Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,2,Mod(7,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.7");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.f (of order \(3\), degree \(2\), 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: | \(2.73088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} - 324 x^{6} - 1701 x^{5} + 243 x^{4} - 4374 x^{3} + 8748 x^{2} + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 7.9 | ||
Root | \(0.339544 - 1.69844i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.7 |
Dual form | 342.2.f.g.49.9 |
$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.64067 | − | 0.555168i | 0.947240 | − | 0.320526i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.467593 | − | 0.809895i | 0.209114 | − | 0.362196i | −0.742322 | − | 0.670044i | \(-0.766275\pi\) |
0.951436 | + | 0.307848i | \(0.0996087\pi\) | |||||||
\(6\) | −1.64067 | + | 0.555168i | −0.669800 | + | 0.226646i | ||||
\(7\) | −0.568176 | + | 0.984110i | −0.214750 | + | 0.371959i | −0.953195 | − | 0.302355i | \(-0.902227\pi\) |
0.738445 | + | 0.674314i | \(0.235560\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.38358 | − | 1.82169i | 0.794526 | − | 0.607230i | ||||
\(10\) | −0.467593 | + | 0.809895i | −0.147866 | + | 0.256111i | ||||
\(11\) | 0.0397925 | − | 0.0689226i | 0.0119979 | − | 0.0207809i | −0.859964 | − | 0.510354i | \(-0.829514\pi\) |
0.871962 | + | 0.489574i | \(0.162848\pi\) | |||||||
\(12\) | 1.64067 | − | 0.555168i | 0.473620 | − | 0.160263i | ||||
\(13\) | 6.63538 | 1.84032 | 0.920162 | − | 0.391539i | \(-0.128057\pi\) | ||||
0.920162 | + | 0.391539i | \(0.128057\pi\) | |||||||
\(14\) | 0.568176 | − | 0.984110i | 0.151851 | − | 0.263014i | ||||
\(15\) | 0.317537 | − | 1.58836i | 0.0819877 | − | 0.410113i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.10797 | − | 1.91906i | −0.268722 | − | 0.465440i | 0.699810 | − | 0.714329i | \(-0.253268\pi\) |
−0.968532 | + | 0.248889i | \(0.919935\pi\) | |||||||
\(18\) | −2.38358 | + | 1.82169i | −0.561815 | + | 0.429377i | ||||
\(19\) | −4.19489 | − | 1.18444i | −0.962374 | − | 0.271728i | ||||
\(20\) | 0.467593 | − | 0.809895i | 0.104557 | − | 0.181098i | ||||
\(21\) | −0.385842 | + | 1.93003i | −0.0841976 | + | 0.421167i | ||||
\(22\) | −0.0397925 | + | 0.0689226i | −0.00848378 | + | 0.0146943i | ||||
\(23\) | −0.138465 | −0.0288719 | −0.0144359 | − | 0.999896i | \(-0.504595\pi\) | ||||
−0.0144359 | + | 0.999896i | \(0.504595\pi\) | |||||||
\(24\) | −1.64067 | + | 0.555168i | −0.334900 | + | 0.113323i | ||||
\(25\) | 2.06271 | + | 3.57272i | 0.412543 | + | 0.714545i | ||||
\(26\) | −6.63538 | −1.30131 | ||||||||
\(27\) | 2.89931 | − | 4.31207i | 0.557973 | − | 0.829859i | ||||
\(28\) | −0.568176 | + | 0.984110i | −0.107375 | + | 0.185979i | ||||
\(29\) | −2.94499 | − | 5.10087i | −0.546871 | − | 0.947208i | −0.998487 | − | 0.0549955i | \(-0.982486\pi\) |
0.451616 | − | 0.892213i | \(-0.350848\pi\) | |||||||
\(30\) | −0.317537 | + | 1.58836i | −0.0579741 | + | 0.289994i | ||||
\(31\) | 1.71503 | + | 2.97052i | 0.308029 | + | 0.533522i | 0.977931 | − | 0.208928i | \(-0.0669973\pi\) |
−0.669902 | + | 0.742449i | \(0.733664\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.0270226 | − | 0.135171i | 0.00470403 | − | 0.0235302i | ||||
\(34\) | 1.10797 | + | 1.91906i | 0.190015 | + | 0.329116i | ||||
\(35\) | 0.531351 | + | 0.920326i | 0.0898146 | + | 0.155564i | ||||
\(36\) | 2.38358 | − | 1.82169i | 0.397263 | − | 0.303615i | ||||
\(37\) | −1.58712 | −0.260922 | −0.130461 | − | 0.991453i | \(-0.541646\pi\) | ||||
−0.130461 | + | 0.991453i | \(0.541646\pi\) | |||||||
\(38\) | 4.19489 | + | 1.18444i | 0.680501 | + | 0.192141i | ||||
\(39\) | 10.8865 | − | 3.68375i | 1.74323 | − | 0.589872i | ||||
\(40\) | −0.467593 | + | 0.809895i | −0.0739330 | + | 0.128056i | ||||
\(41\) | 1.15143 | − | 1.99433i | 0.179823 | − | 0.311462i | −0.761997 | − | 0.647581i | \(-0.775781\pi\) |
0.941820 | + | 0.336118i | \(0.109114\pi\) | |||||||
\(42\) | 0.385842 | − | 1.93003i | 0.0595367 | − | 0.297810i | ||||
\(43\) | 3.30138 | 0.503456 | 0.251728 | − | 0.967798i | \(-0.419001\pi\) | ||||
0.251728 | + | 0.967798i | \(0.419001\pi\) | |||||||
\(44\) | 0.0397925 | − | 0.0689226i | 0.00599894 | − | 0.0103905i | ||||
\(45\) | −0.360834 | − | 2.78226i | −0.0537900 | − | 0.414755i | ||||
\(46\) | 0.138465 | 0.0204155 | ||||||||
\(47\) | −2.46002 | − | 4.26088i | −0.358830 | − | 0.621513i | 0.628935 | − | 0.777458i | \(-0.283491\pi\) |
−0.987766 | + | 0.155945i | \(0.950158\pi\) | |||||||
\(48\) | 1.64067 | − | 0.555168i | 0.236810 | − | 0.0801316i | ||||
\(49\) | 2.85435 | + | 4.94388i | 0.407765 | + | 0.706269i | ||||
\(50\) | −2.06271 | − | 3.57272i | −0.291712 | − | 0.505259i | ||||
\(51\) | −2.88321 | − | 2.53343i | −0.403730 | − | 0.354751i | ||||
\(52\) | 6.63538 | 0.920162 | ||||||||
\(53\) | −4.22378 | + | 7.31580i | −0.580181 | + | 1.00490i | 0.415277 | + | 0.909695i | \(0.363685\pi\) |
−0.995457 | + | 0.0952074i | \(0.969649\pi\) | |||||||
\(54\) | −2.89931 | + | 4.31207i | −0.394547 | + | 0.586799i | ||||
\(55\) | −0.0372134 | − | 0.0644555i | −0.00501785 | − | 0.00869117i | ||||
\(56\) | 0.568176 | − | 0.984110i | 0.0759257 | − | 0.131507i | ||||
\(57\) | −7.53998 | + | 0.385604i | −0.998695 | + | 0.0510745i | ||||
\(58\) | 2.94499 | + | 5.10087i | 0.386696 | + | 0.669777i | ||||
\(59\) | −3.81301 | + | 6.60433i | −0.496412 | + | 0.859810i | −0.999991 | − | 0.00413867i | \(-0.998683\pi\) |
0.503580 | + | 0.863949i | \(0.332016\pi\) | |||||||
\(60\) | 0.317537 | − | 1.58836i | 0.0409939 | − | 0.205057i | ||||
\(61\) | 1.54050 | + | 2.66822i | 0.197240 | + | 0.341630i | 0.947633 | − | 0.319363i | \(-0.103469\pi\) |
−0.750392 | + | 0.660993i | \(0.770135\pi\) | |||||||
\(62\) | −1.71503 | − | 2.97052i | −0.217809 | − | 0.377257i | ||||
\(63\) | 0.438452 | + | 3.38074i | 0.0552398 | + | 0.425934i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.10266 | − | 5.37396i | 0.384837 | − | 0.666558i | ||||
\(66\) | −0.0270226 | + | 0.135171i | −0.00332625 | + | 0.0166383i | ||||
\(67\) | −10.8359 | −1.32381 | −0.661906 | − | 0.749587i | \(-0.730252\pi\) | ||||
−0.661906 | + | 0.749587i | \(0.730252\pi\) | |||||||
\(68\) | −1.10797 | − | 1.91906i | −0.134361 | − | 0.232720i | ||||
\(69\) | −0.227174 | + | 0.0768711i | −0.0273486 | + | 0.00925420i | ||||
\(70\) | −0.531351 | − | 0.920326i | −0.0635085 | − | 0.110000i | ||||
\(71\) | 6.23133 | + | 10.7930i | 0.739523 | + | 1.28089i | 0.952710 | + | 0.303880i | \(0.0982821\pi\) |
−0.213188 | + | 0.977011i | \(0.568385\pi\) | |||||||
\(72\) | −2.38358 | + | 1.82169i | −0.280907 | + | 0.214688i | ||||
\(73\) | −6.81871 | − | 11.8104i | −0.798070 | − | 1.38230i | −0.920872 | − | 0.389866i | \(-0.872521\pi\) |
0.122802 | − | 0.992431i | \(-0.460812\pi\) | |||||||
\(74\) | 1.58712 | 0.184499 | ||||||||
\(75\) | 5.36769 | + | 4.71650i | 0.619807 | + | 0.544614i | ||||
\(76\) | −4.19489 | − | 1.18444i | −0.481187 | − | 0.135864i | ||||
\(77\) | 0.0452183 | + | 0.0783203i | 0.00515310 | + | 0.00892543i | ||||
\(78\) | −10.8865 | + | 3.68375i | −1.23265 | + | 0.417102i | ||||
\(79\) | −6.12676 | −0.689315 | −0.344657 | − | 0.938729i | \(-0.612005\pi\) | ||||
−0.344657 | + | 0.938729i | \(0.612005\pi\) | |||||||
\(80\) | 0.467593 | − | 0.809895i | 0.0522785 | − | 0.0905490i | ||||
\(81\) | 2.36288 | − | 8.68428i | 0.262543 | − | 0.964920i | ||||
\(82\) | −1.15143 | + | 1.99433i | −0.127154 | + | 0.220237i | ||||
\(83\) | −4.76093 | + | 8.24617i | −0.522580 | + | 0.905135i | 0.477075 | + | 0.878863i | \(0.341697\pi\) |
−0.999655 | + | 0.0262725i | \(0.991636\pi\) | |||||||
\(84\) | −0.385842 | + | 1.93003i | −0.0420988 | + | 0.210583i | ||||
\(85\) | −2.07231 | −0.224774 | ||||||||
\(86\) | −3.30138 | −0.355997 | ||||||||
\(87\) | −7.66359 | − | 6.73387i | −0.821623 | − | 0.721947i | ||||
\(88\) | −0.0397925 | + | 0.0689226i | −0.00424189 | + | 0.00734717i | ||||
\(89\) | −4.11336 | + | 7.12456i | −0.436016 | + | 0.755201i | −0.997378 | − | 0.0723688i | \(-0.976944\pi\) |
0.561362 | + | 0.827570i | \(0.310277\pi\) | |||||||
\(90\) | 0.360834 | + | 2.78226i | 0.0380352 | + | 0.293276i | ||||
\(91\) | −3.77006 | + | 6.52994i | −0.395210 | + | 0.684524i | ||||
\(92\) | −0.138465 | −0.0144359 | ||||||||
\(93\) | 4.46294 | + | 3.92151i | 0.462785 | + | 0.406642i | ||||
\(94\) | 2.46002 | + | 4.26088i | 0.253731 | + | 0.439476i | ||||
\(95\) | −2.92077 | + | 2.84359i | −0.299665 | + | 0.291746i | ||||
\(96\) | −1.64067 | + | 0.555168i | −0.167450 | + | 0.0566616i | ||||
\(97\) | −14.9427 | −1.51720 | −0.758601 | − | 0.651555i | \(-0.774117\pi\) | ||||
−0.758601 | + | 0.651555i | \(0.774117\pi\) | |||||||
\(98\) | −2.85435 | − | 4.94388i | −0.288333 | − | 0.499408i | ||||
\(99\) | −0.0307072 | − | 0.236772i | −0.00308619 | − | 0.0237965i | ||||
\(100\) | 2.06271 | + | 3.57272i | 0.206271 | + | 0.357272i | ||||
\(101\) | −0.318675 | − | 0.551961i | −0.0317093 | − | 0.0549222i | 0.849735 | − | 0.527210i | \(-0.176762\pi\) |
−0.881445 | + | 0.472287i | \(0.843428\pi\) | |||||||
\(102\) | 2.88321 | + | 2.53343i | 0.285480 | + | 0.250847i | ||||
\(103\) | 2.96826 | + | 5.14118i | 0.292472 | + | 0.506576i | 0.974394 | − | 0.224849i | \(-0.0721889\pi\) |
−0.681922 | + | 0.731425i | \(0.738856\pi\) | |||||||
\(104\) | −6.63538 | −0.650653 | ||||||||
\(105\) | 1.38270 | + | 1.21496i | 0.134938 | + | 0.118568i | ||||
\(106\) | 4.22378 | − | 7.31580i | 0.410250 | − | 0.710573i | ||||
\(107\) | −16.7256 | −1.61692 | −0.808461 | − | 0.588550i | \(-0.799699\pi\) | ||||
−0.808461 | + | 0.588550i | \(0.799699\pi\) | |||||||
\(108\) | 2.89931 | − | 4.31207i | 0.278987 | − | 0.414930i | ||||
\(109\) | −1.01969 | − | 1.76615i | −0.0976685 | − | 0.169167i | 0.813051 | − | 0.582193i | \(-0.197805\pi\) |
−0.910719 | + | 0.413026i | \(0.864472\pi\) | |||||||
\(110\) | 0.0372134 | + | 0.0644555i | 0.00354816 | + | 0.00614559i | ||||
\(111\) | −2.60394 | + | 0.881120i | −0.247155 | + | 0.0836322i | ||||
\(112\) | −0.568176 | + | 0.984110i | −0.0536876 | + | 0.0929896i | ||||
