Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(45,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.g (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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 45.2 | ||
Root | \(-1.52769 - 2.64604i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.45 |
Dual form | 322.2.g.a.229.2 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.86037 | − | 1.07408i | −1.07408 | − | 0.620123i | −0.144790 | − | 0.989462i | \(-0.546251\pi\) |
−0.929294 | + | 0.369340i | \(0.879584\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.264227 | + | 0.457654i | 0.118166 | + | 0.204669i | 0.919041 | − | 0.394162i | \(-0.128965\pi\) |
−0.800875 | + | 0.598832i | \(0.795632\pi\) | |||||||
\(6\) | 2.14817i | 0.876986i | ||||||||
\(7\) | 1.26346 | + | 2.32458i | 0.477545 | + | 0.878607i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.807314 | + | 1.39831i | 0.269105 | + | 0.466103i | ||||
\(10\) | 0.264227 | − | 0.457654i | 0.0835558 | − | 0.144723i | ||||
\(11\) | 1.77580 | + | 1.02526i | 0.535423 | + | 0.309127i | 0.743222 | − | 0.669045i | \(-0.233297\pi\) |
−0.207799 | + | 0.978172i | \(0.566630\pi\) | |||||||
\(12\) | 1.86037 | − | 1.07408i | 0.537042 | − | 0.310061i | ||||
\(13\) | 3.70082i | 1.02642i | 0.858262 | + | 0.513212i | \(0.171544\pi\) | ||||
−0.858262 | + | 0.513212i | \(0.828456\pi\) | |||||||
\(14\) | 1.38141 | − | 2.25648i | 0.369197 | − | 0.603070i | ||||
\(15\) | − | 1.13521i | − | 0.293109i | ||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.44977 | − | 5.97518i | 0.836692 | − | 1.44919i | −0.0559526 | − | 0.998433i | \(-0.517820\pi\) |
0.892645 | − | 0.450760i | \(-0.148847\pi\) | |||||||
\(18\) | 0.807314 | − | 1.39831i | 0.190286 | − | 0.329585i | ||||
\(19\) | 0.264227 | + | 0.457654i | 0.0606178 | + | 0.104993i | 0.894742 | − | 0.446584i | \(-0.147360\pi\) |
−0.834124 | + | 0.551577i | \(0.814026\pi\) | |||||||
\(20\) | −0.528453 | −0.118166 | ||||||||
\(21\) | 0.146281 | − | 5.68164i | 0.0319212 | − | 1.23983i | ||||
\(22\) | − | 2.05052i | − | 0.437171i | ||||||
\(23\) | 3.94348 | + | 2.72928i | 0.822273 | + | 0.569094i | ||||
\(24\) | −1.86037 | − | 1.07408i | −0.379746 | − | 0.219247i | ||||
\(25\) | 2.36037 | − | 4.08828i | 0.472074 | − | 0.817656i | ||||
\(26\) | 3.20501 | − | 1.85041i | 0.628554 | − | 0.362896i | ||||
\(27\) | 2.97601i | 0.572734i | ||||||||
\(28\) | −2.64487 | − | 0.0680958i | −0.499834 | − | 0.0128689i | ||||
\(29\) | 3.68928 | 0.685082 | 0.342541 | − | 0.939503i | \(-0.388713\pi\) | ||||
0.342541 | + | 0.939503i | \(0.388713\pi\) | |||||||
\(30\) | −0.983118 | + | 0.567604i | −0.179492 | + | 0.103630i | ||||
\(31\) | −4.28231 | − | 2.47239i | −0.769126 | − | 0.444055i | 0.0634370 | − | 0.997986i | \(-0.479794\pi\) |
−0.832563 | + | 0.553931i | \(0.813127\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.20243 | − | 3.81471i | −0.383393 | − | 0.664056i | ||||
\(34\) | −6.89954 | −1.18326 | ||||||||
\(35\) | −0.730011 | + | 1.19245i | −0.123394 | + | 0.201560i | ||||
\(36\) | −1.61463 | −0.269105 | ||||||||
\(37\) | 7.50830 | − | 4.33492i | 1.23436 | − | 0.712656i | 0.266421 | − | 0.963857i | \(-0.414159\pi\) |
0.967935 | + | 0.251201i | \(0.0808255\pi\) | |||||||
\(38\) | 0.264227 | − | 0.457654i | 0.0428632 | − | 0.0742413i | ||||
\(39\) | 3.97500 | − | 6.88490i | 0.636509 | − | 1.10247i | ||||
\(40\) | 0.264227 | + | 0.457654i | 0.0417779 | + | 0.0723615i | ||||
\(41\) | 3.70082i | 0.577972i | 0.957333 | + | 0.288986i | \(0.0933180\pi\) | ||||
−0.957333 | + | 0.288986i | \(0.906682\pi\) | |||||||
\(42\) | −4.99358 | + | 2.71414i | −0.770526 | + | 0.418800i | ||||
\(43\) | 8.98453i | 1.37013i | 0.728483 | + | 0.685064i | \(0.240226\pi\) | ||||
−0.728483 | + | 0.685064i | \(0.759774\pi\) | |||||||
\(44\) | −1.77580 | + | 1.02526i | −0.267712 | + | 0.154563i | ||||
\(45\) | −0.426628 | + | 0.738941i | −0.0635979 | + | 0.110155i | ||||
\(46\) | 0.391884 | − | 4.77979i | 0.0577801 | − | 0.704742i | ||||
\(47\) | −1.70501 | + | 0.984386i | −0.248701 | + | 0.143588i | −0.619169 | − | 0.785258i | \(-0.712531\pi\) |
0.370468 | + | 0.928845i | \(0.379197\pi\) | |||||||
\(48\) | 2.14817i | 0.310061i | ||||||||
\(49\) | −3.80731 | + | 5.87404i | −0.543902 | + | 0.839149i | ||||
\(50\) | −4.72074 | −0.667613 | ||||||||
\(51\) | −12.8357 | + | 7.41069i | −1.79736 | + | 1.03770i | ||||
\(52\) | −3.20501 | − | 1.85041i | −0.444455 | − | 0.256606i | ||||
\(53\) | 11.8526 | + | 6.84309i | 1.62808 | + | 0.939970i | 0.984666 | + | 0.174448i | \(0.0558141\pi\) |
0.643410 | + | 0.765522i | \(0.277519\pi\) | |||||||
\(54\) | 2.57730 | − | 1.48801i | 0.350726 | − | 0.202492i | ||||
\(55\) | 1.08360i | 0.146113i | ||||||||
\(56\) | 1.26346 | + | 2.32458i | 0.168838 | + | 0.310635i | ||||
\(57\) | − | 1.13521i | − | 0.150362i | ||||||
\(58\) | −1.84464 | − | 3.19501i | −0.242213 | − | 0.419525i | ||||
\(59\) | −5.00305 | − | 2.88851i | −0.651341 | − | 0.376052i | 0.137629 | − | 0.990484i | \(-0.456052\pi\) |
−0.788970 | + | 0.614432i | \(0.789385\pi\) | |||||||
\(60\) | 0.983118 | + | 0.567604i | 0.126920 | + | 0.0732773i | ||||
\(61\) | 2.92132 | + | 5.05987i | 0.374036 | + | 0.647850i | 0.990182 | − | 0.139782i | \(-0.0446402\pi\) |
−0.616146 | + | 0.787632i | \(0.711307\pi\) | |||||||
\(62\) | 4.94479i | 0.627988i | ||||||||
\(63\) | −2.23046 | + | 3.64338i | −0.281012 | + | 0.459022i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.69370 | + | 0.977857i | −0.210077 | + | 0.121288i | ||||
\(66\) | −2.20243 | + | 3.81471i | −0.271100 | + | 0.469559i | ||||
\(67\) | −0.710579 | − | 0.410253i | −0.0868110 | − | 0.0501204i | 0.455966 | − | 0.889997i | \(-0.349294\pi\) |
−0.542777 | + | 0.839877i | \(0.682627\pi\) | |||||||
\(68\) | 3.44977 | + | 5.97518i | 0.418346 | + | 0.724597i | ||||
\(69\) | −4.40485 | − | 9.31309i | −0.530282 | − | 1.12116i | ||||
\(70\) | 1.39769 | + | 0.0359855i | 0.167056 | + | 0.00430109i | ||||
\(71\) | 1.03146 | 0.122412 | 0.0612059 | − | 0.998125i | \(-0.480505\pi\) | ||||
0.0612059 | + | 0.998125i | \(0.480505\pi\) | |||||||
\(72\) | 0.807314 | + | 1.39831i | 0.0951429 | + | 0.164792i | ||||
\(73\) | −4.28231 | − | 2.47239i | −0.501206 | − | 0.289372i | 0.228005 | − | 0.973660i | \(-0.426780\pi\) |
−0.729212 | + | 0.684288i | \(0.760113\pi\) | |||||||
\(74\) | −7.50830 | − | 4.33492i | −0.872822 | − | 0.503924i | ||||
\(75\) | −8.78231 | + | 5.07047i | −1.01409 | + | 0.585487i | ||||
\(76\) | −0.528453 | −0.0606178 | ||||||||
\(77\) | −0.139632 | + | 5.42336i | −0.0159125 | + | 0.618049i | ||||
\(78\) | −7.94999 | −0.900159 | ||||||||
\(79\) | −10.3493 | + | 5.97518i | −1.16439 | + | 0.672260i | −0.952352 | − | 0.305002i | \(-0.901343\pi\) |
−0.212037 | + | 0.977262i | \(0.568010\pi\) | |||||||
\(80\) | 0.264227 | − | 0.457654i | 0.0295414 | − | 0.0511673i | ||||
\(81\) | 5.61843 | − | 9.73141i | 0.624270 | − | 1.08127i | ||||
\(82\) | 3.20501 | − | 1.85041i | 0.353934 | − | 0.204344i | ||||
\(83\) | 16.4544 | 1.80610 | 0.903051 | − | 0.429533i | \(-0.141322\pi\) | ||||
0.903051 | + | 0.429533i | \(0.141322\pi\) | |||||||
\(84\) | 4.84730 | + | 2.96750i | 0.528884 | + | 0.323781i | ||||
\(85\) | 3.64609 | 0.395474 | ||||||||
\(86\) | 7.78083 | − | 4.49227i | 0.839029 | − | 0.484414i | ||||
\(87\) | −6.86342 | − | 3.96259i | −0.735835 | − | 0.424835i | ||||
\(88\) | 1.77580 | + | 1.02526i | 0.189301 | + | 0.109293i | ||||
\(89\) | −3.81582 | − | 6.60920i | −0.404476 | − | 0.700574i | 0.589784 | − | 0.807561i | \(-0.299213\pi\) |
−0.994260 | + | 0.106987i | \(0.965880\pi\) | |||||||
\(90\) | 0.853256 | 0.0899410 | ||||||||
\(91\) | −8.60285 | + | 4.67586i | −0.901824 | + | 0.490163i | ||||
\(92\) | −4.33536 | + | 2.05052i | −0.451993 | + | 0.213781i | ||||
\(93\) | 5.31112 | + | 9.19912i | 0.550737 | + | 0.953905i | ||||
\(94\) | 1.70501 | + | 0.984386i | 0.175858 | + | 0.101532i | ||||
\(95\) | −0.139632 | + | 0.241849i | −0.0143259 | + | 0.0248132i | ||||
\(96\) | 1.86037 | − | 1.07408i | 0.189873 | − | 0.109623i | ||||
\(97\) | −11.1402 | −1.13112 | −0.565558 | − | 0.824709i | \(-0.691339\pi\) | ||||
−0.565558 | + | 0.824709i | \(0.691339\pi\) | |||||||
\(98\) | 6.99073 | + | 0.360210i | 0.706170 | + | 0.0363867i | ||||
\(99\) | 3.31082i | 0.332750i | ||||||||
\(100\) | 2.36037 | + | 4.08828i | 0.236037 | + | 0.408828i | ||||
\(101\) | −2.58111 | − | 1.49020i | −0.256830 | − | 0.148281i | 0.366058 | − | 0.930592i | \(-0.380707\pi\) |
−0.622887 | + | 0.782311i | \(0.714041\pi\) | |||||||
\(102\) | 12.8357 | + | 7.41069i | 1.27092 | + | 0.733768i | ||||
\(103\) | 0.881293 | + | 1.52644i | 0.0868363 | + | 0.150405i | 0.906172 | − | 0.422909i | \(-0.138991\pi\) |
−0.819336 | + | 0.573314i | \(0.805658\pi\) | |||||||
\(104\) | 3.70082i | 0.362896i | ||||||||
\(105\) | 2.63888 | − | 1.43429i | 0.257528 | − | 0.139973i | ||||
\(106\) | − | 13.6862i | − | 1.32932i | ||||||
\(107\) | 7.69873 | − | 4.44487i | 0.744265 | − | 0.429701i | −0.0793532 | − | 0.996847i | \(-0.525285\pi\) |
0.823618 | + | 0.567145i | \(0.191952\pi\) | |||||||
\(108\) | −2.57730 | − | 1.48801i | −0.248001 | − | 0.143183i | ||||
\(109\) | −6.00504 | − | 3.46701i | −0.575178 | − | 0.332079i | 0.184037 | − | 0.982919i | \(-0.441083\pi\) |
−0.759215 | + | 0.650840i | \(0.774417\pi\) | |||||||
\(110\) | 0.938427 | − | 0.541801i | 0.0894755 | − | 0.0516587i | ||||
\(111\) | −18.6243 | −1.76774 | ||||||||
\(112\) | 1.38141 | − | 2.25648i | 0.130531 | − | 0.213217i | ||||
\(113\) | − | 5.00860i | − | 0.471169i | −0.971854 | − | 0.235585i | \(-0.924299\pi\) | ||
0.971854 | − | 0.235585i | \(-0.0757005\pi\) | |||||||
\(114\) | −0.983118 | + | 0.567604i | −0.0920775 | + | 0.0531609i | ||||
\(115\) | −0.207092 | + | 2.52590i | −0.0193115 | + | 0.235541i | ||||
\(116\) | −1.84464 | + | 3.19501i | −0.171270 | + | 0.296649i | ||||
