Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(49,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.q (of order \(6\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(1.78384 + 0.477979i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.349 |
Dual form | 570.2.q.c.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.22489 | − | 0.223342i | −0.994999 | − | 0.0998815i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 1.07560i | 0.406538i | 0.979123 | + | 0.203269i | \(0.0651565\pi\) | ||||
−0.979123 | + | 0.203269i | \(0.934843\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 2.03848 | − | 0.919023i | 0.644624 | − | 0.290621i | ||||
\(11\) | 0.410555 | 0.123787 | 0.0618935 | − | 0.998083i | \(-0.480286\pi\) | ||||
0.0618935 | + | 0.998083i | \(0.480286\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 3.30892 | + | 1.91041i | 0.917729 | + | 0.529851i | 0.882910 | − | 0.469543i | \(-0.155581\pi\) |
0.0348191 | + | 0.999394i | \(0.488914\pi\) | |||||||
\(14\) | −0.537799 | − | 0.931495i | −0.143733 | − | 0.248952i | ||||
\(15\) | −2.03848 | + | 0.919023i | −0.526333 | + | 0.237291i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.08642 | − | 0.627244i | 0.263495 | − | 0.152129i | −0.362433 | − | 0.932010i | \(-0.618054\pi\) |
0.625928 | + | 0.779881i | \(0.284720\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 3.85480 | − | 2.03482i | 0.884352 | − | 0.466820i | ||||
\(20\) | −1.30586 | + | 1.81514i | −0.292000 | + | 0.405877i | ||||
\(21\) | 0.537799 | + | 0.931495i | 0.117357 | + | 0.203269i | ||||
\(22\) | −0.355551 | + | 0.205277i | −0.0758037 | + | 0.0437653i | ||||
\(23\) | 3.23263 | + | 1.86636i | 0.674051 | + | 0.389164i | 0.797610 | − | 0.603174i | \(-0.206097\pi\) |
−0.123559 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 4.90024 | + | 0.993820i | 0.980047 | + | 0.198764i | ||||
\(26\) | −3.82081 | −0.749323 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.931495 | + | 0.537799i | 0.176036 | + | 0.101634i | ||||
\(29\) | 1.18789 | − | 2.05749i | 0.220586 | − | 0.382067i | −0.734400 | − | 0.678717i | \(-0.762536\pi\) |
0.954986 | + | 0.296650i | \(0.0958696\pi\) | |||||||
\(30\) | 1.30586 | − | 1.81514i | 0.238417 | − | 0.331397i | ||||
\(31\) | 7.75919 | 1.39359 | 0.696796 | − | 0.717270i | \(-0.254608\pi\) | ||||
0.696796 | + | 0.717270i | \(0.254608\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0.355551 | − | 0.205277i | 0.0618935 | − | 0.0357342i | ||||
\(34\) | −0.627244 | + | 1.08642i | −0.107571 | + | 0.186319i | ||||
\(35\) | 0.240226 | − | 2.39308i | 0.0406056 | − | 0.404505i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | − | 2.08017i | − | 0.341978i | −0.985273 | − | 0.170989i | \(-0.945304\pi\) | ||
0.985273 | − | 0.170989i | \(-0.0546963\pi\) | |||||||
\(38\) | −2.32094 | + | 3.68961i | −0.376507 | + | 0.598534i | ||||
\(39\) | 3.82081 | 0.611819 | ||||||||
\(40\) | 0.223342 | − | 2.22489i | 0.0353134 | − | 0.351785i | ||||
\(41\) | −2.80171 | − | 4.85270i | −0.437554 | − | 0.757865i | 0.559947 | − | 0.828529i | \(-0.310822\pi\) |
−0.997500 | + | 0.0706636i | \(0.977488\pi\) | |||||||
\(42\) | −0.931495 | − | 0.537799i | −0.143733 | − | 0.0829841i | ||||
\(43\) | −1.92233 | + | 1.10986i | −0.293153 | + | 0.169252i | −0.639363 | − | 0.768905i | \(-0.720802\pi\) |
0.346210 | + | 0.938157i | \(0.387469\pi\) | |||||||
\(44\) | 0.205277 | − | 0.355551i | 0.0309467 | − | 0.0536013i | ||||
\(45\) | −1.30586 | + | 1.81514i | −0.194667 | + | 0.270585i | ||||
\(46\) | −3.73273 | −0.550360 | ||||||||
\(47\) | −3.58819 | − | 2.07164i | −0.523391 | − | 0.302180i | 0.214930 | − | 0.976629i | \(-0.431048\pi\) |
−0.738321 | + | 0.674450i | \(0.764381\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 5.84309 | 0.834727 | ||||||||
\(50\) | −4.74064 | + | 1.58945i | −0.670428 | + | 0.224781i | ||||
\(51\) | 0.627244 | − | 1.08642i | 0.0878317 | − | 0.152129i | ||||
\(52\) | 3.30892 | − | 1.91041i | 0.458864 | − | 0.264926i | ||||
\(53\) | 4.32940 | + | 2.49958i | 0.594689 | + | 0.343344i | 0.766949 | − | 0.641708i | \(-0.221774\pi\) |
−0.172261 | + | 0.985051i | \(0.555107\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −0.913438 | − | 0.0916940i | −0.123168 | − | 0.0123640i | ||||
\(56\) | −1.07560 | −0.143733 | ||||||||
\(57\) | 2.32094 | − | 3.68961i | 0.307417 | − | 0.488701i | ||||
\(58\) | 2.37579i | 0.311956i | ||||||||
\(59\) | 1.25650 | + | 2.17633i | 0.163583 | + | 0.283334i | 0.936151 | − | 0.351598i | \(-0.114362\pi\) |
−0.772568 | + | 0.634932i | \(0.781028\pi\) | |||||||
\(60\) | −0.223342 | + | 2.22489i | −0.0288333 | + | 0.287232i | ||||
\(61\) | −3.37731 | + | 5.84967i | −0.432420 | + | 0.748973i | −0.997081 | − | 0.0763496i | \(-0.975674\pi\) |
0.564661 | + | 0.825323i | \(0.309007\pi\) | |||||||
\(62\) | −6.71965 | + | 3.87959i | −0.853397 | + | 0.492709i | ||||
\(63\) | 0.931495 | + | 0.537799i | 0.117357 | + | 0.0677563i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.93529 | − | 4.98945i | −0.860217 | − | 0.618866i | ||||
\(66\) | −0.205277 | + | 0.355551i | −0.0252679 | + | 0.0437653i | ||||
\(67\) | −8.07251 | − | 4.66066i | −0.986214 | − | 0.569391i | −0.0820733 | − | 0.996626i | \(-0.526154\pi\) |
−0.904140 | + | 0.427236i | \(0.859488\pi\) | |||||||
\(68\) | − | 1.25449i | − | 0.152129i | ||||||
\(69\) | 3.73273 | 0.449367 | ||||||||
\(70\) | 0.988499 | + | 2.19258i | 0.118148 | + | 0.262064i | ||||
\(71\) | 4.79760 | + | 8.30969i | 0.569371 | + | 0.986179i | 0.996628 | + | 0.0820491i | \(0.0261464\pi\) |
−0.427258 | + | 0.904130i | \(0.640520\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 6.02521 | − | 3.47866i | 0.705198 | − | 0.407146i | −0.104083 | − | 0.994569i | \(-0.533191\pi\) |
0.809280 | + | 0.587422i | \(0.199857\pi\) | |||||||
\(74\) | 1.04009 | + | 1.80148i | 0.120907 | + | 0.209418i | ||||
\(75\) | 4.74064 | − | 1.58945i | 0.547402 | − | 0.183533i | ||||
\(76\) | 0.165192 | − | 4.35577i | 0.0189488 | − | 0.499641i | ||||
\(77\) | 0.441592i | 0.0503240i | ||||||||
\(78\) | −3.30892 | + | 1.91041i | −0.374661 | + | 0.216311i | ||||
\(79\) | 4.47277 | + | 7.74707i | 0.503226 | + | 0.871613i | 0.999993 | + | 0.00372912i | \(0.00118702\pi\) |
−0.496767 | + | 0.867884i | \(0.665480\pi\) | |||||||
\(80\) | 0.919023 | + | 2.03848i | 0.102750 | + | 0.227909i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.85270 | + | 2.80171i | 0.535892 | + | 0.309397i | ||||
\(83\) | 9.12070i | 1.00113i | 0.865700 | + | 0.500563i | \(0.166874\pi\) | ||||
−0.865700 | + | 0.500563i | \(0.833126\pi\) | |||||||
\(84\) | 1.07560 | 0.117357 | ||||||||
\(85\) | −2.55725 | + | 1.15290i | −0.277372 | + | 0.125050i | ||||
\(86\) | 1.10986 | − | 1.92233i | 0.119679 | − | 0.207291i | ||||
\(87\) | − | 2.37579i | − | 0.254711i | ||||||
\(88\) | 0.410555i | 0.0437653i | ||||||||
\(89\) | −2.72783 | + | 4.72474i | −0.289149 | + | 0.500821i | −0.973607 | − | 0.228231i | \(-0.926706\pi\) |
0.684458 | + | 0.729053i | \(0.260039\pi\) | |||||||
\(90\) | 0.223342 | − | 2.22489i | 0.0235423 | − | 0.234524i | ||||
\(91\) | −2.05483 | + | 3.55906i | −0.215404 | + | 0.373091i | ||||
\(92\) | 3.23263 | − | 1.86636i | 0.337025 | − | 0.194582i | ||||
\(93\) | 6.71965 | − | 3.87959i | 0.696796 | − | 0.402295i | ||||
\(94\) | 4.14328 | 0.427347 | ||||||||
\(95\) | −9.03096 | + | 3.66631i | −0.926556 | + | 0.376156i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.5315 | + | 6.08034i | −1.06931 | + | 0.617365i | −0.927992 | − | 0.372599i | \(-0.878467\pi\) |
−0.141316 | + | 0.989965i | \(0.545133\pi\) | |||||||
\(98\) | −5.06026 | + | 2.92155i | −0.511164 | + | 0.295121i | ||||
\(99\) | 0.205277 | − | 0.355551i | 0.0206312 | − | 0.0357342i | ||||
\(100\) | 3.31079 | − | 3.74682i | 0.331079 | − | 0.374682i | ||||
\(101\) | −1.54404 | + | 2.67436i | −0.153638 | + | 0.266109i | −0.932562 | − | 0.361009i | \(-0.882432\pi\) |
0.778924 | + | 0.627118i | \(0.215766\pi\) | |||||||
\(102\) | 1.25449i | 0.124213i | ||||||||
\(103\) | − | 14.7954i | − | 1.45784i | −0.684600 | − | 0.728919i | \(-0.740023\pi\) | ||
0.684600 | − | 0.728919i | \(-0.259977\pi\) | |||||||
\(104\) | −1.91041 | + | 3.30892i | −0.187331 | + | 0.324466i | ||||
\(105\) | −0.988499 | − | 2.19258i | −0.0964676 | − | 0.213974i | ||||
\(106\) | −4.99916 | −0.485561 | ||||||||
\(107\) | − | 5.37650i | − | 0.519766i | −0.965640 | − | 0.259883i | \(-0.916316\pi\) | ||
0.965640 | − | 0.259883i | \(-0.0836840\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 8.16051 | + | 14.1344i | 0.781636 | + | 1.35383i | 0.930988 | + | 0.365049i | \(0.118948\pi\) |
−0.149353 | + | 0.988784i | \(0.547719\pi\) | |||||||
\(110\) | 0.836907 | − | 0.377309i | 0.0797960 | − | 0.0359750i | ||||
\(111\) | −1.04009 | − | 1.80148i | −0.0987205 | − | 0.170989i | ||||
\(112\) | 0.931495 | − | 0.537799i | 0.0880180 | − | 0.0508172i | ||||
\(113\) | − | 9.79888i | − | 0.921801i | −0.887452 | − | 0.460900i | \(-0.847527\pi\) | ||
0.887452 | − | 0.460900i | \(-0.152473\pi\) | |||||||
\(114\) | −0.165192 | + | 4.35577i | −0.0154716 | + | 0.407955i | ||||
\(115\) | −6.77541 | − | 4.87443i | −0.631810 | − | 0.454543i | ||||
\(116\) | −1.18789 | − | 2.05749i | −0.110293 | − | 0.191033i | ||||
\(117\) | 3.30892 | − | 1.91041i | 0.305910 | − | 0.176617i | ||||
\(118\) | −2.17633 | − | 1.25650i | −0.200347 | − | 0.115670i | ||||
\(119\) | 0.674662 | + | 1.16855i | 0.0618461 | + | 0.107121i | ||||
\(120\) | −0.919023 | − | 2.03848i | −0.0838950 | − | 0.186087i | ||||
\(121\) | −10.8314 | −0.984677 | ||||||||
\(122\) | − | 6.75461i | − | 0.611534i | ||||||
\(123\) | −4.85270 | − | 2.80171i | −0.437554 | − | 0.252622i | ||||
\(124\) | 3.87959 | − | 6.71965i | 0.348398 | − | 0.603443i | ||||
\(125\) | −10.6805 | − | 3.30556i | −0.955294 | − | 0.295659i | ||||