\(113\) | 8.92114 | + | 15.4519i | 0.839231 | + | 1.45359i | 0.890539 | + | 0.454907i | \(0.150328\pi\) |
−0.0513082 | + | 0.998683i | \(0.516339\pi\) | |||||||
\(114\) | 7.53998 | − | 0.385604i | 0.706184 | − | 0.0361151i | ||||
\(115\) | −0.0647451 | + | 0.112142i | −0.00603752 | + | 0.0104573i | ||||
\(116\) | −2.94499 | − | 5.10087i | −0.273435 | − | 0.473604i | ||||
\(117\) | 15.8159 | − | 12.0876i | 1.46218 | − | 1.11750i | ||||
\(118\) | 3.81301 | − | 6.60433i | 0.351016 | − | 0.607977i | ||||
\(119\) | 2.51808 | 0.230832 | ||||||||
\(120\) | −0.317537 | + | 1.58836i | −0.0289870 | + | 0.144997i | ||||
\(121\) | 5.49683 | + | 9.52079i | 0.499712 | + | 0.865527i | ||||
\(122\) | −1.54050 | − | 2.66822i | −0.139470 | − | 0.241569i | ||||
\(123\) | 0.781921 | − | 3.91127i | 0.0705034 | − | 0.352667i | ||||
\(124\) | 1.71503 | + | 2.97052i | 0.154015 | + | 0.266761i | ||||
\(125\) | 8.53397 | 0.763302 | ||||||||
\(126\) | −0.438452 | − | 3.38074i | −0.0390604 | − | 0.301181i | ||||
\(127\) | 0.409265 | − | 0.708868i | 0.0363164 | − | 0.0629019i | −0.847296 | − | 0.531121i | \(-0.821771\pi\) |
0.883612 | + | 0.468219i | \(0.155104\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.41647 | − | 1.83282i | 0.476893 | − | 0.161371i | ||||
\(130\) | −3.10266 | + | 5.37396i | −0.272121 | + | 0.471328i | ||||
\(131\) | 1.91686 | − | 3.32010i | 0.167477 | − | 0.290079i | −0.770055 | − | 0.637977i | \(-0.779771\pi\) |
0.937532 | + | 0.347899i | \(0.113105\pi\) | |||||||
\(132\) | 0.0270226 | − | 0.135171i | 0.00235202 | − | 0.0117651i | ||||
\(133\) | 3.54905 | − | 3.45527i | 0.307742 | − | 0.299610i | ||||
\(134\) | 10.8359 | 0.936076 | ||||||||
\(135\) | −2.13663 | − | 4.36444i | −0.183892 | − | 0.375631i | ||||
\(136\) | 1.10797 | + | 1.91906i | 0.0950075 | + | 0.164558i | ||||
\(137\) | −1.47091 | − | 2.54770i | −0.125669 | − | 0.217665i | 0.796325 | − | 0.604868i | \(-0.206774\pi\) |
−0.921994 | + | 0.387204i | \(0.873441\pi\) | |||||||
\(138\) | 0.227174 | − | 0.0768711i | 0.0193384 | − | 0.00654370i | ||||
\(139\) | −11.2341 | −0.952867 | −0.476433 | − | 0.879211i | \(-0.658071\pi\) | ||||
−0.476433 | + | 0.879211i | \(0.658071\pi\) | |||||||
\(140\) | 0.531351 | + | 0.920326i | 0.0449073 | + | 0.0777818i | ||||
\(141\) | −6.40157 | − | 5.62496i | −0.539110 | − | 0.473707i | ||||
\(142\) | −6.23133 | − | 10.7930i | −0.522922 | − | 0.905727i | ||||
\(143\) | 0.264038 | − | 0.457328i | 0.0220800 | − | 0.0382436i | ||||
\(144\) | 2.38358 | − | 1.82169i | 0.198631 | − | 0.151808i | ||||
\(145\) | −5.50823 | −0.457433 | ||||||||
\(146\) | 6.81871 | + | 11.8104i | 0.564320 | + | 0.977432i | ||||
\(147\) | 7.42773 | + | 6.52662i | 0.612628 | + | 0.538307i | ||||
\(148\) | −1.58712 | −0.130461 | ||||||||
\(149\) | 8.84481 | − | 15.3197i | 0.724595 | − | 1.25503i | −0.234546 | − | 0.972105i | \(-0.575360\pi\) |
0.959141 | − | 0.282930i | \(-0.0913064\pi\) | |||||||
\(150\) | −5.36769 | − | 4.71650i | −0.438270 | − | 0.385101i | ||||
\(151\) | 6.93789 | − | 12.0168i | 0.564597 | − | 0.977912i | −0.432490 | − | 0.901639i | \(-0.642365\pi\) |
0.997087 | − | 0.0762726i | \(-0.0243019\pi\) | |||||||
\(152\) | 4.19489 | + | 1.18444i | 0.340251 | + | 0.0960704i | ||||
\(153\) | −6.13686 | − | 2.55585i | −0.496136 | − | 0.206628i | ||||
\(154\) | −0.0452183 | − | 0.0783203i | −0.00364379 | − | 0.00631123i | ||||
\(155\) | 3.20775 | 0.257653 | ||||||||
\(156\) | 10.8865 | − | 3.68375i | 0.871614 | − | 0.294936i | ||||
\(157\) | 7.76796 | − | 13.4545i | 0.619951 | − | 1.07379i | −0.369543 | − | 0.929214i | \(-0.620486\pi\) |
0.989494 | − | 0.144573i | \(-0.0461809\pi\) | |||||||
\(158\) | 6.12676 | 0.487419 | ||||||||
\(159\) | −2.86832 | + | 14.3477i | −0.227473 | + | 1.13785i | ||||
\(160\) | −0.467593 | + | 0.809895i | −0.0369665 | + | 0.0640278i | ||||
\(161\) | 0.0786723 | − | 0.136264i | 0.00620025 | − | 0.0107391i | ||||
\(162\) | −2.36288 | + | 8.68428i | −0.185646 | + | 0.682302i | ||||
\(163\) | −22.6136 | −1.77124 | −0.885618 | − | 0.464415i | \(-0.846265\pi\) | ||||
−0.885618 | + | 0.464415i | \(0.846265\pi\) | |||||||
\(164\) | 1.15143 | − | 1.99433i | 0.0899114 | − | 0.155731i | ||||
\(165\) | −0.0968384 | − | 0.0850903i | −0.00753886 | − | 0.00662427i | ||||
\(166\) | 4.76093 | − | 8.24617i | 0.369520 | − | 0.640027i | ||||
\(167\) | 6.88495 | 0.532773 | 0.266387 | − | 0.963866i | \(-0.414170\pi\) | ||||
0.266387 | + | 0.963866i | \(0.414170\pi\) | |||||||
\(168\) | 0.385842 | − | 1.93003i | 0.0297683 | − | 0.148905i | ||||
\(169\) | 31.0283 | 2.38679 | ||||||||
\(170\) | 2.07231 | 0.158939 | ||||||||
\(171\) | −12.1565 | + | 4.81860i | −0.929633 | + | 0.368488i | ||||
\(172\) | 3.30138 | 0.251728 | ||||||||
\(173\) | −0.888179 | −0.0675270 | −0.0337635 | − | 0.999430i | \(-0.510749\pi\) | ||||
−0.0337635 | + | 0.999430i | \(0.510749\pi\) | |||||||
\(174\) | 7.66359 | + | 6.73387i | 0.580975 | + | 0.510493i | ||||
\(175\) | −4.68794 | −0.354375 | ||||||||
\(176\) | 0.0397925 | − | 0.0689226i | 0.00299947 | − | 0.00519523i | ||||
\(177\) | −2.58937 | + | 12.9524i | −0.194629 | + | 0.973559i | ||||
\(178\) | 4.11336 | − | 7.12456i | 0.308310 | − | 0.534008i | ||||
\(179\) | 11.8427 | 0.885162 | 0.442581 | − | 0.896729i | \(-0.354063\pi\) | ||||
0.442581 | + | 0.896729i | \(0.354063\pi\) | |||||||
\(180\) | −0.360834 | − | 2.78226i | −0.0268950 | − | 0.207377i | ||||
\(181\) | 8.04715 | − | 13.9381i | 0.598140 | − | 1.03601i | −0.394956 | − | 0.918700i | \(-0.629240\pi\) |
0.993096 | − | 0.117308i | \(-0.0374265\pi\) | |||||||
\(182\) | 3.77006 | − | 6.52994i | 0.279456 | − | 0.484032i | ||||
\(183\) | 4.00875 | + | 3.52242i | 0.296335 | + | 0.260385i | ||||
\(184\) | 0.138465 | 0.0102078 | ||||||||
\(185\) | −0.742128 | + | 1.28540i | −0.0545624 | + | 0.0945048i | ||||
\(186\) | −4.46294 | − | 3.92151i | −0.327238 | − | 0.287539i | ||||
\(187\) | −0.176355 | −0.0128964 | ||||||||
\(188\) | −2.46002 | − | 4.26088i | −0.179415 | − | 0.310756i | ||||
\(189\) | 2.59623 | + | 5.30326i | 0.188848 | + | 0.385755i | ||||
\(190\) | 2.92077 | − | 2.84359i | 0.211895 | − | 0.206296i | ||||
\(191\) | 0.636975 | − | 1.10327i | 0.0460899 | − | 0.0798301i | −0.842060 | − | 0.539384i | \(-0.818657\pi\) |
0.888150 | + | 0.459554i | \(0.151991\pi\) | |||||||
\(192\) | 1.64067 | − | 0.555168i | 0.118405 | − | 0.0400658i | ||||
\(193\) | −4.05430 | + | 7.02226i | −0.291835 | + | 0.505473i | −0.974244 | − | 0.225498i | \(-0.927599\pi\) |
0.682409 | + | 0.730971i | \(0.260932\pi\) | |||||||
\(194\) | 14.9427 | 1.07282 | ||||||||
\(195\) | 2.10698 | − | 10.5394i | 0.150884 | − | 0.754741i | ||||
\(196\) | 2.85435 | + | 4.94388i | 0.203882 | + | 0.353134i | ||||
\(197\) | 20.1767 | 1.43753 | 0.718767 | − | 0.695251i | \(-0.244707\pi\) | ||||
0.718767 | + | 0.695251i | \(0.244707\pi\) | |||||||
\(198\) | 0.0307072 | + | 0.236772i | 0.00218227 | + | 0.0168266i | ||||
\(199\) | 3.27803 | − | 5.67772i | 0.232374 | − | 0.402483i | −0.726132 | − | 0.687555i | \(-0.758684\pi\) |
0.958506 | + | 0.285072i | \(0.0920174\pi\) | |||||||
\(200\) | −2.06271 | − | 3.57272i | −0.145856 | − | 0.252630i | ||||
\(201\) | −17.7780 | + | 6.01572i | −1.25397 | + | 0.424316i | ||||
\(202\) | 0.318675 | + | 0.551961i | 0.0224219 | + | 0.0388359i | ||||
\(203\) | 6.69309 | 0.469763 | ||||||||
\(204\) | −2.88321 | − | 2.53343i | −0.201865 | − | 0.177375i | ||||
\(205\) | −1.07680 | − | 1.86507i | −0.0752069 | − | 0.130262i | ||||
\(206\) | −2.96826 | − | 5.14118i | −0.206809 | − | 0.358203i | ||||
\(207\) | −0.330041 | + | 0.252240i | −0.0229395 | + | 0.0175319i | ||||
\(208\) | 6.63538 | 0.460081 | ||||||||
\(209\) | −0.248559 | + | 0.241991i | −0.0171932 | + | 0.0167389i | ||||
\(210\) | −1.38270 | − | 1.21496i | −0.0954157 | − | 0.0838402i | ||||
\(211\) | −5.53735 | + | 9.59098i | −0.381207 | + | 0.660270i | −0.991235 | − | 0.132110i | \(-0.957825\pi\) |
0.610028 | + | 0.792380i | \(0.291158\pi\) | |||||||
\(212\) | −4.22378 | + | 7.31580i | −0.290090 | + | 0.502451i | ||||
\(213\) | 16.2155 | + | 14.2483i | 1.11106 | + | 0.976274i | ||||
\(214\) | 16.7256 | 1.14334 | ||||||||
\(215\) | 1.54370 | − | 2.67377i | 0.105280 | − | 0.182350i | ||||
\(216\) | −2.89931 | + | 4.31207i | −0.197273 | + | 0.293399i | ||||
\(217\) | −3.89776 | −0.264597 | ||||||||
\(218\) | 1.01969 | + | 1.76615i | 0.0690621 | + | 0.119619i | ||||
\(219\) | −17.7440 | − | 15.5913i | −1.19903 | − | 1.05356i | ||||
\(220\) | −0.0372134 | − | 0.0644555i | −0.00250893 | − | 0.00434559i | ||||
\(221\) | −7.35179 | − | 12.7337i | −0.494535 | − | 0.856560i | ||||
\(222\) | 2.60394 | − | 0.881120i | 0.174765 | − | 0.0591369i | ||||
\(223\) | 0.747365 | 0.0500473 | 0.0250236 | − | 0.999687i | \(-0.492034\pi\) | ||||
0.0250236 | + | 0.999687i | \(0.492034\pi\) | |||||||
\(224\) | 0.568176 | − | 0.984110i | 0.0379629 | − | 0.0657536i | ||||
\(225\) | 11.4250 | + | 4.75824i | 0.761669 | + | 0.317216i | ||||
\(226\) | −8.92114 | − | 15.4519i | −0.593426 | − | 1.02784i | ||||
\(227\) | −14.1895 | + | 24.5769i | −0.941790 | + | 1.63123i | −0.179735 | + | 0.983715i | \(0.557524\pi\) |
−0.762054 | + | 0.647513i | \(0.775809\pi\) | |||||||
\(228\) | −7.53998 | + | 0.385604i | −0.499347 | + | 0.0255373i | ||||
\(229\) | 3.63731 | + | 6.30001i | 0.240360 | + | 0.416316i | 0.960817 | − | 0.277184i | \(-0.0894011\pi\) |
−0.720457 | + | 0.693500i | \(0.756068\pi\) | |||||||
\(230\) | 0.0647451 | − | 0.112142i | 0.00426917 | − | 0.00739442i | ||||
\(231\) | 0.117669 | + | 0.103394i | 0.00774205 | + | 0.00680282i | ||||
\(232\) | 2.94499 | + | 5.10087i | 0.193348 | + | 0.334889i | ||||
\(233\) | −8.86740 | − | 15.3588i | −0.580923 | − | 1.00619i | −0.995370 | − | 0.0961148i | \(-0.969358\pi\) |
0.414447 | − | 0.910073i | \(-0.363975\pi\) | |||||||
\(234\) | −15.8159 | + | 12.0876i | −1.03392 | + | 0.790192i | ||||
\(235\) | −4.60115 | −0.300146 | ||||||||
\(236\) | −3.81301 | + | 6.60433i | −0.248206 | + | 0.429905i | ||||
\(237\) | −10.0520 | + | 3.40138i | −0.652946 | + | 0.220943i | ||||
\(238\) | −2.51808 | −0.163223 | ||||||||
