Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [385,2,Mod(221,385)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(385, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("385.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 385 = 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 385.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.07424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 241 x^{16} - 411 x^{15} + 1702 x^{14} - 2261 x^{13} + \cdots + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.5 | ||
Root | \(0.533037 - 0.923247i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 385.331 |
Dual form | 385.2.i.d.221.5 |
$q$-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 \(\left(\mathbb{Z}/385\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(276\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.533037 | + | 0.923247i | −0.376914 | + | 0.652834i | −0.990612 | − | 0.136707i | \(-0.956348\pi\) |
0.613697 | + | 0.789541i | \(0.289681\pi\) | |||||||
\(3\) | −1.53745 | − | 2.66295i | −0.887650 | − | 1.53745i | −0.842646 | − | 0.538468i | \(-0.819003\pi\) |
−0.0450040 | − | 0.998987i | \(-0.514330\pi\) | |||||||
\(4\) | 0.431743 | + | 0.747801i | 0.215871 | + | 0.373900i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 3.27808 | 1.33827 | ||||||||
\(7\) | −2.62595 | − | 0.323104i | −0.992515 | − | 0.122122i | ||||
\(8\) | −3.05269 | −1.07929 | ||||||||
\(9\) | −3.22753 | + | 5.59025i | −1.07584 | + | 1.86342i | ||||
\(10\) | 0.533037 | + | 0.923247i | 0.168561 | + | 0.291956i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 1.32757 | − | 2.29942i | 0.383236 | − | 0.663785i | ||||
\(13\) | 2.06228 | 0.571973 | 0.285986 | − | 0.958234i | \(-0.407679\pi\) | ||||
0.285986 | + | 0.958234i | \(0.407679\pi\) | |||||||
\(14\) | 1.69803 | − | 2.25217i | 0.453818 | − | 0.601919i | ||||
\(15\) | −3.07491 | −0.793938 | ||||||||
\(16\) | 0.763711 | − | 1.32279i | 0.190928 | − | 0.330696i | ||||
\(17\) | 0.561652 | + | 0.972810i | 0.136221 | + | 0.235941i | 0.926063 | − | 0.377369i | \(-0.123171\pi\) |
−0.789842 | + | 0.613310i | \(0.789838\pi\) | |||||||
\(18\) | −3.44079 | − | 5.95963i | −0.811002 | − | 1.40470i | ||||
\(19\) | −4.23532 | + | 7.33580i | −0.971650 | + | 1.68295i | −0.281076 | + | 0.959685i | \(0.590691\pi\) |
−0.690574 | + | 0.723262i | \(0.742642\pi\) | |||||||
\(20\) | 0.863486 | 0.193081 | ||||||||
\(21\) | 3.17687 | + | 7.48953i | 0.693249 | + | 1.63435i | ||||
\(22\) | 1.06607 | 0.227288 | ||||||||
\(23\) | −1.99963 | + | 3.46346i | −0.416951 | + | 0.722181i | −0.995631 | − | 0.0933740i | \(-0.970235\pi\) |
0.578680 | + | 0.815555i | \(0.303568\pi\) | |||||||
\(24\) | 4.69337 | + | 8.12916i | 0.958030 | + | 1.65936i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −1.09927 | + | 1.90399i | −0.215585 | + | 0.373403i | ||||
\(27\) | 10.6240 | 2.04459 | ||||||||
\(28\) | −0.892117 | − | 2.10318i | −0.168594 | − | 0.397464i | ||||
\(29\) | −4.01868 | −0.746250 | −0.373125 | − | 0.927781i | \(-0.621714\pi\) | ||||
−0.373125 | + | 0.927781i | \(0.621714\pi\) | |||||||
\(30\) | 1.63904 | − | 2.83890i | 0.299247 | − | 0.518310i | ||||
\(31\) | 0.162793 | + | 0.281965i | 0.0292384 | + | 0.0506424i | 0.880274 | − | 0.474465i | \(-0.157358\pi\) |
−0.851036 | + | 0.525107i | \(0.824025\pi\) | |||||||
\(32\) | −2.23852 | − | 3.87722i | −0.395717 | − | 0.685403i | ||||
\(33\) | −1.53745 | + | 2.66295i | −0.267637 | + | 0.463560i | ||||
\(34\) | −1.19753 | −0.205374 | ||||||||
\(35\) | −1.59279 | + | 2.11259i | −0.269231 | + | 0.357092i | ||||
\(36\) | −5.57386 | −0.928977 | ||||||||
\(37\) | −2.70461 | + | 4.68452i | −0.444635 | + | 0.770131i | −0.998027 | − | 0.0627905i | \(-0.980000\pi\) |
0.553392 | + | 0.832921i | \(0.313333\pi\) | |||||||
\(38\) | −4.51517 | − | 7.82050i | −0.732457 | − | 1.26865i | ||||
\(39\) | −3.17066 | − | 5.49174i | −0.507711 | − | 0.879382i | ||||
\(40\) | −1.52634 | + | 2.64371i | −0.241336 | + | 0.418007i | ||||
\(41\) | 1.23247 | 0.192480 | 0.0962399 | − | 0.995358i | \(-0.469318\pi\) | ||||
0.0962399 | + | 0.995358i | \(0.469318\pi\) | |||||||
\(42\) | −8.60807 | − | 1.05916i | −1.32825 | − | 0.163432i | ||||
\(43\) | −12.0838 | −1.84276 | −0.921381 | − | 0.388660i | \(-0.872938\pi\) | ||||
−0.921381 | + | 0.388660i | \(0.872938\pi\) | |||||||
\(44\) | 0.431743 | − | 0.747801i | 0.0650877 | − | 0.112735i | ||||
\(45\) | 3.22753 | + | 5.59025i | 0.481132 | + | 0.833346i | ||||
\(46\) | −2.13175 | − | 3.69230i | −0.314310 | − | 0.544400i | ||||
