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 | 349.10 | ||
Root | \(0.320085 - 1.19457i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.349 |
Dual form | 570.2.q.c.49.10 |
$q$-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 | ||||
\(5\) | 2.21950 | − | 0.271659i | 0.992593 | − | 0.121490i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 4.03495i | 1.52507i | 0.646949 | + | 0.762533i | \(0.276045\pi\) | ||||
−0.646949 | + | 0.762533i | \(0.723955\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.78632 | − | 1.34502i | 0.564883 | − | 0.425331i | ||||
\(11\) | −1.47054 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 4.38320 | + | 2.53064i | 1.21568 | + | 0.701874i | 0.963991 | − | 0.265934i | \(-0.0856805\pi\) |
0.251690 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(14\) | 2.01747 | + | 3.49437i | 0.539192 | + | 0.933909i | ||||
\(15\) | −1.78632 | + | 1.34502i | −0.461225 | + | 0.347282i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.0812933 | − | 0.0469347i | 0.0197165 | − | 0.0113833i | −0.490109 | − | 0.871661i | \(-0.663043\pi\) |
0.509826 | + | 0.860278i | \(0.329710\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −4.00172 | + | 1.72807i | −0.918058 | + | 0.396447i | ||||
\(20\) | 0.874489 | − | 2.05798i | 0.195542 | − | 0.460178i | ||||
\(21\) | −2.01747 | − | 3.49437i | −0.440249 | − | 0.762533i | ||||
\(22\) | −1.27352 | + | 0.735269i | −0.271516 | + | 0.156760i | ||||
\(23\) | 2.22178 | + | 1.28274i | 0.463273 | + | 0.267471i | 0.713419 | − | 0.700737i | \(-0.247145\pi\) |
−0.250147 | + | 0.968208i | \(0.580479\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 4.85240 | − | 1.20590i | 0.970481 | − | 0.241179i | ||||
\(26\) | 5.06128 | 0.992599 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 3.49437 | + | 2.01747i | 0.660373 | + | 0.381267i | ||||
\(29\) | 2.10491 | − | 3.64581i | 0.390872 | − | 0.677011i | −0.601693 | − | 0.798728i | \(-0.705507\pi\) |
0.992565 | + | 0.121717i | \(0.0388401\pi\) | |||||||
\(30\) | −0.874489 | + | 2.05798i | −0.159659 | + | 0.375733i | ||||
\(31\) | 4.26558 | 0.766120 | 0.383060 | − | 0.923723i | \(-0.374870\pi\) | ||||
0.383060 | + | 0.923723i | \(0.374870\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 1.27352 | − | 0.735269i | 0.221692 | − | 0.127994i | ||||
\(34\) | 0.0469347 | − | 0.0812933i | 0.00804924 | − | 0.0139417i | ||||
\(35\) | 1.09613 | + | 8.95558i | 0.185280 | + | 1.51377i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 1.53807i | 0.252858i | 0.991976 | + | 0.126429i | \(0.0403515\pi\) | ||||
−0.991976 | + | 0.126429i | \(0.959648\pi\) | |||||||
\(38\) | −2.60156 | + | 3.49741i | −0.422028 | + | 0.567356i | ||||
\(39\) | −5.06128 | −0.810454 | ||||||||
\(40\) | −0.271659 | − | 2.21950i | −0.0429531 | − | 0.350935i | ||||
\(41\) | −3.88123 | − | 6.72248i | −0.606146 | − | 1.04987i | −0.991869 | − | 0.127261i | \(-0.959382\pi\) |
0.385724 | − | 0.922614i | \(-0.373952\pi\) | |||||||
\(42\) | −3.49437 | − | 2.01747i | −0.539192 | − | 0.311303i | ||||
\(43\) | 3.97202 | − | 2.29325i | 0.605727 | − | 0.349717i | −0.165564 | − | 0.986199i | \(-0.552944\pi\) |
0.771291 | + | 0.636482i | \(0.219611\pi\) | |||||||
\(44\) | −0.735269 | + | 1.27352i | −0.110846 | + | 0.191991i | ||||
\(45\) | 0.874489 | − | 2.05798i | 0.130361 | − | 0.306785i | ||||
\(46\) | 2.56549 | 0.378261 | ||||||||
\(47\) | −3.49530 | − | 2.01801i | −0.509842 | − | 0.294358i | 0.222927 | − | 0.974835i | \(-0.428439\pi\) |
−0.732769 | + | 0.680478i | \(0.761772\pi\) | |||||||
\(48\) | 0.866025 | + | 0.500000i | 0.125000 | + | 0.0721688i | ||||
\(49\) | −9.28080 | −1.32583 | ||||||||
\(50\) | 3.59936 | − | 3.47054i | 0.509026 | − | 0.490808i | ||||
\(51\) | −0.0469347 | + | 0.0812933i | −0.00657218 | + | 0.0113833i | ||||
\(52\) | 4.38320 | − | 2.53064i | 0.607840 | − | 0.350937i | ||||
\(53\) | 9.22964 | + | 5.32873i | 1.26779 | + | 0.731958i | 0.974569 | − | 0.224087i | \(-0.0719401\pi\) |
0.293219 | + | 0.956045i | \(0.405273\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −3.26387 | + | 0.399485i | −0.440100 | + | 0.0538666i | ||||
\(56\) | 4.03495 | 0.539192 | ||||||||
\(57\) | 2.60156 | − | 3.49741i | 0.344584 | − | 0.463244i | ||||
\(58\) | − | 4.20982i | − | 0.552777i | ||||||
\(59\) | −3.07599 | − | 5.32777i | −0.400460 | − | 0.693617i | 0.593321 | − | 0.804966i | \(-0.297816\pi\) |
−0.993781 | + | 0.111349i | \(0.964483\pi\) | |||||||
\(60\) | 0.271659 | + | 2.21950i | 0.0350710 | + | 0.286537i | ||||
\(61\) | 0.653722 | − | 1.13228i | 0.0837005 | − | 0.144974i | −0.821136 | − | 0.570732i | \(-0.806659\pi\) |
0.904837 | + | 0.425759i | \(0.139993\pi\) | |||||||
\(62\) | 3.69410 | − | 2.13279i | 0.469151 | − | 0.270864i | ||||
\(63\) | 3.49437 | + | 2.01747i | 0.440249 | + | 0.254178i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 10.4160 | + | 4.42603i | 1.29195 | + | 0.548982i | ||||
\(66\) | 0.735269 | − | 1.27352i | 0.0905054 | − | 0.156760i | ||||
\(67\) | −9.31187 | − | 5.37621i | −1.13763 | − | 0.656808i | −0.191784 | − | 0.981437i | \(-0.561427\pi\) |
−0.945842 | + | 0.324629i | \(0.894761\pi\) | |||||||
\(68\) | − | 0.0938694i | − | 0.0113833i | ||||||
\(69\) | −2.56549 | −0.308849 | ||||||||
\(70\) | 5.42707 | + | 7.20770i | 0.648659 | + | 0.861485i | ||||
\(71\) | 4.33806 | + | 7.51373i | 0.514833 | + | 0.891716i | 0.999852 | + | 0.0172126i | \(0.00547923\pi\) |
−0.485019 | + | 0.874503i | \(0.661187\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −11.0108 | + | 6.35711i | −1.28872 | + | 0.744044i | −0.978426 | − | 0.206596i | \(-0.933761\pi\) |
−0.310296 | + | 0.950640i | \(0.600428\pi\) | |||||||
\(74\) | 0.769037 | + | 1.33201i | 0.0893987 | + | 0.154843i | ||||
\(75\) | −3.59936 | + | 3.47054i | −0.415618 | + | 0.400743i | ||||
\(76\) | −0.504306 | + | 4.32963i | −0.0578479 | + | 0.496642i | ||||
\(77\) | − | 5.93355i | − | 0.676190i | ||||||
\(78\) | −4.38320 | + | 2.53064i | −0.496300 | + | 0.286539i | ||||
\(79\) | −6.48112 | − | 11.2256i | −0.729183 | − | 1.26298i | −0.957229 | − | 0.289332i | \(-0.906567\pi\) |
0.228046 | − | 0.973650i | \(-0.426766\pi\) | |||||||
\(80\) | −1.34502 | − | 1.78632i | −0.150377 | − | 0.199716i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −6.72248 | − | 3.88123i | −0.742374 | − | 0.428610i | ||||
\(83\) | − | 2.06328i | − | 0.226475i | −0.993568 | − | 0.113237i | \(-0.963878\pi\) | ||
0.993568 | − | 0.113237i | \(-0.0361221\pi\) | |||||||
\(84\) | −4.03495 | −0.440249 | ||||||||
\(85\) | 0.167681 | − | 0.126256i | 0.0181875 | − | 0.0136944i | ||||
\(86\) | 2.29325 | − | 3.97202i | 0.247287 | − | 0.428314i | ||||
\(87\) | 4.20982i | 0.451340i | ||||||||
\(88\) | 1.47054i | 0.156760i | ||||||||
\(89\) | −0.813846 | + | 1.40962i | −0.0862675 | + | 0.149420i | −0.905931 | − | 0.423426i | \(-0.860827\pi\) |
0.819663 | + | 0.572846i | \(0.194161\pi\) | |||||||
\(90\) | −0.271659 | − | 2.21950i | −0.0286354 | − | 0.233956i | ||||
\(91\) | −10.2110 | + | 17.6860i | −1.07040 | + | 1.85399i | ||||
\(92\) | 2.22178 | − | 1.28274i | 0.231636 | − | 0.133735i | ||||
\(93\) | −3.69410 | + | 2.13279i | −0.383060 | + | 0.221160i | ||||
\(94\) | −4.03603 | −0.416285 | ||||||||
\(95\) | −8.41239 | + | 4.92257i | −0.863093 | + | 0.505045i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.3479 | + | 5.97438i | −1.05067 | + | 0.606607i | −0.922838 | − | 0.385188i | \(-0.874136\pi\) |
−0.127836 | + | 0.991795i | \(0.540803\pi\) | |||||||
\(98\) | −8.03741 | + | 4.64040i | −0.811901 | + | 0.468751i | ||||
\(99\) | −0.735269 | + | 1.27352i | −0.0738974 | + | 0.127994i | ||||
\(100\) | 1.38186 | − | 4.80525i | 0.138186 | − | 0.480525i | ||||
\(101\) | −0.252103 | + | 0.436656i | −0.0250852 | + | 0.0434489i | −0.878295 | − | 0.478118i | \(-0.841319\pi\) |
0.853210 | + | 0.521567i | \(0.174652\pi\) | |||||||
\(102\) | 0.0938694i | 0.00929446i | ||||||||
\(103\) | 5.33797i | 0.525966i | 0.964800 | + | 0.262983i | \(0.0847063\pi\) | ||||
−0.964800 | + | 0.262983i | \(0.915294\pi\) | |||||||
\(104\) | 2.53064 | − | 4.38320i | 0.248150 | − | 0.429808i | ||||
\(105\) | −5.42707 | − | 7.20770i | −0.529628 | − | 0.703399i | ||||
\(106\) | 10.6575 | 1.03514 | ||||||||
\(107\) | − | 17.9275i | − | 1.73312i | −0.499076 | − | 0.866558i | \(-0.666327\pi\) | ||
0.499076 | − | 0.866558i | \(-0.333673\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −4.43631 | − | 7.68392i | −0.424922 | − | 0.735986i | 0.571492 | − | 0.820608i | \(-0.306365\pi\) |
−0.996413 | + | 0.0846222i | \(0.973032\pi\) | |||||||
\(110\) | −2.62685 | + | 1.97790i | −0.250460 | + | 0.188585i | ||||
\(111\) | −0.769037 | − | 1.33201i | −0.0729937 | − | 0.126429i | ||||
\(112\) | 3.49437 | − | 2.01747i | 0.330187 | − | 0.190633i | ||||
\(113\) | − | 15.8667i | − | 1.49261i | −0.665603 | − | 0.746306i | \(-0.731826\pi\) | ||
0.665603 | − | 0.746306i | \(-0.268174\pi\) | |||||||
\(114\) | 0.504306 | − | 4.32963i | 0.0472326 | − | 0.405507i | ||||
\(115\) | 5.27972 | + | 2.24349i | 0.492336 | + | 0.209207i | ||||
\(116\) | −2.10491 | − | 3.64581i | −0.195436 | − | 0.338505i | ||||
\(117\) | 4.38320 | − | 2.53064i | 0.405227 | − | 0.233958i | ||||
\(118\) | −5.32777 | − | 3.07599i | −0.490461 | − | 0.283168i | ||||
\(119\) | 0.189379 | + | 0.328014i | 0.0173604 | + | 0.0300690i | ||||
\(120\) | 1.34502 | + | 1.78632i | 0.122783 | + | 0.163068i | ||||
\(121\) | −8.83752 | −0.803410 | ||||||||
\(122\) | − | 1.30744i | − | 0.118370i | ||||||
\(123\) | 6.72248 | + | 3.88123i | 0.606146 | + | 0.349958i | ||||
\(124\) | 2.13279 | − | 3.69410i | 0.191530 | − | 0.331740i | ||||
\(125\) | 10.4423 | − | 3.99469i | 0.933991 | − | 0.357296i | ||||
\(126\) | 4.03495 | 0.359462 | ||||||||