\(126\) | −1.07560 | −0.0958218 | ||||||||
\(127\) | −15.8129 | − | 9.12955i | −1.40316 | − | 0.810117i | −0.408448 | − | 0.912782i | \(-0.633930\pi\) |
−0.994716 | + | 0.102665i | \(0.967263\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −1.10986 | + | 1.92233i | −0.0977177 | + | 0.169252i | ||||
\(130\) | 8.50087 | + | 0.853346i | 0.745575 | + | 0.0748434i | ||||
\(131\) | −9.70176 | − | 16.8039i | −0.847647 | − | 1.46817i | −0.883302 | − | 0.468804i | \(-0.844685\pi\) |
0.0356553 | − | 0.999364i | \(-0.488648\pi\) | |||||||
\(132\) | − | 0.410555i | − | 0.0357342i | ||||||
\(133\) | 2.18865 | + | 4.14621i | 0.189780 | + | 0.359522i | ||||
\(134\) | 9.32133 | 0.805240 | ||||||||
\(135\) | −0.223342 | + | 2.22489i | −0.0192222 | + | 0.191488i | ||||
\(136\) | 0.627244 | + | 1.08642i | 0.0537857 | + | 0.0931596i | ||||
\(137\) | 7.65772 | + | 4.42119i | 0.654244 | + | 0.377728i | 0.790080 | − | 0.613004i | \(-0.210039\pi\) |
−0.135837 | + | 0.990731i | \(0.543372\pi\) | |||||||
\(138\) | −3.23263 | + | 1.86636i | −0.275180 | + | 0.158875i | ||||
\(139\) | 5.28333 | − | 9.15100i | 0.448127 | − | 0.776178i | −0.550138 | − | 0.835074i | \(-0.685425\pi\) |
0.998264 | + | 0.0588961i | \(0.0187581\pi\) | |||||||
\(140\) | −1.95236 | − | 1.40458i | −0.165004 | − | 0.118709i | ||||
\(141\) | −4.14328 | −0.348927 | ||||||||
\(142\) | −8.30969 | − | 4.79760i | −0.697334 | − | 0.402606i | ||||
\(143\) | 1.35849 | + | 0.784326i | 0.113603 | + | 0.0655886i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −3.10245 | + | 4.31238i | −0.257645 | + | 0.358124i | ||||
\(146\) | −3.47866 | + | 6.02521i | −0.287896 | + | 0.498650i | ||||
\(147\) | 5.06026 | − | 2.92155i | 0.417364 | − | 0.240965i | ||||
\(148\) | −1.80148 | − | 1.04009i | −0.148081 | − | 0.0854945i | ||||
\(149\) | 1.18192 | + | 2.04715i | 0.0968267 | + | 0.167709i | 0.910370 | − | 0.413796i | \(-0.135797\pi\) |
−0.813543 | + | 0.581505i | \(0.802464\pi\) | |||||||
\(150\) | −3.31079 | + | 3.74682i | −0.270325 | + | 0.305927i | ||||
\(151\) | −4.02935 | −0.327904 | −0.163952 | − | 0.986468i | \(-0.552424\pi\) | ||||
−0.163952 | + | 0.986468i | \(0.552424\pi\) | |||||||
\(152\) | 2.03482 | + | 3.85480i | 0.165046 | + | 0.312666i | ||||
\(153\) | − | 1.25449i | − | 0.101419i | ||||||
\(154\) | −0.220796 | − | 0.382430i | −0.0177922 | − | 0.0308171i | ||||
\(155\) | −17.2633 | − | 1.73295i | −1.38662 | − | 0.139194i | ||||
\(156\) | 1.91041 | − | 3.30892i | 0.152955 | − | 0.264926i | ||||
\(157\) | −16.8513 | + | 9.72912i | −1.34488 | + | 0.776469i | −0.987520 | − | 0.157497i | \(-0.949658\pi\) |
−0.357364 | + | 0.933965i | \(0.616324\pi\) | |||||||
\(158\) | −7.74707 | − | 4.47277i | −0.616324 | − | 0.355835i | ||||
\(159\) | 4.99916 | 0.396459 | ||||||||
\(160\) | −1.81514 | − | 1.30586i | −0.143499 | − | 0.103238i | ||||
\(161\) | −2.00745 | + | 3.47701i | −0.158210 | + | 0.274027i | ||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | − | 13.4340i | − | 1.05223i | −0.850412 | − | 0.526117i | \(-0.823647\pi\) | ||
0.850412 | − | 0.526117i | \(-0.176353\pi\) | |||||||
\(164\) | −5.60342 | −0.437554 | ||||||||
\(165\) | −0.836907 | + | 0.377309i | −0.0651531 | + | 0.0293735i | ||||
\(166\) | −4.56035 | − | 7.89876i | −0.353952 | − | 0.613063i | ||||
\(167\) | 3.38132 | + | 1.95221i | 0.261655 | + | 0.151066i | 0.625089 | − | 0.780553i | \(-0.285063\pi\) |
−0.363435 | + | 0.931620i | \(0.618396\pi\) | |||||||
\(168\) | −0.931495 | + | 0.537799i | −0.0718664 | + | 0.0414921i | ||||
\(169\) | 0.799296 | + | 1.38442i | 0.0614843 | + | 0.106494i | ||||
\(170\) | 1.63819 | − | 2.27707i | 0.125643 | − | 0.174643i | ||||
\(171\) | 0.165192 | − | 4.35577i | 0.0126325 | − | 0.333094i | ||||
\(172\) | 2.21972i | 0.169252i | ||||||||
\(173\) | −13.1394 | + | 7.58604i | −0.998970 | + | 0.576756i | −0.907943 | − | 0.419093i | \(-0.862348\pi\) |
−0.0910267 | + | 0.995848i | \(0.529015\pi\) | |||||||
\(174\) | 1.18789 | + | 2.05749i | 0.0900540 | + | 0.155978i | ||||
\(175\) | −1.06895 | + | 5.27068i | −0.0808050 | + | 0.398426i | ||||
\(176\) | −0.205277 | − | 0.355551i | −0.0154734 | − | 0.0268007i | ||||
\(177\) | 2.17633 | + | 1.25650i | 0.163583 | + | 0.0944445i | ||||
\(178\) | − | 5.45566i | − | 0.408919i | ||||||
\(179\) | −8.91162 | −0.666085 | −0.333043 | − | 0.942912i | \(-0.608075\pi\) | ||||
−0.333043 | + | 0.942912i | \(0.608075\pi\) | |||||||
\(180\) | 0.919023 | + | 2.03848i | 0.0685000 | + | 0.151939i | ||||
\(181\) | 4.61274 | − | 7.98950i | 0.342862 | − | 0.593855i | −0.642101 | − | 0.766620i | \(-0.721937\pi\) |
0.984963 | + | 0.172765i | \(0.0552702\pi\) | |||||||
\(182\) | − | 4.10965i | − | 0.304628i | ||||||
\(183\) | 6.75461i | 0.499315i | ||||||||
\(184\) | −1.86636 | + | 3.23263i | −0.137590 | + | 0.238313i | ||||
\(185\) | −0.464589 | + | 4.62814i | −0.0341573 | + | 0.340268i | ||||
\(186\) | −3.87959 | + | 6.71965i | −0.284466 | + | 0.492709i | ||||
\(187\) | 0.446034 | − | 0.257518i | 0.0326172 | − | 0.0188316i | ||||
\(188\) | −3.58819 | + | 2.07164i | −0.261695 | + | 0.151090i | ||||
\(189\) | 1.07560 | 0.0782382 | ||||||||
\(190\) | 5.98788 | − | 7.69060i | 0.434407 | − | 0.557935i | ||||
\(191\) | 19.7445 | 1.42867 | 0.714333 | − | 0.699806i | \(-0.246730\pi\) | ||||
0.714333 | + | 0.699806i | \(0.246730\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −11.9562 | + | 6.90289i | −0.860623 | + | 0.496881i | −0.864221 | − | 0.503113i | \(-0.832188\pi\) |
0.00359794 | + | 0.999994i | \(0.498855\pi\) | |||||||
\(194\) | 6.08034 | − | 10.5315i | 0.436543 | − | 0.756115i | ||||
\(195\) | −8.50087 | − | 0.853346i | −0.608760 | − | 0.0611094i | ||||
\(196\) | 2.92155 | − | 5.06026i | 0.208682 | − | 0.361447i | ||||
\(197\) | 8.42005i | 0.599904i | 0.953954 | + | 0.299952i | \(0.0969706\pi\) | ||||
−0.953954 | + | 0.299952i | \(0.903029\pi\) | |||||||
\(198\) | 0.410555i | 0.0291769i | ||||||||
\(199\) | 3.33252 | − | 5.77210i | 0.236236 | − | 0.409173i | −0.723395 | − | 0.690434i | \(-0.757419\pi\) |
0.959631 | + | 0.281261i | \(0.0907528\pi\) | |||||||
\(200\) | −0.993820 | + | 4.90024i | −0.0702737 | + | 0.346499i | ||||
\(201\) | −9.32133 | −0.657476 | ||||||||
\(202\) | − | 3.08809i | − | 0.217277i | ||||||
\(203\) | 2.21303 | + | 1.27769i | 0.155324 | + | 0.0896766i | ||||
\(204\) | −0.627244 | − | 1.08642i | −0.0439159 | − | 0.0760645i | ||||
\(205\) | 5.14967 | + | 11.4225i | 0.359669 | + | 0.797779i | ||||
\(206\) | 7.39772 | + | 12.8132i | 0.515424 | + | 0.892740i | ||||
\(207\) | 3.23263 | − | 1.86636i | 0.224684 | − | 0.129721i | ||||
\(208\) | − | 3.82081i | − | 0.264926i | ||||||
\(209\) | 1.58261 | − | 0.835406i | 0.109471 | − | 0.0577863i | ||||
\(210\) | 1.95236 | + | 1.40458i | 0.134725 | + | 0.0969254i | ||||
\(211\) | −6.10606 | − | 10.5760i | −0.420359 | − | 0.728083i | 0.575616 | − | 0.817720i | \(-0.304762\pi\) |
−0.995974 | + | 0.0896377i | \(0.971429\pi\) | |||||||
\(212\) | 4.32940 | − | 2.49958i | 0.297344 | − | 0.171672i | ||||
\(213\) | 8.30969 | + | 4.79760i | 0.569371 | + | 0.328726i | ||||
\(214\) | 2.68825 | + | 4.65618i | 0.183765 | + | 0.318290i | ||||
\(215\) | 4.52485 | − | 2.03997i | 0.308592 | − | 0.139125i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.34576i | 0.566547i | ||||||||
\(218\) | −14.1344 | − | 8.16051i | −0.957304 | − | 0.552700i | ||||
\(219\) | 3.47866 | − | 6.02521i | 0.235066 | − | 0.407146i | ||||
\(220\) | −0.536128 | + | 0.745213i | −0.0361458 | + | 0.0502423i | ||||
\(221\) | 4.79316 | 0.322423 | ||||||||
\(222\) | 1.80148 | + | 1.04009i | 0.120907 | + | 0.0698060i | ||||
\(223\) | 0.493682 | − | 0.285027i | 0.0330594 | − | 0.0190868i | −0.483379 | − | 0.875411i | \(-0.660591\pi\) |
0.516439 | + | 0.856324i | \(0.327257\pi\) | |||||||
\(224\) | −0.537799 | + | 0.931495i | −0.0359332 | + | 0.0622381i | ||||
\(225\) | 3.31079 | − | 3.74682i | 0.220719 | − | 0.249788i | ||||
\(226\) | 4.89944 | + | 8.48608i | 0.325906 | + | 0.564485i | ||||
\(227\) | − | 2.46316i | − | 0.163486i | −0.996653 | − | 0.0817428i | \(-0.973951\pi\) | ||
0.996653 | − | 0.0817428i | \(-0.0260486\pi\) | |||||||
\(228\) | −2.03482 | − | 3.85480i | −0.134759 | − | 0.255290i | ||||
\(229\) | 11.0250 | 0.728553 | 0.364276 | − | 0.931291i | \(-0.381316\pi\) | ||||
0.364276 | + | 0.931291i | \(0.381316\pi\) | |||||||
\(230\) | 8.30489 | + | 0.833673i | 0.547608 | + | 0.0549708i | ||||
\(231\) | 0.220796 | + | 0.382430i | 0.0145273 | + | 0.0251620i | ||||
\(232\) | 2.05749 | + | 1.18789i | 0.135081 | + | 0.0779890i | ||||
\(233\) | 14.9579 | − | 8.63595i | 0.979925 | − | 0.565760i | 0.0776772 | − | 0.996979i | \(-0.475250\pi\) |
0.902247 | + | 0.431219i | \(0.141916\pi\) | |||||||
\(234\) | −1.91041 | + | 3.30892i | −0.124887 | + | 0.216311i | ||||
\(235\) | 7.52062 | + | 5.41055i | 0.490591 | + | 0.352946i | ||||
\(236\) | 2.51301 | 0.163583 | ||||||||
\(237\) | 7.74707 | + | 4.47277i | 0.503226 | + | 0.290538i | ||||
\(238\) | −1.16855 | − | 0.674662i | −0.0757457 | − | 0.0437318i | ||||
\(239\) | −6.90743 | −0.446805 | −0.223402 | − | 0.974726i | \(-0.571716\pi\) | ||||
−0.223402 | + | 0.974726i | \(0.571716\pi\) | |||||||
\(240\) | 1.81514 | + | 1.30586i | 0.117167 | + | 0.0842931i | ||||
\(241\) | −11.0140 | + | 19.0767i | −0.709471 | + | 1.22884i | 0.255582 | + | 0.966787i | \(0.417733\pi\) |
−0.965053 | + | 0.262053i | \(0.915600\pi\) | |||||||
\(242\) | 9.38031 | − | 5.41572i | 0.602989 | − | 0.348136i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 3.37731 | + | 5.84967i | 0.216210 | + | 0.374487i | ||||
\(245\) | −13.0002 | − | 1.30501i | −0.830553 | − | 0.0833738i | ||||
\(246\) | 5.60342 | 0.357261 | ||||||||
\(247\) | 16.6426 | + | 0.631167i | 1.05894 | + | 0.0401602i | ||||
\(248\) | 7.75919i | 0.492709i | ||||||||