\(239\) | 12.0318 | + | 20.8396i | 0.778270 | + | 1.34800i | 0.932938 | + | 0.360037i | \(0.117236\pi\) |
−0.154667 | + | 0.987967i | \(0.549431\pi\) | |||||||
\(240\) | 0.317537 | − | 1.58836i | 0.0204969 | − | 0.102528i | ||||
\(241\) | −5.35131 | − | 9.26873i | −0.344708 | − | 0.597052i | 0.640593 | − | 0.767881i | \(-0.278689\pi\) |
−0.985301 | + | 0.170829i | \(0.945355\pi\) | |||||||
\(242\) | −5.49683 | − | 9.52079i | −0.353350 | − | 0.612020i | ||||
\(243\) | −0.944527 | − | 15.5598i | −0.0605914 | − | 0.998163i | ||||
\(244\) | 1.54050 | + | 2.66822i | 0.0986201 | + | 0.170815i | ||||
\(245\) | 5.33870 | 0.341077 | ||||||||
\(246\) | −0.781921 | + | 3.91127i | −0.0498535 | + | 0.249373i | ||||
\(247\) | −27.8347 | − | 7.85918i | −1.77108 | − | 0.500068i | ||||
\(248\) | −1.71503 | − | 2.97052i | −0.108905 | − | 0.188628i | ||||
\(249\) | −3.23309 | + | 16.1723i | −0.204889 | + | 1.02488i | ||||
\(250\) | −8.53397 | −0.539736 | ||||||||
\(251\) | 7.87511 | − | 13.6401i | 0.497073 | − | 0.860955i | −0.502921 | − | 0.864332i | \(-0.667742\pi\) |
0.999994 | + | 0.00337672i | \(0.00107485\pi\) | |||||||
\(252\) | 0.438452 | + | 3.38074i | 0.0276199 | + | 0.212967i | ||||
\(253\) | −0.00550985 | + | 0.00954334i | −0.000346401 | + | 0.000599985i | ||||
\(254\) | −0.409265 | + | 0.708868i | −0.0256796 | + | 0.0444783i | ||||
\(255\) | −3.39998 | + | 1.15048i | −0.212915 | + | 0.0720460i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.24788 | −0.327353 | −0.163677 | − | 0.986514i | \(-0.552335\pi\) | ||||
−0.163677 | + | 0.986514i | \(0.552335\pi\) | |||||||
\(258\) | −5.41647 | + | 1.83282i | −0.337215 | + | 0.114106i | ||||
\(259\) | 0.901766 | − | 1.56190i | 0.0560330 | − | 0.0970520i | ||||
\(260\) | 3.10266 | − | 5.37396i | 0.192419 | − | 0.333279i | ||||
\(261\) | −16.3118 | − | 6.79346i | −1.00968 | − | 0.420505i | ||||
\(262\) | −1.91686 | + | 3.32010i | −0.118424 | + | 0.205117i | ||||
\(263\) | −9.00516 | −0.555282 | −0.277641 | − | 0.960685i | \(-0.589553\pi\) | ||||
−0.277641 | + | 0.960685i | \(0.589553\pi\) | |||||||
\(264\) | −0.0270226 | + | 0.135171i | −0.00166313 | + | 0.00831917i | ||||
\(265\) | 3.95002 | + | 6.84164i | 0.242648 | + | 0.420278i | ||||
\(266\) | −3.54905 | + | 3.45527i | −0.217606 | + | 0.211856i | ||||
\(267\) | −2.79334 | + | 13.9726i | −0.170950 | + | 0.855111i | ||||
\(268\) | −10.8359 | −0.661906 | ||||||||
\(269\) | 6.28989 | + | 10.8944i | 0.383501 | + | 0.664243i | 0.991560 | − | 0.129648i | \(-0.0413849\pi\) |
−0.608059 | + | 0.793892i | \(0.708052\pi\) | |||||||
\(270\) | 2.13663 | + | 4.36444i | 0.130031 | + | 0.265611i | ||||
\(271\) | −2.79712 | − | 4.84476i | −0.169913 | − | 0.294298i | 0.768476 | − | 0.639879i | \(-0.221015\pi\) |
−0.938389 | + | 0.345581i | \(0.887682\pi\) | |||||||
\(272\) | −1.10797 | − | 1.91906i | −0.0671805 | − | 0.116360i | ||||
\(273\) | −2.56021 | + | 12.8065i | −0.154951 | + | 0.775083i | ||||
\(274\) | 1.47091 | + | 2.54770i | 0.0888612 | + | 0.153912i | ||||
\(275\) | 0.328322 | 0.0197985 | ||||||||
\(276\) | −0.227174 | + | 0.0768711i | −0.0136743 | + | 0.00462710i | ||||
\(277\) | 7.72542 | − | 13.3808i | 0.464175 | − | 0.803975i | −0.534988 | − | 0.844859i | \(-0.679684\pi\) |
0.999164 | + | 0.0408839i | \(0.0130174\pi\) | |||||||
\(278\) | 11.2341 | 0.673778 | ||||||||
\(279\) | 9.49929 | + | 3.95621i | 0.568708 | + | 0.236852i | ||||
\(280\) | −0.531351 | − | 0.920326i | −0.0317543 | − | 0.0550000i | ||||
\(281\) | −4.41799 | − | 7.65218i | −0.263555 | − | 0.456491i | 0.703629 | − | 0.710568i | \(-0.251562\pi\) |
−0.967184 | + | 0.254077i | \(0.918228\pi\) | |||||||
\(282\) | 6.40157 | + | 5.62496i | 0.381208 | + | 0.334961i | ||||
\(283\) | 13.3232 | − | 23.0765i | 0.791982 | − | 1.37175i | −0.132756 | − | 0.991149i | \(-0.542383\pi\) |
0.924738 | − | 0.380604i | \(-0.124284\pi\) | |||||||
\(284\) | 6.23133 | + | 10.7930i | 0.369761 | + | 0.640445i | ||||
\(285\) | −3.21334 | + | 6.28690i | −0.190342 | + | 0.372404i | ||||
\(286\) | −0.264038 | + | 0.457328i | −0.0156129 | + | 0.0270423i | ||||
\(287\) | 1.30843 | + | 2.26626i | 0.0772340 | + | 0.133773i | ||||
\(288\) | −2.38358 | + | 1.82169i | −0.140454 | + | 0.107344i | ||||
\(289\) | 6.04481 | − | 10.4699i | 0.355577 | − | 0.615878i | ||||
\(290\) | 5.50823 | 0.323454 | ||||||||
\(291\) | −24.5160 | + | 8.29571i | −1.43715 | + | 0.486303i | ||||
\(292\) | −6.81871 | − | 11.8104i | −0.399035 | − | 0.691149i | ||||
\(293\) | −4.55284 | − | 7.88575i | −0.265980 | − | 0.460690i | 0.701840 | − | 0.712335i | \(-0.252362\pi\) |
−0.967820 | + | 0.251644i | \(0.919029\pi\) | |||||||
\(294\) | −7.42773 | − | 6.52662i | −0.433194 | − | 0.380640i | ||||
\(295\) | 3.56587 | + | 6.17628i | 0.207613 | + | 0.359597i | ||||
\(296\) | 1.58712 | 0.0922497 | ||||||||
\(297\) | −0.181828 | − | 0.371416i | −0.0105508 | − | 0.0215518i | ||||
\(298\) | −8.84481 | + | 15.3197i | −0.512366 | + | 0.887444i | ||||
\(299\) | −0.918766 | −0.0531336 | ||||||||
\(300\) | 5.36769 | + | 4.71650i | 0.309904 | + | 0.272307i | ||||
\(301\) | −1.87577 | + | 3.24892i | −0.108117 | + | 0.187265i | ||||
\(302\) | −6.93789 | + | 12.0168i | −0.399231 | + | 0.691488i | ||||
\(303\) | −0.829271 | − | 0.728667i | −0.0476403 | − | 0.0418608i | ||||
\(304\) | −4.19489 | − | 1.18444i | −0.240594 | − | 0.0679320i | ||||
\(305\) | 2.88130 | 0.164983 | ||||||||
\(306\) | 6.13686 | + | 2.55585i | 0.350821 | + | 0.146108i | ||||
\(307\) | 4.46612 | + | 7.73555i | 0.254895 | + | 0.441491i | 0.964867 | − | 0.262739i | \(-0.0846257\pi\) |
−0.709972 | + | 0.704230i | \(0.751292\pi\) | |||||||
\(308\) | 0.0452183 | + | 0.0783203i | 0.00257655 | + | 0.00446271i | ||||
\(309\) | 7.72415 | + | 6.78709i | 0.439412 | + | 0.386104i | ||||
\(310\) | −3.20775 | −0.182188 | ||||||||
\(311\) | 0.795438 | + | 1.37774i | 0.0451051 | + | 0.0781244i | 0.887697 | − | 0.460429i | \(-0.152304\pi\) |
−0.842591 | + | 0.538553i | \(0.818971\pi\) | |||||||
\(312\) | −10.8865 | + | 3.68375i | −0.616324 | + | 0.208551i | ||||
\(313\) | 2.53074 | + | 4.38337i | 0.143046 | + | 0.247763i | 0.928642 | − | 0.370977i | \(-0.120977\pi\) |
−0.785596 | + | 0.618739i | \(0.787644\pi\) | |||||||
\(314\) | −7.76796 | + | 13.4545i | −0.438372 | + | 0.759282i | ||||
\(315\) | 2.94306 | + | 1.22571i | 0.165823 | + | 0.0690611i | ||||
\(316\) | −6.12676 | −0.344657 | ||||||||
\(317\) | −16.0375 | − | 27.7777i | −0.900755 | − | 1.56015i | −0.826516 | − | 0.562913i | \(-0.809680\pi\) |
−0.0742392 | − | 0.997240i | \(-0.523653\pi\) | |||||||
\(318\) | 2.86832 | − | 14.3477i | 0.160847 | − | 0.804579i | ||||
\(319\) | −0.468754 | −0.0262452 | ||||||||
\(320\) | 0.467593 | − | 0.809895i | 0.0261393 | − | 0.0452745i | ||||
\(321\) | −27.4411 | + | 9.28549i | −1.53161 | + | 0.518266i | ||||
\(322\) | −0.0786723 | + | 0.136264i | −0.00438424 | + | 0.00759372i | ||||
\(323\) | 2.37481 | + | 9.36256i | 0.132138 | + | 0.520947i | ||||
\(324\) | 2.36288 | − | 8.68428i | 0.131271 | − | 0.482460i | ||||
\(325\) | 13.6869 | + | 23.7064i | 0.759212 | + | 1.31499i | ||||
\(326\) | 22.6136 | 1.25245 | ||||||||
\(327\) | −2.65348 | − | 2.33157i | −0.146738 | − | 0.128936i | ||||
\(328\) | −1.15143 | + | 1.99433i | −0.0635769 | + | 0.110118i | ||||
\(329\) | 5.59089 | 0.308236 | ||||||||
\(330\) | 0.0968384 | + | 0.0850903i | 0.00533078 | + | 0.00468407i | ||||
\(331\) | −2.26128 | + | 3.91666i | −0.124291 | + | 0.215279i | −0.921456 | − | 0.388483i | \(-0.872999\pi\) |
0.797164 | + | 0.603762i | \(0.206332\pi\) | |||||||
\(332\) | −4.76093 | + | 8.24617i | −0.261290 | + | 0.452568i | ||||
\(333\) | −3.78303 | + | 2.89125i | −0.207309 | + | 0.158440i | ||||
\(334\) | −6.88495 | −0.376728 | ||||||||
\(335\) | −5.06677 | + | 8.77591i | −0.276827 | + | 0.479479i | ||||
\(336\) | −0.385842 | + | 1.93003i | −0.0210494 | + | 0.105292i | ||||
\(337\) | 0.468804 | − | 0.811992i | 0.0255374 | − | 0.0442320i | −0.852974 | − | 0.521953i | \(-0.825204\pi\) |
0.878512 | + | 0.477721i | \(0.158537\pi\) | |||||||
\(338\) | −31.0283 | −1.68772 | ||||||||
\(339\) | 23.2150 | + | 20.3987i | 1.26087 | + | 1.10790i | ||||
\(340\) | −2.07231 | −0.112387 | ||||||||
\(341\) | 0.272982 | 0.0147828 | ||||||||
\(342\) | 12.1565 | − | 4.81860i | 0.657350 | − | 0.260560i | ||||
\(343\) | −14.4416 | −0.779771 | ||||||||
\(344\) | −3.30138 | −0.177999 | ||||||||
\(345\) | −0.0439677 | + | 0.219932i | −0.00236714 | + | 0.0118407i | ||||
\(346\) | 0.888179 | 0.0477488 | ||||||||
\(347\) | 8.49448 | − | 14.7129i | 0.456008 | − | 0.789828i | −0.542738 | − | 0.839902i | \(-0.682612\pi\) |
0.998746 | + | 0.0500739i | \(0.0159457\pi\) | |||||||
\(348\) | −7.66359 | − | 6.73387i | −0.410811 | − | 0.360973i | ||||
\(349\) | 11.0932 | − | 19.2139i | 0.593804 | − | 1.02850i | −0.399910 | − | 0.916554i | \(-0.630959\pi\) |
0.993714 | − | 0.111945i | \(-0.0357079\pi\) | |||||||
\(350\) | 4.68794 | 0.250581 | ||||||||
\(351\) | 19.2380 | − | 28.6123i | 1.02685 | − | 1.52721i | ||||
\(352\) | −0.0397925 | + | 0.0689226i | −0.00212095 | + | 0.00367359i | ||||
\(353\) | 8.74572 | − | 15.1480i | 0.465488 | − | 0.806248i | −0.533736 | − | 0.845651i | \(-0.679212\pi\) |
0.999223 | + | 0.0394032i | \(0.0125457\pi\) | |||||||
\(354\) | 2.58937 | − | 12.9524i | 0.137623 | − | 0.688410i | ||||
\(355\) | 11.6549 | 0.618578 | ||||||||
\(356\) | −4.11336 | + | 7.12456i | −0.218008 | + | 0.377601i | ||||
\(357\) | 4.13134 | − | 1.39796i | 0.218654 | − | 0.0739879i | ||||
\(358\) | −11.8427 | −0.625904 | ||||||||
\(359\) | 8.96717 | + | 15.5316i | 0.473269 | + | 0.819726i | 0.999532 | − | 0.0305960i | \(-0.00974054\pi\) |
−0.526263 | + | 0.850322i | \(0.676407\pi\) | |||||||
\(360\) | 0.360834 | + | 2.78226i | 0.0190176 | + | 0.146638i | ||||
\(361\) | 16.1942 | + | 9.93715i | 0.852328 | + | 0.523008i | ||||
\(362\) | −8.04715 | + | 13.9381i | −0.422949 | + | 0.732569i | ||||
\(363\) | 14.3041 | + | 12.5688i | 0.750771 | + | 0.659690i | ||||
\(364\) | −3.77006 | + | 6.52994i | −0.197605 | + | 0.342262i | ||||
\(365\) | −12.7535 | −0.667550 | ||||||||
\(366\) | −4.00875 | − | 3.52242i | −0.209541 | − | 0.184120i | ||||