\(127\) | −5.77290 | − | 3.33298i | −0.512262 | − | 0.295755i | 0.221501 | − | 0.975160i | \(-0.428904\pi\) |
−0.733763 | + | 0.679406i | \(0.762238\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −2.29325 | + | 3.97202i | −0.201909 | + | 0.349717i | ||||
\(130\) | 11.2335 | − | 1.37494i | 0.985247 | − | 0.120590i | ||||
\(131\) | −3.53784 | − | 6.12771i | −0.309102 | − | 0.535381i | 0.669064 | − | 0.743205i | \(-0.266695\pi\) |
−0.978166 | + | 0.207824i | \(0.933362\pi\) | |||||||
\(132\) | − | 1.47054i | − | 0.127994i | ||||||
\(133\) | −6.97268 | − | 16.1467i | −0.604608 | − | 1.40010i | ||||
\(134\) | −10.7524 | −0.928867 | ||||||||
\(135\) | 0.271659 | + | 2.21950i | 0.0233807 | + | 0.191025i | ||||
\(136\) | −0.0469347 | − | 0.0812933i | −0.00402462 | − | 0.00697084i | ||||
\(137\) | −16.3302 | − | 9.42826i | −1.39519 | − | 0.805511i | −0.401302 | − | 0.915946i | \(-0.631442\pi\) |
−0.993883 | + | 0.110435i | \(0.964775\pi\) | |||||||
\(138\) | −2.22178 | + | 1.28274i | −0.189130 | + | 0.109194i | ||||
\(139\) | −9.99616 | + | 17.3139i | −0.847864 | + | 1.46854i | 0.0352474 | + | 0.999379i | \(0.488778\pi\) |
−0.883111 | + | 0.469164i | \(0.844555\pi\) | |||||||
\(140\) | 8.30383 | + | 3.52852i | 0.701802 | + | 0.298214i | ||||
\(141\) | 4.03603 | 0.339895 | ||||||||
\(142\) | 7.51373 | + | 4.33806i | 0.630538 | + | 0.364042i | ||||
\(143\) | −6.44566 | − | 3.72141i | −0.539014 | − | 0.311200i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 3.68144 | − | 8.66372i | 0.305727 | − | 0.719483i | ||||
\(146\) | −6.35711 | + | 11.0108i | −0.526119 | + | 0.911264i | ||||
\(147\) | 8.03741 | − | 4.64040i | 0.662914 | − | 0.382734i | ||||
\(148\) | 1.33201 | + | 0.769037i | 0.109491 | + | 0.0632144i | ||||
\(149\) | 6.10397 | + | 10.5724i | 0.500056 | + | 0.866123i | 1.00000 | 6.51503e-5i | \(2.07380e-5\pi\) | |
−0.499944 | + | 0.866058i | \(0.666646\pi\) | |||||||
\(150\) | −1.38186 | + | 4.80525i | −0.112829 | + | 0.392347i | ||||
\(151\) | 19.9109 | 1.62032 | 0.810161 | − | 0.586207i | \(-0.199380\pi\) | ||||
0.810161 | + | 0.586207i | \(0.199380\pi\) | |||||||
\(152\) | 1.72807 | + | 4.00172i | 0.140165 | + | 0.324582i | ||||
\(153\) | − | 0.0938694i | − | 0.00758889i | ||||||
\(154\) | −2.96677 | − | 5.13860i | −0.239069 | − | 0.414080i | ||||
\(155\) | 9.46747 | − | 1.15878i | 0.760445 | − | 0.0930756i | ||||
\(156\) | −2.53064 | + | 4.38320i | −0.202613 | + | 0.350937i | ||||
\(157\) | −14.0594 | + | 8.11721i | −1.12206 | + | 0.647824i | −0.941927 | − | 0.335817i | \(-0.890988\pi\) |
−0.180137 | + | 0.983641i | \(0.557654\pi\) | |||||||
\(158\) | −11.2256 | − | 6.48112i | −0.893063 | − | 0.515610i | ||||
\(159\) | −10.6575 | −0.845192 | ||||||||
\(160\) | −2.05798 | − | 0.874489i | −0.162697 | − | 0.0691344i | ||||
\(161\) | −5.17581 | + | 8.96476i | −0.407911 | + | 0.706522i | ||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | − | 2.05750i | − | 0.161156i | −0.996748 | − | 0.0805780i | \(-0.974323\pi\) | ||
0.996748 | − | 0.0805780i | \(-0.0256766\pi\) | |||||||
\(164\) | −7.76245 | −0.606146 | ||||||||
\(165\) | 2.62685 | − | 1.97790i | 0.204500 | − | 0.153979i | ||||
\(166\) | −1.03164 | − | 1.78686i | −0.0800709 | − | 0.138687i | ||||
\(167\) | 18.8169 | + | 10.8639i | 1.45609 | + | 0.840676i | 0.998816 | − | 0.0486476i | \(-0.0154911\pi\) |
0.457278 | + | 0.889324i | \(0.348824\pi\) | |||||||
\(168\) | −3.49437 | + | 2.01747i | −0.269596 | + | 0.155651i | ||||
\(169\) | 6.30829 | + | 10.9263i | 0.485253 | + | 0.840483i | ||||
\(170\) | 0.0820878 | − | 0.193181i | 0.00629584 | − | 0.0148163i | ||||
\(171\) | −0.504306 | + | 4.32963i | −0.0385652 | + | 0.331095i | ||||
\(172\) | − | 4.58649i | − | 0.349717i | ||||||
\(173\) | 20.0963 | − | 11.6026i | 1.52790 | − | 0.882132i | 0.528447 | − | 0.848966i | \(-0.322774\pi\) |
0.999450 | − | 0.0331655i | \(-0.0105588\pi\) | |||||||
\(174\) | 2.10491 | + | 3.64581i | 0.159573 | + | 0.276388i | ||||
\(175\) | 4.86573 | + | 19.5792i | 0.367815 | + | 1.48005i | ||||
\(176\) | 0.735269 | + | 1.27352i | 0.0554230 | + | 0.0959955i | ||||
\(177\) | 5.32777 | + | 3.07599i | 0.400460 | + | 0.231206i | ||||
\(178\) | 1.62769i | 0.122001i | ||||||||
\(179\) | −6.37559 | −0.476534 | −0.238267 | − | 0.971200i | \(-0.576579\pi\) | ||||
−0.238267 | + | 0.971200i | \(0.576579\pi\) | |||||||
\(180\) | −1.34502 | − | 1.78632i | −0.100252 | − | 0.133144i | ||||
\(181\) | 4.39603 | − | 7.61415i | 0.326755 | − | 0.565955i | −0.655111 | − | 0.755532i | \(-0.727378\pi\) |
0.981866 | + | 0.189577i | \(0.0607116\pi\) | |||||||
\(182\) | 20.4220i | 1.51378i | ||||||||
\(183\) | 1.30744i | 0.0966491i | ||||||||
\(184\) | 1.28274 | − | 2.22178i | 0.0945652 | − | 0.163792i | ||||
\(185\) | 0.417831 | + | 3.41376i | 0.0307196 | + | 0.250985i | ||||
\(186\) | −2.13279 | + | 3.69410i | −0.156384 | + | 0.270864i | ||||
\(187\) | −0.119545 | + | 0.0690193i | −0.00874200 | + | 0.00504719i | ||||
\(188\) | −3.49530 | + | 2.01801i | −0.254921 | + | 0.147179i | ||||
\(189\) | −4.03495 | −0.293499 | ||||||||
\(190\) | −4.82406 | + | 8.46926i | −0.349974 | + | 0.614425i | ||||
\(191\) | 12.9659 | 0.938177 | 0.469088 | − | 0.883151i | \(-0.344583\pi\) | ||||
0.469088 | + | 0.883151i | \(0.344583\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 5.29710 | − | 3.05828i | 0.381294 | − | 0.220140i | −0.297087 | − | 0.954850i | \(-0.596015\pi\) |
0.678381 | + | 0.734710i | \(0.262682\pi\) | |||||||
\(194\) | −5.97438 | + | 10.3479i | −0.428936 | + | 0.742939i | ||||
\(195\) | −11.2335 | + | 1.37494i | −0.804451 | + | 0.0984617i | ||||
\(196\) | −4.64040 | + | 8.03741i | −0.331457 | + | 0.574101i | ||||
\(197\) | 7.34941i | 0.523624i | 0.965119 | + | 0.261812i | \(0.0843200\pi\) | ||||
−0.965119 | + | 0.261812i | \(0.915680\pi\) | |||||||
\(198\) | 1.47054i | 0.104507i | ||||||||
\(199\) | 1.71780 | − | 2.97531i | 0.121771 | − | 0.210914i | −0.798695 | − | 0.601736i | \(-0.794476\pi\) |
0.920466 | + | 0.390822i | \(0.127809\pi\) | |||||||
\(200\) | −1.20590 | − | 4.85240i | −0.0852698 | − | 0.343117i | ||||
\(201\) | 10.7524 | 0.758417 | ||||||||
\(202\) | 0.504207i | 0.0354759i | ||||||||
\(203\) | 14.7107 | + | 8.49321i | 1.03249 | + | 0.596106i | ||||
\(204\) | 0.0469347 | + | 0.0812933i | 0.00328609 | + | 0.00569167i | ||||
\(205\) | −10.4406 | − | 13.8662i | −0.729205 | − | 0.968458i | ||||
\(206\) | 2.66899 | + | 4.62282i | 0.185957 | + | 0.322087i | ||||
\(207\) | 2.22178 | − | 1.28274i | 0.154424 | − | 0.0891569i | ||||
\(208\) | − | 5.06128i | − | 0.350937i | ||||||
\(209\) | 5.88469 | − | 2.54120i | 0.407052 | − | 0.175778i | ||||
\(210\) | −8.30383 | − | 3.52852i | −0.573019 | − | 0.243491i | ||||
\(211\) | 2.01970 | + | 3.49822i | 0.139042 | + | 0.240827i | 0.927134 | − | 0.374730i | \(-0.122264\pi\) |
−0.788092 | + | 0.615557i | \(0.788931\pi\) | |||||||
\(212\) | 9.22964 | − | 5.32873i | 0.633894 | − | 0.365979i | ||||
\(213\) | −7.51373 | − | 4.33806i | −0.514833 | − | 0.297239i | ||||
\(214\) | −8.96375 | − | 15.5257i | −0.612749 | − | 1.06131i | ||||
\(215\) | 8.19293 | − | 6.16891i | 0.558754 | − | 0.420716i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 17.2114i | 1.16838i | ||||||||
\(218\) | −7.68392 | − | 4.43631i | −0.520421 | − | 0.300465i | ||||
\(219\) | 6.35711 | − | 11.0108i | 0.429574 | − | 0.744044i | ||||
\(220\) | −1.28597 | + | 3.02634i | −0.0867001 | + | 0.204035i | ||||
\(221\) | 0.475100 | 0.0319587 | ||||||||
\(222\) | −1.33201 | − | 0.769037i | −0.0893987 | − | 0.0516144i | ||||
\(223\) | 15.6334 | − | 9.02593i | 1.04689 | − | 0.604421i | 0.125111 | − | 0.992143i | \(-0.460071\pi\) |
0.921776 | + | 0.387722i | \(0.126738\pi\) | |||||||
\(224\) | 2.01747 | − | 3.49437i | 0.134798 | − | 0.233477i | ||||
\(225\) | 1.38186 | − | 4.80525i | 0.0921243 | − | 0.320350i | ||||
\(226\) | −7.93334 | − | 13.7409i | −0.527718 | − | 0.914034i | ||||
\(227\) | 26.8513i | 1.78219i | 0.453820 | + | 0.891093i | \(0.350061\pi\) | ||||
−0.453820 | + | 0.891093i | \(0.649939\pi\) | |||||||
\(228\) | −1.72807 | − | 4.00172i | −0.114444 | − | 0.265020i | ||||
\(229\) | 13.7131 | 0.906190 | 0.453095 | − | 0.891462i | \(-0.350320\pi\) | ||||
0.453095 | + | 0.891462i | \(0.350320\pi\) | |||||||
\(230\) | 5.69412 | − | 0.696938i | 0.375459 | − | 0.0459548i | ||||
\(231\) | 2.96677 | + | 5.13860i | 0.195199 | + | 0.338095i | ||||
\(232\) | −3.64581 | − | 2.10491i | −0.239359 | − | 0.138194i | ||||
\(233\) | 0.00572506 | − | 0.00330537i | 0.000375061 | − | 0.000216542i | −0.499812 | − | 0.866134i | \(-0.666598\pi\) |
0.500188 | + | 0.865917i | \(0.333264\pi\) | |||||||
\(234\) | 2.53064 | − | 4.38320i | 0.165433 | − | 0.286539i | ||||
\(235\) | −8.30605 | − | 3.52946i | −0.541827 | − | 0.230237i | ||||
\(236\) | −6.15198 | −0.400460 | ||||||||
\(237\) | 11.2256 | + | 6.48112i | 0.729183 | + | 0.420994i | ||||
\(238\) | 0.328014 | + | 0.189379i | 0.0212620 | + | 0.0122756i | ||||
\(239\) | 4.67499 | 0.302400 | 0.151200 | − | 0.988503i | \(-0.451686\pi\) | ||||
0.151200 | + | 0.988503i | \(0.451686\pi\) | |||||||
\(240\) | 2.05798 | + | 0.874489i | 0.132842 | + | 0.0564480i | ||||
\(241\) | 13.9044 | − | 24.0831i | 0.895659 | − | 1.55133i | 0.0626717 | − | 0.998034i | \(-0.480038\pi\) |
0.832987 | − | 0.553292i | \(-0.186629\pi\) | |||||||
\(242\) | −7.65351 | + | 4.41876i | −0.491986 | + | 0.284049i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −0.653722 | − | 1.13228i | −0.0418503 | − | 0.0724868i | ||||
\(245\) | −20.5988 | + | 2.52121i | −1.31601 | + | 0.161074i | ||||
\(246\) | 7.76245 | 0.494916 | ||||||||
\(247\) | −21.9135 | − | 2.55244i | −1.39432 | − | 0.162408i | ||||
\(248\) | − | 4.26558i | − | 0.270864i | ||||||
\(249\) | 1.03164 | + | 1.78686i | 0.0653776 | + | 0.113237i | ||||