\(117\) | −5.17489 | + | 2.98773i | −0.478419 | + | 0.276215i | ||||
\(118\) | 5.77702i | 0.531818i | ||||||||
\(119\) | 18.2484 | + | 0.469830i | 1.67283 | + | 0.0430692i | ||||
\(120\) | − | 1.13521i | − | 0.103630i | ||||||
\(121\) | −3.39769 | − | 5.88498i | −0.308881 | − | 0.534998i | ||||
\(122\) | 2.92132 | − | 5.05987i | 0.264484 | − | 0.458099i | ||||
\(123\) | 3.97500 | − | 6.88490i | 0.358413 | − | 0.620790i | ||||
\(124\) | 4.28231 | − | 2.47239i | 0.384563 | − | 0.222027i | ||||
\(125\) | 5.13696 | 0.459463 | ||||||||
\(126\) | 4.27049 | + | 0.109949i | 0.380445 | + | 0.00979507i | ||||
\(127\) | −3.31072 | −0.293779 | −0.146890 | − | 0.989153i | \(-0.546926\pi\) | ||||
−0.146890 | + | 0.989153i | \(0.546926\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 9.65015 | − | 16.7145i | 0.849648 | − | 1.47163i | ||||
\(130\) | 1.69370 | + | 0.977857i | 0.148547 | + | 0.0857637i | ||||
\(131\) | −14.1457 | + | 8.16704i | −1.23592 | + | 0.713557i | −0.968257 | − | 0.249956i | \(-0.919584\pi\) |
−0.267661 | + | 0.963513i | \(0.586251\pi\) | |||||||
\(132\) | 4.40485 | 0.383393 | ||||||||
\(133\) | −0.730011 | + | 1.19245i | −0.0633000 | + | 0.103398i | ||||
\(134\) | 0.820506i | 0.0708809i | ||||||||
\(135\) | −1.36198 | + | 0.786342i | −0.117221 | + | 0.0676776i | ||||
\(136\) | 3.44977 | − | 5.97518i | 0.295815 | − | 0.512367i | ||||
\(137\) | −8.49141 | − | 4.90252i | −0.725470 | − | 0.418851i | 0.0912924 | − | 0.995824i | \(-0.470900\pi\) |
−0.816763 | + | 0.576974i | \(0.804234\pi\) | |||||||
\(138\) | −5.86295 | + | 8.47126i | −0.499087 | + | 0.721122i | ||||
\(139\) | − | 18.4468i | − | 1.56464i | −0.622879 | − | 0.782318i | \(-0.714037\pi\) | ||
0.622879 | − | 0.782318i | \(-0.285963\pi\) | |||||||
\(140\) | −0.667682 | − | 1.22843i | −0.0564295 | − | 0.103821i | ||||
\(141\) | 4.22926 | 0.356168 | ||||||||
\(142\) | −0.515730 | − | 0.893270i | −0.0432791 | − | 0.0749616i | ||||
\(143\) | −3.79430 | + | 6.57192i | −0.317295 | + | 0.549571i | ||||
\(144\) | 0.807314 | − | 1.39831i | 0.0672762 | − | 0.116526i | ||||
\(145\) | 0.974806 | + | 1.68841i | 0.0809532 | + | 0.140215i | ||||
\(146\) | 4.94479i | 0.409233i | ||||||||
\(147\) | 13.3922 | − | 6.83851i | 1.10457 | − | 0.564030i | ||||
\(148\) | 8.66983i | 0.712656i | ||||||||
\(149\) | 3.55160 | − | 2.05052i | 0.290958 | − | 0.167985i | −0.347416 | − | 0.937711i | \(-0.612941\pi\) |
0.638374 | + | 0.769726i | \(0.279607\pi\) | |||||||
\(150\) | 8.78231 | + | 5.07047i | 0.717073 | + | 0.414002i | ||||
\(151\) | −0.885372 | + | 1.53351i | −0.0720506 | + | 0.124795i | −0.899800 | − | 0.436303i | \(-0.856288\pi\) |
0.827749 | + | 0.561098i | \(0.189621\pi\) | |||||||
\(152\) | 0.264227 | + | 0.457654i | 0.0214316 | + | 0.0371207i | ||||
\(153\) | 11.1402 | 0.900631 | ||||||||
\(154\) | 4.76658 | − | 2.59075i | 0.384102 | − | 0.208769i | ||||
\(155\) | − | 2.61309i | − | 0.209888i | ||||||
\(156\) | 3.97500 | + | 6.88490i | 0.318254 | + | 0.551233i | ||||
\(157\) | −3.73372 | + | 6.46700i | −0.297983 | + | 0.516123i | −0.975675 | − | 0.219224i | \(-0.929647\pi\) |
0.677691 | + | 0.735347i | \(0.262981\pi\) | |||||||
\(158\) | 10.3493 | + | 5.97518i | 0.823347 | + | 0.475360i | ||||
\(159\) | −14.7001 | − | 25.4613i | −1.16579 | − | 2.01921i | ||||
\(160\) | −0.528453 | −0.0417779 | ||||||||
\(161\) | −1.36197 | + | 12.6153i | −0.107338 | + | 0.994223i | ||||
\(162\) | −11.2369 | −0.882851 | ||||||||
\(163\) | 2.80731 | + | 4.86241i | 0.219886 | + | 0.380853i | 0.954773 | − | 0.297336i | \(-0.0960982\pi\) |
−0.734887 | + | 0.678189i | \(0.762765\pi\) | |||||||
\(164\) | −3.20501 | − | 1.85041i | −0.250269 | − | 0.144493i | ||||
\(165\) | 1.16388 | − | 2.01590i | 0.0906079 | − | 0.156938i | ||||
\(166\) | −8.22719 | − | 14.2499i | −0.638554 | − | 1.10601i | ||||
\(167\) | − | 4.65513i | − | 0.360225i | −0.983646 | − | 0.180112i | \(-0.942354\pi\) | ||
0.983646 | − | 0.180112i | \(-0.0576461\pi\) | |||||||
\(168\) | 0.146281 | − | 5.68164i | 0.0112858 | − | 0.438348i | ||||
\(169\) | −0.696095 | −0.0535458 | ||||||||
\(170\) | −1.82304 | − | 3.15760i | −0.139821 | − | 0.242177i | ||||
\(171\) | −0.426628 | + | 0.738941i | −0.0326250 | + | 0.0565082i | ||||
\(172\) | −7.78083 | − | 4.49227i | −0.593283 | − | 0.342532i | ||||
\(173\) | −12.8049 | + | 7.39291i | −0.973538 | + | 0.562072i | −0.900313 | − | 0.435243i | \(-0.856662\pi\) |
−0.0732248 | + | 0.997315i | \(0.523329\pi\) | |||||||
\(174\) | 7.92519i | 0.600807i | ||||||||
\(175\) | 12.4858 | + | 0.321462i | 0.943835 | + | 0.0243003i | ||||
\(176\) | − | 2.05052i | − | 0.154563i | ||||||
\(177\) | 6.20501 | + | 10.7474i | 0.466397 | + | 0.807823i | ||||
\(178\) | −3.81582 | + | 6.60920i | −0.286008 | + | 0.495381i | ||||
\(179\) | −1.69269 | + | 2.93182i | −0.126517 | + | 0.219134i | −0.922325 | − | 0.386415i | \(-0.873713\pi\) |
0.795808 | + | 0.605549i | \(0.207047\pi\) | |||||||
\(180\) | −0.426628 | − | 0.738941i | −0.0317990 | − | 0.0550774i | ||||
\(181\) | 10.2869 | 0.764622 | 0.382311 | − | 0.924034i | \(-0.375128\pi\) | ||||
0.382311 | + | 0.924034i | \(0.375128\pi\) | |||||||
\(182\) | 8.35084 | + | 5.11236i | 0.619005 | + | 0.378953i | ||||
\(183\) | − | 12.5510i | − | 0.927794i | ||||||
\(184\) | 3.94348 | + | 2.72928i | 0.290717 | + | 0.201205i | ||||
\(185\) | 3.96779 | + | 2.29080i | 0.291717 | + | 0.168423i | ||||
\(186\) | 5.31112 | − | 9.19912i | 0.389430 | − | 0.674512i | ||||
\(187\) | 12.2522 | − | 7.07381i | 0.895969 | − | 0.517288i | ||||
\(188\) | − | 1.96877i | − | 0.143588i | ||||||
\(189\) | −6.91797 | + | 3.76009i | −0.503208 | + | 0.273506i | ||||
\(190\) | 0.279263 | 0.0202599 | ||||||||
\(191\) | 3.36116 | − | 1.94057i | 0.243205 | − | 0.140414i | −0.373444 | − | 0.927653i | \(-0.621823\pi\) |
0.616649 | + | 0.787238i | \(0.288490\pi\) | |||||||
\(192\) | −1.86037 | − | 1.07408i | −0.134261 | − | 0.0775154i | ||||
\(193\) | −6.84769 | + | 11.8605i | −0.492907 | + | 0.853740i | −0.999967 | − | 0.00817078i | \(-0.997399\pi\) |
0.507059 | + | 0.861911i | \(0.330732\pi\) | |||||||
\(194\) | 5.57010 | + | 9.64769i | 0.399910 | + | 0.692664i | ||||
\(195\) | 4.20120 | 0.300854 | ||||||||
\(196\) | −3.18341 | − | 6.23425i | −0.227387 | − | 0.445304i | ||||
\(197\) | 20.4976 | 1.46039 | 0.730196 | − | 0.683238i | \(-0.239429\pi\) | ||||
0.730196 | + | 0.683238i | \(0.239429\pi\) | |||||||
\(198\) | 2.86725 | − | 1.65541i | 0.203767 | − | 0.117645i | ||||
\(199\) | 10.4428 | − | 18.0875i | 0.740272 | − | 1.28219i | −0.212099 | − | 0.977248i | \(-0.568030\pi\) |
0.952371 | − | 0.304941i | \(-0.0986368\pi\) | |||||||
\(200\) | 2.36037 | − | 4.08828i | 0.166903 | − | 0.289085i | ||||
\(201\) | 0.881293 | + | 1.52644i | 0.0621616 | + | 0.107667i | ||||
\(202\) | 2.98040i | 0.209700i | ||||||||
\(203\) | 4.66127 | + | 8.57601i | 0.327157 | + | 0.601918i | ||||
\(204\) | − | 14.8214i | − | 1.03770i | ||||||
\(205\) | −1.69370 | + | 0.977857i | −0.118293 | + | 0.0682965i | ||||
\(206\) | 0.881293 | − | 1.52644i | 0.0614026 | − | 0.106352i | ||||
\(207\) | −0.632747 | + | 7.71759i | −0.0439789 | + | 0.536409i | ||||
\(208\) | 3.20501 | − | 1.85041i | 0.222227 | − | 0.128303i | ||||
\(209\) | 1.08360i | 0.0749543i | ||||||||
\(210\) | −2.56157 | − | 1.56819i | −0.176765 | − | 0.108215i | ||||
\(211\) | −26.0807 | −1.79547 | −0.897736 | − | 0.440533i | \(-0.854789\pi\) | ||||
−0.897736 | + | 0.440533i | \(0.854789\pi\) | |||||||
\(212\) | −11.8526 | + | 6.84309i | −0.814038 | + | 0.469985i | ||||
\(213\) | −1.91889 | − | 1.10787i | −0.131480 | − | 0.0759103i | ||||
\(214\) | −7.69873 | − | 4.44487i | −0.526275 | − | 0.303845i | ||||
\(215\) | −4.11181 | + | 2.37395i | −0.280423 | + | 0.161902i | ||||
\(216\) | 2.97601i | 0.202492i | ||||||||
\(217\) | 0.336719 | − | 13.0783i | 0.0228580 | − | 0.887816i | ||||
\(218\) | 6.93402i | 0.469631i | ||||||||
\(219\) | 5.31112 | + | 9.19912i | 0.358892 | + | 0.621619i | ||||
\(220\) | −0.938427 | − | 0.541801i | −0.0632687 | − | 0.0365282i | ||||
\(221\) | 22.1131 | + | 12.7670i | 1.48749 | + | 0.858801i | ||||
\(222\) | 9.31213 | + | 16.1291i | 0.624989 | + | 1.08251i | ||||
\(223\) | 3.15541i | 0.211302i | 0.994403 | + | 0.105651i | \(0.0336926\pi\) | ||||
−0.994403 | + | 0.105651i | \(0.966307\pi\) | |||||||
\(224\) | −2.64487 | − | 0.0680958i | −0.176718 | − | 0.00454984i | ||||
\(225\) | 7.62223 | 0.508149 | ||||||||
\(226\) | −4.33757 | + | 2.50430i | −0.288531 | + | 0.166584i | ||||
\(227\) | 3.89612 | − | 6.74828i | 0.258595 | − | 0.447899i | −0.707271 | − | 0.706943i | \(-0.750074\pi\) |
0.965866 | + | 0.259043i | \(0.0834072\pi\) | |||||||
\(228\) | 0.983118 | + | 0.567604i | 0.0651086 | + | 0.0375905i | ||||
\(229\) | −2.83922 | − | 4.91767i | −0.187621 | − | 0.324969i | 0.756836 | − | 0.653605i | \(-0.226744\pi\) |
−0.944456 | + | 0.328636i | \(0.893411\pi\) | |||||||
\(230\) | 2.29104 | − | 1.08360i | 0.151067 | − | 0.0714506i | ||||
\(231\) | 6.08491 | − | 9.93947i | 0.400358 | − | 0.653969i | ||||
\(232\) | 3.68928 | 0.242213 | ||||||||
\(233\) | −14.2518 | − | 24.6849i | −0.933669 | − | 1.61716i | −0.776991 | − | 0.629512i | \(-0.783255\pi\) |
−0.156678 | − | 0.987650i | \(-0.550078\pi\) | |||||||
\(234\) | 5.17489 | + | 2.98773i | 0.338293 | + | 0.195314i | ||||
\(235\) | −0.901017 | − | 0.520202i | −0.0587759 | − | 0.0339343i | ||||
\(236\) | 5.00305 | − | 2.88851i | 0.325671 | − | 0.188026i | ||||
\(237\) | 25.6714 | 1.66754 | ||||||||
\(238\) | −8.71733 | − | 16.0385i | −0.565060 | − | 1.03962i | ||||
\(239\) | 2.10460 | 0.136135 | 0.0680676 | − | 0.997681i | \(-0.478317\pi\) | ||||
0.0680676 | + | 0.997681i | \(0.478317\pi\) | |||||||
\(240\) | −0.983118 | + | 0.567604i | −0.0634600 | + | 0.0366387i | ||||
\(241\) | −7.60361 | + | 13.1698i | −0.489792 | + | 0.848344i | −0.999931 | − | 0.0117478i | \(-0.996260\pi\) |
