Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (of order \(4\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.4 | ||
Root | \(-0.794932 - 0.794932i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.253 |
Dual form | 370.2.h.e.117.4 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.794932 | + | 0.794932i | −0.458954 | + | 0.458954i | −0.898312 | − | 0.439358i | \(-0.855206\pi\) |
0.439358 | + | 0.898312i | \(0.355206\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.22550 | − | 0.217179i | 0.995272 | − | 0.0971252i | ||||
\(6\) | 0.794932 | − | 0.794932i | 0.324530 | − | 0.324530i | ||||
\(7\) | 2.93770 | − | 2.93770i | 1.11035 | − | 1.11035i | 0.117242 | − | 0.993103i | \(-0.462595\pi\) |
0.993103 | − | 0.117242i | \(-0.0374053\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.73617i | 0.578722i | ||||||||
\(10\) | −2.22550 | + | 0.217179i | −0.703764 | + | 0.0686779i | ||||
\(11\) | − | 3.55539i | − | 1.07199i | −0.844221 | − | 0.535995i | \(-0.819937\pi\) | ||
0.844221 | − | 0.535995i | \(-0.180063\pi\) | |||||||
\(12\) | −0.794932 | + | 0.794932i | −0.229477 | + | 0.229477i | ||||
\(13\) | −4.41538 | −1.22461 | −0.612303 | − | 0.790623i | \(-0.709757\pi\) | ||||
−0.612303 | + | 0.790623i | \(0.709757\pi\) | |||||||
\(14\) | −2.93770 | + | 2.93770i | −0.785133 | + | 0.785133i | ||||
\(15\) | −1.59648 | + | 1.94176i | −0.412208 | + | 0.501360i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.37801i | − | 1.30436i | −0.758065 | − | 0.652179i | \(-0.773855\pi\) | ||
0.758065 | − | 0.652179i | \(-0.226145\pi\) | |||||||
\(18\) | − | 1.73617i | − | 0.409218i | ||||||
\(19\) | 1.98590 | + | 1.98590i | 0.455597 | + | 0.455597i | 0.897207 | − | 0.441610i | \(-0.145592\pi\) |
−0.441610 | + | 0.897207i | \(0.645592\pi\) | |||||||
\(20\) | 2.22550 | − | 0.217179i | 0.497636 | − | 0.0485626i | ||||
\(21\) | 4.67054i | 1.01920i | ||||||||
\(22\) | 3.55539i | 0.758011i | ||||||||
\(23\) | 5.90774 | 1.23185 | 0.615925 | − | 0.787805i | \(-0.288783\pi\) | ||||
0.615925 | + | 0.787805i | \(0.288783\pi\) | |||||||
\(24\) | 0.794932 | − | 0.794932i | 0.162265 | − | 0.162265i | ||||
\(25\) | 4.90567 | − | 0.966660i | 0.981133 | − | 0.193332i | ||||
\(26\) | 4.41538 | 0.865928 | ||||||||
\(27\) | −3.76493 | − | 3.76493i | −0.724561 | − | 0.724561i | ||||
\(28\) | 2.93770 | − | 2.93770i | 0.555173 | − | 0.555173i | ||||
\(29\) | 2.18437 | − | 2.18437i | 0.405627 | − | 0.405627i | −0.474584 | − | 0.880210i | \(-0.657401\pi\) |
0.880210 | + | 0.474584i | \(0.157401\pi\) | |||||||
\(30\) | 1.59648 | − | 1.94176i | 0.291475 | − | 0.354515i | ||||
\(31\) | 5.42197 | + | 5.42197i | 0.973815 | + | 0.973815i | 0.999666 | − | 0.0258507i | \(-0.00822946\pi\) |
−0.0258507 | + | 0.999666i | \(0.508229\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.82629 | + | 2.82629i | 0.491994 | + | 0.491994i | ||||
\(34\) | 5.37801i | 0.922321i | ||||||||
\(35\) | 5.89983 | − | 7.17584i | 0.997253 | − | 1.21294i | ||||
\(36\) | 1.73617i | 0.289361i | ||||||||
\(37\) | −3.88900 | + | 4.67714i | −0.639348 | + | 0.768918i | ||||
\(38\) | −1.98590 | − | 1.98590i | −0.322156 | − | 0.322156i | ||||
\(39\) | 3.50993 | − | 3.50993i | 0.562039 | − | 0.562039i | ||||
\(40\) | −2.22550 | + | 0.217179i | −0.351882 | + | 0.0343389i | ||||
\(41\) | 6.34477i | 0.990886i | 0.868640 | + | 0.495443i | \(0.164994\pi\) | ||||
−0.868640 | + | 0.495443i | \(0.835006\pi\) | |||||||
\(42\) | − | 4.67054i | − | 0.720680i | ||||||
\(43\) | 1.78544 | 0.272277 | 0.136139 | − | 0.990690i | \(-0.456531\pi\) | ||||
0.136139 | + | 0.990690i | \(0.456531\pi\) | |||||||
\(44\) | − | 3.55539i | − | 0.535995i | ||||||
\(45\) | 0.377058 | + | 3.86383i | 0.0562085 | + | 0.575986i | ||||
\(46\) | −5.90774 | −0.871049 | ||||||||
\(47\) | 1.82646 | − | 1.82646i | 0.266417 | − | 0.266417i | −0.561238 | − | 0.827655i | \(-0.689675\pi\) |
0.827655 | + | 0.561238i | \(0.189675\pi\) | |||||||
\(48\) | −0.794932 | + | 0.794932i | −0.114739 | + | 0.114739i | ||||
\(49\) | − | 10.2601i | − | 1.46573i | ||||||
\(50\) | −4.90567 | + | 0.966660i | −0.693766 | + | 0.136706i | ||||
\(51\) | 4.27515 | + | 4.27515i | 0.598641 | + | 0.598641i | ||||
\(52\) | −4.41538 | −0.612303 | ||||||||
\(53\) | −9.57437 | − | 9.57437i | −1.31514 | − | 1.31514i | −0.917573 | − | 0.397567i | \(-0.869855\pi\) |
−0.397567 | − | 0.917573i | \(-0.630145\pi\) | |||||||
\(54\) | 3.76493 | + | 3.76493i | 0.512342 | + | 0.512342i | ||||
\(55\) | −0.772154 | − | 7.91250i | −0.104117 | − | 1.06692i | ||||
\(56\) | −2.93770 | + | 2.93770i | −0.392566 | + | 0.392566i | ||||
\(57\) | −3.15731 | −0.418197 | ||||||||
\(58\) | −2.18437 | + | 2.18437i | −0.286821 | + | 0.286821i | ||||
\(59\) | 4.44588 | + | 4.44588i | 0.578805 | + | 0.578805i | 0.934574 | − | 0.355769i | \(-0.115781\pi\) |
−0.355769 | + | 0.934574i | \(0.615781\pi\) | |||||||
\(60\) | −1.59648 | + | 1.94176i | −0.206104 | + | 0.250680i | ||||
\(61\) | 1.44033 | + | 1.44033i | 0.184416 | + | 0.184416i | 0.793277 | − | 0.608861i | \(-0.208373\pi\) |
−0.608861 | + | 0.793277i | \(0.708373\pi\) | |||||||
\(62\) | −5.42197 | − | 5.42197i | −0.688591 | − | 0.688591i | ||||
\(63\) | 5.10033 | + | 5.10033i | 0.642581 | + | 0.642581i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.82642 | + | 0.958927i | −1.21882 | + | 0.118940i | ||||
\(66\) | −2.82629 | − | 2.82629i | −0.347893 | − | 0.347893i | ||||
\(67\) | 7.88856 | + | 7.88856i | 0.963741 | + | 0.963741i | 0.999365 | − | 0.0356245i | \(-0.0113420\pi\) |
−0.0356245 | + | 0.999365i | \(0.511342\pi\) | |||||||
\(68\) | − | 5.37801i | − | 0.652179i | ||||||
\(69\) | −4.69625 | + | 4.69625i | −0.565363 | + | 0.565363i | ||||
\(70\) | −5.89983 | + | 7.17584i | −0.705165 | + | 0.857677i | ||||
\(71\) | −11.2579 | −1.33606 | −0.668032 | − | 0.744132i | \(-0.732863\pi\) | ||||
−0.668032 | + | 0.744132i | \(0.732863\pi\) | |||||||
\(72\) | − | 1.73617i | − | 0.204609i | ||||||
\(73\) | −4.02333 | + | 4.02333i | −0.470896 | + | 0.470896i | −0.902204 | − | 0.431309i | \(-0.858052\pi\) |
0.431309 | + | 0.902204i | \(0.358052\pi\) | |||||||
\(74\) | 3.88900 | − | 4.67714i | 0.452087 | − | 0.543707i | ||||
\(75\) | −3.13124 | + | 4.66810i | −0.361565 | + | 0.539026i | ||||
\(76\) | 1.98590 | + | 1.98590i | 0.227799 | + | 0.227799i | ||||
\(77\) | −10.4447 | − | 10.4447i | −1.19028 | − | 1.19028i | ||||
\(78\) | −3.50993 | + | 3.50993i | −0.397421 | + | 0.397421i | ||||
\(79\) | 2.03059 | + | 2.03059i | 0.228459 | + | 0.228459i | 0.812049 | − | 0.583590i | \(-0.198352\pi\) |
−0.583590 | + | 0.812049i | \(0.698352\pi\) | |||||||
\(80\) | 2.22550 | − | 0.217179i | 0.248818 | − | 0.0242813i | ||||
\(81\) | 0.777232 | 0.0863591 | ||||||||
\(82\) | − | 6.34477i | − | 0.700662i | ||||||
\(83\) | −4.51281 | − | 4.51281i | −0.495345 | − | 0.495345i | 0.414640 | − | 0.909985i | \(-0.363907\pi\) |
−0.909985 | + | 0.414640i | \(0.863907\pi\) | |||||||
\(84\) | 4.67054i | 0.509598i | ||||||||
\(85\) | −1.16799 | − | 11.9687i | −0.126686 | − | 1.29819i | ||||
\(86\) | −1.78544 | −0.192529 | ||||||||
\(87\) | 3.47285i | 0.372328i | ||||||||
\(88\) | 3.55539i | 0.379006i | ||||||||
\(89\) | 2.13937 | − | 2.13937i | 0.226773 | − | 0.226773i | −0.584570 | − | 0.811343i | \(-0.698737\pi\) |
0.811343 | + | 0.584570i | \(0.198737\pi\) | |||||||
\(90\) | −0.377058 | − | 3.86383i | −0.0397454 | − | 0.407283i | ||||
\(91\) | −12.9711 | + | 12.9711i | −1.35974 | + | 1.35974i | ||||
\(92\) | 5.90774 | 0.615925 | ||||||||
\(93\) | −8.62020 | −0.893873 | ||||||||
\(94\) | −1.82646 | + | 1.82646i | −0.188385 | + | 0.188385i | ||||
\(95\) | 4.85091 | + | 3.98832i | 0.497693 | + | 0.409193i | ||||
\(96\) | 0.794932 | − | 0.794932i | 0.0811324 | − | 0.0811324i | ||||
\(97\) | 5.91995i | 0.601080i | 0.953769 | + | 0.300540i | \(0.0971669\pi\) | ||||
−0.953769 | + | 0.300540i | \(0.902833\pi\) | |||||||
\(98\) | 10.2601i | 1.03643i | ||||||||
\(99\) | 6.17274 | 0.620384 | ||||||||
\(100\) | 4.90567 | − | 0.966660i | 0.490567 | − | 0.0966660i | ||||
\(101\) | 9.23382i | 0.918799i | 0.888230 | + | 0.459399i | \(0.151935\pi\) | ||||
−0.888230 | + | 0.459399i | \(0.848065\pi\) | |||||||
\(102\) | −4.27515 | − | 4.27515i | −0.423303 | − | 0.423303i | ||||
\(103\) | 8.03931i | 0.792137i | 0.918221 | + | 0.396068i | \(0.129626\pi\) | ||||
−0.918221 | + | 0.396068i | \(0.870374\pi\) | |||||||
\(104\) | 4.41538 | 0.432964 | ||||||||
\(105\) | 1.01434 | + | 10.3943i | 0.0989896 | + | 1.01438i | ||||
\(106\) | 9.57437 | + | 9.57437i | 0.929945 | + | 0.929945i | ||||
\(107\) | 4.60753 | − | 4.60753i | 0.445427 | − | 0.445427i | −0.448404 | − | 0.893831i | \(-0.648007\pi\) |
0.893831 | + | 0.448404i | \(0.148007\pi\) | |||||||
\(108\) | −3.76493 | − | 3.76493i | −0.362281 | − | 0.362281i | ||||
\(109\) | −14.6123 | − | 14.6123i | −1.39961 | − | 1.39961i | −0.801166 | − | 0.598443i | \(-0.795786\pi\) |
−0.598443 | − | 0.801166i | \(-0.704214\pi\) | |||||||
\(110\) | 0.772154 | + | 7.91250i | 0.0736220 | + | 0.754428i | ||||
\(111\) | −0.626522 | − | 6.80950i | −0.0594668 | − | 0.646329i | ||||
\(112\) | 2.93770 | − | 2.93770i | 0.277586 | − | 0.277586i | ||||
\(113\) | 8.61849i | 0.810759i | 0.914148 | + | 0.405380i | \(0.132861\pi\) | ||||
−0.914148 | + | 0.405380i | \(0.867139\pi\) | |||||||
\(114\) | 3.15731 | 0.295710 | ||||||||
\(115\) | 13.1477 | − | 1.28304i | 1.22603 | − | 0.119644i | ||||