\(249\) | 4.56035 | + | 7.89876i | 0.289000 | + | 0.500563i | ||||
\(250\) | 10.9024 | − | 2.47755i | 0.689527 | − | 0.156694i | ||||
\(251\) | 10.5663 | − | 18.3014i | 0.666940 | − | 1.15517i | −0.311815 | − | 0.950143i | \(-0.600937\pi\) |
0.978755 | − | 0.205032i | \(-0.0657298\pi\) | |||||||
\(252\) | 0.931495 | − | 0.537799i | 0.0586786 | − | 0.0338781i | ||||
\(253\) | 1.32717 | + | 0.766244i | 0.0834387 | + | 0.0481734i | ||||
\(254\) | 18.2591 | 1.14568 | ||||||||
\(255\) | −1.63819 | + | 2.27707i | −0.102587 | + | 0.142595i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 22.8775 | + | 13.2083i | 1.42706 | + | 0.823913i | 0.996888 | − | 0.0788341i | \(-0.0251197\pi\) |
0.430172 | + | 0.902747i | \(0.358453\pi\) | |||||||
\(258\) | − | 2.21972i | − | 0.138194i | ||||||
\(259\) | 2.23743 | 0.139027 | ||||||||
\(260\) | −7.78864 | + | 3.51141i | −0.483031 | + | 0.217769i | ||||
\(261\) | −1.18789 | − | 2.05749i | −0.0735287 | − | 0.127356i | ||||
\(262\) | 16.8039 | + | 9.70176i | 1.03815 | + | 0.599377i | ||||
\(263\) | 20.7173 | − | 11.9611i | 1.27748 | − | 0.737555i | 0.301097 | − | 0.953593i | \(-0.402647\pi\) |
0.976385 | + | 0.216039i | \(0.0693138\pi\) | |||||||
\(264\) | 0.205277 | + | 0.355551i | 0.0126340 | + | 0.0218826i | ||||
\(265\) | −9.07416 | − | 6.52821i | −0.557421 | − | 0.401025i | ||||
\(266\) | −3.96853 | − | 2.49640i | −0.243326 | − | 0.153064i | ||||
\(267\) | 5.45566i | 0.333881i | ||||||||
\(268\) | −8.07251 | + | 4.66066i | −0.493107 | + | 0.284695i | ||||
\(269\) | −3.89266 | − | 6.74229i | −0.237340 | − | 0.411085i | 0.722610 | − | 0.691256i | \(-0.242942\pi\) |
−0.959950 | + | 0.280171i | \(0.909609\pi\) | |||||||
\(270\) | −0.919023 | − | 2.03848i | −0.0559300 | − | 0.124058i | ||||
\(271\) | −0.421189 | − | 0.729521i | −0.0255854 | − | 0.0443152i | 0.852949 | − | 0.521994i | \(-0.174812\pi\) |
−0.878535 | + | 0.477679i | \(0.841478\pi\) | |||||||
\(272\) | −1.08642 | − | 0.627244i | −0.0658738 | − | 0.0380322i | ||||
\(273\) | 4.10965i | 0.248728i | ||||||||
\(274\) | −8.84238 | −0.534188 | ||||||||
\(275\) | 2.01182 | + | 0.408018i | 0.121317 | + | 0.0246044i | ||||
\(276\) | 1.86636 | − | 3.23263i | 0.112342 | − | 0.194582i | ||||
\(277\) | 5.55485i | 0.333758i | 0.985977 | + | 0.166879i | \(0.0533690\pi\) | ||||
−0.985977 | + | 0.166879i | \(0.946631\pi\) | |||||||
\(278\) | 10.5667i | 0.633747i | ||||||||
\(279\) | 3.87959 | − | 6.71965i | 0.232265 | − | 0.402295i | ||||
\(280\) | 2.39308 | + | 0.240226i | 0.143014 | + | 0.0143562i | ||||
\(281\) | −8.05993 | + | 13.9602i | −0.480815 | + | 0.832796i | −0.999758 | − | 0.0220130i | \(-0.992992\pi\) |
0.518943 | + | 0.854809i | \(0.326326\pi\) | |||||||
\(282\) | 3.58819 | − | 2.07164i | 0.213673 | − | 0.123364i | ||||
\(283\) | 4.78552 | − | 2.76292i | 0.284469 | − | 0.164239i | −0.350976 | − | 0.936385i | \(-0.614150\pi\) |
0.635445 | + | 0.772146i | \(0.280817\pi\) | |||||||
\(284\) | 9.59521 | 0.569371 | ||||||||
\(285\) | −5.98788 | + | 7.69060i | −0.354691 | + | 0.455552i | ||||
\(286\) | −1.56865 | −0.0927563 | ||||||||
\(287\) | 5.21956 | − | 3.01351i | 0.308101 | − | 0.177882i | ||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | −7.71313 | + | 13.3595i | −0.453714 | + | 0.785855i | ||||
\(290\) | 0.530612 | − | 5.28585i | 0.0311586 | − | 0.310396i | ||||
\(291\) | −6.08034 | + | 10.5315i | −0.356436 | + | 0.617365i | ||||
\(292\) | − | 6.95732i | − | 0.407146i | ||||||
\(293\) | 0.546541i | 0.0319293i | 0.999873 | + | 0.0159646i | \(0.00508192\pi\) | ||||
−0.999873 | + | 0.0159646i | \(0.994918\pi\) | |||||||
\(294\) | −2.92155 | + | 5.06026i | −0.170388 | + | 0.295121i | ||||
\(295\) | −2.30951 | − | 5.12271i | −0.134465 | − | 0.298256i | ||||
\(296\) | 2.08017 | 0.120907 | ||||||||
\(297\) | − | 0.410555i | − | 0.0238228i | ||||||
\(298\) | −2.04715 | − | 1.18192i | −0.118588 | − | 0.0684668i | ||||
\(299\) | 7.13102 | + | 12.3513i | 0.412397 | + | 0.714293i | ||||
\(300\) | 0.993820 | − | 4.90024i | 0.0573782 | − | 0.282915i | ||||
\(301\) | −1.19376 | − | 2.06766i | −0.0688073 | − | 0.119178i | ||||
\(302\) | 3.48952 | − | 2.01468i | 0.200799 | − | 0.115932i | ||||
\(303\) | 3.08809i | 0.177406i | ||||||||
\(304\) | −3.68961 | − | 2.32094i | −0.211614 | − | 0.133115i | ||||
\(305\) | 8.82060 | − | 12.2606i | 0.505066 | − | 0.702037i | ||||
\(306\) | 0.627244 | + | 1.08642i | 0.0358571 | + | 0.0621064i | ||||
\(307\) | −21.2877 | + | 12.2904i | −1.21495 | + | 0.701452i | −0.963834 | − | 0.266505i | \(-0.914131\pi\) |
−0.251117 | + | 0.967957i | \(0.580798\pi\) | |||||||
\(308\) | 0.382430 | + | 0.220796i | 0.0217909 | + | 0.0125810i | ||||
\(309\) | −7.39772 | − | 12.8132i | −0.420842 | − | 0.728919i | ||||
\(310\) | 15.8169 | − | 7.13088i | 0.898342 | − | 0.405007i | ||||
\(311\) | 21.5698 | 1.22311 | 0.611556 | − | 0.791201i | \(-0.290544\pi\) | ||||
0.611556 | + | 0.791201i | \(0.290544\pi\) | |||||||
\(312\) | 3.82081i | 0.216311i | ||||||||
\(313\) | 25.3785 | + | 14.6523i | 1.43447 | + | 0.828194i | 0.997458 | − | 0.0712588i | \(-0.0227016\pi\) |
0.437017 | + | 0.899453i | \(0.356035\pi\) | |||||||
\(314\) | 9.72912 | − | 16.8513i | 0.549046 | − | 0.950976i | ||||
\(315\) | −1.95236 | − | 1.40458i | −0.110003 | − | 0.0791392i | ||||
\(316\) | 8.94554 | 0.503226 | ||||||||
\(317\) | −7.10418 | − | 4.10160i | −0.399011 | − | 0.230369i | 0.287046 | − | 0.957917i | \(-0.407327\pi\) |
−0.686057 | + | 0.727548i | \(0.740660\pi\) | |||||||
\(318\) | −4.32940 | + | 2.49958i | −0.242781 | + | 0.140169i | ||||
\(319\) | 0.487695 | − | 0.844713i | 0.0273057 | − | 0.0472948i | ||||
\(320\) | 2.22489 | + | 0.223342i | 0.124375 | + | 0.0124852i | ||||
\(321\) | −2.68825 | − | 4.65618i | −0.150043 | − | 0.259883i | ||||
\(322\) | − | 4.01491i | − | 0.223742i | ||||||
\(323\) | 2.91160 | − | 4.62857i | 0.162006 | − | 0.257540i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 14.3159 | + | 12.6499i | 0.794103 | + | 0.701691i | ||||
\(326\) | 6.71701 | + | 11.6342i | 0.372021 | + | 0.644359i | ||||
\(327\) | 14.1344 | + | 8.16051i | 0.781636 | + | 0.451277i | ||||
\(328\) | 4.85270 | − | 2.80171i | 0.267946 | − | 0.154699i | ||||
\(329\) | 2.22825 | − | 3.85944i | 0.122847 | − | 0.212778i | ||||
\(330\) | 0.536128 | − | 0.745213i | 0.0295129 | − | 0.0410226i | ||||
\(331\) | −27.0826 | −1.48860 | −0.744298 | − | 0.667847i | \(-0.767216\pi\) | ||||
−0.744298 | + | 0.667847i | \(0.767216\pi\) | |||||||
\(332\) | 7.89876 | + | 4.56035i | 0.433501 | + | 0.250282i | ||||
\(333\) | −1.80148 | − | 1.04009i | −0.0987205 | − | 0.0569963i | ||||
\(334\) | −3.90441 | −0.213640 | ||||||||
\(335\) | 16.9195 | + | 12.1724i | 0.924410 | + | 0.665048i | ||||
\(336\) | 0.537799 | − | 0.931495i | 0.0293393 | − | 0.0508172i | ||||
\(337\) | −23.9964 | + | 13.8543i | −1.30717 | + | 0.754693i | −0.981622 | − | 0.190834i | \(-0.938881\pi\) |
−0.325544 | + | 0.945527i | \(0.605547\pi\) | |||||||
\(338\) | −1.38442 | − | 0.799296i | −0.0753026 | − | 0.0434760i | ||||
\(339\) | −4.89944 | − | 8.48608i | −0.266101 | − | 0.460900i | ||||
\(340\) | −0.280179 | + | 2.79109i | −0.0151949 | + | 0.151368i | ||||
\(341\) | 3.18557 | 0.172508 | ||||||||
\(342\) | 2.03482 | + | 3.85480i | 0.110031 | + | 0.208444i | ||||
\(343\) | 13.8140i | 0.745885i | ||||||||
\(344\) | −1.10986 | − | 1.92233i | −0.0598396 | − | 0.103645i | ||||
\(345\) | −8.30489 | − | 0.833673i | −0.447120 | − | 0.0448835i | ||||
\(346\) | 7.58604 | − | 13.1394i | 0.407828 | − | 0.706379i | ||||
\(347\) | 2.04836 | − | 1.18262i | 0.109962 | − | 0.0634865i | −0.444010 | − | 0.896022i | \(-0.646445\pi\) |
0.553972 | + | 0.832535i | \(0.313111\pi\) | |||||||
\(348\) | −2.05749 | − | 1.18789i | −0.110293 | − | 0.0636778i | ||||
\(349\) | −16.7894 | −0.898718 | −0.449359 | − | 0.893351i | \(-0.648348\pi\) | ||||
−0.449359 | + | 0.893351i | \(0.648348\pi\) | |||||||
\(350\) | −1.70960 | − | 5.09902i | −0.0913821 | − | 0.272554i | ||||
\(351\) | 1.91041 | − | 3.30892i | 0.101970 | − | 0.176617i | ||||
\(352\) | 0.355551 | + | 0.205277i | 0.0189509 | + | 0.0109413i | ||||
\(353\) | − | 23.0018i | − | 1.22426i | −0.790756 | − | 0.612132i | \(-0.790312\pi\) | ||
0.790756 | − | 0.612132i | \(-0.209688\pi\) | |||||||
\(354\) | −2.51301 | −0.133565 | ||||||||
\(355\) | −8.81822 | − | 19.5596i | −0.468023 | − | 1.03812i | ||||
\(356\) | 2.72783 | + | 4.72474i | 0.144575 | + | 0.250411i | ||||
\(357\) | 1.16855 | + | 0.674662i | 0.0618461 | + | 0.0357069i | ||||
\(358\) | 7.71769 | − | 4.45581i | 0.407892 | − | 0.235497i | ||||
\(359\) | 1.84432 | + | 3.19445i | 0.0973393 | + | 0.168597i | 0.910583 | − | 0.413327i | \(-0.135633\pi\) |
−0.813243 | + | 0.581924i | \(0.802300\pi\) | |||||||
\(360\) | −1.81514 | − | 1.30586i | −0.0956661 | − | 0.0688250i | ||||
\(361\) | 10.7190 | − | 15.6877i | 0.564157 | − | 0.825667i | ||||
\(362\) | 9.22548i | 0.484881i | ||||||||
\(363\) | −9.38031 | + | 5.41572i | −0.492338 | + | 0.284252i | ||||
\(364\) | 2.05483 | + | 3.55906i | 0.107702 | + | 0.186546i | ||||
\(365\) | −14.1823 | + | 6.39394i | −0.742338 | + | 0.334674i | ||||
\(366\) | −3.37731 | − | 5.84967i | −0.176535 | − | 0.305767i | ||||
\(367\) | 9.72280 | + | 5.61346i | 0.507526 | + | 0.293020i | 0.731816 | − | 0.681502i | \(-0.238673\pi\) |
−0.224290 | + | 0.974522i | \(0.572006\pi\) | |||||||
\(368\) | − | 3.73273i | − | 0.194582i | ||||||
\(369\) | −5.60342 | −0.291702 | ||||||||
\(370\) | −1.91173 | − | 4.24038i | −0.0993859 | − | 0.220447i | ||||
\(371\) | −2.68854 | + | 4.65669i | −0.139582 | + | 0.241763i | ||||
\(372\) | − | 7.75919i | − | 0.402295i | ||||||
\(373\) | − | 2.73993i | − | 0.141868i | −0.997481 | − | 0.0709340i | \(-0.977402\pi\) | ||
0.997481 | − | 0.0709340i | \(-0.0225980\pi\) | |||||||