\(367\) | −10.4730 | − | 18.1398i | −0.546687 | − | 0.946889i | −0.998499 | − | 0.0547761i | \(-0.982556\pi\) |
0.451812 | − | 0.892113i | \(-0.350778\pi\) | |||||||
\(368\) | −0.138465 | −0.00721797 | ||||||||
\(369\) | −0.888538 | − | 6.85119i | −0.0462554 | − | 0.356658i | ||||
\(370\) | 0.742128 | − | 1.28540i | 0.0385814 | − | 0.0668250i | ||||
\(371\) | −4.79970 | − | 8.31333i | −0.249188 | − | 0.431606i | ||||
\(372\) | 4.46294 | + | 3.92151i | 0.231393 | + | 0.203321i | ||||
\(373\) | 6.12723 | + | 10.6127i | 0.317256 | + | 0.549503i | 0.979914 | − | 0.199419i | \(-0.0639053\pi\) |
−0.662659 | + | 0.748922i | \(0.730572\pi\) | |||||||
\(374\) | 0.176355 | 0.00911911 | ||||||||
\(375\) | 14.0014 | − | 4.73779i | 0.723030 | − | 0.244658i | ||||
\(376\) | 2.46002 | + | 4.26088i | 0.126866 | + | 0.219738i | ||||
\(377\) | −19.5411 | − | 33.8462i | −1.00642 | − | 1.74317i | ||||
\(378\) | −2.59623 | − | 5.30326i | −0.133536 | − | 0.272770i | ||||
\(379\) | 31.8645 | 1.63677 | 0.818384 | − | 0.574672i | \(-0.194870\pi\) | ||||
0.818384 | + | 0.574672i | \(0.194870\pi\) | |||||||
\(380\) | −2.92077 | + | 2.84359i | −0.149832 | + | 0.145873i | ||||
\(381\) | 0.277927 | − | 1.39023i | 0.0142386 | − | 0.0712235i | ||||
\(382\) | −0.636975 | + | 1.10327i | −0.0325905 | + | 0.0564484i | ||||
\(383\) | 16.3299 | − | 28.2842i | 0.834419 | − | 1.44526i | −0.0600844 | − | 0.998193i | \(-0.519137\pi\) |
0.894503 | − | 0.447062i | \(-0.147530\pi\) | |||||||
\(384\) | −1.64067 | + | 0.555168i | −0.0837249 | + | 0.0283308i | ||||
\(385\) | 0.0845750 | 0.00431034 | ||||||||
\(386\) | 4.05430 | − | 7.02226i | 0.206358 | − | 0.357423i | ||||
\(387\) | 7.86910 | − | 6.01410i | 0.400009 | − | 0.305714i | ||||
\(388\) | −14.9427 | −0.758601 | ||||||||
\(389\) | 18.4772 | + | 32.0034i | 0.936830 | + | 1.62264i | 0.771338 | + | 0.636426i | \(0.219588\pi\) |
0.165492 | + | 0.986211i | \(0.447079\pi\) | |||||||
\(390\) | −2.10698 | + | 10.5394i | −0.106691 | + | 0.533682i | ||||
\(391\) | 0.153415 | + | 0.265722i | 0.00775851 | + | 0.0134381i | ||||
\(392\) | −2.85435 | − | 4.94388i | −0.144167 | − | 0.249704i | ||||
\(393\) | 1.30172 | − | 6.51137i | 0.0656631 | − | 0.328455i | ||||
\(394\) | −20.1767 | −1.01649 | ||||||||
\(395\) | −2.86483 | + | 4.96204i | −0.144145 | + | 0.249667i | ||||
\(396\) | −0.0307072 | − | 0.236772i | −0.00154309 | − | 0.0118982i | ||||
\(397\) | 8.42840 | + | 14.5984i | 0.423009 | + | 0.732673i | 0.996232 | − | 0.0867261i | \(-0.0276405\pi\) |
−0.573223 | + | 0.819399i | \(0.694307\pi\) | |||||||
\(398\) | −3.27803 | + | 5.67772i | −0.164313 | + | 0.284599i | ||||
\(399\) | 3.90456 | − | 7.63926i | 0.195472 | − | 0.382441i | ||||
\(400\) | 2.06271 | + | 3.57272i | 0.103136 | + | 0.178636i | ||||
\(401\) | −6.87472 | + | 11.9074i | −0.343307 | + | 0.594625i | −0.985045 | − | 0.172299i | \(-0.944880\pi\) |
0.641738 | + | 0.766924i | \(0.278214\pi\) | |||||||
\(402\) | 17.7780 | − | 6.01572i | 0.886688 | − | 0.300037i | ||||
\(403\) | 11.3799 | + | 19.7106i | 0.566873 | + | 0.981853i | ||||
\(404\) | −0.318675 | − | 0.551961i | −0.0158547 | − | 0.0274611i | ||||
\(405\) | −5.92849 | − | 5.97440i | −0.294589 | − | 0.296870i | ||||
\(406\) | −6.69309 | −0.332172 | ||||||||
\(407\) | −0.0631556 | + | 0.109389i | −0.00313051 | + | 0.00542220i | ||||
\(408\) | 2.88321 | + | 2.53343i | 0.142740 | + | 0.125423i | ||||
\(409\) | 14.4996 | 0.716961 | 0.358481 | − | 0.933537i | \(-0.383295\pi\) | ||||
0.358481 | + | 0.933537i | \(0.383295\pi\) | |||||||
\(410\) | 1.07680 | + | 1.86507i | 0.0531793 | + | 0.0921093i | ||||
\(411\) | −3.82768 | − | 3.36332i | −0.188806 | − | 0.165900i | ||||
\(412\) | 2.96826 | + | 5.14118i | 0.146236 | + | 0.253288i | ||||
\(413\) | −4.33292 | − | 7.50484i | −0.213209 | − | 0.369289i | ||||
\(414\) | 0.330041 | − | 0.252240i | 0.0162206 | − | 0.0123969i | ||||
\(415\) | 4.45236 | + | 7.71171i | 0.218558 | + | 0.378553i | ||||
\(416\) | −6.63538 | −0.325326 | ||||||||
\(417\) | −18.4315 | + | 6.23683i | −0.902593 | + | 0.305419i | ||||
\(418\) | 0.248559 | − | 0.241991i | 0.0121574 | − | 0.0118362i | ||||
\(419\) | −0.703380 | − | 1.21829i | −0.0343624 | − | 0.0595174i | 0.848333 | − | 0.529463i | \(-0.177607\pi\) |
−0.882695 | + | 0.469946i | \(0.844273\pi\) | |||||||
\(420\) | 1.38270 | + | 1.21496i | 0.0674691 | + | 0.0592840i | ||||
\(421\) | −29.2010 | −1.42317 | −0.711585 | − | 0.702600i | \(-0.752022\pi\) | ||||
−0.711585 | + | 0.702600i | \(0.752022\pi\) | |||||||
\(422\) | 5.53735 | − | 9.59098i | 0.269554 | − | 0.466881i | ||||
\(423\) | −13.6256 | − | 5.67474i | −0.662501 | − | 0.275915i | ||||
\(424\) | 4.22378 | − | 7.31580i | 0.205125 | − | 0.355287i | ||||
\(425\) | 4.57084 | − | 7.91693i | 0.221718 | − | 0.384028i | ||||
\(426\) | −16.2155 | − | 14.2483i | −0.785641 | − | 0.690330i | ||||
\(427\) | −3.50109 | −0.169430 | ||||||||
\(428\) | −16.7256 | −0.808461 | ||||||||
\(429\) | 0.179305 | − | 0.896908i | 0.00865694 | − | 0.0433031i | ||||
\(430\) | −1.54370 | + | 2.67377i | −0.0744440 | + | 0.128941i | ||||
\(431\) | −14.7626 | + | 25.5695i | −0.711087 | + | 1.23164i | 0.253362 | + | 0.967372i | \(0.418464\pi\) |
−0.964449 | + | 0.264268i | \(0.914870\pi\) | |||||||
\(432\) | 2.89931 | − | 4.31207i | 0.139493 | − | 0.207465i | ||||
\(433\) | −0.0851720 | + | 0.147522i | −0.00409310 | + | 0.00708946i | −0.868065 | − | 0.496451i | \(-0.834636\pi\) |
0.863972 | + | 0.503541i | \(0.167970\pi\) | |||||||
\(434\) | 3.89776 | 0.187099 | ||||||||
\(435\) | −9.03717 | + | 3.05799i | −0.433299 | + | 0.146619i | ||||
\(436\) | −1.01969 | − | 1.76615i | −0.0488342 | − | 0.0845834i | ||||
\(437\) | 0.580844 | + | 0.164002i | 0.0277856 | + | 0.00784530i | ||||
\(438\) | 17.7440 | + | 15.5913i | 0.847839 | + | 0.744983i | ||||
\(439\) | −4.15010 | −0.198074 | −0.0990368 | − | 0.995084i | \(-0.531576\pi\) | ||||
−0.0990368 | + | 0.995084i | \(0.531576\pi\) | |||||||
\(440\) | 0.0372134 | + | 0.0644555i | 0.00177408 | + | 0.00307279i | ||||
\(441\) | 15.8098 | + | 6.58438i | 0.752847 | + | 0.313542i | ||||
\(442\) | 7.35179 | + | 12.7337i | 0.349689 | + | 0.605679i | ||||
\(443\) | −11.7195 | − | 20.2988i | −0.556810 | − | 0.964423i | −0.997760 | − | 0.0668916i | \(-0.978692\pi\) |
0.440950 | − | 0.897532i | \(-0.354642\pi\) | |||||||
\(444\) | −2.60394 | + | 0.881120i | −0.123578 | + | 0.0418161i | ||||
\(445\) | 3.84676 | + | 6.66279i | 0.182354 | + | 0.315846i | ||||
\(446\) | −0.747365 | −0.0353888 | ||||||||
\(447\) | 6.00641 | − | 30.0448i | 0.284093 | − | 1.42107i | ||||
\(448\) | −0.568176 | + | 0.984110i | −0.0268438 | + | 0.0464948i | ||||
\(449\) | −37.0884 | −1.75031 | −0.875155 | − | 0.483842i | \(-0.839241\pi\) | ||||
−0.875155 | + | 0.483842i | \(0.839241\pi\) | |||||||
\(450\) | −11.4250 | − | 4.75824i | −0.538581 | − | 0.224306i | ||||
\(451\) | −0.0916363 | − | 0.158719i | −0.00431498 | − | 0.00747377i | ||||
\(452\) | 8.92114 | + | 15.4519i | 0.419615 | + | 0.726795i | ||||
\(453\) | 4.71144 | − | 23.5672i | 0.221363 | − | 1.10728i | ||||
\(454\) | 14.1895 | − | 24.5769i | 0.665946 | − | 1.15345i | ||||
\(455\) | 3.52571 | + | 6.10671i | 0.165288 | + | 0.286287i | ||||
\(456\) | 7.53998 | − | 0.385604i | 0.353092 | − | 0.0180576i | ||||
\(457\) | −17.9019 | + | 31.0069i | −0.837413 | + | 1.45044i | 0.0546368 | + | 0.998506i | \(0.482600\pi\) |
−0.892050 | + | 0.451936i | \(0.850733\pi\) | |||||||
\(458\) | −3.63731 | − | 6.30001i | −0.169960 | − | 0.294380i | ||||
\(459\) | −11.4875 | − | 0.786308i | −0.536189 | − | 0.0367017i | ||||
\(460\) | −0.0647451 | + | 0.112142i | −0.00301876 | + | 0.00522864i | ||||
\(461\) | 5.84450 | 0.272205 | 0.136103 | − | 0.990695i | \(-0.456542\pi\) | ||||
0.136103 | + | 0.990695i | \(0.456542\pi\) | |||||||
\(462\) | −0.117669 | − | 0.103394i | −0.00547446 | − | 0.00481032i | ||||
\(463\) | −0.657422 | − | 1.13869i | −0.0305530 | − | 0.0529194i | 0.850345 | − | 0.526226i | \(-0.176394\pi\) |
−0.880898 | + | 0.473307i | \(0.843060\pi\) | |||||||
\(464\) | −2.94499 | − | 5.10087i | −0.136718 | − | 0.236802i | ||||
\(465\) | 5.26285 | − | 1.78084i | 0.244059 | − | 0.0825845i | ||||
\(466\) | 8.86740 | + | 15.3588i | 0.410775 | + | 0.711482i | ||||
\(467\) | 16.6029 | 0.768290 | 0.384145 | − | 0.923273i | \(-0.374496\pi\) | ||||
0.384145 | + | 0.923273i | \(0.374496\pi\) | |||||||
\(468\) | 15.8159 | − | 12.0876i | 0.731092 | − | 0.558750i | ||||
\(469\) | 6.15668 | − | 10.6637i | 0.284289 | − | 0.492403i | ||||
\(470\) | 4.60115 | 0.212235 | ||||||||
\(471\) | 5.27513 | − | 26.3869i | 0.243065 | − | 1.21584i | ||||
\(472\) | 3.81301 | − | 6.60433i | 0.175508 | − | 0.303989i | ||||
\(473\) | 0.131370 | − | 0.227540i | 0.00604041 | − | 0.0104623i | ||||
\(474\) | 10.0520 | − | 3.40138i | 0.461703 | − | 0.156231i | ||||
\(475\) | −4.42120 | − | 17.4303i | −0.202858 | − | 0.799759i | ||||
\(476\) | 2.51808 | 0.115416 | ||||||||
\(477\) | 3.25942 | + | 25.1322i | 0.149239 | + | 1.15072i | ||||
\(478\) | −12.0318 | − | 20.8396i | −0.550320 | − | 0.953183i | ||||
\(479\) | 16.6278 | + | 28.8001i | 0.759742 | + | 1.31591i | 0.942982 | + | 0.332843i | \(0.108008\pi\) |
−0.183240 | + | 0.983068i | \(0.558659\pi\) | |||||||
\(480\) | −0.317537 | + | 1.58836i | −0.0144935 | + | 0.0724984i | ||||
\(481\) | −10.5312 | −0.480180 | ||||||||
\(482\) | 5.35131 | + | 9.26873i | 0.243745 | + | 0.422179i | ||||
\(483\) | 0.0534255 | − | 0.267241i | 0.00243094 | − | 0.0121599i | ||||
\(484\) | 5.49683 | + | 9.52079i | 0.249856 | + | 0.432763i | ||||
\(485\) | −6.98711 | + | 12.1020i | −0.317268 | + | 0.549525i | ||||
\(486\) | 0.944527 | + | 15.5598i | 0.0428446 | + | 0.705808i | ||||
\(487\) | −10.0490 | −0.455366 | −0.227683 | − | 0.973735i | \(-0.573115\pi\) | ||||
−0.227683 | + | 0.973735i | \(0.573115\pi\) | |||||||
\(488\) | −1.54050 | − | 2.66822i | −0.0697350 | − | 0.120785i | ||||
\(489\) | −37.1014 | + | 12.5544i | −1.67778 | + | 0.567727i | ||||
\(490\) | −5.33870 | −0.241178 | ||||||||
\(491\) | 19.3339 | − | 33.4873i | 0.872527 | − | 1.51126i | 0.0131528 | − | 0.999913i | \(-0.495813\pi\) |