\(116\) | 2.18437 | − | 2.18437i | 0.202813 | − | 0.202813i | ||||
\(117\) | − | 7.66584i | − | 0.708707i | ||||||
\(118\) | −4.44588 | − | 4.44588i | −0.409277 | − | 0.409277i | ||||
\(119\) | −15.7990 | − | 15.7990i | −1.44829 | − | 1.44829i | ||||
\(120\) | 1.59648 | − | 1.94176i | 0.145738 | − | 0.177258i | ||||
\(121\) | −1.64079 | −0.149163 | ||||||||
\(122\) | −1.44033 | − | 1.44033i | −0.130402 | − | 0.130402i | ||||
\(123\) | −5.04366 | − | 5.04366i | −0.454772 | − | 0.454772i | ||||
\(124\) | 5.42197 | + | 5.42197i | 0.486908 | + | 0.486908i | ||||
\(125\) | 10.7076 | − | 3.21670i | 0.957717 | − | 0.287711i | ||||
\(126\) | −5.10033 | − | 5.10033i | −0.454373 | − | 0.454373i | ||||
\(127\) | −4.22966 | + | 4.22966i | −0.375322 | + | 0.375322i | −0.869411 | − | 0.494089i | \(-0.835502\pi\) |
0.494089 | + | 0.869411i | \(0.335502\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.41931 | + | 1.41931i | −0.124963 | + | 0.124963i | ||||
\(130\) | 9.82642 | − | 0.958927i | 0.861834 | − | 0.0841034i | ||||
\(131\) | −15.2680 | − | 15.2680i | −1.33397 | − | 1.33397i | −0.901783 | − | 0.432188i | \(-0.857742\pi\) |
−0.432188 | − | 0.901783i | \(-0.642258\pi\) | |||||||
\(132\) | 2.82629 | + | 2.82629i | 0.245997 | + | 0.245997i | ||||
\(133\) | 11.6680 | 1.01174 | ||||||||
\(134\) | −7.88856 | − | 7.88856i | −0.681468 | − | 0.681468i | ||||
\(135\) | −9.19650 | − | 7.56118i | −0.791509 | − | 0.650762i | ||||
\(136\) | 5.37801i | 0.461160i | ||||||||
\(137\) | −14.4220 | + | 14.4220i | −1.23215 | + | 1.23215i | −0.269015 | + | 0.963136i | \(0.586698\pi\) |
−0.963136 | + | 0.269015i | \(0.913302\pi\) | |||||||
\(138\) | 4.69625 | − | 4.69625i | 0.399772 | − | 0.399772i | ||||
\(139\) | 1.56244 | 0.132525 | 0.0662624 | − | 0.997802i | \(-0.478893\pi\) | ||||
0.0662624 | + | 0.997802i | \(0.478893\pi\) | |||||||
\(140\) | 5.89983 | − | 7.17584i | 0.498627 | − | 0.606469i | ||||
\(141\) | 2.90383i | 0.244547i | ||||||||
\(142\) | 11.2579 | 0.944740 | ||||||||
\(143\) | 15.6984i | 1.31277i | ||||||||
\(144\) | 1.73617i | 0.144680i | ||||||||
\(145\) | 4.38690 | − | 5.33570i | 0.364312 | − | 0.443105i | ||||
\(146\) | 4.02333 | − | 4.02333i | 0.332973 | − | 0.332973i | ||||
\(147\) | 8.15611 | + | 8.15611i | 0.672705 | + | 0.672705i | ||||
\(148\) | −3.88900 | + | 4.67714i | −0.319674 | + | 0.384459i | ||||
\(149\) | 8.42600i | 0.690285i | 0.938550 | + | 0.345142i | \(0.112169\pi\) | ||||
−0.938550 | + | 0.345142i | \(0.887831\pi\) | |||||||
\(150\) | 3.13124 | − | 4.66810i | 0.255665 | − | 0.381149i | ||||
\(151\) | − | 9.65715i | − | 0.785887i | −0.919563 | − | 0.392944i | \(-0.871457\pi\) | ||
0.919563 | − | 0.392944i | \(-0.128543\pi\) | |||||||
\(152\) | −1.98590 | − | 1.98590i | −0.161078 | − | 0.161078i | ||||
\(153\) | 9.33711 | 0.754861 | ||||||||
\(154\) | 10.4447 | + | 10.4447i | 0.841654 | + | 0.841654i | ||||
\(155\) | 13.2441 | + | 10.8890i | 1.06379 | + | 0.874629i | ||||
\(156\) | 3.50993 | − | 3.50993i | 0.281019 | − | 0.281019i | ||||
\(157\) | −13.7789 | + | 13.7789i | −1.09968 | + | 1.09968i | −0.105231 | + | 0.994448i | \(0.533558\pi\) |
−0.994448 | + | 0.105231i | \(0.966442\pi\) | |||||||
\(158\) | −2.03059 | − | 2.03059i | −0.161545 | − | 0.161545i | ||||
\(159\) | 15.2219 | 1.20718 | ||||||||
\(160\) | −2.22550 | + | 0.217179i | −0.175941 | + | 0.0171695i | ||||
\(161\) | 17.3552 | − | 17.3552i | 1.36778 | − | 1.36778i | ||||
\(162\) | −0.777232 | −0.0610651 | ||||||||
\(163\) | 9.92434i | 0.777334i | 0.921378 | + | 0.388667i | \(0.127064\pi\) | ||||
−0.921378 | + | 0.388667i | \(0.872936\pi\) | |||||||
\(164\) | 6.34477i | 0.495443i | ||||||||
\(165\) | 6.90371 | + | 5.67609i | 0.537453 | + | 0.441883i | ||||
\(166\) | 4.51281 | + | 4.51281i | 0.350262 | + | 0.350262i | ||||
\(167\) | − | 17.7622i | − | 1.37448i | −0.726431 | − | 0.687239i | \(-0.758822\pi\) | ||
0.726431 | − | 0.687239i | \(-0.241178\pi\) | |||||||
\(168\) | − | 4.67054i | − | 0.360340i | ||||||
\(169\) | 6.49561 | 0.499662 | ||||||||
\(170\) | 1.16799 | + | 11.9687i | 0.0895806 | + | 0.917960i | ||||
\(171\) | −3.44786 | + | 3.44786i | −0.263664 | + | 0.263664i | ||||
\(172\) | 1.78544 | 0.136139 | ||||||||
\(173\) | −4.93605 | + | 4.93605i | −0.375281 | + | 0.375281i | −0.869396 | − | 0.494116i | \(-0.835492\pi\) |
0.494116 | + | 0.869396i | \(0.335492\pi\) | |||||||
\(174\) | − | 3.47285i | − | 0.263276i | ||||||
\(175\) | 11.5716 | − | 17.2511i | 0.874732 | − | 1.30406i | ||||
\(176\) | − | 3.55539i | − | 0.267998i | ||||||
\(177\) | −7.06835 | −0.531290 | ||||||||
\(178\) | −2.13937 | + | 2.13937i | −0.160353 | + | 0.160353i | ||||
\(179\) | 3.68868 | − | 3.68868i | 0.275705 | − | 0.275705i | −0.555687 | − | 0.831392i | \(-0.687545\pi\) |
0.831392 | + | 0.555687i | \(0.187545\pi\) | |||||||
\(180\) | 0.377058 | + | 3.86383i | 0.0281042 | + | 0.287993i | ||||
\(181\) | −5.35458 | −0.398002 | −0.199001 | − | 0.979999i | \(-0.563770\pi\) | ||||
−0.199001 | + | 0.979999i | \(0.563770\pi\) | |||||||
\(182\) | 12.9711 | − | 12.9711i | 0.961479 | − | 0.961479i | ||||
\(183\) | −2.28994 | −0.169277 | ||||||||
\(184\) | −5.90774 | −0.435525 | ||||||||
\(185\) | −7.63918 | + | 11.2536i | −0.561644 | + | 0.827379i | ||||
\(186\) | 8.62020 | 0.632064 | ||||||||
\(187\) | −19.1209 | −1.39826 | ||||||||
\(188\) | 1.82646 | − | 1.82646i | 0.133209 | − | 0.133209i | ||||
\(189\) | −22.1205 | −1.60903 | ||||||||
\(190\) | −4.85091 | − | 3.98832i | −0.351922 | − | 0.289343i | ||||
\(191\) | 10.0773 | − | 10.0773i | 0.729166 | − | 0.729166i | −0.241288 | − | 0.970454i | \(-0.577570\pi\) |
0.970454 | + | 0.241288i | \(0.0775698\pi\) | |||||||
\(192\) | −0.794932 | + | 0.794932i | −0.0573693 | + | 0.0573693i | ||||
\(193\) | 24.7844 | 1.78402 | 0.892011 | − | 0.452014i | \(-0.149294\pi\) | ||||
0.892011 | + | 0.452014i | \(0.149294\pi\) | |||||||
\(194\) | − | 5.91995i | − | 0.425028i | ||||||
\(195\) | 7.04905 | − | 8.57362i | 0.504793 | − | 0.613970i | ||||
\(196\) | − | 10.2601i | − | 0.732867i | ||||||
\(197\) | 11.3006 | − | 11.3006i | 0.805132 | − | 0.805132i | −0.178760 | − | 0.983893i | \(-0.557209\pi\) |
0.983893 | + | 0.178760i | \(0.0572087\pi\) | |||||||
\(198\) | −6.17274 | −0.438678 | ||||||||
\(199\) | −6.90680 | + | 6.90680i | −0.489610 | + | 0.489610i | −0.908183 | − | 0.418573i | \(-0.862530\pi\) |
0.418573 | + | 0.908183i | \(0.362530\pi\) | |||||||
\(200\) | −4.90567 | + | 0.966660i | −0.346883 | + | 0.0683532i | ||||
\(201\) | −12.5417 | −0.884626 | ||||||||
\(202\) | − | 9.23382i | − | 0.649689i | ||||||
\(203\) | − | 12.8340i | − | 0.900771i | ||||||
\(204\) | 4.27515 | + | 4.27515i | 0.299321 | + | 0.299321i | ||||
\(205\) | 1.37795 | + | 14.1203i | 0.0962400 | + | 0.986202i | ||||
\(206\) | − | 8.03931i | − | 0.560125i | ||||||
\(207\) | 10.2568i | 0.712898i | ||||||||
\(208\) | −4.41538 | −0.306152 | ||||||||
\(209\) | 7.06065 | − | 7.06065i | 0.488396 | − | 0.488396i | ||||
\(210\) | −1.01434 | − | 10.3943i | −0.0699962 | − | 0.717273i | ||||
\(211\) | −22.7919 | −1.56906 | −0.784531 | − | 0.620090i | \(-0.787096\pi\) | ||||
−0.784531 | + | 0.620090i | \(0.787096\pi\) | |||||||
\(212\) | −9.57437 | − | 9.57437i | −0.657570 | − | 0.657570i | ||||
\(213\) | 8.94925 | − | 8.94925i | 0.613193 | − | 0.613193i | ||||
\(214\) | −4.60753 | + | 4.60753i | −0.314964 | + | 0.314964i | ||||
\(215\) | 3.97349 | − | 0.387760i | 0.270990 | − | 0.0264450i | ||||
\(216\) | 3.76493 | + | 3.76493i | 0.256171 | + | 0.256171i | ||||
\(217\) | 31.8562 | 2.16254 | ||||||||
\(218\) | 14.6123 | + | 14.6123i | 0.989673 | + | 0.989673i | ||||
\(219\) | − | 6.39655i | − | 0.432239i | ||||||
\(220\) | −0.772154 | − | 7.91250i | −0.0520586 | − | 0.533461i | ||||
\(221\) | 23.7460i | 1.59733i | ||||||||
\(222\) | 0.626522 | + | 6.80950i | 0.0420494 | + | 0.457024i | ||||
\(223\) | −7.23324 | − | 7.23324i | −0.484373 | − | 0.484373i | 0.422152 | − | 0.906525i | \(-0.361275\pi\) |
−0.906525 | + | 0.422152i | \(0.861275\pi\) | |||||||
\(224\) | −2.93770 | + | 2.93770i | −0.196283 | + | 0.196283i | ||||
\(225\) | 1.67828 | + | 8.51705i | 0.111885 | + | 0.567803i | ||||
\(226\) | − | 8.61849i | − | 0.573293i | ||||||
\(227\) | − | 3.53828i | − | 0.234844i | −0.993082 | − | 0.117422i | \(-0.962537\pi\) | ||
0.993082 | − | 0.117422i | \(-0.0374630\pi\) | |||||||
\(228\) | −3.15731 | −0.209098 | ||||||||
\(229\) | 10.2694i | 0.678622i | 0.940674 | + | 0.339311i | \(0.110194\pi\) | ||||
−0.940674 | + | 0.339311i | \(0.889806\pi\) | |||||||
\(230\) | −13.1477 | + | 1.28304i | −0.866931 | + | 0.0846008i | ||||
\(231\) | 16.6056 | 1.09257 | ||||||||
\(232\) | −2.18437 | + | 2.18437i | −0.143411 | + | 0.143411i | ||||
\(233\) | −0.731820 | + | 0.731820i | −0.0479431 | + | 0.0479431i | −0.730672 | − | 0.682729i | \(-0.760793\pi\) |
0.682729 | + | 0.730672i | \(0.260793\pi\) | |||||||
\(234\) | 7.66584i | 0.501131i | ||||||||
\(235\) | 3.66812 | − | 4.46146i | 0.239282 | − | 0.291033i | ||||
\(236\) | 4.44588 | + | 4.44588i | 0.289402 | + | 0.289402i | ||||
\(237\) | −3.22836 | −0.209704 | ||||||||
\(238\) | 15.7990 | + | 15.7990i | 1.02409 | + | 1.02409i | ||||
\(239\) | 6.25677 | + | 6.25677i | 0.404717 | + | 0.404717i | 0.879892 | − | 0.475175i | \(-0.157615\pi\) |
−0.475175 | + | 0.879892i | \(0.657615\pi\) | |||||||
\(240\) | −1.59648 | + | 1.94176i | −0.103052 | + | 0.125340i | ||||
