Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(79,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.i (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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 7x^{8} - 8x^{7} + 41x^{6} - 40x^{5} + 59x^{4} - 10x^{3} + 18x^{2} - 4x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.3 | ||
Root | \(-0.281188 - 0.487032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.79 |
Dual form | 273.2.i.e.235.3 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0388377 | + | 0.0672688i | −0.0274624 | + | 0.0475663i | −0.879430 | − | 0.476028i | \(-0.842076\pi\) |
0.851968 | + | 0.523595i | \(0.175409\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.996983 | + | 1.72683i | 0.498492 | + | 0.863413i | ||||
\(5\) | 1.10121 | − | 1.90736i | 0.492478 | − | 0.852996i | −0.507485 | − | 0.861661i | \(-0.669425\pi\) |
0.999962 | + | 0.00866451i | \(0.00275803\pi\) | |||||||
\(6\) | −0.0776754 | −0.0317108 | ||||||||
\(7\) | 2.64490 | − | 0.0672688i | 0.999677 | − | 0.0254252i | ||||
\(8\) | −0.310233 | −0.109684 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.0855372 | + | 0.148155i | 0.0270492 | + | 0.0468506i | ||||
\(11\) | −1.45815 | − | 2.52558i | −0.439647 | − | 0.761492i | 0.558015 | − | 0.829831i | \(-0.311563\pi\) |
−0.997662 | + | 0.0683394i | \(0.978230\pi\) | |||||||
\(12\) | −0.996983 | + | 1.72683i | −0.287804 | + | 0.498492i | ||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.0981965 | + | 0.180532i | −0.0262441 | + | 0.0482491i | ||||
\(15\) | 2.20243 | 0.568664 | ||||||||
\(16\) | −1.98192 | + | 3.43278i | −0.495479 | + | 0.858196i | ||||
\(17\) | 0.196971 | + | 0.341163i | 0.0477724 | + | 0.0827443i | 0.888923 | − | 0.458057i | \(-0.151454\pi\) |
−0.841150 | + | 0.540801i | \(0.818121\pi\) | |||||||
\(18\) | −0.0388377 | − | 0.0672688i | −0.00915413 | − | 0.0158554i | ||||
\(19\) | −0.0623756 | + | 0.108038i | −0.0143099 | + | 0.0247855i | −0.873092 | − | 0.487556i | \(-0.837888\pi\) |
0.858782 | + | 0.512342i | \(0.171222\pi\) | |||||||
\(20\) | 4.39156 | 0.981984 | ||||||||
\(21\) | 1.38070 | + | 2.25691i | 0.301294 | + | 0.492499i | ||||
\(22\) | 0.226524 | 0.0482951 | ||||||||
\(23\) | −1.69094 | + | 2.92879i | −0.352585 | + | 0.610695i | −0.986702 | − | 0.162543i | \(-0.948031\pi\) |
0.634117 | + | 0.773237i | \(0.281364\pi\) | |||||||
\(24\) | −0.155116 | − | 0.268670i | −0.0316630 | − | 0.0548419i | ||||
\(25\) | 0.0746586 | + | 0.129313i | 0.0149317 | + | 0.0258625i | ||||
\(26\) | 0.0388377 | − | 0.0672688i | 0.00761670 | − | 0.0131925i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.75308 | + | 4.50021i | 0.520283 | + | 0.850459i | ||||
\(29\) | −0.642223 | −0.119258 | −0.0596289 | − | 0.998221i | \(-0.518992\pi\) | ||||
−0.0596289 | + | 0.998221i | \(0.518992\pi\) | |||||||
\(30\) | −0.0855372 | + | 0.148155i | −0.0156169 | + | 0.0270492i | ||||
\(31\) | −2.97890 | − | 5.15961i | −0.535026 | − | 0.926693i | −0.999162 | − | 0.0409288i | \(-0.986968\pi\) |
0.464136 | − | 0.885764i | \(-0.346365\pi\) | |||||||
\(32\) | −0.464179 | − | 0.803982i | −0.0820560 | − | 0.142125i | ||||
\(33\) | 1.45815 | − | 2.52558i | 0.253831 | − | 0.439647i | ||||
\(34\) | −0.0305996 | −0.00524778 | ||||||||
\(35\) | 2.78429 | − | 5.11884i | 0.470631 | − | 0.865242i | ||||
\(36\) | −1.99397 | −0.332328 | ||||||||
\(37\) | −2.09335 | + | 3.62579i | −0.344145 | + | 0.596076i | −0.985198 | − | 0.171420i | \(-0.945164\pi\) |
0.641053 | + | 0.767496i | \(0.278498\pi\) | |||||||
\(38\) | −0.00484505 | − | 0.00839187i | −0.000785970 | − | 0.00136134i | ||||
\(39\) | −0.500000 | − | 0.866025i | −0.0800641 | − | 0.138675i | ||||
\(40\) | −0.341633 | + | 0.591725i | −0.0540168 | + | 0.0935599i | ||||
\(41\) | 0.434984 | 0.0679331 | 0.0339665 | − | 0.999423i | \(-0.489186\pi\) | ||||
0.0339665 | + | 0.999423i | \(0.489186\pi\) | |||||||
\(42\) | −0.205443 | + | 0.00522513i | −0.0317006 | + | 0.000806255i | ||||
\(43\) | −6.74934 | −1.02927 | −0.514633 | − | 0.857411i | \(-0.672072\pi\) | ||||
−0.514633 | + | 0.857411i | \(0.672072\pi\) | |||||||
\(44\) | 2.90749 | − | 5.03593i | 0.438321 | − | 0.759194i | ||||
\(45\) | 1.10121 | + | 1.90736i | 0.164159 | + | 0.284332i | ||||
\(46\) | −0.131344 | − | 0.227495i | −0.0193656 | − | 0.0335423i | ||||
\(47\) | 4.73160 | − | 8.19538i | 0.690175 | − | 1.19542i | −0.281605 | − | 0.959530i | \(-0.590867\pi\) |
0.971780 | − | 0.235888i | \(-0.0757999\pi\) | |||||||
\(48\) | −3.96384 | −0.572130 | ||||||||
\(49\) | 6.99095 | − | 0.355838i | 0.998707 | − | 0.0508340i | ||||
\(50\) | −0.0115983 | −0.00164024 | ||||||||
\(51\) | −0.196971 | + | 0.341163i | −0.0275814 | + | 0.0477724i | ||||
\(52\) | −0.996983 | − | 1.72683i | −0.138257 | − | 0.239468i | ||||
\(53\) | −6.21691 | − | 10.7680i | −0.853959 | − | 1.47910i | −0.877608 | − | 0.479380i | \(-0.840862\pi\) |
0.0236487 | − | 0.999720i | \(-0.492472\pi\) | |||||||
\(54\) | 0.0388377 | − | 0.0672688i | 0.00528514 | − | 0.00915413i | ||||
\(55\) | −6.42292 | −0.866066 | ||||||||
\(56\) | −0.820534 | + | 0.0208690i | −0.109648 | + | 0.00278874i | ||||
\(57\) | −0.124751 | −0.0165237 | ||||||||
\(58\) | 0.0249424 | − | 0.0432016i | 0.00327510 | − | 0.00567265i | ||||
\(59\) | 3.66778 | + | 6.35277i | 0.477504 | + | 0.827061i | 0.999668 | − | 0.0257845i | \(-0.00820837\pi\) |
−0.522164 | + | 0.852845i | \(0.674875\pi\) | |||||||
\(60\) | 2.19578 | + | 3.80321i | 0.283474 | + | 0.490992i | ||||
\(61\) | 1.19697 | − | 2.07321i | 0.153256 | − | 0.265448i | −0.779166 | − | 0.626817i | \(-0.784357\pi\) |
0.932423 | + | 0.361369i | \(0.117691\pi\) | |||||||
\(62\) | 0.462775 | 0.0587724 | ||||||||
\(63\) | −1.26419 | + | 2.32418i | −0.159273 | + | 0.292819i | ||||
\(64\) | −7.85556 | −0.981945 | ||||||||
\(65\) | −1.10121 | + | 1.90736i | −0.136589 | + | 0.236579i | ||||
\(66\) | 0.113262 | + | 0.196176i | 0.0139416 | + | 0.0241475i | ||||
\(67\) | −3.07024 | − | 5.31781i | −0.375089 | − | 0.649674i | 0.615251 | − | 0.788331i | \(-0.289055\pi\) |
−0.990340 | + | 0.138658i | \(0.955721\pi\) | |||||||
\(68\) | −0.392753 | + | 0.680269i | −0.0476283 | + | 0.0824947i | ||||
\(69\) | −3.38187 | −0.407130 | ||||||||
\(70\) | 0.236203 | + | 0.386100i | 0.0282317 | + | 0.0461477i | ||||
\(71\) | −14.0826 | −1.67129 | −0.835646 | − | 0.549269i | \(-0.814906\pi\) | ||||
−0.835646 | + | 0.549269i | \(0.814906\pi\) | |||||||
\(72\) | 0.155116 | − | 0.268670i | 0.0182806 | − | 0.0316630i | ||||
\(73\) | 3.77647 | + | 6.54105i | 0.442003 | + | 0.765571i | 0.997838 | − | 0.0657211i | \(-0.0209348\pi\) |
−0.555835 | + | 0.831293i | \(0.687601\pi\) | |||||||
\(74\) | −0.162602 | − | 0.281635i | −0.0189021 | − | 0.0327394i | ||||
\(75\) | −0.0746586 | + | 0.129313i | −0.00862084 | + | 0.0149317i | ||||
\(76\) | −0.248750 | −0.0285335 | ||||||||
\(77\) | −4.02654 | − | 6.58181i | −0.458866 | − | 0.750067i | ||||
\(78\) | 0.0776754 | 0.00879500 | ||||||||
\(79\) | 1.18736 | − | 2.05657i | 0.133589 | − | 0.231382i | −0.791469 | − | 0.611210i | \(-0.790683\pi\) |
0.925057 | + | 0.379827i | \(0.124017\pi\) | |||||||
\(80\) | 4.36503 | + | 7.56045i | 0.488025 | + | 0.845284i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.0168938 | + | 0.0292609i | −0.00186561 | + | 0.00323132i | ||||
\(83\) | −9.78804 | −1.07438 | −0.537189 | − | 0.843462i | \(-0.680514\pi\) | ||||
−0.537189 | + | 0.843462i | \(0.680514\pi\) | |||||||
\(84\) | −2.52076 | + | 4.63434i | −0.275037 | + | 0.505648i | ||||
\(85\) | 0.867628 | 0.0941074 | ||||||||
\(86\) | 0.262129 | − | 0.454020i | 0.0282661 | − | 0.0489583i | ||||
\(87\) | −0.321111 | − | 0.556181i | −0.0344268 | − | 0.0596289i | ||||
\(88\) | 0.452365 | + | 0.783519i | 0.0482222 | + | 0.0835234i | ||||
\(89\) | 3.20182 | − | 5.54571i | 0.339392 | − | 0.587844i | −0.644927 | − | 0.764244i | \(-0.723112\pi\) |
0.984318 | + | 0.176401i | \(0.0564454\pi\) | |||||||
\(90\) | −0.171074 | −0.0180328 | ||||||||
\(91\) | −2.64490 | + | 0.0672688i | −0.277260 | + | 0.00705169i | ||||
\(92\) | −6.74335 | −0.703042 | ||||||||
\(93\) | 2.97890 | − | 5.15961i | 0.308898 | − | 0.535026i | ||||
\(94\) | 0.367529 | + | 0.636579i | 0.0379077 | + | 0.0656581i | ||||
\(95\) | 0.137378 | + | 0.237945i | 0.0140946 | + | 0.0244126i | ||||
\(96\) | 0.464179 | − | 0.803982i | 0.0473751 | − | 0.0820560i | ||||
\(97\) | 14.9096 | 1.51384 | 0.756919 | − | 0.653509i | \(-0.226704\pi\) | ||||
0.756919 | + | 0.653509i | \(0.226704\pi\) | |||||||
\(98\) | −0.247575 | + | 0.484093i | −0.0250089 | + | 0.0489008i | ||||
\(99\) | 2.91629 | 0.293098 | ||||||||
\(100\) | −0.148867 | + | 0.257845i | −0.0148867 | + | 0.0257845i | ||||
\(101\) | 9.99103 | + | 17.3050i | 0.994145 | + | 1.72191i | 0.590653 | + | 0.806926i | \(0.298870\pi\) |
0.403492 | + | 0.914983i | \(0.367796\pi\) | |||||||
\(102\) | −0.0152998 | − | 0.0265000i | −0.00151490 | − | 0.00262389i | ||||
\(103\) | 7.33724 | − | 12.7085i | 0.722960 | − | 1.25220i | −0.236849 | − | 0.971547i | \(-0.576115\pi\) |
0.959808 | − | 0.280656i | \(-0.0905520\pi\) | |||||||
\(104\) | 0.310233 | 0.0304208 | ||||||||
\(105\) | 5.82519 | − | 0.148155i | 0.568480 | − | 0.0144584i | ||||
\(106\) | 0.965802 | 0.0938070 | ||||||||
\(107\) | 2.51986 | − | 4.36453i | 0.243604 | − | 0.421935i | −0.718134 | − | 0.695905i | \(-0.755003\pi\) |
0.961738 | + | 0.273970i | \(0.0883368\pi\) | |||||||
\(108\) | −0.996983 | − | 1.72683i | −0.0959348 | − | 0.166164i | ||||
\(109\) | 0.0613411 | + | 0.106246i | 0.00587542 | + | 0.0101765i | 0.868948 | − | 0.494903i | \(-0.164796\pi\) |
−0.863073 | + | 0.505080i | \(0.831463\pi\) | |||||||
\(110\) | 0.249451 | − | 0.432062i | 0.0237842 | − | 0.0411955i | ||||
\(111\) | −4.18670 | −0.397384 | ||||||||
\(112\) | −5.01105 | + | 9.21267i | −0.473499 | + | 0.870516i | ||||
\(113\) | −4.16138 | −0.391470 | −0.195735 | − | 0.980657i | \(-0.562709\pi\) | ||||
−0.195735 | + | 0.980657i | \(0.562709\pi\) | |||||||