\(250\) | 7.04598 | − | 8.68068i | 0.445627 | − | 0.549014i | ||||
\(251\) | 3.03259 | − | 5.25259i | 0.191415 | − | 0.331541i | −0.754304 | − | 0.656525i | \(-0.772026\pi\) |
0.945719 | + | 0.324984i | \(0.105359\pi\) | |||||||
\(252\) | 3.49437 | − | 2.01747i | 0.220124 | − | 0.127089i | ||||
\(253\) | −3.26721 | − | 1.88633i | −0.205408 | − | 0.118592i | ||||
\(254\) | −6.66597 | −0.418260 | ||||||||
\(255\) | −0.0820878 | + | 0.193181i | −0.00514054 | + | 0.0120975i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.11707 | + | 0.644941i | 0.0696809 | + | 0.0402303i | 0.534436 | − | 0.845209i | \(-0.320524\pi\) |
−0.464755 | + | 0.885439i | \(0.653858\pi\) | |||||||
\(258\) | 4.58649i | 0.285543i | ||||||||
\(259\) | −6.20604 | −0.385625 | ||||||||
\(260\) | 9.04106 | − | 6.80751i | 0.560703 | − | 0.422184i | ||||
\(261\) | −2.10491 | − | 3.64581i | −0.130291 | − | 0.225670i | ||||
\(262\) | −6.12771 | − | 3.53784i | −0.378571 | − | 0.218568i | ||||
\(263\) | −24.4863 | + | 14.1372i | −1.50989 | + | 0.871737i | −0.509959 | + | 0.860199i | \(0.670339\pi\) |
−0.999933 | + | 0.0115378i | \(0.996327\pi\) | |||||||
\(264\) | −0.735269 | − | 1.27352i | −0.0452527 | − | 0.0783800i | ||||
\(265\) | 21.9328 | + | 9.31984i | 1.34732 | + | 0.572513i | ||||
\(266\) | −14.1119 | − | 10.4971i | −0.865255 | − | 0.643621i | ||||
\(267\) | − | 1.62769i | − | 0.0996131i | ||||||
\(268\) | −9.31187 | + | 5.37621i | −0.568813 | + | 0.328404i | ||||
\(269\) | −13.8782 | − | 24.0377i | −0.846169 | − | 1.46561i | −0.884602 | − | 0.466346i | \(-0.845570\pi\) |
0.0384337 | − | 0.999261i | \(-0.487763\pi\) | |||||||
\(270\) | 1.34502 | + | 1.78632i | 0.0818551 | + | 0.108712i | ||||
\(271\) | −5.42826 | − | 9.40202i | −0.329743 | − | 0.571132i | 0.652718 | − | 0.757601i | \(-0.273629\pi\) |
−0.982461 | + | 0.186469i | \(0.940296\pi\) | |||||||
\(272\) | −0.0812933 | − | 0.0469347i | −0.00492913 | − | 0.00284584i | ||||
\(273\) | − | 20.4220i | − | 1.23600i | ||||||
\(274\) | −18.8565 | −1.13916 | ||||||||
\(275\) | −7.13565 | + | 1.77332i | −0.430296 | + | 0.106935i | ||||
\(276\) | −1.28274 | + | 2.22178i | −0.0772122 | + | 0.133735i | ||||
\(277\) | 24.5237i | 1.47349i | 0.676173 | + | 0.736743i | \(0.263637\pi\) | ||||
−0.676173 | + | 0.736743i | \(0.736363\pi\) | |||||||
\(278\) | 19.9923i | 1.19906i | ||||||||
\(279\) | 2.13279 | − | 3.69410i | 0.127687 | − | 0.221160i | ||||
\(280\) | 8.95558 | − | 1.09613i | 0.535199 | − | 0.0655063i | ||||
\(281\) | 3.29709 | − | 5.71073i | 0.196688 | − | 0.340674i | −0.750765 | − | 0.660570i | \(-0.770315\pi\) |
0.947453 | + | 0.319896i | \(0.103648\pi\) | |||||||
\(282\) | 3.49530 | − | 2.01801i | 0.208142 | − | 0.120171i | ||||
\(283\) | 20.4709 | − | 11.8189i | 1.21687 | − | 0.702559i | 0.252621 | − | 0.967565i | \(-0.418707\pi\) |
0.964247 | + | 0.265006i | \(0.0853740\pi\) | |||||||
\(284\) | 8.67611 | 0.514833 | ||||||||
\(285\) | 4.82406 | − | 8.46926i | 0.285753 | − | 0.501676i | ||||
\(286\) | −7.44281 | −0.440103 | ||||||||
\(287\) | 27.1248 | − | 15.6605i | 1.60113 | − | 0.924412i | ||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −8.49559 | + | 14.7148i | −0.499741 | + | 0.865577i | ||||
\(290\) | −1.14364 | − | 9.34372i | −0.0671567 | − | 0.548682i | ||||
\(291\) | 5.97438 | − | 10.3479i | 0.350225 | − | 0.606607i | ||||
\(292\) | 12.7142i | 0.744044i | ||||||||
\(293\) | 23.0123i | 1.34439i | 0.740374 | + | 0.672195i | \(0.234648\pi\) | ||||
−0.740374 | + | 0.672195i | \(0.765352\pi\) | |||||||
\(294\) | 4.64040 | − | 8.03741i | 0.270634 | − | 0.468751i | ||||
\(295\) | −8.27451 | − | 10.9894i | −0.481761 | − | 0.639827i | ||||
\(296\) | 1.53807 | 0.0893987 | ||||||||
\(297\) | − | 1.47054i | − | 0.0853293i | ||||||
\(298\) | 10.5724 | + | 6.10397i | 0.612442 | + | 0.353593i | ||||
\(299\) | 6.49233 | + | 11.2451i | 0.375461 | + | 0.650318i | ||||
\(300\) | 1.20590 | + | 4.85240i | 0.0696225 | + | 0.280154i | ||||
\(301\) | 9.25313 | + | 16.0269i | 0.533341 | + | 0.923774i | ||||
\(302\) | 17.2433 | − | 9.95543i | 0.992241 | − | 0.572870i | ||||
\(303\) | − | 0.504207i | − | 0.0289659i | ||||||
\(304\) | 3.49741 | + | 2.60156i | 0.200590 | + | 0.149209i | ||||
\(305\) | 1.14335 | − | 2.69069i | 0.0654678 | − | 0.154068i | ||||
\(306\) | −0.0469347 | − | 0.0812933i | −0.00268308 | − | 0.00464723i | ||||
\(307\) | 22.0807 | − | 12.7483i | 1.26021 | − | 0.727584i | 0.287097 | − | 0.957902i | \(-0.407310\pi\) |
0.973116 | + | 0.230318i | \(0.0739765\pi\) | |||||||
\(308\) | −5.13860 | − | 2.96677i | −0.292799 | − | 0.169048i | ||||
\(309\) | −2.66899 | − | 4.62282i | −0.151833 | − | 0.262983i | ||||
\(310\) | 7.61968 | − | 5.73727i | 0.432768 | − | 0.325855i | ||||
\(311\) | −30.3172 | −1.71913 | −0.859565 | − | 0.511027i | \(-0.829265\pi\) | ||||
−0.859565 | + | 0.511027i | \(0.829265\pi\) | |||||||
\(312\) | 5.06128i | 0.286539i | ||||||||
\(313\) | −6.54063 | − | 3.77623i | −0.369698 | − | 0.213445i | 0.303628 | − | 0.952791i | \(-0.401802\pi\) |
−0.673327 | + | 0.739345i | \(0.735135\pi\) | |||||||
\(314\) | −8.11721 | + | 14.0594i | −0.458081 | + | 0.793419i | ||||
\(315\) | 8.30383 | + | 3.52852i | 0.467868 | + | 0.198809i | ||||
\(316\) | −12.9622 | −0.729183 | ||||||||
\(317\) | 12.1344 | + | 7.00579i | 0.681535 | + | 0.393484i | 0.800433 | − | 0.599422i | \(-0.204603\pi\) |
−0.118898 | + | 0.992906i | \(0.537936\pi\) | |||||||
\(318\) | −9.22964 | + | 5.32873i | −0.517572 | + | 0.298821i | ||||
\(319\) | −3.09535 | + | 5.36131i | −0.173307 | + | 0.300176i | ||||
\(320\) | −2.21950 | + | 0.271659i | −0.124074 | + | 0.0151862i | ||||
\(321\) | 8.96375 | + | 15.5257i | 0.500308 | + | 0.866558i | ||||
\(322\) | 10.3516i | 0.576873i | ||||||||
\(323\) | −0.244207 | + | 0.328300i | −0.0135880 | + | 0.0182671i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 24.3207 | + | 6.99400i | 1.34907 | + | 0.387957i | ||||
\(326\) | −1.02875 | − | 1.78185i | −0.0569773 | − | 0.0986875i | ||||
\(327\) | 7.68392 | + | 4.43631i | 0.424922 | + | 0.245329i | ||||
\(328\) | −6.72248 | + | 3.88123i | −0.371187 | + | 0.214305i | ||||
\(329\) | 8.14258 | − | 14.1034i | 0.448915 | − | 0.777544i | ||||
\(330\) | 1.28597 | − | 3.02634i | 0.0707903 | − | 0.166594i | ||||
\(331\) | −2.20541 | −0.121220 | −0.0606102 | − | 0.998162i | \(-0.519305\pi\) | ||||
−0.0606102 | + | 0.998162i | \(0.519305\pi\) | |||||||
\(332\) | −1.78686 | − | 1.03164i | −0.0980665 | − | 0.0566187i | ||||
\(333\) | 1.33201 | + | 0.769037i | 0.0729937 | + | 0.0421429i | ||||
\(334\) | 21.7279 | 1.18890 | ||||||||
\(335\) | −22.1282 | − | 9.40287i | −1.20899 | − | 0.513734i | ||||
\(336\) | −2.01747 | + | 3.49437i | −0.110062 | + | 0.190633i | ||||
\(337\) | 3.35026 | − | 1.93428i | 0.182500 | − | 0.105367i | −0.405966 | − | 0.913888i | \(-0.633065\pi\) |
0.588467 | + | 0.808521i | \(0.299732\pi\) | |||||||
\(338\) | 10.9263 | + | 6.30829i | 0.594311 | + | 0.343126i | ||||
\(339\) | 7.93334 | + | 13.7409i | 0.430880 | + | 0.746306i | ||||
\(340\) | −0.0255005 | − | 0.208344i | −0.00138296 | − | 0.0112990i | ||||
\(341\) | −6.27270 | −0.339685 | ||||||||
\(342\) | 1.72807 | + | 4.00172i | 0.0934434 | + | 0.216388i | ||||
\(343\) | − | 9.20290i | − | 0.496910i | ||||||
\(344\) | −2.29325 | − | 3.97202i | −0.123644 | − | 0.214157i | ||||
\(345\) | −5.69412 | + | 0.696938i | −0.306561 | + | 0.0375219i | ||||
\(346\) | 11.6026 | − | 20.0963i | 0.623761 | − | 1.08039i | ||||
\(347\) | 10.6406 | − | 6.14337i | 0.571219 | − | 0.329793i | −0.186417 | − | 0.982471i | \(-0.559688\pi\) |
0.757636 | + | 0.652677i | \(0.226354\pi\) | |||||||
\(348\) | 3.64581 | + | 2.10491i | 0.195436 | + | 0.112835i | ||||
\(349\) | 23.1329 | 1.23828 | 0.619139 | − | 0.785282i | \(-0.287482\pi\) | ||||
0.619139 | + | 0.785282i | \(0.287482\pi\) | |||||||
\(350\) | 14.0034 | + | 14.5232i | 0.748515 | + | 0.776298i | ||||
\(351\) | −2.53064 | + | 4.38320i | −0.135076 | + | 0.233958i | ||||
\(352\) | 1.27352 | + | 0.735269i | 0.0678791 | + | 0.0391900i | ||||
\(353\) | − | 2.27216i | − | 0.120935i | −0.998170 | − | 0.0604674i | \(-0.980741\pi\) | ||
0.998170 | − | 0.0604674i | \(-0.0192591\pi\) | |||||||
\(354\) | 6.15198 | 0.326974 | ||||||||
\(355\) | 11.6695 | + | 15.4983i | 0.619353 | + | 0.822564i | ||||
\(356\) | 0.813846 | + | 1.40962i | 0.0431338 | + | 0.0747098i | ||||
\(357\) | −0.328014 | − | 0.189379i | −0.0173604 | − | 0.0100230i | ||||
\(358\) | −5.52142 | + | 3.18779i | −0.291816 | + | 0.168480i | ||||
\(359\) | −10.3404 | − | 17.9101i | −0.545746 | − | 0.945260i | −0.998560 | − | 0.0536549i | \(-0.982913\pi\) |
0.452813 | − | 0.891605i | \(-0.350420\pi\) | |||||||
\(360\) | −2.05798 | − | 0.874489i | −0.108465 | − | 0.0460896i | ||||
\(361\) | 13.0275 | − | 13.8305i | 0.685660 | − | 0.727922i | ||||
\(362\) | − | 8.79207i | − | 0.462101i | ||||||
\(363\) | 7.65351 | − | 4.41876i | 0.401705 | − | 0.231925i | ||||
\(364\) | 10.2110 | + | 17.6860i | 0.535202 | + | 0.926997i | ||||
\(365\) | −22.7117 | + | 17.1008i | −1.18878 | + | 0.895099i | ||||
\(366\) | 0.653722 | + | 1.13228i | 0.0341706 | + | 0.0591852i | ||||
\(367\) | −31.7744 | − | 18.3450i | −1.65861 | − | 0.957600i | −0.973357 | − | 0.229296i | \(-0.926358\pi\) |
−0.685255 | − | 0.728304i | \(-0.740309\pi\) | |||||||
\(368\) | − | 2.56549i | − | 0.133735i | ||||||
\(369\) | −7.76245 | −0.404097 | ||||||||
\(370\) | 2.06873 | + | 2.74749i | 0.107548 | + | 0.142835i | ||||
\(371\) | −21.5012 | + | 37.2411i | −1.11628 | + | 1.93346i | ||||
\(372\) | 4.26558i | 0.221160i | ||||||||
\(373\) | 19.5380i | 1.01164i | 0.862640 | + | 0.505819i | \(0.168810\pi\) | ||||
−0.862640 | + | 0.505819i | \(0.831190\pi\) | |||||||
\(374\) | −0.0690193 | + | 0.119545i | −0.00356890 | + | 0.00618152i | ||||