0.510139 | + | 0.860092i | \(0.329594\pi\) | |||||||
\(242\) | −3.39769 | + | 5.88498i | −0.218412 | + | 0.378301i | ||||
\(243\) | −13.1728 | + | 7.60532i | −0.845035 | + | 0.487881i | ||||
\(244\) | −5.84264 | −0.374036 | ||||||||
\(245\) | −3.69427 | − | 0.190354i | −0.236018 | − | 0.0121613i | ||||
\(246\) | −7.94999 | −0.506873 | ||||||||
\(247\) | −1.69370 | + | 0.977857i | −0.107767 | + | 0.0622195i | ||||
\(248\) | −4.28231 | − | 2.47239i | −0.271927 | − | 0.156997i | ||||
\(249\) | −30.6112 | − | 17.6734i | −1.93991 | − | 1.12001i | ||||
\(250\) | −2.56848 | − | 4.44874i | −0.162445 | − | 0.281363i | ||||
\(251\) | −21.0463 | −1.32843 | −0.664214 | − | 0.747543i | \(-0.731234\pi\) | ||||
−0.664214 | + | 0.747543i | \(0.731234\pi\) | |||||||
\(252\) | −2.04003 | − | 3.75333i | −0.128510 | − | 0.236437i | ||||
\(253\) | 4.20461 | + | 8.88973i | 0.264342 | + | 0.558893i | ||||
\(254\) | 1.65536 | + | 2.86717i | 0.103867 | + | 0.179902i | ||||
\(255\) | −6.78307 | − | 3.91620i | −0.424772 | − | 0.245242i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 19.3956 | − | 11.1981i | 1.20987 | − | 0.698517i | 0.247136 | − | 0.968981i | \(-0.420511\pi\) |
0.962730 | + | 0.270464i | \(0.0871772\pi\) | |||||||
\(258\) | −19.3003 | −1.20158 | ||||||||
\(259\) | 19.5633 | + | 11.9766i | 1.21561 | + | 0.744189i | ||||
\(260\) | − | 1.95571i | − | 0.121288i | ||||||
\(261\) | 2.97840 | + | 5.15875i | 0.184359 | + | 0.319319i | ||||
\(262\) | 14.1457 | + | 8.16704i | 0.873926 | + | 0.504561i | ||||
\(263\) | −8.30098 | − | 4.79257i | −0.511860 | − | 0.295523i | 0.221738 | − | 0.975106i | \(-0.428827\pi\) |
−0.733598 | + | 0.679584i | \(0.762160\pi\) | |||||||
\(264\) | −2.20243 | − | 3.81471i | −0.135550 | − | 0.234779i | ||||
\(265\) | 7.23251i | 0.444289i | ||||||||
\(266\) | 1.39769 | + | 0.0359855i | 0.0856981 | + | 0.00220641i | ||||
\(267\) | 16.3941i | 1.00330i | ||||||||
\(268\) | 0.710579 | − | 0.410253i | 0.0434055 | − | 0.0250602i | ||||
\(269\) | −14.7823 | − | 8.53457i | −0.901293 | − | 0.520362i | −0.0236738 | − | 0.999720i | \(-0.507536\pi\) |
−0.877620 | + | 0.479358i | \(0.840870\pi\) | |||||||
\(270\) | 1.36198 | + | 0.786342i | 0.0828877 | + | 0.0478553i | ||||
\(271\) | 12.9093 | − | 7.45316i | 0.784182 | − | 0.452747i | −0.0537286 | − | 0.998556i | \(-0.517111\pi\) |
0.837910 | + | 0.545808i | \(0.183777\pi\) | |||||||
\(272\) | −6.89954 | −0.418346 | ||||||||
\(273\) | 21.0267 | + | 0.541361i | 1.27260 | + | 0.0327647i | ||||
\(274\) | 9.80504i | 0.592344i | ||||||||
\(275\) | 8.38308 | − | 4.83997i | 0.505519 | − | 0.291861i | ||||
\(276\) | 10.2678 | + | 0.841833i | 0.618049 | + | 0.0506724i | ||||
\(277\) | −14.9407 | + | 25.8781i | −0.897701 | + | 1.55486i | −0.0672747 | + | 0.997734i | \(0.521430\pi\) |
−0.830426 | + | 0.557129i | \(0.811903\pi\) | |||||||
\(278\) | −15.9754 | + | 9.22340i | −0.958140 | + | 0.553183i | ||||
\(279\) | − | 7.98399i | − | 0.477989i | ||||||
\(280\) | −0.730011 | + | 1.19245i | −0.0436265 | + | 0.0712622i | ||||
\(281\) | 21.7934i | 1.30009i | 0.759897 | + | 0.650044i | \(0.225249\pi\) | ||||
−0.759897 | + | 0.650044i | \(0.774751\pi\) | |||||||
\(282\) | −2.11463 | − | 3.66264i | −0.125924 | − | 0.218107i | ||||
\(283\) | −13.3641 | + | 23.1474i | −0.794416 | + | 1.37597i | 0.128793 | + | 0.991671i | \(0.458890\pi\) |
−0.923209 | + | 0.384297i | \(0.874444\pi\) | |||||||
\(284\) | −0.515730 | + | 0.893270i | −0.0306029 | + | 0.0530058i | ||||
\(285\) | 0.519532 | − | 0.299952i | 0.0307744 | − | 0.0177676i | ||||
\(286\) | 7.58860 | 0.448723 | ||||||||
\(287\) | −8.60285 | + | 4.67586i | −0.507810 | + | 0.276007i | ||||
\(288\) | −1.61463 | −0.0951429 | ||||||||
\(289\) | −15.3018 | − | 26.5036i | −0.900108 | − | 1.55903i | ||||
\(290\) | 0.974806 | − | 1.68841i | 0.0572426 | − | 0.0991470i | ||||
\(291\) | 20.7249 | + | 11.9655i | 1.21491 | + | 0.701430i | ||||
\(292\) | 4.28231 | − | 2.47239i | 0.250603 | − | 0.144686i | ||||
\(293\) | −21.3877 | −1.24948 | −0.624741 | − | 0.780832i | \(-0.714795\pi\) | ||||
−0.624741 | + | 0.780832i | \(0.714795\pi\) | |||||||
\(294\) | −12.6184 | − | 8.17875i | −0.735922 | − | 0.476994i | ||||
\(295\) | − | 3.05289i | − | 0.177746i | ||||||
\(296\) | 7.50830 | − | 4.33492i | 0.436411 | − | 0.251962i | ||||
\(297\) | −3.05118 | + | 5.28480i | −0.177047 | + | 0.306655i | ||||
\(298\) | −3.55160 | − | 2.05052i | −0.205738 | − | 0.118783i | ||||
\(299\) | −10.1006 | + | 14.5941i | −0.584131 | + | 0.844000i | ||||
\(300\) | − | 10.1409i | − | 0.585487i | ||||||
\(301\) | −20.8852 | + | 11.3516i | −1.20381 | + | 0.654298i | ||||
\(302\) | 1.77074 | 0.101895 | ||||||||
\(303\) | 3.20120 | + | 5.54465i | 0.183904 | + | 0.318532i | ||||
\(304\) | 0.264227 | − | 0.457654i | 0.0151544 | − | 0.0262483i | ||||
\(305\) | −1.54378 | + | 2.67391i | −0.0883966 | + | 0.153107i | ||||
\(306\) | −5.57010 | − | 9.64769i | −0.318421 | − | 0.551522i | ||||
\(307\) | 2.16565i | 0.123600i | 0.998089 | + | 0.0618001i | \(0.0196841\pi\) | ||||
−0.998089 | + | 0.0618001i | \(0.980316\pi\) | |||||||
\(308\) | −4.62695 | − | 2.83260i | −0.263645 | − | 0.161403i | ||||
\(309\) | − | 3.78633i | − | 0.215397i | ||||||
\(310\) | −2.26300 | + | 1.30654i | −0.128530 | + | 0.0742067i | ||||
\(311\) | 16.2365 | + | 9.37413i | 0.920686 | + | 0.531558i | 0.883854 | − | 0.467763i | \(-0.154940\pi\) |
0.0368318 | + | 0.999321i | \(0.488273\pi\) | |||||||
\(312\) | 3.97500 | − | 6.88490i | 0.225040 | − | 0.389780i | ||||
\(313\) | 15.6552 | + | 27.1156i | 0.884883 | + | 1.53266i | 0.845847 | + | 0.533425i | \(0.179095\pi\) |
0.0390359 | + | 0.999238i | \(0.487571\pi\) | |||||||
\(314\) | 7.46744 | 0.421412 | ||||||||
\(315\) | −2.25675 | − | 0.0581031i | −0.127154 | − | 0.00327374i | ||||
\(316\) | − | 11.9504i | − | 0.672260i | ||||||
\(317\) | −14.3234 | − | 24.8089i | −0.804484 | − | 1.39341i | −0.916639 | − | 0.399717i | \(-0.869108\pi\) |
0.112154 | − | 0.993691i | \(-0.464225\pi\) | |||||||
\(318\) | −14.7001 | + | 25.4613i | −0.824341 | + | 1.42780i | ||||
\(319\) | 6.55141 | + | 3.78246i | 0.366809 | + | 0.211777i | ||||
\(320\) | 0.264227 | + | 0.457654i | 0.0147707 | + | 0.0255836i | ||||
\(321\) | −19.0966 | −1.06587 | ||||||||
\(322\) | 11.6061 | − | 5.12814i | 0.646784 | − | 0.285780i | ||||
\(323\) | 3.64609 | 0.202874 | ||||||||
\(324\) | 5.61843 | + | 9.73141i | 0.312135 | + | 0.540634i | ||||
\(325\) | 15.1300 | + | 8.73531i | 0.839261 | + | 0.484548i | ||||
\(326\) | 2.80731 | − | 4.86241i | 0.155483 | − | 0.269304i | ||||
\(327\) | 7.44772 | + | 12.8998i | 0.411860 | + | 0.713362i | ||||
\(328\) | 3.70082i | 0.204344i | ||||||||
\(329\) | −4.44250 | − | 2.71968i | −0.244923 | − | 0.149941i | ||||
\(330\) | −2.32776 | −0.128139 | ||||||||
\(331\) | −13.6550 | − | 23.6512i | −0.750547 | − | 1.29998i | −0.947558 | − | 0.319584i | \(-0.896457\pi\) |
0.197011 | − | 0.980401i | \(-0.436876\pi\) | |||||||
\(332\) | −8.22719 | + | 14.2499i | −0.451526 | + | 0.782065i | ||||
\(333\) | 12.1231 | + | 6.99928i | 0.664342 | + | 0.383558i | ||||
\(334\) | −4.03146 | + | 2.32756i | −0.220592 | + | 0.127359i | ||||
\(335\) | − | 0.433599i | − | 0.0236901i | ||||||
\(336\) | −4.99358 | + | 2.71414i | −0.272422 | + | 0.148068i | ||||
\(337\) | − | 3.09092i | − | 0.168373i | −0.996450 | − | 0.0841866i | \(-0.973171\pi\) | ||
0.996450 | − | 0.0841866i | \(-0.0268292\pi\) | |||||||
\(338\) | 0.348047 | + | 0.602836i | 0.0189313 | + | 0.0327899i | ||||
\(339\) | −5.37966 | + | 9.31784i | −0.292183 | + | 0.506076i | ||||
\(340\) | −1.82304 | + | 3.15760i | −0.0988684 | + | 0.171245i | ||||
\(341\) | −5.06968 | − | 8.78094i | −0.274539 | − | 0.475515i | ||||
\(342\) | 0.853256 | 0.0461388 | ||||||||
\(343\) | −18.4651 | − | 1.42875i | −0.997020 | − | 0.0771452i | ||||
\(344\) | 8.98453i | 0.484414i | ||||||||
\(345\) | 3.09830 | − | 4.47667i | 0.166807 | − | 0.241016i | ||||
\(346\) | 12.8049 | + | 7.39291i | 0.688395 | + | 0.397445i | ||||
\(347\) | 2.72415 | − | 4.71836i | 0.146240 | − | 0.253295i | −0.783595 | − | 0.621272i | \(-0.786616\pi\) |
0.929835 | + | 0.367977i | \(0.119950\pi\) | |||||||
\(348\) | 6.86342 | − | 3.96259i | 0.367918 | − | 0.212417i | ||||
\(349\) | 7.05311i | 0.377544i | 0.982021 | + | 0.188772i | \(0.0604508\pi\) | ||||
−0.982021 | + | 0.188772i | \(0.939549\pi\) | |||||||
\(350\) | −5.96448 | − | 10.9737i | −0.318815 | − | 0.586570i | ||||
\(351\) | −11.0137 | −0.587868 | ||||||||
\(352\) | −1.77580 | + | 1.02526i | −0.0946504 | + | 0.0546464i | ||||
\(353\) | 7.67718 | + | 4.43242i | 0.408615 | + | 0.235914i | 0.690195 | − | 0.723624i | \(-0.257525\pi\) |
−0.281579 | + | 0.959538i | \(0.590858\pi\) | |||||||
\(354\) | 6.20501 | − | 10.7474i | 0.329792 | − | 0.571217i | ||||
\(355\) | 0.272539 | + | 0.472052i | 0.0144649 | + | 0.0250539i | ||||
\(356\) | 7.63165 | 0.404476 | ||||||||
\(357\) | −33.4442 | − | 20.4744i | −1.77005 | − | 1.08362i | ||||
\(358\) | 3.38537 | 0.178922 | ||||||||
\(359\) | 8.33391 | − | 4.81159i | 0.439847 | − | 0.253946i | −0.263686 | − | 0.964609i | \(-0.584938\pi\) |
0.703533 | + | 0.710663i | \(0.251605\pi\) | |||||||
\(360\) | −0.426628 | + | 0.738941i | −0.0224853 | + | 0.0389456i | ||||
\(361\) | 9.36037 | − | 16.2126i | 0.492651 | − | 0.853297i | ||||
\(362\) | −5.14347 | − | 8.90875i | −0.270335 | − | 0.468233i | ||||
\(363\) | 14.5976i | 0.766177i | ||||||||
\(364\) | 0.252011 | − | 9.78822i | 0.0132089 | − | 0.513042i | ||||
\(365\) | − | 2.61309i | − | 0.136775i | ||||||
\(366\) | −10.8695 | + | 6.27548i | −0.568155 | + | 0.328025i | ||||
\(367\) | 12.1036 | − | 20.9640i | 0.631802 | − | 1.09431i | −0.355381 | − | 0.934722i | \(-0.615649\pi\) |
0.987183 | − | 0.159592i | \(-0.0510178\pi\) | |||||||
\(368\) | 0.391884 | − | 4.77979i | 0.0204284 | − | 0.249164i | ||||