\(114\) | 0.00484505 | − | 0.00839187i | 0.000453780 | − | 0.000785970i | ||||
\(115\) | 3.72417 | + | 6.45044i | 0.347280 | + | 0.601507i | ||||
\(116\) | −0.640285 | − | 1.10901i | −0.0594490 | − | 0.102969i | ||||
\(117\) | 0.500000 | − | 0.866025i | 0.0462250 | − | 0.0800641i | ||||
\(118\) | −0.569792 | −0.0524536 | ||||||||
\(119\) | 0.543917 | + | 0.889092i | 0.0498608 | + | 0.0815029i | ||||
\(120\) | −0.683265 | −0.0623733 | ||||||||
\(121\) | 1.24762 | − | 2.16095i | 0.113420 | − | 0.196450i | ||||
\(122\) | 0.0929752 | + | 0.161038i | 0.00841758 | + | 0.0145797i | ||||
\(123\) | 0.217492 | + | 0.376707i | 0.0196106 | + | 0.0339665i | ||||
\(124\) | 5.93983 | − | 10.2881i | 0.533412 | − | 0.923897i | ||||
\(125\) | 11.3410 | 1.01437 | ||||||||
\(126\) | −0.107247 | − | 0.175307i | −0.00955430 | − | 0.0156175i | ||||
\(127\) | 14.9711 | 1.32847 | 0.664237 | − | 0.747522i | \(-0.268756\pi\) | ||||
0.664237 | + | 0.747522i | \(0.268756\pi\) | |||||||
\(128\) | 1.23345 | − | 2.13640i | 0.109023 | − | 0.188833i | ||||
\(129\) | −3.37467 | − | 5.84510i | −0.297123 | − | 0.514633i | ||||
\(130\) | −0.0855372 | − | 0.148155i | −0.00750210 | − | 0.0129940i | ||||
\(131\) | −9.37108 | + | 16.2312i | −0.818755 | + | 1.41812i | 0.0878454 | + | 0.996134i | \(0.472002\pi\) |
−0.906600 | + | 0.421991i | \(0.861331\pi\) | |||||||
\(132\) | 5.81499 | 0.506130 | ||||||||
\(133\) | −0.157709 | + | 0.289944i | −0.0136751 | + | 0.0251414i | ||||
\(134\) | 0.476964 | 0.0412034 | ||||||||
\(135\) | −1.10121 | + | 1.90736i | −0.0947773 | + | 0.164159i | ||||
\(136\) | −0.0611068 | − | 0.105840i | −0.00523987 | − | 0.00907572i | ||||
\(137\) | 6.79525 | + | 11.7697i | 0.580557 | + | 1.00555i | 0.995413 | + | 0.0956675i | \(0.0304986\pi\) |
−0.414856 | + | 0.909887i | \(0.636168\pi\) | |||||||
\(138\) | 0.131344 | − | 0.227495i | 0.0111808 | − | 0.0193656i | ||||
\(139\) | −15.7292 | −1.33413 | −0.667066 | − | 0.744999i | \(-0.732450\pi\) | ||||
−0.667066 | + | 0.744999i | \(0.732450\pi\) | |||||||
\(140\) | 11.6152 | − | 0.295416i | 0.981666 | − | 0.0249672i | ||||
\(141\) | 9.46321 | 0.796946 | ||||||||
\(142\) | 0.546934 | − | 0.947317i | 0.0458977 | − | 0.0794971i | ||||
\(143\) | 1.45815 | + | 2.52558i | 0.121936 | + | 0.211200i | ||||
\(144\) | −1.98192 | − | 3.43278i | −0.165160 | − | 0.286065i | ||||
\(145\) | −0.707224 | + | 1.22495i | −0.0587318 | + | 0.101726i | ||||
\(146\) | −0.586678 | −0.0485538 | ||||||||
\(147\) | 3.80364 | + | 5.87642i | 0.313719 | + | 0.484679i | ||||
\(148\) | −8.34815 | −0.686213 | ||||||||
\(149\) | −1.67404 | + | 2.89953i | −0.137143 | + | 0.237539i | −0.926414 | − | 0.376506i | \(-0.877125\pi\) |
0.789271 | + | 0.614045i | \(0.210459\pi\) | |||||||
\(150\) | −0.00579914 | − | 0.0100444i | −0.000473498 | − | 0.000820122i | ||||
\(151\) | 10.2238 | + | 17.7082i | 0.832003 | + | 1.44107i | 0.896448 | + | 0.443150i | \(0.146139\pi\) |
−0.0644447 | + | 0.997921i | \(0.520528\pi\) | |||||||
\(152\) | 0.0193510 | − | 0.0335168i | 0.00156957 | − | 0.00271857i | ||||
\(153\) | −0.393942 | −0.0318483 | ||||||||
\(154\) | 0.599132 | − | 0.0152380i | 0.0482795 | − | 0.00122791i | ||||
\(155\) | −13.1216 | −1.05395 | ||||||||
\(156\) | 0.996983 | − | 1.72683i | 0.0798225 | − | 0.138257i | ||||
\(157\) | −5.10068 | − | 8.83464i | −0.407079 | − | 0.705081i | 0.587482 | − | 0.809237i | \(-0.300119\pi\) |
−0.994561 | + | 0.104156i | \(0.966786\pi\) | |||||||
\(158\) | 0.0922287 | + | 0.159745i | 0.00733732 | + | 0.0127086i | ||||
\(159\) | 6.21691 | − | 10.7680i | 0.493033 | − | 0.853959i | ||||
\(160\) | −2.04464 | −0.161643 | ||||||||
\(161\) | −4.27534 | + | 7.86009i | −0.336944 | + | 0.619462i | ||||
\(162\) | 0.0776754 | 0.00610275 | ||||||||
\(163\) | −7.79177 | + | 13.4957i | −0.610299 | + | 1.05707i | 0.380891 | + | 0.924620i | \(0.375617\pi\) |
−0.991190 | + | 0.132449i | \(0.957716\pi\) | |||||||
\(164\) | 0.433672 | + | 0.751142i | 0.0338641 | + | 0.0586543i | ||||
\(165\) | −3.21146 | − | 5.56241i | −0.250012 | − | 0.433033i | ||||
\(166\) | 0.380145 | − | 0.658430i | 0.0295050 | − | 0.0511041i | ||||
\(167\) | 1.53310 | 0.118635 | 0.0593174 | − | 0.998239i | \(-0.481108\pi\) | ||||
0.0593174 | + | 0.998239i | \(0.481108\pi\) | |||||||
\(168\) | −0.428340 | − | 0.700168i | −0.0330471 | − | 0.0540192i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.0336966 | + | 0.0583643i | −0.00258442 | + | 0.00447634i | ||||
\(171\) | −0.0623756 | − | 0.108038i | −0.00476998 | − | 0.00826185i | ||||
\(172\) | −6.72898 | − | 11.6549i | −0.513080 | − | 0.888681i | ||||
\(173\) | 6.99222 | − | 12.1109i | 0.531609 | − | 0.920773i | −0.467711 | − | 0.883882i | \(-0.654921\pi\) |
0.999319 | − | 0.0368914i | \(-0.0117456\pi\) | |||||||
\(174\) | 0.0498849 | 0.00378176 | ||||||||
\(175\) | 0.206163 | + | 0.336996i | 0.0155845 | + | 0.0254745i | ||||
\(176\) | 11.5597 | 0.871345 | ||||||||
\(177\) | −3.66778 | + | 6.35277i | −0.275687 | + | 0.477504i | ||||
\(178\) | 0.248702 | + | 0.430765i | 0.0186410 | + | 0.0322872i | ||||
\(179\) | 10.9652 | + | 18.9923i | 0.819577 | + | 1.41955i | 0.905994 | + | 0.423290i | \(0.139125\pi\) |
−0.0864170 | + | 0.996259i | \(0.527542\pi\) | |||||||
\(180\) | −2.19578 | + | 3.80321i | −0.163664 | + | 0.283474i | ||||
\(181\) | 0.955265 | 0.0710043 | 0.0355021 | − | 0.999370i | \(-0.488697\pi\) | ||||
0.0355021 | + | 0.999370i | \(0.488697\pi\) | |||||||
\(182\) | 0.0981965 | − | 0.180532i | 0.00727881 | − | 0.0133819i | ||||
\(183\) | 2.39394 | 0.176965 | ||||||||
\(184\) | 0.524584 | − | 0.908607i | 0.0386729 | − | 0.0669834i | ||||
\(185\) | 4.61045 | + | 7.98554i | 0.338967 | + | 0.587108i | ||||
\(186\) | 0.231387 | + | 0.400774i | 0.0169661 | + | 0.0293862i | ||||
\(187\) | 0.574424 | − | 0.994932i | 0.0420061 | − | 0.0727566i | ||||
\(188\) | 18.8693 | 1.37619 | ||||||||
\(189\) | −2.64490 | + | 0.0672688i | −0.192388 | + | 0.00489309i | ||||
\(190\) | −0.0213417 | −0.00154829 | ||||||||
\(191\) | −9.84171 | + | 17.0463i | −0.712121 | + | 1.23343i | 0.251938 | + | 0.967743i | \(0.418932\pi\) |
−0.964059 | + | 0.265687i | \(0.914401\pi\) | |||||||
\(192\) | −3.92778 | − | 6.80312i | −0.283463 | − | 0.490973i | ||||
\(193\) | −7.54753 | − | 13.0727i | −0.543283 | − | 0.940993i | −0.998713 | − | 0.0507219i | \(-0.983848\pi\) |
0.455430 | − | 0.890272i | \(-0.349486\pi\) | |||||||
\(194\) | −0.579053 | + | 1.00295i | −0.0415736 | + | 0.0720076i | ||||
\(195\) | −2.20243 | −0.157719 | ||||||||
\(196\) | 7.58433 | + | 11.7174i | 0.541738 | + | 0.836956i | ||||
\(197\) | −11.0323 | −0.786015 | −0.393008 | − | 0.919535i | \(-0.628565\pi\) | ||||
−0.393008 | + | 0.919535i | \(0.628565\pi\) | |||||||
\(198\) | −0.113262 | + | 0.196176i | −0.00804918 | + | 0.0139416i | ||||
\(199\) | −3.58851 | − | 6.21548i | −0.254382 | − | 0.440603i | 0.710345 | − | 0.703854i | \(-0.248539\pi\) |
−0.964728 | + | 0.263250i | \(0.915206\pi\) | |||||||
\(200\) | −0.0231616 | − | 0.0401170i | −0.00163777 | − | 0.00283670i | ||||
\(201\) | 3.07024 | − | 5.31781i | 0.216558 | − | 0.375089i | ||||
\(202\) | −1.55211 | −0.109206 | ||||||||
\(203\) | −1.69861 | + | 0.0432016i | −0.119219 | + | 0.00303216i | ||||
\(204\) | −0.785507 | −0.0549965 | ||||||||
\(205\) | 0.479010 | − | 0.829670i | 0.0334555 | − | 0.0579467i | ||||
\(206\) | 0.569923 | + | 0.987135i | 0.0397084 | + | 0.0687770i | ||||
\(207\) | −1.69094 | − | 2.92879i | −0.117528 | − | 0.203565i | ||||
\(208\) | 1.98192 | − | 3.43278i | 0.137421 | − | 0.238021i | ||||
\(209\) | 0.363811 | 0.0251653 | ||||||||
\(210\) | −0.216271 | + | 0.397608i | −0.0149241 | + | 0.0274375i | ||||
\(211\) | 15.7119 | 1.08165 | 0.540825 | − | 0.841135i | \(-0.318112\pi\) | ||||
0.540825 | + | 0.841135i | \(0.318112\pi\) | |||||||
\(212\) | 12.3963 | − | 21.4711i | 0.851383 | − | 1.47464i | ||||
\(213\) | −7.04128 | − | 12.1958i | −0.482460 | − | 0.835646i | ||||
\(214\) | 0.195731 | + | 0.339017i | 0.0133799 | + | 0.0231747i | ||||
\(215\) | −7.43247 | + | 12.8734i | −0.506890 | + | 0.877959i | ||||
\(216\) | 0.310233 | 0.0211087 | ||||||||
\(217\) | −8.22596 | − | 13.4462i | −0.558415 | − | 0.912790i | ||||
\(218\) | −0.00952939 | −0.000645412 | ||||||||
\(219\) | −3.77647 | + | 6.54105i | −0.255190 | + | 0.442003i | ||||
\(220\) | −6.40354 | − | 11.0913i | −0.431727 | − | 0.747772i | ||||
\(221\) | −0.196971 | − | 0.341163i | −0.0132497 | − | 0.0229491i | ||||
\(222\) | 0.162602 | − | 0.281635i | 0.0109131 | − | 0.0189021i | ||||
\(223\) | 6.20889 | 0.415778 | 0.207889 | − | 0.978152i | \(-0.433341\pi\) | ||||
0.207889 | + | 0.978152i | \(0.433341\pi\) | |||||||
\(224\) | −1.28179 | − | 2.09522i | −0.0856431 | − | 0.139993i | ||||
\(225\) | −0.149317 | −0.00995449 | ||||||||
\(226\) | 0.161619 | − | 0.279932i | 0.0107507 | − | 0.0186208i | ||||
\(227\) | −11.8440 | − | 20.5143i | −0.786111 | − | 1.36158i | −0.928333 | − | 0.371750i | \(-0.878758\pi\) |
0.142221 | − | 0.989835i | \(-0.454575\pi\) | |||||||
\(228\) | −0.124375 | − | 0.215424i | −0.00823692 | − | 0.0142668i | ||||
\(229\) | 4.52113 | − | 7.83083i | 0.298765 | − | 0.517476i | −0.677089 | − | 0.735901i | \(-0.736759\pi\) |
0.975854 | + | 0.218425i | \(0.0700921\pi\) | |||||||
\(230\) | −0.578552 | −0.0381486 | ||||||||
\(231\) | 3.68675 | − | 6.77799i | 0.242570 | − | 0.445959i | ||||
\(232\) | 0.199239 | 0.0130807 | ||||||||
\(233\) | −2.67224 | + | 4.62846i | −0.175065 | + | 0.303221i | −0.940184 | − | 0.340668i | \(-0.889347\pi\) |
0.765119 | + | 0.643889i | \(0.222680\pi\) | |||||||
\(234\) | 0.0388377 | + | 0.0672688i | 0.00253890 | + | 0.00439750i | ||||
\(235\) | −10.4210 | − | 18.0497i | −0.679792 | − | 1.17743i | ||||
\(236\) | −7.31342 | + | 12.6672i | −0.476063 | + | 0.824566i | ||||
\(237\) | 2.37472 | 0.154255 | ||||||||
\(238\) | −0.0809327 | + | 0.00205840i | −0.00524609 | + | 0.000133426i | ||||