\(375\) | −7.04598 | + | 8.68068i | −0.363853 | + | 0.448268i | ||||
\(376\) | −2.01801 | + | 3.49530i | −0.104071 | + | 0.180256i | ||||
\(377\) | 18.4525 | − | 10.6536i | 0.950352 | − | 0.548686i | ||||
\(378\) | −3.49437 | + | 2.01747i | −0.179731 | + | 0.103768i | ||||
\(379\) | −3.46802 | −0.178140 | −0.0890701 | − | 0.996025i | \(-0.528390\pi\) | ||||
−0.0890701 | + | 0.996025i | \(0.528390\pi\) | |||||||
\(380\) | 0.0568730 | + | 9.74663i | 0.00291752 | + | 0.499991i | ||||
\(381\) | 6.66597 | 0.341508 | ||||||||
\(382\) | 11.2288 | − | 6.48293i | 0.574514 | − | 0.331696i | ||||
\(383\) | −21.7388 | + | 12.5509i | −1.11080 | + | 0.641322i | −0.939037 | − | 0.343816i | \(-0.888280\pi\) |
−0.171765 | + | 0.985138i | \(0.554947\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −1.61190 | − | 13.1695i | −0.0821501 | − | 0.671182i | ||||
\(386\) | 3.05828 | − | 5.29710i | 0.155662 | − | 0.269615i | ||||
\(387\) | − | 4.58649i | − | 0.233145i | ||||||
\(388\) | 11.9488i | 0.606607i | ||||||||
\(389\) | 7.02074 | − | 12.1603i | 0.355965 | − | 0.616550i | −0.631317 | − | 0.775525i | \(-0.717485\pi\) |
0.987283 | + | 0.158974i | \(0.0508188\pi\) | |||||||
\(390\) | −9.04106 | + | 6.80751i | −0.457812 | + | 0.344711i | ||||
\(391\) | 0.240821 | 0.0121788 | ||||||||
\(392\) | 9.28080i | 0.468751i | ||||||||
\(393\) | 6.12771 | + | 3.53784i | 0.309102 | + | 0.178460i | ||||
\(394\) | 3.67471 | + | 6.36478i | 0.185129 | + | 0.320653i | ||||
\(395\) | −17.4344 | − | 23.1547i | −0.877221 | − | 1.16504i | ||||
\(396\) | 0.735269 | + | 1.27352i | 0.0369487 | + | 0.0639970i | ||||
\(397\) | −26.6267 | + | 15.3729i | −1.33635 | + | 0.771544i | −0.986265 | − | 0.165172i | \(-0.947182\pi\) |
−0.350089 | + | 0.936716i | \(0.613849\pi\) | |||||||
\(398\) | − | 3.43559i | − | 0.172211i | ||||||
\(399\) | 14.1119 | + | 10.4971i | 0.706478 | + | 0.525514i | ||||
\(400\) | −3.47054 | − | 3.59936i | −0.173527 | − | 0.179968i | ||||
\(401\) | −19.3518 | − | 33.5183i | −0.966381 | − | 1.67382i | −0.705857 | − | 0.708355i | \(-0.749438\pi\) |
−0.260525 | − | 0.965467i | \(-0.583896\pi\) | |||||||
\(402\) | 9.31187 | − | 5.37621i | 0.464434 | − | 0.268141i | ||||
\(403\) | 18.6969 | + | 10.7946i | 0.931357 | + | 0.537719i | ||||
\(404\) | 0.252103 | + | 0.436656i | 0.0125426 | + | 0.0217244i | ||||
\(405\) | −1.34502 | − | 1.78632i | −0.0668344 | − | 0.0887629i | ||||
\(406\) | 16.9864 | 0.843022 | ||||||||
\(407\) | − | 2.26180i | − | 0.112113i | ||||||
\(408\) | 0.0812933 | + | 0.0469347i | 0.00402462 | + | 0.00232361i | ||||
\(409\) | −10.3920 | + | 17.9994i | −0.513850 | + | 0.890014i | 0.486021 | + | 0.873947i | \(0.338448\pi\) |
−0.999871 | + | 0.0160671i | \(0.994885\pi\) | |||||||
\(410\) | −15.9749 | − | 6.78818i | −0.788946 | − | 0.335244i | ||||
\(411\) | 18.8565 | 0.930123 | ||||||||
\(412\) | 4.62282 | + | 2.66899i | 0.227750 | + | 0.131491i | ||||
\(413\) | 21.4973 | − | 12.4115i | 1.05781 | − | 0.610728i | ||||
\(414\) | 1.28274 | − | 2.22178i | 0.0630435 | − | 0.109194i | ||||
\(415\) | −0.560510 | − | 4.57947i | −0.0275143 | − | 0.224797i | ||||
\(416\) | −2.53064 | − | 4.38320i | −0.124075 | − | 0.214904i | ||||
\(417\) | − | 19.9923i | − | 0.979029i | ||||||
\(418\) | 3.82569 | − | 5.14308i | 0.187121 | − | 0.251556i | ||||
\(419\) | 36.2672 | 1.77177 | 0.885883 | − | 0.463908i | \(-0.153553\pi\) | ||||
0.885883 | + | 0.463908i | \(0.153553\pi\) | |||||||
\(420\) | −8.95558 | + | 1.09613i | −0.436988 | + | 0.0534857i | ||||
\(421\) | 10.7212 | + | 18.5697i | 0.522519 | + | 0.905030i | 0.999657 | + | 0.0262013i | \(0.00834109\pi\) |
−0.477137 | + | 0.878829i | \(0.658326\pi\) | |||||||
\(422\) | 3.49822 | + | 2.01970i | 0.170291 | + | 0.0983174i | ||||
\(423\) | −3.49530 | + | 2.01801i | −0.169947 | + | 0.0981192i | ||||
\(424\) | 5.32873 | − | 9.22964i | 0.258786 | − | 0.448231i | ||||
\(425\) | 0.337869 | − | 0.325778i | 0.0163891 | − | 0.0158025i | ||||
\(426\) | −8.67611 | −0.420359 | ||||||||
\(427\) | 4.56869 | + | 2.63773i | 0.221094 | + | 0.127649i | ||||
\(428\) | −15.5257 | − | 8.96375i | −0.750461 | − | 0.433279i | ||||
\(429\) | 7.44281 | 0.359342 | ||||||||
\(430\) | 4.01084 | − | 9.43890i | 0.193420 | − | 0.455184i | ||||
\(431\) | 2.91216 | − | 5.04400i | 0.140274 | − | 0.242961i | −0.787326 | − | 0.616537i | \(-0.788535\pi\) |
0.927600 | + | 0.373576i | \(0.121868\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 27.3690 | + | 15.8015i | 1.31527 | + | 0.759371i | 0.982963 | − | 0.183801i | \(-0.0588403\pi\) |
0.332305 | + | 0.943172i | \(0.392174\pi\) | |||||||
\(434\) | 8.60569 | + | 14.9055i | 0.413086 | + | 0.715486i | ||||
\(435\) | 1.14364 | + | 9.34372i | 0.0548332 | + | 0.447997i | ||||
\(436\) | −8.87262 | −0.424922 | ||||||||
\(437\) | −11.1076 | − | 1.29379i | −0.531349 | − | 0.0618904i | ||||
\(438\) | − | 12.7142i | − | 0.607509i | ||||||
\(439\) | −0.932951 | − | 1.61592i | −0.0445273 | − | 0.0771236i | 0.842903 | − | 0.538066i | \(-0.180845\pi\) |
−0.887430 | + | 0.460942i | \(0.847512\pi\) | |||||||
\(440\) | 0.399485 | + | 3.26387i | 0.0190447 | + | 0.155599i | ||||
\(441\) | −4.64040 | + | 8.03741i | −0.220971 | + | 0.382734i | ||||
\(442\) | 0.411448 | − | 0.237550i | 0.0195706 | − | 0.0112991i | ||||
\(443\) | −13.6368 | − | 7.87318i | −0.647902 | − | 0.374066i | 0.139750 | − | 0.990187i | \(-0.455370\pi\) |
−0.787652 | + | 0.616121i | \(0.788703\pi\) | |||||||
\(444\) | −1.53807 | −0.0729937 | ||||||||
\(445\) | −1.42340 | + | 3.34975i | −0.0674755 | + | 0.158794i | ||||
\(446\) | 9.02593 | − | 15.6334i | 0.427390 | − | 0.740262i | ||||
\(447\) | −10.5724 | − | 6.10397i | −0.500056 | − | 0.288708i | ||||
\(448\) | − | 4.03495i | − | 0.190633i | ||||||
\(449\) | −29.7436 | −1.40369 | −0.701845 | − | 0.712330i | \(-0.747640\pi\) | ||||
−0.701845 | + | 0.712330i | \(0.747640\pi\) | |||||||
\(450\) | −1.20590 | − | 4.85240i | −0.0568465 | − | 0.228744i | ||||
\(451\) | 5.70749 | + | 9.88567i | 0.268755 | + | 0.465498i | ||||
\(452\) | −13.7409 | − | 7.93334i | −0.646320 | − | 0.373153i | ||||
\(453\) | −17.2433 | + | 9.95543i | −0.810161 | + | 0.467747i | ||||
\(454\) | 13.4257 | + | 23.2539i | 0.630098 | + | 1.09136i | ||||
\(455\) | −17.8588 | + | 42.0280i | −0.837234 | + | 1.97030i | ||||
\(456\) | −3.49741 | − | 2.60156i | −0.163781 | − | 0.121829i | ||||
\(457\) | − | 12.7891i | − | 0.598250i | −0.954214 | − | 0.299125i | \(-0.903305\pi\) | ||
0.954214 | − | 0.299125i | \(-0.0966948\pi\) | |||||||
\(458\) | 11.8759 | − | 6.85657i | 0.554926 | − | 0.320387i | ||||
\(459\) | 0.0469347 | + | 0.0812933i | 0.00219073 | + | 0.00379445i | ||||
\(460\) | 4.58278 | − | 3.45062i | 0.213673 | − | 0.160886i | ||||
\(461\) | 5.96303 | + | 10.3283i | 0.277726 | + | 0.481035i | 0.970819 | − | 0.239813i | \(-0.0770860\pi\) |
−0.693093 | + | 0.720848i | \(0.743753\pi\) | |||||||
\(462\) | 5.13860 | + | 2.96677i | 0.239069 | + | 0.138027i | ||||
\(463\) | − | 19.3208i | − | 0.897913i | −0.893554 | − | 0.448956i | \(-0.851796\pi\) | ||
0.893554 | − | 0.448956i | \(-0.148204\pi\) | |||||||
\(464\) | −4.20982 | −0.195436 | ||||||||
\(465\) | −7.61968 | + | 5.73727i | −0.353354 | + | 0.266059i | ||||
\(466\) | 0.00330537 | − | 0.00572506i | 0.000153118 | − | 0.000265208i | ||||
\(467\) | 26.7009i | 1.23557i | 0.786347 | + | 0.617785i | \(0.211970\pi\) | ||||
−0.786347 | + | 0.617785i | \(0.788030\pi\) | |||||||
\(468\) | − | 5.06128i | − | 0.233958i | ||||||
\(469\) | 21.6927 | − | 37.5729i | 1.00168 | − | 1.73496i | ||||
\(470\) | −8.95798 | + | 1.09642i | −0.413201 | + | 0.0505742i | ||||
\(471\) | 8.11721 | − | 14.0594i | 0.374021 | − | 0.647824i | ||||
\(472\) | −5.32777 | + | 3.07599i | −0.245231 | + | 0.141584i | ||||
\(473\) | −5.84101 | + | 3.37231i | −0.268570 | + | 0.155059i | ||||
\(474\) | 12.9622 | 0.595375 | ||||||||
\(475\) | −17.3341 | + | 13.2110i | −0.795342 | + | 0.606161i | ||||
\(476\) | 0.378758 | 0.0173604 | ||||||||
\(477\) | 9.22964 | − | 5.32873i | 0.422596 | − | 0.243986i | ||||
\(478\) | 4.04866 | − | 2.33750i | 0.185182 | − | 0.106915i | ||||
\(479\) | −6.79124 | + | 11.7628i | −0.310299 | + | 0.537454i | −0.978427 | − | 0.206592i | \(-0.933763\pi\) |
0.668128 | + | 0.744047i | \(0.267096\pi\) | |||||||
\(480\) | 2.21950 | − | 0.271659i | 0.101306 | − | 0.0123995i | ||||
\(481\) | −3.89231 | + | 6.74168i | −0.177474 | + | 0.307394i | ||||
\(482\) | − | 27.8087i | − | 1.26665i | ||||||
\(483\) | − | 10.3516i | − | 0.471015i | ||||||
\(484\) | −4.41876 | + | 7.65351i | −0.200853 | + | 0.347887i | ||||
\(485\) | −21.3443 | + | 16.0713i | −0.969195 | + | 0.729760i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 8.03640i | 0.364164i | 0.983283 | + | 0.182082i | \(0.0582837\pi\) | ||||
−0.983283 | + | 0.182082i | \(0.941716\pi\) | |||||||
\(488\) | −1.13228 | − | 0.653722i | −0.0512559 | − | 0.0295926i | ||||
\(489\) | 1.02875 | + | 1.78185i | 0.0465217 | + | 0.0805780i | ||||
\(490\) | −16.5785 | + | 12.4828i | −0.748938 | + | 0.563916i | ||||
\(491\) | 10.3390 | + | 17.9077i | 0.466593 | + | 0.808163i | 0.999272 | − | 0.0381546i | \(-0.0121479\pi\) |
−0.532679 | + | 0.846317i | \(0.678815\pi\) | |||||||
\(492\) | 6.72248 | − | 3.88123i | 0.303073 | − | 0.174979i | ||||
\(493\) | − | 0.395174i | − | 0.0177977i | ||||||
\(494\) | −20.2538 | + | 8.74626i | −0.911263 | + | 0.393513i | ||||
\(495\) | −1.28597 | + | 3.02634i | −0.0578000 | + | 0.136024i | ||||
\(496\) | −2.13279 | − | 3.69410i | −0.0957650 | − | 0.165870i | ||||
\(497\) | −30.3175 | + | 17.5038i | −1.35993 | + | 0.785154i | ||||
\(498\) | 1.78686 | + | 1.03164i | 0.0800709 | + | 0.0462290i | ||||
\(499\) | −0.551160 | − | 0.954638i | −0.0246733 | − | 0.0427355i | 0.853425 | − | 0.521216i | \(-0.174521\pi\) |
−0.878098 | + | 0.478480i | \(0.841188\pi\) | |||||||