\(374\) | −0.257518 | + | 0.446034i | −0.0133159 | + | 0.0230639i | ||||
\(375\) | −10.9024 | + | 2.47755i | −0.562996 | + | 0.127940i | ||||
\(376\) | 2.07164 | − | 3.58819i | 0.106837 | − | 0.185047i | ||||
\(377\) | 7.86129 | − | 4.53872i | 0.404877 | − | 0.233756i | ||||
\(378\) | −0.931495 | + | 0.537799i | −0.0479109 | + | 0.0276614i | ||||
\(379\) | −36.3082 | −1.86503 | −0.932515 | − | 0.361132i | \(-0.882390\pi\) | ||||
−0.932515 | + | 0.361132i | \(0.882390\pi\) | |||||||
\(380\) | −1.34036 | + | 9.65419i | −0.0687589 | + | 0.495250i | ||||
\(381\) | −18.2591 | −0.935442 | ||||||||
\(382\) | −17.0993 | + | 9.87227i | −0.874875 | + | 0.505109i | ||||
\(383\) | −9.30230 | + | 5.37069i | −0.475326 | + | 0.274429i | −0.718466 | − | 0.695562i | \(-0.755156\pi\) |
0.243141 | + | 0.969991i | \(0.421822\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 0.0986258 | − | 0.982491i | 0.00502644 | − | 0.0500724i | ||||
\(386\) | 6.90289 | − | 11.9562i | 0.351348 | − | 0.608552i | ||||
\(387\) | 2.21972i | 0.112835i | ||||||||
\(388\) | 12.1607i | 0.617365i | ||||||||
\(389\) | 3.04431 | − | 5.27291i | 0.154353 | − | 0.267347i | −0.778470 | − | 0.627681i | \(-0.784004\pi\) |
0.932823 | + | 0.360334i | \(0.117337\pi\) | |||||||
\(390\) | 7.78864 | − | 3.51141i | 0.394393 | − | 0.177807i | ||||
\(391\) | 4.68266 | 0.236812 | ||||||||
\(392\) | 5.84309i | 0.295121i | ||||||||
\(393\) | −16.8039 | − | 9.70176i | −0.847647 | − | 0.489389i | ||||
\(394\) | −4.21002 | − | 7.29198i | −0.212098 | − | 0.367364i | ||||
\(395\) | −8.22116 | − | 18.2353i | −0.413652 | − | 0.917517i | ||||
\(396\) | −0.205277 | − | 0.355551i | −0.0103156 | − | 0.0178671i | ||||
\(397\) | −19.8802 | + | 11.4778i | −0.997759 | + | 0.576056i | −0.907584 | − | 0.419870i | \(-0.862076\pi\) |
−0.0901743 | + | 0.995926i | \(0.528742\pi\) | |||||||
\(398\) | 6.66504i | 0.334088i | ||||||||
\(399\) | 3.96853 | + | 2.49640i | 0.198675 | + | 0.124976i | ||||
\(400\) | −1.58945 | − | 4.74064i | −0.0794723 | − | 0.237032i | ||||
\(401\) | 9.06197 | + | 15.6958i | 0.452533 | + | 0.783810i | 0.998543 | − | 0.0539687i | \(-0.0171871\pi\) |
−0.546010 | + | 0.837779i | \(0.683854\pi\) | |||||||
\(402\) | 8.07251 | − | 4.66066i | 0.402620 | − | 0.232453i | ||||
\(403\) | 25.6745 | + | 14.8232i | 1.27894 | + | 0.738396i | ||||
\(404\) | 1.54404 | + | 2.67436i | 0.0768190 | + | 0.133054i | ||||
\(405\) | 0.919023 | + | 2.03848i | 0.0456666 | + | 0.101293i | ||||
\(406\) | −2.55539 | −0.126822 | ||||||||
\(407\) | − | 0.854024i | − | 0.0423324i | ||||||
\(408\) | 1.08642 | + | 0.627244i | 0.0537857 | + | 0.0310532i | ||||
\(409\) | 19.7968 | − | 34.2890i | 0.978888 | − | 1.69548i | 0.312431 | − | 0.949941i | \(-0.398857\pi\) |
0.666457 | − | 0.745543i | \(-0.267810\pi\) | |||||||
\(410\) | −10.1710 | − | 7.31730i | −0.502309 | − | 0.361376i | ||||
\(411\) | 8.84238 | 0.436162 | ||||||||
\(412\) | −12.8132 | − | 7.39772i | −0.631263 | − | 0.364460i | ||||
\(413\) | −2.34085 | + | 1.35149i | −0.115186 | + | 0.0665025i | ||||
\(414\) | −1.86636 | + | 3.23263i | −0.0917267 | + | 0.158875i | ||||
\(415\) | 2.03703 | − | 20.2925i | 0.0999940 | − | 0.996121i | ||||
\(416\) | 1.91041 | + | 3.30892i | 0.0936653 | + | 0.162233i | ||||
\(417\) | − | 10.5667i | − | 0.517452i | ||||||
\(418\) | −0.952875 | + | 1.51479i | −0.0466066 | + | 0.0740906i | ||||
\(419\) | 27.5268 | 1.34477 | 0.672385 | − | 0.740201i | \(-0.265270\pi\) | ||||
0.672385 | + | 0.740201i | \(0.265270\pi\) | |||||||
\(420\) | −2.39308 | − | 0.240226i | −0.116770 | − | 0.0117218i | ||||
\(421\) | 0.443296 | + | 0.767812i | 0.0216049 | + | 0.0374209i | 0.876626 | − | 0.481173i | \(-0.159789\pi\) |
−0.855021 | + | 0.518594i | \(0.826456\pi\) | |||||||
\(422\) | 10.5760 | + | 6.10606i | 0.514832 | + | 0.297239i | ||||
\(423\) | −3.58819 | + | 2.07164i | −0.174464 | + | 0.100727i | ||||
\(424\) | −2.49958 | + | 4.32940i | −0.121390 | + | 0.210254i | ||||
\(425\) | 5.94707 | − | 1.99394i | 0.288475 | − | 0.0967203i | ||||
\(426\) | −9.59521 | −0.464889 | ||||||||
\(427\) | −6.29189 | − | 3.63262i | −0.304486 | − | 0.175795i | ||||
\(428\) | −4.65618 | − | 2.68825i | −0.225065 | − | 0.129941i | ||||
\(429\) | 1.56865 | 0.0757352 | ||||||||
\(430\) | −2.89865 | + | 4.02909i | −0.139785 | + | 0.194300i | ||||
\(431\) | −4.26551 | + | 7.38807i | −0.205462 | + | 0.355871i | −0.950280 | − | 0.311397i | \(-0.899203\pi\) |
0.744818 | + | 0.667268i | \(0.232536\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 12.5809 | + | 7.26356i | 0.604597 | + | 0.349064i | 0.770848 | − | 0.637019i | \(-0.219833\pi\) |
−0.166251 | + | 0.986084i | \(0.553166\pi\) | |||||||
\(434\) | −4.17288 | − | 7.22764i | −0.200305 | − | 0.346938i | ||||
\(435\) | −0.530612 | + | 5.28585i | −0.0254409 | + | 0.253437i | ||||
\(436\) | 16.3210 | 0.781636 | ||||||||
\(437\) | 16.2589 | + | 0.616616i | 0.777768 | + | 0.0294968i | ||||
\(438\) | 6.95732i | 0.332433i | ||||||||
\(439\) | 6.98935 | + | 12.1059i | 0.333583 | + | 0.577784i | 0.983212 | − | 0.182469i | \(-0.0584088\pi\) |
−0.649628 | + | 0.760252i | \(0.725075\pi\) | |||||||
\(440\) | 0.0916940 | − | 0.913438i | 0.00437134 | − | 0.0435464i | ||||
\(441\) | 2.92155 | − | 5.06026i | 0.139121 | − | 0.240965i | ||||
\(442\) | −4.15100 | + | 2.39658i | −0.197443 | + | 0.113994i | ||||
\(443\) | −19.1733 | − | 11.0697i | −0.910951 | − | 0.525938i | −0.0302139 | − | 0.999543i | \(-0.509619\pi\) |
−0.880737 | + | 0.473606i | \(0.842952\pi\) | |||||||
\(444\) | −2.08017 | −0.0987205 | ||||||||
\(445\) | 7.12434 | − | 9.90277i | 0.337726 | − | 0.469436i | ||||
\(446\) | −0.285027 | + | 0.493682i | −0.0134964 | + | 0.0233765i | ||||
\(447\) | 2.04715 | + | 1.18192i | 0.0968267 | + | 0.0559029i | ||||
\(448\) | − | 1.07560i | − | 0.0508172i | ||||||
\(449\) | −33.0859 | −1.56142 | −0.780711 | − | 0.624892i | \(-0.785143\pi\) | ||||
−0.780711 | + | 0.624892i | \(0.785143\pi\) | |||||||
\(450\) | −0.993820 | + | 4.90024i | −0.0468491 | + | 0.230999i | ||||
\(451\) | −1.15026 | − | 1.99230i | −0.0541634 | − | 0.0938138i | ||||
\(452\) | −8.48608 | − | 4.89944i | −0.399151 | − | 0.230450i | ||||
\(453\) | −3.48952 | + | 2.01468i | −0.163952 | + | 0.0946577i | ||||
\(454\) | 1.23158 | + | 2.13316i | 0.0578009 | + | 0.100114i | ||||
\(455\) | 5.36664 | − | 7.45958i | 0.251592 | − | 0.349711i | ||||
\(456\) | 3.68961 | + | 2.32094i | 0.172782 | + | 0.108688i | ||||
\(457\) | 29.1810i | 1.36503i | 0.730871 | + | 0.682515i | \(0.239114\pi\) | ||||
−0.730871 | + | 0.682515i | \(0.760886\pi\) | |||||||
\(458\) | −9.54793 | + | 5.51250i | −0.446145 | + | 0.257582i | ||||
\(459\) | −0.627244 | − | 1.08642i | −0.0292772 | − | 0.0507097i | ||||
\(460\) | −7.60908 | + | 3.43046i | −0.354775 | + | 0.159946i | ||||
\(461\) | 10.1373 | + | 17.5583i | 0.472141 | + | 0.817773i | 0.999492 | − | 0.0318749i | \(-0.0101478\pi\) |
−0.527350 | + | 0.849648i | \(0.676814\pi\) | |||||||
\(462\) | −0.382430 | − | 0.220796i | −0.0177922 | − | 0.0102724i | ||||
\(463\) | − | 15.3688i | − | 0.714251i | −0.934057 | − | 0.357125i | \(-0.883757\pi\) | ||
0.934057 | − | 0.357125i | \(-0.116243\pi\) | |||||||
\(464\) | −2.37579 | −0.110293 | ||||||||
\(465\) | −15.8169 | + | 7.13088i | −0.733493 | + | 0.330686i | ||||
\(466\) | −8.63595 | + | 14.9579i | −0.400053 | + | 0.692911i | ||||
\(467\) | − | 38.1609i | − | 1.76587i | −0.469491 | − | 0.882937i | \(-0.655563\pi\) | ||
0.469491 | − | 0.882937i | \(-0.344437\pi\) | |||||||
\(468\) | − | 3.82081i | − | 0.176617i | ||||||
\(469\) | 5.01300 | − | 8.68277i | 0.231479 | − | 0.400933i | ||||
\(470\) | −9.21833 | − | 0.925367i | −0.425210 | − | 0.0426840i | ||||
\(471\) | −9.72912 | + | 16.8513i | −0.448294 | + | 0.776469i | ||||
\(472\) | −2.17633 | + | 1.25650i | −0.100174 | + | 0.0578352i | ||||
\(473\) | −0.789223 | + | 0.455658i | −0.0362885 | + | 0.0209512i | ||||
\(474\) | −8.94554 | −0.410882 | ||||||||
\(475\) | 20.9117 | − | 6.14014i | 0.959494 | − | 0.281729i | ||||
\(476\) | 1.34932 | 0.0618461 | ||||||||
\(477\) | 4.32940 | − | 2.49958i | 0.198230 | − | 0.114448i | ||||
\(478\) | 5.98201 | − | 3.45372i | 0.273611 | − | 0.157969i | ||||
\(479\) | −15.1215 | + | 26.1912i | −0.690918 | + | 1.19670i | 0.280620 | + | 0.959819i | \(0.409460\pi\) |
−0.971538 | + | 0.236886i | \(0.923873\pi\) | |||||||
\(480\) | −2.22489 | − | 0.223342i | −0.101552 | − | 0.0101941i | ||||
\(481\) | 3.97397 | − | 6.88312i | 0.181197 | − | 0.313843i | ||||
\(482\) | − | 22.0279i | − | 1.00334i | ||||||
\(483\) | 4.01491i | 0.182685i | ||||||||
\(484\) | −5.41572 | + | 9.38031i | −0.246169 | + | 0.426378i | ||||
\(485\) | 24.7893 | − | 11.1760i | 1.12562 | − | 0.507474i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − | 37.7499i | − | 1.71061i | −0.518125 | − | 0.855305i | \(-0.673370\pi\) | ||
0.518125 | − | 0.855305i | \(-0.326630\pi\) | |||||||
\(488\) | −5.84967 | − | 3.37731i | −0.264802 | − | 0.152884i | ||||
\(489\) | −6.71701 | − | 11.6342i | −0.303754 | − | 0.526117i | ||||
\(490\) | 11.9110 | − | 5.36994i | 0.538085 | − | 0.242589i | ||||
\(491\) | −10.6495 | − | 18.4456i | −0.480607 | − | 0.832436i | 0.519145 | − | 0.854686i | \(-0.326250\pi\) |
−0.999752 | + | 0.0222498i | \(0.992917\pi\) | |||||||
\(492\) | −4.85270 | + | 2.80171i | −0.218777 | + | 0.126311i | ||||
\(493\) | − | 2.98039i | − | 0.134230i | ||||||
\(494\) | −14.7285 | + | 7.77467i | −0.662665 | + | 0.349799i | ||||
\(495\) | −0.536128 | + | 0.745213i | −0.0240972 | + | 0.0334948i | ||||
\(496\) | −3.87959 | − | 6.71965i | −0.174199 | − | 0.301721i | ||||
\(497\) | −8.93788 | + | 5.16029i | −0.400919 | + | 0.231471i | ||||
\(498\) | −7.89876 | − | 4.56035i | −0.353952 | − | 0.204354i | ||||
\(499\) | −10.2460 | − | 17.7466i | −0.458674 | − | 0.794447i | 0.540217 | − | 0.841526i | \(-0.318342\pi\) |