\(47\) | 0.526841 | − | 0.912516i | 0.0768477 | − | 0.133104i | −0.825041 | − | 0.565073i | \(-0.808848\pi\) |
0.901888 | + | 0.431969i | \(0.142181\pi\) | |||||||
\(48\) | −4.69668 | −0.677908 | ||||||||
\(49\) | 6.79121 | + | 1.69691i | 0.970173 | + | 0.242415i | ||||
\(50\) | 1.06607 | 0.150766 | ||||||||
\(51\) | 1.72703 | − | 2.99130i | 0.241832 | − | 0.418866i | ||||
\(52\) | 0.890373 | + | 1.54217i | 0.123473 | + | 0.213861i | ||||
\(53\) | 0.442221 | + | 0.765949i | 0.0607437 | + | 0.105211i | 0.894798 | − | 0.446471i | \(-0.147319\pi\) |
−0.834054 | + | 0.551682i | \(0.813986\pi\) | |||||||
\(54\) | −5.66300 | + | 9.80860i | −0.770637 | + | 1.33478i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 8.01620 | + | 0.986335i | 1.07121 | + | 0.131805i | ||||
\(57\) | 26.0465 | 3.44994 | ||||||||
\(58\) | 2.14211 | − | 3.71024i | 0.281272 | − | 0.487178i | ||||
\(59\) | −6.93461 | − | 12.0111i | −0.902809 | − | 1.56371i | −0.823831 | − | 0.566836i | \(-0.808167\pi\) |
−0.0789785 | − | 0.996876i | \(-0.525166\pi\) | |||||||
\(60\) | −1.32757 | − | 2.29942i | −0.171389 | − | 0.296854i | ||||
\(61\) | −0.819335 | + | 1.41913i | −0.104905 | + | 0.181701i | −0.913699 | − | 0.406391i | \(-0.866787\pi\) |
0.808794 | + | 0.588092i | \(0.200121\pi\) | |||||||
\(62\) | −0.347098 | −0.0440815 | ||||||||
\(63\) | 10.2816 | − | 13.6369i | 1.29536 | − | 1.71809i | ||||
\(64\) | 7.82769 | 0.978461 | ||||||||
\(65\) | 1.03114 | − | 1.78598i | 0.127897 | − | 0.221524i | ||||
\(66\) | −1.63904 | − | 2.83890i | −0.201752 | − | 0.349445i | ||||
\(67\) | −5.37852 | − | 9.31587i | −0.657091 | − | 1.13811i | −0.981365 | − | 0.192152i | \(-0.938453\pi\) |
0.324274 | − | 0.945963i | \(-0.394880\pi\) | |||||||
\(68\) | −0.484978 | + | 0.840007i | −0.0588123 | + | 0.101866i | ||||
\(69\) | 12.2974 | 1.48043 | ||||||||
\(70\) | −1.10142 | − | 2.59663i | −0.131645 | − | 0.310356i | ||||
\(71\) | 8.18682 | 0.971597 | 0.485799 | − | 0.874071i | \(-0.338529\pi\) | ||||
0.485799 | + | 0.874071i | \(0.338529\pi\) | |||||||
\(72\) | 9.85266 | − | 17.0653i | 1.16115 | − | 2.01117i | ||||
\(73\) | 6.48062 | + | 11.2248i | 0.758499 | + | 1.31376i | 0.943616 | + | 0.331043i | \(0.107400\pi\) |
−0.185117 | + | 0.982717i | \(0.559266\pi\) | |||||||
\(74\) | −2.88332 | − | 4.99405i | −0.335179 | − | 0.580546i | ||||
\(75\) | −1.53745 | + | 2.66295i | −0.177530 | + | 0.307491i | ||||
\(76\) | −7.31428 | −0.839006 | ||||||||
\(77\) | 1.03316 | + | 2.43569i | 0.117739 | + | 0.277573i | ||||
\(78\) | 6.76031 | 0.765454 | ||||||||
\(79\) | −3.71992 | + | 6.44309i | −0.418523 | + | 0.724904i | −0.995791 | − | 0.0916511i | \(-0.970786\pi\) |
0.577268 | + | 0.816555i | \(0.304119\pi\) | |||||||
\(80\) | −0.763711 | − | 1.32279i | −0.0853854 | − | 0.147892i | ||||
\(81\) | −6.65135 | − | 11.5205i | −0.739039 | − | 1.28005i | ||||
\(82\) | −0.656953 | + | 1.13788i | −0.0725484 | + | 0.125657i | ||||
\(83\) | 4.20154 | 0.461179 | 0.230590 | − | 0.973051i | \(-0.425935\pi\) | ||||
0.230590 | + | 0.973051i | \(0.425935\pi\) | |||||||
\(84\) | −4.22908 | + | 5.60921i | −0.461431 | + | 0.612015i | ||||
\(85\) | 1.12330 | 0.121839 | ||||||||
\(86\) | 6.44111 | − | 11.1563i | 0.694563 | − | 1.20302i | ||||
\(87\) | 6.17854 | + | 10.7015i | 0.662409 | + | 1.14733i | ||||
\(88\) | 1.52634 | + | 2.64371i | 0.162709 | + | 0.281820i | ||||
\(89\) | 7.04583 | − | 12.2037i | 0.746856 | − | 1.29359i | −0.202467 | − | 0.979289i | \(-0.564896\pi\) |
0.949323 | − | 0.314303i | \(-0.101771\pi\) | |||||||
\(90\) | −6.88158 | −0.725383 | ||||||||
\(91\) | −5.41543 | − | 0.666329i | −0.567691 | − | 0.0698503i | ||||
\(92\) | −3.45330 | −0.360031 | ||||||||
\(93\) | 0.500573 | − | 0.867017i | 0.0519070 | − | 0.0899055i | ||||
\(94\) | 0.561652 | + | 0.972810i | 0.0579300 | + | 0.100338i | ||||
\(95\) | 4.23532 | + | 7.33580i | 0.434535 | + | 0.752637i | ||||
\(96\) | −6.88323 | + | 11.9221i | −0.702517 | + | 1.21680i | ||||
\(97\) | −16.8254 | −1.70836 | −0.854180 | − | 0.519977i | \(-0.825940\pi\) | ||||
−0.854180 | + | 0.519977i | \(0.825940\pi\) | |||||||
\(98\) | −5.18663 | + | 5.36545i | −0.523929 | + | 0.541992i | ||||
\(99\) | 6.45507 | 0.648759 | ||||||||
\(100\) | 0.431743 | − | 0.747801i | 0.0431743 | − | 0.0747801i | ||||
\(101\) | −7.12645 | − | 12.3434i | −0.709109 | − | 1.22821i | −0.965188 | − | 0.261557i | \(-0.915764\pi\) |
0.256079 | − | 0.966656i | \(-0.417569\pi\) | |||||||
\(102\) | 1.84114 | + | 3.18895i | 0.182300 | + | 0.315753i | ||||
\(103\) | 8.12911 | − | 14.0800i | 0.800985 | − | 1.38735i | −0.117983 | − | 0.993016i | \(-0.537643\pi\) |