\(500\) | 1.76166 | − | 11.0407i | 0.0787840 | − | 0.493754i | ||||
\(501\) | −21.7279 | −0.970729 | ||||||||
\(502\) | − | 6.06517i | − | 0.270702i | ||||||
\(503\) | 21.0518 | + | 12.1543i | 0.938653 | + | 0.541932i | 0.889538 | − | 0.456861i | \(-0.151026\pi\) |
0.0491154 | + | 0.998793i | \(0.484360\pi\) | |||||||
\(504\) | 2.01747 | − | 3.49437i | 0.0898654 | − | 0.155651i | ||||
\(505\) | −0.440923 | + | 1.03765i | −0.0196208 | + | 0.0461746i | ||||
\(506\) | −3.77265 | −0.167715 | ||||||||
\(507\) | −10.9263 | − | 6.30829i | −0.485253 | − | 0.280161i | ||||
\(508\) | −5.77290 | + | 3.33298i | −0.256131 | + | 0.147877i | ||||
\(509\) | −4.96728 | + | 8.60358i | −0.220171 | + | 0.381347i | −0.954860 | − | 0.297057i | \(-0.903995\pi\) |
0.734689 | + | 0.678404i | \(0.237328\pi\) | |||||||
\(510\) | 0.0255005 | + | 0.208344i | 0.00112918 | + | 0.00922561i | ||||
\(511\) | −25.6506 | − | 44.4282i | −1.13472 | − | 1.96539i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.72807 | − | 4.00172i | −0.0762962 | − | 0.176680i | ||||
\(514\) | 1.28988 | 0.0568942 | ||||||||
\(515\) | 1.45011 | + | 11.8477i | 0.0638994 | + | 0.522070i | ||||
\(516\) | 2.29325 | + | 3.97202i | 0.100955 | + | 0.174858i | ||||
\(517\) | 5.13998 | + | 2.96757i | 0.226056 | + | 0.130513i | ||||
\(518\) | −5.37459 | + | 3.10302i | −0.236146 | + | 0.136339i | ||||
\(519\) | −11.6026 | + | 20.0963i | −0.509299 | + | 0.882132i | ||||
\(520\) | 4.42603 | − | 10.4160i | 0.194094 | − | 0.456772i | ||||
\(521\) | −20.9057 | −0.915895 | −0.457947 | − | 0.888979i | \(-0.651415\pi\) | ||||
−0.457947 | + | 0.888979i | \(0.651415\pi\) | |||||||
\(522\) | −3.64581 | − | 2.10491i | −0.159573 | − | 0.0921295i | ||||
\(523\) | 27.3676 | + | 15.8007i | 1.19670 | + | 0.690916i | 0.959818 | − | 0.280622i | \(-0.0905408\pi\) |
0.236883 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(524\) | −7.07568 | −0.309102 | ||||||||
\(525\) | −14.0034 | − | 14.5232i | −0.611160 | − | 0.633845i | ||||
\(526\) | −14.1372 | + | 24.4863i | −0.616411 | + | 1.06766i | ||||
\(527\) | 0.346763 | − | 0.200204i | 0.0151052 | − | 0.00872101i | ||||
\(528\) | −1.27352 | − | 0.735269i | −0.0554230 | − | 0.0319985i | ||||
\(529\) | −8.20913 | − | 14.2186i | −0.356919 | − | 0.618202i | ||||
\(530\) | 23.6543 | − | 2.89520i | 1.02748 | − | 0.125759i | ||||
\(531\) | −6.15198 | −0.266973 | ||||||||
\(532\) | −17.4698 | − | 2.03485i | −0.757413 | − | 0.0882218i | ||||
\(533\) | − | 39.2880i | − | 1.70175i | ||||||
\(534\) | −0.813846 | − | 1.40962i | −0.0352186 | − | 0.0610003i | ||||
\(535\) | −4.87017 | − | 39.7902i | −0.210556 | − | 1.72028i | ||||
\(536\) | −5.37621 | + | 9.31187i | −0.232217 | + | 0.402211i | ||||
\(537\) | 5.52142 | − | 3.18779i | 0.238267 | − | 0.137563i | ||||
\(538\) | −24.0377 | − | 13.8782i | −1.03634 | − | 0.598332i | ||||
\(539\) | 13.6478 | 0.587851 | ||||||||
\(540\) | 2.05798 | + | 0.874489i | 0.0885612 | + | 0.0376320i | ||||
\(541\) | −2.50615 | + | 4.34078i | −0.107748 | + | 0.186625i | −0.914858 | − | 0.403777i | \(-0.867697\pi\) |
0.807110 | + | 0.590402i | \(0.201031\pi\) | |||||||
\(542\) | −9.40202 | − | 5.42826i | −0.403851 | − | 0.233164i | ||||
\(543\) | 8.79207i | 0.377304i | ||||||||
\(544\) | −0.0938694 | −0.00402462 | ||||||||
\(545\) | −11.9338 | − | 15.8493i | −0.511189 | − | 0.678911i | ||||
\(546\) | −10.2110 | − | 17.6860i | −0.436991 | − | 0.756890i | ||||
\(547\) | −30.7554 | − | 17.7566i | −1.31500 | − | 0.759218i | −0.332084 | − | 0.943250i | \(-0.607752\pi\) |
−0.982920 | + | 0.184032i | \(0.941085\pi\) | |||||||
\(548\) | −16.3302 | + | 9.42826i | −0.697593 | + | 0.402755i | ||||
\(549\) | −0.653722 | − | 1.13228i | −0.0279002 | − | 0.0483245i | ||||
\(550\) | −5.29299 | + | 5.10356i | −0.225694 | + | 0.217617i | ||||
\(551\) | −2.12304 | + | 18.2270i | −0.0904445 | + | 0.776495i | ||||
\(552\) | 2.56549i | 0.109194i | ||||||||
\(553\) | 45.2948 | − | 26.1510i | 1.92613 | − | 1.11205i | ||||
\(554\) | 12.2618 | + | 21.2381i | 0.520956 | + | 0.902322i | ||||
\(555\) | −2.06873 | − | 2.74749i | −0.0878128 | − | 0.116624i | ||||
\(556\) | 9.99616 | + | 17.3139i | 0.423932 | + | 0.734271i | ||||
\(557\) | −8.45640 | − | 4.88231i | −0.358309 | − | 0.206870i | 0.310030 | − | 0.950727i | \(-0.399661\pi\) |
−0.668339 | + | 0.743857i | \(0.732994\pi\) | |||||||
\(558\) | − | 4.26558i | − | 0.180576i | ||||||
\(559\) | 23.2135 | 0.981828 | ||||||||
\(560\) | 7.20770 | − | 5.42707i | 0.304581 | − | 0.229336i | ||||
\(561\) | 0.0690193 | − | 0.119545i | 0.00291400 | − | 0.00504719i | ||||
\(562\) | − | 6.59418i | − | 0.278159i | ||||||
\(563\) | 11.5237i | 0.485665i | 0.970068 | + | 0.242833i | \(0.0780766\pi\) | ||||
−0.970068 | + | 0.242833i | \(0.921923\pi\) | |||||||
\(564\) | 2.01801 | − | 3.49530i | 0.0849737 | − | 0.147179i | ||||
\(565\) | −4.31033 | − | 35.2162i | −0.181337 | − | 1.48156i | ||||
\(566\) | 11.8189 | − | 20.4709i | 0.496784 | − | 0.860456i | ||||
\(567\) | 3.49437 | − | 2.01747i | 0.146750 | − | 0.0847259i | ||||
\(568\) | 7.51373 | − | 4.33806i | 0.315269 | − | 0.182021i | ||||
\(569\) | −1.93925 | −0.0812978 | −0.0406489 | − | 0.999173i | \(-0.512943\pi\) | ||||
−0.0406489 | + | 0.999173i | \(0.512943\pi\) | |||||||
\(570\) | −0.0568730 | − | 9.74663i | −0.00238215 | − | 0.408241i | ||||
\(571\) | −38.0052 | −1.59047 | −0.795235 | − | 0.606301i | \(-0.792652\pi\) | ||||
−0.795235 | + | 0.606301i | \(0.792652\pi\) | |||||||
\(572\) | −6.44566 | + | 3.72141i | −0.269507 | + | 0.155600i | ||||
\(573\) | −11.2288 | + | 6.48293i | −0.469088 | + | 0.270828i | ||||
\(574\) | 15.6605 | − | 27.1248i | 0.653658 | − | 1.13217i | ||||
\(575\) | 12.3278 | + | 3.54516i | 0.514106 | + | 0.147843i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 28.3094i | 1.17854i | 0.807938 | + | 0.589268i | \(0.200584\pi\) | ||||
−0.807938 | + | 0.589268i | \(0.799416\pi\) | |||||||
\(578\) | 16.9912i | 0.706740i | ||||||||
\(579\) | −3.05828 | + | 5.29710i | −0.127098 | + | 0.220140i | ||||
\(580\) | −5.66228 | − | 7.52008i | −0.235113 | − | 0.312254i | ||||
\(581\) | 8.32524 | 0.345389 | ||||||||
\(582\) | − | 11.9488i | − | 0.495292i | ||||||
\(583\) | −13.5725 | − | 7.83611i | −0.562117 | − | 0.324539i | ||||
\(584\) | 6.35711 | + | 11.0108i | 0.263059 | + | 0.455632i | ||||
\(585\) | 9.04106 | − | 6.80751i | 0.373802 | − | 0.281456i | ||||
\(586\) | 11.5061 | + | 19.9292i | 0.475314 | + | 0.823267i | ||||
\(587\) | 9.39980 | − | 5.42698i | 0.387971 | − | 0.223995i | −0.293309 | − | 0.956018i | \(-0.594757\pi\) |
0.681281 | + | 0.732022i | \(0.261423\pi\) | |||||||
\(588\) | − | 9.28080i | − | 0.382734i | ||||||
\(589\) | −17.0696 | + | 7.37122i | −0.703342 | + | 0.303726i | ||||
\(590\) | −12.6606 | − | 5.37984i | −0.521230 | − | 0.221484i | ||||
\(591\) | −3.67471 | − | 6.36478i | −0.151157 | − | 0.261812i | ||||
\(592\) | 1.33201 | − | 0.769037i | 0.0547453 | − | 0.0316072i | ||||
\(593\) | −24.0190 | − | 13.8674i | −0.986341 | − | 0.569464i | −0.0821625 | − | 0.996619i | \(-0.526183\pi\) |
−0.904179 | + | 0.427155i | \(0.859516\pi\) | |||||||
\(594\) | −0.735269 | − | 1.27352i | −0.0301685 | − | 0.0522533i | ||||
\(595\) | 0.509436 | + | 0.676583i | 0.0208848 | + | 0.0277372i | ||||
\(596\) | 12.2079 | 0.500056 | ||||||||
\(597\) | 3.43559i | 0.140609i | ||||||||
\(598\) | 11.2451 | + | 6.49233i | 0.459844 | + | 0.265491i | ||||
\(599\) | 15.6071 | − | 27.0323i | 0.637690 | − | 1.10451i | −0.348248 | − | 0.937402i | \(-0.613223\pi\) |
0.985938 | − | 0.167109i | \(-0.0534433\pi\) | |||||||
\(600\) | 3.47054 | + | 3.59936i | 0.141684 | + | 0.146943i | ||||
\(601\) | 42.3271 | 1.72656 | 0.863280 | − | 0.504726i | \(-0.168406\pi\) | ||||
0.863280 | + | 0.504726i | \(0.168406\pi\) | |||||||
\(602\) | 16.0269 | + | 9.25313i | 0.653207 | + | 0.377129i | ||||
\(603\) | −9.31187 | + | 5.37621i | −0.379209 | + | 0.218936i | ||||
\(604\) | 9.95543 | − | 17.2433i | 0.405081 | − | 0.701620i | ||||
\(605\) | −19.6149 | + | 2.40079i | −0.797459 | + | 0.0976060i | ||||
\(606\) | −0.252103 | − | 0.436656i | −0.0102410 | − | 0.0177379i | ||||
\(607\) | 12.9882i | 0.527176i | 0.964635 | + | 0.263588i | \(0.0849059\pi\) | ||||
−0.964635 | + | 0.263588i | \(0.915094\pi\) | |||||||
\(608\) | 4.32963 | + | 0.504306i | 0.175590 | + | 0.0204523i | ||||
\(609\) | −16.9864 | −0.688324 | ||||||||
\(610\) | −0.355179 | − | 2.90188i | −0.0143808 | − | 0.117494i | ||||
\(611\) | −10.2137 | − | 17.6907i | −0.413204 | − | 0.715690i | ||||
\(612\) | −0.0812933 | − | 0.0469347i | −0.00328609 | − | 0.00189722i | ||||
\(613\) | −23.2303 | + | 13.4120i | −0.938264 | + | 0.541707i | −0.889416 | − | 0.457099i | \(-0.848888\pi\) |
−0.0488484 | + | 0.998806i | \(0.515555\pi\) | |||||||
\(614\) | 12.7483 | − | 22.0807i | 0.514480 | − | 0.891105i | ||||
\(615\) | 15.9749 | + | 6.78818i | 0.644172 | + | 0.273726i | ||||
\(616\) | −5.93355 | −0.239069 | ||||||||
\(617\) | 11.9663 | + | 6.90877i | 0.481747 | + | 0.278136i | 0.721144 | − | 0.692785i | \(-0.243617\pi\) |
−0.239398 | + | 0.970922i | \(0.576950\pi\) | |||||||
\(618\) | −4.62282 | − | 2.66899i | −0.185957 | − | 0.107362i | ||||
\(619\) | 36.2091 | 1.45537 | 0.727684 | − | 0.685912i | \(-0.240597\pi\) | ||||
0.727684 | + | 0.685912i | \(0.240597\pi\) | |||||||
\(620\) | 3.73020 | − | 8.77846i | 0.149808 | − | 0.352551i | ||||
\(621\) | −1.28274 | + | 2.22178i | −0.0514748 | + | 0.0891569i | ||||
\(622\) | −26.2555 | + | 15.1586i | −1.05275 | + | 0.607804i | ||||
\(623\) | −5.68775 | − | 3.28383i | −0.227875 | − | 0.131564i | ||||
\(624\) | 2.53064 | + | 4.38320i | 0.101307 | + | 0.175468i | ||||
\(625\) | 22.0916 | − | 11.7030i | 0.883665 | − | 0.468120i | ||||
\(626\) | −7.55247 | −0.301857 | ||||||||