\(239\) | −27.2548 | −1.76297 | −0.881484 | − | 0.472215i | \(-0.843455\pi\) | ||||
−0.881484 | + | 0.472215i | \(0.843455\pi\) | |||||||
\(240\) | −4.36503 | + | 7.56045i | −0.281761 | + | 0.488025i | ||||
\(241\) | 7.83806 | + | 13.5759i | 0.504894 | + | 0.874501i | 0.999984 | + | 0.00565987i | \(0.00180160\pi\) |
−0.495090 | + | 0.868841i | \(0.664865\pi\) | |||||||
\(242\) | 0.0969096 | + | 0.167852i | 0.00622958 | + | 0.0107900i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 4.77344 | 0.305588 | ||||||||
\(245\) | 7.01982 | − | 13.7261i | 0.448480 | − | 0.876928i | ||||
\(246\) | −0.0337875 | −0.00215422 | ||||||||
\(247\) | 0.0623756 | − | 0.108038i | 0.00396886 | − | 0.00687427i | ||||
\(248\) | 0.924153 | + | 1.60068i | 0.0586838 | + | 0.101643i | ||||
\(249\) | −4.89402 | − | 8.47669i | −0.310146 | − | 0.537189i | ||||
\(250\) | −0.440458 | + | 0.762896i | −0.0278570 | + | 0.0482497i | ||||
\(251\) | −18.2218 | −1.15015 | −0.575075 | − | 0.818101i | \(-0.695027\pi\) | ||||
−0.575075 | + | 0.818101i | \(0.695027\pi\) | |||||||
\(252\) | −5.27383 | + | 0.134132i | −0.332220 | + | 0.00844951i | ||||
\(253\) | 9.86253 | 0.620052 | ||||||||
\(254\) | −0.581445 | + | 1.00709i | −0.0364831 | + | 0.0631906i | ||||
\(255\) | 0.433814 | + | 0.751388i | 0.0271665 | + | 0.0470537i | ||||
\(256\) | −7.75975 | − | 13.4403i | −0.484985 | − | 0.840018i | ||||
\(257\) | −7.53068 | + | 13.0435i | −0.469751 | + | 0.813632i | −0.999402 | − | 0.0345833i | \(-0.988990\pi\) |
0.529651 | + | 0.848216i | \(0.322323\pi\) | |||||||
\(258\) | 0.524258 | 0.0326389 | ||||||||
\(259\) | −5.29279 | + | 9.73066i | −0.328878 | + | 0.604634i | ||||
\(260\) | −4.39156 | −0.272353 | ||||||||
\(261\) | 0.321111 | − | 0.556181i | 0.0198763 | − | 0.0344268i | ||||
\(262\) | −0.727902 | − | 1.26076i | −0.0449699 | − | 0.0778902i | ||||
\(263\) | 13.8958 | + | 24.0682i | 0.856852 | + | 1.48411i | 0.874916 | + | 0.484274i | \(0.160916\pi\) |
−0.0180644 | + | 0.999837i | \(0.505750\pi\) | |||||||
\(264\) | −0.452365 | + | 0.783519i | −0.0278411 | + | 0.0482222i | ||||
\(265\) | −27.3846 | −1.68222 | ||||||||
\(266\) | −0.0133792 | − | 0.0218697i | −0.000820329 | − | 0.00134092i | ||||
\(267\) | 6.40363 | 0.391896 | ||||||||
\(268\) | 6.12195 | − | 10.6035i | 0.373958 | − | 0.647714i | ||||
\(269\) | 4.00404 | + | 6.93521i | 0.244131 | + | 0.422847i | 0.961887 | − | 0.273448i | \(-0.0881640\pi\) |
−0.717756 | + | 0.696295i | \(0.754831\pi\) | |||||||
\(270\) | −0.0855372 | − | 0.148155i | −0.00520563 | − | 0.00901641i | ||||
\(271\) | −10.1323 | + | 17.5496i | −0.615490 | + | 1.06606i | 0.374808 | + | 0.927103i | \(0.377709\pi\) |
−0.990298 | + | 0.138958i | \(0.955625\pi\) | |||||||
\(272\) | −1.56152 | −0.0946811 | ||||||||
\(273\) | −1.38070 | − | 2.25691i | −0.0835640 | − | 0.136595i | ||||
\(274\) | −1.05565 | −0.0637740 | ||||||||
\(275\) | 0.217726 | − | 0.377113i | 0.0131294 | − | 0.0227408i | ||||
\(276\) | −3.37167 | − | 5.83991i | −0.202951 | − | 0.351521i | ||||
\(277\) | 14.7169 | + | 25.4905i | 0.884256 | + | 1.53158i | 0.846564 | + | 0.532286i | \(0.178667\pi\) |
0.0376912 | + | 0.999289i | \(0.488000\pi\) | |||||||
\(278\) | 0.610885 | − | 1.05808i | 0.0366385 | − | 0.0634597i | ||||
\(279\) | 5.95780 | 0.356684 | ||||||||
\(280\) | −0.863778 | + | 1.58803i | −0.0516206 | + | 0.0949031i | ||||
\(281\) | −3.76735 | −0.224741 | −0.112371 | − | 0.993666i | \(-0.535844\pi\) | ||||
−0.112371 | + | 0.993666i | \(0.535844\pi\) | |||||||
\(282\) | −0.367529 | + | 0.636579i | −0.0218860 | + | 0.0379077i | ||||
\(283\) | −11.2203 | − | 19.4342i | −0.666980 | − | 1.15524i | −0.978744 | − | 0.205084i | \(-0.934253\pi\) |
0.311764 | − | 0.950160i | \(-0.399080\pi\) | |||||||
\(284\) | −14.0401 | − | 24.3181i | −0.833125 | − | 1.44301i | ||||
\(285\) | −0.137378 | + | 0.237945i | −0.00813755 | + | 0.0140946i | ||||
\(286\) | −0.226524 | −0.0133946 | ||||||||
\(287\) | 1.15049 | − | 0.0292609i | 0.0679111 | − | 0.00172721i | ||||
\(288\) | 0.928358 | 0.0547040 | ||||||||
\(289\) | 8.42240 | − | 14.5880i | 0.495436 | − | 0.858120i | ||||
\(290\) | −0.0549339 | − | 0.0951483i | −0.00322583 | − | 0.00558730i | ||||
\(291\) | 7.45479 | + | 12.9121i | 0.437007 | + | 0.756919i | ||||
\(292\) | −7.53016 | + | 13.0426i | −0.440670 | + | 0.763262i | ||||
\(293\) | 8.13635 | 0.475331 | 0.237665 | − | 0.971347i | \(-0.423618\pi\) | ||||
0.237665 | + | 0.971347i | \(0.423618\pi\) | |||||||
\(294\) | −0.543025 | + | 0.0276399i | −0.0316698 | + | 0.00161199i | ||||
\(295\) | 16.1560 | 0.940639 | ||||||||
\(296\) | 0.649426 | − | 1.12484i | 0.0377471 | − | 0.0653800i | ||||
\(297\) | 1.45815 | + | 2.52558i | 0.0846102 | + | 0.146549i | ||||
\(298\) | −0.130032 | − | 0.225222i | −0.00753255 | − | 0.0130468i | ||||
\(299\) | 1.69094 | − | 2.92879i | 0.0977894 | − | 0.169376i | ||||
\(300\) | −0.297734 | −0.0171897 | ||||||||
\(301\) | −17.8513 | + | 0.454020i | −1.02893 | + | 0.0261693i | ||||
\(302\) | −1.58828 | −0.0913951 | ||||||||
\(303\) | −9.99103 | + | 17.3050i | −0.573970 | + | 0.994145i | ||||
\(304\) | −0.247247 | − | 0.428244i | −0.0141806 | − | 0.0245615i | ||||
\(305\) | −2.63624 | − | 4.56610i | −0.150951 | − | 0.261454i | ||||
\(306\) | 0.0152998 | − | 0.0265000i | 0.000874630 | − | 0.00151490i | ||||
\(307\) | 18.9247 | 1.08009 | 0.540046 | − | 0.841636i | \(-0.318407\pi\) | ||||
0.540046 | + | 0.841636i | \(0.318407\pi\) | |||||||
\(308\) | 7.35126 | − | 13.5151i | 0.418877 | − | 0.770093i | ||||
\(309\) | 14.6745 | 0.834802 | ||||||||
\(310\) | 0.509613 | − | 0.882676i | 0.0289441 | − | 0.0501326i | ||||
\(311\) | −5.80947 | − | 10.0623i | −0.329425 | − | 0.570580i | 0.652973 | − | 0.757381i | \(-0.273521\pi\) |
−0.982398 | + | 0.186801i | \(0.940188\pi\) | |||||||
\(312\) | 0.155116 | + | 0.268670i | 0.00878174 | + | 0.0152104i | ||||
\(313\) | 5.85117 | − | 10.1345i | 0.330727 | − | 0.572837i | −0.651927 | − | 0.758282i | \(-0.726039\pi\) |
0.982655 | + | 0.185445i | \(0.0593726\pi\) | |||||||
\(314\) | 0.792395 | 0.0447174 | ||||||||
\(315\) | 3.04090 | + | 4.97068i | 0.171335 | + | 0.280066i | ||||
\(316\) | 4.73512 | 0.266371 | ||||||||
\(317\) | 16.5034 | − | 28.5848i | 0.926926 | − | 1.60548i | 0.138492 | − | 0.990364i | \(-0.455774\pi\) |
0.788434 | − | 0.615119i | \(-0.210892\pi\) | |||||||
\(318\) | 0.482901 | + | 0.836409i | 0.0270798 | + | 0.0469035i | ||||
\(319\) | 0.936454 | + | 1.62199i | 0.0524314 | + | 0.0908138i | ||||
\(320\) | −8.65065 | + | 14.9834i | −0.483586 | + | 0.837595i | ||||
\(321\) | 5.03973 | 0.281290 | ||||||||
\(322\) | −0.362695 | − | 0.592865i | −0.0202122 | − | 0.0330391i | ||||
\(323\) | −0.0491447 | −0.00273448 | ||||||||
\(324\) | 0.996983 | − | 1.72683i | 0.0553880 | − | 0.0959348i | ||||
\(325\) | −0.0746586 | − | 0.129313i | −0.00414132 | − | 0.00717297i | ||||
\(326\) | −0.605229 | − | 1.04829i | −0.0335205 | − | 0.0580593i | ||||
\(327\) | −0.0613411 | + | 0.106246i | −0.00339217 | + | 0.00587542i | ||||
\(328\) | −0.134946 | −0.00745116 | ||||||||
\(329\) | 11.9633 | − | 21.9942i | 0.659558 | − | 1.21258i | ||||
\(330\) | 0.498902 | 0.0274637 | ||||||||
\(331\) | −7.38730 | + | 12.7952i | −0.406043 | + | 0.703286i | −0.994442 | − | 0.105284i | \(-0.966425\pi\) |
0.588400 | + | 0.808570i | \(0.299758\pi\) | |||||||
\(332\) | −9.75852 | − | 16.9022i | −0.535568 | − | 0.927631i | ||||
\(333\) | −2.09335 | − | 3.62579i | −0.114715 | − | 0.198692i | ||||
\(334\) | −0.0595421 | + | 0.103130i | −0.00325800 | + | 0.00564302i | ||||
\(335\) | −13.5239 | −0.738892 | ||||||||
\(336\) | −10.4839 | + | 0.266643i | −0.571945 | + | 0.0145465i | ||||
\(337\) | −13.0713 | −0.712041 | −0.356020 | − | 0.934478i | \(-0.615867\pi\) | ||||
−0.356020 | + | 0.934478i | \(0.615867\pi\) | |||||||
\(338\) | −0.0388377 | + | 0.0672688i | −0.00211249 | + | 0.00365894i | ||||
\(339\) | −2.08069 | − | 3.60386i | −0.113008 | − | 0.195735i | ||||
\(340\) | 0.865010 | + | 1.49824i | 0.0469118 | + | 0.0812536i | ||||
\(341\) | −8.68734 | + | 15.0469i | −0.470446 | + | 0.814836i | ||||
\(342\) | 0.00969009 | 0.000523980 | ||||||||
\(343\) | 18.4664 | − | 1.41143i | 0.997092 | − | 0.0762100i | ||||
\(344\) | 2.09387 | 0.112894 | ||||||||
\(345\) | −3.72417 | + | 6.45044i | −0.200502 | + | 0.347280i | ||||
\(346\) | 0.543123 | + | 0.940717i | 0.0291985 | + | 0.0505733i | ||||
\(347\) | −3.18975 | − | 5.52481i | −0.171235 | − | 0.296587i | 0.767617 | − | 0.640909i | \(-0.221442\pi\) |
−0.938852 | + | 0.344322i | \(0.888109\pi\) | |||||||
\(348\) | 0.640285 | − | 1.10901i | 0.0343229 | − | 0.0594490i | ||||
\(349\) | −10.3287 | −0.552881 | −0.276441 | − | 0.961031i | \(-0.589155\pi\) | ||||
−0.276441 | + | 0.961031i | \(0.589155\pi\) | |||||||
\(350\) | −0.0306762 | 0.000780203i | −0.00163971 | 4.17036e-5i | ||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −1.35368 | + | 2.34464i | −0.0721515 | + | 0.124970i | ||||
\(353\) | 15.0759 | + | 26.1122i | 0.802407 | + | 1.38981i | 0.918028 | + | 0.396516i | \(0.129781\pi\) |
−0.115620 | + | 0.993293i | \(0.536886\pi\) | |||||||
\(354\) | −0.284896 | − | 0.493454i | −0.0151420 | − | 0.0262268i | ||||
\(355\) | −15.5079 | + | 26.8605i | −0.823074 | + | 1.42561i | ||||
\(356\) | 12.7686 | 0.676736 | ||||||||
\(357\) | −0.498018 | + | 0.915592i | −0.0263579 | + | 0.0484583i | ||||
\(358\) | −1.70345 | −0.0900302 | ||||||||
\(359\) | 14.5886 | − | 25.2681i | 0.769955 | − | 1.33360i | −0.167631 | − | 0.985850i | \(-0.553612\pi\) |
0.937587 | − | 0.347752i | \(-0.113055\pi\) | |||||||
\(360\) | −0.341633 | − | 0.591725i | −0.0180056 | − | 0.0311866i | ||||
\(361\) | 9.49222 | + | 16.4410i | 0.499590 | + | 0.865316i | ||||
\(362\) | −0.0371003 | + | 0.0642595i | −0.00194995 | + | 0.00337741i | ||||
\(363\) | 2.49525 | 0.130966 | ||||||||
\(364\) | −2.75308 | − | 4.50021i | −0.144301 | − | 0.235875i | ||||
\(365\) | 16.6348 | 0.870706 | ||||||||
\(366\) | −0.0929752 | + | 0.161038i | −0.00485989 | + | 0.00841758i | ||||