−0.998891 | + | 0.0470789i | \(0.985009\pi\) | |||||||
\(500\) | −8.20296 | + | 7.59681i | −0.366847 | + | 0.339740i | ||||
\(501\) | 3.90441 | 0.174436 | ||||||||
\(502\) | 21.1326i | 0.943196i | ||||||||
\(503\) | −3.26234 | − | 1.88351i | −0.145461 | − | 0.0839817i | 0.425503 | − | 0.904957i | \(-0.360097\pi\) |
−0.570964 | + | 0.820975i | \(0.693430\pi\) | |||||||
\(504\) | −0.537799 | + | 0.931495i | −0.0239555 | + | 0.0414921i | ||||
\(505\) | 4.03262 | − | 5.60530i | 0.179449 | − | 0.249432i | ||||
\(506\) | −1.53249 | −0.0681274 | ||||||||
\(507\) | 1.38442 | + | 0.799296i | 0.0614843 | + | 0.0354980i | ||||
\(508\) | −15.8129 | + | 9.12955i | −0.701582 | + | 0.405058i | ||||
\(509\) | −4.50733 | + | 7.80693i | −0.199784 | + | 0.346036i | −0.948458 | − | 0.316902i | \(-0.897357\pi\) |
0.748674 | + | 0.662938i | \(0.230691\pi\) | |||||||
\(510\) | 0.280179 | − | 2.79109i | 0.0124066 | − | 0.123592i | ||||
\(511\) | 3.74164 | + | 6.48070i | 0.165520 | + | 0.286689i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −2.03482 | − | 3.85480i | −0.0898396 | − | 0.170194i | ||||
\(514\) | −26.4167 | −1.16519 | ||||||||
\(515\) | −3.30444 | + | 32.9182i | −0.145611 | + | 1.45055i | ||||
\(516\) | 1.10986 | + | 1.92233i | 0.0488588 | + | 0.0846260i | ||||
\(517\) | −1.47315 | − | 0.850522i | −0.0647889 | − | 0.0374059i | ||||
\(518\) | −1.93767 | + | 1.11871i | −0.0851362 | + | 0.0491534i | ||||
\(519\) | −7.58604 | + | 13.1394i | −0.332990 | + | 0.576756i | ||||
\(520\) | 4.98945 | − | 6.93529i | 0.218802 | − | 0.304133i | ||||
\(521\) | 7.99789 | 0.350394 | 0.175197 | − | 0.984533i | \(-0.443944\pi\) | ||||
0.175197 | + | 0.984533i | \(0.443944\pi\) | |||||||
\(522\) | 2.05749 | + | 1.18789i | 0.0900540 | + | 0.0519927i | ||||
\(523\) | 10.1372 | + | 5.85269i | 0.443267 | + | 0.255920i | 0.704982 | − | 0.709225i | \(-0.250955\pi\) |
−0.261716 | + | 0.965145i | \(0.584288\pi\) | |||||||
\(524\) | −19.4035 | −0.847647 | ||||||||
\(525\) | 1.70960 | + | 5.09902i | 0.0746132 | + | 0.222539i | ||||
\(526\) | −11.9611 | + | 20.7173i | −0.521530 | + | 0.903316i | ||||
\(527\) | 8.42972 | − | 4.86690i | 0.367204 | − | 0.212006i | ||||
\(528\) | −0.355551 | − | 0.205277i | −0.0154734 | − | 0.00893355i | ||||
\(529\) | −4.53338 | − | 7.85205i | −0.197104 | − | 0.341393i | ||||
\(530\) | 11.1226 | + | 1.11652i | 0.483133 | + | 0.0484986i | ||||
\(531\) | 2.51301 | 0.109055 | ||||||||
\(532\) | 4.68505 | + | 0.177680i | 0.203123 | + | 0.00770341i | ||||
\(533\) | − | 21.4096i | − | 0.927353i | ||||||
\(534\) | −2.72783 | − | 4.72474i | −0.118045 | − | 0.204459i | ||||
\(535\) | −1.20080 | + | 11.9621i | −0.0519150 | + | 0.517167i | ||||
\(536\) | 4.66066 | − | 8.07251i | 0.201310 | − | 0.348679i | ||||
\(537\) | −7.71769 | + | 4.45581i | −0.333043 | + | 0.192282i | ||||
\(538\) | 6.74229 | + | 3.89266i | 0.290681 | + | 0.167825i | ||||
\(539\) | 2.39891 | 0.103328 | ||||||||
\(540\) | 1.81514 | + | 1.30586i | 0.0781111 | + | 0.0561954i | ||||
\(541\) | −12.3595 | + | 21.4072i | −0.531375 | + | 0.920369i | 0.467954 | + | 0.883753i | \(0.344991\pi\) |
−0.999329 | + | 0.0366163i | \(0.988342\pi\) | |||||||
\(542\) | 0.729521 | + | 0.421189i | 0.0313356 | + | 0.0180916i | ||||
\(543\) | − | 9.22548i | − | 0.395903i | ||||||
\(544\) | 1.25449 | 0.0537857 | ||||||||
\(545\) | −14.9994 | − | 33.2701i | −0.642504 | − | 1.42513i | ||||
\(546\) | −2.05483 | − | 3.55906i | −0.0879385 | − | 0.152314i | ||||
\(547\) | −27.0571 | − | 15.6214i | −1.15688 | − | 0.667924i | −0.206324 | − | 0.978484i | \(-0.566150\pi\) |
−0.950554 | + | 0.310560i | \(0.899484\pi\) | |||||||
\(548\) | 7.65772 | − | 4.42119i | 0.327122 | − | 0.188864i | ||||
\(549\) | 3.37731 | + | 5.84967i | 0.144140 | + | 0.249658i | ||||
\(550\) | −1.94629 | + | 0.652554i | −0.0829902 | + | 0.0278250i | ||||
\(551\) | 0.392461 | − | 10.3484i | 0.0167194 | − | 0.440856i | ||||
\(552\) | 3.73273i | 0.158875i | ||||||||
\(553\) | −8.33272 | + | 4.81090i | −0.354343 | + | 0.204580i | ||||
\(554\) | −2.77742 | − | 4.81064i | −0.118001 | − | 0.204384i | ||||
\(555\) | 1.91173 | + | 4.24038i | 0.0811482 | + | 0.179994i | ||||
\(556\) | −5.28333 | − | 9.15100i | −0.224063 | − | 0.388089i | ||||
\(557\) | 1.27137 | + | 0.734027i | 0.0538698 | + | 0.0311017i | 0.526693 | − | 0.850056i | \(-0.323432\pi\) |
−0.472823 | + | 0.881157i | \(0.656765\pi\) | |||||||
\(558\) | 7.75919i | 0.328473i | ||||||||
\(559\) | −8.48113 | −0.358713 | ||||||||
\(560\) | −2.19258 | + | 0.988499i | −0.0926535 | + | 0.0417717i | ||||
\(561\) | 0.257518 | − | 0.446034i | 0.0108724 | − | 0.0188316i | ||||
\(562\) | − | 16.1199i | − | 0.679975i | ||||||
\(563\) | 9.14417i | 0.385381i | 0.981260 | + | 0.192690i | \(0.0617213\pi\) | ||||
−0.981260 | + | 0.192690i | \(0.938279\pi\) | |||||||
\(564\) | −2.07164 | + | 3.58819i | −0.0872318 | + | 0.151090i | ||||
\(565\) | −2.18850 | + | 21.8014i | −0.0920708 | + | 0.917191i | ||||
\(566\) | −2.76292 | + | 4.78552i | −0.116134 | + | 0.201150i | ||||
\(567\) | 0.931495 | − | 0.537799i | 0.0391191 | − | 0.0225854i | ||||
\(568\) | −8.30969 | + | 4.79760i | −0.348667 | + | 0.201303i | ||||
\(569\) | −26.6371 | −1.11668 | −0.558342 | − | 0.829611i | \(-0.688562\pi\) | ||||
−0.558342 | + | 0.829611i | \(0.688562\pi\) | |||||||
\(570\) | 1.34036 | − | 9.65419i | 0.0561414 | − | 0.404370i | ||||
\(571\) | 37.9441 | 1.58791 | 0.793957 | − | 0.607974i | \(-0.208018\pi\) | ||||
0.793957 | + | 0.607974i | \(0.208018\pi\) | |||||||
\(572\) | 1.35849 | − | 0.784326i | 0.0568014 | − | 0.0327943i | ||||
\(573\) | 17.0993 | − | 9.87227i | 0.714333 | − | 0.412420i | ||||
\(574\) | −3.01351 | + | 5.21956i | −0.125782 | + | 0.217860i | ||||
\(575\) | 13.9858 | + | 12.3583i | 0.583250 | + | 0.515376i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 11.2059i | − | 0.466508i | −0.972416 | − | 0.233254i | \(-0.925063\pi\) | ||
0.972416 | − | 0.233254i | \(-0.0749373\pi\) | |||||||
\(578\) | − | 15.4263i | − | 0.641648i | ||||||
\(579\) | −6.90289 | + | 11.9562i | −0.286874 | + | 0.496881i | ||||
\(580\) | 2.18340 | + | 4.84299i | 0.0906609 | + | 0.201094i | ||||
\(581\) | −9.81020 | −0.406996 | ||||||||
\(582\) | − | 12.1607i | − | 0.504077i | ||||||
\(583\) | 1.77745 | + | 1.02621i | 0.0736147 | + | 0.0425014i | ||||
\(584\) | 3.47866 | + | 6.02521i | 0.143948 | + | 0.249325i | ||||
\(585\) | −7.78864 | + | 3.51141i | −0.322021 | + | 0.145179i | ||||
\(586\) | −0.273271 | − | 0.473319i | −0.0112887 | − | 0.0195526i | ||||
\(587\) | −17.3126 | + | 9.99543i | −0.714567 | + | 0.412555i | −0.812750 | − | 0.582613i | \(-0.802030\pi\) |
0.0981828 | + | 0.995168i | \(0.468697\pi\) | |||||||
\(588\) | − | 5.84309i | − | 0.240965i | ||||||
\(589\) | 29.9101 | − | 15.7886i | 1.23243 | − | 0.650557i | ||||
\(590\) | 4.56145 | + | 3.28164i | 0.187792 | + | 0.135103i | ||||
\(591\) | 4.21002 | + | 7.29198i | 0.173177 | + | 0.299952i | ||||
\(592\) | −1.80148 | + | 1.04009i | −0.0740404 | + | 0.0427472i | ||||
\(593\) | 18.6911 | + | 10.7913i | 0.767552 | + | 0.443146i | 0.832001 | − | 0.554775i | \(-0.187196\pi\) |
−0.0644489 | + | 0.997921i | \(0.520529\pi\) | |||||||
\(594\) | 0.205277 | + | 0.355551i | 0.00842263 | + | 0.0145884i | ||||
\(595\) | −1.24006 | − | 2.75057i | −0.0508375 | − | 0.112762i | ||||
\(596\) | 2.36384 | 0.0968267 | ||||||||
\(597\) | − | 6.66504i | − | 0.272782i | ||||||
\(598\) | −12.3513 | − | 7.13102i | −0.505082 | − | 0.291609i | ||||
\(599\) | −22.0781 | + | 38.2403i | −0.902085 | + | 1.56246i | −0.0773019 | + | 0.997008i | \(0.524631\pi\) |
−0.824783 | + | 0.565449i | \(0.808703\pi\) | |||||||
\(600\) | 1.58945 | + | 4.74064i | 0.0648888 | + | 0.193536i | ||||
\(601\) | 22.7911 | 0.929667 | 0.464834 | − | 0.885398i | \(-0.346114\pi\) | ||||
0.464834 | + | 0.885398i | \(0.346114\pi\) | |||||||
\(602\) | 2.06766 | + | 1.19376i | 0.0842714 | + | 0.0486541i | ||||
\(603\) | −8.07251 | + | 4.66066i | −0.328738 | + | 0.189797i | ||||
\(604\) | −2.01468 | + | 3.48952i | −0.0819760 | + | 0.141987i | ||||
\(605\) | 24.0987 | + | 2.41911i | 0.979753 | + | 0.0983510i | ||||
\(606\) | −1.54404 | − | 2.67436i | −0.0627224 | − | 0.108638i | ||||
\(607\) | − | 15.8927i | − | 0.645064i | −0.946559 | − | 0.322532i | \(-0.895466\pi\) | ||
0.946559 | − | 0.322532i | \(-0.104534\pi\) | |||||||
\(608\) | 4.35577 | + | 0.165192i | 0.176650 | + | 0.00669942i | ||||
\(609\) | 2.55539 | 0.103550 | ||||||||
\(610\) | −1.50859 | + | 15.0282i | −0.0610809 | + | 0.608476i | ||||
\(611\) | −7.91534 | − | 13.7098i | −0.320221 | − | 0.554638i | ||||
\(612\) | −1.08642 | − | 0.627244i | −0.0439159 | − | 0.0253548i | ||||
\(613\) | 33.0003 | − | 19.0527i | 1.33287 | − | 0.769532i | 0.347130 | − | 0.937817i | \(-0.387156\pi\) |
0.985738 | + | 0.168285i | \(0.0538230\pi\) | |||||||
\(614\) | 12.2904 | − | 21.2877i | 0.496001 | − | 0.859100i | ||||
\(615\) | 10.1710 | + | 7.31730i | 0.410133 | + | 0.295062i | ||||
\(616\) | −0.441592 | −0.0177922 | ||||||||
\(617\) | −30.0827 | − | 17.3683i | −1.21109 | − | 0.699221i | −0.248090 | − | 0.968737i | \(-0.579803\pi\) |
−0.962996 | + | 0.269516i | \(0.913136\pi\) | |||||||
\(618\) | 12.8132 | + | 7.39772i | 0.515424 | + | 0.297580i | ||||
\(619\) | −19.6805 | −0.791027 | −0.395513 | − | 0.918460i | \(-0.629433\pi\) | ||||
−0.395513 | + | 0.918460i | \(0.629433\pi\) | |||||||
\(620\) | −10.1324 | + | 14.0840i | −0.406928 | + | 0.565627i | ||||
\(621\) | 1.86636 | − | 3.23263i | 0.0748946 | − | 0.129721i | ||||
\(622\) | −18.6800 | + | 10.7849i | −0.749000 | + | 0.432435i | ||||
\(623\) | −5.08192 | − | 2.93405i | −0.203603 | − | 0.117550i | ||||
\(624\) | −1.91041 | − | 3.30892i | −0.0764774 | − | 0.132463i | ||||