\(627\) | −3.82569 | + | 5.14308i | −0.152783 | + | 0.205395i | ||||
\(628\) | 16.2344i | 0.647824i | ||||||||
\(629\) | 0.0721890 | + | 0.125035i | 0.00287837 | + | 0.00498547i | ||||
\(630\) | 8.95558 | − | 1.09613i | 0.356799 | − | 0.0436709i | ||||
\(631\) | −1.00438 | + | 1.73963i | −0.0399836 | + | 0.0692536i | −0.885325 | − | 0.464973i | \(-0.846064\pi\) |
0.845341 | + | 0.534227i | \(0.179397\pi\) | |||||||
\(632\) | −11.2256 | + | 6.48112i | −0.446532 | + | 0.257805i | ||||
\(633\) | −3.49822 | − | 2.01970i | −0.139042 | − | 0.0802758i | ||||
\(634\) | 14.0116 | 0.556471 | ||||||||
\(635\) | −13.7184 | − | 5.82932i | −0.544399 | − | 0.231329i | ||||
\(636\) | −5.32873 | + | 9.22964i | −0.211298 | + | 0.365979i | ||||
\(637\) | −40.6796 | − | 23.4864i | −1.61178 | − | 0.930564i | ||||
\(638\) | 6.19071i | 0.245093i | ||||||||
\(639\) | 8.67611 | 0.343222 | ||||||||
\(640\) | −1.78632 | + | 1.34502i | −0.0706104 | + | 0.0531664i | ||||
\(641\) | −8.04795 | − | 13.9395i | −0.317875 | − | 0.550575i | 0.662170 | − | 0.749354i | \(-0.269636\pi\) |
−0.980044 | + | 0.198779i | \(0.936302\pi\) | |||||||
\(642\) | 15.5257 | + | 8.96375i | 0.612749 | + | 0.353771i | ||||
\(643\) | −34.6016 | + | 19.9773i | −1.36455 | + | 0.787826i | −0.990226 | − | 0.139470i | \(-0.955460\pi\) |
−0.374328 | + | 0.927296i | \(0.622127\pi\) | |||||||
\(644\) | 5.17581 | + | 8.96476i | 0.203955 | + | 0.353261i | ||||
\(645\) | −4.01084 | + | 9.43890i | −0.157927 | + | 0.371656i | ||||
\(646\) | −0.0473389 | + | 0.406420i | −0.00186252 | + | 0.0159904i | ||||
\(647\) | − | 32.2985i | − | 1.26979i | −0.772600 | − | 0.634893i | \(-0.781044\pi\) | ||
0.772600 | − | 0.634893i | \(-0.218956\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 4.52336 | + | 7.83470i | 0.177558 | + | 0.307539i | ||||
\(650\) | 24.5594 | − | 6.10339i | 0.963298 | − | 0.239394i | ||||
\(651\) | −8.60569 | − | 14.9055i | −0.337283 | − | 0.584192i | ||||
\(652\) | −1.78185 | − | 1.02875i | −0.0697826 | − | 0.0402890i | ||||
\(653\) | − | 25.3382i | − | 0.991559i | −0.868448 | − | 0.495780i | \(-0.834882\pi\) | ||
0.868448 | − | 0.495780i | \(-0.165118\pi\) | |||||||
\(654\) | 8.87262 | 0.346947 | ||||||||
\(655\) | −9.51690 | − | 12.6394i | −0.371856 | − | 0.493862i | ||||
\(656\) | −3.88123 | + | 6.72248i | −0.151536 | + | 0.262469i | ||||
\(657\) | 12.7142i | 0.496029i | ||||||||
\(658\) | − | 16.2852i | − | 0.634862i | ||||||
\(659\) | 2.44914 | − | 4.24204i | 0.0954051 | − | 0.165247i | −0.814372 | − | 0.580343i | \(-0.802919\pi\) |
0.909778 | + | 0.415096i | \(0.136252\pi\) | |||||||
\(660\) | −0.399485 | − | 3.26387i | −0.0155499 | − | 0.127046i | ||||
\(661\) | −24.1271 | + | 41.7893i | −0.938435 | + | 1.62542i | −0.170044 | + | 0.985437i | \(0.554391\pi\) |
−0.768391 | + | 0.639980i | \(0.778942\pi\) | |||||||
\(662\) | −1.90994 | + | 1.10271i | −0.0742320 | + | 0.0428579i | ||||
\(663\) | −0.411448 | + | 0.237550i | −0.0159793 | + | 0.00922567i | ||||
\(664\) | −2.06328 | −0.0800709 | ||||||||
\(665\) | −19.8623 | − | 33.9436i | −0.770227 | − | 1.31627i | ||||
\(666\) | 1.53807 | 0.0595991 | ||||||||
\(667\) | 9.35330 | − | 5.40013i | 0.362161 | − | 0.209094i | ||||
\(668\) | 18.8169 | − | 10.8639i | 0.728047 | − | 0.420338i | ||||
\(669\) | −9.02593 | + | 15.6334i | −0.348963 | + | 0.604421i | ||||
\(670\) | −23.8650 | + | 2.92099i | −0.921987 | + | 0.112848i | ||||
\(671\) | −0.961324 | + | 1.66506i | −0.0371115 | + | 0.0642790i | ||||
\(672\) | 4.03495i | 0.155651i | ||||||||
\(673\) | 11.3374i | 0.437025i | 0.975834 | + | 0.218512i | \(0.0701204\pi\) | ||||
−0.975834 | + | 0.218512i | \(0.929880\pi\) | |||||||
\(674\) | 1.93428 | − | 3.35026i | 0.0745055 | − | 0.129047i | ||||
\(675\) | 1.20590 | + | 4.85240i | 0.0464150 | + | 0.186769i | ||||
\(676\) | 12.6166 | 0.485253 | ||||||||
\(677\) | 30.8182i | 1.18444i | 0.805776 | + | 0.592220i | \(0.201748\pi\) | ||||
−0.805776 | + | 0.592220i | \(0.798252\pi\) | |||||||
\(678\) | 13.7409 | + | 7.93334i | 0.527718 | + | 0.304678i | ||||
\(679\) | −24.1063 | − | 41.7534i | −0.925116 | − | 1.60235i | ||||
\(680\) | −0.126256 | − | 0.167681i | −0.00484169 | − | 0.00643026i | ||||
\(681\) | −13.4257 | − | 23.2539i | −0.514473 | − | 0.891093i | ||||
\(682\) | −5.43231 | + | 3.13635i | −0.208014 | + | 0.120097i | ||||
\(683\) | − | 10.5683i | − | 0.404386i | −0.979346 | − | 0.202193i | \(-0.935193\pi\) | ||
0.979346 | − | 0.202193i | \(-0.0648069\pi\) | |||||||
\(684\) | 3.49741 | + | 2.60156i | 0.133727 | + | 0.0994730i | ||||
\(685\) | −38.8063 | − | 16.4898i | −1.48271 | − | 0.630043i | ||||
\(686\) | −4.60145 | − | 7.96995i | −0.175684 | − | 0.304294i | ||||
\(687\) | −11.8759 | + | 6.85657i | −0.453095 | + | 0.261595i | ||||
\(688\) | −3.97202 | − | 2.29325i | −0.151432 | − | 0.0874292i | ||||
\(689\) | 26.9702 | + | 46.7138i | 1.02748 | + | 1.77965i | ||||
\(690\) | −4.58278 | + | 3.45062i | −0.174463 | + | 0.131363i | ||||
\(691\) | −0.570970 | −0.0217207 | −0.0108604 | − | 0.999941i | \(-0.503457\pi\) | ||||
−0.0108604 | + | 0.999941i | \(0.503457\pi\) | |||||||
\(692\) | − | 23.2053i | − | 0.882132i | ||||||
\(693\) | −5.13860 | − | 2.96677i | −0.195199 | − | 0.112698i | ||||
\(694\) | 6.14337 | − | 10.6406i | 0.233199 | − | 0.403913i | ||||
\(695\) | −17.4831 | + | 41.1438i | −0.663171 | + | 1.56067i | ||||
\(696\) | 4.20982 | 0.159573 | ||||||||
\(697\) | −0.631035 | − | 0.364328i | −0.0239022 | − | 0.0137999i | ||||
\(698\) | 20.0337 | − | 11.5665i | 0.758287 | − | 0.437797i | ||||
\(699\) | −0.00330537 | + | 0.00572506i | −0.000125020 | + | 0.000216542i | ||||
\(700\) | 19.3889 | + | 5.57575i | 0.732833 | + | 0.210743i | ||||
\(701\) | 3.36247 | + | 5.82398i | 0.126999 | + | 0.219969i | 0.922513 | − | 0.385967i | \(-0.126132\pi\) |
−0.795514 | + | 0.605936i | \(0.792799\pi\) | |||||||
\(702\) | 5.06128i | 0.191026i | ||||||||
\(703\) | −2.65790 | − | 6.15494i | −0.100245 | − | 0.232138i | ||||
\(704\) | 1.47054 | 0.0554230 | ||||||||
\(705\) | 8.95798 | − | 1.09642i | 0.337377 | − | 0.0412937i | ||||
\(706\) | −1.13608 | − | 1.96775i | −0.0427569 | − | 0.0740571i | ||||
\(707\) | −1.76188 | − | 1.01722i | −0.0662625 | − | 0.0382566i | ||||
\(708\) | 5.32777 | − | 3.07599i | 0.200230 | − | 0.115603i | ||||
\(709\) | −15.4517 | + | 26.7632i | −0.580302 | + | 1.00511i | 0.415141 | + | 0.909757i | \(0.363732\pi\) |
−0.995443 | + | 0.0953554i | \(0.969601\pi\) | |||||||
\(710\) | 17.8552 | + | 7.58716i | 0.670095 | + | 0.284741i | ||||
\(711\) | −12.9622 | −0.486122 | ||||||||
\(712\) | 1.40962 | + | 0.813846i | 0.0528278 | + | 0.0305002i | ||||
\(713\) | 9.47717 | + | 5.47164i | 0.354923 | + | 0.204915i | ||||
\(714\) | −0.378758 | −0.0141747 | ||||||||
\(715\) | −15.3171 | − | 6.50866i | −0.572828 | − | 0.243410i | ||||
\(716\) | −3.18779 | + | 5.52142i | −0.119133 | + | 0.206345i | ||||
\(717\) | −4.04866 | + | 2.33750i | −0.151200 | + | 0.0872954i | ||||
\(718\) | −17.9101 | − | 10.3404i | −0.668400 | − | 0.385901i | ||||
\(719\) | −11.7185 | − | 20.2970i | −0.437025 | − | 0.756949i | 0.560434 | − | 0.828199i | \(-0.310634\pi\) |
−0.997458 | + | 0.0712504i | \(0.977301\pi\) | |||||||
\(720\) | −2.21950 | + | 0.271659i | −0.0827161 | + | 0.0101241i | ||||
\(721\) | −21.5384 | −0.802133 | ||||||||
\(722\) | 4.36691 | − | 18.4914i | 0.162520 | − | 0.688177i | ||||
\(723\) | 27.8087i | 1.03422i | ||||||||
\(724\) | −4.39603 | − | 7.61415i | −0.163377 | − | 0.282978i | ||||
\(725\) | 5.81740 | − | 20.2293i | 0.216053 | − | 0.751296i | ||||
\(726\) | 4.41876 | − | 7.65351i | 0.163995 | − | 0.284049i | ||||
\(727\) | 34.0238 | − | 19.6436i | 1.26187 | − | 0.728543i | 0.288436 | − | 0.957499i | \(-0.406865\pi\) |
0.973437 | + | 0.228957i | \(0.0735314\pi\) | |||||||
\(728\) | 17.6860 | + | 10.2110i | 0.655486 | + | 0.378445i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −11.1184 | + | 26.1656i | −0.411512 | + | 0.968432i | ||||
\(731\) | 0.215266 | − | 0.372851i | 0.00796189 | − | 0.0137904i | ||||
\(732\) | 1.13228 | + | 0.653722i | 0.0418503 | + | 0.0241623i | ||||
\(733\) | 45.2875i | 1.67273i | 0.548171 | + | 0.836366i | \(0.315324\pi\) | ||||
−0.548171 | + | 0.836366i | \(0.684676\pi\) | |||||||
\(734\) | −36.6899 | −1.35425 | ||||||||
\(735\) | 16.5785 | − | 12.4828i | 0.611506 | − | 0.460436i | ||||
\(736\) | −1.28274 | − | 2.22178i | −0.0472826 | − | 0.0818959i | ||||
\(737\) | 13.6935 | + | 7.90592i | 0.504405 | + | 0.291218i | ||||
\(738\) | −6.72248 | + | 3.88123i | −0.247458 | + | 0.142870i | ||||
\(739\) | 15.7422 | + | 27.2663i | 0.579086 | + | 1.00301i | 0.995585 | + | 0.0938695i | \(0.0299237\pi\) |
−0.416499 | + | 0.909136i | \(0.636743\pi\) | |||||||
\(740\) | 3.16532 | + | 1.34503i | 0.116359 | + | 0.0494442i | ||||
\(741\) | 20.2538 | − | 8.74626i | 0.744043 | − | 0.321302i | ||||
\(742\) | 43.0023i | 1.57866i | ||||||||
\(743\) | −40.4415 | + | 23.3489i | −1.48365 | + | 0.856587i | −0.999827 | − | 0.0185770i | \(-0.994086\pi\) |
−0.483826 | + | 0.875164i | \(0.660753\pi\) | |||||||
\(744\) | 2.13279 | + | 3.69410i | 0.0781918 | + | 0.135432i | ||||
\(745\) | 16.4199 | + | 21.8073i | 0.601577 | + | 0.798956i | ||||
\(746\) | 9.76898 | + | 16.9204i | 0.357668 | + | 0.619499i | ||||
\(747\) | −1.78686 | − | 1.03164i | −0.0653776 | − | 0.0377458i | ||||
\(748\) | 0.138039i | 0.00504719i | ||||||||
\(749\) | 72.3365 | 2.64312 | ||||||||
\(750\) | −1.76166 | + | 11.0407i | −0.0643268 | + | 0.403149i | ||||
\(751\) | −14.8807 | + | 25.7741i | −0.543004 | + | 0.940510i | 0.455726 | + | 0.890120i | \(0.349380\pi\) |
−0.998730 | + | 0.0503901i | \(0.983954\pi\) | |||||||
\(752\) | 4.03603i | 0.147179i | ||||||||
\(753\) | 6.06517i | 0.221027i | ||||||||
\(754\) | 10.6536 | − | 18.4525i | 0.387980 | − | 0.672000i | ||||