\(241\) | −6.31560 | + | 6.31560i | −0.406823 | + | 0.406823i | −0.880629 | − | 0.473806i | \(-0.842880\pi\) |
0.473806 | + | 0.880629i | \(0.342880\pi\) | |||||||
\(242\) | 1.64079 | 0.105474 | ||||||||
\(243\) | 10.6769 | − | 10.6769i | 0.684926 | − | 0.684926i | ||||
\(244\) | 1.44033 | + | 1.44033i | 0.0922079 | + | 0.0922079i | ||||
\(245\) | −2.22828 | − | 22.8339i | −0.142360 | − | 1.45880i | ||||
\(246\) | 5.04366 | + | 5.04366i | 0.321572 | + | 0.321572i | ||||
\(247\) | −8.76852 | − | 8.76852i | −0.557927 | − | 0.557927i | ||||
\(248\) | −5.42197 | − | 5.42197i | −0.344296 | − | 0.344296i | ||||
\(249\) | 7.17475 | 0.454681 | ||||||||
\(250\) | −10.7076 | + | 3.21670i | −0.677208 | + | 0.203442i | ||||
\(251\) | 3.90237 | + | 3.90237i | 0.246315 | + | 0.246315i | 0.819457 | − | 0.573141i | \(-0.194275\pi\) |
−0.573141 | + | 0.819457i | \(0.694275\pi\) | |||||||
\(252\) | 5.10033 | + | 5.10033i | 0.321291 | + | 0.321291i | ||||
\(253\) | − | 21.0043i | − | 1.32053i | ||||||
\(254\) | 4.22966 | − | 4.22966i | 0.265393 | − | 0.265393i | ||||
\(255\) | 10.4428 | + | 8.58586i | 0.653954 | + | 0.537668i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.21902i | 0.138419i | 0.997602 | + | 0.0692095i | \(0.0220477\pi\) | ||||
−0.997602 | + | 0.0692095i | \(0.977952\pi\) | |||||||
\(258\) | 1.41931 | − | 1.41931i | 0.0883621 | − | 0.0883621i | ||||
\(259\) | 2.31533 | + | 25.1647i | 0.143868 | + | 1.56366i | ||||
\(260\) | −9.82642 | + | 0.958927i | −0.609409 | + | 0.0594701i | ||||
\(261\) | 3.79242 | + | 3.79242i | 0.234745 | + | 0.234745i | ||||
\(262\) | 15.2680 | + | 15.2680i | 0.943260 | + | 0.943260i | ||||
\(263\) | −11.1111 | + | 11.1111i | −0.685141 | + | 0.685141i | −0.961154 | − | 0.276013i | \(-0.910987\pi\) |
0.276013 | + | 0.961154i | \(0.410987\pi\) | |||||||
\(264\) | −2.82629 | − | 2.82629i | −0.173946 | − | 0.173946i | ||||
\(265\) | −23.3871 | − | 19.2284i | −1.43666 | − | 1.18119i | ||||
\(266\) | −11.6680 | −0.715408 | ||||||||
\(267\) | 3.40131i | 0.208157i | ||||||||
\(268\) | 7.88856 | + | 7.88856i | 0.481870 | + | 0.481870i | ||||
\(269\) | 5.86174i | 0.357396i | 0.983904 | + | 0.178698i | \(0.0571886\pi\) | ||||
−0.983904 | + | 0.178698i | \(0.942811\pi\) | |||||||
\(270\) | 9.19650 | + | 7.56118i | 0.559681 | + | 0.460159i | ||||
\(271\) | −4.91311 | −0.298450 | −0.149225 | − | 0.988803i | \(-0.547678\pi\) | ||||
−0.149225 | + | 0.988803i | \(0.547678\pi\) | |||||||
\(272\) | − | 5.37801i | − | 0.326090i | ||||||
\(273\) | − | 20.6222i | − | 1.24811i | ||||||
\(274\) | 14.4220 | − | 14.4220i | 0.871262 | − | 0.871262i | ||||
\(275\) | −3.43685 | − | 17.4416i | −0.207250 | − | 1.05177i | ||||
\(276\) | −4.69625 | + | 4.69625i | −0.282681 | + | 0.282681i | ||||
\(277\) | 8.21627 | 0.493668 | 0.246834 | − | 0.969058i | \(-0.420610\pi\) | ||||
0.246834 | + | 0.969058i | \(0.420610\pi\) | |||||||
\(278\) | −1.56244 | −0.0937092 | ||||||||
\(279\) | −9.41344 | + | 9.41344i | −0.563568 | + | 0.563568i | ||||
\(280\) | −5.89983 | + | 7.17584i | −0.352582 | + | 0.428838i | ||||
\(281\) | −7.17894 | + | 7.17894i | −0.428259 | + | 0.428259i | −0.888035 | − | 0.459776i | \(-0.847930\pi\) |
0.459776 | + | 0.888035i | \(0.347930\pi\) | |||||||
\(282\) | − | 2.90383i | − | 0.172921i | ||||||
\(283\) | 21.1149i | 1.25515i | 0.778557 | + | 0.627574i | \(0.215952\pi\) | ||||
−0.778557 | + | 0.627574i | \(0.784048\pi\) | |||||||
\(284\) | −11.2579 | −0.668032 | ||||||||
\(285\) | −7.02659 | + | 0.685701i | −0.416219 | + | 0.0406174i | ||||
\(286\) | − | 15.6984i | − | 0.928266i | ||||||
\(287\) | 18.6390 | + | 18.6390i | 1.10023 | + | 1.10023i | ||||
\(288\) | − | 1.73617i | − | 0.102305i | ||||||
\(289\) | −11.9230 | −0.701352 | ||||||||
\(290\) | −4.38690 | + | 5.33570i | −0.257608 | + | 0.313323i | ||||
\(291\) | −4.70596 | − | 4.70596i | −0.275868 | − | 0.275868i | ||||
\(292\) | −4.02333 | + | 4.02333i | −0.235448 | + | 0.235448i | ||||
\(293\) | 8.03410 | + | 8.03410i | 0.469357 | + | 0.469357i | 0.901706 | − | 0.432349i | \(-0.142315\pi\) |
−0.432349 | + | 0.901706i | \(0.642315\pi\) | |||||||
\(294\) | −8.15611 | − | 8.15611i | −0.475674 | − | 0.475674i | ||||
\(295\) | 10.8598 | + | 8.92875i | 0.632285 | + | 0.519852i | ||||
\(296\) | 3.88900 | − | 4.67714i | 0.226044 | − | 0.271854i | ||||
\(297\) | −13.3858 | + | 13.3858i | −0.776722 | + | 0.776722i | ||||
\(298\) | − | 8.42600i | − | 0.488105i | ||||||
\(299\) | −26.0849 | −1.50853 | ||||||||
\(300\) | −3.13124 | + | 4.66810i | −0.180782 | + | 0.269513i | ||||
\(301\) | 5.24509 | − | 5.24509i | 0.302322 | − | 0.302322i | ||||
\(302\) | 9.65715i | 0.555706i | ||||||||
\(303\) | −7.34026 | − | 7.34026i | −0.421687 | − | 0.421687i | ||||
\(304\) | 1.98590 | + | 1.98590i | 0.113899 | + | 0.113899i | ||||
\(305\) | 3.51827 | + | 2.89265i | 0.201455 | + | 0.165633i | ||||
\(306\) | −9.33711 | −0.533767 | ||||||||
\(307\) | 3.81755 | + | 3.81755i | 0.217879 | + | 0.217879i | 0.807604 | − | 0.589725i | \(-0.200764\pi\) |
−0.589725 | + | 0.807604i | \(0.700764\pi\) | |||||||
\(308\) | −10.4447 | − | 10.4447i | −0.595140 | − | 0.595140i | ||||
\(309\) | −6.39071 | − | 6.39071i | −0.363555 | − | 0.363555i | ||||
\(310\) | −13.2441 | − | 10.8890i | −0.752215 | − | 0.618456i | ||||
\(311\) | 8.92270 | + | 8.92270i | 0.505960 | + | 0.505960i | 0.913284 | − | 0.407324i | \(-0.133538\pi\) |
−0.407324 | + | 0.913284i | \(0.633538\pi\) | |||||||
\(312\) | −3.50993 | + | 3.50993i | −0.198711 | + | 0.198711i | ||||
\(313\) | −29.7794 | −1.68323 | −0.841616 | − | 0.540076i | \(-0.818395\pi\) | ||||
−0.841616 | + | 0.540076i | \(0.818395\pi\) | |||||||
\(314\) | 13.7789 | − | 13.7789i | 0.777591 | − | 0.777591i | ||||
\(315\) | 12.4584 | + | 10.2431i | 0.701954 | + | 0.577132i | ||||
\(316\) | 2.03059 | + | 2.03059i | 0.114229 | + | 0.114229i | ||||
\(317\) | −16.2699 | − | 16.2699i | −0.913808 | − | 0.913808i | 0.0827610 | − | 0.996569i | \(-0.473626\pi\) |
−0.996569 | + | 0.0827610i | \(0.973626\pi\) | |||||||
\(318\) | −15.2219 | −0.853604 | ||||||||
\(319\) | −7.76627 | − | 7.76627i | −0.434828 | − | 0.434828i | ||||
\(320\) | 2.22550 | − | 0.217179i | 0.124409 | − | 0.0121407i | ||||
\(321\) | 7.32535i | 0.408861i | ||||||||
\(322\) | −17.3552 | + | 17.3552i | −0.967165 | + | 0.967165i | ||||
\(323\) | 10.6802 | − | 10.6802i | 0.594262 | − | 0.594262i | ||||
\(324\) | 0.777232 | 0.0431795 | ||||||||
\(325\) | −21.6604 | + | 4.26818i | −1.20150 | + | 0.236756i | ||||
\(326\) | − | 9.92434i | − | 0.549658i | ||||||
\(327\) | 23.2316 | 1.28471 | ||||||||
\(328\) | − | 6.34477i | − | 0.350331i | ||||||
\(329\) | − | 10.7312i | − | 0.591630i | ||||||
\(330\) | −6.90371 | − | 5.67609i | −0.380037 | − | 0.312459i | ||||
\(331\) | 15.6327 | − | 15.6327i | 0.859250 | − | 0.859250i | −0.132000 | − | 0.991250i | \(-0.542140\pi\) |
0.991250 | + | 0.132000i | \(0.0421399\pi\) | |||||||
\(332\) | −4.51281 | − | 4.51281i | −0.247672 | − | 0.247672i | ||||
\(333\) | −8.12030 | − | 6.75195i | −0.444990 | − | 0.370004i | ||||
\(334\) | 17.7622i | 0.971903i | ||||||||
\(335\) | 19.2692 | + | 15.8427i | 1.05279 | + | 0.865581i | ||||
\(336\) | 4.67054i | 0.254799i | ||||||||
\(337\) | 22.0252 | + | 22.0252i | 1.19979 | + | 1.19979i | 0.974230 | + | 0.225558i | \(0.0724204\pi\) |
0.225558 | + | 0.974230i | \(0.427580\pi\) | |||||||
\(338\) | −6.49561 | −0.353315 | ||||||||
\(339\) | −6.85111 | − | 6.85111i | −0.372101 | − | 0.372101i | ||||
\(340\) | −1.16799 | − | 11.9687i | −0.0633431 | − | 0.649096i | ||||
\(341\) | 19.2772 | − | 19.2772i | 1.04392 | − | 1.04392i | ||||
\(342\) | 3.44786 | − | 3.44786i | 0.186439 | − | 0.186439i | ||||
\(343\) | −9.57729 | − | 9.57729i | −0.517125 | − | 0.517125i | ||||
\(344\) | −1.78544 | −0.0962646 | ||||||||
\(345\) | −9.43157 | + | 11.4714i | −0.507779 | + | 0.617601i | ||||
\(346\) | 4.93605 | − | 4.93605i | 0.265364 | − | 0.265364i | ||||
\(347\) | −35.2079 | −1.89006 | −0.945029 | − | 0.326987i | \(-0.893967\pi\) | ||||
−0.945029 | + | 0.326987i | \(0.893967\pi\) | |||||||
\(348\) | 3.47285i | 0.186164i | ||||||||
\(349\) | − | 7.00272i | − | 0.374847i | −0.982279 | − | 0.187423i | \(-0.939986\pi\) | ||
0.982279 | − | 0.187423i | \(-0.0600137\pi\) | |||||||
\(350\) | −11.5716 | + | 17.2511i | −0.618529 | + | 0.922111i | ||||
\(351\) | 16.6236 | + | 16.6236i | 0.887303 | + | 0.887303i | ||||
\(352\) | 3.55539i | 0.189503i | ||||||||
\(353\) | 24.1991i | 1.28799i | 0.765030 | + | 0.643995i | \(0.222724\pi\) | ||||
−0.765030 | + | 0.643995i | \(0.777276\pi\) | |||||||
\(354\) | 7.06835 | 0.375679 | ||||||||
\(355\) | −25.0544 | + | 2.44497i | −1.32975 | + | 0.129766i | ||||
\(356\) | 2.13937 | − | 2.13937i | 0.113387 | − | 0.113387i | ||||
\(357\) | 25.1182 | 1.32940 | ||||||||
\(358\) | −3.68868 | + | 3.68868i | −0.194953 | + | 0.194953i | ||||
\(359\) | − | 5.19872i | − | 0.274378i | −0.990545 | − | 0.137189i | \(-0.956193\pi\) | ||
0.990545 | − | 0.137189i | \(-0.0438067\pi\) | |||||||
\(360\) | −0.377058 | − | 3.86383i | −0.0198727 | − | 0.203642i | ||||
\(361\) | − | 11.1124i | − | 0.584862i | ||||||
\(362\) | 5.35458 | 0.281430 | ||||||||
\(363\) | 1.30432 | − | 1.30432i | 0.0684588 | − | 0.0684588i | ||||
\(364\) | −12.9711 | + | 12.9711i | −0.679868 | + | 0.679868i | ||||
\(365\) | −8.08013 | + | 9.82769i | −0.422933 | + | 0.514405i | ||||