0.859374 | − | 0.511347i | \(-0.170853\pi\) | |||||||
\(492\) | 0.781921 | − | 3.91127i | 0.0352517 | − | 0.176334i | ||||
\(493\) | −6.52591 | + | 11.3032i | −0.293912 | + | 0.509071i | ||||
\(494\) | 27.8347 | + | 7.85918i | 1.25234 | + | 0.353601i | ||||
\(495\) | −0.206119 | − | 0.0858433i | −0.00926436 | − | 0.00385837i | ||||
\(496\) | 1.71503 | + | 2.97052i | 0.0770073 | + | 0.133380i | ||||
\(497\) | −14.1620 | −0.635251 | ||||||||
\(498\) | 3.23309 | − | 16.1723i | 0.144878 | − | 0.724700i | ||||
\(499\) | 17.8984 | − | 31.0009i | 0.801240 | − | 1.38779i | −0.117560 | − | 0.993066i | \(-0.537507\pi\) |
0.918800 | − | 0.394723i | \(-0.129159\pi\) | |||||||
\(500\) | 8.53397 | 0.381651 | ||||||||
\(501\) | 11.2959 | − | 3.82230i | 0.504664 | − | 0.170768i | ||||
\(502\) | −7.87511 | + | 13.6401i | −0.351484 | + | 0.608787i | ||||
\(503\) | −11.6716 | + | 20.2158i | −0.520410 | + | 0.901377i | 0.479308 | + | 0.877647i | \(0.340888\pi\) |
−0.999718 | + | 0.0237301i | \(0.992446\pi\) | |||||||
\(504\) | −0.438452 | − | 3.38074i | −0.0195302 | − | 0.150590i | ||||
\(505\) | −0.596041 | −0.0265235 | ||||||||
\(506\) | 0.00550985 | − | 0.00954334i | 0.000244943 | − | 0.000424253i | ||||
\(507\) | 50.9071 | − | 17.2259i | 2.26086 | − | 0.765029i | ||||
\(508\) | 0.409265 | − | 0.708868i | 0.0181582 | − | 0.0314509i | ||||
\(509\) | −43.7873 | −1.94084 | −0.970419 | − | 0.241427i | \(-0.922384\pi\) | ||||
−0.970419 | + | 0.241427i | \(0.922384\pi\) | |||||||
\(510\) | 3.39998 | − | 1.15048i | 0.150554 | − | 0.0509442i | ||||
\(511\) | 15.4969 | 0.685543 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.2697 | + | 14.6546i | −0.762475 | + | 0.647018i | ||||
\(514\) | 5.24788 | 0.231474 | ||||||||
\(515\) | 5.55176 | 0.244640 | ||||||||
\(516\) | 5.41647 | − | 1.83282i | 0.238447 | − | 0.0806854i | ||||
\(517\) | −0.391561 | −0.0172208 | ||||||||
\(518\) | −0.901766 | + | 1.56190i | −0.0396213 | + | 0.0686261i | ||||
\(519\) | −1.45721 | + | 0.493089i | −0.0639643 | + | 0.0216442i | ||||
\(520\) | −3.10266 | + | 5.37396i | −0.136061 | + | 0.235664i | ||||
\(521\) | 14.0255 | 0.614470 | 0.307235 | − | 0.951634i | \(-0.400596\pi\) | ||||
0.307235 | + | 0.951634i | \(0.400596\pi\) | |||||||
\(522\) | 16.3118 | + | 6.79346i | 0.713949 | + | 0.297342i | ||||
\(523\) | −1.68513 | + | 2.91874i | −0.0736858 | + | 0.127627i | −0.900514 | − | 0.434827i | \(-0.856810\pi\) |
0.826828 | + | 0.562454i | \(0.190143\pi\) | |||||||
\(524\) | 1.91686 | − | 3.32010i | 0.0837385 | − | 0.145039i | ||||
\(525\) | −7.69134 | + | 2.60259i | −0.335678 | + | 0.113586i | ||||
\(526\) | 9.00516 | 0.392644 | ||||||||
\(527\) | 3.80040 | − | 6.58249i | 0.165548 | − | 0.286738i | ||||
\(528\) | 0.0270226 | − | 0.135171i | 0.00117601 | − | 0.00588254i | ||||
\(529\) | −22.9808 | −0.999166 | ||||||||
\(530\) | −3.95002 | − | 6.84164i | −0.171578 | − | 0.297182i | ||||
\(531\) | 2.94244 | + | 22.6880i | 0.127691 | + | 0.984577i | ||||
\(532\) | 3.54905 | − | 3.45527i | 0.153871 | − | 0.149805i | ||||
\(533\) | 7.64016 | − | 13.2331i | 0.330932 | − | 0.573191i | ||||
\(534\) | 2.79334 | − | 13.9726i | 0.120880 | − | 0.604655i | ||||
\(535\) | −7.82076 | + | 13.5460i | −0.338121 | + | 0.585643i | ||||
\(536\) | 10.8359 | 0.468038 | ||||||||
\(537\) | 19.4299 | − | 6.57466i | 0.838460 | − | 0.283718i | ||||
\(538\) | −6.28989 | − | 10.8944i | −0.271176 | − | 0.469691i | ||||
\(539\) | 0.454327 | 0.0195692 | ||||||||
\(540\) | −2.13663 | − | 4.36444i | −0.0919459 | − | 0.187815i | ||||
\(541\) | −4.05201 | + | 7.01829i | −0.174210 | + | 0.301740i | −0.939887 | − | 0.341484i | \(-0.889070\pi\) |
0.765678 | + | 0.643224i | \(0.222404\pi\) | |||||||
\(542\) | 2.79712 | + | 4.84476i | 0.120147 | + | 0.208100i | ||||
\(543\) | 5.46472 | − | 27.3352i | 0.234514 | − | 1.17307i | ||||
\(544\) | 1.10797 | + | 1.91906i | 0.0475038 | + | 0.0822789i | ||||
\(545\) | −1.90720 | −0.0816954 | ||||||||
\(546\) | 2.56021 | − | 12.8065i | 0.109567 | − | 0.548067i | ||||
\(547\) | 17.8887 | + | 30.9841i | 0.764865 | + | 1.32479i | 0.940318 | + | 0.340298i | \(0.110528\pi\) |
−0.175452 | + | 0.984488i | \(0.556139\pi\) | |||||||
\(548\) | −1.47091 | − | 2.54770i | −0.0628344 | − | 0.108832i | ||||
\(549\) | 8.53256 | + | 3.55359i | 0.364161 | + | 0.151664i | ||||
\(550\) | −0.328322 | −0.0139997 | ||||||||
\(551\) | 6.31226 | + | 24.8857i | 0.268911 | + | 1.06017i | ||||
\(552\) | 0.227174 | − | 0.0768711i | 0.00966919 | − | 0.00327185i | ||||
\(553\) | 3.48108 | − | 6.02941i | 0.148031 | − | 0.256396i | ||||
\(554\) | −7.72542 | + | 13.3808i | −0.328222 | + | 0.568497i | ||||
\(555\) | −0.503971 | + | 2.52093i | −0.0213924 | + | 0.107007i | ||||
\(556\) | −11.2341 | −0.476433 | ||||||||
\(557\) | 12.8280 | − | 22.2187i | 0.543538 | − | 0.941436i | −0.455159 | − | 0.890410i | \(-0.650418\pi\) |
0.998697 | − | 0.0510256i | \(-0.0162490\pi\) | |||||||
\(558\) | −9.49929 | − | 3.95621i | −0.402137 | − | 0.167480i | ||||
\(559\) | 21.9059 | 0.926522 | ||||||||
\(560\) | 0.531351 | + | 0.920326i | 0.0224537 | + | 0.0388909i | ||||
\(561\) | −0.289340 | + | 0.0979067i | −0.0122160 | + | 0.00413363i | ||||
\(562\) | 4.41799 | + | 7.65218i | 0.186362 | + | 0.322788i | ||||
\(563\) | −19.7952 | − | 34.2862i | −0.834267 | − | 1.44499i | −0.894626 | − | 0.446816i | \(-0.852558\pi\) |
0.0603587 | − | 0.998177i | \(-0.480776\pi\) | |||||||
\(564\) | −6.40157 | − | 5.62496i | −0.269555 | − | 0.236853i | ||||
\(565\) | 16.6859 | 0.701980 | ||||||||
\(566\) | −13.3232 | + | 23.0765i | −0.560016 | + | 0.969976i | ||||
\(567\) | 7.20375 | + | 7.25954i | 0.302529 | + | 0.304872i | ||||
\(568\) | −6.23133 | − | 10.7930i | −0.261461 | − | 0.452863i | ||||
\(569\) | 8.34476 | − | 14.4535i | 0.349830 | − | 0.605924i | −0.636389 | − | 0.771369i | \(-0.719573\pi\) |
0.986219 | + | 0.165445i | \(0.0529059\pi\) | |||||||
\(570\) | 3.21334 | − | 6.28690i | 0.134592 | − | 0.263329i | ||||
\(571\) | 17.0306 | + | 29.4979i | 0.712710 | + | 1.23445i | 0.963836 | + | 0.266496i | \(0.0858659\pi\) |
−0.251126 | + | 0.967954i | \(0.580801\pi\) | |||||||
\(572\) | 0.264038 | − | 0.457328i | 0.0110400 | − | 0.0191218i | ||||
\(573\) | 0.432563 | − | 2.16373i | 0.0180706 | − | 0.0903912i | ||||
\(574\) | −1.30843 | − | 2.26626i | −0.0546127 | − | 0.0945919i | ||||
\(575\) | −0.285613 | − | 0.494696i | −0.0119109 | − | 0.0206303i | ||||
\(576\) | 2.38358 | − | 1.82169i | 0.0993157 | − | 0.0759038i | ||||
\(577\) | 13.8354 | 0.575975 | 0.287987 | − | 0.957634i | \(-0.407014\pi\) | ||||
0.287987 | + | 0.957634i | \(0.407014\pi\) | |||||||
\(578\) | −6.04481 | + | 10.4699i | −0.251431 | + | 0.435491i | ||||
\(579\) | −2.75323 | + | 13.7720i | −0.114420 | + | 0.572345i | ||||
\(580\) | −5.50823 | −0.228717 | ||||||||
\(581\) | −5.41009 | − | 9.37056i | −0.224449 | − | 0.388756i | ||||
\(582\) | 24.5160 | − | 8.29571i | 1.01622 | − | 0.343868i | ||||
\(583\) | 0.336149 | + | 0.582228i | 0.0139219 | + | 0.0241134i | ||||
\(584\) | 6.81871 | + | 11.8104i | 0.282160 | + | 0.488716i | ||||
\(585\) | −2.39427 | − | 18.4613i | −0.0989909 | − | 0.763283i | ||||
\(586\) | 4.55284 | + | 7.88575i | 0.188076 | + | 0.325757i | ||||
\(587\) | −32.5972 | −1.34543 | −0.672716 | − | 0.739901i | \(-0.734872\pi\) | ||||
−0.672716 | + | 0.739901i | \(0.734872\pi\) | |||||||
\(588\) | 7.42773 | + | 6.52662i | 0.306314 | + | 0.269153i | ||||
\(589\) | −3.67598 | − | 14.4924i | −0.151466 | − | 0.597148i | ||||
\(590\) | −3.56587 | − | 6.17628i | −0.146805 | − | 0.254273i | ||||
\(591\) | 33.1033 | − | 11.2015i | 1.36169 | − | 0.460767i | ||||
\(592\) | −1.58712 | −0.0652304 | ||||||||
\(593\) | −22.3884 | + | 38.7779i | −0.919383 | + | 1.59242i | −0.119028 | + | 0.992891i | \(0.537978\pi\) |
−0.800355 | + | 0.599526i | \(0.795356\pi\) | |||||||
\(594\) | 0.181828 | + | 0.371416i | 0.00746051 | + | 0.0152394i | ||||
\(595\) | 1.17744 | − | 2.03938i | 0.0482703 | − | 0.0836066i | ||||
\(596\) | 8.84481 | − | 15.3197i | 0.362297 | − | 0.627517i | ||||
\(597\) | 2.22608 | − | 11.1351i | 0.0911072 | − | 0.455730i | ||||
\(598\) | 0.918766 | 0.0375711 | ||||||||
\(599\) | 13.1482 | 0.537222 | 0.268611 | − | 0.963249i | \(-0.413435\pi\) | ||||
0.268611 | + | 0.963249i | \(0.413435\pi\) | |||||||
\(600\) | −5.36769 | − | 4.71650i | −0.219135 | − | 0.192550i | ||||
\(601\) | −5.57735 | + | 9.66025i | −0.227505 | + | 0.394050i | −0.957068 | − | 0.289864i | \(-0.906390\pi\) |
0.729563 | + | 0.683913i | \(0.239723\pi\) | |||||||
\(602\) | 1.87577 | − | 3.24892i | 0.0764505 | − | 0.132416i | ||||
\(603\) | −25.8281 | + | 19.7396i | −1.05180 | + | 0.803858i | ||||
\(604\) | 6.93789 | − | 12.0168i | 0.282299 | − | 0.488956i | ||||
\(605\) | 10.2811 | 0.417987 | ||||||||
\(606\) | 0.829271 | + | 0.728667i | 0.0336868 | + | 0.0296001i | ||||
\(607\) | −22.8386 | − | 39.5577i | −0.926991 | − | 1.60560i | −0.788327 | − | 0.615257i | \(-0.789052\pi\) |
−0.138665 | − | 0.990339i | \(-0.544281\pi\) | |||||||
\(608\) | 4.19489 | + | 1.18444i | 0.170125 | + | 0.0480352i | ||||
\(609\) | 10.9811 | − | 3.71579i | 0.444978 | − | 0.150571i | ||||
\(610\) | −2.88130 | −0.116660 | ||||||||
\(611\) | −16.3232 | − | 28.2725i | −0.660364 | − | 1.14378i | ||||
\(612\) | −6.13686 | − | 2.55585i | −0.248068 | − | 0.103314i | ||||
\(613\) | −8.80325 | − | 15.2477i | −0.355560 | − | 0.615848i | 0.631654 | − | 0.775251i | \(-0.282376\pi\) |
−0.987214 | + | 0.159403i | \(0.949043\pi\) | |||||||
\(614\) | −4.46612 | − | 7.73555i | −0.180238 | − | 0.312181i | ||||
\(615\) | −2.80210 | − | 2.46216i | −0.112991 | − | 0.0992837i | ||||
\(616\) | −0.0452183 | − | 0.0783203i | −0.00182190 | − | 0.00315562i | ||||
\(617\) | −17.9178 | −0.721344 | −0.360672 | − | 0.932693i | \(-0.617453\pi\) | ||||
−0.360672 | + | 0.932693i | \(0.617453\pi\) | |||||||
\(618\) | −7.72415 | − | 6.78709i | −0.310711 | − | 0.273017i | ||||
\(619\) | −8.69227 | + | 15.0555i | −0.349372 | + | 0.605130i | −0.986138 | − | 0.165927i | \(-0.946938\pi\) |
0.636766 | + | 0.771057i | \(0.280272\pi\) | |||||||