0.918968 | − | 0.394332i | \(-0.129024\pi\) | |||||||
\(104\) | −6.29549 | −0.617323 | ||||||||
\(105\) | 8.07455 | + | 0.993515i | 0.787996 | + | 0.0969571i | ||||
\(106\) | −0.942881 | −0.0915807 | ||||||||
\(107\) | −4.29016 | + | 7.43078i | −0.414745 | + | 0.718360i | −0.995402 | − | 0.0957886i | \(-0.969463\pi\) |
0.580656 | + | 0.814149i | \(0.302796\pi\) | |||||||
\(108\) | 4.58685 | + | 7.94465i | 0.441369 | + | 0.764474i | ||||
\(109\) | −2.07085 | − | 3.58681i | −0.198351 | − | 0.343555i | 0.749643 | − | 0.661843i | \(-0.230225\pi\) |
−0.947994 | + | 0.318288i | \(0.896892\pi\) | |||||||
\(110\) | 0.533037 | − | 0.923247i | 0.0508231 | − | 0.0880282i | ||||
\(111\) | 16.6329 | 1.57872 | ||||||||
\(112\) | −2.43286 | + | 3.22681i | −0.229884 | + | 0.304905i | ||||
\(113\) | 2.95520 | 0.278002 | 0.139001 | − | 0.990292i | \(-0.455611\pi\) | ||||
0.139001 | + | 0.990292i | \(0.455611\pi\) | |||||||
\(114\) | −13.8837 | + | 24.0473i | −1.30033 | + | 2.25224i | ||||
\(115\) | 1.99963 | + | 3.46346i | 0.186466 | + | 0.322969i | ||||
\(116\) | −1.73504 | − | 3.00517i | −0.161094 | − | 0.279023i | ||||
\(117\) | −6.65607 | + | 11.5286i | −0.615354 | + | 1.06582i | ||||
\(118\) | 14.7856 | 1.36113 | ||||||||
\(119\) | −1.16055 | − | 2.73602i | −0.106388 | − | 0.250811i | ||||
\(120\) | 9.38674 | 0.856888 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −0.873471 | − | 1.51290i | −0.0790804 | − | 0.136971i | ||||
\(123\) | −1.89487 | − | 3.28201i | −0.170855 | − | 0.295929i | ||||
\(124\) | −0.140569 | + | 0.243473i | −0.0126235 | + | 0.0218645i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 7.10976 | + | 16.7614i | 0.633388 | + | 1.49322i | ||||
\(127\) | −6.78852 | −0.602383 | −0.301192 | − | 0.953564i | \(-0.597384\pi\) | ||||
−0.301192 | + | 0.953564i | \(0.597384\pi\) | |||||||
\(128\) | 0.304582 | − | 0.527552i | 0.0269215 | − | 0.0466294i | ||||
\(129\) | 18.5783 | + | 32.1786i | 1.63573 | + | 2.83316i | ||||
\(130\) | 1.09927 | + | 1.90399i | 0.0964123 | + | 0.166991i | ||||
\(131\) | 2.06094 | − | 3.56966i | 0.180065 | − | 0.311883i | −0.761837 | − | 0.647769i | \(-0.775702\pi\) |
0.941903 | + | 0.335886i | \(0.109036\pi\) | |||||||
\(132\) | −2.65514 | −0.231100 | ||||||||
\(133\) | 13.4920 | − | 17.8950i | 1.16990 | − | 1.55169i | ||||
\(134\) | 11.4678 | 0.990668 | ||||||||
\(135\) | 5.31201 | − | 9.20067i | 0.457185 | − | 0.791868i | ||||
\(136\) | −1.71455 | − | 2.96969i | −0.147021 | − | 0.254648i | ||||
\(137\) | −5.75396 | − | 9.96615i | −0.491594 | − | 0.851465i | 0.508359 | − | 0.861145i | \(-0.330252\pi\) |
−0.999953 | + | 0.00967958i | \(0.996919\pi\) | |||||||
\(138\) | −6.55495 | + | 11.3535i | −0.557994 | + | 0.966474i | ||||
\(139\) | −0.783249 | −0.0664343 | −0.0332172 | − | 0.999448i | \(-0.510575\pi\) | ||||
−0.0332172 | + | 0.999448i | \(0.510575\pi\) | |||||||
\(140\) | −2.26747 | − | 0.278995i | −0.191636 | − | 0.0235794i | ||||
\(141\) | −3.23998 | −0.272855 | ||||||||
\(142\) | −4.36388 | + | 7.55846i | −0.366209 | + | 0.634292i | ||||
\(143\) | −1.03114 | − | 1.78598i | −0.0862281 | − | 0.149351i | ||||
\(144\) | 4.92980 | + | 8.53867i | 0.410817 | + | 0.711556i | ||||
\(145\) | −2.00934 | + | 3.48028i | −0.166867 | + | 0.289022i | ||||
\(146\) | −13.8176 | −1.14356 | ||||||||
\(147\) | −5.92240 | − | 20.6936i | −0.488471 | − | 1.70678i | ||||
\(148\) | −4.67078 | −0.383936 | ||||||||
\(149\) | −5.48695 | + | 9.50368i | −0.449509 | + | 0.778572i | −0.998354 | − | 0.0573521i | \(-0.981734\pi\) |
0.548845 | + | 0.835924i | \(0.315068\pi\) | |||||||
\(150\) | −1.63904 | − | 2.83890i | −0.133827 | − | 0.231795i | ||||
\(151\) | 4.81317 | + | 8.33666i | 0.391691 | + | 0.678428i | 0.992673 | − | 0.120834i | \(-0.0385570\pi\) |
−0.600982 | + | 0.799263i | \(0.705224\pi\) | |||||||
\(152\) | 12.9291 | − | 22.3939i | 1.04869 | − | 1.81639i | ||||
\(153\) | −7.25101 | −0.586209 | ||||||||
\(154\) | −2.79946 | − | 0.344453i | −0.225587 | − | 0.0277568i | ||||
\(155\) | 0.325585 | 0.0261516 | ||||||||
\(156\) | 2.73782 | − | 4.74204i | 0.219201 | − | 0.379667i | ||||
\(157\) | 9.67603 | + | 16.7594i | 0.772231 | + | 1.33754i | 0.936337 | + | 0.351101i | \(0.114193\pi\) |
−0.164106 | + | 0.986443i | \(0.552474\pi\) | |||||||
\(158\) | −3.96571 | − | 6.86881i | −0.315495 | − | 0.546453i | ||||
\(159\) | 1.35979 | − | 2.35522i | 0.107838 | − | 0.186781i | ||||
\(160\) | −4.47703 | −0.353940 | ||||||||
\(161\) | 6.36998 | − | 8.44877i | 0.502024 | − | 0.665857i | ||||
\(162\) | 14.1817 | 1.11422 | ||||||||