\(366\) | 2.28994 | 0.119697 | ||||||||
\(367\) | 22.4335 | − | 22.4335i | 1.17102 | − | 1.17102i | 0.189049 | − | 0.981968i | \(-0.439460\pi\) |
0.981968 | − | 0.189049i | \(-0.0605405\pi\) | |||||||
\(368\) | 5.90774 | 0.307962 | ||||||||
\(369\) | −11.0156 | −0.573448 | ||||||||
\(370\) | 7.63918 | − | 11.2536i | 0.397142 | − | 0.585045i | ||||
\(371\) | −56.2532 | −2.92052 | ||||||||
\(372\) | −8.62020 | −0.446937 | ||||||||
\(373\) | −10.4263 | + | 10.4263i | −0.539852 | + | 0.539852i | −0.923486 | − | 0.383633i | \(-0.874673\pi\) |
0.383633 | + | 0.923486i | \(0.374673\pi\) | |||||||
\(374\) | 19.1209 | 0.988719 | ||||||||
\(375\) | −5.95476 | + | 11.0689i | −0.307502 | + | 0.571595i | ||||
\(376\) | −1.82646 | + | 1.82646i | −0.0941927 | + | 0.0941927i | ||||
\(377\) | −9.64481 | + | 9.64481i | −0.496733 | + | 0.496733i | ||||
\(378\) | 22.1205 | 1.13775 | ||||||||
\(379\) | − | 15.9233i | − | 0.817925i | −0.912551 | − | 0.408963i | \(-0.865891\pi\) | ||
0.912551 | − | 0.408963i | \(-0.134109\pi\) | |||||||
\(380\) | 4.85091 | + | 3.98832i | 0.248847 | + | 0.204597i | ||||
\(381\) | − | 6.72459i | − | 0.344511i | ||||||
\(382\) | −10.0773 | + | 10.0773i | −0.515598 | + | 0.515598i | ||||
\(383\) | 24.2531 | 1.23928 | 0.619638 | − | 0.784888i | \(-0.287279\pi\) | ||||
0.619638 | + | 0.784888i | \(0.287279\pi\) | |||||||
\(384\) | 0.794932 | − | 0.794932i | 0.0405662 | − | 0.0405662i | ||||
\(385\) | −25.5129 | − | 20.9762i | −1.30026 | − | 1.06905i | ||||
\(386\) | −24.7844 | −1.26149 | ||||||||
\(387\) | 3.09982i | 0.157573i | ||||||||
\(388\) | 5.91995i | 0.300540i | ||||||||
\(389\) | 19.7499 | + | 19.7499i | 1.00136 | + | 1.00136i | 0.999999 | + | 0.00136297i | \(0.000433846\pi\) |
0.00136297 | + | 0.999999i | \(0.499566\pi\) | |||||||
\(390\) | −7.04905 | + | 8.57362i | −0.356943 | + | 0.434142i | ||||
\(391\) | − | 31.7719i | − | 1.60677i | ||||||
\(392\) | 10.2601i | 0.518215i | ||||||||
\(393\) | 24.2741 | 1.22446 | ||||||||
\(394\) | −11.3006 | + | 11.3006i | −0.569314 | + | 0.569314i | ||||
\(395\) | 4.96006 | + | 4.07806i | 0.249568 | + | 0.205190i | ||||
\(396\) | 6.17274 | 0.310192 | ||||||||
\(397\) | −1.71599 | − | 1.71599i | −0.0861232 | − | 0.0861232i | 0.662733 | − | 0.748856i | \(-0.269397\pi\) |
−0.748856 | + | 0.662733i | \(0.769397\pi\) | |||||||
\(398\) | 6.90680 | − | 6.90680i | 0.346206 | − | 0.346206i | ||||
\(399\) | −9.27524 | + | 9.27524i | −0.464343 | + | 0.464343i | ||||
\(400\) | 4.90567 | − | 0.966660i | 0.245283 | − | 0.0483330i | ||||
\(401\) | 9.29247 | + | 9.29247i | 0.464044 | + | 0.464044i | 0.899978 | − | 0.435934i | \(-0.143582\pi\) |
−0.435934 | + | 0.899978i | \(0.643582\pi\) | |||||||
\(402\) | 12.5417 | 0.625525 | ||||||||
\(403\) | −23.9401 | − | 23.9401i | −1.19254 | − | 1.19254i | ||||
\(404\) | 9.23382i | 0.459399i | ||||||||
\(405\) | 1.72973 | − | 0.168798i | 0.0859508 | − | 0.00838764i | ||||
\(406\) | 12.8340i | 0.636941i | ||||||||
\(407\) | 16.6291 | + | 13.8269i | 0.824272 | + | 0.685374i | ||||
\(408\) | −4.27515 | − | 4.27515i | −0.211652 | − | 0.211652i | ||||
\(409\) | 18.3866 | − | 18.3866i | 0.909160 | − | 0.909160i | −0.0870446 | − | 0.996204i | \(-0.527742\pi\) |
0.996204 | + | 0.0870446i | \(0.0277423\pi\) | |||||||
\(410\) | −1.37795 | − | 14.1203i | −0.0680520 | − | 0.697350i | ||||
\(411\) | − | 22.9290i | − | 1.13100i | ||||||
\(412\) | 8.03931i | 0.396068i | ||||||||
\(413\) | 26.1213 | 1.28535 | ||||||||
\(414\) | − | 10.2568i | − | 0.504095i | ||||||
\(415\) | −11.0233 | − | 9.06315i | −0.541113 | − | 0.444892i | ||||
\(416\) | 4.41538 | 0.216482 | ||||||||
\(417\) | −1.24204 | + | 1.24204i | −0.0608228 | + | 0.0608228i | ||||
\(418\) | −7.06065 | + | 7.06065i | −0.345348 | + | 0.345348i | ||||
\(419\) | 8.04256i | 0.392905i | 0.980513 | + | 0.196452i | \(0.0629421\pi\) | ||||
−0.980513 | + | 0.196452i | \(0.937058\pi\) | |||||||
\(420\) | 1.01434 | + | 10.3943i | 0.0494948 | + | 0.507188i | ||||
\(421\) | 11.0268 | + | 11.0268i | 0.537416 | + | 0.537416i | 0.922769 | − | 0.385353i | \(-0.125920\pi\) |
−0.385353 | + | 0.922769i | \(0.625920\pi\) | |||||||
\(422\) | 22.7919 | 1.10949 | ||||||||
\(423\) | 3.17104 | + | 3.17104i | 0.154181 | + | 0.154181i | ||||
\(424\) | 9.57437 | + | 9.57437i | 0.464972 | + | 0.464972i | ||||
\(425\) | −5.19871 | − | 26.3827i | −0.252174 | − | 1.27975i | ||||
\(426\) | −8.94925 | + | 8.94925i | −0.433593 | + | 0.433593i | ||||
\(427\) | 8.46253 | 0.409530 | ||||||||
\(428\) | 4.60753 | − | 4.60753i | 0.222713 | − | 0.222713i | ||||
\(429\) | −12.4792 | − | 12.4792i | −0.602500 | − | 0.602500i | ||||
\(430\) | −3.97349 | + | 0.387760i | −0.191619 | + | 0.0186994i | ||||
\(431\) | 9.69563 | + | 9.69563i | 0.467022 | + | 0.467022i | 0.900948 | − | 0.433926i | \(-0.142872\pi\) |
−0.433926 | + | 0.900948i | \(0.642872\pi\) | |||||||
\(432\) | −3.76493 | − | 3.76493i | −0.181140 | − | 0.181140i | ||||
\(433\) | −7.39679 | − | 7.39679i | −0.355467 | − | 0.355467i | 0.506672 | − | 0.862139i | \(-0.330876\pi\) |
−0.862139 | + | 0.506672i | \(0.830876\pi\) | |||||||
\(434\) | −31.8562 | −1.52915 | ||||||||
\(435\) | 0.754228 | + | 7.72880i | 0.0361624 | + | 0.370568i | ||||
\(436\) | −14.6123 | − | 14.6123i | −0.699804 | − | 0.699804i | ||||
\(437\) | 11.7322 | + | 11.7322i | 0.561227 | + | 0.561227i | ||||
\(438\) | 6.39655i | 0.305639i | ||||||||
\(439\) | 21.3840 | − | 21.3840i | 1.02060 | − | 1.02060i | 0.0208186 | − | 0.999783i | \(-0.493373\pi\) |
0.999783 | − | 0.0208186i | \(-0.00662725\pi\) | |||||||
\(440\) | 0.772154 | + | 7.91250i | 0.0368110 | + | 0.377214i | ||||
\(441\) | 17.8133 | 0.848252 | ||||||||
\(442\) | − | 23.7460i | − | 1.12948i | ||||||
\(443\) | −0.537851 | + | 0.537851i | −0.0255541 | + | 0.0255541i | −0.719768 | − | 0.694214i | \(-0.755752\pi\) |
0.694214 | + | 0.719768i | \(0.255752\pi\) | |||||||
\(444\) | −0.626522 | − | 6.80950i | −0.0297334 | − | 0.323165i | ||||
\(445\) | 4.29654 | − | 5.22579i | 0.203676 | − | 0.247726i | ||||
\(446\) | 7.23324 | + | 7.23324i | 0.342504 | + | 0.342504i | ||||
\(447\) | −6.69810 | − | 6.69810i | −0.316809 | − | 0.316809i | ||||
\(448\) | 2.93770 | − | 2.93770i | 0.138793 | − | 0.138793i | ||||
\(449\) | −17.9014 | − | 17.9014i | −0.844820 | − | 0.844820i | 0.144661 | − | 0.989481i | \(-0.453791\pi\) |
−0.989481 | + | 0.144661i | \(0.953791\pi\) | |||||||
\(450\) | −1.67828 | − | 8.51705i | −0.0791150 | − | 0.401498i | ||||
\(451\) | 22.5581 | 1.06222 | ||||||||
\(452\) | 8.61849i | 0.405380i | ||||||||
\(453\) | 7.67678 | + | 7.67678i | 0.360686 | + | 0.360686i | ||||
\(454\) | 3.53828i | 0.166060i | ||||||||
\(455\) | −26.0500 | + | 31.6841i | −1.22124 | + | 1.48537i | ||||
\(456\) | 3.15731 | 0.147855 | ||||||||
\(457\) | − | 10.3305i | − | 0.483240i | −0.970371 | − | 0.241620i | \(-0.922321\pi\) | ||
0.970371 | − | 0.241620i | \(-0.0776787\pi\) | |||||||
\(458\) | − | 10.2694i | − | 0.479858i | ||||||
\(459\) | −20.2478 | + | 20.2478i | −0.945088 | + | 0.945088i | ||||
\(460\) | 13.1477 | − | 1.28304i | 0.613013 | − | 0.0598218i | ||||
\(461\) | −19.5325 | + | 19.5325i | −0.909718 | + | 0.909718i | −0.996249 | − | 0.0865312i | \(-0.972422\pi\) |
0.0865312 | + | 0.996249i | \(0.472422\pi\) | |||||||
\(462\) | −16.6056 | −0.772562 | ||||||||
\(463\) | 13.2709 | 0.616752 | 0.308376 | − | 0.951265i | \(-0.400214\pi\) | ||||
0.308376 | + | 0.951265i | \(0.400214\pi\) | |||||||
\(464\) | 2.18437 | − | 2.18437i | 0.101407 | − | 0.101407i | ||||
\(465\) | −19.1842 | + | 1.87212i | −0.889647 | + | 0.0868176i | ||||
\(466\) | 0.731820 | − | 0.731820i | 0.0339009 | − | 0.0339009i | ||||
\(467\) | 40.7473i | 1.88556i | 0.333414 | + | 0.942780i | \(0.391799\pi\) | ||||
−0.333414 | + | 0.942780i | \(0.608201\pi\) | |||||||
\(468\) | − | 7.66584i | − | 0.354353i | ||||||
\(469\) | 46.3484 | 2.14017 | ||||||||
\(470\) | −3.66812 | + | 4.46146i | −0.169198 | + | 0.205792i | ||||
\(471\) | − | 21.9066i | − | 1.00941i | ||||||
\(472\) | −4.44588 | − | 4.44588i | −0.204638 | − | 0.204638i | ||||
\(473\) | − | 6.34794i | − | 0.291879i | ||||||
\(474\) | 3.22836 | 0.148283 | ||||||||
\(475\) | 11.6619 | + | 7.82248i | 0.535083 | + | 0.358920i | ||||
\(476\) | −15.7990 | − | 15.7990i | −0.724144 | − | 0.724144i | ||||
\(477\) | 16.6227 | − | 16.6227i | 0.761100 | − | 0.761100i | ||||
\(478\) | −6.25677 | − | 6.25677i | −0.286178 | − | 0.286178i | ||||
\(479\) | 8.91382 | + | 8.91382i | 0.407283 | + | 0.407283i | 0.880790 | − | 0.473507i | \(-0.157012\pi\) |
−0.473507 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(480\) | 1.59648 | − | 1.94176i | 0.0728688 | − | 0.0886288i | ||||
\(481\) | 17.1714 | − | 20.6514i | 0.782950 | − | 0.941622i | ||||
\(482\) | 6.31560 | − | 6.31560i | 0.287667 | − | 0.287667i | ||||
\(483\) | 27.5924i | 1.25550i | ||||||||
\(484\) | −1.64079 | −0.0745813 | ||||||||
\(485\) | 1.28569 | + | 13.1748i | 0.0583800 | + | 0.598238i | ||||
\(486\) | −10.6769 | + | 10.6769i | −0.484316 | + | 0.484316i | ||||
\(487\) | − | 27.7847i | − | 1.25904i | −0.776983 | − | 0.629522i | \(-0.783251\pi\) | ||
0.776983 | − | 0.629522i | \(-0.216749\pi\) | |||||||
\(488\) | −1.44033 | − | 1.44033i | −0.0652008 | − | 0.0652008i | ||||
\(489\) | −7.88918 | − | 7.88918i | −0.356761 | − | 0.356761i | ||||
\(490\) | 2.22828 | + | 22.8339i | 0.100663 | + | 1.03153i | ||||