\(369\) | −5.17489 | + | 2.98773i | −0.269394 | + | 0.155535i | ||||
\(370\) | − | 4.58160i | − | 0.238186i | ||||||
\(371\) | −0.931971 | + | 36.1982i | −0.0483855 | + | 1.87932i | ||||
\(372\) | −10.6222 | −0.550737 | ||||||||
\(373\) | 0.0491634 | − | 0.0283845i | 0.00254558 | − | 0.00146969i | −0.498727 | − | 0.866759i | \(-0.666199\pi\) |
0.501272 | + | 0.865290i | \(0.332866\pi\) | |||||||
\(374\) | −12.2522 | − | 7.07381i | −0.633546 | − | 0.365778i | ||||
\(375\) | −9.55663 | − | 5.51752i | −0.493502 | − | 0.284924i | ||||
\(376\) | −1.70501 | + | 0.984386i | −0.0879290 | + | 0.0507659i | ||||
\(377\) | 13.6534i | 0.703184i | ||||||||
\(378\) | 6.71532 | + | 4.11109i | 0.345399 | + | 0.211452i | ||||
\(379\) | − | 20.4003i | − | 1.04789i | −0.851751 | − | 0.523946i | \(-0.824459\pi\) | ||
0.851751 | − | 0.523946i | \(-0.175541\pi\) | |||||||
\(380\) | −0.139632 | − | 0.241849i | −0.00716295 | − | 0.0124066i | ||||
\(381\) | 6.15916 | + | 3.55599i | 0.315544 | + | 0.182179i | ||||
\(382\) | −3.36116 | − | 1.94057i | −0.171972 | − | 0.0992880i | ||||
\(383\) | −6.47291 | − | 11.2114i | −0.330750 | − | 0.572877i | 0.651909 | − | 0.758297i | \(-0.273969\pi\) |
−0.982659 | + | 0.185421i | \(0.940635\pi\) | |||||||
\(384\) | 2.14817i | 0.109623i | ||||||||
\(385\) | −2.51892 | + | 1.36909i | −0.128376 | + | 0.0697754i | ||||
\(386\) | 13.6954 | 0.697076 | ||||||||
\(387\) | −12.5632 | + | 7.25334i | −0.638621 | + | 0.368708i | ||||
\(388\) | 5.57010 | − | 9.64769i | 0.282779 | − | 0.489787i | ||||
\(389\) | −30.9988 | − | 17.8972i | −1.57170 | − | 0.907422i | −0.995961 | − | 0.0897885i | \(-0.971381\pi\) |
−0.575740 | − | 0.817633i | \(-0.695286\pi\) | |||||||
\(390\) | −2.10060 | − | 3.63835i | −0.106368 | − | 0.184235i | ||||
\(391\) | 29.9120 | − | 14.1476i | 1.51272 | − | 0.715476i | ||||
\(392\) | −3.80731 | + | 5.87404i | −0.192298 | + | 0.296684i | ||||
\(393\) | 35.0883 | 1.76997 | ||||||||
\(394\) | −10.2488 | − | 17.7514i | −0.516326 | − | 0.894304i | ||||
\(395\) | −5.46913 | − | 3.15760i | −0.275182 | − | 0.158876i | ||||
\(396\) | −2.86725 | − | 1.65541i | −0.144085 | − | 0.0831875i | ||||
\(397\) | 18.9349 | − | 10.9321i | 0.950315 | − | 0.548664i | 0.0571360 | − | 0.998366i | \(-0.481803\pi\) |
0.893179 | + | 0.449702i | \(0.148470\pi\) | |||||||
\(398\) | −20.8857 | −1.04690 | ||||||||
\(399\) | 2.63888 | − | 1.43429i | 0.132109 | − | 0.0718045i | ||||
\(400\) | −4.72074 | −0.236037 | ||||||||
\(401\) | 15.0987 | − | 8.71723i | 0.753993 | − | 0.435318i | −0.0731420 | − | 0.997322i | \(-0.523303\pi\) |
0.827135 | + | 0.562004i | \(0.189969\pi\) | |||||||
\(402\) | 0.881293 | − | 1.52644i | 0.0439549 | − | 0.0761321i | ||||
\(403\) | 9.14989 | − | 15.8481i | 0.455788 | − | 0.789449i | ||||
\(404\) | 2.58111 | − | 1.49020i | 0.128415 | − | 0.0741403i | ||||
\(405\) | 5.93816 | 0.295069 | ||||||||
\(406\) | 5.09641 | − | 8.32478i | 0.252930 | − | 0.413152i | ||||
\(407\) | 17.7776 | 0.881204 | ||||||||
\(408\) | −12.8357 | + | 7.41069i | −0.635461 | + | 0.366884i | ||||
\(409\) | 28.6772 | + | 16.5568i | 1.41800 | + | 0.818680i | 0.996123 | − | 0.0879749i | \(-0.0280395\pi\) |
0.421873 | + | 0.906655i | \(0.361373\pi\) | |||||||
\(410\) | 1.69370 | + | 0.977857i | 0.0836457 | + | 0.0482929i | ||||
\(411\) | 10.5314 | + | 18.2410i | 0.519478 | + | 0.899762i | ||||
\(412\) | −1.76259 | −0.0868363 | ||||||||
\(413\) | 0.393391 | − | 15.2795i | 0.0193575 | − | 0.751855i | ||||
\(414\) | 7.00000 | − | 3.31082i | 0.344031 | − | 0.162718i | ||||
\(415\) | 4.34769 | + | 7.53041i | 0.213419 | + | 0.369653i | ||||
\(416\) | −3.20501 | − | 1.85041i | −0.157138 | − | 0.0907239i | ||||
\(417\) | −19.8134 | + | 34.3178i | −0.970267 | + | 1.68055i | ||||
\(418\) | 0.938427 | − | 0.541801i | 0.0459000 | − | 0.0265004i | ||||
\(419\) | 22.9995 | 1.12360 | 0.561799 | − | 0.827274i | \(-0.310110\pi\) | ||||
0.561799 | + | 0.827274i | \(0.310110\pi\) | |||||||
\(420\) | −0.0773029 | + | 3.00248i | −0.00377199 | + | 0.146506i | ||||
\(421\) | 13.9931i | 0.681984i | 0.940066 | + | 0.340992i | \(0.110763\pi\) | ||||
−0.940066 | + | 0.340992i | \(0.889237\pi\) | |||||||
\(422\) | 13.0404 | + | 22.5866i | 0.634795 | + | 1.09950i | ||||
\(423\) | −2.75295 | − | 1.58942i | −0.133853 | − | 0.0772801i | ||||
\(424\) | 11.8526 | + | 6.84309i | 0.575612 | + | 0.332330i | ||||
\(425\) | −16.2855 | − | 28.2072i | −0.789961 | − | 1.36825i | ||||
\(426\) | 2.21575i | 0.107353i | ||||||||
\(427\) | −8.07108 | + | 13.1838i | −0.390587 | + | 0.638009i | ||||
\(428\) | 8.88973i | 0.429701i | ||||||||
\(429\) | 14.1176 | − | 8.15079i | 0.681603 | − | 0.393524i | ||||
\(430\) | 4.11181 | + | 2.37395i | 0.198289 | + | 0.114482i | ||||
\(431\) | −13.0194 | − | 7.51677i | −0.627124 | − | 0.362070i | 0.152514 | − | 0.988301i | \(-0.451263\pi\) |
−0.779637 | + | 0.626231i | \(0.784597\pi\) | |||||||
\(432\) | 2.57730 | − | 1.48801i | 0.124001 | − | 0.0715917i | ||||
\(433\) | 8.50153 | 0.408557 | 0.204279 | − | 0.978913i | \(-0.434515\pi\) | ||||
0.204279 | + | 0.978913i | \(0.434515\pi\) | |||||||
\(434\) | −11.4945 | + | 6.24756i | −0.551755 | + | 0.299893i | ||||
\(435\) | − | 4.18809i | − | 0.200804i | ||||||
\(436\) | 6.00504 | − | 3.46701i | 0.287589 | − | 0.166040i | ||||
\(437\) | −0.207092 | + | 2.52590i | −0.00990657 | + | 0.120830i | ||||
\(438\) | 5.31112 | − | 9.19912i | 0.253775 | − | 0.439551i | ||||
\(439\) | 1.54965 | − | 0.894688i | 0.0739606 | − | 0.0427012i | −0.462564 | − | 0.886586i | \(-0.653070\pi\) |
0.536524 | + | 0.843885i | \(0.319737\pi\) | |||||||
\(440\) | 1.08360i | 0.0516587i | ||||||||
\(441\) | −11.2874 | − | 0.581605i | −0.537496 | − | 0.0276955i | ||||
\(442\) | − | 25.5340i | − | 1.21453i | ||||||
\(443\) | −7.21146 | − | 12.4906i | −0.342627 | − | 0.593447i | 0.642293 | − | 0.766459i | \(-0.277983\pi\) |
−0.984920 | + | 0.173012i | \(0.944650\pi\) | |||||||
\(444\) | 9.31213 | − | 16.1291i | 0.441934 | − | 0.765452i | ||||
\(445\) | 2.01649 | − | 3.49265i | 0.0955906 | − | 0.165568i | ||||
\(446\) | 2.73266 | − | 1.57770i | 0.129395 | − | 0.0747065i | ||||
\(447\) | −8.80970 | −0.416685 | ||||||||
\(448\) | 1.26346 | + | 2.32458i | 0.0596931 | + | 0.109826i | ||||
\(449\) | 9.65218 | 0.455515 | 0.227757 | − | 0.973718i | \(-0.426861\pi\) | ||||
0.227757 | + | 0.973718i | \(0.426861\pi\) | |||||||
\(450\) | −3.81112 | − | 6.60105i | −0.179658 | − | 0.311176i | ||||
\(451\) | −3.79430 | + | 6.57192i | −0.178667 | + | 0.309459i | ||||
\(452\) | 4.33757 | + | 2.50430i | 0.204022 | + | 0.117792i | ||||
\(453\) | 3.29424 | − | 1.90193i | 0.154777 | − | 0.0893604i | ||||
\(454\) | −7.79225 | −0.365708 | ||||||||
\(455\) | −4.41303 | − | 2.70164i | −0.206886 | − | 0.126655i | ||||
\(456\) | − | 1.13521i | − | 0.0531609i | ||||||
\(457\) | 31.2955 | − | 18.0685i | 1.46394 | − | 0.845208i | 0.464753 | − | 0.885440i | \(-0.346143\pi\) |
0.999190 | + | 0.0402319i | \(0.0128097\pi\) | |||||||
\(458\) | −2.83922 | + | 4.91767i | −0.132668 | + | 0.229787i | ||||
\(459\) | 17.7822 | + | 10.2666i | 0.830002 | + | 0.479202i | ||||
\(460\) | −2.08395 | − | 1.44230i | −0.0971645 | − | 0.0672474i | ||||
\(461\) | − | 27.5367i | − | 1.28251i | −0.767326 | − | 0.641257i | \(-0.778413\pi\) | ||
0.767326 | − | 0.641257i | \(-0.221587\pi\) | |||||||
\(462\) | −11.6503 | − | 0.299952i | −0.542020 | − | 0.0139550i | ||||
\(463\) | −0.186065 | −0.00864718 | −0.00432359 | − | 0.999991i | \(-0.501376\pi\) | ||||
−0.00432359 | + | 0.999991i | \(0.501376\pi\) | |||||||
\(464\) | −1.84464 | − | 3.19501i | −0.0856352 | − | 0.148325i | ||||
\(465\) | −2.80668 | + | 4.86131i | −0.130157 | + | 0.225438i | ||||
\(466\) | −14.2518 | + | 24.6849i | −0.660203 | + | 1.14351i | ||||
\(467\) | 8.66213 | + | 15.0032i | 0.400835 | + | 0.694267i | 0.993827 | − | 0.110941i | \(-0.0353866\pi\) |
−0.592992 | + | 0.805209i | \(0.702053\pi\) | |||||||
\(468\) | − | 5.97545i | − | 0.276215i | ||||||
\(469\) | 0.0558730 | − | 2.17014i | 0.00257998 | − | 0.100208i | ||||
\(470\) | 1.04040i | 0.0479903i | ||||||||
\(471\) | 13.8922 | − | 8.02066i | 0.640119 | − | 0.369573i | ||||
\(472\) | −5.00305 | − | 2.88851i | −0.230284 | − | 0.132954i | ||||
\(473\) | −9.21146 | + | 15.9547i | −0.423544 | + | 0.733599i | ||||
\(474\) | −12.8357 | − | 22.2321i | −0.589563 | − | 1.02115i | ||||
\(475\) | 2.49469 | 0.114464 | ||||||||
\(476\) | −9.53110 | + | 15.5687i | −0.436857 | + | 0.713590i | ||||
\(477\) | 22.0981i | 1.01180i | ||||||||
\(478\) | −1.05230 | − | 1.82264i | −0.0481310 | − | 0.0833654i | ||||
\(479\) | 16.1836 | − | 28.0309i | 0.739449 | − | 1.28076i | −0.213294 | − | 0.976988i | \(-0.568419\pi\) |
0.952744 | − | 0.303776i | \(-0.0982473\pi\) | |||||||
\(480\) | 0.983118 | + | 0.567604i | 0.0448730 | + | 0.0259074i | ||||
\(481\) | 16.0428 | + | 27.7869i | 0.731487 | + | 1.26697i | ||||
\(482\) | 15.2072 | 0.692670 | ||||||||
\(483\) | 16.0836 | − | 22.0062i | 0.731830 | − | 1.00132i | ||||
\(484\) | 6.79539 | 0.308881 | ||||||||
\(485\) | −2.94354 | − | 5.09836i | −0.133659 | − | 0.231504i | ||||
\(486\) | 13.1728 | + | 7.60532i | 0.597530 | + | 0.344984i | ||||
\(487\) | −15.0010 | + | 25.9825i | −0.679759 | + | 1.17738i | 0.295294 | + | 0.955407i | \(0.404583\pi\) |
−0.975053 | + | 0.221971i | \(0.928751\pi\) | |||||||
\(488\) | 2.92132 | + | 5.05987i | 0.132242 | + | 0.229050i | ||||
\(489\) | − | 12.0612i | − | 0.545425i | ||||||
\(490\) | 1.68229 | + | 3.29451i | 0.0759979 | + | 0.148831i | ||||
\(491\) | −11.9761 | −0.540476 | −0.270238 | − | 0.962794i | \(-0.587102\pi\) | ||||
−0.270238 | + | 0.962794i | \(0.587102\pi\) | |||||||
\(492\) | 3.97500 | + | 6.88490i | 0.179207 | + | 0.310395i | ||||
\(493\) | 12.7272 | − | 22.0441i | 0.573203 | − | 0.992816i | ||||
\(494\) | 1.69370 | + | 0.977857i | 0.0762030 | + | 0.0439958i | ||||