\(367\) | 2.24216 | + | 3.88353i | 0.117040 | + | 0.202719i | 0.918593 | − | 0.395204i | \(-0.129326\pi\) |
−0.801554 | + | 0.597923i | \(0.795993\pi\) | |||||||
\(368\) | −6.70260 | − | 11.6092i | −0.349397 | − | 0.605173i | ||||
\(369\) | −0.217492 | + | 0.376707i | −0.0113222 | + | 0.0196106i | ||||
\(370\) | −0.716237 | −0.0372354 | ||||||||
\(371\) | −17.1674 | − | 28.0621i | −0.891289 | − | 1.45691i | ||||
\(372\) | 11.8797 | 0.615932 | ||||||||
\(373\) | −11.9946 | + | 20.7752i | −0.621055 | + | 1.07570i | 0.368235 | + | 0.929733i | \(0.379962\pi\) |
−0.989290 | + | 0.145966i | \(0.953371\pi\) | |||||||
\(374\) | 0.0446186 | + | 0.0772817i | 0.00230717 | + | 0.00399614i | ||||
\(375\) | 5.67050 | + | 9.82159i | 0.292823 | + | 0.507185i | ||||
\(376\) | −1.46790 | + | 2.54248i | −0.0757011 | + | 0.131118i | ||||
\(377\) | 0.642223 | 0.0330762 | ||||||||
\(378\) | 0.0981965 | − | 0.180532i | 0.00505069 | − | 0.00928555i | ||||
\(379\) | 20.2228 | 1.03878 | 0.519389 | − | 0.854538i | \(-0.326160\pi\) | ||||
0.519389 | + | 0.854538i | \(0.326160\pi\) | |||||||
\(380\) | −0.273926 | + | 0.474455i | −0.0140521 | + | 0.0243390i | ||||
\(381\) | 7.48557 | + | 12.9654i | 0.383498 | + | 0.664237i | ||||
\(382\) | −0.764459 | − | 1.32408i | −0.0391131 | − | 0.0677459i | ||||
\(383\) | 11.5409 | − | 19.9895i | 0.589714 | − | 1.02141i | −0.404555 | − | 0.914513i | \(-0.632574\pi\) |
0.994270 | − | 0.106901i | \(-0.0340929\pi\) | |||||||
\(384\) | 2.46690 | 0.125888 | ||||||||
\(385\) | −16.9879 | + | 0.432062i | −0.865786 | + | 0.0220199i | ||||
\(386\) | 1.17251 | 0.0596794 | ||||||||
\(387\) | 3.37467 | − | 5.84510i | 0.171544 | − | 0.297123i | ||||
\(388\) | 14.8646 | + | 25.7462i | 0.754635 | + | 1.30707i | ||||
\(389\) | 16.6685 | + | 28.8706i | 0.845124 | + | 1.46380i | 0.885513 | + | 0.464615i | \(0.153807\pi\) |
−0.0403885 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(390\) | 0.0855372 | − | 0.148155i | 0.00433134 | − | 0.00750210i | ||||
\(391\) | −1.33226 | −0.0673754 | ||||||||
\(392\) | −2.16882 | + | 0.110393i | −0.109542 | + | 0.00557567i | ||||
\(393\) | −18.7422 | −0.945417 | ||||||||
\(394\) | 0.428467 | − | 0.742127i | 0.0215859 | − | 0.0373878i | ||||
\(395\) | −2.61508 | − | 4.52944i | −0.131579 | − | 0.227901i | ||||
\(396\) | 2.90749 | + | 5.03593i | 0.146107 | + | 0.253065i | ||||
\(397\) | 10.0940 | − | 17.4834i | 0.506605 | − | 0.877465i | −0.493366 | − | 0.869822i | \(-0.664234\pi\) |
0.999971 | − | 0.00764315i | \(-0.00243291\pi\) | |||||||
\(398\) | 0.557477 | 0.0279438 | ||||||||
\(399\) | −0.329954 | + | 0.00839187i | −0.0165184 | + | 0.000420119i | ||||
\(400\) | −0.591869 | −0.0295935 | ||||||||
\(401\) | 2.10744 | − | 3.65019i | 0.105240 | − | 0.182282i | −0.808596 | − | 0.588364i | \(-0.799772\pi\) |
0.913836 | + | 0.406083i | \(0.133105\pi\) | |||||||
\(402\) | 0.238482 | + | 0.413063i | 0.0118944 | + | 0.0206017i | ||||
\(403\) | 2.97890 | + | 5.15961i | 0.148390 | + | 0.257018i | ||||
\(404\) | −19.9218 | + | 34.5055i | −0.991146 | + | 1.71671i | ||||
\(405\) | −2.20243 | −0.109439 | ||||||||
\(406\) | 0.0630641 | − | 0.115942i | 0.00312982 | − | 0.00575408i | ||||
\(407\) | 12.2096 | 0.605210 | ||||||||
\(408\) | 0.0611068 | − | 0.105840i | 0.00302524 | − | 0.00523987i | ||||
\(409\) | −3.72314 | − | 6.44866i | −0.184097 | − | 0.318866i | 0.759175 | − | 0.650887i | \(-0.225603\pi\) |
−0.943272 | + | 0.332021i | \(0.892269\pi\) | |||||||
\(410\) | 0.0372073 | + | 0.0644449i | 0.00183754 | + | 0.00318271i | ||||
\(411\) | −6.79525 | + | 11.7697i | −0.335185 | + | 0.580557i | ||||
\(412\) | 29.2604 | 1.44156 | ||||||||
\(413\) | 10.1282 | + | 16.5557i | 0.498378 | + | 0.814653i | ||||
\(414\) | 0.262688 | 0.0129104 | ||||||||
\(415\) | −10.7787 | + | 18.6693i | −0.529107 | + | 0.916440i | ||||
\(416\) | 0.464179 | + | 0.803982i | 0.0227583 | + | 0.0394184i | ||||
\(417\) | −7.86459 | − | 13.6219i | −0.385131 | − | 0.667066i | ||||
\(418\) | −0.0141296 | + | 0.0244731i | −0.000691100 | + | 0.00119702i | ||||
\(419\) | −12.2817 | −0.600000 | −0.300000 | − | 0.953939i | \(-0.596987\pi\) | ||||
−0.300000 | + | 0.953939i | \(0.596987\pi\) | |||||||
\(420\) | 6.06345 | + | 9.91138i | 0.295866 | + | 0.483626i | ||||
\(421\) | 26.9884 | 1.31533 | 0.657667 | − | 0.753309i | \(-0.271544\pi\) | ||||
0.657667 | + | 0.753309i | \(0.271544\pi\) | |||||||
\(422\) | −0.610212 | + | 1.05692i | −0.0297047 | + | 0.0514500i | ||||
\(423\) | 4.73160 | + | 8.19538i | 0.230058 | + | 0.398473i | ||||
\(424\) | 1.92869 | + | 3.34059i | 0.0936655 | + | 0.162233i | ||||
\(425\) | −0.0294112 | + | 0.0509416i | −0.00142665 | + | 0.00247103i | ||||
\(426\) | 1.09387 | 0.0529981 | ||||||||
\(427\) | 3.02640 | − | 5.56396i | 0.146458 | − | 0.269259i | ||||
\(428\) | 10.0490 | 0.485739 | ||||||||
\(429\) | −1.45815 | + | 2.52558i | −0.0703999 | + | 0.121936i | ||||
\(430\) | −0.577320 | − | 0.999947i | −0.0278408 | − | 0.0482217i | ||||
\(431\) | 10.1583 | + | 17.5948i | 0.489310 | + | 0.847511i | 0.999924 | − | 0.0122995i | \(-0.00391516\pi\) |
−0.510614 | + | 0.859810i | \(0.670582\pi\) | |||||||
\(432\) | 1.98192 | − | 3.43278i | 0.0953551 | − | 0.165160i | ||||
\(433\) | −9.02891 | −0.433902 | −0.216951 | − | 0.976183i | \(-0.569611\pi\) | ||||
−0.216951 | + | 0.976183i | \(0.569611\pi\) | |||||||
\(434\) | 1.22399 | − | 0.0311303i | 0.0587534 | − | 0.00149430i | ||||
\(435\) | −1.41445 | −0.0678176 | ||||||||
\(436\) | −0.122312 | + | 0.211851i | −0.00585769 | + | 0.0101458i | ||||
\(437\) | −0.210946 | − | 0.365370i | −0.0100909 | − | 0.0174780i | ||||
\(438\) | −0.293339 | − | 0.508078i | −0.0140163 | − | 0.0242769i | ||||
\(439\) | −5.01746 | + | 8.69049i | −0.239470 | + | 0.414774i | −0.960562 | − | 0.278065i | \(-0.910307\pi\) |
0.721092 | + | 0.692839i | \(0.243640\pi\) | |||||||
\(440\) | 1.99260 | 0.0949935 | ||||||||
\(441\) | −3.18731 | + | 6.23226i | −0.151777 | + | 0.296774i | ||||
\(442\) | 0.0305996 | 0.00145547 | ||||||||
\(443\) | 16.8205 | − | 29.1339i | 0.799165 | − | 1.38419i | −0.120996 | − | 0.992653i | \(-0.538609\pi\) |
0.920161 | − | 0.391541i | \(-0.128058\pi\) | |||||||
\(444\) | −4.17407 | − | 7.22971i | −0.198093 | − | 0.343107i | ||||
\(445\) | −7.05176 | − | 12.2140i | −0.334286 | − | 0.579000i | ||||
\(446\) | −0.241139 | + | 0.417665i | −0.0114183 | + | 0.0197770i | ||||
\(447\) | −3.34809 | −0.158359 | ||||||||
\(448\) | −20.7771 | + | 0.528435i | −0.981628 | + | 0.0249662i | ||||
\(449\) | 1.21577 | 0.0573759 | 0.0286879 | − | 0.999588i | \(-0.490867\pi\) | ||||
0.0286879 | + | 0.999588i | \(0.490867\pi\) | |||||||
\(450\) | 0.00579914 | − | 0.0100444i | 0.000273374 | − | 0.000473498i | ||||
\(451\) | −0.634270 | − | 1.09859i | −0.0298666 | − | 0.0517305i | ||||
\(452\) | −4.14883 | − | 7.18599i | −0.195145 | − | 0.338000i | ||||
\(453\) | −10.2238 | + | 17.7082i | −0.480357 | + | 0.832003i | ||||
\(454\) | 1.83997 | 0.0863540 | ||||||||
\(455\) | −2.78429 | + | 5.11884i | −0.130529 | + | 0.239975i | ||||
\(456\) | 0.0387019 | 0.00181238 | ||||||||
\(457\) | 14.2167 | − | 24.6241i | 0.665029 | − | 1.15186i | −0.314248 | − | 0.949341i | \(-0.601752\pi\) |
0.979277 | − | 0.202524i | \(-0.0649144\pi\) | |||||||
\(458\) | 0.351181 | + | 0.608263i | 0.0164096 | + | 0.0284222i | ||||
\(459\) | −0.196971 | − | 0.341163i | −0.00919381 | − | 0.0159241i | ||||
\(460\) | −7.42586 | + | 12.8620i | −0.346233 | + | 0.599692i | ||||
\(461\) | 30.9864 | 1.44318 | 0.721590 | − | 0.692320i | \(-0.243412\pi\) | ||||
0.721590 | + | 0.692320i | \(0.243412\pi\) | |||||||
\(462\) | 0.312763 | + | 0.511245i | 0.0145510 | + | 0.0237853i | ||||
\(463\) | −14.7992 | −0.687779 | −0.343889 | − | 0.939010i | \(-0.611745\pi\) | ||||
−0.343889 | + | 0.939010i | \(0.611745\pi\) | |||||||
\(464\) | 1.27283 | − | 2.20461i | 0.0590898 | − | 0.102346i | ||||
\(465\) | −6.56081 | − | 11.3637i | −0.304250 | − | 0.526977i | ||||
\(466\) | −0.207568 | − | 0.359518i | −0.00961538 | − | 0.0166543i | ||||
\(467\) | 0.914979 | − | 1.58479i | 0.0423402 | − | 0.0733353i | −0.844079 | − | 0.536219i | \(-0.819852\pi\) |
0.886419 | + | 0.462884i | \(0.153185\pi\) | |||||||
\(468\) | 1.99397 | 0.0921711 | ||||||||
\(469\) | −8.47818 | − | 13.8585i | −0.391486 | − | 0.639927i | ||||
\(470\) | 1.61891 | 0.0746748 | ||||||||
\(471\) | 5.10068 | − | 8.83464i | 0.235027 | − | 0.407079i | ||||
\(472\) | −1.13786 | − | 1.97084i | −0.0523745 | − | 0.0907152i | ||||
\(473\) | 9.84152 | + | 17.0460i | 0.452514 | + | 0.783777i | ||||
\(474\) | −0.0922287 | + | 0.159745i | −0.00423621 | + | 0.00733732i | ||||
\(475\) | −0.0186275 | −0.000854689 | ||||||||
\(476\) | −0.993031 | + | 1.82566i | −0.0455155 | + | 0.0836790i | ||||
\(477\) | 12.4338 | 0.569306 | ||||||||
\(478\) | 1.05851 | − | 1.83340i | 0.0484153 | − | 0.0838578i | ||||
\(479\) | −4.67330 | − | 8.09439i | −0.213528 | − | 0.369842i | 0.739288 | − | 0.673389i | \(-0.235162\pi\) |
−0.952816 | + | 0.303547i | \(0.901829\pi\) | |||||||
\(480\) | −1.02232 | − | 1.77071i | −0.0466623 | − | 0.0808215i | ||||
\(481\) | 2.09335 | − | 3.62579i | 0.0954486 | − | 0.165322i | ||||
\(482\) | −1.21765 | −0.0554623 | ||||||||
\(483\) | −8.94471 | + | 0.227495i | −0.406998 | + | 0.0103514i | ||||
\(484\) | 4.97544 | 0.226156 | ||||||||
\(485\) | 16.4186 | − | 28.4379i | 0.745531 | − | 1.29130i | ||||
\(486\) | 0.0388377 | + | 0.0672688i | 0.00176171 | + | 0.00305138i | ||||
\(487\) | −11.6870 | − | 20.2424i | −0.529587 | − | 0.917272i | −0.999404 | − | 0.0345080i | \(-0.989014\pi\) |
0.469817 | − | 0.882764i | \(-0.344320\pi\) | |||||||
\(488\) | −0.371340 | + | 0.643179i | −0.0168098 | + | 0.0291154i | ||||
\(489\) | −15.5835 | −0.704712 | ||||||||
\(490\) | 0.650705 | + | 1.00530i | 0.0293959 | + | 0.0454150i | ||||
\(491\) | −21.4726 | −0.969044 | −0.484522 | − | 0.874779i | \(-0.661007\pi\) | ||||
−0.484522 | + | 0.874779i | \(0.661007\pi\) | |||||||