\(620\) | 3.20775 | 0.128826 | ||||||||
\(621\) | −0.401453 | + | 0.597070i | −0.0161097 | + | 0.0239596i | ||||
\(622\) | −0.795438 | − | 1.37774i | −0.0318942 | − | 0.0552423i | ||||
\(623\) | −4.67423 | − | 8.09600i | −0.187269 | − | 0.324360i | ||||
\(624\) | 10.8865 | − | 3.68375i | 0.435807 | − | 0.147468i | ||||
\(625\) | −6.32314 | + | 10.9520i | −0.252926 | + | 0.438080i | ||||
\(626\) | −2.53074 | − | 4.38337i | −0.101149 | − | 0.175195i | ||||
\(627\) | −0.273458 | + | 0.535019i | −0.0109208 | + | 0.0213666i | ||||
\(628\) | 7.76796 | − | 13.4545i | 0.309975 | − | 0.536893i | ||||
\(629\) | 1.75848 | + | 3.04578i | 0.0701153 | + | 0.121443i | ||||
\(630\) | −2.94306 | − | 1.22571i | −0.117255 | − | 0.0488335i | ||||
\(631\) | −15.6412 | + | 27.0914i | −0.622668 | + | 1.07849i | 0.366319 | + | 0.930489i | \(0.380618\pi\) |
−0.988987 | + | 0.148003i | \(0.952715\pi\) | |||||||
\(632\) | 6.12676 | 0.243710 | ||||||||
\(633\) | −3.76035 | + | 18.8098i | −0.149461 | + | 0.747621i | ||||
\(634\) | 16.0375 | + | 27.7777i | 0.636930 | + | 1.10320i | ||||
\(635\) | −0.382739 | − | 0.662924i | −0.0151885 | − | 0.0263073i | ||||
\(636\) | −2.86832 | + | 14.3477i | −0.113736 | + | 0.568923i | ||||
\(637\) | 18.9397 | + | 32.8045i | 0.750419 | + | 1.29976i | ||||
\(638\) | 0.468754 | 0.0185581 | ||||||||
\(639\) | 34.5143 | + | 14.3743i | 1.36537 | + | 0.568640i | ||||
\(640\) | −0.467593 | + | 0.809895i | −0.0184832 | + | 0.0320139i | ||||
\(641\) | −9.47055 | −0.374064 | −0.187032 | − | 0.982354i | \(-0.559887\pi\) | ||||
−0.187032 | + | 0.982354i | \(0.559887\pi\) | |||||||
\(642\) | 27.4411 | − | 9.28549i | 1.08301 | − | 0.366469i | ||||
\(643\) | 4.13256 | − | 7.15781i | 0.162972 | − | 0.282277i | −0.772961 | − | 0.634454i | \(-0.781225\pi\) |
0.935933 | + | 0.352177i | \(0.114559\pi\) | |||||||
\(644\) | 0.0786723 | − | 0.136264i | 0.00310012 | − | 0.00536957i | ||||
\(645\) | 1.04831 | − | 5.24379i | 0.0412772 | − | 0.206474i | ||||
\(646\) | −2.37481 | − | 9.36256i | −0.0934356 | − | 0.368365i | ||||
\(647\) | −19.0963 | −0.750754 | −0.375377 | − | 0.926872i | \(-0.622487\pi\) | ||||
−0.375377 | + | 0.926872i | \(0.622487\pi\) | |||||||
\(648\) | −2.36288 | + | 8.68428i | −0.0928229 | + | 0.341151i | ||||
\(649\) | 0.303458 | + | 0.525605i | 0.0119118 | + | 0.0206318i | ||||
\(650\) | −13.6869 | − | 23.7064i | −0.536844 | − | 0.929841i | ||||
\(651\) | −6.39493 | + | 2.16391i | −0.250637 | + | 0.0848104i | ||||
\(652\) | −22.6136 | −0.885618 | ||||||||
\(653\) | 4.14981 | + | 7.18769i | 0.162395 | + | 0.281276i | 0.935727 | − | 0.352725i | \(-0.114745\pi\) |
−0.773332 | + | 0.634001i | \(0.781412\pi\) | |||||||
\(654\) | 2.65348 | + | 2.33157i | 0.103759 | + | 0.0911716i | ||||
\(655\) | −1.79262 | − | 3.10492i | −0.0700436 | − | 0.121319i | ||||
\(656\) | 1.15143 | − | 1.99433i | 0.0449557 | − | 0.0778655i | ||||
\(657\) | −37.7677 | − | 15.7293i | −1.47346 | − | 0.613659i | ||||
\(658\) | −5.59089 | −0.217956 | ||||||||
\(659\) | 4.91963 | + | 8.52104i | 0.191641 | + | 0.331933i | 0.945794 | − | 0.324766i | \(-0.105286\pi\) |
−0.754153 | + | 0.656699i | \(0.771952\pi\) | |||||||
\(660\) | −0.0968384 | − | 0.0850903i | −0.00376943 | − | 0.00331213i | ||||
\(661\) | 44.1357 | 1.71668 | 0.858340 | − | 0.513082i | \(-0.171496\pi\) | ||||
0.858340 | + | 0.513082i | \(0.171496\pi\) | |||||||
\(662\) | 2.26128 | − | 3.91666i | 0.0878873 | − | 0.152225i | ||||
\(663\) | −19.1312 | − | 16.8103i | −0.742993 | − | 0.652856i | ||||
\(664\) | 4.76093 | − | 8.24617i | 0.184760 | − | 0.320014i | ||||
\(665\) | −1.13889 | − | 4.49002i | −0.0441643 | − | 0.174115i | ||||
\(666\) | 3.78303 | − | 2.89125i | 0.146590 | − | 0.112034i | ||||
\(667\) | 0.407777 | + | 0.706291i | 0.0157892 | + | 0.0273477i | ||||
\(668\) | 6.88495 | 0.266387 | ||||||||
\(669\) | 1.22618 | − | 0.414913i | 0.0474068 | − | 0.0160415i | ||||
\(670\) | 5.06677 | − | 8.77591i | 0.195747 | − | 0.339043i | ||||
\(671\) | 0.245201 | 0.00946586 | ||||||||
\(672\) | 0.385842 | − | 1.93003i | 0.0148842 | − | 0.0744525i | ||||
\(673\) | −12.6558 | + | 21.9205i | −0.487845 | + | 0.844972i | −0.999902 | − | 0.0139794i | \(-0.995550\pi\) |
0.512058 | + | 0.858951i | \(0.328883\pi\) | |||||||
\(674\) | −0.468804 | + | 0.811992i | −0.0180577 | + | 0.0312768i | ||||
\(675\) | 21.3863 | + | 1.46388i | 0.823159 | + | 0.0563446i | ||||
\(676\) | 31.0283 | 1.19340 | ||||||||
\(677\) | 14.4291 | − | 24.9919i | 0.554554 | − | 0.960516i | −0.443384 | − | 0.896332i | \(-0.646222\pi\) |
0.997938 | − | 0.0641840i | \(-0.0204445\pi\) | |||||||
\(678\) | −23.2150 | − | 20.3987i | −0.891567 | − | 0.783406i | ||||
\(679\) | 8.49009 | − | 14.7053i | 0.325820 | − | 0.564336i | ||||
\(680\) | 2.07231 | 0.0794696 | ||||||||
\(681\) | −9.63592 | + | 48.2001i | −0.369249 | + | 1.84703i | ||||
\(682\) | −0.272982 | −0.0104530 | ||||||||
\(683\) | 24.9816 | 0.955893 | 0.477947 | − | 0.878389i | \(-0.341381\pi\) | ||||
0.477947 | + | 0.878389i | \(0.341381\pi\) | |||||||
\(684\) | −12.1565 | + | 4.81860i | −0.464816 | + | 0.184244i | ||||
\(685\) | −2.75116 | −0.105116 | ||||||||
\(686\) | 14.4416 | 0.551381 | ||||||||
\(687\) | 9.46518 | + | 8.31690i | 0.361119 | + | 0.317309i | ||||
\(688\) | 3.30138 | 0.125864 | ||||||||
\(689\) | −28.0264 | + | 48.5431i | −1.06772 | + | 1.84935i | ||||
\(690\) | 0.0439677 | − | 0.219932i | 0.00167382 | − | 0.00837267i | ||||
\(691\) | 9.20873 | − | 15.9500i | 0.350317 | − | 0.606766i | −0.635988 | − | 0.771699i | \(-0.719407\pi\) |
0.986305 | + | 0.164933i | \(0.0527407\pi\) | |||||||
\(692\) | −0.888179 | −0.0337635 | ||||||||
\(693\) | 0.250457 | + | 0.104309i | 0.00951406 | + | 0.00396237i | ||||
\(694\) | −8.49448 | + | 14.7129i | −0.322446 | + | 0.558493i | ||||
\(695\) | −5.25300 | + | 9.09847i | −0.199258 | + | 0.345125i | ||||
\(696\) | 7.66359 | + | 6.73387i | 0.290487 | + | 0.255247i | ||||
\(697\) | −5.10298 | −0.193289 | ||||||||
\(698\) | −11.0932 | + | 19.2139i | −0.419883 | + | 0.727258i | ||||
\(699\) | −23.0752 | − | 20.2758i | −0.872783 | − | 0.766900i | ||||
\(700\) | −4.68794 | −0.177187 | ||||||||
\(701\) | −9.04527 | − | 15.6669i | −0.341635 | − | 0.591729i | 0.643101 | − | 0.765781i | \(-0.277647\pi\) |
−0.984737 | + | 0.174052i | \(0.944314\pi\) | |||||||
\(702\) | −19.2380 | + | 28.6123i | −0.726093 | + | 1.07990i | ||||
\(703\) | 6.65781 | + | 1.87985i | 0.251104 | + | 0.0708997i | ||||
\(704\) | 0.0397925 | − | 0.0689226i | 0.00149974 | − | 0.00259762i | ||||
\(705\) | −7.54896 | + | 2.55441i | −0.284310 | + | 0.0962047i | ||||
\(706\) | −8.74572 | + | 15.1480i | −0.329149 | + | 0.570103i | ||||
\(707\) | 0.724254 | 0.0272384 | ||||||||
\(708\) | −2.58937 | + | 12.9524i | −0.0973145 | + | 0.486780i | ||||
\(709\) | −11.6354 | − | 20.1531i | −0.436977 | − | 0.756866i | 0.560478 | − | 0.828169i | \(-0.310618\pi\) |
−0.997455 | + | 0.0713033i | \(0.977284\pi\) | |||||||
\(710\) | −11.6549 | −0.437401 | ||||||||
\(711\) | −14.6036 | + | 11.1611i | −0.547678 | + | 0.418573i | ||||
\(712\) | 4.11336 | − | 7.12456i | 0.154155 | − | 0.267004i | ||||
\(713\) | −0.237471 | − | 0.411313i | −0.00889338 | − | 0.0154038i | ||||
\(714\) | −4.13134 | + | 1.39796i | −0.154611 | + | 0.0523173i | ||||
\(715\) | −0.246925 | − | 0.427686i | −0.00923447 | − | 0.0159946i | ||||
\(716\) | 11.8427 | 0.442581 | ||||||||
\(717\) | 31.3096 | + | 27.5113i | 1.16928 | + | 1.02743i | ||||
\(718\) | −8.96717 | − | 15.5316i | −0.334652 | − | 0.579634i | ||||
\(719\) | 12.5242 | + | 21.6926i | 0.467075 | + | 0.808997i | 0.999292 | − | 0.0376103i | \(-0.0119745\pi\) |
−0.532218 | + | 0.846608i | \(0.678641\pi\) | |||||||
\(720\) | −0.360834 | − | 2.78226i | −0.0134475 | − | 0.103689i | ||||
\(721\) | −6.74599 | −0.251234 | ||||||||
\(722\) | −16.1942 | − | 9.93715i | −0.602687 | − | 0.369823i | ||||
\(723\) | −13.9254 | − | 12.2360i | −0.517892 | − | 0.455063i | ||||
\(724\) | 8.04715 | − | 13.9381i | 0.299070 | − | 0.518004i | ||||
\(725\) | 12.1493 | − | 21.0433i | 0.451215 | − | 0.781527i | ||||
\(726\) | −14.3041 | − | 12.5688i | −0.530875 | − | 0.466472i | ||||
\(727\) | −28.6838 | −1.06382 | −0.531911 | − | 0.846800i | \(-0.678526\pi\) | ||||
−0.531911 | + | 0.846800i | \(0.678526\pi\) | |||||||
\(728\) | 3.77006 | − | 6.52994i | 0.139728 | − | 0.242016i | ||||
\(729\) | −10.1880 | − | 25.0041i | −0.377332 | − | 0.926078i | ||||
\(730\) | 12.7535 | 0.472029 | ||||||||
\(731\) | −3.65783 | − | 6.33554i | −0.135290 | − | 0.234328i | ||||
\(732\) | 4.00875 | + | 3.52242i | 0.148168 | + | 0.130192i | ||||
\(733\) | −9.80946 | − | 16.9905i | −0.362321 | − | 0.627558i | 0.626022 | − | 0.779806i | \(-0.284682\pi\) |
−0.988342 | + | 0.152248i | \(0.951349\pi\) | |||||||
\(734\) | 10.4730 | + | 18.1398i | 0.386566 | + | 0.669552i | ||||
\(735\) | 8.75903 | − | 2.96388i | 0.323082 | − | 0.109324i | ||||
\(736\) | 0.138465 | 0.00510388 | ||||||||
\(737\) | −0.431186 | + | 0.746835i | −0.0158829 | + | 0.0275100i | ||||
\(738\) | 0.888538 | + | 6.85119i | 0.0327075 | + | 0.252196i | ||||
\(739\) | 7.81031 | + | 13.5278i | 0.287307 | + | 0.497630i | 0.973166 | − | 0.230104i | \(-0.0739067\pi\) |
−0.685859 | + | 0.727734i | \(0.740573\pi\) | |||||||
\(740\) | −0.742128 | + | 1.28540i | −0.0272812 | + | 0.0472524i | ||||
\(741\) | −50.0306 | + | 2.55863i | −1.83792 | + | 0.0939936i | ||||
\(742\) | 4.79970 | + | 8.31333i | 0.176203 | + | 0.305192i | ||||
\(743\) | 16.2184 | − | 28.0912i | 0.594997 | − | 1.03056i | −0.398551 | − | 0.917146i | \(-0.630487\pi\) |
0.993547 | − | 0.113418i | \(-0.0361800\pi\) | |||||||
\(744\) | −4.46294 | − | 3.92151i | −0.163619 | − | 0.143770i | ||||
\(745\) | −8.27154 | − | 14.3267i | −0.303046 | − | 0.524891i | ||||
\(746\) | −6.12723 | − | 10.6127i | −0.224334 | − | 0.388557i | ||||
\(747\) | 3.67393 | + | 28.3283i | 0.134422 | + | 1.03648i | ||||
\(748\) | −0.176355 | −0.00644819 | ||||||||
\(749\) | 9.50306 | − | 16.4598i | 0.347234 | − | 0.601428i | ||||
\(750\) | −14.0014 | + | 4.73779i | −0.511259 | + | 0.173000i | ||||