\(491\) | −7.19820 | −0.324850 | −0.162425 | − | 0.986721i | \(-0.551932\pi\) | ||||
−0.162425 | + | 0.986721i | \(0.551932\pi\) | |||||||
\(492\) | −5.04366 | − | 5.04366i | −0.227386 | − | 0.227386i | ||||
\(493\) | −11.7475 | − | 11.7475i | −0.529083 | − | 0.529083i | ||||
\(494\) | 8.76852 | + | 8.76852i | 0.394514 | + | 0.394514i | ||||
\(495\) | 13.7374 | − | 1.34059i | 0.617451 | − | 0.0602549i | ||||
\(496\) | 5.42197 | + | 5.42197i | 0.243454 | + | 0.243454i | ||||
\(497\) | −33.0722 | + | 33.0722i | −1.48349 | + | 1.48349i | ||||
\(498\) | −7.17475 | −0.321508 | ||||||||
\(499\) | −0.378337 | + | 0.378337i | −0.0169367 | + | 0.0169367i | −0.715524 | − | 0.698588i | \(-0.753812\pi\) |
0.698588 | + | 0.715524i | \(0.253812\pi\) | |||||||
\(500\) | 10.7076 | − | 3.21670i | 0.478859 | − | 0.143855i | ||||
\(501\) | 14.1197 | + | 14.1197i | 0.630823 | + | 0.630823i | ||||
\(502\) | −3.90237 | − | 3.90237i | −0.174171 | − | 0.174171i | ||||
\(503\) | 22.0885 | 0.984876 | 0.492438 | − | 0.870348i | \(-0.336106\pi\) | ||||
0.492438 | + | 0.870348i | \(0.336106\pi\) | |||||||
\(504\) | −5.10033 | − | 5.10033i | −0.227187 | − | 0.227187i | ||||
\(505\) | 2.00539 | + | 20.5498i | 0.0892385 | + | 0.914455i | ||||
\(506\) | 21.0043i | 0.933756i | ||||||||
\(507\) | −5.16357 | + | 5.16357i | −0.229322 | + | 0.229322i | ||||
\(508\) | −4.22966 | + | 4.22966i | −0.187661 | + | 0.187661i | ||||
\(509\) | 24.8176 | 1.10002 | 0.550011 | − | 0.835157i | \(-0.314624\pi\) | ||||
0.550011 | + | 0.835157i | \(0.314624\pi\) | |||||||
\(510\) | −10.4428 | − | 8.58586i | −0.462415 | − | 0.380188i | ||||
\(511\) | 23.6387i | 1.04571i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 14.9536i | − | 0.660216i | ||||||
\(514\) | − | 2.21902i | − | 0.0978769i | ||||||
\(515\) | 1.74597 | + | 17.8915i | 0.0769364 | + | 0.788392i | ||||
\(516\) | −1.41931 | + | 1.41931i | −0.0624814 | + | 0.0624814i | ||||
\(517\) | −6.49379 | − | 6.49379i | −0.285597 | − | 0.285597i | ||||
\(518\) | −2.31533 | − | 25.1647i | −0.101730 | − | 1.10568i | ||||
\(519\) | − | 7.84764i | − | 0.344473i | ||||||
\(520\) | 9.82642 | − | 0.958927i | 0.430917 | − | 0.0420517i | ||||
\(521\) | − | 2.41522i | − | 0.105813i | −0.998599 | − | 0.0529064i | \(-0.983151\pi\) | ||
0.998599 | − | 0.0529064i | \(-0.0168485\pi\) | |||||||
\(522\) | −3.79242 | − | 3.79242i | −0.165990 | − | 0.165990i | ||||
\(523\) | 24.1447 | 1.05577 | 0.527887 | − | 0.849315i | \(-0.322985\pi\) | ||||
0.527887 | + | 0.849315i | \(0.322985\pi\) | |||||||
\(524\) | −15.2680 | − | 15.2680i | −0.666986 | − | 0.666986i | ||||
\(525\) | 4.51483 | + | 22.9121i | 0.197043 | + | 0.999967i | ||||
\(526\) | 11.1111 | − | 11.1111i | 0.484468 | − | 0.484468i | ||||
\(527\) | 29.1594 | − | 29.1594i | 1.27020 | − | 1.27020i | ||||
\(528\) | 2.82629 | + | 2.82629i | 0.122999 | + | 0.122999i | ||||
\(529\) | 11.9014 | 0.517453 | ||||||||
\(530\) | 23.3871 | + | 19.2284i | 1.01587 | + | 0.835227i | ||||
\(531\) | −7.71879 | + | 7.71879i | −0.334967 | + | 0.334967i | ||||
\(532\) | 11.6680 | 0.505870 | ||||||||
\(533\) | − | 28.0146i | − | 1.21345i | ||||||
\(534\) | − | 3.40131i | − | 0.147189i | ||||||
\(535\) | 9.25339 | − | 11.2547i | 0.400059 | − | 0.486583i | ||||
\(536\) | −7.88856 | − | 7.88856i | −0.340734 | − | 0.340734i | ||||
\(537\) | 5.86451i | 0.253072i | ||||||||
\(538\) | − | 5.86174i | − | 0.252717i | ||||||
\(539\) | −36.4788 | −1.57125 | ||||||||
\(540\) | −9.19650 | − | 7.56118i | −0.395754 | − | 0.325381i | ||||
\(541\) | 12.3532 | − | 12.3532i | 0.531107 | − | 0.531107i | −0.389795 | − | 0.920902i | \(-0.627454\pi\) |
0.920902 | + | 0.389795i | \(0.127454\pi\) | |||||||
\(542\) | 4.91311 | 0.211036 | ||||||||
\(543\) | 4.25652 | − | 4.25652i | 0.182665 | − | 0.182665i | ||||
\(544\) | 5.37801i | 0.230580i | ||||||||
\(545\) | −35.6932 | − | 29.3462i | −1.52893 | − | 1.25705i | ||||
\(546\) | 20.6222i | 0.882550i | ||||||||
\(547\) | −34.8143 | −1.48855 | −0.744277 | − | 0.667871i | \(-0.767206\pi\) | ||||
−0.744277 | + | 0.667871i | \(0.767206\pi\) | |||||||
\(548\) | −14.4220 | + | 14.4220i | −0.616075 | + | 0.616075i | ||||
\(549\) | −2.50066 | + | 2.50066i | −0.106725 | + | 0.106725i | ||||
\(550\) | 3.43685 | + | 17.4416i | 0.146548 | + | 0.743710i | ||||
\(551\) | 8.67587 | 0.369605 | ||||||||
\(552\) | 4.69625 | − | 4.69625i | 0.199886 | − | 0.199886i | ||||
\(553\) | 11.9305 | 0.507336 | ||||||||
\(554\) | −8.21627 | −0.349076 | ||||||||
\(555\) | −2.87320 | − | 15.0185i | −0.121961 | − | 0.637498i | ||||
\(556\) | 1.56244 | 0.0662624 | ||||||||
\(557\) | 31.3271 | 1.32737 | 0.663685 | − | 0.748012i | \(-0.268992\pi\) | ||||
0.663685 | + | 0.748012i | \(0.268992\pi\) | |||||||
\(558\) | 9.41344 | − | 9.41344i | 0.398503 | − | 0.398503i | ||||
\(559\) | −7.88341 | −0.333433 | ||||||||
\(560\) | 5.89983 | − | 7.17584i | 0.249313 | − | 0.303235i | ||||
\(561\) | 15.1998 | − | 15.1998i | 0.641737 | − | 0.641737i | ||||
\(562\) | 7.17894 | − | 7.17894i | 0.302825 | − | 0.302825i | ||||
\(563\) | 22.9644 | 0.967836 | 0.483918 | − | 0.875113i | \(-0.339213\pi\) | ||||
0.483918 | + | 0.875113i | \(0.339213\pi\) | |||||||
\(564\) | 2.90383i | 0.122273i | ||||||||
\(565\) | 1.87175 | + | 19.1804i | 0.0787452 | + | 0.806926i | ||||
\(566\) | − | 21.1149i | − | 0.887524i | ||||||
\(567\) | 2.28327 | − | 2.28327i | 0.0958884 | − | 0.0958884i | ||||
\(568\) | 11.2579 | 0.472370 | ||||||||
\(569\) | 30.2581 | − | 30.2581i | 1.26849 | − | 1.26849i | 0.321616 | − | 0.946870i | \(-0.395774\pi\) |
0.946870 | − | 0.321616i | \(-0.104226\pi\) | |||||||
\(570\) | 7.02659 | − | 0.685701i | 0.294312 | − | 0.0287209i | ||||
\(571\) | 25.3502 | 1.06087 | 0.530436 | − | 0.847725i | \(-0.322028\pi\) | ||||
0.530436 | + | 0.847725i | \(0.322028\pi\) | |||||||
\(572\) | 15.6984i | 0.656383i | ||||||||
\(573\) | 16.0215i | 0.669307i | ||||||||
\(574\) | −18.6390 | − | 18.6390i | −0.777977 | − | 0.777977i | ||||
\(575\) | 28.9814 | − | 5.71078i | 1.20861 | − | 0.238156i | ||||
\(576\) | 1.73617i | 0.0723402i | ||||||||
\(577\) | 29.6723i | 1.23527i | 0.786464 | + | 0.617637i | \(0.211910\pi\) | ||||
−0.786464 | + | 0.617637i | \(0.788090\pi\) | |||||||
\(578\) | 11.9230 | 0.495931 | ||||||||
\(579\) | −19.7019 | + | 19.7019i | −0.818784 | + | 0.818784i | ||||
\(580\) | 4.38690 | − | 5.33570i | 0.182156 | − | 0.221553i | ||||
\(581\) | −26.5145 | −1.10001 | ||||||||
\(582\) | 4.70596 | + | 4.70596i | 0.195068 | + | 0.195068i | ||||
\(583\) | −34.0406 | + | 34.0406i | −1.40982 | + | 1.40982i | ||||
\(584\) | 4.02333 | − | 4.02333i | 0.166487 | − | 0.166487i | ||||
\(585\) | −1.66486 | − | 17.0603i | −0.0688333 | − | 0.705356i | ||||
\(586\) | −8.03410 | − | 8.03410i | −0.331886 | − | 0.331886i | ||||
\(587\) | −16.9046 | −0.697726 | −0.348863 | − | 0.937174i | \(-0.613432\pi\) | ||||
−0.348863 | + | 0.937174i | \(0.613432\pi\) | |||||||
\(588\) | 8.15611 | + | 8.15611i | 0.336352 | + | 0.336352i | ||||
\(589\) | 21.5350i | 0.887335i | ||||||||
\(590\) | −10.8598 | − | 8.92875i | −0.447093 | − | 0.367591i | ||||
\(591\) | 17.9664i | 0.739038i | ||||||||
\(592\) | −3.88900 | + | 4.67714i | −0.159837 | + | 0.192229i | ||||
\(593\) | 13.2570 | + | 13.2570i | 0.544398 | + | 0.544398i | 0.924815 | − | 0.380417i | \(-0.124220\pi\) |
−0.380417 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(594\) | 13.3858 | − | 13.3858i | 0.549226 | − | 0.549226i | ||||
\(595\) | −38.5917 | − | 31.7293i | −1.58211 | − | 1.30078i | ||||
\(596\) | 8.42600i | 0.345142i | ||||||||
\(597\) | − | 10.9809i | − | 0.449417i | ||||||
\(598\) | 26.0849 | 1.06669 | ||||||||
\(599\) | 9.47521i | 0.387147i | 0.981086 | + | 0.193573i | \(0.0620077\pi\) | ||||
−0.981086 | + | 0.193573i | \(0.937992\pi\) | |||||||
\(600\) | 3.13124 | − | 4.66810i | 0.127832 | − | 0.190574i | ||||
\(601\) | −0.0866615 | −0.00353500 | −0.00176750 | − | 0.999998i | \(-0.500563\pi\) | ||||
−0.00176750 | + | 0.999998i | \(0.500563\pi\) | |||||||
\(602\) | −5.24509 | + | 5.24509i | −0.213774 | + | 0.213774i | ||||
\(603\) | −13.6958 | + | 13.6958i | −0.557738 | + | 0.557738i | ||||
\(604\) | − | 9.65715i | − | 0.392944i | ||||||
\(605\) | −3.65157 | + | 0.356344i | −0.148457 | + | 0.0144875i | ||||
\(606\) | 7.34026 | + | 7.34026i | 0.298178 | + | 0.298178i | ||||
\(607\) | −24.7793 | −1.00576 | −0.502880 | − | 0.864356i | \(-0.667726\pi\) | ||||
−0.502880 | + | 0.864356i | \(0.667726\pi\) | |||||||
\(608\) | −1.98590 | − | 1.98590i | −0.0805390 | − | 0.0805390i | ||||
\(609\) | 10.2022 | + | 10.2022i | 0.413413 | + | 0.413413i | ||||
\(610\) | −3.51827 | − | 2.89265i | −0.142450 | − | 0.117120i | ||||
\(611\) | −8.06454 | + | 8.06454i | −0.326256 | + | 0.326256i | ||||
\(612\) | 9.33711 | 0.377430 | ||||||||
\(613\) | −3.88165 | + | 3.88165i | −0.156779 | + | 0.156779i | −0.781138 | − | 0.624359i | \(-0.785360\pi\) |
0.624359 | + | 0.781138i | \(0.285360\pi\) | |||||||
\(614\) | −3.81755 | − | 3.81755i | −0.154064 | − | 0.154064i | ||||
\(615\) | −12.3200 | − | 10.1293i | −0.496791 | − | 0.408452i | ||||
\(616\) | 10.4447 | + | 10.4447i | 0.420827 | + | 0.420827i | ||||
\(617\) | −34.7871 | − | 34.7871i | −1.40047 | − | 1.40047i | −0.798563 | − | 0.601911i | \(-0.794406\pi\) |
−0.601911 | − | 0.798563i | \(-0.705594\pi\) | |||||||
\(618\) | 6.39071 | + | 6.39071i | 0.257072 | + | 0.257072i | ||||