\(495\) | −1.51521 | + | 0.874807i | −0.0681036 | + | 0.0393196i | ||||
\(496\) | 4.94479i | 0.222027i | ||||||||
\(497\) | 1.30321 | + | 2.39771i | 0.0584571 | + | 0.107552i | ||||
\(498\) | 35.3468i | 1.58393i | ||||||||
\(499\) | 20.1372 | + | 34.8787i | 0.901465 | + | 1.56138i | 0.825593 | + | 0.564266i | \(0.190841\pi\) |
0.0758721 | + | 0.997118i | \(0.475826\pi\) | |||||||
\(500\) | −2.56848 | + | 4.44874i | −0.114866 | + | 0.198953i | ||||
\(501\) | −5.00000 | + | 8.66025i | −0.223384 | + | 0.386912i | ||||
\(502\) | 10.5231 | + | 18.2266i | 0.469670 | + | 0.813493i | ||||
\(503\) | 19.6812 | 0.877540 | 0.438770 | − | 0.898599i | \(-0.355414\pi\) | ||||
0.438770 | + | 0.898599i | \(0.355414\pi\) | |||||||
\(504\) | −2.23046 | + | 3.64338i | −0.0993527 | + | 0.162289i | ||||
\(505\) | − | 1.57500i | − | 0.0700868i | ||||||
\(506\) | 5.59643 | − | 8.08617i | 0.248792 | − | 0.359474i | ||||
\(507\) | 1.29499 | + | 0.747664i | 0.0575126 | + | 0.0332049i | ||||
\(508\) | 1.65536 | − | 2.86717i | 0.0734448 | − | 0.127210i | ||||
\(509\) | 25.0722 | − | 14.4755i | 1.11131 | − | 0.641613i | 0.172139 | − | 0.985073i | \(-0.444932\pi\) |
0.939168 | + | 0.343459i | \(0.111599\pi\) | |||||||
\(510\) | 7.83241i | 0.346825i | ||||||||
\(511\) | 0.336719 | − | 13.0783i | 0.0148956 | − | 0.578552i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.36198 | + | 0.786342i | −0.0601331 | + | 0.0347179i | ||||
\(514\) | −19.3956 | − | 11.1981i | −0.855505 | − | 0.493926i | ||||
\(515\) | −0.465722 | + | 0.806654i | −0.0205222 | + | 0.0355454i | ||||
\(516\) | 9.65015 | + | 16.7145i | 0.424824 | + | 0.735817i | ||||
\(517\) | −4.03700 | −0.177547 | ||||||||
\(518\) | 0.590379 | − | 22.9306i | 0.0259398 | − | 1.00751i | ||||
\(519\) | 31.7624 | 1.39422 | ||||||||
\(520\) | −1.69370 | + | 0.977857i | −0.0742735 | + | 0.0428818i | ||||
\(521\) | −14.5786 | + | 25.2508i | −0.638698 | + | 1.10626i | 0.347021 | + | 0.937857i | \(0.387193\pi\) |
−0.985719 | + | 0.168400i | \(0.946140\pi\) | |||||||
\(522\) | 2.97840 | − | 5.15875i | 0.130361 | − | 0.225792i | ||||
\(523\) | −8.36986 | − | 14.4970i | −0.365989 | − | 0.633911i | 0.622946 | − | 0.782265i | \(-0.285936\pi\) |
−0.988934 | + | 0.148354i | \(0.952602\pi\) | |||||||
\(524\) | − | 16.3341i | − | 0.713557i | ||||||
\(525\) | −22.8828 | − | 14.0088i | −0.998689 | − | 0.611394i | ||||
\(526\) | 9.58514i | 0.417932i | ||||||||
\(527\) | −29.5460 | + | 17.0584i | −1.28704 | + | 0.743075i | ||||
\(528\) | −2.20243 | + | 3.81471i | −0.0958483 | + | 0.166014i | ||||
\(529\) | 8.10208 | + | 21.5257i | 0.352264 | + | 0.935901i | ||||
\(530\) | 6.26353 | − | 3.61625i | 0.272071 | − | 0.157080i | ||||
\(531\) | − | 9.32774i | − | 0.404789i | ||||||
\(532\) | −0.667682 | − | 1.22843i | −0.0289477 | − | 0.0532592i | ||||
\(533\) | −13.6961 | −0.593244 | ||||||||
\(534\) | 14.1977 | − | 8.19703i | 0.614394 | − | 0.354720i | ||||
\(535\) | 4.06842 | + | 2.34890i | 0.175893 | + | 0.101552i | ||||
\(536\) | −0.710579 | − | 0.410253i | −0.0306923 | − | 0.0177202i | ||||
\(537\) | 6.29804 | − | 3.63617i | 0.271780 | − | 0.156913i | ||||
\(538\) | 17.0691i | 0.735903i | ||||||||
\(539\) | −12.7834 | + | 6.52764i | −0.550621 | + | 0.281165i | ||||
\(540\) | − | 1.57268i | − | 0.0676776i | ||||||
\(541\) | 13.9445 | + | 24.1526i | 0.599522 | + | 1.03840i | 0.992892 | + | 0.119022i | \(0.0379759\pi\) |
−0.393370 | + | 0.919380i | \(0.628691\pi\) | |||||||
\(542\) | −12.9093 | − | 7.45316i | −0.554500 | − | 0.320141i | ||||
\(543\) | −19.1375 | − | 11.0490i | −0.821268 | − | 0.474160i | ||||
\(544\) | 3.44977 | + | 5.97518i | 0.147908 | + | 0.256184i | ||||
\(545\) | − | 3.66431i | − | 0.156962i | ||||||
\(546\) | −10.0445 | − | 18.4804i | −0.429866 | − | 0.790887i | ||||
\(547\) | −29.2861 | −1.25219 | −0.626093 | − | 0.779749i | \(-0.715347\pi\) | ||||
−0.626093 | + | 0.779749i | \(0.715347\pi\) | |||||||
\(548\) | 8.49141 | − | 4.90252i | 0.362735 | − | 0.209425i | ||||
\(549\) | −4.71684 | + | 8.16981i | −0.201310 | + | 0.348679i | ||||
\(550\) | −8.38308 | − | 4.83997i | −0.357456 | − | 0.206377i | ||||
\(551\) | 0.974806 | + | 1.68841i | 0.0415281 | + | 0.0719288i | ||||
\(552\) | −4.40485 | − | 9.31309i | −0.187483 | − | 0.396392i | ||||
\(553\) | −26.9658 | − | 16.5083i | −1.14670 | − | 0.702006i | ||||
\(554\) | 29.8814 | 1.26954 | ||||||||
\(555\) | −4.92103 | − | 8.52347i | −0.208886 | − | 0.361801i | ||||
\(556\) | 15.9754 | + | 9.22340i | 0.677507 | + | 0.391159i | ||||
\(557\) | −22.9683 | − | 13.2608i | −0.973199 | − | 0.561877i | −0.0729893 | − | 0.997333i | \(-0.523254\pi\) |
−0.900210 | + | 0.435456i | \(0.856587\pi\) | |||||||
\(558\) | −6.91434 | + | 3.99199i | −0.292707 | + | 0.168995i | ||||
\(559\) | −33.2502 | −1.40633 | ||||||||
\(560\) | 1.39769 | + | 0.0359855i | 0.0590633 | + | 0.00152066i | ||||
\(561\) | −30.3915 | −1.28313 | ||||||||
\(562\) | 18.8737 | − | 10.8967i | 0.796138 | − | 0.459650i | ||||
\(563\) | 11.2503 | − | 19.4861i | 0.474145 | − | 0.821243i | −0.525417 | − | 0.850845i | \(-0.676091\pi\) |
0.999562 | + | 0.0296019i | \(0.00942395\pi\) | |||||||
\(564\) | −2.11463 | + | 3.66264i | −0.0890419 | + | 0.154225i | ||||
\(565\) | 2.29221 | − | 1.32341i | 0.0964339 | − | 0.0556761i | ||||
\(566\) | 26.7283 | 1.12347 | ||||||||
\(567\) | 29.7201 | + | 0.765183i | 1.24813 | + | 0.0321347i | ||||
\(568\) | 1.03146 | 0.0432791 | ||||||||
\(569\) | −39.9445 | + | 23.0619i | −1.67456 | + | 0.966807i | −0.709525 | + | 0.704680i | \(0.751091\pi\) |
−0.965033 | + | 0.262127i | \(0.915576\pi\) | |||||||
\(570\) | −0.519532 | − | 0.299952i | −0.0217608 | − | 0.0125636i | ||||
\(571\) | 8.35014 | + | 4.82096i | 0.349442 | + | 0.201751i | 0.664440 | − | 0.747342i | \(-0.268670\pi\) |
−0.314997 | + | 0.949093i | \(0.602004\pi\) | |||||||
\(572\) | −3.79430 | − | 6.57192i | −0.158648 | − | 0.274786i | ||||
\(573\) | −8.33733 | −0.348297 | ||||||||
\(574\) | 8.35084 | + | 5.11236i | 0.348557 | + | 0.213386i | ||||
\(575\) | 20.4661 | − | 9.67994i | 0.853496 | − | 0.403682i | ||||
\(576\) | 0.807314 | + | 1.39831i | 0.0336381 | + | 0.0582629i | ||||
\(577\) | −5.57577 | − | 3.21917i | −0.232122 | − | 0.134016i | 0.379428 | − | 0.925221i | \(-0.376121\pi\) |
−0.611551 | + | 0.791205i | \(0.709454\pi\) | |||||||
\(578\) | −15.3018 | + | 26.5036i | −0.636473 | + | 1.10240i | ||||
\(579\) | 25.4784 | − | 14.7100i | 1.05885 | − | 0.611326i | ||||
\(580\) | −1.94961 | −0.0809532 | ||||||||
\(581\) | 20.7895 | + | 38.2495i | 0.862495 | + | 1.58685i | ||||
\(582\) | − | 23.9310i | − | 0.991972i | ||||||
\(583\) | 14.0319 | + | 24.3039i | 0.581140 | + | 1.00656i | ||||
\(584\) | −4.28231 | − | 2.47239i | −0.177203 | − | 0.102308i | ||||
\(585\) | −2.73469 | − | 1.57887i | −0.113066 | − | 0.0652784i | ||||
\(586\) | 10.6938 | + | 18.5223i | 0.441758 | + | 0.765148i | ||||
\(587\) | − | 23.4844i | − | 0.969303i | −0.874707 | − | 0.484652i | \(-0.838946\pi\) | ||
0.874707 | − | 0.484652i | \(-0.161054\pi\) | |||||||
\(588\) | −0.773792 | + | 15.0173i | −0.0319106 | + | 0.619301i | ||||
\(589\) | − | 2.61309i | − | 0.107670i | ||||||
\(590\) | −2.64388 | + | 1.52644i | −0.108847 | + | 0.0628427i | ||||
\(591\) | −38.1330 | − | 22.0161i | −1.56858 | − | 0.905622i | ||||
\(592\) | −7.50830 | − | 4.33492i | −0.308589 | − | 0.178164i | ||||
\(593\) | −4.62619 | + | 2.67093i | −0.189975 | + | 0.109682i | −0.591971 | − | 0.805959i | \(-0.701650\pi\) |
0.401996 | + | 0.915641i | \(0.368317\pi\) | |||||||
\(594\) | 6.10236 | 0.250383 | ||||||||
\(595\) | 4.60670 | + | 8.47561i | 0.188856 | + | 0.347466i | ||||
\(596\) | 4.10103i | 0.167985i | ||||||||
\(597\) | −38.8550 | + | 22.4330i | −1.59023 | + | 0.918120i | ||||
\(598\) | 17.6892 | + | 1.45029i | 0.723364 | + | 0.0593069i | ||||
\(599\) | −7.02881 | + | 12.1742i | −0.287189 | + | 0.497426i | −0.973138 | − | 0.230224i | \(-0.926054\pi\) |
0.685948 | + | 0.727650i | \(0.259388\pi\) | |||||||
\(600\) | −8.78231 | + | 5.07047i | −0.358536 | + | 0.207001i | ||||
\(601\) | − | 13.0270i | − | 0.531383i | −0.964058 | − | 0.265691i | \(-0.914400\pi\) | ||
0.964058 | − | 0.265691i | \(-0.0856002\pi\) | |||||||
\(602\) | 20.2734 | + | 12.4113i | 0.826283 | + | 0.505848i | ||||
\(603\) | − | 1.32481i | − | 0.0539505i | ||||||
\(604\) | −0.885372 | − | 1.53351i | −0.0360253 | − | 0.0623976i | ||||
\(605\) | 1.79552 | − | 3.10994i | 0.0729984 | − | 0.126437i | ||||
\(606\) | 3.20120 | − | 5.54465i | 0.130040 | − | 0.225236i | ||||
\(607\) | 34.3614 | − | 19.8386i | 1.39469 | − | 0.805222i | 0.400856 | − | 0.916141i | \(-0.368713\pi\) |
0.993829 | + | 0.110919i | \(0.0353794\pi\) | |||||||
\(608\) | −0.528453 | −0.0214316 | ||||||||
\(609\) | 0.539672 | − | 20.9611i | 0.0218686 | − | 0.849388i | ||||
\(610\) | 3.08756 | 0.125012 | ||||||||
\(611\) | −3.64304 | − | 6.30993i | −0.147382 | − | 0.255272i | ||||
\(612\) | −5.57010 | + | 9.64769i | −0.225158 | + | 0.389985i | ||||
\(613\) | −22.8371 | − | 13.1850i | −0.922380 | − | 0.532537i | −0.0379867 | − | 0.999278i | \(-0.512094\pi\) |
−0.884394 | + | 0.466742i | \(0.845428\pi\) | |||||||
\(614\) | 1.87551 | − | 1.08283i | 0.0756893 | − | 0.0436993i | ||||
\(615\) | 4.20120 | 0.169409 | ||||||||
\(616\) | −0.139632 | + | 5.42336i | −0.00562592 | + | 0.218513i | ||||
\(617\) | 10.7491i | 0.432744i | 0.976311 | + | 0.216372i | \(0.0694224\pi\) | ||||
−0.976311 | + | 0.216372i | \(0.930578\pi\) | |||||||
\(618\) | −3.27906 | + | 1.89316i | −0.131903 | + | 0.0761543i | ||||
\(619\) | −17.9379 | + | 31.0694i | −0.720985 | + | 1.24878i | 0.239620 | + | 0.970867i | \(0.422977\pi\) |
−0.960605 | + | 0.277917i | \(0.910356\pi\) | |||||||
\(620\) | 2.26300 | + | 1.30654i | 0.0908843 | + | 0.0524721i | ||||
\(621\) | −8.12237 | + | 11.7358i | −0.325939 | + | 0.470943i | ||||
\(622\) | − | 18.7483i | − | 0.751737i | ||||||