\(625\) | 23.0246 | + | 9.73991i | 0.920986 | + | 0.389596i | ||||
\(626\) | −29.3045 | −1.17124 | ||||||||
\(627\) | 0.952875 | − | 1.51479i | 0.0380542 | − | 0.0604948i | ||||
\(628\) | 19.4582i | 0.776469i | ||||||||
\(629\) | −1.30477 | − | 2.25994i | −0.0520248 | − | 0.0901095i | ||||
\(630\) | 2.39308 | + | 0.240226i | 0.0953426 | + | 0.00957082i | ||||
\(631\) | −10.0442 | + | 17.3970i | −0.399851 | + | 0.692563i | −0.993707 | − | 0.112008i | \(-0.964272\pi\) |
0.593856 | + | 0.804571i | \(0.297605\pi\) | |||||||
\(632\) | −7.74707 | + | 4.47277i | −0.308162 | + | 0.177917i | ||||
\(633\) | −10.5760 | − | 6.10606i | −0.420359 | − | 0.242694i | ||||
\(634\) | 8.20320 | 0.325791 | ||||||||
\(635\) | 33.1428 | + | 23.8439i | 1.31523 | + | 0.946216i | ||||
\(636\) | 2.49958 | − | 4.32940i | 0.0991148 | − | 0.171672i | ||||
\(637\) | 19.3343 | + | 11.1627i | 0.766053 | + | 0.442281i | ||||
\(638\) | 0.975391i | 0.0386161i | ||||||||
\(639\) | 9.59521 | 0.379581 | ||||||||
\(640\) | −2.03848 | + | 0.919023i | −0.0805780 | + | 0.0363276i | ||||
\(641\) | 10.1096 | + | 17.5104i | 0.399306 | + | 0.691618i | 0.993640 | − | 0.112600i | \(-0.0359179\pi\) |
−0.594335 | + | 0.804218i | \(0.702585\pi\) | |||||||
\(642\) | 4.65618 | + | 2.68825i | 0.183765 | + | 0.106097i | ||||
\(643\) | 11.6160 | − | 6.70652i | 0.458092 | − | 0.264479i | −0.253150 | − | 0.967427i | \(-0.581467\pi\) |
0.711241 | + | 0.702948i | \(0.248133\pi\) | |||||||
\(644\) | 2.00745 | + | 3.47701i | 0.0791048 | + | 0.137014i | ||||
\(645\) | 2.89865 | − | 4.02909i | 0.114134 | − | 0.158645i | ||||
\(646\) | −0.207231 | + | 5.46426i | −0.00815341 | + | 0.214988i | ||||
\(647\) | − | 36.1642i | − | 1.42176i | −0.703313 | − | 0.710880i | \(-0.748297\pi\) | ||
0.703313 | − | 0.710880i | \(-0.251703\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 0.515863 | + | 0.893501i | 0.0202494 | + | 0.0350730i | ||||
\(650\) | −18.7229 | − | 3.79720i | −0.734372 | − | 0.148938i | ||||
\(651\) | 4.17288 | + | 7.22764i | 0.163548 | + | 0.283274i | ||||
\(652\) | −11.6342 | − | 6.71701i | −0.455631 | − | 0.263058i | ||||
\(653\) | 28.2889i | 1.10703i | 0.832839 | + | 0.553515i | \(0.186714\pi\) | ||||
−0.832839 | + | 0.553515i | \(0.813286\pi\) | |||||||
\(654\) | −16.3210 | −0.638203 | ||||||||
\(655\) | 17.8323 | + | 39.5537i | 0.696766 | + | 1.54549i | ||||
\(656\) | −2.80171 | + | 4.85270i | −0.109388 | + | 0.189466i | ||||
\(657\) | − | 6.95732i | − | 0.271431i | ||||||
\(658\) | 4.45650i | 0.173732i | ||||||||
\(659\) | −3.15825 | + | 5.47025i | −0.123028 | + | 0.213091i | −0.920960 | − | 0.389656i | \(-0.872594\pi\) |
0.797932 | + | 0.602747i | \(0.205927\pi\) | |||||||
\(660\) | −0.0916940 | + | 0.913438i | −0.00356918 | + | 0.0355555i | ||||
\(661\) | 12.4189 | − | 21.5102i | 0.483039 | − | 0.836649i | −0.516771 | − | 0.856124i | \(-0.672866\pi\) |
0.999810 | + | 0.0194748i | \(0.00619942\pi\) | |||||||
\(662\) | 23.4543 | − | 13.5413i | 0.911575 | − | 0.526298i | ||||
\(663\) | 4.15100 | − | 2.39658i | 0.161211 | − | 0.0930754i | ||||
\(664\) | −9.12070 | −0.353952 | ||||||||
\(665\) | −3.94348 | − | 9.71367i | −0.152921 | − | 0.376680i | ||||
\(666\) | 2.08017 | 0.0806050 | ||||||||
\(667\) | 7.68005 | − | 4.43408i | 0.297373 | − | 0.171688i | ||||
\(668\) | 3.38132 | − | 1.95221i | 0.130827 | − | 0.0755331i | ||||
\(669\) | 0.285027 | − | 0.493682i | 0.0110198 | − | 0.0190868i | ||||
\(670\) | −20.7389 | − | 2.08184i | −0.801213 | − | 0.0804286i | ||||
\(671\) | −1.38657 | + | 2.40161i | −0.0535279 | + | 0.0927131i | ||||
\(672\) | 1.07560i | 0.0414921i | ||||||||
\(673\) | − | 28.1903i | − | 1.08665i | −0.839521 | − | 0.543327i | \(-0.817164\pi\) | ||
0.839521 | − | 0.543327i | \(-0.182836\pi\) | |||||||
\(674\) | 13.8543 | − | 23.9964i | 0.533648 | − | 0.924306i | ||||
\(675\) | 0.993820 | − | 4.90024i | 0.0382521 | − | 0.188610i | ||||
\(676\) | 1.59859 | 0.0614843 | ||||||||
\(677\) | 16.9194i | 0.650266i | 0.945668 | + | 0.325133i | \(0.105409\pi\) | ||||
−0.945668 | + | 0.325133i | \(0.894591\pi\) | |||||||
\(678\) | 8.48608 | + | 4.89944i | 0.325906 | + | 0.188162i | ||||
\(679\) | −6.54000 | − | 11.3276i | −0.250982 | − | 0.434714i | ||||
\(680\) | −1.15290 | − | 2.55725i | −0.0442118 | − | 0.0980659i | ||||
\(681\) | −1.23158 | − | 2.13316i | −0.0471942 | − | 0.0817428i | ||||
\(682\) | −2.75879 | + | 1.59279i | −0.105639 | + | 0.0609909i | ||||
\(683\) | 46.8587i | 1.79300i | 0.443044 | + | 0.896500i | \(0.353899\pi\) | ||||
−0.443044 | + | 0.896500i | \(0.646101\pi\) | |||||||
\(684\) | −3.68961 | − | 2.32094i | −0.141076 | − | 0.0887435i | ||||
\(685\) | −16.0501 | − | 11.5469i | −0.613244 | − | 0.441186i | ||||
\(686\) | −6.90700 | − | 11.9633i | −0.263710 | − | 0.456760i | ||||
\(687\) | 9.54793 | − | 5.51250i | 0.364276 | − | 0.210315i | ||||
\(688\) | 1.92233 | + | 1.10986i | 0.0732883 | + | 0.0423130i | ||||
\(689\) | 9.55042 | + | 16.5418i | 0.363842 | + | 0.630193i | ||||
\(690\) | 7.60908 | − | 3.43046i | 0.289673 | − | 0.130595i | ||||
\(691\) | −19.4802 | −0.741061 | −0.370531 | − | 0.928820i | \(-0.620824\pi\) | ||||
−0.370531 | + | 0.928820i | \(0.620824\pi\) | |||||||
\(692\) | 15.1721i | 0.576756i | ||||||||
\(693\) | 0.382430 | + | 0.220796i | 0.0145273 | + | 0.00838734i | ||||
\(694\) | −1.18262 | + | 2.04836i | −0.0448917 | + | 0.0777547i | ||||
\(695\) | −13.7986 | + | 19.1800i | −0.523411 | + | 0.727537i | ||||
\(696\) | 2.37579 | 0.0900540 | ||||||||
\(697\) | −6.08766 | − | 3.51471i | −0.230586 | − | 0.133129i | ||||
\(698\) | 14.5401 | − | 8.39471i | 0.550350 | − | 0.317745i | ||||
\(699\) | 8.63595 | − | 14.9579i | 0.326642 | − | 0.565760i | ||||
\(700\) | 4.03007 | + | 3.56108i | 0.152322 | + | 0.134596i | ||||
\(701\) | −24.8870 | − | 43.1055i | −0.939968 | − | 1.62807i | −0.765527 | − | 0.643404i | \(-0.777522\pi\) |
−0.174441 | − | 0.984668i | \(-0.555812\pi\) | |||||||
\(702\) | 3.82081i | 0.144207i | ||||||||
\(703\) | −4.23278 | − | 8.01865i | −0.159642 | − | 0.302429i | ||||
\(704\) | −0.410555 | −0.0154734 | ||||||||
\(705\) | 9.21833 | + | 0.925367i | 0.347182 | + | 0.0348514i | ||||
\(706\) | 11.5009 | + | 19.9202i | 0.432843 | + | 0.749706i | ||||
\(707\) | −2.87653 | − | 1.66077i | −0.108183 | − | 0.0624596i | ||||
\(708\) | 2.17633 | − | 1.25650i | 0.0817914 | − | 0.0472223i | ||||
\(709\) | −12.3260 | + | 21.3493i | −0.462913 | + | 0.801790i | −0.999105 | − | 0.0423070i | \(-0.986529\pi\) |
0.536191 | + | 0.844097i | \(0.319863\pi\) | |||||||
\(710\) | 17.4166 | + | 12.5300i | 0.653634 | + | 0.470243i | ||||
\(711\) | 8.94554 | 0.335484 | ||||||||
\(712\) | −4.72474 | − | 2.72783i | −0.177067 | − | 0.102230i | ||||
\(713\) | 25.0826 | + | 14.4815i | 0.939352 | + | 0.542335i | ||||
\(714\) | −1.34932 | −0.0504972 | ||||||||
\(715\) | −2.84732 | − | 2.04844i | −0.106484 | − | 0.0766075i | ||||
\(716\) | −4.45581 | + | 7.71769i | −0.166521 | + | 0.288423i | ||||
\(717\) | −5.98201 | + | 3.45372i | −0.223402 | + | 0.128981i | ||||
\(718\) | −3.19445 | − | 1.84432i | −0.119216 | − | 0.0688293i | ||||
\(719\) | −16.3306 | − | 28.2854i | −0.609027 | − | 1.05487i | −0.991401 | − | 0.130858i | \(-0.958227\pi\) |
0.382374 | − | 0.924008i | \(-0.375107\pi\) | |||||||
\(720\) | 2.22489 | + | 0.223342i | 0.0829166 | + | 0.00832346i | ||||
\(721\) | 15.9139 | 0.592666 | ||||||||
\(722\) | −1.43908 | + | 18.9454i | −0.0535569 | + | 0.705076i | ||||
\(723\) | 22.0279i | 0.819227i | ||||||||
\(724\) | −4.61274 | − | 7.98950i | −0.171431 | − | 0.296927i | ||||
\(725\) | 7.86573 | − | 8.90164i | 0.292126 | − | 0.330599i | ||||
\(726\) | 5.41572 | − | 9.38031i | 0.200996 | − | 0.348136i | ||||
\(727\) | 9.05449 | − | 5.22761i | 0.335813 | − | 0.193881i | −0.322606 | − | 0.946533i | \(-0.604559\pi\) |
0.658419 | + | 0.752652i | \(0.271226\pi\) | |||||||
\(728\) | −3.55906 | − | 2.05483i | −0.131908 | − | 0.0761569i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 9.08530 | − | 12.6285i | 0.336262 | − | 0.467401i | ||||
\(731\) | −1.39231 | + | 2.41154i | −0.0514963 | + | 0.0891942i | ||||
\(732\) | 5.84967 | + | 3.37731i | 0.216210 | + | 0.124829i | ||||
\(733\) | − | 20.8146i | − | 0.768804i | −0.923166 | − | 0.384402i | \(-0.874408\pi\) | ||
0.923166 | − | 0.384402i | \(-0.125592\pi\) | |||||||
\(734\) | −11.2269 | −0.414393 | ||||||||
\(735\) | −11.9110 | + | 5.36994i | −0.439344 | + | 0.198073i | ||||
\(736\) | 1.86636 | + | 3.23263i | 0.0687950 | + | 0.119157i | ||||
\(737\) | −3.31421 | − | 1.91346i | −0.122080 | − | 0.0704831i | ||||
\(738\) | 4.85270 | − | 2.80171i | 0.178631 | − | 0.103132i | ||||
\(739\) | 1.61058 | + | 2.78961i | 0.0592461 | + | 0.102617i | 0.894127 | − | 0.447813i | \(-0.147797\pi\) |
−0.834881 | + | 0.550430i | \(0.814464\pi\) | |||||||
\(740\) | 3.77580 | + | 2.71642i | 0.138801 | + | 0.0998575i | ||||
\(741\) | 14.7285 | − | 7.77467i | 0.541064 | − | 0.285610i | ||||
\(742\) | − | 5.37708i | − | 0.197399i | ||||||
\(743\) | −36.4504 | + | 21.0447i | −1.33724 | + | 0.772054i | −0.986397 | − | 0.164381i | \(-0.947437\pi\) |
−0.350840 | + | 0.936435i | \(0.614104\pi\) | |||||||
\(744\) | 3.87959 | + | 6.71965i | 0.142233 | + | 0.246354i | ||||
\(745\) | −2.17243 | − | 4.81864i | −0.0795915 | − | 0.176541i | ||||
\(746\) | 1.36996 | + | 2.37285i | 0.0501579 | + | 0.0868761i | ||||
\(747\) | 7.89876 | + | 4.56035i | 0.289000 | + | 0.166854i | ||||
\(748\) | − | 0.515036i | − | 0.0188316i | ||||||
\(749\) | 5.78295 | 0.211304 | ||||||||
\(750\) | 8.20296 | − | 7.59681i | 0.299530 | − | 0.277396i | ||||
\(751\) | −15.3356 | + | 26.5620i | −0.559602 | + | 0.969259i | 0.437927 | + | 0.899010i | \(0.355713\pi\) |
−0.997529 | + | 0.0702491i | \(0.977621\pi\) | |||||||
\(752\) | 4.14328i | 0.151090i | ||||||||
\(753\) | − | 21.1326i | − | 0.770116i | ||||||