\(619\) | −14.8991 | −0.598845 | −0.299422 | − | 0.954121i | \(-0.596794\pi\) | ||||
−0.299422 | + | 0.954121i | \(0.596794\pi\) | |||||||
\(620\) | 13.2441 | + | 10.8890i | 0.531897 | + | 0.437315i | ||||
\(621\) | −22.2422 | − | 22.2422i | −0.892550 | − | 0.892550i | ||||
\(622\) | −8.92270 | − | 8.92270i | −0.357768 | − | 0.357768i | ||||
\(623\) | − | 12.5697i | − | 0.503593i | ||||||
\(624\) | 3.50993 | − | 3.50993i | 0.140510 | − | 0.140510i | ||||
\(625\) | 23.1311 | − | 9.48423i | 0.925245 | − | 0.379369i | ||||
\(626\) | 29.7794 | 1.19022 | ||||||||
\(627\) | 11.2255i | 0.448303i | ||||||||
\(628\) | −13.7789 | + | 13.7789i | −0.549840 | + | 0.549840i | ||||
\(629\) | 25.1537 | + | 20.9151i | 1.00294 | + | 0.833939i | ||||
\(630\) | −12.4584 | − | 10.2431i | −0.496356 | − | 0.408094i | ||||
\(631\) | −26.9215 | − | 26.9215i | −1.07173 | − | 1.07173i | −0.997220 | − | 0.0745080i | \(-0.976261\pi\) |
−0.0745080 | − | 0.997220i | \(-0.523739\pi\) | |||||||
\(632\) | −2.03059 | − | 2.03059i | −0.0807724 | − | 0.0807724i | ||||
\(633\) | 18.1180 | − | 18.1180i | 0.720128 | − | 0.720128i | ||||
\(634\) | 16.2699 | + | 16.2699i | 0.646160 | + | 0.646160i | ||||
\(635\) | −8.49450 | + | 10.3317i | −0.337094 | + | 0.410000i | ||||
\(636\) | 15.2219 | 0.603589 | ||||||||
\(637\) | 45.3024i | 1.79495i | ||||||||
\(638\) | 7.76627 | + | 7.76627i | 0.307470 | + | 0.307470i | ||||
\(639\) | − | 19.5455i | − | 0.773210i | ||||||
\(640\) | −2.22550 | + | 0.217179i | −0.0879705 | + | 0.00858474i | ||||
\(641\) | −13.9581 | −0.551314 | −0.275657 | − | 0.961256i | \(-0.588895\pi\) | ||||
−0.275657 | + | 0.961256i | \(0.588895\pi\) | |||||||
\(642\) | − | 7.32535i | − | 0.289109i | ||||||
\(643\) | 32.7954i | 1.29332i | 0.762777 | + | 0.646662i | \(0.223836\pi\) | ||||
−0.762777 | + | 0.646662i | \(0.776164\pi\) | |||||||
\(644\) | 17.3552 | − | 17.3552i | 0.683889 | − | 0.683889i | ||||
\(645\) | −2.85042 | + | 3.46690i | −0.112235 | + | 0.136509i | ||||
\(646\) | −10.6802 | + | 10.6802i | −0.420207 | + | 0.420207i | ||||
\(647\) | 0.428355 | 0.0168404 | 0.00842020 | − | 0.999965i | \(-0.497320\pi\) | ||||
0.00842020 | + | 0.999965i | \(0.497320\pi\) | |||||||
\(648\) | −0.777232 | −0.0305325 | ||||||||
\(649\) | 15.8068 | − | 15.8068i | 0.620473 | − | 0.620473i | ||||
\(650\) | 21.6604 | − | 4.26818i | 0.849591 | − | 0.167412i | ||||
\(651\) | −25.3235 | + | 25.3235i | −0.992508 | + | 0.992508i | ||||
\(652\) | 9.92434i | 0.388667i | ||||||||
\(653\) | − | 35.6290i | − | 1.39427i | −0.716939 | − | 0.697136i | \(-0.754457\pi\) | ||
0.716939 | − | 0.697136i | \(-0.245543\pi\) | |||||||
\(654\) | −23.2316 | −0.908429 | ||||||||
\(655\) | −37.2948 | − | 30.6630i | −1.45723 | − | 1.19810i | ||||
\(656\) | 6.34477i | 0.247722i | ||||||||
\(657\) | −6.98517 | − | 6.98517i | −0.272518 | − | 0.272518i | ||||
\(658\) | 10.7312i | 0.418346i | ||||||||
\(659\) | −23.0667 | −0.898552 | −0.449276 | − | 0.893393i | \(-0.648318\pi\) | ||||
−0.449276 | + | 0.893393i | \(0.648318\pi\) | |||||||
\(660\) | 6.90371 | + | 5.67609i | 0.268727 | + | 0.220942i | ||||
\(661\) | 2.71363 | + | 2.71363i | 0.105548 | + | 0.105548i | 0.757909 | − | 0.652361i | \(-0.226221\pi\) |
−0.652361 | + | 0.757909i | \(0.726221\pi\) | |||||||
\(662\) | −15.6327 | + | 15.6327i | −0.607581 | + | 0.607581i | ||||
\(663\) | −18.8764 | − | 18.8764i | −0.733100 | − | 0.733100i | ||||
\(664\) | 4.51281 | + | 4.51281i | 0.175131 | + | 0.175131i | ||||
\(665\) | 25.9670 | − | 2.53403i | 1.00696 | − | 0.0982655i | ||||
\(666\) | 8.12030 | + | 6.75195i | 0.314655 | + | 0.261633i | ||||
\(667\) | 12.9047 | − | 12.9047i | 0.499671 | − | 0.499671i | ||||
\(668\) | − | 17.7622i | − | 0.687239i | ||||||
\(669\) | 11.4999 | 0.444610 | ||||||||
\(670\) | −19.2692 | − | 15.8427i | −0.744433 | − | 0.612058i | ||||
\(671\) | 5.12095 | − | 5.12095i | 0.197692 | − | 0.197692i | ||||
\(672\) | − | 4.67054i | − | 0.180170i | ||||||
\(673\) | −19.5626 | − | 19.5626i | −0.754083 | − | 0.754083i | 0.221156 | − | 0.975238i | \(-0.429017\pi\) |
−0.975238 | + | 0.221156i | \(0.929017\pi\) | |||||||
\(674\) | −22.0252 | − | 22.0252i | −0.848378 | − | 0.848378i | ||||
\(675\) | −22.1089 | − | 14.8301i | −0.850972 | − | 0.570810i | ||||
\(676\) | 6.49561 | 0.249831 | ||||||||
\(677\) | −23.4376 | − | 23.4376i | −0.900781 | − | 0.900781i | 0.0947229 | − | 0.995504i | \(-0.469803\pi\) |
−0.995504 | + | 0.0947229i | \(0.969803\pi\) | |||||||
\(678\) | 6.85111 | + | 6.85111i | 0.263115 | + | 0.263115i | ||||
\(679\) | 17.3910 | + | 17.3910i | 0.667406 | + | 0.667406i | ||||
\(680\) | 1.16799 | + | 11.9687i | 0.0447903 | + | 0.458980i | ||||
\(681\) | 2.81269 | + | 2.81269i | 0.107783 | + | 0.107783i | ||||
\(682\) | −19.2772 | + | 19.2772i | −0.738163 | + | 0.738163i | ||||
\(683\) | −15.8368 | −0.605977 | −0.302988 | − | 0.952994i | \(-0.597984\pi\) | ||||
−0.302988 | + | 0.952994i | \(0.597984\pi\) | |||||||
\(684\) | −3.44786 | + | 3.44786i | −0.131832 | + | 0.131832i | ||||
\(685\) | −28.9639 | + | 35.2281i | −1.10665 | + | 1.34600i | ||||
\(686\) | 9.57729 | + | 9.57729i | 0.365663 | + | 0.365663i | ||||
\(687\) | −8.16348 | − | 8.16348i | −0.311456 | − | 0.311456i | ||||
\(688\) | 1.78544 | 0.0680693 | ||||||||
\(689\) | 42.2745 | + | 42.2745i | 1.61053 | + | 1.61053i | ||||
\(690\) | 9.43157 | − | 11.4714i | 0.359054 | − | 0.436710i | ||||
\(691\) | − | 25.5077i | − | 0.970358i | −0.874415 | − | 0.485179i | \(-0.838754\pi\) | ||
0.874415 | − | 0.485179i | \(-0.161246\pi\) | |||||||
\(692\) | −4.93605 | + | 4.93605i | −0.187640 | + | 0.187640i | ||||
\(693\) | 18.1337 | − | 18.1337i | 0.688841 | − | 0.688841i | ||||
\(694\) | 35.2079 | 1.33647 | ||||||||
\(695\) | 3.47721 | − | 0.339330i | 0.131898 | − | 0.0128715i | ||||
\(696\) | − | 3.47285i | − | 0.131638i | ||||||
\(697\) | 34.1222 | 1.29247 | ||||||||
\(698\) | 7.00272i | 0.265057i | ||||||||
\(699\) | − | 1.16349i | − | 0.0440074i | ||||||
\(700\) | 11.5716 | − | 17.2511i | 0.437366 | − | 0.652031i | ||||
\(701\) | 6.69201 | − | 6.69201i | 0.252754 | − | 0.252754i | −0.569345 | − | 0.822099i | \(-0.692803\pi\) |
0.822099 | + | 0.569345i | \(0.192803\pi\) | |||||||
\(702\) | −16.6236 | − | 16.6236i | −0.627418 | − | 0.627418i | ||||
\(703\) | −17.0115 | + | 1.56518i | −0.641602 | + | 0.0590318i | ||||
\(704\) | − | 3.55539i | − | 0.133999i | ||||||
\(705\) | 0.630650 | + | 6.46246i | 0.0237516 | + | 0.243390i | ||||
\(706\) | − | 24.1991i | − | 0.910746i | ||||||
\(707\) | 27.1262 | + | 27.1262i | 1.02018 | + | 1.02018i | ||||
\(708\) | −7.06835 | −0.265645 | ||||||||
\(709\) | −9.99501 | − | 9.99501i | −0.375370 | − | 0.375370i | 0.494058 | − | 0.869429i | \(-0.335513\pi\) |
−0.869429 | + | 0.494058i | \(0.835513\pi\) | |||||||
\(710\) | 25.0544 | − | 2.44497i | 0.940274 | − | 0.0917581i | ||||
\(711\) | −3.52544 | + | 3.52544i | −0.132214 | + | 0.132214i | ||||
\(712\) | −2.13937 | + | 2.13937i | −0.0801764 | + | 0.0801764i | ||||
\(713\) | 32.0316 | + | 32.0316i | 1.19959 | + | 1.19959i | ||||
\(714\) | −25.1182 | −0.940025 | ||||||||
\(715\) | 3.40936 | + | 34.9367i | 0.127503 | + | 1.30656i | ||||
\(716\) | 3.68868 | − | 3.68868i | 0.137853 | − | 0.137853i | ||||
\(717\) | −9.94742 | −0.371493 | ||||||||
\(718\) | 5.19872i | 0.194014i | ||||||||
\(719\) | 19.0225i | 0.709421i | 0.934976 | + | 0.354711i | \(0.115421\pi\) | ||||
−0.934976 | + | 0.354711i | \(0.884579\pi\) | |||||||
\(720\) | 0.377058 | + | 3.86383i | 0.0140521 | + | 0.143996i | ||||
\(721\) | 23.6171 | + | 23.6171i | 0.879545 | + | 0.879545i | ||||
\(722\) | 11.1124i | 0.413560i | ||||||||
\(723\) | − | 10.0409i | − | 0.373427i | ||||||
\(724\) | −5.35458 | −0.199001 | ||||||||
\(725\) | 8.60423 | − | 12.8273i | 0.319553 | − | 0.476394i | ||||
\(726\) | −1.30432 | + | 1.30432i | −0.0484077 | + | 0.0484077i | ||||
\(727\) | 32.8141 | 1.21701 | 0.608504 | − | 0.793551i | \(-0.291770\pi\) | ||||
0.608504 | + | 0.793551i | \(0.291770\pi\) | |||||||
\(728\) | 12.9711 | − | 12.9711i | 0.480739 | − | 0.480739i | ||||
\(729\) | 19.3066i | 0.715059i | ||||||||
\(730\) | 8.08013 | − | 9.82769i | 0.299059 | − | 0.363739i | ||||
\(731\) | − | 9.60212i | − | 0.355147i | ||||||
\(732\) | −2.28994 | −0.0846384 | ||||||||
\(733\) | −30.2477 | + | 30.2477i | −1.11722 | + | 1.11722i | −0.125077 | + | 0.992147i | \(0.539918\pi\) |
−0.992147 | + | 0.125077i | \(0.960082\pi\) | |||||||
\(734\) | −22.4335 | + | 22.4335i | −0.828034 | + | 0.828034i | ||||
\(735\) | 19.9227 | + | 16.3801i | 0.734861 | + | 0.604188i | ||||
\(736\) | −5.90774 | −0.217762 | ||||||||
\(737\) | 28.0469 | − | 28.0469i | 1.03312 | − | 1.03312i | ||||
\(738\) | 11.0156 | 0.405489 | ||||||||
\(739\) | 27.9037 | 1.02646 | 0.513228 | − | 0.858253i | \(-0.328450\pi\) | ||||
0.513228 | + | 0.858253i | \(0.328450\pi\) | |||||||
\(740\) | −7.63918 | + | 11.2536i | −0.280822 | + | 0.413690i | ||||
\(741\) | 13.9408 | 0.512126 | ||||||||
\(742\) | 56.2532 | 2.06512 | ||||||||
\(743\) | −10.9502 | + | 10.9502i | −0.401723 | + | 0.401723i | −0.878840 | − | 0.477117i | \(-0.841682\pi\) |
0.477117 | + | 0.878840i | \(0.341682\pi\) | |||||||
\(744\) | 8.62020 | 0.316032 | ||||||||
\(745\) | 1.82995 | + | 18.7520i | 0.0670440 | + | 0.687021i | ||||
\(746\) | 10.4263 | − | 10.4263i | 0.381733 | − | 0.381733i | ||||
\(747\) | 7.83498 | − | 7.83498i | 0.286667 | − | 0.286667i | ||||