\(163\) | −8.05931 | + | 13.9591i | −0.631254 | + | 1.09336i | 0.356042 | + | 0.934470i | \(0.384126\pi\) |
−0.987296 | + | 0.158894i | \(0.949207\pi\) | |||||||
\(164\) | 0.532111 | + | 0.921643i | 0.0415509 | + | 0.0719682i | ||||
\(165\) | 1.53745 | + | 2.66295i | 0.119691 | + | 0.207310i | ||||
\(166\) | −2.23958 | + | 3.87906i | −0.173825 | + | 0.301074i | ||||
\(167\) | −9.27253 | −0.717530 | −0.358765 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358765 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(168\) | −9.69799 | − | 22.8632i | −0.748216 | − | 1.76393i | ||||
\(169\) | −8.74702 | −0.672847 | ||||||||
\(170\) | −0.598763 | + | 1.03709i | −0.0459230 | + | 0.0795410i | ||||
\(171\) | −27.3393 | − | 47.3531i | −2.09069 | − | 3.62118i | ||||
\(172\) | −5.21709 | − | 9.03627i | −0.397800 | − | 0.689009i | ||||
\(173\) | 9.62070 | − | 16.6635i | 0.731448 | − | 1.26691i | −0.224816 | − | 0.974401i | \(-0.572178\pi\) |
0.956264 | − | 0.292505i | \(-0.0944887\pi\) | |||||||
\(174\) | −13.1736 | −0.998685 | ||||||||
\(175\) | 1.03316 | + | 2.43569i | 0.0780994 | + | 0.184121i | ||||
\(176\) | −1.52742 | −0.115134 | ||||||||
\(177\) | −21.3233 | + | 36.9330i | −1.60276 | + | 2.77606i | ||||
\(178\) | 7.51137 | + | 13.0101i | 0.563001 | + | 0.975147i | ||||
\(179\) | 4.17161 | + | 7.22544i | 0.311801 | + | 0.540055i | 0.978752 | − | 0.205046i | \(-0.0657345\pi\) |
−0.666952 | + | 0.745101i | \(0.732401\pi\) | |||||||
\(180\) | −2.78693 | + | 4.82710i | −0.207725 | + | 0.359791i | ||||
\(181\) | −18.9132 | −1.40580 | −0.702902 | − | 0.711287i | \(-0.748113\pi\) | ||||
−0.702902 | + | 0.711287i | \(0.748113\pi\) | |||||||
\(182\) | 3.50181 | − | 4.64460i | 0.259572 | − | 0.344281i | ||||
\(183\) | 5.03876 | 0.372476 | ||||||||
\(184\) | 6.10424 | − | 10.5729i | 0.450011 | − | 0.779441i | ||||
\(185\) | 2.70461 | + | 4.68452i | 0.198847 | + | 0.344413i | ||||
\(186\) | 0.533648 | + | 0.924305i | 0.0391289 | + | 0.0677733i | ||||
\(187\) | 0.561652 | − | 0.972810i | 0.0410721 | − | 0.0711389i | ||||
\(188\) | 0.909840 | 0.0663569 | ||||||||
\(189\) | −27.8981 | − | 3.43266i | −2.02929 | − | 0.249689i | ||||
\(190\) | −9.03034 | −0.655130 | ||||||||
\(191\) | −0.597017 | + | 1.03406i | −0.0431986 | + | 0.0748222i | −0.886816 | − | 0.462122i | \(-0.847088\pi\) |
0.843618 | + | 0.536944i | \(0.180421\pi\) | |||||||
\(192\) | −12.0347 | − | 20.8447i | −0.868531 | − | 1.50434i | ||||
\(193\) | 11.1045 | + | 19.2335i | 0.799319 | + | 1.38446i | 0.920060 | + | 0.391777i | \(0.128140\pi\) |
−0.120741 | + | 0.992684i | \(0.538527\pi\) | |||||||
\(194\) | 8.96856 | − | 15.5340i | 0.643905 | − | 1.11528i | ||||
\(195\) | −6.34131 | −0.454111 | ||||||||
\(196\) | 1.66311 | + | 5.81110i | 0.118793 | + | 0.415078i | ||||
\(197\) | −5.35087 | −0.381234 | −0.190617 | − | 0.981664i | \(-0.561049\pi\) | ||||
−0.190617 | + | 0.981664i | \(0.561049\pi\) | |||||||
\(198\) | −3.44079 | + | 5.95963i | −0.244526 | + | 0.423532i | ||||
\(199\) | 5.51146 | + | 9.54613i | 0.390697 | + | 0.676707i | 0.992542 | − | 0.121906i | \(-0.0389007\pi\) |
−0.601845 | + | 0.798613i | \(0.705567\pi\) | |||||||
\(200\) | 1.52634 | + | 2.64371i | 0.107929 | + | 0.186938i | ||||
\(201\) | −16.5385 | + | 28.6455i | −1.16653 | + | 2.02050i | ||||
\(202\) | 15.1947 | 1.06909 | ||||||||
\(203\) | 10.5528 | + | 1.29845i | 0.740665 | + | 0.0911334i | ||||
\(204\) | 2.98253 | 0.208819 | ||||||||
\(205\) | 0.616236 | − | 1.06735i | 0.0430398 | − | 0.0745471i | ||||
\(206\) | 8.66624 | + | 15.0104i | 0.603805 | + | 1.04582i | ||||
\(207\) | −12.9077 | − | 22.3569i | −0.897150 | − | 1.55391i | ||||
\(208\) | 1.57498 | − | 2.72795i | 0.109205 | − | 0.189149i | ||||
\(209\) | 8.47065 | 0.585927 | ||||||||
\(210\) | −5.22130 | + | 6.92523i | −0.360304 | + | 0.477886i | ||||
\(211\) | 4.84291 | 0.333400 | 0.166700 | − | 0.986008i | \(-0.446689\pi\) | ||||
0.166700 | + | 0.986008i | \(0.446689\pi\) | |||||||
\(212\) | −0.381851 | + | 0.661386i | −0.0262257 | + | 0.0454242i | ||||
\(213\) | −12.5869 | − | 21.8011i | −0.862438 | − | 1.49379i | ||||
\(214\) | −4.57363 | − | 7.92176i | −0.312647 | − | 0.541520i | ||||
\(215\) | −6.04190 | + | 10.4649i | −0.412054 | + | 0.713699i | ||||
\(216\) | −32.4318 | −2.20671 | ||||||||
\(217\) | −0.336381 | − | 0.793025i | −0.0228350 | − | 0.0538340i | ||||
\(218\) | 4.41536 | 0.299046 | ||||||||
\(219\) | 19.9273 | − | 34.5151i | 1.34656 | − | 2.33232i | ||||
\(220\) | −0.431743 | − | 0.747801i | −0.0291081 | − | 0.0504167i | ||||