\(755\) | 44.1922 | − | 5.40896i | 1.60832 | − | 0.196852i | ||||
\(756\) | −2.01747 | + | 3.49437i | −0.0733748 | + | 0.127089i | ||||
\(757\) | −11.2784 | + | 6.51161i | −0.409922 | + | 0.236668i | −0.690756 | − | 0.723088i | \(-0.742722\pi\) |
0.280834 | + | 0.959756i | \(0.409389\pi\) | |||||||
\(758\) | −3.00339 | + | 1.73401i | −0.109088 | + | 0.0629820i | ||||
\(759\) | 3.77265 | 0.136939 | ||||||||
\(760\) | 4.92257 | + | 8.41239i | 0.178560 | + | 0.305150i | ||||
\(761\) | 43.4538 | 1.57520 | 0.787600 | − | 0.616187i | \(-0.211324\pi\) | ||||
0.787600 | + | 0.616187i | \(0.211324\pi\) | |||||||
\(762\) | 5.77290 | − | 3.33298i | 0.209130 | − | 0.120741i | ||||
\(763\) | 31.0042 | − | 17.9003i | 1.12243 | − | 0.648034i | ||||
\(764\) | 6.48293 | − | 11.2288i | 0.234544 | − | 0.406242i | ||||
\(765\) | −0.0255005 | − | 0.208344i | −0.000921972 | − | 0.00753268i | ||||
\(766\) | −12.5509 | + | 21.7388i | −0.453483 | + | 0.785456i | ||||
\(767\) | − | 31.1369i | − | 1.12429i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −23.6418 | + | 40.9487i | −0.852544 | + | 1.47665i | 0.0263617 | + | 0.999652i | \(0.491608\pi\) |
−0.878905 | + | 0.476996i | \(0.841725\pi\) | |||||||
\(770\) | −7.98072 | − | 10.5992i | −0.287605 | − | 0.381969i | ||||
\(771\) | −1.28988 | −0.0464539 | ||||||||
\(772\) | − | 6.11656i | − | 0.220140i | ||||||
\(773\) | 11.4692 | + | 6.62172i | 0.412517 | + | 0.238167i | 0.691871 | − | 0.722022i | \(-0.256787\pi\) |
−0.279354 | + | 0.960188i | \(0.590120\pi\) | |||||||
\(774\) | −2.29325 | − | 3.97202i | −0.0824290 | − | 0.142771i | ||||
\(775\) | 20.6983 | − | 5.14385i | 0.743505 | − | 0.184772i | ||||
\(776\) | 5.97438 | + | 10.3479i | 0.214468 | + | 0.371469i | ||||
\(777\) | 5.37459 | − | 3.10302i | 0.192812 | − | 0.111320i | ||||
\(778\) | − | 14.0415i | − | 0.503411i | ||||||
\(779\) | 27.1485 | + | 20.1944i | 0.972696 | + | 0.723541i | ||||
\(780\) | −4.42603 | + | 10.4160i | −0.158477 | + | 0.372953i | ||||
\(781\) | −6.37928 | − | 11.0492i | −0.228269 | − | 0.395373i | ||||
\(782\) | 0.208557 | − | 0.120411i | 0.00745799 | − | 0.00430587i | ||||
\(783\) | 3.64581 | + | 2.10491i | 0.130291 | + | 0.0752234i | ||||
\(784\) | 4.64040 | + | 8.03741i | 0.165729 | + | 0.287050i | ||||
\(785\) | −28.9999 | + | 21.8356i | −1.03505 | + | 0.779345i | ||||
\(786\) | 7.07568 | 0.252381 | ||||||||
\(787\) | − | 21.7913i | − | 0.776775i | −0.921496 | − | 0.388388i | \(-0.873032\pi\) | ||
0.921496 | − | 0.388388i | \(-0.126968\pi\) | |||||||
\(788\) | 6.36478 | + | 3.67471i | 0.226736 | + | 0.130906i | ||||
\(789\) | 14.1372 | − | 24.4863i | 0.503297 | − | 0.871737i | ||||
\(790\) | −26.6760 | − | 11.3353i | −0.949089 | − | 0.403293i | ||||
\(791\) | 64.0212 | 2.27633 | ||||||||
\(792\) | 1.27352 | + | 0.735269i | 0.0452527 | + | 0.0261267i | ||||
\(793\) | 5.73079 | − | 3.30867i | 0.203506 | − | 0.117494i | ||||
\(794\) | −15.3729 | + | 26.6267i | −0.545564 | + | 0.944945i | ||||
\(795\) | −23.6543 | + | 2.89520i | −0.838932 | + | 0.102682i | ||||
\(796\) | −1.71780 | − | 2.97531i | −0.0608857 | − | 0.105457i | ||||
\(797\) | 14.8524i | 0.526099i | 0.964782 | + | 0.263049i | \(0.0847283\pi\) | ||||
−0.964782 | + | 0.263049i | \(0.915272\pi\) | |||||||
\(798\) | 17.4698 | + | 2.03485i | 0.618425 | + | 0.0720328i | ||||
\(799\) | −0.378860 | −0.0134031 | ||||||||
\(800\) | −4.80525 | − | 1.38186i | −0.169891 | − | 0.0488563i | ||||
\(801\) | 0.813846 | + | 1.40962i | 0.0287558 | + | 0.0498066i | ||||
\(802\) | −33.5183 | − | 19.3518i | −1.18357 | − | 0.683335i | ||||
\(803\) | 16.1919 | − | 9.34838i | 0.571399 | − | 0.329897i | ||||
\(804\) | 5.37621 | − | 9.31187i | 0.189604 | − | 0.328404i | ||||
\(805\) | −9.05237 | + | 21.3034i | −0.319054 | + | 0.750846i | ||||
\(806\) | 21.5893 | 0.760450 | ||||||||
\(807\) | 24.0377 | + | 13.8782i | 0.846169 | + | 0.488536i | ||||
\(808\) | 0.436656 | + | 0.252103i | 0.0153615 | + | 0.00886897i | ||||
\(809\) | 0.338772 | 0.0119106 | 0.00595530 | − | 0.999982i | \(-0.498104\pi\) | ||||
0.00595530 | + | 0.999982i | \(0.498104\pi\) | |||||||
\(810\) | −2.05798 | − | 0.874489i | −0.0723099 | − | 0.0307264i | ||||
\(811\) | −2.04652 | + | 3.54467i | −0.0718629 | + | 0.124470i | −0.899718 | − | 0.436472i | \(-0.856228\pi\) |
0.827855 | + | 0.560942i | \(0.189561\pi\) | |||||||
\(812\) | 14.7107 | − | 8.49321i | 0.516243 | − | 0.298053i | ||||
\(813\) | 9.40202 | + | 5.42826i | 0.329743 | + | 0.190377i | ||||
\(814\) | −1.13090 | − | 1.95877i | −0.0396380 | − | 0.0686550i | ||||
\(815\) | −0.558939 | − | 4.56664i | −0.0195788 | − | 0.159962i | ||||
\(816\) | 0.0938694 | 0.00328609 | ||||||||
\(817\) | −11.9320 | + | 16.0409i | −0.417448 | + | 0.561199i | ||||
\(818\) | 20.7839i | 0.726694i | ||||||||
\(819\) | 10.2110 | + | 17.6860i | 0.356801 | + | 0.617998i | ||||
\(820\) | −17.2288 | + | 2.10874i | −0.601656 | + | 0.0736404i | ||||
\(821\) | 17.2054 | − | 29.8007i | 0.600474 | − | 1.04005i | −0.392275 | − | 0.919848i | \(-0.628312\pi\) |
0.992749 | − | 0.120203i | \(-0.0383547\pi\) | |||||||
\(822\) | 16.3302 | − | 9.42826i | 0.569582 | − | 0.328848i | ||||
\(823\) | 10.3009 | + | 5.94720i | 0.359065 | + | 0.207306i | 0.668671 | − | 0.743559i | \(-0.266864\pi\) |
−0.309605 | + | 0.950865i | \(0.600197\pi\) | |||||||
\(824\) | 5.33797 | 0.185957 | ||||||||
\(825\) | 5.29299 | − | 5.10356i | 0.184278 | − | 0.177683i | ||||
\(826\) | 12.4115 | − | 21.4973i | 0.431850 | − | 0.747986i | ||||
\(827\) | −10.5632 | − | 6.09865i | −0.367318 | − | 0.212071i | 0.304968 | − | 0.952363i | \(-0.401354\pi\) |
−0.672286 | + | 0.740292i | \(0.734687\pi\) | |||||||
\(828\) | − | 2.56549i | − | 0.0891569i | ||||||
\(829\) | 33.0048 | 1.14631 | 0.573153 | − | 0.819449i | \(-0.305720\pi\) | ||||
0.573153 | + | 0.819449i | \(0.305720\pi\) | |||||||
\(830\) | −2.77515 | − | 3.68568i | −0.0963268 | − | 0.127932i | ||||
\(831\) | −12.2618 | − | 21.2381i | −0.425358 | − | 0.736743i | ||||
\(832\) | −4.38320 | − | 2.53064i | −0.151960 | − | 0.0877342i | ||||
\(833\) | −0.754467 | + | 0.435592i | −0.0261407 | + | 0.0150924i | ||||
\(834\) | −9.99616 | − | 17.3139i | −0.346139 | − | 0.599530i | ||||
\(835\) | 44.7154 | + | 19.0008i | 1.54744 | + | 0.657549i | ||||
\(836\) | 0.741602 | − | 6.36689i | 0.0256488 | − | 0.220203i | ||||
\(837\) | 4.26558i | 0.147440i | ||||||||
\(838\) | 31.4083 | − | 18.1336i | 1.08498 | − | 0.626414i | ||||
\(839\) | −8.97119 | − | 15.5386i | −0.309720 | − | 0.536451i | 0.668581 | − | 0.743639i | \(-0.266902\pi\) |
−0.978301 | + | 0.207189i | \(0.933569\pi\) | |||||||
\(840\) | −7.20770 | + | 5.42707i | −0.248689 | + | 0.187252i | ||||
\(841\) | 5.63869 | + | 9.76650i | 0.194438 | + | 0.336776i | ||||
\(842\) | 18.5697 | + | 10.7212i | 0.639953 | + | 0.369477i | ||||
\(843\) | 6.59418i | 0.227116i | ||||||||
\(844\) | 4.03940 | 0.139042 | ||||||||
\(845\) | 16.9695 | + | 22.5372i | 0.583769 | + | 0.775304i | ||||
\(846\) | −2.01801 | + | 3.49530i | −0.0693808 | + | 0.120171i | ||||
\(847\) | − | 35.6589i | − | 1.22525i | ||||||
\(848\) | − | 10.6575i | − | 0.365979i | ||||||
\(849\) | −11.8189 | + | 20.4709i | −0.405623 | + | 0.702559i | ||||
\(850\) | 0.129715 | − | 0.451066i | 0.00444918 | − | 0.0154714i | ||||
\(851\) | −1.97295 | + | 3.41726i | −0.0676320 | + | 0.117142i | ||||
\(852\) | −7.51373 | + | 4.33806i | −0.257416 | + | 0.148619i | ||||
\(853\) | 19.4891 | − | 11.2520i | 0.667295 | − | 0.385263i | −0.127756 | − | 0.991806i | \(-0.540777\pi\) |
0.795051 | + | 0.606543i | \(0.207444\pi\) | |||||||
\(854\) | 5.27547 | 0.180523 | ||||||||
\(855\) | 0.0568730 | + | 9.74663i | 0.00194501 | + | 0.333328i | ||||
\(856\) | −17.9275 | −0.612749 | ||||||||
\(857\) | −1.71631 | + | 0.990914i | −0.0586281 | + | 0.0338490i | −0.529028 | − | 0.848605i | \(-0.677443\pi\) |
0.470399 | + | 0.882454i | \(0.344110\pi\) | |||||||
\(858\) | 6.44566 | − | 3.72141i | 0.220051 | − | 0.127047i | ||||
\(859\) | −16.4673 | + | 28.5223i | −0.561858 | + | 0.973167i | 0.435476 | + | 0.900200i | \(0.356580\pi\) |
−0.997334 | + | 0.0729670i | \(0.976753\pi\) | |||||||
\(860\) | −1.24596 | − | 10.1797i | −0.0424870 | − | 0.347126i | ||||
\(861\) | −15.6605 | + | 27.1248i | −0.533710 | + | 0.924412i | ||||
\(862\) | − | 5.82431i | − | 0.198377i | ||||||
\(863\) | − | 1.13901i | − | 0.0387723i | −0.999812 | − | 0.0193862i | \(-0.993829\pi\) | ||
0.999812 | − | 0.0193862i | \(-0.00617119\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 41.4520 | − | 31.2114i | 1.40941 | − | 1.06122i | ||||
\(866\) | 31.6030 | 1.07391 | ||||||||
\(867\) | − | 16.9912i | − | 0.577051i | ||||||
\(868\) | 14.9055 | + | 8.60569i | 0.505925 | + | 0.292096i | ||||
\(869\) | 9.53074 | + | 16.5077i | 0.323308 | + | 0.559986i | ||||
\(870\) | 5.66228 | + | 7.52008i | 0.191969 | + | 0.254955i | ||||
\(871\) | −27.2105 | − | 47.1300i | −0.921993 | − | 1.59694i | ||||
\(872\) | −7.68392 | + | 4.43631i | −0.260210 | + | 0.150232i | ||||
\(873\) | 11.9488i | 0.404405i | ||||||||
\(874\) | −10.2664 | + | 4.43335i | −0.347265 | + | 0.149960i | ||||
\(875\) | 16.1184 | + | 42.1343i | 0.544901 | + | 1.42440i | ||||
\(876\) | −6.35711 | − | 11.0108i | −0.214787 | − | 0.372022i | ||||
\(877\) | 19.9508 | − | 11.5186i | 0.673692 | − | 0.388956i | −0.123782 | − | 0.992309i | \(-0.539502\pi\) |
0.797474 | + | 0.603353i | \(0.206169\pi\) | |||||||
\(878\) | −1.61592 | − | 0.932951i | −0.0545346 | − | 0.0314856i | ||||
\(879\) | −11.5061 | − | 19.9292i | −0.388092 | − | 0.672195i | ||||
\(880\) | 1.97790 | + | 2.62685i | 0.0666749 | + | 0.0885511i | ||||
\(881\) | −6.22555 | −0.209744 | −0.104872 | − | 0.994486i | \(-0.533443\pi\) | ||||
−0.104872 | + | 0.994486i | \(0.533443\pi\) | |||||||
