | ||||
\(796\) | 3.76144 | − | 11.5765i | 0.133321 | − | 0.410319i | ||||
\(797\) | 1.60888 | + | 1.16892i | 0.0569896 | + | 0.0414053i | 0.615915 | − | 0.787812i | \(-0.288786\pi\) |
−0.558926 | + | 0.829218i | \(0.688786\pi\) | |||||||
\(798\) | 2.24861 | + | 1.63371i | 0.0795998 | + | 0.0578326i | ||||
\(799\) | −2.59861 | + | 7.99771i | −0.0919323 | + | 0.282939i | ||||
\(800\) | −0.453850 | − | 1.39681i | −0.0160460 | − | 0.0493846i | ||||
\(801\) | 11.0322 | − | 8.01537i | 0.389804 | − | 0.283209i | ||||
\(802\) | 0.122952 | 0.00434158 | ||||||||
\(803\) | 8.12410 | − | 8.33447i | 0.286693 | − | 0.294117i | ||||
\(804\) | 0.676236 | 0.0238490 | ||||||||
\(805\) | 6.25635 | − | 4.54551i | 0.220508 | − | 0.160208i | ||||
\(806\) | 0.224466 | + | 0.690836i | 0.00790648 | + | 0.0243337i | ||||
\(807\) | 5.11985 | − | 15.7573i | 0.180227 | − | 0.554682i | ||||
\(808\) | 5.06365 | + | 3.67896i | 0.178139 | + | 0.129425i | ||||
\(809\) | −23.2682 | − | 16.9053i | −0.818067 | − | 0.594360i | 0.0980914 | − | 0.995177i | \(-0.468726\pi\) |
−0.916158 | + | 0.400817i | \(0.868726\pi\) | |||||||
\(810\) | 0.580698 | − | 1.78720i | 0.0204036 | − | 0.0627960i | ||||
\(811\) | −15.3327 | − | 47.1892i | −0.538404 | − | 1.65704i | −0.736176 | − | 0.676790i | \(-0.763370\pi\) |
0.197772 | − | 0.980248i | \(-0.436630\pi\) | |||||||
\(812\) | −3.77340 | + | 2.74154i | −0.132421 | + | 0.0962091i | ||||
\(813\) | −28.8309 | −1.01114 | ||||||||
\(814\) | 0.531889 | − | 3.66041i | 0.0186427 | − | 0.128297i | ||||
\(815\) | −19.4437 | −0.681082 | ||||||||
\(816\) | −3.66140 | + | 2.66016i | −0.128174 | + | 0.0931242i | ||||
\(817\) | −9.45336 | − | 29.0945i | −0.330731 | − | 1.01789i | ||||
\(818\) | 4.52821 | − | 13.9364i | 0.158325 | − | 0.487274i | ||||
\(819\) | −0.748606 | − | 0.543894i | −0.0261584 | − | 0.0190052i | ||||
\(820\) | −0.721020 | − | 0.523852i | −0.0251791 | − | 0.0182937i | ||||
\(821\) | 8.94597 | − | 27.5329i | 0.312217 | − | 0.960904i | −0.664668 | − | 0.747138i | \(-0.731427\pi\) |
0.976885 | − | 0.213765i | \(-0.0685728\pi\) | |||||||
\(822\) | −6.77368 | − | 20.8472i | −0.236259 | − | 0.727131i | ||||
\(823\) | 21.4122 | − | 15.5569i | 0.746384 | − | 0.542279i | −0.148320 | − | 0.988939i | \(-0.547387\pi\) |
0.894704 | + | 0.446660i | \(0.147387\pi\) | |||||||
\(824\) | −14.6616 | −0.510762 | ||||||||
\(825\) | −4.80099 | + | 0.823434i | −0.167149 | + | 0.0286683i | ||||
\(826\) | −1.48516 | −0.0516753 | ||||||||
\(827\) | 3.69477 | − | 2.68440i | 0.128480 | − | 0.0933459i | −0.521689 | − | 0.853135i | \(-0.674698\pi\) |
0.650169 | + | 0.759790i | \(0.274698\pi\) | |||||||
\(828\) | −1.27168 | − | 3.91383i | −0.0441940 | − | 0.136015i | ||||