\(221\) | 1.15828 | + | 2.00620i | 0.0779145 | + | 0.134952i | ||||
\(222\) | −8.86593 | + | 15.3562i | −0.595042 | + | 1.03064i | ||||
\(223\) | −10.7581 | −0.720412 | −0.360206 | − | 0.932873i | \(-0.617294\pi\) | ||||
−0.360206 | + | 0.932873i | \(0.617294\pi\) | |||||||
\(224\) | 4.62548 | + | 10.9047i | 0.309053 | + | 0.728598i | ||||
\(225\) | 6.45507 | 0.430338 | ||||||||
\(226\) | −1.57523 | + | 2.72838i | −0.104783 | + | 0.181489i | ||||
\(227\) | −2.31224 | − | 4.00491i | −0.153469 | − | 0.265815i | 0.779032 | − | 0.626984i | \(-0.215711\pi\) |
−0.932500 | + | 0.361169i | \(0.882378\pi\) | |||||||
\(228\) | 11.2454 | + | 19.4776i | 0.744744 | + | 1.28993i | ||||
\(229\) | 0.827005 | − | 1.43241i | 0.0546500 | − | 0.0946566i | −0.837406 | − | 0.546581i | \(-0.815929\pi\) |
0.892056 | + | 0.451924i | \(0.149262\pi\) | |||||||
\(230\) | −4.26350 | −0.281127 | ||||||||
\(231\) | 4.89769 | − | 6.49601i | 0.322244 | − | 0.427406i | ||||
\(232\) | 12.2678 | 0.805419 | ||||||||
\(233\) | −1.04515 | + | 1.81025i | −0.0684700 | + | 0.118594i | −0.898228 | − | 0.439530i | \(-0.855145\pi\) |
0.829758 | + | 0.558123i | \(0.188478\pi\) | |||||||
\(234\) | −7.09586 | − | 12.2904i | −0.463871 | − | 0.803448i | ||||
\(235\) | −0.526841 | − | 0.912516i | −0.0343673 | − | 0.0595260i | ||||
\(236\) | 5.98794 | − | 10.3714i | 0.389782 | − | 0.675121i | ||||
\(237\) | 22.8768 | 1.48601 | ||||||||
\(238\) | 3.14464 | + | 0.386925i | 0.203837 | + | 0.0250806i | ||||
\(239\) | −13.1060 | −0.847754 | −0.423877 | − | 0.905720i | \(-0.639331\pi\) | ||||
−0.423877 | + | 0.905720i | \(0.639331\pi\) | |||||||
\(240\) | −2.34834 | + | 4.06745i | −0.151585 | + | 0.262553i | ||||
\(241\) | −2.96322 | − | 5.13244i | −0.190877 | − | 0.330609i | 0.754664 | − | 0.656112i | \(-0.227800\pi\) |
−0.945541 | + | 0.325502i | \(0.894467\pi\) | |||||||
\(242\) | −0.533037 | − | 0.923247i | −0.0342649 | − | 0.0593486i | ||||
\(243\) | −4.51627 | + | 7.82242i | −0.289719 | + | 0.501808i | ||||
\(244\) | −1.41497 | −0.0905840 | ||||||||
\(245\) | 4.86517 | − | 5.03290i | 0.310824 | − | 0.321540i | ||||
\(246\) | 4.04014 | 0.257590 | ||||||||
\(247\) | −8.73441 | + | 15.1284i | −0.555757 | + | 0.962600i | ||||
\(248\) | −0.496955 | − | 0.860752i | −0.0315567 | − | 0.0546578i | ||||
\(249\) | −6.45968 | − | 11.1885i | −0.409366 | − | 0.709042i | ||||
\(250\) | 0.533037 | − | 0.923247i | 0.0337122 | − | 0.0583913i | ||||
\(251\) | 8.12067 | 0.512572 | 0.256286 | − | 0.966601i | \(-0.417501\pi\) | ||||
0.256286 | + | 0.966601i | \(0.417501\pi\) | |||||||
\(252\) | 14.6367 | + | 1.80093i | 0.922023 | + | 0.113448i | ||||
\(253\) | 3.99926 | 0.251431 | ||||||||
\(254\) | 3.61853 | − | 6.26748i | 0.227047 | − | 0.393257i | ||||
\(255\) | −1.72703 | − | 2.99130i | −0.108151 | − | 0.187323i | ||||
\(256\) | 8.15240 | + | 14.1204i | 0.509525 | + | 0.882523i | ||||
\(257\) | −13.1908 | + | 22.8471i | −0.822818 | + | 1.42516i | 0.0807568 | + | 0.996734i | \(0.474266\pi\) |
−0.903575 | + | 0.428429i | \(0.859067\pi\) | |||||||
\(258\) | −39.6117 | −2.46612 | ||||||||
\(259\) | 8.61575 | − | 11.4274i | 0.535357 | − | 0.710067i | ||||
\(260\) | 1.78075 | 0.110437 | ||||||||
\(261\) | 12.9704 | − | 22.4654i | 0.802850 | − | 1.39058i | ||||
\(262\) | 2.19712 | + | 3.80552i | 0.135738 | + | 0.235106i | ||||
\(263\) | 10.3845 | + | 17.9865i | 0.640337 | + | 1.10910i | 0.985358 | + | 0.170501i | \(0.0545385\pi\) |
−0.345021 | + | 0.938595i | \(0.612128\pi\) | |||||||
\(264\) | 4.69337 | − | 8.12916i | 0.288857 | − | 0.500315i | ||||
\(265\) | 0.884442 | 0.0543308 | ||||||||
\(266\) | 9.32977 | + | 21.9951i | 0.572045 | + | 1.34861i | ||||
\(267\) | −43.3306 | −2.65179 | ||||||||
\(268\) | 4.64428 | − | 8.04412i | 0.283694 | − | 0.491373i | ||||
\(269\) | 5.33628 | + | 9.24271i | 0.325359 | + | 0.563538i | 0.981585 | − | 0.191026i | \(-0.0611816\pi\) |
−0.656226 | + | 0.754564i | \(0.727848\pi\) | |||||||
\(270\) | 5.66300 | + | 9.80860i | 0.344639 | + | 0.596933i | ||||
\(271\) | 2.62181 | − | 4.54110i | 0.159263 | − | 0.275852i | −0.775340 | − | 0.631544i | \(-0.782421\pi\) |
0.934603 | + | 0.355692i | \(0.115755\pi\) | |||||||
\(272\) | 1.71576 | 0.104033 | ||||||||
\(273\) | 6.55158 | + | 15.4455i | 0.396520 | + | 0.934802i | ||||
\(274\) | 12.2683 | 0.741155 | ||||||||
\(275\) | −0.500000 | + | 0.866025i | −0.0301511 | + | 0.0522233i | ||||
\(276\) | 5.30929 | + | 9.19597i | 0.319582 | + | 0.553532i | ||||
\(277\) | 9.18831 | + | 15.9146i | 0.552072 | + | 0.956216i | 0.998125 | + | 0.0612099i | \(0.0194959\pi\) |