\(754\) | −4.53872 | + | 7.86129i | −0.165290 | + | 0.286291i | ||||
\(755\) | 8.96485 | + | 0.899923i | 0.326264 | + | 0.0327515i | ||||
\(756\) | 0.537799 | − | 0.931495i | 0.0195595 | − | 0.0338781i | ||||
\(757\) | −24.7684 | + | 14.3000i | −0.900221 | + | 0.519743i | −0.877272 | − | 0.479994i | \(-0.840639\pi\) |
−0.0229494 | + | 0.999737i | \(0.507306\pi\) | |||||||
\(758\) | 31.4439 | − | 18.1541i | 1.14209 | − | 0.659387i | ||||
\(759\) | 1.53249 | 0.0556258 | ||||||||
\(760\) | −3.66631 | − | 9.03096i | −0.132991 | − | 0.327587i | ||||
\(761\) | 35.0855 | 1.27185 | 0.635924 | − | 0.771752i | \(-0.280619\pi\) | ||||
0.635924 | + | 0.771752i | \(0.280619\pi\) | |||||||
\(762\) | 15.8129 | − | 9.12955i | 0.572839 | − | 0.330729i | ||||
\(763\) | −15.2029 | + | 8.77743i | −0.550384 | + | 0.317764i | ||||
\(764\) | 9.87227 | − | 17.0993i | 0.357166 | − | 0.618630i | ||||
\(765\) | −0.280179 | + | 2.79109i | −0.0101299 | + | 0.100912i | ||||
\(766\) | 5.37069 | − | 9.30230i | 0.194051 | − | 0.336106i | ||||
\(767\) | 9.60172i | 0.346698i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 9.23956 | − | 16.0034i | 0.333187 | − | 0.577097i | −0.649948 | − | 0.759979i | \(-0.725209\pi\) |
0.983135 | + | 0.182882i | \(0.0585426\pi\) | |||||||
\(770\) | 0.405833 | + | 0.900175i | 0.0146252 | + | 0.0324401i | ||||
\(771\) | 26.4167 | 0.951373 | ||||||||
\(772\) | 13.8058i | 0.496881i | ||||||||
\(773\) | −39.7340 | − | 22.9404i | −1.42913 | − | 0.825110i | −0.432080 | − | 0.901835i | \(-0.642220\pi\) |
−0.997052 | + | 0.0767251i | \(0.975554\pi\) | |||||||
\(774\) | −1.10986 | − | 1.92233i | −0.0398931 | − | 0.0690968i | ||||
\(775\) | 38.0219 | + | 7.71124i | 1.36579 | + | 0.276996i | ||||
\(776\) | −6.08034 | − | 10.5315i | −0.218272 | − | 0.378058i | ||||
\(777\) | 1.93767 | − | 1.11871i | 0.0695134 | − | 0.0401336i | ||||
\(778\) | 6.08863i | 0.218288i | ||||||||
\(779\) | −20.6744 | − | 13.0052i | −0.740738 | − | 0.465961i | ||||
\(780\) | −4.98945 | + | 6.93529i | −0.178651 | + | 0.248323i | ||||
\(781\) | 1.96968 | + | 3.41158i | 0.0704807 | + | 0.122076i | ||||
\(782\) | −4.05530 | + | 2.34133i | −0.145017 | + | 0.0837257i | ||||
\(783\) | −2.05749 | − | 1.18789i | −0.0735287 | − | 0.0424518i | ||||
\(784\) | −2.92155 | − | 5.06026i | −0.104341 | − | 0.180724i | ||||
\(785\) | 39.6652 | − | 17.8826i | 1.41571 | − | 0.638257i | ||||
\(786\) | 19.4035 | 0.692101 | ||||||||
\(787\) | − | 30.3497i | − | 1.08185i | −0.841071 | − | 0.540925i | \(-0.818074\pi\) | ||
0.841071 | − | 0.540925i | \(-0.181926\pi\) | |||||||
\(788\) | 7.29198 | + | 4.21002i | 0.259766 | + | 0.149976i | ||||
\(789\) | 11.9611 | − | 20.7173i | 0.425827 | − | 0.737555i | ||||
\(790\) | 16.2374 | + | 11.6816i | 0.577700 | + | 0.415614i | ||||
\(791\) | 10.5396 | 0.374747 | ||||||||
\(792\) | 0.355551 | + | 0.205277i | 0.0126340 | + | 0.00729421i | ||||
\(793\) | −22.3505 | + | 12.9041i | −0.793689 | + | 0.458236i | ||||
\(794\) | 11.4778 | − | 19.8802i | 0.407333 | − | 0.705522i | ||||
\(795\) | −11.1226 | − | 1.11652i | −0.394476 | − | 0.0395989i | ||||
\(796\) | −3.33252 | − | 5.77210i | −0.118118 | − | 0.204587i | ||||
\(797\) | 24.0936i | 0.853441i | 0.904384 | + | 0.426720i | \(0.140331\pi\) | ||||
−0.904384 | + | 0.426720i | \(0.859669\pi\) | |||||||
\(798\) | −4.68505 | − | 0.177680i | −0.165849 | − | 0.00628981i | ||||
\(799\) | −5.19769 | −0.183881 | ||||||||
\(800\) | 3.74682 | + | 3.31079i | 0.132470 | + | 0.117054i | ||||
\(801\) | 2.72783 | + | 4.72474i | 0.0963831 | + | 0.166940i | ||||
\(802\) | −15.6958 | − | 9.06197i | −0.554238 | − | 0.319989i | ||||
\(803\) | 2.47368 | − | 1.42818i | 0.0872943 | − | 0.0503994i | ||||
\(804\) | −4.66066 | + | 8.07251i | −0.164369 | + | 0.284695i | ||||
\(805\) | 5.24292 | − | 7.28761i | 0.184789 | − | 0.256854i | ||||
\(806\) | −29.6464 | −1.04425 | ||||||||
\(807\) | −6.74229 | − | 3.89266i | −0.237340 | − | 0.137028i | ||||
\(808\) | −2.67436 | − | 1.54404i | −0.0940837 | − | 0.0543192i | ||||
\(809\) | −41.5203 | −1.45978 | −0.729888 | − | 0.683567i | \(-0.760428\pi\) | ||||
−0.729888 | + | 0.683567i | \(0.760428\pi\) | |||||||
\(810\) | −1.81514 | − | 1.30586i | −0.0637774 | − | 0.0458833i | ||||
\(811\) | 9.91162 | − | 17.1674i | 0.348044 | − | 0.602830i | −0.637858 | − | 0.770154i | \(-0.720179\pi\) |
0.985902 | + | 0.167324i | \(0.0535126\pi\) | |||||||
\(812\) | 2.21303 | − | 1.27769i | 0.0776622 | − | 0.0448383i | ||||
\(813\) | −0.729521 | − | 0.421189i | −0.0255854 | − | 0.0147717i | ||||
\(814\) | 0.427012 | + | 0.739607i | 0.0149668 | + | 0.0259232i | ||||
\(815\) | −3.00038 | + | 29.8892i | −0.105099 | + | 1.04697i | ||||
\(816\) | −1.25449 | −0.0439159 | ||||||||
\(817\) | −5.15184 | + | 8.18990i | −0.180240 | + | 0.286528i | ||||
\(818\) | 39.5936i | 1.38436i | ||||||||
\(819\) | 2.05483 | + | 3.55906i | 0.0718014 | + | 0.124364i | ||||
\(820\) | 12.4670 | + | 1.25148i | 0.435366 | + | 0.0437035i | ||||
\(821\) | 27.0794 | − | 46.9029i | 0.945078 | − | 1.63692i | 0.189484 | − | 0.981884i | \(-0.439319\pi\) |
0.755595 | − | 0.655039i | \(-0.227348\pi\) | |||||||
\(822\) | −7.65772 | + | 4.42119i | −0.267094 | + | 0.154207i | ||||
\(823\) | 8.46807 | + | 4.88904i | 0.295178 | + | 0.170421i | 0.640275 | − | 0.768146i | \(-0.278820\pi\) |
−0.345096 | + | 0.938567i | \(0.612154\pi\) | |||||||
\(824\) | 14.7954 | 0.515424 | ||||||||
\(825\) | 1.94629 | − | 0.652554i | 0.0677612 | − | 0.0227190i | ||||
\(826\) | 1.35149 | − | 2.34085i | 0.0470244 | − | 0.0814486i | ||||
\(827\) | 37.0141 | + | 21.3701i | 1.28711 | + | 0.743110i | 0.978137 | − | 0.207962i | \(-0.0666830\pi\) |
0.308968 | + | 0.951072i | \(0.400016\pi\) | |||||||
\(828\) | − | 3.73273i | − | 0.129721i | ||||||
\(829\) | −39.3417 | −1.36639 | −0.683197 | − | 0.730234i | \(-0.739411\pi\) | ||||
−0.683197 | + | 0.730234i | \(0.739411\pi\) | |||||||
\(830\) | 8.38214 | + | 18.5924i | 0.290948 | + | 0.645350i | ||||
\(831\) | 2.77742 | + | 4.81064i | 0.0963477 | + | 0.166879i | ||||
\(832\) | −3.30892 | − | 1.91041i | −0.114716 | − | 0.0662314i | ||||
\(833\) | 6.34804 | − | 3.66504i | 0.219947 | − | 0.126986i | ||||
\(834\) | 5.28333 | + | 9.15100i | 0.182947 | + | 0.316873i | ||||
\(835\) | −7.08705 | − | 5.09863i | −0.245257 | − | 0.176445i | ||||
\(836\) | 0.0678204 | − | 1.78828i | 0.00234562 | − | 0.0618490i | ||||
\(837\) | − | 7.75919i | − | 0.268197i | ||||||
\(838\) | −23.8389 | + | 13.7634i | −0.823500 | + | 0.475448i | ||||
\(839\) | −8.04689 | − | 13.9376i | −0.277809 | − | 0.481180i | 0.693031 | − | 0.720908i | \(-0.256275\pi\) |
−0.970840 | + | 0.239728i | \(0.922942\pi\) | |||||||
\(840\) | 2.19258 | − | 0.988499i | 0.0756513 | − | 0.0341065i | ||||
\(841\) | 11.6778 | + | 20.2266i | 0.402683 | + | 0.697468i | ||||
\(842\) | −0.767812 | − | 0.443296i | −0.0264605 | − | 0.0152770i | ||||
\(843\) | 16.1199i | 0.555197i | ||||||||
\(844\) | −12.2121 | −0.420359 | ||||||||
\(845\) | −1.46914 | − | 3.25870i | −0.0505401 | − | 0.112103i | ||||
\(846\) | 2.07164 | − | 3.58819i | 0.0712245 | − | 0.123364i | ||||
\(847\) | − | 11.6503i | − | 0.400308i | ||||||
\(848\) | − | 4.99916i | − | 0.171672i | ||||||
\(849\) | 2.76292 | − | 4.78552i | 0.0948232 | − | 0.164239i | ||||
\(850\) | −4.15335 | + | 4.70034i | −0.142459 | + | 0.161220i | ||||
\(851\) | 3.88235 | − | 6.72443i | 0.133085 | − | 0.230511i | ||||
\(852\) | 8.30969 | − | 4.79760i | 0.284685 | − | 0.164363i | ||||
\(853\) | −6.70983 | + | 3.87392i | −0.229740 | + | 0.132641i | −0.610452 | − | 0.792053i | \(-0.709012\pi\) |
0.380712 | + | 0.924694i | \(0.375679\pi\) | |||||||
\(854\) | 7.26524 | 0.248612 | ||||||||
\(855\) | −1.34036 | + | 9.65419i | −0.0458393 | + | 0.330166i | ||||
\(856\) | 5.37650 | 0.183765 | ||||||||
\(857\) | −22.3760 | + | 12.9188i | −0.764349 | + | 0.441297i | −0.830855 | − | 0.556489i | \(-0.812148\pi\) |
0.0665062 | + | 0.997786i | \(0.478815\pi\) | |||||||
\(858\) | −1.35849 | + | 0.784326i | −0.0463782 | + | 0.0267764i | ||||
\(859\) | 5.48101 | − | 9.49338i | 0.187010 | − | 0.323910i | −0.757242 | − | 0.653134i | \(-0.773454\pi\) |
0.944252 | + | 0.329224i | \(0.106787\pi\) | |||||||
\(860\) | 0.495756 | − | 4.93862i | 0.0169051 | − | 0.168406i | ||||
\(861\) | 3.01351 | − | 5.21956i | 0.102700 | − | 0.177882i | ||||
\(862\) | − | 8.53101i | − | 0.290567i | ||||||
\(863\) | − | 9.48221i | − | 0.322778i | −0.986891 | − | 0.161389i | \(-0.948403\pi\) | ||
0.986891 | − | 0.161389i | \(-0.0515974\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 30.9279 | − | 13.9435i | 1.05158 | − | 0.474093i | ||||
\(866\) | −14.5271 | −0.493652 | ||||||||
\(867\) | 15.4263i | 0.523903i | ||||||||
\(868\) | 7.22764 | + | 4.17288i | 0.245322 | + | 0.141637i | ||||
\(869\) | 1.83632 | + | 3.18060i | 0.0622928 | + | 0.107894i | ||||
\(870\) | −2.18340 | − | 4.84299i | −0.0740243 | − | 0.164193i | ||||
\(871\) | −17.8075 | − | 30.8435i | −0.603385 | − | 1.04509i | ||||
\(872\) | −14.1344 | + | 8.16051i | −0.478652 | + | 0.276350i | ||||
\(873\) | 12.1607i | 0.411577i | ||||||||
\(874\) | −14.3889 | + | 7.59544i | −0.486712 | + | 0.256919i | ||||
\(875\) | 3.55545 | − | 11.4879i | 0.120196 | − | 0.388363i | ||||
\(876\) | −3.47866 | − | 6.02521i | −0.117533 | − | 0.203573i | ||||
\(877\) | −27.0267 | + | 15.6039i | −0.912626 | + | 0.526905i | −0.881275 | − | 0.472603i | \(-0.843314\pi\) |
−0.0313511 | + | 0.999508i | \(0.509981\pi\) | |||||||
\(878\) | −12.1059 | − | 6.98935i | −0.408555 | − | 0.235879i | ||||
\(879\) | 0.273271 | + | 0.473319i | 0.00921719 | + | 0.0159646i | ||||
\(880\) | 0.377309 | + | 0.836907i | 0.0127191 | + | 0.0282121i | ||||
\(881\) | −59.2914 | −1.99758 | −0.998789 | − | 0.0492058i | \(-0.984331\pi\) | ||||
−0.998789 | + | 0.0492058i | \(0.984331\pi\) | |||||||