\(829\) | 15.5139 | − | 47.7467i | 0.538818 | − | 1.65831i | −0.196432 | − | 0.980517i | \(-0.562936\pi\) |
0.735251 | − | 0.677795i | \(-0.237064\pi\) | |||||||
\(830\) | −4.80338 | − | 3.48986i | −0.166728 | − | 0.121135i | ||||
\(831\) | 13.5410 | + | 9.83813i | 0.469733 | + | 0.341281i | ||||
\(832\) | 0.285942 | − | 0.880039i | 0.00991326 | − | 0.0305099i | ||||
\(833\) | 1.39853 | + | 4.30423i | 0.0484562 | + | 0.149133i | ||||
\(834\) | 4.52525 | − | 3.28779i | 0.156697 | − | 0.113847i | ||||
\(835\) | −19.1900 | −0.664096 | ||||||||
\(836\) | 8.26641 | + | 4.07972i | 0.285900 | + | 0.141100i | ||||
\(837\) | 0.785006 | 0.0271338 | ||||||||
\(838\) | 5.21775 | − | 3.79091i | 0.180244 | − | 0.130955i | ||||
\(839\) | 2.37859 | + | 7.32053i | 0.0821179 | + | 0.252733i | 0.983683 | − | 0.179911i | \(-0.0575809\pi\) |
−0.901565 | + | 0.432644i | \(0.857581\pi\) | |||||||
\(840\) | 0.580698 | − | 1.78720i | 0.0200360 | − | 0.0616644i | ||||
\(841\) | 5.86164 | + | 4.25873i | 0.202126 | + | 0.146853i | ||||
\(842\) | 20.8638 | + | 15.1584i | 0.719015 | + | 0.522395i | ||||
\(843\) | −0.392595 | + | 1.20828i | −0.0135217 | + | 0.0416155i | ||||
\(844\) | −5.68784 | − | 17.5054i | −0.195783 | − | 0.602559i | ||||
\(845\) | 18.4620 | − | 13.4134i | 0.635113 | − | 0.461436i | ||||
\(846\) | −1.85810 | −0.0638829 | ||||||||
\(847\) | 10.3713 | − | 3.66547i | 0.356363 | − | 0.125947i | ||||
\(848\) | 4.58394 | 0.157413 | ||||||||
\(849\) | −19.1636 | + | 13.9231i | −0.657692 | + | 0.477841i | ||||
\(850\) | −2.05401 | − | 6.32158i | −0.0704518 | − | 0.216828i | ||||
\(851\) | −1.41824 | + | 4.36489i | −0.0486165 | + | 0.149626i | ||||
\(852\) | 4.30172 | + | 3.12538i | 0.147374 | + | 0.107074i | ||||
\(853\) | 31.0499 | + | 22.5591i | 1.06313 | + | 0.772409i | 0.974665 | − | 0.223670i | \(-0.0718039\pi\) |
0.0884648 | + | 0.996079i | \(0.471804\pi\) | |||||||
\(854\) | 4.41651 | − | 13.5926i | 0.151130 | − | 0.465130i | ||||
\(855\) | −1.61401 | − | 4.96741i | −0.0551980 | − | 0.169882i | ||||
\(856\) | 5.24861 | − | 3.81334i | 0.179394 | − | 0.130337i | ||||
\(857\) | 14.1029 | 0.481747 | 0.240874 | − | 0.970557i | \(-0.422566\pi\) | ||||
0.240874 | + | 0.970557i | \(0.422566\pi\) | |||||||
\(858\) | −2.75205 | − | 1.35822i | −0.0939535 | − | 0.0463688i | ||||
\(859\) | 53.5036 | 1.82552 | 0.912760 | − | 0.408496i | \(-0.133947\pi\) | ||||
0.912760 | + | 0.408496i | \(0.133947\pi\) | |||||||
\(860\) | −16.7330 | + | 12.1572i | −0.570591 | + | 0.414558i | ||||
\(861\) | 0.146556 | + | 0.451054i | 0.00499462 | + | 0.0153719i | ||||
\(862\) | 7.35154 | − | 22.6257i | 0.250394 | − | 0.770634i | ||||
\(863\) | −40.7757 | − | 29.6253i | −1.38802 | − | 1.00846i | −0.996079 | − | 0.0884682i | \(-0.971803\pi\) |