\(748\) | −19.1209 | −0.699130 | ||||||||
\(749\) | − | 27.0711i | − | 0.989155i | ||||||
\(750\) | 5.95476 | − | 11.0689i | 0.217437 | − | 0.404178i | ||||
\(751\) | − | 44.1738i | − | 1.61193i | −0.591966 | − | 0.805963i | \(-0.701648\pi\) | ||
0.591966 | − | 0.805963i | \(-0.298352\pi\) | |||||||
\(752\) | 1.82646 | − | 1.82646i | 0.0666043 | − | 0.0666043i | ||||
\(753\) | −6.20423 | −0.226095 | ||||||||
\(754\) | 9.64481 | − | 9.64481i | 0.351243 | − | 0.351243i | ||||
\(755\) | −2.09733 | − | 21.4919i | −0.0763295 | − | 0.782172i | ||||
\(756\) | −22.1205 | −0.804513 | ||||||||
\(757\) | 3.52885i | 0.128258i | 0.997942 | + | 0.0641291i | \(0.0204269\pi\) | ||||
−0.997942 | + | 0.0641291i | \(0.979573\pi\) | |||||||
\(758\) | 15.9233i | 0.578361i | ||||||||
\(759\) | 16.6970 | + | 16.6970i | 0.606063 | + | 0.606063i | ||||
\(760\) | −4.85091 | − | 3.98832i | −0.175961 | − | 0.144672i | ||||
\(761\) | − | 15.9891i | − | 0.579605i | −0.957086 | − | 0.289803i | \(-0.906410\pi\) | ||
0.957086 | − | 0.289803i | \(-0.0935896\pi\) | |||||||
\(762\) | 6.72459i | 0.243606i | ||||||||
\(763\) | −85.8533 | −3.10810 | ||||||||
\(764\) | 10.0773 | − | 10.0773i | 0.364583 | − | 0.364583i | ||||
\(765\) | 20.7797 | − | 2.02782i | 0.751292 | − | 0.0733160i | ||||
\(766\) | −24.2531 | −0.876301 | ||||||||
\(767\) | −19.6303 | − | 19.6303i | −0.708808 | − | 0.708808i | ||||
\(768\) | −0.794932 | + | 0.794932i | −0.0286846 | + | 0.0286846i | ||||
\(769\) | −10.5741 | + | 10.5741i | −0.381313 | + | 0.381313i | −0.871575 | − | 0.490262i | \(-0.836901\pi\) |
0.490262 | + | 0.871575i | \(0.336901\pi\) | |||||||
\(770\) | 25.5129 | + | 20.9762i | 0.919421 | + | 0.755929i | ||||
\(771\) | −1.76397 | − | 1.76397i | −0.0635280 | − | 0.0635280i | ||||
\(772\) | 24.7844 | 0.892011 | ||||||||
\(773\) | −5.39429 | − | 5.39429i | −0.194019 | − | 0.194019i | 0.603411 | − | 0.797430i | \(-0.293808\pi\) |
−0.797430 | + | 0.603411i | \(0.793808\pi\) | |||||||
\(774\) | − | 3.09982i | − | 0.111421i | ||||||
\(775\) | 31.8396 | + | 21.3572i | 1.14371 | + | 0.767173i | ||||
\(776\) | − | 5.91995i | − | 0.212514i | ||||||
\(777\) | −21.8448 | − | 18.1637i | −0.783678 | − | 0.651620i | ||||
\(778\) | −19.7499 | − | 19.7499i | −0.708070 | − | 0.708070i | ||||
\(779\) | −12.6001 | + | 12.6001i | −0.451445 | + | 0.451445i | ||||
\(780\) | 7.04905 | − | 8.57362i | 0.252397 | − | 0.306985i | ||||
\(781\) | 40.0261i | 1.43225i | ||||||||
\(782\) | 31.7719i | 1.13616i | ||||||||
\(783\) | −16.4480 | −0.587803 | ||||||||
\(784\) | − | 10.2601i | − | 0.366433i | ||||||
\(785\) | −27.6725 | + | 33.6575i | −0.987674 | + | 1.20129i | ||||
\(786\) | −24.2741 | −0.865827 | ||||||||
\(787\) | −20.2260 | + | 20.2260i | −0.720978 | + | 0.720978i | −0.968804 | − | 0.247827i | \(-0.920284\pi\) |
0.247827 | + | 0.968804i | \(0.420284\pi\) | |||||||
\(788\) | 11.3006 | − | 11.3006i | 0.402566 | − | 0.402566i | ||||
\(789\) | − | 17.6652i | − | 0.628897i | ||||||
\(790\) | −4.96006 | − | 4.07806i | −0.176471 | − | 0.145091i | ||||
\(791\) | 25.3185 | + | 25.3185i | 0.900223 | + | 0.900223i | ||||
\(792\) | −6.17274 | −0.219339 | ||||||||
\(793\) | −6.35962 | − | 6.35962i | −0.225837 | − | 0.225837i | ||||
\(794\) | 1.71599 | + | 1.71599i | 0.0608983 | + | 0.0608983i | ||||
\(795\) | 33.8764 | − | 3.30588i | 1.20147 | − | 0.117247i | ||||
\(796\) | −6.90680 | + | 6.90680i | −0.244805 | + | 0.244805i | ||||
\(797\) | −40.0646 | −1.41916 | −0.709580 | − | 0.704625i | \(-0.751115\pi\) | ||||
−0.709580 | + | 0.704625i | \(0.751115\pi\) | |||||||
\(798\) | 9.27524 | − | 9.27524i | 0.328340 | − | 0.328340i | ||||
\(799\) | −9.82274 | − | 9.82274i | −0.347504 | − | 0.347504i | ||||
\(800\) | −4.90567 | + | 0.966660i | −0.173442 | + | 0.0341766i | ||||
\(801\) | 3.71431 | + | 3.71431i | 0.131239 | + | 0.131239i | ||||
\(802\) | −9.29247 | − | 9.29247i | −0.328129 | − | 0.328129i | ||||
\(803\) | 14.3045 | + | 14.3045i | 0.504795 | + | 0.504795i | ||||
\(804\) | −12.5417 | −0.442313 | ||||||||
\(805\) | 34.8547 | − | 42.3930i | 1.22847 | − | 1.49416i | ||||
\(806\) | 23.9401 | + | 23.9401i | 0.843254 | + | 0.843254i | ||||
\(807\) | −4.65968 | − | 4.65968i | −0.164029 | − | 0.164029i | ||||
\(808\) | − | 9.23382i | − | 0.324844i | ||||||
\(809\) | −33.6427 | + | 33.6427i | −1.18282 | + | 1.18282i | −0.203803 | + | 0.979012i | \(0.565330\pi\) |
−0.979012 | + | 0.203803i | \(0.934670\pi\) | |||||||
\(810\) | −1.72973 | + | 0.168798i | −0.0607764 | + | 0.00593096i | ||||
\(811\) | −11.9502 | −0.419628 | −0.209814 | − | 0.977741i | \(-0.567286\pi\) | ||||
−0.209814 | + | 0.977741i | \(0.567286\pi\) | |||||||
\(812\) | − | 12.8340i | − | 0.450386i | ||||||
\(813\) | 3.90559 | − | 3.90559i | 0.136975 | − | 0.136975i | ||||
\(814\) | −16.6291 | − | 13.8269i | −0.582848 | − | 0.484633i | ||||
\(815\) | 2.15535 | + | 22.0866i | 0.0754988 | + | 0.773659i | ||||
\(816\) | 4.27515 | + | 4.27515i | 0.149660 | + | 0.149660i | ||||
\(817\) | 3.54571 | + | 3.54571i | 0.124049 | + | 0.124049i | ||||
\(818\) | −18.3866 | + | 18.3866i | −0.642873 | + | 0.642873i | ||||
\(819\) | −22.5199 | − | 22.5199i | −0.786909 | − | 0.786909i | ||||
\(820\) | 1.37795 | + | 14.1203i | 0.0481200 | + | 0.493101i | ||||
\(821\) | −23.5565 | −0.822126 | −0.411063 | − | 0.911607i | \(-0.634842\pi\) | ||||
−0.411063 | + | 0.911607i | \(0.634842\pi\) | |||||||
\(822\) | 22.9290i | 0.799739i | ||||||||
\(823\) | 12.5168 | + | 12.5168i | 0.436309 | + | 0.436309i | 0.890768 | − | 0.454459i | \(-0.150167\pi\) |
−0.454459 | + | 0.890768i | \(0.650167\pi\) | |||||||
\(824\) | − | 8.03931i | − | 0.280063i | ||||||
\(825\) | 16.5969 | + | 11.1328i | 0.577830 | + | 0.387594i | ||||
\(826\) | −26.1213 | −0.908877 | ||||||||
\(827\) | 2.77988i | 0.0966659i | 0.998831 | + | 0.0483329i | \(0.0153908\pi\) | ||||
−0.998831 | + | 0.0483329i | \(0.984609\pi\) | |||||||
\(828\) | 10.2568i | 0.356449i | ||||||||
\(829\) | −20.9695 | + | 20.9695i | −0.728301 | + | 0.728301i | −0.970281 | − | 0.241980i | \(-0.922203\pi\) |
0.241980 | + | 0.970281i | \(0.422203\pi\) | |||||||
\(830\) | 11.0233 | + | 9.06315i | 0.382625 | + | 0.314586i | ||||
\(831\) | −6.53137 | + | 6.53137i | −0.226571 | + | 0.226571i | ||||
\(832\) | −4.41538 | −0.153076 | ||||||||
\(833\) | −55.1791 | −1.91184 | ||||||||
\(834\) | 1.24204 | − | 1.24204i | 0.0430082 | − | 0.0430082i | ||||
\(835\) | −3.85756 | − | 39.5297i | −0.133496 | − | 1.36798i | ||||
\(836\) | 7.06065 | − | 7.06065i | 0.244198 | − | 0.244198i | ||||
\(837\) | − | 40.8267i | − | 1.41118i | ||||||
\(838\) | − | 8.04256i | − | 0.277825i | ||||||
\(839\) | −28.7182 | −0.991464 | −0.495732 | − | 0.868476i | \(-0.665100\pi\) | ||||
−0.495732 | + | 0.868476i | \(0.665100\pi\) | |||||||
\(840\) | −1.01434 | − | 10.3943i | −0.0349981 | − | 0.358636i | ||||
\(841\) | 19.4571i | 0.670934i | ||||||||
\(842\) | −11.0268 | − | 11.0268i | −0.380010 | − | 0.380010i | ||||
\(843\) | − | 11.4135i | − | 0.393103i | ||||||
\(844\) | −22.7919 | −0.784531 | ||||||||
\(845\) | 14.4560 | − | 1.41071i | 0.497300 | − | 0.0485298i | ||||
\(846\) | −3.17104 | − | 3.17104i | −0.109023 | − | 0.109023i | ||||
\(847\) | −4.82014 | + | 4.82014i | −0.165622 | + | 0.165622i | ||||
\(848\) | −9.57437 | − | 9.57437i | −0.328785 | − | 0.328785i | ||||
\(849\) | −16.7849 | − | 16.7849i | −0.576056 | − | 0.576056i | ||||
\(850\) | 5.19871 | + | 26.3827i | 0.178314 | + | 0.904920i | ||||
\(851\) | −22.9752 | + | 27.6314i | −0.787580 | + | 0.947191i | ||||
\(852\) | 8.94925 | − | 8.94925i | 0.306596 | − | 0.306596i | ||||
\(853\) | − | 11.9189i | − | 0.408097i | −0.978961 | − | 0.204048i | \(-0.934590\pi\) | ||
0.978961 | − | 0.204048i | \(-0.0654100\pi\) | |||||||
\(854\) | −8.46253 | −0.289582 | ||||||||
\(855\) | −6.92439 | + | 8.42199i | −0.236809 | + | 0.288026i | ||||
\(856\) | −4.60753 | + | 4.60753i | −0.157482 | + | 0.157482i | ||||
\(857\) | − | 17.5942i | − | 0.601008i | −0.953781 | − | 0.300504i | \(-0.902845\pi\) | ||
0.953781 | − | 0.300504i | \(-0.0971548\pi\) | |||||||
\(858\) | 12.4792 | + | 12.4792i | 0.426032 | + | 0.426032i | ||||
\(859\) | 15.4861 | + | 15.4861i | 0.528379 | + | 0.528379i | 0.920089 | − | 0.391710i | \(-0.128116\pi\) |
−0.391710 | + | 0.920089i | \(0.628116\pi\) | |||||||
\(860\) | 3.97349 | − | 0.387760i | 0.135495 | − | 0.0132225i | ||||
\(861\) | −29.6335 | −1.00991 | ||||||||
\(862\) | −9.69563 | − | 9.69563i | −0.330234 | − | 0.330234i | ||||
\(863\) | −22.0613 | − | 22.0613i | −0.750974 | − | 0.750974i | 0.223687 | − | 0.974661i | \(-0.428191\pi\) |
−0.974661 | + | 0.223687i | \(0.928191\pi\) | |||||||
\(864\) | 3.76493 | + | 3.76493i | 0.128086 | + | 0.128086i | ||||
\(865\) | −9.91315 | + | 12.0572i | −0.337057 | + | 0.409956i | ||||
\(866\) | 7.39679 | + | 7.39679i | 0.251353 | + | 0.251353i | ||||
\(867\) | 9.47796 | − | 9.47796i | 0.321888 | − | 0.321888i | ||||
\(868\) | 31.8562 | 1.08127 | ||||||||
\(869\) | 7.21953 | − | 7.21953i | 0.244906 | − | 0.244906i | ||||
\(870\) | −0.754228 | − | 7.72880i | −0.0255707 | − | 0.262031i | ||||
\(871\) | −34.8310 | − | 34.8310i | −1.18020 | − | 1.18020i | ||||
\(872\) | 14.6123 | + | 14.6123i | 0.494836 | + | 0.494836i | ||||
\(873\) | −10.2780 | −0.347858 | ||||||||
\(874\) | −11.7322 | − | 11.7322i | −0.396848 | − | 0.396848i | ||||
\(875\) | 22.0060 | − | 40.9054i | 0.743939 | − | 1.38286i | ||||