\(492\) | −0.433672 | + | 0.751142i | −0.0195514 | + | 0.0338641i | ||||
\(493\) | −0.126499 | − | 0.219103i | −0.00569723 | − | 0.00986790i | ||||
\(494\) | 0.00484505 | + | 0.00839187i | 0.000217989 | + | 0.000377568i | ||||
\(495\) | 3.21146 | − | 5.56241i | 0.144344 | − | 0.250012i | ||||
\(496\) | 23.6157 | 1.06038 | ||||||||
\(497\) | −37.2469 | + | 0.947317i | −1.67075 | + | 0.0424930i | ||||
\(498\) | 0.760290 | 0.0340694 | ||||||||
\(499\) | 11.0957 | − | 19.2184i | 0.496714 | − | 0.860333i | −0.503279 | − | 0.864124i | \(-0.667873\pi\) |
0.999993 | + | 0.00379076i | \(0.00120664\pi\) | |||||||
\(500\) | 11.3068 | + | 19.5839i | 0.505655 | + | 0.875819i | ||||
\(501\) | 0.766550 | + | 1.32770i | 0.0342469 | + | 0.0593174i | ||||
\(502\) | 0.707693 | − | 1.22576i | 0.0315859 | − | 0.0547083i | ||||
\(503\) | 17.3231 | 0.772399 | 0.386200 | − | 0.922415i | \(-0.373788\pi\) | ||||
0.386200 | + | 0.922415i | \(0.373788\pi\) | |||||||
\(504\) | 0.392194 | − | 0.721037i | 0.0174697 | − | 0.0321176i | ||||
\(505\) | 44.0090 | 1.95838 | ||||||||
\(506\) | −0.383038 | + | 0.663441i | −0.0170281 | + | 0.0294936i | ||||
\(507\) | 0.500000 | + | 0.866025i | 0.0222058 | + | 0.0384615i | ||||
\(508\) | 14.9260 | + | 25.8526i | 0.662233 | + | 1.14702i | ||||
\(509\) | 13.4306 | − | 23.2625i | 0.595303 | − | 1.03109i | −0.398202 | − | 0.917298i | \(-0.630366\pi\) |
0.993504 | − | 0.113796i | \(-0.0363011\pi\) | |||||||
\(510\) | −0.0673933 | −0.00298423 | ||||||||
\(511\) | 10.4284 | + | 17.0463i | 0.461325 | + | 0.754086i | ||||
\(512\) | 6.13928 | 0.271321 | ||||||||
\(513\) | 0.0623756 | − | 0.108038i | 0.00275395 | − | 0.00476998i | ||||
\(514\) | −0.584948 | − | 1.01316i | −0.0258010 | − | 0.0446886i | ||||
\(515\) | −16.1597 | − | 27.9895i | −0.712083 | − | 1.23336i | ||||
\(516\) | 6.72898 | − | 11.6549i | 0.296227 | − | 0.513080i | ||||
\(517\) | −27.5975 | −1.21374 | ||||||||
\(518\) | −0.449010 | − | 0.733956i | −0.0197284 | − | 0.0322482i | ||||
\(519\) | 13.9844 | 0.613849 | ||||||||
\(520\) | 0.341633 | − | 0.591725i | 0.0149816 | − | 0.0259489i | ||||
\(521\) | 5.10145 | + | 8.83598i | 0.223499 | + | 0.387111i | 0.955868 | − | 0.293797i | \(-0.0949188\pi\) |
−0.732369 | + | 0.680908i | \(0.761585\pi\) | |||||||
\(522\) | 0.0249424 | + | 0.0432016i | 0.00109170 | + | 0.00189088i | ||||
\(523\) | −5.95733 | + | 10.3184i | −0.260496 | + | 0.451192i | −0.966374 | − | 0.257141i | \(-0.917219\pi\) |
0.705878 | + | 0.708334i | \(0.250553\pi\) | |||||||
\(524\) | −37.3712 | −1.63257 | ||||||||
\(525\) | −0.188766 | + | 0.347040i | −0.00823841 | + | 0.0151461i | ||||
\(526\) | −2.15872 | −0.0941248 | ||||||||
\(527\) | 1.17351 | − | 2.03258i | 0.0511190 | − | 0.0885408i | ||||
\(528\) | 5.77985 | + | 10.0110i | 0.251536 | + | 0.435673i | ||||
\(529\) | 5.78146 | + | 10.0138i | 0.251368 | + | 0.435382i | ||||
\(530\) | 1.06355 | − | 1.84213i | 0.0461978 | − | 0.0800170i | ||||
\(531\) | −7.33555 | −0.318336 | ||||||||
\(532\) | −0.657917 | + | 0.0167331i | −0.0285243 | + | 0.000725472i | ||||
\(533\) | −0.434984 | −0.0188412 | ||||||||
\(534\) | −0.248702 | + | 0.430765i | −0.0107624 | + | 0.0186410i | ||||
\(535\) | −5.54981 | − | 9.61256i | −0.239939 | − | 0.415587i | ||||
\(536\) | 0.952488 | + | 1.64976i | 0.0411412 | + | 0.0712587i | ||||
\(537\) | −10.9652 | + | 18.9923i | −0.473183 | + | 0.819577i | ||||
\(538\) | −0.622031 | −0.0268177 | ||||||||
\(539\) | −11.0925 | − | 17.1374i | −0.477789 | − | 0.738158i | ||||
\(540\) | −4.39156 | −0.188983 | ||||||||
\(541\) | −9.98434 | + | 17.2934i | −0.429260 | + | 0.743501i | −0.996808 | − | 0.0798401i | \(-0.974559\pi\) |
0.567547 | + | 0.823341i | \(0.307892\pi\) | |||||||
\(542\) | −0.787026 | − | 1.36317i | −0.0338057 | − | 0.0585532i | ||||
\(543\) | 0.477632 | + | 0.827283i | 0.0204972 | + | 0.0355021i | ||||
\(544\) | 0.182859 | − | 0.316722i | 0.00784004 | − | 0.0135793i | ||||
\(545\) | 0.270199 | 0.0115740 | ||||||||
\(546\) | 0.205443 | − | 0.00522513i | 0.00879216 | − | 0.000223615i | ||||
\(547\) | −16.7640 | −0.716778 | −0.358389 | − | 0.933572i | \(-0.616674\pi\) | ||||
−0.358389 | + | 0.933572i | \(0.616674\pi\) | |||||||
\(548\) | −13.5495 | + | 23.4684i | −0.578806 | + | 1.00252i | ||||
\(549\) | 1.19697 | + | 2.07321i | 0.0510855 | + | 0.0884826i | ||||
\(550\) | 0.0169120 | + | 0.0292924i | 0.000721129 | + | 0.00124903i | ||||
\(551\) | 0.0400590 | − | 0.0693843i | 0.00170657 | − | 0.00295587i | ||||
\(552\) | 1.04917 | 0.0446556 | ||||||||
\(553\) | 3.00210 | − | 5.51929i | 0.127662 | − | 0.234704i | ||||
\(554\) | −2.28629 | −0.0971351 | ||||||||
\(555\) | −4.61045 | + | 7.98554i | −0.195703 | + | 0.338967i | ||||
\(556\) | −15.6817 | − | 27.1616i | −0.665054 | − | 1.15191i | ||||
\(557\) | −11.6898 | − | 20.2474i | −0.495314 | − | 0.857909i | 0.504671 | − | 0.863311i | \(-0.331614\pi\) |
−0.999985 | + | 0.00540254i | \(0.998280\pi\) | |||||||
\(558\) | −0.231387 | + | 0.400774i | −0.00979540 | + | 0.0169661i | ||||
\(559\) | 6.74934 | 0.285467 | ||||||||
\(560\) | 12.0536 | + | 19.7030i | 0.509359 | + | 0.832603i | ||||
\(561\) | 1.14885 | 0.0485044 | ||||||||
\(562\) | 0.146315 | − | 0.253425i | 0.00617193 | − | 0.0106901i | ||||
\(563\) | −21.0019 | − | 36.3763i | −0.885124 | − | 1.53308i | −0.845571 | − | 0.533863i | \(-0.820740\pi\) |
−0.0395532 | − | 0.999217i | \(-0.512593\pi\) | |||||||
\(564\) | 9.43466 | + | 16.3413i | 0.397271 | + | 0.688093i | ||||
\(565\) | −4.58257 | + | 7.93725i | −0.192790 | + | 0.333922i | ||||
\(566\) | 1.74309 | 0.0732675 | ||||||||
\(567\) | −1.38070 | − | 2.25691i | −0.0579841 | − | 0.0947814i | ||||
\(568\) | 4.36887 | 0.183314 | ||||||||
\(569\) | −6.28982 | + | 10.8943i | −0.263683 | + | 0.456712i | −0.967218 | − | 0.253948i | \(-0.918271\pi\) |
0.703535 | + | 0.710661i | \(0.251604\pi\) | |||||||
\(570\) | −0.0106709 | − | 0.0184825i | −0.000446953 | − | 0.000774146i | ||||
\(571\) | 4.39938 | + | 7.61995i | 0.184108 | + | 0.318885i | 0.943276 | − | 0.332011i | \(-0.107727\pi\) |
−0.759167 | + | 0.650895i | \(0.774394\pi\) | |||||||
\(572\) | −2.90749 | + | 5.03593i | −0.121568 | + | 0.210563i | ||||
\(573\) | −19.6834 | −0.822287 | ||||||||
\(574\) | −0.0427139 | + | 0.0785284i | −0.00178284 | + | 0.00327771i | ||||
\(575\) | −0.504972 | −0.0210588 | ||||||||
\(576\) | 3.92778 | − | 6.80312i | 0.163658 | − | 0.283463i | ||||
\(577\) | −0.706850 | − | 1.22430i | −0.0294266 | − | 0.0509683i | 0.850937 | − | 0.525268i | \(-0.176035\pi\) |
−0.880364 | + | 0.474299i | \(0.842701\pi\) | |||||||
\(578\) | 0.654213 | + | 1.13313i | 0.0272117 | + | 0.0471320i | ||||
\(579\) | 7.54753 | − | 13.0727i | 0.313664 | − | 0.543283i | ||||
\(580\) | −2.82036 | −0.117109 | ||||||||
\(581\) | −25.8884 | + | 0.658430i | −1.07403 | + | 0.0273163i | ||||
\(582\) | −1.15811 | −0.0480051 | ||||||||
\(583\) | −18.1303 | + | 31.4027i | −0.750882 | + | 1.30057i | ||||
\(584\) | −1.17159 | − | 2.02925i | −0.0484806 | − | 0.0839708i | ||||
\(585\) | −1.10121 | − | 1.90736i | −0.0455296 | − | 0.0788595i | ||||
\(586\) | −0.315997 | + | 0.547323i | −0.0130537 | + | 0.0226097i | ||||
\(587\) | −24.3046 | −1.00316 | −0.501580 | − | 0.865111i | \(-0.667248\pi\) | ||||
−0.501580 | + | 0.865111i | \(0.667248\pi\) | |||||||
\(588\) | −6.35539 | + | 12.4269i | −0.262092 | + | 0.512477i | ||||
\(589\) | 0.743243 | 0.0306248 | ||||||||
\(590\) | −0.627462 | + | 1.08680i | −0.0258322 | + | 0.0447427i | ||||
\(591\) | −5.51613 | − | 9.55421i | −0.226903 | − | 0.393008i | ||||
\(592\) | −8.29770 | − | 14.3720i | −0.341033 | − | 0.590687i | ||||
\(593\) | 13.3532 | − | 23.1283i | 0.548348 | − | 0.949767i | −0.450040 | − | 0.893009i | \(-0.648590\pi\) |
0.998388 | − | 0.0567584i | \(-0.0180765\pi\) | |||||||
\(594\) | −0.226524 | −0.00929439 | ||||||||
\(595\) | 2.29478 | − | 0.0583643i | 0.0940770 | − | 0.00239270i | ||||
\(596\) | −6.67597 | −0.273459 | ||||||||
\(597\) | 3.58851 | − | 6.21548i | 0.146868 | − | 0.254382i | ||||
\(598\) | 0.131344 | + | 0.227495i | 0.00537106 | + | 0.00930295i | ||||
\(599\) | 16.8268 | + | 29.1449i | 0.687526 | + | 1.19083i | 0.972636 | + | 0.232335i | \(0.0746364\pi\) |
−0.285110 | + | 0.958495i | \(0.592030\pi\) | |||||||
\(600\) | 0.0231616 | − | 0.0401170i | 0.000945567 | − | 0.00163777i | ||||
\(601\) | −12.5737 | −0.512890 | −0.256445 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256445 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(602\) | 0.662762 | − | 1.21847i | 0.0270122 | − | 0.0496611i | ||||
\(603\) | 6.14047 | 0.250059 | ||||||||
\(604\) | −20.3860 | + | 35.3095i | −0.829493 | + | 1.43672i | ||||
\(605\) | −2.74780 | − | 4.75933i | −0.111714 | − | 0.193494i | ||||
\(606\) | −0.776057 | − | 1.34417i | −0.0315252 | − | 0.0546032i | ||||
\(607\) | −10.7209 | + | 18.5691i | −0.435146 | + | 0.753695i | −0.997308 | − | 0.0733326i | \(-0.976637\pi\) |
0.562162 | + | 0.827027i | \(0.309970\pi\) | |||||||
\(608\) | 0.115814 | 0.00469687 | ||||||||
\(609\) | −0.886720 | − | 1.44944i | −0.0359317 | − | 0.0587343i | ||||
\(610\) | 0.409542 | 0.0165819 | ||||||||
\(611\) | −4.73160 | + | 8.19538i | −0.191420 | + | 0.331549i | ||||
\(612\) | −0.392753 | − | 0.680269i | −0.0158761 | − | 0.0274982i | ||||
\(613\) | −15.3631 | − | 26.6096i | −0.620509 | − | 1.07475i | −0.989391 | − | 0.145276i | \(-0.953593\pi\) |
0.368882 | − | 0.929476i | \(-0.379740\pi\) | |||||||
\(614\) | −0.734993 | + | 1.27304i | −0.0296619 | + | 0.0513759i | ||||
\(615\) | 0.958020 | 0.0386311 | ||||||||
\(616\) | 1.24916 | + | 2.04190i | 0.0503302 | + | 0.0822703i | ||||
\(617\) | 0.216739 | 0.00872559 | 0.00436279 | − | 0.999990i | \(-0.498611\pi\) | ||||
0.00436279 | + | 0.999990i | \(0.498611\pi\) | |||||||
\(618\) | −0.569923 | + | 0.987135i | −0.0229257 | + | 0.0397084i | ||||
\(619\) | −15.2490 | − | 26.4121i | −0.612909 | − | 1.06159i | −0.990747 | − | 0.135718i | \(-0.956666\pi\) |