−0.391944 | − | 0.919989i | \(-0.628197\pi\) | |||||||
\(864\) | −0.809017 | − | 0.587785i | −0.0275233 | − | 0.0199969i | ||||
\(865\) | −5.84530 | + | 17.9900i | −0.198746 | + | 0.611678i | ||||
\(866\) | 7.93826 | + | 24.4314i | 0.269753 | + | 0.830214i | ||||
\(867\) | −2.81722 | + | 2.04683i | −0.0956777 | + | 0.0695139i | ||||
\(868\) | 0.785006 | 0.0266448 | ||||||||
\(869\) | −13.0512 | + | 2.23846i | −0.442732 | + | 0.0759346i | ||||
\(870\) | 8.76483 | 0.297156 | ||||||||
\(871\) | −0.506234 | + | 0.367801i | −0.0171531 | + | 0.0124624i | ||||
\(872\) | −1.29848 | − | 3.99631i | −0.0439721 | − | 0.135332i | ||||
\(873\) | 1.46266 | − | 4.50162i | 0.0495037 | − | 0.152357i | ||||
\(874\) | −9.25357 | − | 6.72311i | −0.313007 | − | 0.227413i | ||||
\(875\) | 9.83426 | + | 7.14501i | 0.332459 | + | 0.241545i | ||||
\(876\) | −1.08442 | + | 3.33751i | −0.0366392 | + | 0.112764i | ||||
\(877\) | 4.55852 | + | 14.0297i | 0.153930 | + | 0.473748i | 0.998051 | − | 0.0624048i | \(-0.0198770\pi\) |
−0.844121 | + | 0.536153i | \(0.819877\pi\) | |||||||
\(878\) | −25.7844 | + | 18.7334i | −0.870180 | + | 0.632223i | ||||
\(879\) | 13.2956 | 0.448449 | ||||||||
\(880\) | 0.896227 | − | 6.16775i | 0.0302118 | − | 0.207915i | ||||
\(881\) | 38.4292 | 1.29471 | 0.647356 | − | 0.762188i | \(-0.275875\pi\) | ||||
0.647356 | + | 0.762188i | \(0.275875\pi\) | |||||||
\(882\) | −0.809017 | + | 0.587785i | −0.0272410 | + | 0.0197918i | ||||
\(883\) | 4.05289 | + | 12.4735i | 0.136391 | + | 0.419767i | 0.995804 | − | 0.0915146i | \(-0.0291708\pi\) |
−0.859413 | + | 0.511282i | \(0.829171\pi\) | |||||||
\(884\) | 1.29410 | − | 3.98282i | 0.0435252 | − | 0.133957i | ||||
\(885\) | 2.25787 | + | 1.64044i | 0.0758975 | + | 0.0551427i | ||||
\(886\) | −10.5860 | − | 7.69118i | −0.355643 | − | 0.258390i | ||||
\(887\) | −9.73558 | + | 29.9630i | −0.326889 | + | 1.00606i | 0.643692 | + | 0.765285i | \(0.277402\pi\) |
−0.970581 | + | 0.240776i | \(0.922598\pi\) | |||||||
\(888\) | 0.344630 | + | 1.06066i | 0.0115650 | + | 0.0355935i | ||||
\(889\) | −0.493038 | + | 0.358213i | −0.0165360 | + | 0.0120141i | ||||
\(890\) | −25.6255 | −0.858970 | ||||||||
\(891\) | −2.31504 | + | 2.37499i | −0.0775569 | + | 0.0795652i | ||||
\(892\) | −23.7621 | −0.795615 | ||||||||
\(893\) | −4.17814 | + | 3.03560i | −0.139816 | + | 0.101582i | ||||
\(894\) | 6.61459 | + | 20.3576i | 0.221225 | + | 0.680860i | ||||
\(895\) | −0.950390 | + | 2.92500i | −0.0317680 | + | 0.0977720i | ||||
\(896\) | −0.809017 | − | 0.587785i | −0.0270274 | − | 0.0196365i | ||||
\(897\) | 3.08070 | + | 2.23826i | 0.102862 | + | 0.0747333i | ||||
\(898\) | 10.9803 | − | 33.7938i | 0.366416 | − | 1.12771i | ||||
\(899\) | 1.13144 | + | 3.48221i | 0.0377356 | + | 0.116138i | ||||