−0.446053 | + | 0.895006i | \(0.647171\pi\) | |||||||
\(278\) | 0.417501 | − | 0.723133i | 0.0250400 | − | 0.0433706i | ||||
\(279\) | −2.10168 | −0.125824 | ||||||||
\(280\) | 4.86229 | − | 6.44907i | 0.290578 | − | 0.385405i | ||||
\(281\) | −2.89615 | −0.172770 | −0.0863849 | − | 0.996262i | \(-0.527531\pi\) | ||||
−0.0863849 | + | 0.996262i | \(0.527531\pi\) | |||||||
\(282\) | 1.72703 | − | 2.99130i | 0.102843 | − | 0.178129i | ||||
\(283\) | −2.19606 | − | 3.80369i | −0.130542 | − | 0.226106i | 0.793344 | − | 0.608774i | \(-0.208338\pi\) |
−0.923886 | + | 0.382669i | \(0.875005\pi\) | |||||||
\(284\) | 3.53460 | + | 6.12211i | 0.209740 | + | 0.363280i | ||||
\(285\) | 13.0232 | − | 22.5569i | 0.771430 | − | 1.33616i | ||||
\(286\) | 2.19854 | 0.130002 | ||||||||
\(287\) | −3.23641 | − | 0.398216i | −0.191039 | − | 0.0235060i | ||||
\(288\) | 28.8996 | 1.70292 | ||||||||
\(289\) | 7.86909 | − | 13.6297i | 0.462888 | − | 0.801745i | ||||
\(290\) | −2.14211 | − | 3.71024i | −0.125789 | − | 0.217873i | ||||
\(291\) | 25.8683 | + | 44.8052i | 1.51643 | + | 2.62653i | ||||
\(292\) | −5.59592 | + | 9.69242i | −0.327477 | + | 0.567206i | ||||
\(293\) | −21.0343 | −1.22884 | −0.614418 | − | 0.788981i | \(-0.710609\pi\) | ||||
−0.614418 | + | 0.788981i | \(0.710609\pi\) | |||||||
\(294\) | 22.2621 | + | 5.56260i | 1.29835 | + | 0.324418i | ||||
\(295\) | −13.8692 | −0.807497 | ||||||||
\(296\) | 8.25633 | − | 14.3004i | 0.479890 | − | 0.831193i | ||||
\(297\) | −5.31201 | − | 9.20067i | −0.308234 | − | 0.533877i | ||||
\(298\) | −5.84950 | − | 10.1316i | −0.338852 | − | 0.586910i | ||||
\(299\) | −4.12379 | + | 7.14261i | −0.238485 | + | 0.413068i | ||||
\(300\) | −2.65514 | −0.153295 | ||||||||
\(301\) | 31.7314 | + | 3.90432i | 1.82897 | + | 0.225041i | ||||
\(302\) | −10.2624 | −0.590535 | ||||||||
\(303\) | −21.9132 | + | 37.9548i | −1.25888 | + | 2.18045i | ||||
\(304\) | 6.46912 | + | 11.2049i | 0.371030 | + | 0.642642i | ||||
\(305\) | 0.819335 | + | 1.41913i | 0.0469150 | + | 0.0812591i | ||||
\(306\) | 3.86506 | − | 6.69447i | 0.220950 | − | 0.382697i | ||||
\(307\) | 24.8681 | 1.41930 | 0.709648 | − | 0.704556i | \(-0.248854\pi\) | ||||
0.709648 | + | 0.704556i | \(0.248854\pi\) | |||||||
\(308\) | −1.37535 | + | 1.82419i | −0.0783679 | + | 0.103943i | ||||
\(309\) | −49.9926 | −2.84398 | ||||||||
\(310\) | −0.173549 | + | 0.300596i | −0.00985692 | + | 0.0170727i | ||||
\(311\) | 12.1742 | + | 21.0864i | 0.690336 | + | 1.19570i | 0.971728 | + | 0.236104i | \(0.0758708\pi\) |
−0.281391 | + | 0.959593i | \(0.590796\pi\) | |||||||
\(312\) | 9.67903 | + | 16.7646i | 0.547967 | + | 0.949107i | ||||
\(313\) | −0.574509 | + | 0.995079i | −0.0324732 | + | 0.0562452i | −0.881805 | − | 0.471614i | \(-0.843672\pi\) |
0.849332 | + | 0.527859i | \(0.177005\pi\) | |||||||
\(314\) | −20.6307 | −1.16426 | ||||||||
\(315\) | −6.66911 | − | 15.7225i | −0.375762 | − | 0.885865i | ||||
\(316\) | −6.42419 | −0.361389 | ||||||||
\(317\) | −9.67734 | + | 16.7616i | −0.543533 | + | 0.941428i | 0.455164 | + | 0.890408i | \(0.349581\pi\) |
−0.998698 | + | 0.0510201i | \(0.983753\pi\) | |||||||
\(318\) | 1.44964 | + | 2.51084i | 0.0812916 | + | 0.140801i | ||||
\(319\) | 2.00934 | + | 3.48028i | 0.112501 | + | 0.194858i | ||||
\(320\) | 3.91385 | − | 6.77898i | 0.218791 | − | 0.378956i | ||||
\(321\) | 26.3837 | 1.47260 | ||||||||
\(322\) | 4.40487 | + | 10.3846i | 0.245474 | + | 0.578710i | ||||
\(323\) | −9.51511 | −0.529435 | ||||||||
\(324\) | 5.74335 | − | 9.94777i | 0.319075 | − | 0.552654i | ||||
\(325\) | −1.03114 | − | 1.78598i | −0.0571973 | − | 0.0990685i | ||||
\(326\) | −8.59182 | − | 14.8815i | −0.475857 | − | 0.824208i | ||||
\(327\) | −6.36767 | + | 11.0291i | −0.352133 | + | 0.609912i | ||||
\(328\) | −3.76235 | −0.207741 | ||||||||
\(329\) | −1.67830 | + | 2.22600i | −0.0925274 | + | 0.122723i | ||||
\(330\) | −3.27808 | −0.180452 | ||||||||
\(331\) | 1.62987 | − | 2.82301i | 0.0895856 | − | 0.155167i | −0.817750 | − | 0.575573i | \(-0.804779\pi\) |
0.907336 | + | 0.420406i | \(0.138112\pi\) | |||||||
\(332\) | 1.81399 | + | 3.14192i | 0.0995554 | + | 0.172435i | ||||
\(333\) | −17.4584 | − | 30.2389i | −0.956717 | − | 1.65708i | ||||
\(334\) | 4.94260 | − | 8.56084i | 0.270447 | − | 0.468428i | ||||
\(335\) | −10.7570 | −0.587720 | ||||||||
\(336\) | 12.3332 | + | 1.51752i | 0.672834 | + | 0.0827873i | ||||
\(337\) | −0.431489 | −0.0235047 | −0.0117523 | − | 0.999931i | \(-0.503741\pi\) | ||||
−0.0117523 | + | 0.999931i | \(0.503741\pi\) | |||||||