\(882\) | 9.28080i | 0.312501i | ||||||||
\(883\) | −28.2402 | − | 16.3045i | −0.950360 | − | 0.548691i | −0.0571672 | − | 0.998365i | \(-0.518207\pi\) |
−0.893193 | + | 0.449674i | \(0.851540\pi\) | |||||||
\(884\) | 0.237550 | − | 0.411448i | 0.00798967 | − | 0.0138385i | ||||
\(885\) | 12.6606 | + | 5.37984i | 0.425583 | + | 0.180841i | ||||
\(886\) | −15.7464 | −0.529009 | ||||||||
\(887\) | −3.26261 | − | 1.88367i | −0.109548 | − | 0.0632474i | 0.444225 | − | 0.895915i | \(-0.353479\pi\) |
−0.553773 | + | 0.832668i | \(0.686812\pi\) | |||||||
\(888\) | −1.33201 | + | 0.769037i | −0.0446993 | + | 0.0258072i | ||||
\(889\) | 13.4484 | − | 23.2933i | 0.451045 | − | 0.781234i | ||||
\(890\) | 0.442177 | + | 3.61267i | 0.0148218 | + | 0.121097i | ||||
\(891\) | 0.735269 | + | 1.27352i | 0.0246325 | + | 0.0426647i | ||||
\(892\) | − | 18.0519i | − | 0.604421i | ||||||
\(893\) | 17.4745 | + | 2.03539i | 0.584762 | + | 0.0681118i | ||||
\(894\) | −12.2079 | −0.408294 | ||||||||
\(895\) | −14.1506 | + | 1.73199i | −0.473004 | + | 0.0578939i | ||||
\(896\) | −2.01747 | − | 3.49437i | −0.0673991 | − | 0.116739i | ||||
\(897\) | −11.2451 | − | 6.49233i | −0.375461 | − | 0.216773i | ||||
\(898\) | −25.7588 | + | 14.8718i | −0.859581 | + | 0.496279i | ||||
\(899\) | 8.97866 | − | 15.5515i | 0.299455 | − | 0.518671i | ||||
\(900\) | −3.47054 | − | 3.59936i | −0.115685 | − | 0.119979i | ||||
\(901\) | 1.00041 | 0.0333285 | ||||||||
\(902\) | 9.88567 | + | 5.70749i | 0.329157 | + | 0.190039i | ||||
\(903\) | −16.0269 | − | 9.25313i | −0.533341 | − | 0.307925i | ||||
\(904\) | −15.8667 | −0.527718 | ||||||||
\(905\) | 7.68856 | − | 18.0939i | 0.255576 | − | 0.601461i | ||||
\(906\) | −9.95543 | + | 17.2433i | −0.330747 | + | 0.572870i | ||||
\(907\) | −8.85151 | + | 5.11042i | −0.293910 | + | 0.169689i | −0.639704 | − | 0.768622i | \(-0.720943\pi\) |
0.345794 | + | 0.938310i | \(0.387610\pi\) | |||||||
\(908\) | 23.2539 | + | 13.4257i | 0.771709 | + | 0.445547i | ||||
\(909\) | 0.252103 | + | 0.436656i | 0.00836174 | + | 0.0144830i | ||||
\(910\) | 5.54782 | + | 45.3267i | 0.183909 | + | 1.50257i | ||||
\(911\) | −18.6042 | −0.616383 | −0.308192 | − | 0.951324i | \(-0.599724\pi\) | ||||
−0.308192 | + | 0.951324i | \(0.599724\pi\) | |||||||
\(912\) | −4.32963 | − | 0.504306i | −0.143368 | − | 0.0166992i | ||||
\(913\) | 3.03414i | 0.100415i | ||||||||
\(914\) | −6.39456 | − | 11.0757i | −0.211513 | − | 0.366352i | ||||
\(915\) | 0.355179 | + | 2.90188i | 0.0117419 | + | 0.0959332i | ||||
\(916\) | 6.85657 | − | 11.8759i | 0.226548 | − | 0.392392i | ||||
\(917\) | 24.7250 | − | 14.2750i | 0.816492 | − | 0.471402i | ||||
\(918\) | 0.0812933 | + | 0.0469347i | 0.00268308 | + | 0.00154908i | ||||
\(919\) | 35.5145 | 1.17152 | 0.585758 | − | 0.810486i | \(-0.300797\pi\) | ||||
0.585758 | + | 0.810486i | \(0.300797\pi\) | |||||||
\(920\) | 2.24349 | − | 5.27972i | 0.0739657 | − | 0.174067i | ||||
\(921\) | −12.7483 | + | 22.0807i | −0.420071 | + | 0.727584i | ||||
\(922\) | 10.3283 | + | 5.96303i | 0.340143 | + | 0.196382i | ||||
\(923\) | 43.9123i | 1.44539i | ||||||||
\(924\) | 5.93355 | 0.195199 | ||||||||
\(925\) | 1.85476 | + | 7.46335i | 0.0609841 | + | 0.245393i | ||||
\(926\) | −9.66039 | − | 16.7323i | −0.317460 | − | 0.549857i | ||||
\(927\) | 4.62282 | + | 2.66899i | 0.151833 | + | 0.0876610i | ||||
\(928\) | −3.64581 | + | 2.10491i | −0.119680 | + | 0.0690971i | ||||
\(929\) | 2.13612 | + | 3.69987i | 0.0700838 | + | 0.121389i | 0.898938 | − | 0.438076i | \(-0.144340\pi\) |
−0.828854 | + | 0.559465i | \(0.811007\pi\) | |||||||
\(930\) | −3.73020 | + | 8.77846i | −0.122318 | + | 0.287857i | ||||
\(931\) | 37.1392 | − | 16.0379i | 1.21719 | − | 0.525621i | ||||
\(932\) | − | 0.00661073i | − | 0.000216542i | ||||||
\(933\) | 26.2555 | − | 15.1586i | 0.859565 | − | 0.496270i | ||||
\(934\) | 13.3504 | + | 23.1237i | 0.436840 | + | 0.756629i | ||||
\(935\) | −0.246581 | + | 0.185664i | −0.00806406 | + | 0.00607187i | ||||
\(936\) | −2.53064 | − | 4.38320i | −0.0827166 | − | 0.143269i | ||||
\(937\) | 44.5676 | + | 25.7311i | 1.45596 | + | 0.840599i | 0.998809 | − | 0.0487891i | \(-0.0155362\pi\) |
0.457152 | + | 0.889389i | \(0.348870\pi\) | |||||||
\(938\) | − | 43.3854i | − | 1.41658i | ||||||
\(939\) | 7.55247 | 0.246465 | ||||||||
\(940\) | −7.20963 | + | 5.42852i | −0.235152 | + | 0.177059i | ||||
\(941\) | −30.2442 | + | 52.3845i | −0.985934 | + | 1.70769i | −0.348222 | + | 0.937412i | \(0.613214\pi\) |
−0.637712 | + | 0.770275i | \(0.720119\pi\) | |||||||
\(942\) | − | 16.2344i | − | 0.528946i | ||||||
\(943\) | − | 19.9145i | − | 0.648505i | ||||||
\(944\) | −3.07599 | + | 5.32777i | −0.100115 | + | 0.173404i | ||||
\(945\) | −8.95558 | + | 1.09613i | −0.291325 | + | 0.0356571i | ||||
\(946\) | −3.37231 | + | 5.84101i | −0.109643 | + | 0.189908i | ||||
\(947\) | 10.0415 | − | 5.79749i | 0.326306 | − | 0.188393i | −0.327894 | − | 0.944715i | \(-0.606339\pi\) |
0.654200 | + | 0.756322i | \(0.273005\pi\) | |||||||
\(948\) | 11.2256 | − | 6.48112i | 0.364592 | − | 0.210497i | ||||
\(949\) | −64.3503 | −2.08890 | ||||||||
\(950\) | −8.40627 | + | 20.1081i | −0.272736 | + | 0.652392i | ||||
\(951\) | −14.0116 | −0.454357 | ||||||||
\(952\) | 0.328014 | − | 0.189379i | 0.0106310 | − | 0.00613781i | ||||
\(953\) | −22.5443 | + | 13.0160i | −0.730282 | + | 0.421629i | −0.818525 | − | 0.574470i | \(-0.805208\pi\) |
0.0882433 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(954\) | 5.32873 | − | 9.22964i | 0.172524 | − | 0.298821i | ||||
\(955\) | 28.7778 | − | 3.52229i | 0.931227 | − | 0.113979i | ||||
\(956\) | 2.33750 | − | 4.04866i | 0.0756000 | − | 0.130943i | ||||
\(957\) | − | 6.19071i | − | 0.200117i | ||||||
\(958\) | 13.5825i | 0.438830i | ||||||||
\(959\) | 38.0425 | − | 65.8916i | 1.22846 | − | 2.12775i | ||||
\(960\) | 1.78632 | − | 1.34502i | 0.0576532 | − | 0.0434102i | ||||
\(961\) | −12.8049 | −0.413060 | ||||||||
\(962\) | 7.78462i | 0.250986i | ||||||||
\(963\) | −15.5257 | − | 8.96375i | −0.500308 | − | 0.288853i | ||||
\(964\) | −13.9044 | − | 24.0831i | −0.447829 | − | 0.775663i | ||||
\(965\) | 10.9261 | − | 8.22688i | 0.351725 | − | 0.264833i | ||||
\(966\) | −5.17581 | − | 8.96476i | −0.166529 | − | 0.288436i | ||||
\(967\) | 14.9595 | − | 8.63685i | 0.481064 | − | 0.277743i | −0.239796 | − | 0.970823i | \(-0.577080\pi\) |
0.720860 | + | 0.693081i | \(0.243747\pi\) | |||||||
\(968\) | 8.83752i | 0.284049i | ||||||||
\(969\) | 0.0473389 | − | 0.406420i | 0.00152075 | − | 0.0130561i | ||||
\(970\) | −10.4491 | + | 24.5903i | −0.335499 | + | 0.789547i | ||||
\(971\) | 5.47052 | + | 9.47522i | 0.175557 | + | 0.304074i | 0.940354 | − | 0.340198i | \(-0.110494\pi\) |
−0.764797 | + | 0.644272i | \(0.777161\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −69.8605 | − | 40.3340i | −2.23963 | − | 1.29305i | ||||
\(974\) | 4.01820 | + | 6.95973i | 0.128752 | + | 0.223004i | ||||
\(975\) | −24.5594 | + | 6.10339i | −0.786530 | + | 0.195465i | ||||
\(976\) | −1.30744 | −0.0418503 | ||||||||
\(977\) | − | 9.01488i | − | 0.288412i | −0.989548 | − | 0.144206i | \(-0.953937\pi\) | ||
0.989548 | − | 0.144206i | \(-0.0460627\pi\) | |||||||
\(978\) | 1.78185 | + | 1.02875i | 0.0569773 | + | 0.0328958i | ||||
\(979\) | 1.19679 | − | 2.07290i | 0.0382496 | − | 0.0662503i | ||||
\(980\) | −8.11595 | + | 19.0997i | −0.259255 | + | 0.610117i | ||||
\(981\) | −8.87262 | −0.283281 | ||||||||
\(982\) | 17.9077 | + | 10.3390i | 0.571457 | + | 0.329931i | ||||
\(983\) | −12.8956 | + | 7.44527i | −0.411305 | + | 0.237467i | −0.691350 | − | 0.722520i | \(-0.742984\pi\) |
0.280045 | + | 0.959987i | \(0.409651\pi\) | |||||||
\(984\) | 3.88123 | − | 6.72248i | 0.123729 | − | 0.214305i | ||||
\(985\) | 1.99653 | + | 16.3121i | 0.0636149 | + | 0.519745i | ||||
\(986\) | −0.197587 | − | 0.342231i | −0.00629245 | − | 0.0108988i | ||||
\(987\) | 16.2852i | 0.518362i | ||||||||
\(988\) | −13.1672 | + | 17.7014i | −0.418905 | + | 0.563157i | ||||
\(989\) | 11.7666 | 0.374156 | ||||||||
\(990\) | 0.399485 | + | 3.26387i | 0.0126965 | + | 0.103733i | ||||
\(991\) | −23.1717 | − | 40.1346i | −0.736075 | − | 1.27492i | −0.954250 | − | 0.299009i | \(-0.903344\pi\) |
0.218176 | − | 0.975910i | \(-0.429989\pi\) | |||||||
\(992\) | −3.69410 | − | 2.13279i | −0.117288 | − | 0.0677161i | ||||
\(993\) | 1.90994 | − | 1.10271i | 0.0606102 | − | 0.0349933i | ||||
\(994\) | −17.5038 | + | 30.3175i | −0.555188 | + | 0.961613i | ||||
\(995\) | 3.00439 | − | 7.07037i | 0.0952454 | − | 0.224146i | ||||
\(996\) | 2.06328 | 0.0653776 | ||||||||
\(997\) | 26.1990 | + | 15.1260i | 0.829730 | + | 0.479045i | 0.853760 | − | 0.520667i | \(-0.174317\pi\) |
−0.0240304 | + | 0.999711i | \(0.507650\pi\) | |||||||
\(998\) | −0.954638 | − | 0.551160i | −0.0302185 | − | 0.0174467i | ||||
\(999\) | −1.53807 | −0.0486625 |
(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.349.10 | yes | 20 | |
3.2 | odd | 2 | 1710.2.t.c.919.1 | 20 | |||
5.4 | even | 2 | inner | 570.2.q.c.349.2 | yes | 20 | |
15.14 | odd | 2 | 1710.2.t.c.919.9 | 20 | |||
19.11 | even | 3 | inner | 570.2.q.c.49.2 | ✓ | 20 | |
57.11 | odd | 6 | 1710.2.t.c.1189.9 | 20 | |||
95.49 | even | 6 | inner | 570.2.q.c.49.10 | yes | 20 | |
285.239 | odd | 6 | 1710.2.t.c.1189.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.c.49.2 | ✓ | 20 | 19.11 | even | 3 | inner | |
570.2.q.c.49.10 | yes | 20 | 95.49 | even | 6 | inner | |
570.2.q.c.349.2 | yes | 20 | 5.4 | even | 2 | inner | |
570.2.q.c.349.10 | yes | 20 | 1.1 | even | 1 | trivial | |
1710.2.t.c.919.1 | 20 | 3.2 | odd | 2 | |||
1710.2.t.c.919.9 | 20 | 15.14 | odd | 2 | |||
1710.2.t.c.1189.1 | 20 | 285.239 | odd | 6 | |||
1710.2.t.c.1189.9 | 20 | 57.11 | odd | 6 |