\(882\) | 5.84309i | 0.196747i | ||||||||
\(883\) | −10.3188 | − | 5.95754i | −0.347254 | − | 0.200487i | 0.316221 | − | 0.948685i | \(-0.397586\pi\) |
−0.663475 | + | 0.748198i | \(0.730919\pi\) | |||||||
\(884\) | 2.39658 | − | 4.15100i | 0.0806057 | − | 0.139613i | ||||
\(885\) | −4.56145 | − | 3.28164i | −0.153331 | − | 0.110311i | ||||
\(886\) | 22.1394 | 0.743788 | ||||||||
\(887\) | 31.9783 | + | 18.4627i | 1.07372 | + | 0.619915i | 0.929197 | − | 0.369585i | \(-0.120500\pi\) |
0.144528 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(888\) | 1.80148 | − | 1.04009i | 0.0604537 | − | 0.0349030i | ||||
\(889\) | 9.81972 | − | 17.0083i | 0.329343 | − | 0.570439i | ||||
\(890\) | −1.21848 | + | 12.1382i | −0.0408434 | + | 0.406874i | ||||
\(891\) | −0.205277 | − | 0.355551i | −0.00687705 | − | 0.0119114i | ||||
\(892\) | − | 0.570054i | − | 0.0190868i | ||||||
\(893\) | −18.0472 | − | 0.684437i | −0.603925 | − | 0.0229038i | ||||
\(894\) | −2.36384 | −0.0790587 | ||||||||
\(895\) | 19.8273 | + | 1.99034i | 0.662755 | + | 0.0665296i | ||||
\(896\) | 0.537799 | + | 0.931495i | 0.0179666 | + | 0.0311190i | ||||
\(897\) | 12.3513 | + | 7.13102i | 0.412397 | + | 0.238098i | ||||
\(898\) | 28.6533 | − | 16.5430i | 0.956172 | − | 0.552046i | ||||
\(899\) | 9.21709 | − | 15.9645i | 0.307407 | − | 0.532445i | ||||
\(900\) | −1.58945 | − | 4.74064i | −0.0529815 | − | 0.158021i | ||||
\(901\) | 6.27138 | 0.208930 | ||||||||
\(902\) | 1.99230 | + | 1.15026i | 0.0663364 | + | 0.0382993i | ||||
\(903\) | −2.06766 | − | 1.19376i | −0.0688073 | − | 0.0397259i | ||||
\(904\) | 9.79888 | 0.325906 | ||||||||
\(905\) | −12.0472 | + | 16.7455i | −0.400463 | + | 0.556640i | ||||
\(906\) | 2.01468 | − | 3.48952i | 0.0669331 | − | 0.115932i | ||||
\(907\) | 32.6223 | − | 18.8345i | 1.08321 | − | 0.625389i | 0.151446 | − | 0.988466i | \(-0.451607\pi\) |
0.931759 | + | 0.363077i | \(0.118274\pi\) | |||||||
\(908\) | −2.13316 | − | 1.23158i | −0.0707914 | − | 0.0408714i | ||||
\(909\) | 1.54404 | + | 2.67436i | 0.0512127 | + | 0.0887029i | ||||
\(910\) | −0.917857 | + | 9.14351i | −0.0304267 | + | 0.303104i | ||||
\(911\) | −39.7301 | −1.31632 | −0.658159 | − | 0.752879i | \(-0.728665\pi\) | ||||
−0.658159 | + | 0.752879i | \(0.728665\pi\) | |||||||
\(912\) | −4.35577 | − | 0.165192i | −0.144234 | − | 0.00547005i | ||||
\(913\) | 3.74455i | 0.123926i | ||||||||
\(914\) | −14.5905 | − | 25.2715i | −0.482611 | − | 0.835907i | ||||
\(915\) | 1.50859 | − | 15.0282i | 0.0498724 | − | 0.496819i | ||||
\(916\) | 5.51250 | − | 9.54793i | 0.182138 | − | 0.315472i | ||||
\(917\) | 18.0743 | − | 10.4352i | 0.596865 | − | 0.344600i | ||||
\(918\) | 1.08642 | + | 0.627244i | 0.0358571 | + | 0.0207021i | ||||
\(919\) | −9.04072 | −0.298226 | −0.149113 | − | 0.988820i | \(-0.547642\pi\) | ||||
−0.149113 | + | 0.988820i | \(0.547642\pi\) | |||||||
\(920\) | 4.87443 | − | 6.77541i | 0.160705 | − | 0.223379i | ||||
\(921\) | −12.2904 | + | 21.2877i | −0.404984 | + | 0.701452i | ||||
\(922\) | −17.5583 | − | 10.1373i | −0.578253 | − | 0.333854i | ||||
\(923\) | 36.6615i | 1.20673i | ||||||||
\(924\) | 0.441592 | 0.0145273 | ||||||||
\(925\) | 2.06732 | − | 10.1933i | 0.0679729 | − | 0.335155i | ||||
\(926\) | 7.68442 | + | 13.3098i | 0.252526 | + | 0.437387i | ||||
\(927\) | −12.8132 | − | 7.39772i | −0.420842 | − | 0.242973i | ||||
\(928\) | 2.05749 | − | 1.18789i | 0.0675405 | − | 0.0389945i | ||||
\(929\) | 16.8764 | + | 29.2308i | 0.553696 | + | 0.959030i | 0.998004 | + | 0.0631559i | \(0.0201165\pi\) |
−0.444307 | + | 0.895874i | \(0.646550\pi\) | |||||||
\(930\) | 10.1324 | − | 14.0840i | 0.332256 | − | 0.461832i | ||||
\(931\) | 22.5240 | − | 11.8897i | 0.738193 | − | 0.389668i | ||||
\(932\) | − | 17.2719i | − | 0.565760i | ||||||
\(933\) | 18.6800 | − | 10.7849i | 0.611556 | − | 0.353082i | ||||
\(934\) | 19.0804 | + | 33.0483i | 0.624331 | + | 1.08137i | ||||
\(935\) | −1.04989 | + | 0.473330i | −0.0343351 | + | 0.0154795i | ||||
\(936\) | 1.91041 | + | 3.30892i | 0.0624435 | + | 0.108155i | ||||
\(937\) | 46.3764 | + | 26.7754i | 1.51505 | + | 0.874715i | 0.999844 | + | 0.0176489i | \(0.00561812\pi\) |
0.515207 | + | 0.857066i | \(0.327715\pi\) | |||||||
\(938\) | 10.0260i | 0.327360i | ||||||||
\(939\) | 29.3045 | 0.956317 | ||||||||
\(940\) | 8.44599 | − | 3.80777i | 0.275478 | − | 0.124196i | ||||
\(941\) | −20.1287 | + | 34.8639i | −0.656177 | + | 1.13653i | 0.325421 | + | 0.945569i | \(0.394494\pi\) |
−0.981597 | + | 0.190962i | \(0.938839\pi\) | |||||||
\(942\) | − | 19.4582i | − | 0.633984i | ||||||
\(943\) | − | 20.9160i | − | 0.681120i | ||||||
\(944\) | 1.25650 | − | 2.17633i | 0.0408957 | − | 0.0708334i | ||||
\(945\) | −2.39308 | − | 0.240226i | −0.0778469 | − | 0.00781454i | ||||
\(946\) | 0.455658 | − | 0.789223i | 0.0148147 | − | 0.0256599i | ||||
\(947\) | −44.0513 | + | 25.4330i | −1.43147 | + | 0.826462i | −0.997233 | − | 0.0743353i | \(-0.976316\pi\) |
−0.434240 | + | 0.900797i | \(0.642983\pi\) | |||||||
\(948\) | 7.74707 | − | 4.47277i | 0.251613 | − | 0.145269i | ||||
\(949\) | 26.5826 | 0.862907 | ||||||||
\(950\) | −15.0400 | + | 15.7734i | −0.487962 | + | 0.511755i | ||||
\(951\) | −8.20320 | −0.266007 | ||||||||
\(952\) | −1.16855 | + | 0.674662i | −0.0378729 | + | 0.0218659i | ||||
\(953\) | −7.79497 | + | 4.50043i | −0.252504 | + | 0.145783i | −0.620910 | − | 0.783882i | \(-0.713237\pi\) |
0.368406 | + | 0.929665i | \(0.379904\pi\) | |||||||
\(954\) | −2.49958 | + | 4.32940i | −0.0809269 | + | 0.140169i | ||||
\(955\) | −43.9294 | − | 4.40978i | −1.42152 | − | 0.142697i | ||||
\(956\) | −3.45372 | + | 5.98201i | −0.111701 | + | 0.193472i | ||||
\(957\) | − | 0.975391i | − | 0.0315299i | ||||||
\(958\) | − | 30.2429i | − | 0.977105i | ||||||
\(959\) | −4.75542 | + | 8.23663i | −0.153560 | + | 0.265975i | ||||
\(960\) | 2.03848 | − | 0.919023i | 0.0657916 | − | 0.0296614i | ||||
\(961\) | 29.2050 | 0.942097 | ||||||||
\(962\) | 7.94794i | 0.256252i | ||||||||
\(963\) | −4.65618 | − | 2.68825i | −0.150043 | − | 0.0866276i | ||||
\(964\) | 11.0140 | + | 19.0767i | 0.354736 | + | 0.614420i | ||||
\(965\) | 28.1428 | − | 12.6878i | 0.905948 | − | 0.408436i | ||||
\(966\) | −2.00745 | − | 3.47701i | −0.0645888 | − | 0.111871i | ||||
\(967\) | 27.4733 | − | 15.8617i | 0.883480 | − | 0.510078i | 0.0116759 | − | 0.999932i | \(-0.496283\pi\) |
0.871804 | + | 0.489854i | \(0.162950\pi\) | |||||||
\(968\) | − | 10.8314i | − | 0.348136i | ||||||
\(969\) | 0.207231 | − | 5.46426i | 0.00665723 | − | 0.175537i | ||||
\(970\) | −15.8802 | + | 22.0733i | −0.509882 | + | 0.708731i | ||||
\(971\) | −8.90105 | − | 15.4171i | −0.285648 | − | 0.494758i | 0.687118 | − | 0.726546i | \(-0.258876\pi\) |
−0.972766 | + | 0.231788i | \(0.925542\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | 9.84279 | + | 5.68274i | 0.315545 | + | 0.182180i | ||||
\(974\) | 18.8749 | + | 32.6923i | 0.604792 | + | 1.04753i | ||||
\(975\) | 18.7229 | + | 3.79720i | 0.599612 | + | 0.121608i | ||||
\(976\) | 6.75461 | 0.216210 | ||||||||
\(977\) | − | 31.9251i | − | 1.02137i | −0.859767 | − | 0.510687i | \(-0.829391\pi\) | ||
0.859767 | − | 0.510687i | \(-0.170609\pi\) | |||||||
\(978\) | 11.6342 | + | 6.71701i | 0.372021 | + | 0.214786i | ||||
\(979\) | −1.11992 | + | 1.93976i | −0.0357929 | + | 0.0619951i | ||||
\(980\) | −7.63027 | + | 10.6060i | −0.243740 | + | 0.338797i | ||||
\(981\) | 16.3210 | 0.521090 | ||||||||
\(982\) | 18.4456 | + | 10.6495i | 0.588621 | + | 0.339841i | ||||
\(983\) | 30.9561 | − | 17.8725i | 0.987346 | − | 0.570045i | 0.0828663 | − | 0.996561i | \(-0.473593\pi\) |
0.904480 | + | 0.426516i | \(0.140259\pi\) | |||||||
\(984\) | 2.80171 | − | 4.85270i | 0.0893153 | − | 0.154699i | ||||
\(985\) | 1.88055 | − | 18.7336i | 0.0599192 | − | 0.596904i | ||||
\(986\) | 1.49020 | + | 2.58110i | 0.0474576 | + | 0.0821989i | ||||
\(987\) | − | 4.45650i | − | 0.141852i | ||||||
\(988\) | 8.86789 | − | 14.0973i | 0.282125 | − | 0.448495i | ||||
\(989\) | −8.28560 | −0.263467 | ||||||||
\(990\) | 0.0916940 | − | 0.913438i | 0.00291423 | − | 0.0290310i | ||||
\(991\) | 17.1480 | + | 29.7012i | 0.544724 | + | 0.943490i | 0.998624 | + | 0.0524376i | \(0.0166991\pi\) |
−0.453900 | + | 0.891053i | \(0.649968\pi\) | |||||||
\(992\) | 6.71965 | + | 3.87959i | 0.213349 | + | 0.123177i | ||||
\(993\) | −23.4543 | + | 13.5413i | −0.744298 | + | 0.429721i | ||||
\(994\) | 5.16029 | − | 8.93788i | 0.163674 | − | 0.283492i | ||||
\(995\) | −8.70363 | + | 12.0980i | −0.275924 | + | 0.383531i | ||||
\(996\) | 9.12070 | 0.289000 | ||||||||
\(997\) | −2.35098 | − | 1.35734i | −0.0744561 | − | 0.0429873i | 0.462310 | − | 0.886719i | \(-0.347021\pi\) |
−0.536766 | + | 0.843731i | \(0.680354\pi\) | |||||||
\(998\) | 17.7466 | + | 10.2460i | 0.561759 | + | 0.324332i | ||||
\(999\) | −2.08017 | −0.0658137 |
(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 | 570.2.q.c.349.1 | yes | 20 | |
3.2 | odd | 2 | 1710.2.t.c.919.10 | 20 | |||
5.4 | even | 2 | inner | 570.2.q.c.349.9 | yes | 20 | |
15.14 | odd | 2 | 1710.2.t.c.919.2 | 20 | |||
19.11 | even | 3 | inner | 570.2.q.c.49.9 | yes | 20 | |
57.11 | odd | 6 | 1710.2.t.c.1189.2 | 20 | |||
95.49 | even | 6 | inner | 570.2.q.c.49.1 | ✓ | 20 | |
285.239 | odd | 6 | 1710.2.t.c.1189.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.c.49.1 | ✓ | 20 | 95.49 | even | 6 | inner | |
570.2.q.c.49.9 | yes | 20 | 19.11 | even | 3 | inner | |
570.2.q.c.349.1 | yes | 20 | 1.1 | even | 1 | trivial | |
570.2.q.c.349.9 | yes | 20 | 5.4 | even | 2 | inner | |
1710.2.t.c.919.2 | 20 | 15.14 | odd | 2 | |||
1710.2.t.c.919.10 | 20 | 3.2 | odd | 2 | |||
1710.2.t.c.1189.2 | 20 | 57.11 | odd | 6 | |||
1710.2.t.c.1189.10 | 20 | 285.239 | odd | 6 |