0.377838 | − | 0.925872i | \(-0.376668\pi\) | |||||||
\(620\) | −13.0820 | − | 22.6588i | −0.525387 | − | 0.909997i | ||||
\(621\) | 1.69094 | − | 2.92879i | 0.0678550 | − | 0.117528i | ||||
\(622\) | 0.902505 | 0.0361871 | ||||||||
\(623\) | 8.09542 | − | 14.8832i | 0.324336 | − | 0.596283i | ||||
\(624\) | 3.96384 | 0.158680 | ||||||||
\(625\) | 12.1156 | − | 20.9848i | 0.484622 | − | 0.839391i | ||||
\(626\) | 0.454492 | + | 0.787202i | 0.0181651 | + | 0.0314629i | ||||
\(627\) | 0.181905 | + | 0.315069i | 0.00726460 | + | 0.0125827i | ||||
\(628\) | 10.1706 | − | 17.6160i | 0.405851 | − | 0.702954i | ||||
\(629\) | −1.64932 | −0.0657626 | ||||||||
\(630\) | −0.452474 | + | 0.0115080i | −0.0180270 | + | 0.000458489i | ||||
\(631\) | −14.0505 | −0.559343 | −0.279671 | − | 0.960096i | \(-0.590226\pi\) | ||||
−0.279671 | + | 0.960096i | \(0.590226\pi\) | |||||||
\(632\) | −0.368358 | + | 0.638015i | −0.0146525 | + | 0.0253789i | ||||
\(633\) | 7.85593 | + | 13.6069i | 0.312245 | + | 0.540825i | ||||
\(634\) | 1.28191 | + | 2.22034i | 0.0509112 | + | 0.0881808i | ||||
\(635\) | 16.4864 | − | 28.5553i | 0.654244 | − | 1.13318i | ||||
\(636\) | 24.7926 | 0.983092 | ||||||||
\(637\) | −6.99095 | + | 0.355838i | −0.276992 | + | 0.0140988i | ||||
\(638\) | −0.145479 | −0.00575956 | ||||||||
\(639\) | 7.04128 | − | 12.1958i | 0.278549 | − | 0.482460i | ||||
\(640\) | −2.71658 | − | 4.70526i | −0.107382 | − | 0.185992i | ||||
\(641\) | 9.08657 | + | 15.7384i | 0.358898 | + | 0.621629i | 0.987777 | − | 0.155874i | \(-0.0498193\pi\) |
−0.628879 | + | 0.777503i | \(0.716486\pi\) | |||||||
\(642\) | −0.195731 | + | 0.339017i | −0.00772490 | + | 0.0133799i | ||||
\(643\) | −7.27895 | −0.287054 | −0.143527 | − | 0.989646i | \(-0.545844\pi\) | ||||
−0.143527 | + | 0.989646i | \(0.545844\pi\) | |||||||
\(644\) | −17.8354 | + | 0.453617i | −0.702815 | + | 0.0178750i | ||||
\(645\) | −14.8649 | −0.585306 | ||||||||
\(646\) | 0.00190867 | − | 0.00330591i | 7.50955e−5 | − | 0.000130069i | ||||
\(647\) | −8.88985 | − | 15.3977i | −0.349496 | − | 0.605345i | 0.636664 | − | 0.771141i | \(-0.280314\pi\) |
−0.986160 | + | 0.165797i | \(0.946980\pi\) | |||||||
\(648\) | 0.155116 | + | 0.268670i | 0.00609355 | + | 0.0105543i | ||||
\(649\) | 10.6963 | − | 18.5265i | 0.419867 | − | 0.727230i | ||||
\(650\) | 0.0115983 | 0.000454922 | ||||||||
\(651\) | 7.53180 | − | 13.8470i | 0.295195 | − | 0.542707i | ||||
\(652\) | −31.0731 | −1.21692 | ||||||||
\(653\) | −4.06627 | + | 7.04298i | −0.159125 | + | 0.275613i | −0.934554 | − | 0.355823i | \(-0.884201\pi\) |
0.775428 | + | 0.631436i | \(0.217534\pi\) | |||||||
\(654\) | −0.00476470 | − | 0.00825270i | −0.000186314 | − | 0.000322706i | ||||
\(655\) | 20.6391 | + | 35.7480i | 0.806437 | + | 1.39679i | ||||
\(656\) | −0.862103 | + | 1.49321i | −0.0336595 | + | 0.0582999i | ||||
\(657\) | −7.55295 | −0.294669 | ||||||||
\(658\) | 1.01490 | + | 1.65896i | 0.0395648 | + | 0.0646731i | ||||
\(659\) | 10.0958 | 0.393278 | 0.196639 | − | 0.980476i | \(-0.436997\pi\) | ||||
0.196639 | + | 0.980476i | \(0.436997\pi\) | |||||||
\(660\) | 6.40354 | − | 11.0913i | 0.249257 | − | 0.431727i | ||||
\(661\) | −12.1727 | − | 21.0838i | −0.473464 | − | 0.820064i | 0.526074 | − | 0.850439i | \(-0.323663\pi\) |
−0.999539 | + | 0.0303745i | \(0.990330\pi\) | |||||||
\(662\) | −0.573811 | − | 0.993870i | −0.0223018 | − | 0.0386279i | ||||
\(663\) | 0.196971 | − | 0.341163i | 0.00764971 | − | 0.0132497i | ||||
\(664\) | 3.03657 | 0.117842 | ||||||||
\(665\) | 0.379356 | + | 0.620099i | 0.0147108 | + | 0.0240464i | ||||
\(666\) | 0.325204 | 0.0126014 | ||||||||
\(667\) | 1.08596 | − | 1.88094i | 0.0420485 | − | 0.0728301i | ||||
\(668\) | 1.52848 | + | 2.64740i | 0.0591385 | + | 0.102431i | ||||
\(669\) | 3.10445 | + | 5.37706i | 0.120025 | + | 0.207889i | ||||
\(670\) | 0.525239 | − | 0.909740i | 0.0202917 | − | 0.0351463i | ||||
\(671\) | −6.98143 | −0.269515 | ||||||||
\(672\) | 1.17362 | − | 2.15767i | 0.0452735 | − | 0.0832340i | ||||
\(673\) | −39.4811 | −1.52189 | −0.760943 | − | 0.648819i | \(-0.775263\pi\) | ||||
−0.760943 | + | 0.648819i | \(0.775263\pi\) | |||||||
\(674\) | 0.507660 | − | 0.879294i | 0.0195543 | − | 0.0338691i | ||||
\(675\) | −0.0746586 | − | 0.129313i | −0.00287361 | − | 0.00497724i | ||||
\(676\) | 0.996983 | + | 1.72683i | 0.0383455 | + | 0.0664164i | ||||
\(677\) | −8.99151 | + | 15.5738i | −0.345572 | + | 0.598548i | −0.985457 | − | 0.169922i | \(-0.945648\pi\) |
0.639886 | + | 0.768470i | \(0.278982\pi\) | |||||||
\(678\) | 0.323237 | 0.0124138 | ||||||||
\(679\) | 39.4343 | − | 1.00295i | 1.51335 | − | 0.0384897i | ||||
\(680\) | −0.269167 | −0.0103221 | ||||||||
\(681\) | 11.8440 | − | 20.5143i | 0.453862 | − | 0.786111i | ||||
\(682\) | −0.674793 | − | 1.16878i | −0.0258391 | − | 0.0447547i | ||||
\(683\) | −7.66325 | − | 13.2731i | −0.293226 | − | 0.507882i | 0.681345 | − | 0.731963i | \(-0.261395\pi\) |
−0.974571 | + | 0.224080i | \(0.928062\pi\) | |||||||
\(684\) | 0.124375 | − | 0.215424i | 0.00475559 | − | 0.00823692i | ||||
\(685\) | 29.9321 | 1.14365 | ||||||||
\(686\) | −0.622247 | + | 1.29703i | −0.0237575 | + | 0.0495208i | ||||
\(687\) | 9.04226 | 0.344984 | ||||||||
\(688\) | 13.3766 | − | 23.1690i | 0.509980 | − | 0.883311i | ||||
\(689\) | 6.21691 | + | 10.7680i | 0.236846 | + | 0.410229i | ||||
\(690\) | −0.289276 | − | 0.501041i | −0.0110125 | − | 0.0190743i | ||||
\(691\) | 12.6299 | − | 21.8757i | 0.480466 | − | 0.832191i | −0.519283 | − | 0.854602i | \(-0.673801\pi\) |
0.999749 | + | 0.0224112i | \(0.00713432\pi\) | |||||||
\(692\) | 27.8845 | 1.06001 | ||||||||
\(693\) | 7.71329 | − | 0.196176i | 0.293004 | − | 0.00745209i | ||||
\(694\) | 0.495530 | 0.0188101 | ||||||||
\(695\) | −17.3212 | + | 30.0012i | −0.657030 | + | 1.13801i | ||||
\(696\) | 0.0996193 | + | 0.172546i | 0.00377606 | + | 0.00654033i | ||||
\(697\) | 0.0856792 | + | 0.148401i | 0.00324533 | + | 0.00562108i | ||||
\(698\) | 0.401142 | − | 0.694798i | 0.0151834 | − | 0.0262985i | ||||
\(699\) | −5.34449 | −0.202147 | ||||||||
\(700\) | −0.376392 | + | 0.691987i | −0.0142263 | + | 0.0261547i | ||||
\(701\) | 37.6169 | 1.42077 | 0.710385 | − | 0.703813i | \(-0.248521\pi\) | ||||
0.710385 | + | 0.703813i | \(0.248521\pi\) | |||||||
\(702\) | −0.0388377 | + | 0.0672688i | −0.00146583 | + | 0.00253890i | ||||
\(703\) | −0.261148 | − | 0.452322i | −0.00984939 | − | 0.0170596i | ||||
\(704\) | 11.4546 | + | 19.8399i | 0.431710 | + | 0.747743i | ||||
\(705\) | 10.4210 | − | 18.0497i | 0.392478 | − | 0.679792i | ||||
\(706\) | −2.34205 | −0.0881441 | ||||||||
\(707\) | 27.5893 | + | 45.0978i | 1.03760 | + | 1.69608i | ||||
\(708\) | −14.6268 | −0.549710 | ||||||||
\(709\) | −5.36331 | + | 9.28953i | −0.201423 | + | 0.348876i | −0.948987 | − | 0.315314i | \(-0.897890\pi\) |
0.747564 | + | 0.664190i | \(0.231223\pi\) | |||||||
\(710\) | −1.20458 | − | 2.08640i | −0.0452071 | − | 0.0783011i | ||||
\(711\) | 1.18736 | + | 2.05657i | 0.0445295 | + | 0.0771274i | ||||
\(712\) | −0.993308 | + | 1.72046i | −0.0372258 | + | 0.0644770i | ||||
\(713\) | 20.1485 | 0.754569 | ||||||||
\(714\) | −0.0422490 | − | 0.0690606i | −0.00158113 | − | 0.00258453i | ||||
\(715\) | 6.42292 | 0.240203 | ||||||||
\(716\) | −21.8642 | + | 37.8700i | −0.817105 | + | 1.41527i | ||||
\(717\) | −13.6274 | − | 23.6034i | −0.508925 | − | 0.881484i | ||||
\(718\) | 1.13317 | + | 1.96271i | 0.0422896 | + | 0.0732478i | ||||
\(719\) | −6.17034 | + | 10.6873i | −0.230115 | + | 0.398571i | −0.957842 | − | 0.287296i | \(-0.907244\pi\) |
0.727727 | + | 0.685867i | \(0.240577\pi\) | |||||||
\(720\) | −8.73006 | −0.325350 | ||||||||
\(721\) | 18.5513 | − | 34.1061i | 0.690888 | − | 1.27018i | ||||
\(722\) | −1.47462 | −0.0548798 | ||||||||
\(723\) | −7.83806 | + | 13.5759i | −0.291500 | + | 0.504894i | ||||
\(724\) | 0.952383 | + | 1.64958i | 0.0353950 | + | 0.0613060i | ||||
\(725\) | −0.0479475 | − | 0.0830475i | −0.00178072 | − | 0.00308431i | ||||
\(726\) | −0.0969096 | + | 0.167852i | −0.00359665 | + | 0.00622958i | ||||
\(727\) | 46.5464 | 1.72631 | 0.863155 | − | 0.504939i | \(-0.168485\pi\) | ||||
0.863155 | + | 0.504939i | \(0.168485\pi\) | |||||||
\(728\) | 0.820534 | − | 0.0208690i | 0.0304110 | − | 0.000773457i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.646058 | + | 1.11900i | −0.0239117 | + | 0.0414162i | ||||
\(731\) | −1.32942 | − | 2.30263i | −0.0491705 | − | 0.0851658i | ||||
\(732\) | 2.38672 | + | 4.13392i | 0.0882157 | + | 0.152794i | ||||
\(733\) | −18.9421 | + | 32.8088i | −0.699644 | + | 1.21182i | 0.268946 | + | 0.963155i | \(0.413325\pi\) |
−0.968590 | + | 0.248664i | \(0.920009\pi\) | |||||||
\(734\) | −0.348321 | −0.0128568 | ||||||||
\(735\) | 15.3971 | − | 0.783708i | 0.567929 | − | 0.0289075i | ||||
\(736\) | 3.13959 | 0.115727 | ||||||||
\(737\) | −8.95371 | + | 15.5083i | −0.329814 | + | 0.571255i | ||||
\(738\) | −0.0168938 | − | 0.0292609i | −0.000621868 | − | 0.00107711i | ||||
\(739\) | −9.48912 | − | 16.4356i | −0.349063 | − | 0.604595i | 0.637020 | − | 0.770847i | \(-0.280167\pi\) |
−0.986083 | + | 0.166252i | \(0.946833\pi\) | |||||||
\(740\) | −9.19309 | + | 15.9229i | −0.337945 | + | 0.585337i | ||||
\(741\) | 0.124751 | 0.00458285 | ||||||||
\(742\) | 2.55445 | − | 0.0649684i | 0.0937767 | − | 0.00238507i | ||||
\(743\) | 20.2127 | 0.741534 | 0.370767 | − | 0.928726i | \(-0.379095\pi\) | ||||
0.370767 | + | 0.928726i | \(0.379095\pi\) | |||||||
\(744\) | −0.924153 | + | 1.60068i | −0.0338811 | + | 0.0586838i | ||||
\(745\) | 3.68696 | + | 6.38600i | 0.135080 | + | 0.233965i | ||||
\(746\) | −0.931682 | − | 1.61372i | −0.0341113 | − | 0.0590825i | ||||
\(747\) | 4.89402 | − | 8.47669i | 0.179063 | − | 0.310146i | ||||
\(748\) | 2.29077 | 0.0837587 | ||||||||
\(749\) | 6.37118 | − | 11.7132i | 0.232798 | − | 0.427992i | ||||