\(623\) | 10.5424 | − | 17.2207i | 0.422374 | − | 0.689931i | ||||
\(624\) | −7.94999 | −0.318254 | ||||||||
\(625\) | −10.4445 | − | 18.0904i | −0.417781 | − | 0.723618i | ||||
\(626\) | 15.6552 | − | 27.1156i | 0.625707 | − | 1.08376i | ||||
\(627\) | 1.16388 | − | 2.01590i | 0.0464809 | − | 0.0805073i | ||||
\(628\) | −3.73372 | − | 6.46700i | −0.148992 | − | 0.258061i | ||||
\(629\) | − | 59.8179i | − | 2.38510i | ||||||
\(630\) | 1.07806 | + | 1.98346i | 0.0429509 | + | 0.0790229i | ||||
\(631\) | − | 33.2092i | − | 1.32204i | −0.750370 | − | 0.661018i | \(-0.770124\pi\) | ||
0.750370 | − | 0.661018i | \(-0.229876\pi\) | |||||||
\(632\) | −10.3493 | + | 5.97518i | −0.411674 | + | 0.237680i | ||||
\(633\) | 48.5198 | + | 28.0129i | 1.92849 | + | 1.11341i | ||||
\(634\) | −14.3234 | + | 24.8089i | −0.568856 | + | 0.985288i | ||||
\(635\) | −0.874781 | − | 1.51517i | −0.0347146 | − | 0.0601275i | ||||
\(636\) | 29.4002 | 1.16579 | ||||||||
\(637\) | −21.7388 | − | 14.0902i | −0.861322 | − | 0.558274i | ||||
\(638\) | − | 7.56492i | − | 0.299498i | ||||||
\(639\) | 0.832712 | + | 1.44230i | 0.0329416 | + | 0.0570565i | ||||
\(640\) | 0.264227 | − | 0.457654i | 0.0104445 | − | 0.0180904i | ||||
\(641\) | −4.72515 | − | 2.72807i | −0.186632 | − | 0.107752i | 0.403773 | − | 0.914859i | \(-0.367699\pi\) |
−0.590405 | + | 0.807107i | \(0.701032\pi\) | |||||||
\(642\) | 9.54832 | + | 16.5382i | 0.376842 | + | 0.652710i | ||||
\(643\) | 19.3950 | 0.764865 | 0.382432 | − | 0.923983i | \(-0.375086\pi\) | ||||
0.382432 | + | 0.923983i | \(0.375086\pi\) | |||||||
\(644\) | −10.2442 | − | 7.48713i | −0.403676 | − | 0.295034i | ||||
\(645\) | 10.1993 | 0.401597 | ||||||||
\(646\) | −1.82304 | − | 3.15760i | −0.0717267 | − | 0.124234i | ||||
\(647\) | −32.8996 | − | 18.9946i | −1.29342 | − | 0.746755i | −0.314159 | − | 0.949370i | \(-0.601723\pi\) |
−0.979258 | + | 0.202615i | \(0.935056\pi\) | |||||||
\(648\) | 5.61843 | − | 9.73141i | 0.220713 | − | 0.382286i | ||||
\(649\) | −5.92294 | − | 10.2588i | −0.232496 | − | 0.402694i | ||||
\(650\) | − | 17.4706i | − | 0.685254i | ||||||
\(651\) | −14.6737 | + | 23.9689i | −0.575106 | + | 0.939414i | ||||
\(652\) | −5.61463 | −0.219886 | ||||||||
\(653\) | 3.32891 | + | 5.76584i | 0.130270 | + | 0.225635i | 0.923781 | − | 0.382922i | \(-0.125082\pi\) |
−0.793510 | + | 0.608557i | \(0.791749\pi\) | |||||||
\(654\) | 7.44772 | − | 12.8998i | 0.291229 | − | 0.504423i | ||||
\(655\) | −7.47536 | − | 4.31590i | −0.292086 | − | 0.168636i | ||||
\(656\) | 3.20501 | − | 1.85041i | 0.125135 | − | 0.0722464i | ||||
\(657\) | − | 7.98399i | − | 0.311485i | ||||||
\(658\) | −0.134065 | + | 5.20716i | −0.00522641 | + | 0.202996i | ||||
\(659\) | − | 7.65972i | − | 0.298380i | −0.988809 | − | 0.149190i | \(-0.952333\pi\) | ||
0.988809 | − | 0.149190i | \(-0.0476667\pi\) | |||||||
\(660\) | 1.16388 | + | 2.01590i | 0.0453040 | + | 0.0784688i | ||||
\(661\) | −11.6853 | + | 20.2395i | −0.454504 | + | 0.787225i | −0.998660 | − | 0.0517599i | \(-0.983517\pi\) |
0.544155 | + | 0.838985i | \(0.316850\pi\) | |||||||
\(662\) | −13.6550 | + | 23.6512i | −0.530717 | + | 0.919228i | ||||
\(663\) | −27.4257 | − | 47.5026i | −1.06512 | − | 1.84485i | ||||
\(664\) | 16.4544 | 0.638554 | ||||||||
\(665\) | −0.738616 | − | 0.0190167i | −0.0286423 | − | 0.000737434i | ||||
\(666\) | − | 13.9986i | − | 0.542433i | ||||||
\(667\) | 14.5486 | + | 10.0691i | 0.563324 | + | 0.389876i | ||||
\(668\) | 4.03146 | + | 2.32756i | 0.155982 | + | 0.0900562i | ||||
\(669\) | 3.38917 | − | 5.87022i | 0.131033 | − | 0.226956i | ||||
\(670\) | −0.375508 | + | 0.216800i | −0.0145071 | + | 0.00837570i | ||||
\(671\) | 11.9804i | 0.462499i | ||||||||
\(672\) | 4.84730 | + | 2.96750i | 0.186989 | + | 0.114474i | ||||
\(673\) | −32.0944 | −1.23715 | −0.618575 | − | 0.785726i | \(-0.712290\pi\) | ||||
−0.618575 | + | 0.785726i | \(0.712290\pi\) | |||||||
\(674\) | −2.67682 | + | 1.54546i | −0.103107 | + | 0.0595289i | ||||
\(675\) | 12.1668 | + | 7.02449i | 0.468299 | + | 0.270373i | ||||
\(676\) | 0.348047 | − | 0.602836i | 0.0133864 | − | 0.0231860i | ||||
\(677\) | −5.30587 | − | 9.19004i | −0.203921 | − | 0.353202i | 0.745867 | − | 0.666095i | \(-0.232035\pi\) |
−0.949788 | + | 0.312893i | \(0.898702\pi\) | |||||||
\(678\) | 10.7593 | 0.413209 | ||||||||
\(679\) | −14.0752 | − | 25.8962i | −0.540158 | − | 0.993806i | ||||
\(680\) | 3.64609 | 0.139821 | ||||||||
\(681\) | −14.4965 | + | 8.36953i | −0.555505 | + | 0.320721i | ||||
\(682\) | −5.06968 | + | 8.78094i | −0.194128 | + | 0.336240i | ||||
\(683\) | 20.7369 | − | 35.9173i | 0.793474 | − | 1.37434i | −0.130330 | − | 0.991471i | \(-0.541604\pi\) |
0.923804 | − | 0.382866i | \(-0.125063\pi\) | |||||||
\(684\) | −0.426628 | − | 0.738941i | −0.0163125 | − | 0.0282541i | ||||
\(685\) | − | 5.18151i | − | 0.197975i | ||||||
\(686\) | 7.99520 | + | 16.7056i | 0.305258 | + | 0.637822i | ||||
\(687\) | 12.1982i | 0.465392i | ||||||||
\(688\) | 7.78083 | − | 4.49227i | 0.296642 | − | 0.171266i | ||||
\(689\) | −25.3251 | + | 43.8643i | −0.964808 | + | 1.67110i | ||||
\(690\) | −5.42606 | − | 0.444869i | −0.206566 | − | 0.0169359i | ||||
\(691\) | −3.74856 | + | 2.16423i | −0.142602 | + | 0.0823313i | −0.569603 | − | 0.821920i | \(-0.692903\pi\) |
0.427002 | + | 0.904251i | \(0.359570\pi\) | |||||||
\(692\) | − | 14.7858i | − | 0.562072i | ||||||
\(693\) | −7.69625 | + | 4.18310i | −0.292356 | + | 0.158903i | ||||
\(694\) | −5.44829 | −0.206814 | ||||||||
\(695\) | 8.44225 | − | 4.87414i | 0.320233 | − | 0.184887i | ||||
\(696\) | −6.86342 | − | 3.96259i | −0.260157 | − | 0.150202i | ||||
\(697\) | 22.1131 | + | 12.7670i | 0.837593 | + | 0.483584i | ||||
\(698\) | 6.10817 | − | 3.52655i | 0.231198 | − | 0.133482i | ||||
\(699\) | 61.2307i | 2.31596i | ||||||||
\(700\) | −6.52127 | + | 10.6523i | −0.246481 | + | 0.402617i | ||||
\(701\) | 4.85553i | 0.183391i | 0.995787 | + | 0.0916954i | \(0.0292286\pi\) | ||||
−0.995787 | + | 0.0916954i | \(0.970771\pi\) | |||||||
\(702\) | 5.50685 | + | 9.53814i | 0.207843 | + | 0.359994i | ||||
\(703\) | 3.96779 | + | 2.29080i | 0.149648 | + | 0.0863992i | ||||
\(704\) | 1.77580 | + | 1.02526i | 0.0669279 | + | 0.0386409i | ||||
\(705\) | 1.11748 | + | 1.93554i | 0.0420868 | + | 0.0728965i | ||||
\(706\) | − | 8.86485i | − | 0.333633i | ||||||
\(707\) | 0.202953 | − | 7.88279i | 0.00763284 | − | 0.296463i | ||||
\(708\) | −12.4100 | −0.466397 | ||||||||
\(709\) | −12.1318 | + | 7.00431i | −0.455620 | + | 0.263052i | −0.710201 | − | 0.703999i | \(-0.751396\pi\) |
0.254581 | + | 0.967051i | \(0.418062\pi\) | |||||||
\(710\) | 0.272539 | − | 0.472052i | 0.0102282 | − | 0.0177158i | ||||
\(711\) | −16.7103 | − | 9.64769i | −0.626685 | − | 0.361817i | ||||
\(712\) | −3.81582 | − | 6.60920i | −0.143004 | − | 0.247690i | ||||
\(713\) | −10.1394 | − | 21.4374i | −0.379722 | − | 0.802839i | ||||
\(714\) | −1.00927 | + | 39.2007i | −0.0377711 | + | 1.46705i | ||||
\(715\) | −4.01022 | −0.149974 | ||||||||
\(716\) | −1.69269 | − | 2.93182i | −0.0632587 | − | 0.109567i | ||||
\(717\) | −3.91533 | − | 2.26052i | −0.146221 | − | 0.0844205i | ||||
\(718\) | −8.33391 | − | 4.81159i | −0.311019 | − | 0.179567i | ||||
\(719\) | −29.9439 | + | 17.2881i | −1.11672 | + | 0.644739i | −0.940562 | − | 0.339623i | \(-0.889700\pi\) |
−0.176159 | + | 0.984362i | \(0.556367\pi\) | |||||||
\(720\) | 0.853256 | 0.0317990 | ||||||||
\(721\) | −2.43485 | + | 3.97724i | −0.0906787 | + | 0.148120i | ||||
\(722\) | −18.7207 | −0.696714 | ||||||||
\(723\) | 28.2910 | − | 16.3338i | 1.05215 | − | 0.607462i | ||||
\(724\) | −5.14347 | + | 8.90875i | −0.191155 | + | 0.331091i | ||||
\(725\) | 8.70805 | − | 15.0828i | 0.323409 | − | 0.560161i | ||||
\(726\) | 12.6419 | − | 7.29882i | 0.469186 | − | 0.270885i | ||||
\(727\) | −29.9681 | −1.11146 | −0.555728 | − | 0.831364i | \(-0.687560\pi\) | ||||
−0.555728 | + | 0.831364i | \(0.687560\pi\) | |||||||
\(728\) | −8.60285 | + | 4.67586i | −0.318843 | + | 0.173299i | ||||
\(729\) | −1.03559 | −0.0383550 | ||||||||
\(730\) | −2.26300 | + | 1.30654i | −0.0837574 | + | 0.0483574i | ||||
\(731\) | 53.6842 | + | 30.9946i | 1.98558 | + | 1.14638i | ||||
\(732\) | 10.8695 | + | 6.27548i | 0.401747 | + | 0.231949i | ||||
\(733\) | 23.8350 | + | 41.2834i | 0.880366 | + | 1.52484i | 0.850934 | + | 0.525272i | \(0.176036\pi\) |
0.0294318 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(734\) | −24.2072 | −0.893503 | ||||||||
\(735\) | 6.66825 | + | 4.32209i | 0.245962 | + | 0.159423i | ||||
\(736\) | −4.33536 | + | 2.05052i | −0.159804 | + | 0.0755830i | ||||
\(737\) | −0.841230 | − | 1.45705i | −0.0309871 | − | 0.0536712i | ||||
\(738\) | 5.17489 | + | 2.98773i | 0.190490 | + | 0.109980i | ||||
\(739\) | 0.172792 | − | 0.299285i | 0.00635626 | − | 0.0110094i | −0.862830 | − | 0.505495i | \(-0.831310\pi\) |
0.869186 | + | 0.494485i | \(0.164643\pi\) | |||||||
\(740\) | −3.96779 | + | 2.29080i | −0.145859 | + | 0.0842115i | ||||
\(741\) | 4.20120 | 0.154335 | ||||||||
\(742\) | 31.8146 | − | 17.2920i | 1.16795 | − | 0.634809i | ||||
\(743\) | − | 14.5735i | − | 0.534650i | −0.963606 | − | 0.267325i | \(-0.913860\pi\) | ||
0.963606 | − | 0.267325i | \(-0.0861397\pi\) | |||||||
\(744\) | 5.31112 | + | 9.19912i | 0.194715 | + | 0.337256i | ||||
\(745\) | 1.87685 | + | 1.08360i | 0.0687626 | + | 0.0397001i | ||||
\(746\) | −0.0491634 | − | 0.0283845i | −0.00180000 | − | 0.00103923i | ||||
\(747\) | 13.2838 | + | 23.0083i | 0.486030 | + | 0.841829i | ||||
\(748\) | 14.1476i | 0.517288i | ||||||||
\(749\) | 20.0595 | + | 12.2804i | 0.732959 | + | 0.448715i | ||||
\(750\) | 11.0350i | 0.402943i | ||||||||
\(751\) | −40.0662 | + | 23.1322i | −1.46204 | + | 0.844107i | −0.999105 | − | 0.0422873i | \(-0.986536\pi\) |
−0.462931 | + | 0.886394i | \(0.653202\pi\) | |||||||