\(900\) | 1.18820 | − | 0.863274i | 0.0396065 | − | 0.0287758i | ||||
\(901\) | 20.7457 | 0.691139 | ||||||||
\(902\) | 0.731964 | + | 1.39228i | 0.0243717 | + | 0.0463578i | ||||
\(903\) | 11.0065 | 0.366273 | ||||||||
\(904\) | −15.9851 | + | 11.6139i | −0.531657 | + | 0.386272i | ||||
\(905\) | 12.4661 | + | 38.3667i | 0.414388 | + | 1.27535i | ||||
\(906\) | −3.30357 | + | 10.1673i | −0.109754 | + | 0.337787i | ||||
\(907\) | 47.7435 | + | 34.6877i | 1.58530 | + | 1.15179i | 0.910286 | + | 0.413981i | \(0.135862\pi\) |
0.675013 | + | 0.737806i | \(0.264138\pi\) | |||||||
\(908\) | −14.7780 | − | 10.7369i | −0.490426 | − | 0.356315i | ||||
\(909\) | −1.93414 | + | 5.95268i | −0.0641514 | + | 0.197438i | ||||
\(910\) | 0.537336 | + | 1.65375i | 0.0178125 | + | 0.0548213i | ||||
\(911\) | −20.2420 | + | 14.7067i | −0.670647 | + | 0.487254i | −0.870242 | − | 0.492625i | \(-0.836037\pi\) |
0.199595 | + | 0.979879i | \(0.436037\pi\) | |||||||
\(912\) | −2.77943 | −0.0920361 | ||||||||
\(913\) | 4.87629 | + | 9.27525i | 0.161382 | + | 0.306966i | ||||
\(914\) | 16.0161 | 0.529765 | ||||||||
\(915\) | −21.7282 | + | 15.7864i | −0.718311 | + | 0.521883i | ||||
\(916\) | 8.10364 | + | 24.9405i | 0.267752 | + | 0.824056i | ||||
\(917\) | 5.18619 | − | 15.9615i | 0.171263 | − | 0.527094i | ||||
\(918\) | −3.66140 | − | 2.66016i | −0.120844 | − | 0.0877984i | ||||
\(919\) | 43.2550 | + | 31.4266i | 1.42685 | + | 1.03667i | 0.990593 | + | 0.136845i | \(0.0436961\pi\) |
0.436257 | + | 0.899822i | \(0.356304\pi\) | |||||||
\(920\) | −2.38971 | + | 7.35479i | −0.0787866 | + | 0.242480i | ||||
\(921\) | −3.68133 | − | 11.3300i | −0.121304 | − | 0.373335i | ||||
\(922\) | 3.58648 | − | 2.60573i | 0.118114 | − | 0.0858152i | ||||
\(923\) | −4.92017 | −0.161949 | ||||||||
\(924\) | −2.31504 | + | 2.37499i | −0.0761593 | + | 0.0781314i | ||||
\(925\) | −1.63795 | −0.0538555 | ||||||||
\(926\) | 19.6231 | − | 14.2570i | 0.644855 | − | 0.468515i | ||||
\(927\) | −4.53070 | − | 13.9440i | −0.148808 | − | 0.457983i | ||||
\(928\) | 1.44131 | − | 4.43590i | 0.0473134 | − | 0.145616i | ||||
\(929\) | 38.1776 | + | 27.7376i | 1.25256 | + | 0.910042i | 0.998368 | − | 0.0571108i | \(-0.0181888\pi\) |
0.254197 | + | 0.967152i | \(0.418189\pi\) | |||||||
\(930\) | −1.19343 | − | 0.867081i | −0.0391342 | − | 0.0284327i | ||||
\(931\) | −0.858891 | + | 2.64339i | −0.0281490 | + | 0.0866338i | ||||
\(932\) | −8.33599 | − | 25.6555i | −0.273054 | − | 0.840375i | ||||
\(933\) | 24.0948 | − | 17.5059i | 0.788828 | − | 0.573117i | ||||
\(934\) | −7.56541 | −0.247548 | ||||||||
\(935\) | 4.05609 | − | 27.9136i | 0.132648 | − | 0.912873i | ||||
\(936\) | 0.925328 | 0.0302453 | ||||||||