\(338\) | 4.66248 | − | 8.07566i | 0.253606 | − | 0.439258i | ||||
\(339\) | −4.54348 | − | 7.86955i | −0.246768 | − | 0.427415i | ||||
\(340\) | 0.484978 | + | 0.840007i | 0.0263017 | + | 0.0455558i | ||||
\(341\) | 0.162793 | − | 0.281965i | 0.00881571 | − | 0.0152693i | ||||
\(342\) | 58.2915 | 3.15204 | ||||||||
\(343\) | −17.2851 | − | 6.65026i | −0.933307 | − | 0.359080i | ||||
\(344\) | 36.8881 | 1.98887 | ||||||||
\(345\) | 6.14868 | − | 10.6498i | 0.331034 | − | 0.573367i | ||||
\(346\) | 10.2564 | + | 17.7646i | 0.551387 | + | 0.955030i | ||||
\(347\) | 1.29750 | + | 2.24734i | 0.0696535 | + | 0.120643i | 0.898749 | − | 0.438464i | \(-0.144477\pi\) |
−0.829095 | + | 0.559107i | \(0.811144\pi\) | |||||||
\(348\) | −5.33508 | + | 9.24063i | −0.285990 | + | 0.495350i | ||||
\(349\) | −11.7944 | −0.631340 | −0.315670 | − | 0.948869i | \(-0.602229\pi\) | ||||
−0.315670 | + | 0.948869i | \(0.602229\pi\) | |||||||
\(350\) | −2.79946 | − | 0.344453i | −0.149637 | − | 0.0184118i | ||||
\(351\) | 21.9097 | 1.16945 | ||||||||
\(352\) | −2.23852 | + | 3.87722i | −0.119313 | + | 0.206657i | ||||
\(353\) | 1.03652 | + | 1.79531i | 0.0551685 | + | 0.0955546i | 0.892291 | − | 0.451461i | \(-0.149097\pi\) |
−0.837122 | + | 0.547016i | \(0.815764\pi\) | |||||||
\(354\) | −22.7322 | − | 39.3734i | −1.20820 | − | 2.09267i | ||||
\(355\) | 4.09341 | − | 7.09000i | 0.217256 | − | 0.376298i | ||||
\(356\) | 12.1679 | 0.644899 | ||||||||
\(357\) | −5.50159 | + | 7.29700i | −0.291175 | + | 0.386198i | ||||
\(358\) | −8.89449 | −0.470088 | ||||||||
\(359\) | 15.1378 | − | 26.2195i | 0.798943 | − | 1.38381i | −0.121362 | − | 0.992608i | \(-0.538726\pi\) |
0.920305 | − | 0.391202i | \(-0.127941\pi\) | |||||||
\(360\) | −9.85266 | − | 17.0653i | −0.519281 | − | 0.899420i | ||||
\(361\) | −26.3759 | − | 45.6845i | −1.38821 | − | 2.40445i | ||||
\(362\) | 10.0814 | − | 17.4615i | 0.529868 | − | 0.917758i | ||||
\(363\) | 3.07491 | 0.161391 | ||||||||
\(364\) | −1.83979 | − | 4.33734i | −0.0964313 | − | 0.227339i | ||||
\(365\) | 12.9612 | 0.678422 | ||||||||
\(366\) | −2.68585 | + | 4.65202i | −0.140391 | + | 0.243165i | ||||
\(367\) | −4.01976 | − | 6.96242i | −0.209830 | − | 0.363435i | 0.741831 | − | 0.670587i | \(-0.233958\pi\) |
−0.951661 | + | 0.307151i | \(0.900624\pi\) | |||||||
\(368\) | 3.05427 | + | 5.29016i | 0.159215 | + | 0.275769i | ||||
\(369\) | −3.97785 | + | 6.88983i | −0.207078 | + | 0.358670i | ||||
\(370\) | −5.76663 | −0.299793 | ||||||||
\(371\) | −0.913768 | − | 2.15423i | −0.0474405 | − | 0.111842i | ||||
\(372\) | 0.864474 | 0.0448209 | ||||||||
\(373\) | 14.9828 | − | 25.9510i | 0.775780 | − | 1.34369i | −0.158575 | − | 0.987347i | \(-0.550690\pi\) |
0.934355 | − | 0.356344i | \(-0.115977\pi\) | |||||||
\(374\) | 0.598763 | + | 1.03709i | 0.0309613 | + | 0.0536265i | ||||
\(375\) | 1.53745 | + | 2.66295i | 0.0793938 | + | 0.137514i | ||||
\(376\) | −1.60828 | + | 2.78563i | −0.0829408 | + | 0.143658i | ||||
\(377\) | −8.28763 | −0.426835 | ||||||||
\(378\) | 18.0399 | − | 23.9271i | 0.927874 | − | 1.23068i | ||||
\(379\) | 19.3330 | 0.993068 | 0.496534 | − | 0.868017i | \(-0.334606\pi\) | ||||
0.496534 | + | 0.868017i | \(0.334606\pi\) | |||||||
\(380\) | −3.65714 | + | 6.33436i | −0.187607 | + | 0.324946i | ||||
\(381\) | 10.4370 | + | 18.0775i | 0.534706 | + | 0.926137i | ||||
\(382\) | −0.636464 | − | 1.10239i | −0.0325643 | − | 0.0564031i | ||||
\(383\) | 5.04615 | − | 8.74019i | 0.257846 | − | 0.446603i | −0.707818 | − | 0.706395i | \(-0.750320\pi\) |
0.965665 | + | 0.259791i | \(0.0836538\pi\) | |||||||
\(384\) | −1.87312 | −0.0955875 | ||||||||
\(385\) | 2.62595 | + | 0.323104i | 0.133831 | + | 0.0164669i | ||||
\(386\) | −23.6764 | −1.20510 | ||||||||
\(387\) | 39.0009 | − | 67.5515i | 1.98253 | − | 3.43384i | ||||
\(388\) | −7.26424 | − | 12.5820i | −0.368786 | − | 0.638756i | ||||
\(389\) | −13.6428 | − | 23.6300i | −0.691717 | − | 1.19809i | −0.971275 | − | 0.237960i | \(-0.923521\pi\) |
0.279559 | − | 0.960129i | \(-0.409812\pi\) | |||||||
\(390\) | 3.38016 | − | 5.85460i | 0.171161 | − | 0.296459i | ||||
\(391\) | −4.49238 | −0.227189 | ||||||||
\(392\) | −20.7314 | − | 5.18013i | −1.04710 | − | 0.261636i | ||||
\(393\) | −12.6744 | −0.639340 | ||||||||
\(394\) | 2.85221 | − | 4.94018i | 0.143692 | − | 0.248883i | ||||
\(395\) | 3.71992 | + | 6.44309i | 0.187169 | + | 0.324187i | ||||
\(396\) | 2.78693 | + | 4.82710i | 0.140048 | + | 0.242571i | ||||
\(397\) | 12.6298 | − | 21.8754i | 0.633870 | − | 1.09789i | −0.352883 | − | 0.935667i | \(-0.614799\pi\) |