\(752\) | 1.70501 | + | 0.984386i | 0.0621752 | + | 0.0358969i | ||||
\(753\) | 39.1538 | + | 22.6054i | 1.42684 | + | 0.823788i | ||||
\(754\) | 11.8242 | − | 6.82668i | 0.430611 | − | 0.248613i | ||||
\(755\) | −0.935756 | −0.0340557 | ||||||||
\(756\) | 0.202654 | − | 7.87118i | 0.00737046 | − | 0.286272i | ||||
\(757\) | − | 5.74054i | − | 0.208644i | −0.994544 | − | 0.104322i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104322i | \(-0.0332672\pi\) | |||||||
\(758\) | −17.6672 | + | 10.2001i | −0.641701 | + | 0.370486i | ||||
\(759\) | 1.72619 | − | 21.0543i | 0.0626568 | − | 0.764222i | ||||
\(760\) | −0.139632 | + | 0.241849i | −0.00506497 | + | 0.00877278i | ||||
\(761\) | −38.7314 | + | 22.3616i | −1.40401 | + | 0.810607i | −0.994801 | − | 0.101834i | \(-0.967529\pi\) |
−0.409210 | + | 0.912440i | \(0.634196\pi\) | |||||||
\(762\) | − | 7.11199i | − | 0.257640i | ||||||
\(763\) | 0.472178 | − | 18.3396i | 0.0170940 | − | 0.663939i | ||||
\(764\) | 3.88113i | 0.140414i | ||||||||
\(765\) | 2.94354 | + | 5.09836i | 0.106424 | + | 0.184331i | ||||
\(766\) | −6.47291 | + | 11.2114i | −0.233876 | + | 0.405085i | ||||
\(767\) | 10.6899 | − | 18.5154i | 0.385989 | − | 0.668552i | ||||
\(768\) | 1.86037 | − | 1.07408i | 0.0671303 | − | 0.0387577i | ||||
\(769\) | 30.7425 | 1.10860 | 0.554301 | − | 0.832316i | \(-0.312986\pi\) | ||||
0.554301 | + | 0.832316i | \(0.312986\pi\) | |||||||
\(770\) | 2.44513 | + | 1.49690i | 0.0881163 | + | 0.0539445i | ||||
\(771\) | −48.1107 | −1.73266 | ||||||||
\(772\) | −6.84769 | − | 11.8605i | −0.246454 | − | 0.426870i | ||||
\(773\) | −14.1519 | + | 24.5119i | −0.509009 | + | 0.881630i | 0.490936 | + | 0.871196i | \(0.336655\pi\) |
−0.999946 | + | 0.0104345i | \(0.996679\pi\) | |||||||
\(774\) | 12.5632 | + | 7.25334i | 0.451573 | + | 0.260716i | ||||
\(775\) | −20.2157 | + | 11.6715i | −0.726168 | + | 0.419253i | ||||
\(776\) | −11.1402 | −0.399910 | ||||||||
\(777\) | −23.5311 | − | 43.2935i | −0.844173 | − | 1.55315i | ||||
\(778\) | 35.7943i | 1.28329i | ||||||||
\(779\) | −1.69370 | + | 0.977857i | −0.0606830 | + | 0.0350353i | ||||
\(780\) | −2.10060 | + | 3.63835i | −0.0752136 | + | 0.130274i | ||||
\(781\) | 1.83166 | + | 1.05751i | 0.0655421 | + | 0.0378407i | ||||
\(782\) | −27.2082 | − | 18.8308i | −0.972964 | − | 0.673387i | ||||
\(783\) | 10.9793i | 0.392370i | ||||||||
\(784\) | 6.99073 | + | 0.360210i | 0.249669 | + | 0.0128646i | ||||
\(785\) | −3.94620 | −0.140846 | ||||||||
\(786\) | −17.5442 | − | 30.3874i | −0.625780 | − | 1.08388i | ||||
\(787\) | 1.87582 | − | 3.24902i | 0.0668659 | − | 0.115815i | −0.830654 | − | 0.556789i | \(-0.812033\pi\) |
0.897520 | + | 0.440973i | \(0.145367\pi\) | |||||||
\(788\) | −10.2488 | + | 17.7514i | −0.365098 | + | 0.632368i | ||||
\(789\) | 10.2952 | + | 17.8319i | 0.366521 | + | 0.634832i | ||||
\(790\) | 6.31521i | 0.224685i | ||||||||
\(791\) | 11.6429 | − | 6.32819i | 0.413973 | − | 0.225005i | ||||
\(792\) | 3.31082i | 0.117645i | ||||||||
\(793\) | −18.7257 | + | 10.8113i | −0.664969 | + | 0.383920i | ||||
\(794\) | −18.9349 | − | 10.9321i | −0.671974 | − | 0.387964i | ||||
\(795\) | 7.76832 | − | 13.4551i | 0.275514 | − | 0.477204i | ||||
\(796\) | 10.4428 | + | 18.0875i | 0.370136 | + | 0.641095i | ||||
\(797\) | −14.8394 | −0.525637 | −0.262819 | − | 0.964845i | \(-0.584652\pi\) | ||||
−0.262819 | + | 0.964845i | \(0.584652\pi\) | |||||||
\(798\) | −2.56157 | − | 1.56819i | −0.0906787 | − | 0.0555132i | ||||
\(799\) | 13.5836i | 0.480554i | ||||||||
\(800\) | 2.36037 | + | 4.08828i | 0.0834516 | + | 0.144542i | ||||
\(801\) | 6.16113 | − | 10.6714i | 0.217693 | − | 0.377055i | ||||
\(802\) | −15.0987 | − | 8.71723i | −0.533153 | − | 0.307816i | ||||
\(803\) | −5.06968 | − | 8.78094i | −0.178905 | − | 0.309873i | ||||
\(804\) | −1.76259 | −0.0621616 | ||||||||
\(805\) | −6.13330 | + | 2.70998i | −0.216170 | + | 0.0955143i | ||||
\(806\) | −18.2998 | −0.644582 | ||||||||
\(807\) | 18.3337 | + | 31.7549i | 0.645377 | + | 1.11783i | ||||
\(808\) | −2.58111 | − | 1.49020i | −0.0908030 | − | 0.0524251i | ||||
\(809\) | −23.3360 | + | 40.4191i | −0.820450 | + | 1.42106i | 0.0848982 | + | 0.996390i | \(0.472943\pi\) |
−0.905348 | + | 0.424671i | \(0.860390\pi\) | |||||||
\(810\) | −2.96908 | − | 5.14260i | −0.104323 | − | 0.180692i | ||||
\(811\) | − | 10.5200i | − | 0.369409i | −0.982794 | − | 0.184704i | \(-0.940867\pi\) | ||
0.982794 | − | 0.184704i | \(-0.0591328\pi\) | |||||||
\(812\) | −9.75768 | − | 0.251224i | −0.342427 | − | 0.00881625i | ||||
\(813\) | −32.0213 | −1.12304 | ||||||||
\(814\) | −8.88881 | − | 15.3959i | −0.311553 | − | 0.539625i | ||||
\(815\) | −1.48353 | + | 2.56956i | −0.0519660 | + | 0.0900077i | ||||
\(816\) | 12.8357 | + | 7.41069i | 0.449339 | + | 0.259426i | ||||
\(817\) | −4.11181 | + | 2.37395i | −0.143854 | + | 0.0830541i | ||||
\(818\) | − | 33.1136i | − | 1.15779i | ||||||
\(819\) | −13.4835 | − | 8.25455i | −0.471151 | − | 0.288437i | ||||
\(820\) | − | 1.95571i | − | 0.0682965i | ||||||
\(821\) | 7.02805 | + | 12.1729i | 0.245281 | + | 0.424839i | 0.962210 | − | 0.272307i | \(-0.0877866\pi\) |
−0.716930 | + | 0.697145i | \(0.754453\pi\) | |||||||
\(822\) | 10.5314 | − | 18.2410i | 0.367326 | − | 0.636228i | ||||
\(823\) | 3.49718 | − | 6.05730i | 0.121904 | − | 0.211144i | −0.798614 | − | 0.601843i | \(-0.794433\pi\) |
0.920519 | + | 0.390699i | \(0.127767\pi\) | |||||||
\(824\) | 0.881293 | + | 1.52644i | 0.0307013 | + | 0.0531762i | ||||
\(825\) | −20.7941 | −0.723959 | ||||||||
\(826\) | −13.4291 | + | 7.29906i | −0.467259 | + | 0.253967i | ||||
\(827\) | 36.9598i | 1.28522i | 0.766194 | + | 0.642609i | \(0.222148\pi\) | ||||
−0.766194 | + | 0.642609i | \(0.777852\pi\) | |||||||
\(828\) | −6.36725 | − | 4.40677i | −0.221277 | − | 0.153146i | ||||
\(829\) | 3.07501 | + | 1.77536i | 0.106800 | + | 0.0616608i | 0.552448 | − | 0.833547i | \(-0.313694\pi\) |
−0.445649 | + | 0.895208i | \(0.647027\pi\) | |||||||
\(830\) | 4.34769 | − | 7.53041i | 0.150910 | − | 0.261384i | ||||
\(831\) | 55.5905 | − | 32.0952i | 1.92841 | − | 1.11337i | ||||
\(832\) | 3.70082i | 0.128303i | ||||||||
\(833\) | 21.9641 | + | 43.0135i | 0.761010 | + | 1.49033i | ||||
\(834\) | 39.6268 | 1.37216 | ||||||||
\(835\) | 2.13044 | − | 1.23001i | 0.0737269 | − | 0.0425662i | ||||
\(836\) | −0.938427 | − | 0.541801i | −0.0324562 | − | 0.0187386i | ||||
\(837\) | 7.35787 | − | 12.7442i | 0.254325 | − | 0.440504i | ||||
\(838\) | −11.4997 | − | 19.9181i | −0.397252 | − | 0.688060i | ||||
\(839\) | −4.89386 | −0.168955 | −0.0844774 | − | 0.996425i | \(-0.526922\pi\) | ||||
−0.0844774 | + | 0.996425i | \(0.526922\pi\) | |||||||
\(840\) | 2.63888 | − | 1.43429i | 0.0910499 | − | 0.0494878i | ||||
\(841\) | −15.3892 | −0.530663 | ||||||||
\(842\) | 12.1184 | − | 6.99657i | 0.417628 | − | 0.241118i | ||||
\(843\) | 23.4080 | − | 40.5438i | 0.806214 | − | 1.39640i | ||||
\(844\) | 13.0404 | − | 22.5866i | 0.448868 | − | 0.777462i | ||||
\(845\) | −0.183927 | − | 0.318571i | −0.00632728 | − | 0.0109592i | ||||
\(846\) | 3.17884i | 0.109291i | ||||||||
\(847\) | 9.38722 | − | 15.3337i | 0.322549 | − | 0.526871i | ||||
\(848\) | − | 13.6862i | − | 0.469985i | ||||||
\(849\) | 49.7245 | − | 28.7084i | 1.70654 | − | 0.985271i | ||||
\(850\) | −16.2855 | + | 28.2072i | −0.558587 | + | 0.967501i | ||||
\(851\) | 41.4400 | + | 3.39757i | 1.42055 | + | 0.116467i | ||||
\(852\) | 1.91889 | − | 1.10787i | 0.0657402 | − | 0.0379551i | ||||
\(853\) | 15.0374i | 0.514871i | 0.966296 | + | 0.257435i | \(0.0828774\pi\) | ||||
−0.966296 | + | 0.257435i | \(0.917123\pi\) | |||||||
\(854\) | 15.4530 | + | 0.397859i | 0.528792 | + | 0.0136145i | ||||
\(855\) | −0.450906 | −0.0154207 | ||||||||
\(856\) | 7.69873 | − | 4.44487i | 0.263137 | − | 0.151922i | ||||
\(857\) | −21.1705 | − | 12.2228i | −0.723171 | − | 0.417523i | 0.0927480 | − | 0.995690i | \(-0.470435\pi\) |
−0.815919 | + | 0.578167i | \(0.803768\pi\) | |||||||
\(858\) | −14.1176 | − | 8.15079i | −0.481966 | − | 0.278263i | ||||
\(859\) | −39.3337 | + | 22.7093i | −1.34205 | + | 0.774833i | −0.987108 | − | 0.160056i | \(-0.948833\pi\) |
−0.354942 | + | 0.934889i | \(0.615499\pi\) | |||||||
\(860\) | − | 4.74791i | − | 0.161902i | ||||||
\(861\) | 21.0267 | + | 0.541361i | 0.716589 | + | 0.0184495i | ||||
\(862\) | 15.0335i | 0.512044i | ||||||||
\(863\) | 15.5188 | + | 26.8793i | 0.528265 | + | 0.914982i | 0.999457 | + | 0.0329515i | \(0.0104907\pi\) |
−0.471192 | + | 0.882031i | \(0.656176\pi\) | |||||||
\(864\) | −2.57730 | − | 1.48801i | −0.0876816 | − | 0.0506230i | ||||
\(865\) | −6.76679 | − | 3.90681i | −0.230078 | − | 0.132835i | ||||
\(866\) | −4.25076 | − | 7.36254i | −0.144447 | − | 0.250189i | ||||
\(867\) | 65.7419i | 2.23271i | ||||||||
\(868\) | 11.1578 | + | 6.83078i | 0.378721 | + | 0.231852i | ||||
\(869\) | −24.5044 | −0.831255 | ||||||||
\(870\) | −3.62700 | + | 2.09405i | −0.122967 | + | 0.0709948i | ||||
\(871\) | 1.51827 | − | 2.62973i | 0.0514447 | − | 0.0891049i | ||||
\(872\) | −6.00504 | − | 3.46701i | −0.203356 | − | 0.117408i | ||||
\(873\) | −8.99363 | − | 15.5774i | −0.304388 | − | 0.527216i | ||||
\(874\) | 2.29104 | − | 1.08360i | 0.0774955 | − | 0.0366534i | ||||
\(875\) | 6.49036 | + | 11.9413i | 0.219414 | + | 0.403688i | ||||
\(876\) | −10.6222 | −0.358892 | ||||||||
\(877\) | 13.4970 | + | 23.3775i | 0.455761 | + | 0.789401i | 0.998732 | − | 0.0503507i | \(-0.0160339\pi\) |
−0.542971 | + | 0.839752i | \(0.682701\pi\) | |||||||
\(878\) | −1.54965 | − | 0.894688i | −0.0522980 | − | 0.0301943i | ||||
\(879\) | 39.7890 | + | 22.9722i | 1.34205 | + | 0.774832i | ||||
\(880\) | 0.938427 | − | 0.541801i | 0.0316344 | − | 0.0182641i | ||||
\(881\) | 41.9616 | 1.41372 | 0.706860 | − | 0.707353i | \(-0.250111\pi\) | ||||