\(937\) | 10.6396 | − | 7.73009i | 0.347579 | − | 0.252531i | −0.400274 | − | 0.916396i | \(-0.631085\pi\) |
0.747853 | + | 0.663865i | \(0.231085\pi\) | |||||||
\(938\) | 0.208968 | + | 0.643138i | 0.00682306 | + | 0.0209992i | ||||
\(939\) | 0.189918 | − | 0.584508i | 0.00619774 | − | 0.0190747i | ||||
\(940\) | 2.82485 | + | 2.05237i | 0.0921365 | + | 0.0669411i | ||||
\(941\) | 35.2047 | + | 25.5777i | 1.14764 | + | 0.833808i | 0.988165 | − | 0.153394i | \(-0.0490203\pi\) |
0.159474 | + | 0.987202i | \(0.449020\pi\) | |||||||
\(942\) | −1.44114 | + | 4.43537i | −0.0469549 | + | 0.144512i | ||||
\(943\) | −0.603115 | − | 1.85620i | −0.0196401 | − | 0.0604461i | ||||
\(944\) | 1.20152 | − | 0.872955i | 0.0391061 | − | 0.0284123i | ||||
\(945\) | 1.87918 | 0.0611297 | ||||||||
\(946\) | 35.9790 | − | 6.17088i | 1.16978 | − | 0.200633i | ||||
\(947\) | −60.4254 | −1.96356 | −0.981780 | − | 0.190020i | \(-0.939145\pi\) | ||||
−0.981780 | + | 0.190020i | \(0.939145\pi\) | |||||||
\(948\) | 3.23004 | − | 2.34676i | 0.104907 | − | 0.0762193i | ||||
\(949\) | −1.00345 | − | 3.08829i | −0.0325732 | − | 0.100250i | ||||
\(950\) | 1.26144 | − | 3.88233i | 0.0409267 | − | 0.125959i | ||||
\(951\) | 20.7646 | + | 15.0863i | 0.673337 | + | 0.489208i | ||||
\(952\) | −3.66140 | − | 2.66016i | −0.118667 | − | 0.0862163i | ||||
\(953\) | 1.81298 | − | 5.57979i | 0.0587283 | − | 0.180747i | −0.917389 | − | 0.397992i | \(-0.869707\pi\) |
0.976117 | + | 0.217245i | \(0.0697071\pi\) | |||||||
\(954\) | 1.41651 | + | 4.35958i | 0.0458613 | + | 0.141147i | ||||
\(955\) | −10.2812 | + | 7.46976i | −0.332693 | + | 0.241716i | ||||
\(956\) | −7.60591 | −0.245993 | ||||||||
\(957\) | −13.8719 | − | 6.84620i | −0.448416 | − | 0.221306i | ||||
\(958\) | 17.7051 | 0.572024 | ||||||||
\(959\) | 17.7337 | − | 12.8843i | 0.572652 | − | 0.416056i | ||||
\(960\) | 0.580698 | + | 1.78720i | 0.0187419 | + | 0.0576818i | ||||
\(961\) | −9.38910 | + | 28.8967i | −0.302874 | + | 0.932151i | ||||
\(962\) | −0.834880 | − | 0.606576i | −0.0269176 | − | 0.0195568i | ||||
\(963\) | 5.24861 | + | 3.81334i | 0.169134 | + | 0.122883i | ||||
\(964\) | −5.41651 | + | 16.6703i | −0.174454 | + | 0.536915i | ||||
\(965\) | 9.03376 | + | 27.8031i | 0.290807 | + | 0.895012i | ||||
\(966\) | 3.32930 | − | 2.41888i | 0.107119 | − | 0.0778262i | ||||
\(967\) | 13.8068 | 0.443998 | 0.221999 | − | 0.975047i | \(-0.428742\pi\) | ||||
0.221999 | + | 0.975047i | \(0.428742\pi\) | |||||||
\(968\) | −6.23607 | + | 9.06154i | −0.200435 | + | 0.291249i | ||||
\(969\) | −12.5790 | −0.404094 | ||||||||
\(970\) | −7.19594 | + | 5.22816i | −0.231048 | + | 0.167866i | ||||
\(971\) | 10.3446 | + | 31.8374i | 0.331974 | + | 1.02171i | 0.968194 | + | 0.250202i | \(0.0804972\pi\) |