\(750\) | −0.880916 | −0.0321665 | ||||||||
\(751\) | 23.5767 | − | 40.8361i | 0.860328 | − | 1.49013i | −0.0112854 | − | 0.999936i | \(-0.503592\pi\) |
0.871613 | − | 0.490195i | \(-0.163074\pi\) | |||||||
\(752\) | 18.7553 | + | 32.4851i | 0.683935 | + | 1.18461i | ||||
\(753\) | −9.11090 | − | 15.7805i | −0.332020 | − | 0.575075i | ||||
\(754\) | −0.0249424 | + | 0.0432016i | −0.000908350 | + | 0.00157331i | ||||
\(755\) | 45.0344 | 1.63897 | ||||||||
\(756\) | −2.75308 | − | 4.50021i | −0.100129 | − | 0.163671i | ||||
\(757\) | −14.7288 | −0.535327 | −0.267664 | − | 0.963512i | \(-0.586252\pi\) | ||||
−0.267664 | + | 0.963512i | \(0.586252\pi\) | |||||||
\(758\) | −0.785408 | + | 1.36037i | −0.0285273 | + | 0.0494107i | ||||
\(759\) | 4.93127 | + | 8.54120i | 0.178994 | + | 0.310026i | ||||
\(760\) | −0.0426191 | − | 0.0738184i | −0.00154596 | − | 0.00267767i | ||||
\(761\) | −20.8747 | + | 36.1560i | −0.756706 | + | 1.31065i | 0.187815 | + | 0.982204i | \(0.439859\pi\) |
−0.944522 | + | 0.328450i | \(0.893474\pi\) | |||||||
\(762\) | −1.16289 | −0.0421270 | ||||||||
\(763\) | 0.169388 | + | 0.276883i | 0.00613226 | + | 0.0100238i | ||||
\(764\) | −39.2481 | −1.41995 | ||||||||
\(765\) | −0.433814 | + | 0.751388i | −0.0156846 | + | 0.0271665i | ||||
\(766\) | 0.896446 | + | 1.55269i | 0.0323899 | + | 0.0561010i | ||||
\(767\) | −3.66778 | − | 6.35277i | −0.132436 | − | 0.229385i | ||||
\(768\) | 7.75975 | − | 13.4403i | 0.280006 | − | 0.484985i | ||||
\(769\) | −34.0121 | −1.22651 | −0.613254 | − | 0.789886i | \(-0.710140\pi\) | ||||
−0.613254 | + | 0.789886i | \(0.710140\pi\) | |||||||
\(770\) | 0.630708 | − | 1.15954i | 0.0227291 | − | 0.0417869i | ||||
\(771\) | −15.0614 | −0.542422 | ||||||||
\(772\) | 15.0495 | − | 26.0665i | 0.541644 | − | 0.938155i | ||||
\(773\) | 8.50125 | + | 14.7246i | 0.305769 | + | 0.529607i | 0.977432 | − | 0.211249i | \(-0.0677532\pi\) |
−0.671663 | + | 0.740856i | \(0.734420\pi\) | |||||||
\(774\) | 0.262129 | + | 0.454020i | 0.00942203 | + | 0.0163194i | ||||
\(775\) | 0.444801 | − | 0.770419i | 0.0159777 | − | 0.0276743i | ||||
\(776\) | −4.62544 | −0.166044 | ||||||||
\(777\) | −11.0734 | + | 0.281635i | −0.397256 | + | 0.0101036i | ||||
\(778\) | −2.58946 | −0.0928366 | ||||||||
\(779\) | −0.0271324 | + | 0.0469947i | −0.000972119 | + | 0.00168376i | ||||
\(780\) | −2.19578 | − | 3.80321i | −0.0786216 | − | 0.136177i | ||||
\(781\) | 20.5344 | + | 35.5666i | 0.734779 | + | 1.27267i | ||||
\(782\) | 0.0517420 | − | 0.0896197i | 0.00185029 | − | 0.00320479i | ||||
\(783\) | 0.642223 | 0.0229512 | ||||||||
\(784\) | −12.6340 | + | 24.7037i | −0.451213 | + | 0.882273i | ||||
\(785\) | −22.4678 | −0.801909 | ||||||||
\(786\) | 0.727902 | − | 1.26076i | 0.0259634 | − | 0.0449699i | ||||
\(787\) | 15.5647 | + | 26.9589i | 0.554822 | + | 0.960980i | 0.997917 | + | 0.0645052i | \(0.0205469\pi\) |
−0.443096 | + | 0.896474i | \(0.646120\pi\) | |||||||
\(788\) | −10.9990 | − | 19.0508i | −0.391822 | − | 0.678656i | ||||
\(789\) | −13.8958 | + | 24.0682i | −0.494704 | + | 0.856852i | ||||
\(790\) | 0.406254 | 0.0144539 | ||||||||
\(791\) | −11.0064 | + | 0.279932i | −0.391344 | + | 0.00995322i | ||||
\(792\) | −0.904729 | −0.0321482 | ||||||||
\(793\) | −1.19697 | + | 2.07321i | −0.0425057 | + | 0.0736220i | ||||
\(794\) | 0.784057 | + | 1.35803i | 0.0278251 | + | 0.0481946i | ||||
\(795\) | −13.6923 | − | 23.7158i | −0.485616 | − | 0.841111i | ||||
\(796\) | 7.15536 | − | 12.3935i | 0.253615 | − | 0.439274i | ||||
\(797\) | 10.5797 | 0.374752 | 0.187376 | − | 0.982288i | \(-0.440002\pi\) | ||||
0.187376 | + | 0.982288i | \(0.440002\pi\) | |||||||
\(798\) | 0.0122501 | − | 0.0225215i | 0.000433650 | − | 0.000797254i | ||||
\(799\) | 3.72795 | 0.131885 | ||||||||
\(800\) | 0.0693100 | − | 0.120048i | 0.00245048 | − | 0.00424435i | ||||
\(801\) | 3.20182 | + | 5.54571i | 0.113131 | + | 0.195948i | ||||
\(802\) | 0.163696 | + | 0.283530i | 0.00578030 | + | 0.0100118i | ||||
\(803\) | 11.0133 | − | 19.0756i | 0.388651 | − | 0.673163i | ||||
\(804\) | 12.2439 | 0.431809 | ||||||||
\(805\) | 10.2839 | + | 16.8102i | 0.362461 | + | 0.592483i | ||||
\(806\) | −0.462775 | −0.0163005 | ||||||||
\(807\) | −4.00404 | + | 6.93521i | −0.140949 | + | 0.244131i | ||||
\(808\) | −3.09955 | − | 5.36857i | −0.109042 | − | 0.188866i | ||||
\(809\) | 9.51307 | + | 16.4771i | 0.334462 | + | 0.579305i | 0.983381 | − | 0.181552i | \(-0.0581122\pi\) |
−0.648920 | + | 0.760857i | \(0.724779\pi\) | |||||||
\(810\) | 0.0855372 | − | 0.148155i | 0.00300547 | − | 0.00520563i | ||||
\(811\) | −24.9894 | −0.877497 | −0.438748 | − | 0.898610i | \(-0.644578\pi\) | ||||
−0.438748 | + | 0.898610i | \(0.644578\pi\) | |||||||
\(812\) | −1.76809 | − | 2.89014i | −0.0620478 | − | 0.101424i | ||||
\(813\) | −20.2645 | −0.710707 | ||||||||
\(814\) | −0.474194 | + | 0.821329i | −0.0166205 | + | 0.0287876i | ||||
\(815\) | 17.1608 | + | 29.7234i | 0.601117 | + | 1.04117i | ||||
\(816\) | −0.780760 | − | 1.35232i | −0.0273321 | − | 0.0473405i | ||||
\(817\) | 0.420994 | − | 0.729183i | 0.0147287 | − | 0.0255109i | ||||
\(818\) | 0.578392 | 0.0202230 | ||||||||
\(819\) | 1.26419 | − | 2.32418i | 0.0441744 | − | 0.0812135i | ||||
\(820\) | 1.91026 | 0.0667092 | ||||||||
\(821\) | −22.8500 | + | 39.5774i | −0.797471 | + | 1.38126i | 0.123788 | + | 0.992309i | \(0.460496\pi\) |
−0.921258 | + | 0.388951i | \(0.872837\pi\) | |||||||
\(822\) | −0.527823 | − | 0.914217i | −0.0184100 | − | 0.0318870i | ||||
\(823\) | 5.18997 | + | 8.98930i | 0.180911 | + | 0.313347i | 0.942191 | − | 0.335076i | \(-0.108762\pi\) |
−0.761280 | + | 0.648423i | \(0.775429\pi\) | |||||||
\(824\) | −2.27625 | + | 3.94258i | −0.0792970 | + | 0.137346i | ||||
\(825\) | 0.435453 | 0.0151605 | ||||||||
\(826\) | −1.50704 | + | 0.0383292i | −0.0524366 | + | 0.00133364i | ||||
\(827\) | −9.56239 | −0.332517 | −0.166258 | − | 0.986082i | \(-0.553169\pi\) | ||||
−0.166258 | + | 0.986082i | \(0.553169\pi\) | |||||||
\(828\) | 3.37167 | − | 5.83991i | 0.117174 | − | 0.202951i | ||||
\(829\) | 8.93681 | + | 15.4790i | 0.310388 | + | 0.537608i | 0.978446 | − | 0.206501i | \(-0.0662076\pi\) |
−0.668058 | + | 0.744109i | \(0.732874\pi\) | |||||||
\(830\) | −0.837241 | − | 1.45014i | −0.0290611 | − | 0.0503353i | ||||
\(831\) | −14.7169 | + | 25.4905i | −0.510525 | + | 0.884256i | ||||
\(832\) | 7.85556 | 0.272343 | ||||||||
\(833\) | 1.49841 | + | 2.31497i | 0.0519169 | + | 0.0802089i | ||||
\(834\) | 1.22177 | 0.0423064 | ||||||||
\(835\) | 1.68827 | − | 2.92417i | 0.0584250 | − | 0.101195i | ||||
\(836\) | 0.362713 | + | 0.628238i | 0.0125447 | + | 0.0217281i | ||||
\(837\) | 2.97890 | + | 5.15961i | 0.102966 | + | 0.178342i | ||||
\(838\) | 0.476992 | − | 0.826175i | 0.0164774 | − | 0.0285397i | ||||
\(839\) | 33.6620 | 1.16214 | 0.581071 | − | 0.813853i | \(-0.302634\pi\) | ||||
0.581071 | + | 0.813853i | \(0.302634\pi\) | |||||||
\(840\) | −1.80716 | + | 0.0459625i | −0.0623531 | + | 0.00158586i | ||||
\(841\) | −28.5876 | −0.985778 | ||||||||
\(842\) | −1.04817 | + | 1.81548i | −0.0361222 | + | 0.0625655i | ||||
\(843\) | −1.88367 | − | 3.26262i | −0.0648772 | − | 0.112371i | ||||
\(844\) | 15.6645 | + | 27.1316i | 0.539193 | + | 0.933910i | ||||
\(845\) | 1.10121 | − | 1.90736i | 0.0378829 | − | 0.0656151i | ||||
\(846\) | −0.735058 | −0.0252718 | ||||||||
\(847\) | 3.15447 | − | 5.79940i | 0.108389 | − | 0.199270i | ||||
\(848\) | 49.2857 | 1.69248 | ||||||||
\(849\) | 11.2203 | − | 19.4342i | 0.385081 | − | 0.666980i | ||||
\(850\) | −0.00228452 | − | 0.00395691i | −7.83585e−5 | − | 0.000135721i | ||||
\(851\) | −7.07945 | − | 12.2620i | −0.242681 | − | 0.420335i | ||||
\(852\) | 14.0401 | − | 24.3181i | 0.481005 | − | 0.833125i | ||||
\(853\) | −45.2796 | −1.55035 | −0.775173 | − | 0.631749i | \(-0.782337\pi\) | ||||
−0.775173 | + | 0.631749i | \(0.782337\pi\) | |||||||
\(854\) | 0.256742 | + | 0.419674i | 0.00878555 | + | 0.0143609i | ||||
\(855\) | −0.274755 | −0.00939643 | ||||||||
\(856\) | −0.781744 | + | 1.35402i | −0.0267195 | + | 0.0462795i | ||||
\(857\) | 22.2861 | + | 38.6006i | 0.761278 | + | 1.31857i | 0.942192 | + | 0.335074i | \(0.108761\pi\) |
−0.180914 | + | 0.983499i | \(0.557905\pi\) | |||||||
\(858\) | −0.113262 | − | 0.196176i | −0.00386670 | − | 0.00669732i | ||||
\(859\) | 19.9505 | − | 34.5552i | 0.680701 | − | 1.17901i | −0.294066 | − | 0.955785i | \(-0.595009\pi\) |
0.974767 | − | 0.223224i | \(-0.0716582\pi\) | |||||||
\(860\) | −29.6402 | −1.01072 | ||||||||
\(861\) | 0.600584 | + | 0.981721i | 0.0204679 | + | 0.0334570i | ||||
\(862\) | −1.57811 | −0.0537505 | ||||||||
\(863\) | 1.55523 | − | 2.69373i | 0.0529406 | − | 0.0916957i | −0.838341 | − | 0.545147i | \(-0.816474\pi\) |
0.891281 | + | 0.453451i | \(0.149807\pi\) | |||||||
\(864\) | 0.464179 | + | 0.803982i | 0.0157917 | + | 0.0273520i | ||||
\(865\) | −15.3998 | − | 26.6733i | −0.523611 | − | 0.906920i | ||||
\(866\) | 0.350662 | − | 0.607364i | 0.0119160 | − | 0.0206391i | ||||
\(867\) | 16.8448 | 0.572080 | ||||||||
\(868\) | 15.0182 | − | 27.6105i | 0.509750 | − | 0.937161i | ||||
\(869\) | −6.92538 | −0.234927 | ||||||||
\(870\) | 0.0549339 | − | 0.0951483i | 0.00186243 | − | 0.00322583i | ||||
\(871\) | 3.07024 | + | 5.31781i | 0.104031 | + | 0.180187i | ||||
\(872\) | −0.0190300 | − | 0.0329610i | −0.000644438 | − | 0.00111620i | ||||
\(873\) | −7.45479 | + | 12.9121i | −0.252306 | + | 0.437007i | ||||
\(874\) | 0.0327707 | 0.00110848 | ||||||||
\(875\) | 29.9957 | − | 0.762896i | 1.01404 | − | 0.0257906i | ||||
\(876\) | −15.0603 | −0.508841 | ||||||||
\(877\) | 2.32137 | − | 4.02073i | 0.0783872 | − | 0.135771i | −0.824167 | − | 0.566347i | \(-0.808356\pi\) |
0.902554 | + | 0.430576i | \(0.141690\pi\) | |||||||
\(878\) | −0.389733 | − | 0.675037i | −0.0131528 | − | 0.0227814i | ||||
\(879\) | 4.06817 | + | 7.04629i | 0.137216 | + | 0.237665i | ||||