0.706860 | + | 0.707353i | \(0.250111\pi\) | |||||||
\(882\) | 5.14003 | + | 10.0660i | 0.173074 | + | 0.338940i | ||||
\(883\) | −10.3346 | −0.347786 | −0.173893 | − | 0.984765i | \(-0.555635\pi\) | ||||
−0.173893 | + | 0.984765i | \(0.555635\pi\) | |||||||
\(884\) | −22.1131 | + | 12.7670i | −0.743743 | + | 0.429400i | ||||
\(885\) | −3.27906 | + | 5.67949i | −0.110224 | + | 0.190914i | ||||
\(886\) | −7.21146 | + | 12.4906i | −0.242274 | + | 0.419631i | ||||
\(887\) | −30.0510 | + | 17.3499i | −1.00901 | + | 0.582554i | −0.910903 | − | 0.412621i | \(-0.864613\pi\) |
−0.0981109 | + | 0.995175i | \(0.531280\pi\) | |||||||
\(888\) | −18.6243 | −0.624989 | ||||||||
\(889\) | −4.18298 | − | 7.69603i | −0.140293 | − | 0.258117i | ||||
\(890\) | −4.03297 | −0.135185 | ||||||||
\(891\) | 19.9544 | − | 11.5207i | 0.668498 | − | 0.385957i | ||||
\(892\) | −2.73266 | − | 1.57770i | −0.0914964 | − | 0.0528254i | ||||
\(893\) | −0.901017 | − | 0.520202i | −0.0301514 | − | 0.0174079i | ||||
\(894\) | 4.40485 | + | 7.62943i | 0.147320 | + | 0.255166i | ||||
\(895\) | −1.78901 | −0.0598001 | ||||||||
\(896\) | 1.38141 | − | 2.25648i | 0.0461497 | − | 0.0753837i | ||||
\(897\) | 34.4661 | − | 16.3016i | 1.15079 | − | 0.544294i | ||||
\(898\) | −4.82609 | − | 8.35903i | −0.161049 | − | 0.278945i | ||||
\(899\) | −15.7986 | − | 9.12134i | −0.526914 | − | 0.304214i | ||||
\(900\) | −3.81112 | + | 6.60105i | −0.127037 | + | 0.220035i | ||||
\(901\) | 81.7773 | − | 47.2142i | 2.72440 | − | 1.57293i | ||||
\(902\) | 7.58860 | 0.252673 | ||||||||
\(903\) | 51.0469 | + | 1.31427i | 1.69873 | + | 0.0437361i | ||||
\(904\) | − | 5.00860i | − | 0.166584i | ||||||
\(905\) | 2.71808 | + | 4.70786i | 0.0903522 | + | 0.156495i | ||||
\(906\) | −3.29424 | − | 1.90193i | −0.109444 | − | 0.0631874i | ||||
\(907\) | −27.5555 | − | 15.9092i | −0.914966 | − | 0.528256i | −0.0329403 | − | 0.999457i | \(-0.510487\pi\) |
−0.882026 | + | 0.471201i | \(0.843820\pi\) | |||||||
\(908\) | 3.89612 | + | 6.74828i | 0.129297 | + | 0.223950i | ||||
\(909\) | − | 4.81224i | − | 0.159612i | ||||||
\(910\) | −0.133176 | + | 5.17262i | −0.00441474 | + | 0.171471i | ||||
\(911\) | − | 3.68229i | − | 0.122000i | −0.998138 | − | 0.0609998i | \(-0.980571\pi\) | ||
0.998138 | − | 0.0609998i | \(-0.0194289\pi\) | |||||||
\(912\) | −0.983118 | + | 0.567604i | −0.0325543 | + | 0.0187952i | ||||
\(913\) | 29.2197 | + | 16.8700i | 0.967029 | + | 0.558315i | ||||
\(914\) | −31.2955 | − | 18.0685i | −1.03516 | − | 0.597653i | ||||
\(915\) | 5.74400 | − | 3.31630i | 0.189891 | − | 0.109634i | ||||
\(916\) | 5.67843 | 0.187621 | ||||||||
\(917\) | −36.8575 | − | 22.5641i | −1.21714 | − | 0.745131i | ||||
\(918\) | − | 20.5331i | − | 0.677694i | ||||||
\(919\) | 45.3869 | − | 26.2041i | 1.49718 | − | 0.864395i | 0.497181 | − | 0.867647i | \(-0.334369\pi\) |
0.999995 | + | 0.00325243i | \(0.00103528\pi\) | |||||||
\(920\) | −0.207092 | + | 2.52590i | −0.00682763 | + | 0.0832764i | ||||
\(921\) | 2.32609 | − | 4.02891i | 0.0766473 | − | 0.132757i | ||||
\(922\) | −23.8475 | + | 13.7684i | −0.785376 | + | 0.453437i | ||||
\(923\) | 3.81725i | 0.125646i | ||||||||
\(924\) | 5.56538 | + | 10.2394i | 0.183087 | + | 0.336852i | ||||
\(925\) | − | 40.9280i | − | 1.34570i | ||||||
\(926\) | 0.0930326 | + | 0.161137i | 0.00305724 | + | 0.00529530i | ||||
\(927\) | −1.42296 | + | 2.46464i | −0.0467361 | + | 0.0809493i | ||||
\(928\) | −1.84464 | + | 3.19501i | −0.0605532 | + | 0.104881i | ||||
\(929\) | −1.47463 | + | 0.851381i | −0.0483812 | + | 0.0279329i | −0.523995 | − | 0.851721i | \(-0.675559\pi\) |
0.475614 | + | 0.879654i | \(0.342226\pi\) | |||||||
\(930\) | 5.61336 | 0.184069 | ||||||||
\(931\) | −3.69427 | − | 0.190354i | −0.121075 | − | 0.00623861i | ||||
\(932\) | 28.5037 | 0.933669 | ||||||||
\(933\) | −20.1372 | − | 34.8787i | −0.659263 | − | 1.14188i | ||||
\(934\) | 8.66213 | − | 15.0032i | 0.283433 | − | 0.490921i | ||||
\(935\) | 6.47472 | + | 3.73818i | 0.211746 | + | 0.122252i | ||||
\(936\) | −5.17489 | + | 2.98773i | −0.169147 | + | 0.0976569i | ||||
\(937\) | 17.8589 | 0.583425 | 0.291713 | − | 0.956506i | \(-0.405775\pi\) | ||||
0.291713 | + | 0.956506i | \(0.405775\pi\) | |||||||
\(938\) | −1.90733 | + | 1.03668i | −0.0622765 | + | 0.0338488i | ||||
\(939\) | − | 67.2599i | − | 2.19495i | ||||||
\(940\) | 0.901017 | − | 0.520202i | 0.0293879 | − | 0.0169671i | ||||
\(941\) | 28.6616 | − | 49.6433i | 0.934341 | − | 1.61833i | 0.158536 | − | 0.987353i | \(-0.449323\pi\) |
0.775805 | − | 0.630973i | \(-0.217344\pi\) | |||||||
\(942\) | −13.8922 | − | 8.02066i | −0.452632 | − | 0.261327i | ||||
\(943\) | −10.1006 | + | 14.5941i | −0.328920 | + | 0.475250i | ||||
\(944\) | 5.77702i | 0.188026i | ||||||||
\(945\) | −3.54873 | − | 2.17252i | −0.115440 | − | 0.0706722i | ||||
\(946\) | 18.4229 | 0.598981 | ||||||||
\(947\) | −1.22926 | − | 2.12913i | −0.0399454 | − | 0.0691875i | 0.845361 | − | 0.534195i | \(-0.179385\pi\) |
−0.885307 | + | 0.465007i | \(0.846052\pi\) | |||||||
\(948\) | −12.8357 | + | 22.2321i | −0.416884 | + | 0.722064i | ||||
\(949\) | 9.14989 | − | 15.8481i | 0.297018 | − | 0.514450i | ||||
\(950\) | −1.24734 | − | 2.16046i | −0.0404692 | − | 0.0700947i | ||||
\(951\) | 61.5383i | 1.99552i | ||||||||
\(952\) | 18.2484 | + | 0.469830i | 0.591435 | + | 0.0152273i | ||||
\(953\) | − | 22.3180i | − | 0.722950i | −0.932382 | − | 0.361475i | \(-0.882273\pi\) | ||
0.932382 | − | 0.361475i | \(-0.117727\pi\) | |||||||
\(954\) | 19.1375 | − | 11.0490i | 0.619599 | − | 0.357726i | ||||
\(955\) | 1.77622 | + | 1.02550i | 0.0574770 | + | 0.0331844i | ||||
\(956\) | −1.05230 | + | 1.82264i | −0.0340338 | + | 0.0589482i | ||||
\(957\) | −8.12536 | − | 14.0735i | −0.262656 | − | 0.454933i | ||||
\(958\) | −32.3673 | −1.04574 | ||||||||
\(959\) | 0.667682 | − | 25.9331i | 0.0215606 | − | 0.837424i | ||||
\(960\) | − | 1.13521i | − | 0.0366387i | ||||||
\(961\) | −3.27455 | − | 5.67168i | −0.105631 | − | 0.182957i | ||||
\(962\) | 16.0428 | − | 27.7869i | 0.517239 | − | 0.895885i | ||||
\(963\) | 12.4306 | + | 7.17680i | 0.400570 | + | 0.231269i | ||||
\(964\) | −7.60361 | − | 13.1698i | −0.244896 | − | 0.424172i | ||||
\(965\) | −7.23737 | −0.232979 | ||||||||
\(966\) | −27.0997 | − | 2.92574i | −0.871919 | − | 0.0941340i | ||||
\(967\) | 52.7700 | 1.69697 | 0.848485 | − | 0.529220i | \(-0.177515\pi\) | ||||
0.848485 | + | 0.529220i | \(0.177515\pi\) | |||||||
\(968\) | −3.39769 | − | 5.88498i | −0.109206 | − | 0.189150i | ||||
\(969\) | −6.78307 | − | 3.91620i | −0.217903 | − | 0.125807i | ||||
\(970\) | −2.94354 | + | 5.09836i | −0.0945113 | + | 0.163698i | ||||
\(971\) | −1.75446 | − | 3.03882i | −0.0563034 | − | 0.0975204i | 0.836500 | − | 0.547967i | \(-0.184598\pi\) |
−0.892803 | + | 0.450447i | \(0.851265\pi\) | |||||||
\(972\) | − | 15.2106i | − | 0.487881i | ||||||
\(973\) | 42.8810 | − | 23.3069i | 1.37470 | − | 0.747184i | ||||
\(974\) | 30.0020 | 0.961325 | ||||||||
\(975\) | −18.7649 | − | 32.5018i | −0.600958 | − | 1.04089i | ||||
\(976\) | 2.92132 | − | 5.05987i | 0.0935091 | − | 0.161963i | ||||
\(977\) | −26.1586 | − | 15.1027i | −0.836887 | − | 0.483177i | 0.0193177 | − | 0.999813i | \(-0.493851\pi\) |
−0.856205 | + | 0.516636i | \(0.827184\pi\) | |||||||
\(978\) | −10.4453 | + | 6.03058i | −0.334003 | + | 0.192837i | ||||
\(979\) | − | 15.6488i | − | 0.500138i | ||||||
\(980\) | 2.01199 | − | 3.10416i | 0.0642706 | − | 0.0991587i | ||||
\(981\) | − | 11.1959i | − | 0.357456i | ||||||
\(982\) | 5.98807 | + | 10.3716i | 0.191087 | + | 0.330973i | ||||
\(983\) | 10.5938 | − | 18.3490i | 0.337890 | − | 0.585243i | −0.646145 | − | 0.763214i | \(-0.723620\pi\) |
0.984036 | + | 0.177971i | \(0.0569534\pi\) | |||||||
\(984\) | 3.97500 | − | 6.88490i | 0.126718 | − | 0.219482i | ||||
\(985\) | 5.41601 | + | 9.38080i | 0.172568 | + | 0.298897i | ||||
\(986\) | −25.4543 | −0.810631 | ||||||||
\(987\) | 5.34352 | + | 9.83123i | 0.170086 | + | 0.312931i | ||||
\(988\) | − | 1.95571i | − | 0.0622195i | ||||||
\(989\) | −24.5213 | + | 35.4303i | −0.779732 | + | 1.12662i | ||||
\(990\) | 1.51521 | + | 0.874807i | 0.0481565 | + | 0.0278032i | ||||
\(991\) | 27.8066 | − | 48.1624i | 0.883305 | − | 1.52993i | 0.0356618 | − | 0.999364i | \(-0.488646\pi\) |
0.847644 | − | 0.530566i | \(-0.178021\pi\) | |||||||
\(992\) | 4.28231 | − | 2.47239i | 0.135963 | − | 0.0784986i | ||||
\(993\) | 58.6665i | 1.86172i | ||||||||
\(994\) | 1.42487 | − | 2.32747i | 0.0451941 | − | 0.0738228i | ||||
\(995\) | 11.0371 | 0.349899 | ||||||||
\(996\) | 30.6112 | − | 17.6734i | 0.969953 | − | 0.560003i | ||||
\(997\) | 5.61807 | + | 3.24359i | 0.177926 | + | 0.102726i | 0.586318 | − | 0.810081i | \(-0.300577\pi\) |
−0.408392 | + | 0.912807i | \(0.633910\pi\) | |||||||
\(998\) | 20.1372 | − | 34.8787i | 0.637432 | − | 1.10406i | ||||
\(999\) | 12.9008 | + | 22.3448i | 0.408162 | + | 0.706958i |
(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 | 322.2.g.a.45.2 | yes | 16 | |
7.3 | odd | 6 | 2254.2.c.c.2253.4 | 16 | |||
7.4 | even | 3 | 2254.2.c.c.2253.13 | 16 | |||
7.5 | odd | 6 | inner | 322.2.g.a.229.1 | yes | 16 | |
23.22 | odd | 2 | inner | 322.2.g.a.45.1 | ✓ | 16 | |
161.45 | even | 6 | 2254.2.c.c.2253.3 | 16 | |||
161.68 | even | 6 | inner | 322.2.g.a.229.2 | yes | 16 | |
161.137 | odd | 6 | 2254.2.c.c.2253.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.g.a.45.1 | ✓ | 16 | 23.22 | odd | 2 | inner | |
322.2.g.a.45.2 | yes | 16 | 1.1 | even | 1 | trivial | |
322.2.g.a.229.1 | yes | 16 | 7.5 | odd | 6 | inner | |
322.2.g.a.229.2 | yes | 16 | 161.68 | even | 6 | inner | |
2254.2.c.c.2253.3 | 16 | 161.45 | even | 6 | |||
2254.2.c.c.2253.4 | 16 | 7.3 | odd | 6 | |||
2254.2.c.c.2253.13 | 16 | 7.4 | even | 3 | |||
2254.2.c.c.2253.14 | 16 | 161.137 | odd | 6 |