\(876\) | − | 6.39655i | − | 0.216120i | ||||||
\(877\) | 23.3891 | − | 23.3891i | 0.789793 | − | 0.789793i | −0.191667 | − | 0.981460i | \(-0.561389\pi\) |
0.981460 | + | 0.191667i | \(0.0613893\pi\) | |||||||
\(878\) | −21.3840 | + | 21.3840i | −0.721675 | + | 0.721675i | ||||
\(879\) | −12.7731 | −0.430827 | ||||||||
\(880\) | −0.772154 | − | 7.91250i | −0.0260293 | − | 0.266730i | ||||
\(881\) | − | 16.5058i | − | 0.556094i | −0.960567 | − | 0.278047i | \(-0.910313\pi\) | ||
0.960567 | − | 0.278047i | \(-0.0896871\pi\) | |||||||
\(882\) | −17.8133 | −0.599805 | ||||||||
\(883\) | 33.7230i | 1.13487i | 0.823418 | + | 0.567435i | \(0.192064\pi\) | ||||
−0.823418 | + | 0.567435i | \(0.807936\pi\) | |||||||
\(884\) | 23.7460i | 0.798663i | ||||||||
\(885\) | −15.7306 | + | 1.53509i | −0.528778 | + | 0.0516016i | ||||
\(886\) | 0.537851 | − | 0.537851i | 0.0180695 | − | 0.0180695i | ||||
\(887\) | 39.4709 | + | 39.4709i | 1.32530 | + | 1.32530i | 0.909417 | + | 0.415885i | \(0.136528\pi\) |
0.415885 | + | 0.909417i | \(0.363472\pi\) | |||||||
\(888\) | 0.626522 | + | 6.80950i | 0.0210247 | + | 0.228512i | ||||
\(889\) | 24.8509i | 0.833473i | ||||||||
\(890\) | −4.29654 | + | 5.22579i | −0.144020 | + | 0.175169i | ||||
\(891\) | − | 2.76336i | − | 0.0925761i | ||||||
\(892\) | −7.23324 | − | 7.23324i | −0.242187 | − | 0.242187i | ||||
\(893\) | 7.25436 | 0.242758 | ||||||||
\(894\) | 6.69810 | + | 6.69810i | 0.224018 | + | 0.224018i | ||||
\(895\) | 7.40805 | − | 9.01025i | 0.247624 | − | 0.301180i | ||||
\(896\) | −2.93770 | + | 2.93770i | −0.0981416 | + | 0.0981416i | ||||
\(897\) | 20.7358 | − | 20.7358i | 0.692347 | − | 0.692347i | ||||
\(898\) | 17.9014 | + | 17.9014i | 0.597378 | + | 0.597378i | ||||
\(899\) | 23.6871 | 0.790011 | ||||||||
\(900\) | 1.67828 | + | 8.51705i | 0.0559427 | + | 0.283902i | ||||
\(901\) | −51.4910 | + | 51.4910i | −1.71541 | + | 1.71541i | ||||
\(902\) | −22.5581 | −0.751103 | ||||||||
\(903\) | 8.33898i | 0.277504i | ||||||||
\(904\) | − | 8.61849i | − | 0.286647i | ||||||
\(905\) | −11.9166 | + | 1.16290i | −0.396121 | + | 0.0386561i | ||||
\(906\) | −7.67678 | − | 7.67678i | −0.255044 | − | 0.255044i | ||||
\(907\) | − | 2.85857i | − | 0.0949173i | −0.998873 | − | 0.0474587i | \(-0.984888\pi\) | ||
0.998873 | − | 0.0474587i | \(-0.0151122\pi\) | |||||||
\(908\) | − | 3.53828i | − | 0.117422i | ||||||
\(909\) | −16.0314 | −0.531729 | ||||||||
\(910\) | 26.0500 | − | 31.6841i | 0.863549 | − | 1.05032i | ||||
\(911\) | 7.44807 | − | 7.44807i | 0.246765 | − | 0.246765i | −0.572876 | − | 0.819642i | \(-0.694172\pi\) |
0.819642 | + | 0.572876i | \(0.194172\pi\) | |||||||
\(912\) | −3.15731 | −0.104549 | ||||||||
\(913\) | −16.0448 | + | 16.0448i | −0.531005 | + | 0.531005i | ||||
\(914\) | 10.3305i | 0.341702i | ||||||||
\(915\) | −5.09624 | + | 0.497325i | −0.168477 | + | 0.0164411i | ||||
\(916\) | 10.2694i | 0.339311i | ||||||||
\(917\) | −89.7056 | −2.96234 | ||||||||
\(918\) | 20.2478 | − | 20.2478i | 0.668278 | − | 0.668278i | ||||
\(919\) | 7.70512 | − | 7.70512i | 0.254168 | − | 0.254168i | −0.568509 | − | 0.822677i | \(-0.692479\pi\) |
0.822677 | + | 0.568509i | \(0.192479\pi\) | |||||||
\(920\) | −13.1477 | + | 1.28304i | −0.433466 | + | 0.0423004i | ||||
\(921\) | −6.06939 | −0.199993 | ||||||||
\(922\) | 19.5325 | − | 19.5325i | 0.643268 | − | 0.643268i | ||||
\(923\) | 49.7079 | 1.63615 | ||||||||
\(924\) | 16.6056 | 0.546284 | ||||||||
\(925\) | −14.5569 | + | 26.7039i | −0.478629 | + | 0.878017i | ||||
\(926\) | −13.2709 | −0.436110 | ||||||||
\(927\) | −13.9576 | −0.458427 | ||||||||
\(928\) | −2.18437 | + | 2.18437i | −0.0717053 | + | 0.0717053i | ||||
\(929\) | 29.3928 | 0.964346 | 0.482173 | − | 0.876076i | \(-0.339848\pi\) | ||||
0.482173 | + | 0.876076i | \(0.339848\pi\) | |||||||
\(930\) | 19.1842 | − | 1.87212i | 0.629076 | − | 0.0613893i | ||||
\(931\) | 20.3756 | − | 20.3756i | 0.667784 | − | 0.667784i | ||||
\(932\) | −0.731820 | + | 0.731820i | −0.0239716 | + | 0.0239716i | ||||
\(933\) | −14.1859 | −0.464425 | ||||||||
\(934\) | − | 40.7473i | − | 1.33329i | ||||||
\(935\) | −42.5535 | + | 4.15265i | −1.39165 | + | 0.135806i | ||||
\(936\) | 7.66584i | 0.250566i | ||||||||
\(937\) | 10.7698 | − | 10.7698i | 0.351834 | − | 0.351834i | −0.508958 | − | 0.860791i | \(-0.669969\pi\) |
0.860791 | + | 0.508958i | \(0.169969\pi\) | |||||||
\(938\) | −46.3484 | −1.51333 | ||||||||
\(939\) | 23.6726 | − | 23.6726i | 0.772527 | − | 0.772527i | ||||
\(940\) | 3.66812 | − | 4.46146i | 0.119641 | − | 0.145517i | ||||
\(941\) | 29.3530 | 0.956880 | 0.478440 | − | 0.878120i | \(-0.341202\pi\) | ||||
0.478440 | + | 0.878120i | \(0.341202\pi\) | |||||||
\(942\) | 21.9066i | 0.713757i | ||||||||
\(943\) | 37.4833i | 1.22062i | ||||||||
\(944\) | 4.44588 | + | 4.44588i | 0.144701 | + | 0.144701i | ||||
\(945\) | −49.2290 | + | 4.80409i | −1.60142 | + | 0.156277i | ||||
\(946\) | 6.34794i | 0.206389i | ||||||||
\(947\) | − | 14.6562i | − | 0.476262i | −0.971233 | − | 0.238131i | \(-0.923465\pi\) | ||
0.971233 | − | 0.238131i | \(-0.0765347\pi\) | |||||||
\(948\) | −3.22836 | −0.104852 | ||||||||
\(949\) | 17.7646 | − | 17.7646i | 0.576662 | − | 0.576662i | ||||
\(950\) | −11.6619 | − | 7.82248i | −0.378361 | − | 0.253795i | ||||
\(951\) | 25.8669 | 0.838793 | ||||||||
\(952\) | 15.7990 | + | 15.7990i | 0.512047 | + | 0.512047i | ||||
\(953\) | 7.12766 | − | 7.12766i | 0.230887 | − | 0.230887i | −0.582176 | − | 0.813063i | \(-0.697798\pi\) |
0.813063 | + | 0.582176i | \(0.197798\pi\) | |||||||
\(954\) | −16.6227 | + | 16.6227i | −0.538179 | + | 0.538179i | ||||
\(955\) | 20.2384 | − | 24.6155i | 0.654898 | − | 0.796539i | ||||
\(956\) | 6.25677 | + | 6.25677i | 0.202358 | + | 0.202358i | ||||
\(957\) | 12.3473 | 0.399132 | ||||||||
\(958\) | −8.91382 | − | 8.91382i | −0.287992 | − | 0.287992i | ||||
\(959\) | 84.7347i | 2.73623i | ||||||||
\(960\) | −1.59648 | + | 1.94176i | −0.0515261 | + | 0.0626701i | ||||
\(961\) | 27.7956i | 0.896632i | ||||||||
\(962\) | −17.1714 | + | 20.6514i | −0.553629 | + | 0.665827i | ||||
\(963\) | 7.99944 | + | 7.99944i | 0.257778 | + | 0.257778i | ||||
\(964\) | −6.31560 | + | 6.31560i | −0.203412 | + | 0.203412i | ||||
\(965\) | 55.1576 | − | 5.38264i | 1.77559 | − | 0.173273i | ||||
\(966\) | − | 27.5924i | − | 0.887769i | ||||||
\(967\) | − | 38.4439i | − | 1.23627i | −0.786071 | − | 0.618136i | \(-0.787888\pi\) | ||
0.786071 | − | 0.618136i | \(-0.212112\pi\) | |||||||
\(968\) | 1.64079 | 0.0527370 | ||||||||
\(969\) | 16.9801i | 0.545478i | ||||||||
\(970\) | −1.28569 | − | 13.1748i | −0.0412809 | − | 0.423018i | ||||
\(971\) | −45.1188 | −1.44793 | −0.723965 | − | 0.689837i | \(-0.757682\pi\) | ||||
−0.723965 | + | 0.689837i | \(0.757682\pi\) | |||||||
\(972\) | 10.6769 | − | 10.6769i | 0.342463 | − | 0.342463i | ||||
\(973\) | 4.58999 | − | 4.58999i | 0.147148 | − | 0.147148i | ||||
\(974\) | 27.7847i | 0.890278i | ||||||||
\(975\) | 13.8256 | − | 20.6115i | 0.442775 | − | 0.660095i | ||||
\(976\) | 1.44033 | + | 1.44033i | 0.0461040 | + | 0.0461040i | ||||
\(977\) | 34.3176 | 1.09792 | 0.548959 | − | 0.835850i | \(-0.315024\pi\) | ||||
0.548959 | + | 0.835850i | \(0.315024\pi\) | |||||||
\(978\) | 7.88918 | + | 7.88918i | 0.252268 | + | 0.252268i | ||||
\(979\) | −7.60630 | − | 7.60630i | −0.243099 | − | 0.243099i | ||||
\(980\) | −2.22828 | − | 22.8339i | −0.0711798 | − | 0.729402i | ||||
\(981\) | 25.3694 | − | 25.3694i | 0.809984 | − | 0.809984i | ||||
\(982\) | 7.19820 | 0.229704 | ||||||||
\(983\) | −35.5214 | + | 35.5214i | −1.13296 | + | 1.13296i | −0.143272 | + | 0.989683i | \(0.545762\pi\) |
−0.989683 | + | 0.143272i | \(0.954238\pi\) | |||||||
\(984\) | 5.04366 | + | 5.04366i | 0.160786 | + | 0.160786i | ||||
\(985\) | 22.6951 | − | 27.6036i | 0.723127 | − | 0.879524i | ||||
\(986\) | 11.7475 | + | 11.7475i | 0.374118 | + | 0.374118i | ||||
\(987\) | 8.53057 | + | 8.53057i | 0.271531 | + | 0.271531i | ||||
\(988\) | −8.76852 | − | 8.76852i | −0.278964 | − | 0.278964i | ||||
\(989\) | 10.5479 | 0.335405 | ||||||||
\(990\) | −13.7374 | + | 1.34059i | −0.436604 | + | 0.0426067i | ||||
\(991\) | 32.2431 | + | 32.2431i | 1.02424 | + | 1.02424i | 0.999699 | + | 0.0245377i | \(0.00781138\pi\) |
0.0245377 | + | 0.999699i | \(0.492189\pi\) | |||||||
\(992\) | −5.42197 | − | 5.42197i | −0.172148 | − | 0.172148i | ||||
\(993\) | 24.8538i | 0.788713i | ||||||||
\(994\) | 33.0722 | − | 33.0722i | 1.04899 | − | 1.04899i | ||||
\(995\) | −13.8710 | + | 16.8711i | −0.439742 | + | 0.534849i | ||||
\(996\) | 7.17475 | 0.227341 | ||||||||
\(997\) | − | 2.02170i | − | 0.0640278i | −0.999487 | − | 0.0320139i | \(-0.989808\pi\) | ||
0.999487 | − | 0.0320139i | \(-0.0101921\pi\) | |||||||
\(998\) | 0.378337 | − | 0.378337i | 0.0119761 | − | 0.0119761i | ||||
\(999\) | 32.2509 | − | 2.96731i | 1.02037 | − | 0.0938815i |
(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 | 370.2.h.e.253.4 | yes | 20 | |
5.2 | odd | 4 | 370.2.g.e.327.7 | yes | 20 | ||
37.6 | odd | 4 | 370.2.g.e.43.7 | ✓ | 20 | ||
185.117 | even | 4 | inner | 370.2.h.e.117.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.7 | ✓ | 20 | 37.6 | odd | 4 | ||
370.2.g.e.327.7 | yes | 20 | 5.2 | odd | 4 | ||
370.2.h.e.117.4 | yes | 20 | 185.117 | even | 4 | inner | |
370.2.h.e.253.4 | yes | 20 | 1.1 | even | 1 | trivial |