\(880\) | 12.7297 | − | 22.0485i | 0.429118 | − | 0.743254i | ||||
\(881\) | −42.8058 | −1.44216 | −0.721082 | − | 0.692850i | \(-0.756355\pi\) | ||||
−0.721082 | + | 0.692850i | \(0.756355\pi\) | |||||||
\(882\) | −0.295449 | − | 0.456453i | −0.00994829 | − | 0.0153696i | ||||
\(883\) | −9.60368 | −0.323190 | −0.161595 | − | 0.986857i | \(-0.551664\pi\) | ||||
−0.161595 | + | 0.986857i | \(0.551664\pi\) | |||||||
\(884\) | 0.392753 | − | 0.680269i | 0.0132097 | − | 0.0228799i | ||||
\(885\) | 8.07801 | + | 13.9915i | 0.271539 | + | 0.470320i | ||||
\(886\) | 1.30654 | + | 2.26299i | 0.0438939 | + | 0.0760266i | ||||
\(887\) | 5.24687 | − | 9.08785i | 0.176173 | − | 0.305140i | −0.764394 | − | 0.644750i | \(-0.776962\pi\) |
0.940567 | + | 0.339610i | \(0.110295\pi\) | |||||||
\(888\) | 1.29885 | 0.0435866 | ||||||||
\(889\) | 39.5971 | − | 1.00709i | 1.32805 | − | 0.0337768i | ||||
\(890\) | 1.09550 | 0.0367211 | ||||||||
\(891\) | −1.45815 | + | 2.52558i | −0.0488497 | + | 0.0846102i | ||||
\(892\) | 6.19016 | + | 10.7217i | 0.207262 | + | 0.358988i | ||||
\(893\) | 0.590273 | + | 1.02238i | 0.0197527 | + | 0.0342127i | ||||
\(894\) | 0.130032 | − | 0.225222i | 0.00434892 | − | 0.00753255i | ||||
\(895\) | 48.3001 | 1.61449 | ||||||||
\(896\) | 3.11863 | − | 5.73352i | 0.104186 | − | 0.191544i | ||||
\(897\) | 3.38187 | 0.112918 | ||||||||
\(898\) | −0.0472178 | + | 0.0817837i | −0.00157568 | + | 0.00272916i | ||||
\(899\) | 1.91312 | + | 3.31362i | 0.0638061 | + | 0.110515i | ||||
\(900\) | −0.148867 | − | 0.257845i | −0.00496223 | − | 0.00859483i | ||||
\(901\) | 2.44910 | − | 4.24197i | 0.0815914 | − | 0.141320i | ||||
\(902\) | 0.0985343 | 0.00328083 | ||||||||
\(903\) | −9.31885 | − | 15.2327i | −0.310112 | − | 0.506912i | ||||
\(904\) | 1.29100 | 0.0429380 | ||||||||
\(905\) | 1.05195 | − | 1.82203i | 0.0349680 | − | 0.0605664i | ||||
\(906\) | −0.794139 | − | 1.37549i | −0.0263835 | − | 0.0456976i | ||||
\(907\) | −27.1740 | − | 47.0667i | −0.902298 | − | 1.56283i | −0.824504 | − | 0.565856i | \(-0.808546\pi\) |
−0.0777940 | − | 0.996969i | \(-0.524788\pi\) | |||||||
\(908\) | 23.6165 | − | 40.9049i | 0.783740 | − | 1.35748i | ||||
\(909\) | −19.9821 | −0.662763 | ||||||||
\(910\) | −0.236203 | − | 0.386100i | −0.00783006 | − | 0.0127991i | ||||
\(911\) | 29.9548 | 0.992445 | 0.496223 | − | 0.868195i | \(-0.334720\pi\) | ||||
0.496223 | + | 0.868195i | \(0.334720\pi\) | |||||||
\(912\) | 0.247247 | − | 0.428244i | 0.00818715 | − | 0.0141806i | ||||
\(913\) | 14.2724 | + | 24.7205i | 0.472347 | + | 0.818129i | ||||
\(914\) | 1.10429 | + | 1.91268i | 0.0365266 | + | 0.0632659i | ||||
\(915\) | 2.63624 | − | 4.56610i | 0.0871514 | − | 0.150951i | ||||
\(916\) | 18.0300 | 0.595727 | ||||||||
\(917\) | −23.6937 | + | 43.5602i | −0.782434 | + | 1.43848i | ||||
\(918\) | 0.0305996 | 0.00100994 | ||||||||
\(919\) | −15.4047 | + | 26.6817i | −0.508153 | + | 0.880147i | 0.491803 | + | 0.870707i | \(0.336338\pi\) |
−0.999955 | + | 0.00943982i | \(0.996995\pi\) | |||||||
\(920\) | −1.15536 | − | 2.00114i | −0.0380910 | − | 0.0659756i | ||||
\(921\) | 9.46237 | + | 16.3893i | 0.311796 | + | 0.540046i | ||||
\(922\) | −1.20344 | + | 2.08442i | −0.0396332 | + | 0.0686467i | ||||
\(923\) | 14.0826 | 0.463533 | ||||||||
\(924\) | 15.3800 | − | 0.391167i | 0.505966 | − | 0.0128685i | ||||
\(925\) | −0.625147 | −0.0205547 | ||||||||
\(926\) | 0.574768 | − | 0.995528i | 0.0188881 | − | 0.0327151i | ||||
\(927\) | 7.33724 | + | 12.7085i | 0.240987 | + | 0.417401i | ||||
\(928\) | 0.298106 | + | 0.516335i | 0.00978582 | + | 0.0169495i | ||||
\(929\) | 9.94398 | − | 17.2235i | 0.326252 | − | 0.565084i | −0.655513 | − | 0.755184i | \(-0.727548\pi\) |
0.981765 | + | 0.190099i | \(0.0608810\pi\) | |||||||
\(930\) | 1.01923 | 0.0334218 | ||||||||
\(931\) | −0.397621 | + | 0.777482i | −0.0130315 | + | 0.0254809i | ||||
\(932\) | −10.6567 | −0.349073 | ||||||||
\(933\) | 5.80947 | − | 10.0623i | 0.190193 | − | 0.329425i | ||||
\(934\) | 0.0710713 | + | 0.123099i | 0.00232552 | + | 0.00402793i | ||||
\(935\) | −1.26513 | − | 2.19126i | −0.0413741 | − | 0.0716620i | ||||
\(936\) | −0.155116 | + | 0.268670i | −0.00507014 | + | 0.00878174i | ||||
\(937\) | −50.6240 | −1.65382 | −0.826908 | − | 0.562338i | \(-0.809902\pi\) | ||||
−0.826908 | + | 0.562338i | \(0.809902\pi\) | |||||||
\(938\) | 1.26152 | − | 0.0320848i | 0.0411901 | − | 0.00104761i | ||||
\(939\) | 11.7023 | 0.381891 | ||||||||
\(940\) | 20.7791 | − | 35.9905i | 0.677741 | − | 1.17388i | ||||
\(941\) | −10.5585 | − | 18.2878i | −0.344197 | − | 0.596167i | 0.641011 | − | 0.767532i | \(-0.278515\pi\) |
−0.985208 | + | 0.171365i | \(0.945182\pi\) | |||||||
\(942\) | 0.396197 | + | 0.686234i | 0.0129088 | + | 0.0223587i | ||||
\(943\) | −0.735531 | + | 1.27398i | −0.0239522 | + | 0.0414864i | ||||
\(944\) | −29.0769 | −0.946373 | ||||||||
\(945\) | −2.78429 | + | 5.11884i | −0.0905729 | + | 0.166516i | ||||
\(946\) | −1.52889 | −0.0497084 | ||||||||
\(947\) | −16.5481 | + | 28.6621i | −0.537741 | + | 0.931394i | 0.461285 | + | 0.887252i | \(0.347389\pi\) |
−0.999025 | + | 0.0441420i | \(0.985945\pi\) | |||||||
\(948\) | 2.36756 | + | 4.10073i | 0.0768947 | + | 0.133186i | ||||
\(949\) | −3.77647 | − | 6.54105i | −0.122590 | − | 0.212331i | ||||
\(950\) | 0.000723449 | − | 0.00125305i | 2.34718e−5 | − | 4.06543e-5i | ||||
\(951\) | 33.0069 | 1.07032 | ||||||||
\(952\) | −0.168741 | − | 0.275826i | −0.00546893 | − | 0.00893956i | ||||
\(953\) | −3.06989 | −0.0994436 | −0.0497218 | − | 0.998763i | \(-0.515833\pi\) | ||||
−0.0497218 | + | 0.998763i | \(0.515833\pi\) | |||||||
\(954\) | −0.482901 | + | 0.836409i | −0.0156345 | + | 0.0270798i | ||||
\(955\) | 21.6756 | + | 37.5433i | 0.701408 | + | 1.21487i | ||||
\(956\) | −27.1726 | − | 47.0643i | −0.878824 | − | 1.52217i | ||||
\(957\) | −0.936454 | + | 1.62199i | −0.0302713 | + | 0.0524314i | ||||
\(958\) | 0.726000 | 0.0234560 | ||||||||
\(959\) | 18.7645 | + | 30.6726i | 0.605936 | + | 0.990469i | ||||
\(960\) | −17.3013 | −0.558397 | ||||||||
\(961\) | −2.24770 | + | 3.89314i | −0.0725066 | + | 0.125585i | ||||
\(962\) | 0.162602 | + | 0.281635i | 0.00524249 | + | 0.00908027i | ||||
\(963\) | 2.51986 | + | 4.36453i | 0.0812015 | + | 0.140645i | ||||
\(964\) | −15.6288 | + | 27.0699i | −0.503370 | + | 0.871863i | ||||
\(965\) | −33.2457 | −1.07022 | ||||||||
\(966\) | 0.332088 | − | 0.610535i | 0.0106848 | − | 0.0196437i | ||||
\(967\) | 10.0334 | 0.322651 | 0.161325 | − | 0.986901i | \(-0.448423\pi\) | ||||
0.161325 | + | 0.986901i | \(0.448423\pi\) | |||||||
\(968\) | −0.387054 | + | 0.670397i | −0.0124404 | + | 0.0215474i | ||||
\(969\) | −0.0245723 | − | 0.0425605i | −0.000789377 | − | 0.00136724i | ||||
\(970\) | 1.27532 | + | 2.20892i | 0.0409481 | + | 0.0709242i | ||||
\(971\) | 9.73484 | − | 16.8612i | 0.312406 | − | 0.541103i | −0.666477 | − | 0.745526i | \(-0.732198\pi\) |
0.978883 | + | 0.204423i | \(0.0655318\pi\) | |||||||
\(972\) | 1.99397 | 0.0639565 | ||||||||
\(973\) | −41.6021 | + | 1.05808i | −1.33370 | + | 0.0339206i | ||||
\(974\) | 1.81558 | 0.0581749 | ||||||||
\(975\) | 0.0746586 | − | 0.129313i | 0.00239099 | − | 0.00414132i | ||||
\(976\) | 4.74460 | + | 8.21788i | 0.151871 | + | 0.263048i | ||||
\(977\) | −0.934264 | − | 1.61819i | −0.0298898 | − | 0.0517706i | 0.850694 | − | 0.525662i | \(-0.176182\pi\) |
−0.880583 | + | 0.473891i | \(0.842849\pi\) | |||||||
\(978\) | 0.605229 | − | 1.04829i | 0.0193531 | − | 0.0335205i | ||||
\(979\) | −18.6749 | −0.596851 | ||||||||
\(980\) | 30.7012 | − | 1.56269i | 0.980714 | − | 0.0499182i | ||||
\(981\) | −0.122682 | −0.00391694 | ||||||||
\(982\) | 0.833946 | − | 1.44444i | 0.0266123 | − | 0.0460938i | ||||
\(983\) | −16.1431 | − | 27.9608i | −0.514886 | − | 0.891810i | −0.999851 | − | 0.0172756i | \(-0.994501\pi\) |
0.484964 | − | 0.874534i | \(-0.338833\pi\) | |||||||
\(984\) | −0.0674732 | − | 0.116867i | −0.00215097 | − | 0.00372558i | ||||
\(985\) | −12.1489 | + | 21.0424i | −0.387095 | + | 0.670468i | ||||
\(986\) | 0.0196517 | 0.000625839 | ||||||||
\(987\) | 25.0292 | − | 0.636579i | 0.796688 | − | 0.0202625i | ||||
\(988\) | 0.248750 | 0.00791378 | ||||||||
\(989\) | 11.4127 | − | 19.7674i | 0.362903 | − | 0.628567i | ||||
\(990\) | 0.249451 | + | 0.432062i | 0.00792808 | + | 0.0137318i | ||||
\(991\) | −28.4183 | − | 49.2219i | −0.902736 | − | 1.56358i | −0.823928 | − | 0.566695i | \(-0.808222\pi\) |
−0.0788081 | − | 0.996890i | \(-0.525111\pi\) | |||||||
\(992\) | −2.76549 | + | 4.78996i | −0.0878043 | + | 0.152082i | ||||
\(993\) | −14.7746 | −0.468858 | ||||||||
\(994\) | 1.38286 | − | 2.54235i | 0.0438616 | − | 0.0806383i | ||||
\(995\) | −15.8068 | −0.501111 | ||||||||
\(996\) | 9.75852 | − | 16.9022i | 0.309210 | − | 0.535568i | ||||
\(997\) | 12.0568 | + | 20.8830i | 0.381843 | + | 0.661371i | 0.991326 | − | 0.131428i | \(-0.0419563\pi\) |
−0.609483 | + | 0.792799i | \(0.708623\pi\) | |||||||
\(998\) | 0.861866 | + | 1.49280i | 0.0272819 | + | 0.0472536i | ||||
\(999\) | 2.09335 | − | 3.62579i | 0.0662307 | − | 0.114715i |
(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 | 273.2.i.e.79.3 | ✓ | 10 | |
3.2 | odd | 2 | 819.2.j.g.352.3 | 10 | |||
7.2 | even | 3 | 1911.2.a.t.1.3 | 5 | |||
7.4 | even | 3 | inner | 273.2.i.e.235.3 | yes | 10 | |
7.5 | odd | 6 | 1911.2.a.u.1.3 | 5 | |||
21.2 | odd | 6 | 5733.2.a.bq.1.3 | 5 | |||
21.5 | even | 6 | 5733.2.a.bp.1.3 | 5 | |||
21.11 | odd | 6 | 819.2.j.g.235.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.i.e.79.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
273.2.i.e.235.3 | yes | 10 | 7.4 | even | 3 | inner | |
819.2.j.g.235.3 | 10 | 21.11 | odd | 6 | |||
819.2.j.g.352.3 | 10 | 3.2 | odd | 2 | |||
1911.2.a.t.1.3 | 5 | 7.2 | even | 3 | |||
1911.2.a.u.1.3 | 5 | 7.5 | odd | 6 | |||
5733.2.a.bp.1.3 | 5 | 21.5 | even | 6 | |||
5733.2.a.bq.1.3 | 5 | 21.2 | odd | 6 |