−0.636220 | + | 0.771508i | \(0.719503\pi\) | |||||||
\(972\) | 0.309017 | − | 0.951057i | 0.00991172 | − | 0.0305052i | ||||
\(973\) | 4.52525 | + | 3.28779i | 0.145073 | + | 0.105402i | ||||
\(974\) | 21.0502 | + | 15.2939i | 0.674492 | + | 0.490047i | ||||
\(975\) | −0.419960 | + | 1.29250i | −0.0134495 | + | 0.0413933i | ||||
\(976\) | 4.41651 | + | 13.5926i | 0.141369 | + | 0.435090i | ||||
\(977\) | 33.0618 | − | 24.0208i | 1.05774 | − | 0.768495i | 0.0840727 | − | 0.996460i | \(-0.473207\pi\) |
0.973669 | + | 0.227965i | \(0.0732072\pi\) | |||||||
\(978\) | −10.3469 | −0.330857 | ||||||||
\(979\) | 40.5570 | + | 20.0161i | 1.29621 | + | 0.639717i | ||||
\(980\) | 1.87918 | 0.0600281 | ||||||||
\(981\) | 3.39947 | − | 2.46986i | 0.108537 | − | 0.0788564i | ||||
\(982\) | 10.9992 | + | 33.8521i | 0.350999 | + | 1.08026i | ||||
\(983\) | 4.75567 | − | 14.6364i | 0.151682 | − | 0.466830i | −0.846127 | − | 0.532981i | \(-0.821072\pi\) |
0.997810 | + | 0.0661506i | \(0.0210718\pi\) | |||||||
\(984\) | −0.383689 | − | 0.278766i | −0.0122316 | − | 0.00888675i | ||||
\(985\) | −29.3974 | − | 21.3584i | −0.936678 | − | 0.680536i | ||||
\(986\) | 6.52300 | − | 20.0757i | 0.207734 | − | 0.639341i | ||||
\(987\) | −0.574186 | − | 1.76716i | −0.0182765 | − | 0.0562494i | ||||
\(988\) | 2.08070 | − | 1.51172i | 0.0661958 | − | 0.0480941i | ||||
\(989\) | −45.2944 | −1.44028 | ||||||||
\(990\) | 6.14283 | − | 1.05358i | 0.195232 | − | 0.0334849i | ||||
\(991\) | −48.7434 | −1.54839 | −0.774193 | − | 0.632950i | \(-0.781844\pi\) | ||||
−0.774193 | + | 0.632950i | \(0.781844\pi\) | |||||||
\(992\) | −0.635083 | + | 0.461415i | −0.0201639 | + | 0.0146499i | ||||
\(993\) | 10.0255 | + | 30.8554i | 0.318150 | + | 0.979166i | ||||
\(994\) | −1.64311 | + | 5.05697i | −0.0521163 | + | 0.160397i | ||||
\(995\) | −18.5054 | − | 13.4449i | −0.586660 | − | 0.426233i | ||||
\(996\) | −2.55611 | − | 1.85712i | −0.0809934 | − | 0.0588451i | ||||
\(997\) | −0.710162 | + | 2.18565i | −0.0224911 | + | 0.0692203i | −0.961672 | − | 0.274202i | \(-0.911586\pi\) |
0.939181 | + | 0.343422i | \(0.111586\pi\) | |||||||
\(998\) | −4.54496 | − | 13.9879i | −0.143868 | − | 0.442780i | ||||
\(999\) | −0.902253 | + | 0.655525i | −0.0285460 | + | 0.0207399i |
(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 | 462.2.j.e.421.1 | yes | 8 | |
11.2 | odd | 10 | 5082.2.a.ca.1.3 | 4 | |||
11.4 | even | 5 | inner | 462.2.j.e.169.1 | ✓ | 8 | |
11.9 | even | 5 | 5082.2.a.cf.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.e.169.1 | ✓ | 8 | 11.4 | even | 5 | inner | |
462.2.j.e.421.1 | yes | 8 | 1.1 | even | 1 | trivial | |
5082.2.a.ca.1.3 | 4 | 11.2 | odd | 10 | |||
5082.2.a.cf.1.3 | 4 | 11.9 | even | 5 |