\(751\) | −17.0078 | −0.620623 | −0.310312 | − | 0.950635i | \(-0.600433\pi\) | ||||
−0.310312 | + | 0.950635i | \(0.600433\pi\) | |||||||
\(752\) | −2.46002 | − | 4.26088i | −0.0897076 | − | 0.155378i | ||||
\(753\) | 5.34790 | − | 26.7509i | 0.194888 | − | 0.974856i | ||||
\(754\) | 19.5411 | + | 33.8462i | 0.711646 | + | 1.23261i | ||||
\(755\) | −6.48822 | − | 11.2379i | −0.236131 | − | 0.408990i | ||||
\(756\) | 2.59623 | + | 5.30326i | 0.0944241 | + | 0.192878i | ||||
\(757\) | 17.2273 | + | 29.8386i | 0.626139 | + | 1.08450i | 0.988320 | + | 0.152396i | \(0.0486989\pi\) |
−0.362181 | + | 0.932108i | \(0.617968\pi\) | |||||||
\(758\) | −31.8645 | −1.15737 | ||||||||
\(759\) | −0.00374168 | + | 0.0187163i | −0.000135814 | + | 0.000679360i | ||||
\(760\) | 2.92077 | − | 2.84359i | 0.105948 | − | 0.103148i | ||||
\(761\) | 15.8669 | + | 27.4822i | 0.575174 | + | 0.996230i | 0.996023 | + | 0.0890994i | \(0.0283989\pi\) |
−0.420849 | + | 0.907131i | \(0.638268\pi\) | |||||||
\(762\) | −0.277927 | + | 1.39023i | −0.0100682 | + | 0.0503626i | ||||
\(763\) | 2.31745 | 0.0838974 | ||||||||
\(764\) | 0.636975 | − | 1.10327i | 0.0230450 | − | 0.0399150i | ||||
\(765\) | −4.93952 | + | 3.77512i | −0.178589 | + | 0.136490i | ||||
\(766\) | −16.3299 | + | 28.2842i | −0.590023 | + | 1.02195i | ||||
\(767\) | −25.3008 | + | 43.8222i | −0.913558 | + | 1.58233i | ||||
\(768\) | 1.64067 | − | 0.555168i | 0.0592025 | − | 0.0200329i | ||||
\(769\) | −30.1599 | −1.08759 | −0.543797 | − | 0.839217i | \(-0.683014\pi\) | ||||
−0.543797 | + | 0.839217i | \(0.683014\pi\) | |||||||
\(770\) | −0.0845750 | −0.00304787 | ||||||||
\(771\) | −8.61002 | + | 2.91345i | −0.310082 | + | 0.104925i | ||||
\(772\) | −4.05430 | + | 7.02226i | −0.145917 | + | 0.252736i | ||||
\(773\) | −20.0303 | + | 34.6935i | −0.720440 | + | 1.24784i | 0.240384 | + | 0.970678i | \(0.422727\pi\) |
−0.960824 | + | 0.277161i | \(0.910607\pi\) | |||||||
\(774\) | −7.86910 | + | 6.01410i | −0.282849 | + | 0.216172i | ||||
\(775\) | −7.07524 | + | 12.2547i | −0.254150 | + | 0.440201i | ||||
\(776\) | 14.9427 | 0.536412 | ||||||||
\(777\) | 0.612379 | − | 3.06320i | 0.0219690 | − | 0.109892i | ||||
\(778\) | −18.4772 | − | 32.0034i | −0.662439 | − | 1.14738i | ||||
\(779\) | −7.19227 | + | 7.00221i | −0.257690 | + | 0.250880i | ||||
\(780\) | 2.10698 | − | 10.5394i | 0.0754420 | − | 0.377370i | ||||
\(781\) | 0.991840 | 0.0354908 | ||||||||
\(782\) | −0.153415 | − | 0.265722i | −0.00548609 | − | 0.00950219i | ||||
\(783\) | −30.5338 | − | 2.09001i | −1.09119 | − | 0.0746910i | ||||
\(784\) | 2.85435 | + | 4.94388i | 0.101941 | + | 0.176567i | ||||
\(785\) | −7.26449 | − | 12.5825i | −0.259281 | − | 0.449088i | ||||
\(786\) | −1.30172 | + | 6.51137i | −0.0464308 | + | 0.232253i | ||||
\(787\) | −3.20276 | − | 5.54735i | −0.114166 | − | 0.197742i | 0.803280 | − | 0.595602i | \(-0.203086\pi\) |
−0.917446 | + | 0.397860i | \(0.869753\pi\) | |||||||
\(788\) | 20.1767 | 0.718767 | ||||||||
\(789\) | −14.7745 | + | 4.99938i | −0.525985 | + | 0.177983i | ||||
\(790\) | 2.86483 | − | 4.96204i | 0.101926 | − | 0.176541i | ||||
\(791\) | −20.2751 | −0.720900 | ||||||||
\(792\) | 0.0307072 | + | 0.236772i | 0.00109113 | + | 0.00841332i | ||||
\(793\) | 10.2218 | + | 17.7046i | 0.362986 | + | 0.628710i | ||||
\(794\) | −8.42840 | − | 14.5984i | −0.299113 | − | 0.518078i | ||||
\(795\) | 10.2789 | + | 9.03193i | 0.364556 | + | 0.320329i | ||||
\(796\) | 3.27803 | − | 5.67772i | 0.116187 | − | 0.201242i | ||||
\(797\) | 22.6941 | + | 39.3074i | 0.803867 | + | 1.39234i | 0.917053 | + | 0.398764i | \(0.130561\pi\) |
−0.113187 | + | 0.993574i | \(0.536106\pi\) | |||||||
\(798\) | −3.90456 | + | 7.63926i | −0.138220 | + | 0.270427i | ||||
\(799\) | −5.45124 | + | 9.44183i | −0.192851 | + | 0.334028i | ||||
\(800\) | −2.06271 | − | 3.57272i | −0.0729279 | − | 0.126315i | ||||
\(801\) | 3.17422 | + | 24.4752i | 0.112155 | + | 0.864789i | ||||
\(802\) | 6.87472 | − | 11.9074i | 0.242755 | − | 0.420464i | ||||
\(803\) | −1.08533 | −0.0383006 | ||||||||
\(804\) | −17.7780 | + | 6.01572i | −0.626983 | + | 0.212158i | ||||
\(805\) | −0.0735733 | − | 0.127433i | −0.00259312 | − | 0.00449141i | ||||
\(806\) | −11.3799 | − | 19.7106i | −0.400840 | − | 0.694275i | ||||
\(807\) | 16.3678 | + | 14.3821i | 0.576175 | + | 0.506276i | ||||
\(808\) | 0.318675 | + | 0.551961i | 0.0112109 | + | 0.0194179i | ||||
\(809\) | −37.1208 | −1.30510 | −0.652548 | − | 0.757747i | \(-0.726300\pi\) | ||||
−0.652548 | + | 0.757747i | \(0.726300\pi\) | |||||||
\(810\) | 5.92849 | + | 5.97440i | 0.208306 | + | 0.209919i | ||||
\(811\) | 13.6434 | − | 23.6311i | 0.479085 | − | 0.829799i | −0.520628 | − | 0.853784i | \(-0.674302\pi\) |
0.999712 | + | 0.0239847i | \(0.00763531\pi\) | |||||||
\(812\) | 6.69309 | 0.234881 | ||||||||
\(813\) | −7.27880 | − | 6.39576i | −0.255279 | − | 0.224309i | ||||
\(814\) | 0.0631556 | − | 0.109389i | 0.00221360 | − | 0.00383407i | ||||
\(815\) | −10.5740 | + | 18.3147i | −0.370390 | + | 0.641535i | ||||
\(816\) | −2.88321 | − | 2.53343i | −0.100932 | − | 0.0886877i | ||||
\(817\) | −13.8489 | − | 3.91027i | −0.484513 | − | 0.136803i | ||||
\(818\) | −14.4996 | −0.506968 | ||||||||
\(819\) | 2.90930 | + | 22.4325i | 0.101659 | + | 0.783856i | ||||
\(820\) | −1.07680 | − | 1.86507i | −0.0376035 | − | 0.0651311i | ||||
\(821\) | −7.78257 | − | 13.4798i | −0.271614 | − | 0.470449i | 0.697662 | − | 0.716428i | \(-0.254224\pi\) |
−0.969275 | + | 0.245979i | \(0.920891\pi\) | |||||||
\(822\) | 3.82768 | + | 3.36332i | 0.133506 | + | 0.117309i | ||||
\(823\) | −6.77770 | −0.236256 | −0.118128 | − | 0.992998i | \(-0.537689\pi\) | ||||
−0.118128 | + | 0.992998i | \(0.537689\pi\) | |||||||
\(824\) | −2.96826 | − | 5.14118i | −0.103404 | − | 0.179102i | ||||
\(825\) | 0.538667 | − | 0.182274i | 0.0187540 | − | 0.00634595i | ||||
\(826\) | 4.33292 | + | 7.50484i | 0.150762 | + | 0.261127i | ||||
\(827\) | 22.2662 | − | 38.5662i | 0.774272 | − | 1.34108i | −0.160931 | − | 0.986966i | \(-0.551450\pi\) |
0.935203 | − | 0.354112i | \(-0.115217\pi\) | |||||||
\(828\) | −0.330041 | + | 0.252240i | −0.0114697 | + | 0.00876594i | ||||
\(829\) | 13.0200 | 0.452204 | 0.226102 | − | 0.974104i | \(-0.427402\pi\) | ||||
0.226102 | + | 0.974104i | \(0.427402\pi\) | |||||||
\(830\) | −4.45236 | − | 7.71171i | −0.154544 | − | 0.267677i | ||||
\(831\) | 5.24624 | − | 26.2424i | 0.181990 | − | 0.910338i | ||||
\(832\) | 6.63538 | 0.230040 | ||||||||
\(833\) | 6.32506 | − | 10.9553i | 0.219150 | − | 0.379580i | ||||
\(834\) | 18.4315 | − | 6.23683i | 0.638230 | − | 0.215964i | ||||
\(835\) | 3.21936 | − | 5.57609i | 0.111410 | − | 0.192968i | ||||
\(836\) | −0.248559 | + | 0.241991i | −0.00859661 | + | 0.00836944i | ||||
\(837\) | 17.7815 | + | 1.21713i | 0.614620 | + | 0.0420702i | ||||
\(838\) | 0.703380 | + | 1.21829i | 0.0242979 | + | 0.0420852i | ||||
\(839\) | −2.58115 | −0.0891113 | −0.0445557 | − | 0.999007i | \(-0.514187\pi\) | ||||
−0.0445557 | + | 0.999007i | \(0.514187\pi\) | |||||||
\(840\) | −1.38270 | − | 1.21496i | −0.0477078 | − | 0.0419201i | ||||
\(841\) | −2.84592 | + | 4.92929i | −0.0981353 | + | 0.169975i | ||||
\(842\) | 29.2010 | 1.00633 | ||||||||
\(843\) | −11.4967 | − | 10.1020i | −0.395967 | − | 0.347930i | ||||
\(844\) | −5.53735 | + | 9.59098i | −0.190604 | + | 0.330135i | ||||
\(845\) | 14.5086 | − | 25.1296i | 0.499111 | − | 0.864486i | ||||
\(846\) | 13.6256 | + | 5.67474i | 0.468459 | + | 0.195101i | ||||
\(847\) | −12.4927 | −0.429253 | ||||||||
\(848\) | −4.22378 | + | 7.31580i | −0.145045 | + | 0.251226i | ||||
\(849\) | 9.04763 | − | 45.2574i | 0.310514 | − | 1.55323i | ||||
\(850\) | −4.57084 | + | 7.91693i | −0.156779 | + | 0.271549i | ||||
\(851\) | 0.219761 | 0.00753330 | ||||||||
\(852\) | 16.2155 | + | 14.2483i | 0.555532 | + | 0.488137i | ||||
\(853\) | 45.6154 | 1.56184 | 0.780921 | − | 0.624630i | \(-0.214750\pi\) | ||||
0.780921 | + | 0.624630i | \(0.214750\pi\) | |||||||
\(854\) | 3.50109 | 0.119805 | ||||||||
\(855\) | −1.78175 | + | 12.0987i | −0.0609344 | + | 0.413765i | ||||
\(856\) | 16.7256 | 0.571668 | ||||||||
\(857\) | −1.78120 | −0.0608448 | −0.0304224 | − | 0.999537i | \(-0.509685\pi\) | ||||
−0.0304224 | + | 0.999537i | \(0.509685\pi\) | |||||||
\(858\) | −0.179305 | + | 0.896908i | −0.00612138 | + | 0.0306199i | ||||
\(859\) | 27.2935 | 0.931244 | 0.465622 | − | 0.884984i | \(-0.345831\pi\) | ||||
0.465622 | + | 0.884984i | \(0.345831\pi\) | |||||||
\(860\) | 1.54370 | − | 2.67377i | 0.0526399 | − | 0.0911749i | ||||
\(861\) | 3.40485 | + | 2.99178i | 0.116037 | + | 0.101960i | ||||
\(862\) | 14.7626 | − | 25.5695i | 0.502815 | − | 0.870901i | ||||
\(863\) | 44.6491 | 1.51987 | 0.759937 | − | 0.649997i | \(-0.225230\pi\) | ||||
0.759937 | + | 0.649997i | \(0.225230\pi\) | |||||||
\(864\) | −2.89931 | + | 4.31207i | −0.0986366 | + | 0.146700i | ||||
\(865\) | −0.415307 | + | 0.719332i | −0.0141209 | + | 0.0244580i | ||||
\(866\) | 0.0851720 | − | 0.147522i | 0.00289426 | − | 0.00501301i | ||||
\(867\) | 4.10496 | − | 20.5335i | 0.139412 | − | 0.697356i | ||||
\(868\) | −3.89776 | −0.132299 | ||||||||
\(869\) | −0.243799 | + | 0.422272i | −0.00827031 | + | 0.0143246i | ||||
\(870\) | 9.03717 | − | 3.05799i | 0.306389 | − | 0.103676i | ||||
\(871\) | −71.9001 | −2.43624 | ||||||||
\(872\) | 1.01969 | + | 1.76615i | 0.0345310 | + | 0.0598095i | ||||
\(873\) | −35.6171 | + | 27.2210i | −1.20546 | + | 0.921291i | ||||
\(874\) | −0.580844 | − | 0.164002i | −0.0196474 | − | 0.00554747i | ||||
\(875\) | −4.84880 | + | 8.39837i | −0.163919 | + | 0.283917i | ||||
\(876\) | −17.7440 | − | 15.5913i | −0.599513 | − | 0.526782i | ||||
\(877\) | −14.8318 | + | 25.6894i | −0.500833 | + | 0.867468i | 0.499167 | + | 0.866506i | \(0.333639\pi\) |
−1.00000 | 0.000961840i | \(0.999694\pi\) | ||||||||
\(878\) | 4.15010 | 0.140059 | ||||||||
\(879\) | −11.8476 | − | 10.4103i | −0.399610 | − | 0.351131i | ||||
\(880\) | −0.0372134 | − | 0.0644555i | −0.00125446 | − | 0.00217279i | ||||
\(881\) | 46.3343 | 1.56104 | 0.780521 | − | 0.625130i | \(-0.214954\pi\) | ||||
0.780521 | + | 0.625130i | \(0.214954\pi\) | |||||||
\(882\) | −15.8098 | − | 6.58438i | −0.532344 | − | 0.221708i | ||||
\(883\) | 11.1195 | − | 19.2595i | 0.374201 | − | 0.648135i | −0.616006 | − | 0.787741i | \(-0.711250\pi\) |
0.990207 | + | 0.139606i | \(0.0445838\pi\) | |||||||
\(884\) | −7.35179 | − | 12.7337i | −0.247268 | − | 0.428280i | ||||
\(885\) | 9.27928 | + | 8.15355i | 0.311920 | + | 0.274079i | ||||
\(886\) | 11.7195 | + | 20.2988i | 0.393724 | + | 0.681950i | ||||
\(887\) | −24.2952 | −0.815753 | −0.407876 | − | 0.913037i | \(-0.633731\pi\) | ||||
−0.407876 | + | 0.913037i | \(0.633731\pi\) | |||||||
\(888\) | 2.60394 | − | 0.881120i | 0.0873826 | − | 0.0295685i | ||||
\(889\) | 0.465069 | + | 0.805524i | 0.0155979 | + | 0.0270164i | ||||
\(890\) | −3.84676 | − | 6.66279i | −0.128944 | − | 0.223337i | ||||
\(891\) | −0.504518 | − | 0.508425i | −0.0169020 | − | 0.0170329i | ||||
\(892\) | 0.747365 | 0.0250236 | ||||||||
\(893\) | 5.27278 | + | 20.7876i | 0.176447 | + | 0.695632i | ||||
\(894\) | −6.00641 | + | 30.0448i | −0.200884 | + | 1.00485i | ||||
\(895\) | 5.53755 | − | 9.59131i | 0.185100 | − | 0.320602i | ||||
\(896\) | 0.568176 | − | 0.984110i | 0.0189814 | − | 0.0328768i | ||||
\(897\) | −1.50739 | + | 0.510069i | −0.0503303 | + | 0.0170307i | ||||
\(898\) | 37.0884 | 1.23766 | ||||||||
\(899\) | 10.1015 | − | 17.4963i | 0.336904 | − | 0.583535i | ||||
\(900\) | 11.4250 | + | 4.75824i | 0.380835 | + | 0.158608i | ||||
\(901\) | 18.7193 | 0.623629 | ||||||||
\(902\) | 0.0916363 | + | 0.158719i | 0.00305115 | + | 0.00528475i | ||||
\(903\) | −1.27381 | + | 6.37176i | −0.0423898 | + | 0.212039i | ||||
\(904\) | −8.92114 | − | 15.4519i | −0.296713 | − | 0.513922i | ||||
\(905\) | −7.52558 | − | 13.0347i | −0.250159 | − | 0.433288i | ||||
\(906\) | −4.71144 | + | 23.5672i | −0.156527 | + | 0.782969i | ||||
\(907\) | 22.9849 | 0.763202 | 0.381601 | − | 0.924327i | \(-0.375373\pi\) | ||||
0.381601 | + | 0.924327i | \(0.375373\pi\) | |||||||
\(908\) | −14.1895 | + | 24.5769i | −0.470895 | + | 0.815614i | ||||
\(909\) | −1.76509 | − | 0.735115i | −0.0585443 | − | 0.0243822i | ||||
\(910\) | −3.52571 | − | 6.10671i | −0.116876 | − | 0.202436i | ||||
\(911\) | 26.8163 | − | 46.4473i | 0.888465 | − | 1.53887i | 0.0467748 | − | 0.998905i | \(-0.485106\pi\) |
0.841690 | − | 0.539961i | \(-0.181561\pi\) | |||||||
\(912\) | −7.53998 | + | 0.385604i | −0.249674 | + | 0.0127686i | ||||
\(913\) | 0.378898 | + | 0.656271i | 0.0125397 | + | 0.0217194i | ||||
\(914\) | 17.9019 | − | 31.0069i | 0.592141 | − | 1.02562i | ||||
\(915\) | 4.72726 | − | 1.59961i | 0.156278 | − | 0.0528813i | ||||
\(916\) | 3.63731 | + | 6.30001i | 0.120180 | + | 0.208158i | ||||
\(917\) | 2.17823 | + | 3.77281i | 0.0719315 | + | 0.124589i | ||||
\(918\) | 11.4875 | + | 0.786308i | 0.379143 | + | 0.0259520i | ||||
\(919\) | −40.1397 | −1.32409 | −0.662043 | − | 0.749466i | \(-0.730310\pi\) | ||||
−0.662043 | + | 0.749466i | \(0.730310\pi\) | |||||||
\(920\) | 0.0647451 | − | 0.112142i | 0.00213458 | − | 0.00369721i | ||||
\(921\) | 11.6220 | + | 10.2120i | 0.382956 | + | 0.336497i | ||||
\(922\) | −5.84450 | −0.192478 | ||||||||
\(923\) | 41.3472 | + | 71.6155i | 1.36096 | + | 2.35725i | ||||
\(924\) | 0.117669 | + | 0.103394i | 0.00387103 | + | 0.00340141i | ||||
\(925\) | −3.27378 | − | 5.67036i | −0.107641 | − | 0.186440i | ||||
\(926\) | 0.657422 | + | 1.13869i | 0.0216042 | + | 0.0374196i | ||||
\(927\) | 16.4407 | + | 6.84715i | 0.539985 | + | 0.224890i | ||||
\(928\) | 2.94499 | + | 5.10087i | 0.0966740 | + | 0.167444i | ||||
\(929\) | 35.5441 | 1.16616 | 0.583082 | − | 0.812413i | \(-0.301847\pi\) | ||||
0.583082 | + | 0.812413i | \(0.301847\pi\) | |||||||
\(930\) | −5.26285 | + | 1.78084i | −0.172576 | + | 0.0583960i | ||||
\(931\) | −6.11799 | − | 24.1198i | −0.200509 | − | 0.790496i | ||||
\(932\) | −8.86740 | − | 15.3588i | −0.290461 | − | 0.503094i | ||||
\(933\) | 2.06993 | + | 1.81881i | 0.0677663 | + | 0.0595452i | ||||
\(934\) | −16.6029 | −0.543263 | ||||||||
\(935\) | −0.0824625 | + | 0.142829i | −0.00269681 | + | 0.00467102i | ||||
\(936\) | −15.8159 | + | 12.0876i | −0.516960 | + | 0.395096i | ||||
\(937\) | 22.6726 | − | 39.2701i | 0.740682 | − | 1.28290i | −0.211503 | − | 0.977377i | \(-0.567836\pi\) |
0.952185 | − | 0.305522i | \(-0.0988309\pi\) | |||||||
\(938\) | −6.15668 | + | 10.6637i | −0.201023 | + | 0.348181i | ||||
\(939\) | 6.58561 | + | 5.78667i | 0.214913 | + | 0.188841i | ||||
\(940\) | −4.60115 | −0.150073 | ||||||||
\(941\) | 12.8040 | 0.417398 | 0.208699 | − | 0.977980i | \(-0.433077\pi\) | ||||
0.208699 | + | 0.977980i | \(0.433077\pi\) | |||||||
\(942\) | −5.27513 | + | 26.3869i | −0.171873 | + | 0.859731i | ||||
\(943\) | −0.159432 | + | 0.276144i | −0.00519182 | + | 0.00899250i | ||||
\(944\) | −3.81301 | + | 6.60433i | −0.124103 | + | 0.214952i | ||||
\(945\) | 5.50907 | + | 0.377091i | 0.179210 | + | 0.0122668i | ||||
\(946\) | −0.131370 | + | 0.227540i | −0.00427121 | + | 0.00739796i | ||||
\(947\) | −28.4759 | −0.925344 | −0.462672 | − | 0.886530i | \(-0.653109\pi\) | ||||
−0.462672 | + | 0.886530i | \(0.653109\pi\) | |||||||
\(948\) | −10.0520 | + | 3.40138i | −0.326473 | + | 0.110472i | ||||
\(949\) | −45.2447 | − | 78.3662i | −1.46871 | − | 2.54387i | ||||
\(950\) | 4.42120 | + | 17.4303i | 0.143443 | + | 0.565515i | ||||
\(951\) | −41.7335 | − | 36.6705i | −1.35330 | − | 1.18912i | ||||
\(952\) | −2.51808 | −0.0816116 | ||||||||
\(953\) | −4.47160 | − | 7.74504i | −0.144849 | − | 0.250887i | 0.784467 | − | 0.620170i | \(-0.212936\pi\) |
−0.929317 | + | 0.369284i | \(0.879603\pi\) | |||||||
\(954\) | −3.25942 | − | 25.1322i | −0.105528 | − | 0.813685i | ||||
\(955\) | −0.595691 | − | 1.03177i | −0.0192761 | − | 0.0333872i | ||||
\(956\) | 12.0318 | + | 20.8396i | 0.389135 | + | 0.674002i | ||||
\(957\) | −0.769069 | + | 0.260237i | −0.0248605 | + | 0.00841226i | ||||
\(958\) | −16.6278 | − | 28.8001i | −0.537219 | − | 0.930490i | ||||
\(959\) | 3.34295 | 0.107950 | ||||||||
\(960\) | 0.317537 | − | 1.58836i | 0.0102485 | − | 0.0512641i | ||||
\(961\) | 9.61732 | − | 16.6577i | 0.310236 | − | 0.537345i | ||||
\(962\) | 10.5312 | 0.339539 | ||||||||
\(963\) | −39.8667 | + | 30.4688i | −1.28469 | + | 0.981843i | ||||
\(964\) | −5.35131 | − | 9.26873i | −0.172354 | − | 0.298526i | ||||
\(965\) | 3.79153 | + | 6.56712i | 0.122054 | + | 0.211403i | ||||
\(966\) | −0.0534255 | + | 0.267241i | −0.00171894 | + | 0.00859834i | ||||
\(967\) | −20.6993 | + | 35.8522i | −0.665643 | + | 1.15293i | 0.313467 | + | 0.949599i | \(0.398509\pi\) |
−0.979110 | + | 0.203329i | \(0.934824\pi\) | |||||||
\(968\) | −5.49683 | − | 9.52079i | −0.176675 | − | 0.306010i | ||||
\(969\) | 9.09406 | + | 14.0424i | 0.292143 | + | 0.451108i | ||||
\(970\) | 6.98711 | − | 12.1020i | 0.224343 | − | 0.388573i | ||||
\(971\) | −1.82451 | − | 3.16014i | −0.0585513 | − | 0.101414i | 0.835264 | − | 0.549849i | \(-0.185315\pi\) |
−0.893815 | + | 0.448435i | \(0.851981\pi\) | |||||||
\(972\) | −0.944527 | − | 15.5598i | −0.0302957 | − | 0.499081i | ||||
\(973\) | 6.38296 | − | 11.0556i | 0.204628 | − | 0.354427i | ||||
\(974\) | 10.0490 | 0.321992 | ||||||||
\(975\) | 35.6166 | + | 31.2958i | 1.14065 | + | 1.00227i | ||||
\(976\) | 1.54050 | + | 2.66822i | 0.0493101 | + | 0.0854075i | ||||
\(977\) | 21.3672 | + | 37.0091i | 0.683597 | + | 1.18403i | 0.973875 | + | 0.227083i | \(0.0729189\pi\) |
−0.290278 | + | 0.956942i | \(0.593748\pi\) | |||||||
\(978\) | 37.1014 | − | 12.5544i | 1.18637 | − | 0.401444i | ||||
\(979\) | 0.327362 | + | 0.567007i | 0.0104625 | + | 0.0181216i | ||||
\(980\) | 5.33870 | 0.170539 | ||||||||
\(981\) | −5.64789 | − | 2.35220i | −0.180323 | − | 0.0751001i | ||||
\(982\) | −19.3339 | + | 33.4873i | −0.616970 | + | 1.06862i | ||||
\(983\) | 42.7076 | 1.36216 | 0.681081 | − | 0.732208i | \(-0.261510\pi\) | ||||
0.681081 | + | 0.732208i | \(0.261510\pi\) | |||||||
\(984\) | −0.781921 | + | 3.91127i | −0.0249267 | + | 0.124687i | ||||
\(985\) | 9.43451 | − | 16.3411i | 0.300609 | − | 0.520669i | ||||
\(986\) | 6.52591 | − | 11.3032i | 0.207827 | − | 0.359968i | ||||
\(987\) | 9.17279 | − | 3.10388i | 0.291973 | − | 0.0987977i | ||||
\(988\) | −27.8347 | − | 7.85918i | −0.885540 | − | 0.250034i | ||||
\(989\) | −0.457125 | −0.0145357 | ||||||||
\(990\) | 0.206119 | + | 0.0858433i | 0.00655089 | + | 0.00272828i | ||||
\(991\) | −14.7910 | − | 25.6187i | −0.469851 | − | 0.813806i | 0.529555 | − | 0.848276i | \(-0.322359\pi\) |
−0.999406 | + | 0.0344699i | \(0.989026\pi\) | |||||||
\(992\) | −1.71503 | − | 2.97052i | −0.0544523 | − | 0.0943142i | ||||
\(993\) | −1.53561 | + | 7.68132i | −0.0487312 | + | 0.243759i | ||||
\(994\) | 14.1620 | 0.449190 | ||||||||
\(995\) | −3.06557 | − | 5.30973i | −0.0971852 | − | 0.168330i | ||||
\(996\) | −3.23309 | + | 16.1723i | −0.102444 | + | 0.512440i | ||||
\(997\) | 0.991736 | + | 1.71774i | 0.0314086 | + | 0.0544013i | 0.881302 | − | 0.472553i | \(-0.156667\pi\) |
−0.849894 | + | 0.526954i | \(0.823334\pi\) | |||||||
\(998\) | −17.8984 | + | 31.0009i | −0.566562 | + | 0.981315i | ||||
\(999\) | −4.60157 | + | 6.84380i | −0.145587 | + | 0.216528i |
(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 | 342.2.f.g.7.9 | ✓ | 18 | |
3.2 | odd | 2 | 1026.2.f.g.235.4 | 18 | |||
9.4 | even | 3 | 342.2.h.g.121.3 | yes | 18 | ||
9.5 | odd | 6 | 1026.2.h.g.577.6 | 18 | |||
19.11 | even | 3 | 342.2.h.g.277.3 | yes | 18 | ||
57.11 | odd | 6 | 1026.2.h.g.505.6 | 18 | |||
171.49 | even | 3 | inner | 342.2.f.g.49.9 | yes | 18 | |
171.68 | odd | 6 | 1026.2.f.g.847.4 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.2.f.g.7.9 | ✓ | 18 | 1.1 | even | 1 | trivial | |
342.2.f.g.49.9 | yes | 18 | 171.49 | even | 3 | inner | |
342.2.h.g.121.3 | yes | 18 | 9.4 | even | 3 | ||
342.2.h.g.277.3 | yes | 18 | 19.11 | even | 3 | ||
1026.2.f.g.235.4 | 18 | 3.2 | odd | 2 | |||
1026.2.f.g.847.4 | 18 | 171.68 | odd | 6 | |||
1026.2.h.g.505.6 | 18 | 57.11 | odd | 6 | |||
1026.2.h.g.577.6 | 18 | 9.5 | odd | 6 |