0.986753 | − | 0.162228i | \(-0.0518679\pi\) | |||||||
\(398\) | −11.7512 | −0.589037 | ||||||||
\(399\) | −68.3967 | − | 8.41572i | −3.42412 | − | 0.421313i | ||||
\(400\) | −1.52742 | −0.0763711 | ||||||||
\(401\) | −2.65566 | + | 4.59974i | −0.132617 | + | 0.229700i | −0.924685 | − | 0.380734i | \(-0.875671\pi\) |
0.792067 | + | 0.610434i | \(0.209005\pi\) | |||||||
\(402\) | −17.6312 | − | 30.5382i | −0.879366 | − | 1.52311i | ||||
\(403\) | 0.335723 | + | 0.581490i | 0.0167236 | + | 0.0289661i | ||||
\(404\) | 6.15359 | − | 10.6583i | 0.306153 | − | 0.530272i | ||||
\(405\) | −13.3027 | −0.661017 | ||||||||
\(406\) | −6.82385 | + | 9.05077i | −0.338662 | + | 0.449182i | ||||
\(407\) | 5.40922 | 0.268125 | ||||||||
\(408\) | −5.27208 | + | 9.13151i | −0.261007 | + | 0.452077i | ||||
\(409\) | 15.0340 | + | 26.0397i | 0.743384 | + | 1.28758i | 0.950946 | + | 0.309357i | \(0.100114\pi\) |
−0.207562 | + | 0.978222i | \(0.566553\pi\) | |||||||
\(410\) | 0.656953 | + | 1.13788i | 0.0324446 | + | 0.0561957i | ||||
\(411\) | −17.6929 | + | 30.6450i | −0.872726 | + | 1.51161i | ||||
\(412\) | 14.0387 | 0.691639 | ||||||||
\(413\) | 14.3291 | + | 33.7811i | 0.705089 | + | 1.66226i | ||||
\(414\) | 27.5212 | 1.35259 | ||||||||
\(415\) | 2.10077 | − | 3.63864i | 0.103123 | − | 0.178614i | ||||
\(416\) | −4.61644 | − | 7.99591i | −0.226340 | − | 0.392032i | ||||
\(417\) | 1.20421 | + | 2.08575i | 0.0589704 | + | 0.102140i | ||||
\(418\) | −4.51517 | + | 7.82050i | −0.220844 | + | 0.382513i | ||||
\(419\) | 12.9969 | 0.634938 | 0.317469 | − | 0.948269i | \(-0.397167\pi\) | ||||
0.317469 | + | 0.948269i | \(0.397167\pi\) | |||||||
\(420\) | 2.74318 | + | 6.46710i | 0.133853 | + | 0.315562i | ||||
\(421\) | −2.56078 | −0.124805 | −0.0624024 | − | 0.998051i | \(-0.519876\pi\) | ||||
−0.0624024 | + | 0.998051i | \(0.519876\pi\) | |||||||
\(422\) | −2.58145 | + | 4.47121i | −0.125663 | + | 0.217655i | ||||
\(423\) | 3.40080 | + | 5.89035i | 0.165352 | + | 0.286399i | ||||
\(424\) | −1.34996 | − | 2.33820i | −0.0655600 | − | 0.113553i | ||||
\(425\) | 0.561652 | − | 0.972810i | 0.0272441 | − | 0.0471882i | ||||
\(426\) | 26.8371 | 1.30026 | ||||||||
\(427\) | 2.61006 | − | 3.46183i | 0.126309 | − | 0.167530i | ||||
\(428\) | −7.40898 | −0.358127 | ||||||||
\(429\) | −3.17066 | + | 5.49174i | −0.153081 | + | 0.265144i | ||||
\(430\) | −6.44111 | − | 11.1563i | −0.310618 | − | 0.538006i | ||||
\(431\) | −0.494933 | − | 0.857249i | −0.0238401 | − | 0.0412922i | 0.853859 | − | 0.520504i | \(-0.174256\pi\) |
−0.877699 | + | 0.479212i | \(0.840923\pi\) | |||||||
\(432\) | 8.11368 | − | 14.0533i | 0.390370 | − | 0.676140i | ||||
\(433\) | 32.4815 | 1.56096 | 0.780482 | − | 0.625179i | \(-0.214974\pi\) | ||||
0.780482 | + | 0.625179i | \(0.214974\pi\) | |||||||
\(434\) | 0.911461 | + | 0.112149i | 0.0437516 | + | 0.00538331i | ||||
\(435\) | 12.3571 | 0.592477 | ||||||||
\(436\) | 1.78815 | − | 3.09716i | 0.0856368 | − | 0.148327i | ||||
\(437\) | −16.9381 | − | 29.3377i | −0.810262 | − | 1.40341i | ||||
\(438\) | 21.2440 | + | 36.7957i | 1.01508 | + | 1.75817i | ||||
\(439\) | −1.22046 | + | 2.11390i | −0.0582495 | + | 0.100891i | −0.893680 | − | 0.448705i | \(-0.851885\pi\) |
0.835430 | + | 0.549597i | \(0.185219\pi\) | |||||||
\(440\) | 3.05269 | 0.145531 | ||||||||
\(441\) | −31.4050 | + | 32.4877i | −1.49548 | + | 1.54704i | ||||
\(442\) | −2.46963 | −0.117468 | ||||||||
\(443\) | −14.8963 | + | 25.8012i | −0.707746 | + | 1.22585i | 0.257946 | + | 0.966159i | \(0.416954\pi\) |
−0.965691 | + | 0.259692i | \(0.916379\pi\) | |||||||
\(444\) | 7.18112 | + | 12.4381i | 0.340801 | + | 0.590284i | ||||
\(445\) | −7.04583 | − | 12.2037i | −0.334004 | − | 0.578512i | ||||
\(446\) | 5.73444 | − | 9.93234i | 0.271534 | − | 0.470310i | ||||
\(447\) | 33.7438 | 1.59603 | ||||||||
\(448\) | −20.5551 | − | 2.52916i | −0.971138 | − | 0.119491i | ||||
\(449\) | 32.6965 | 1.54304 | 0.771521 | − | 0.636203i | \(-0.219496\pi\) | ||||
0.771521 | + | 0.636203i | \(0.219496\pi\) | |||||||
\(450\) | −3.44079 | + | 5.95963i | −0.162200 | + | 0.280939i | ||||
\(451\) | −0.616236 | − | 1.06735i | −0.0290174 | − | 0.0502596i | ||||
\(452\) | 1.27589 | + | 2.20990i | 0.0600126 | + | 0.103945i | ||||
\(453\) | 14.8001 | − | 25.6345i | 0.695368 | − | 1.20441i | ||||
\(454\) | 4.93003 | 0.231378 | ||||||||
\(455\) | −3.28477 | + | 4.35674i | −0.153993 | + | 0.204247i | ||||
\(456\) | −79.5118 | −3.72348 | ||||||||
\(457\) | −6.19525 | + | 10.7305i | −0.289801 | + | 0.501951i | −0.973762 | − | 0.227568i | \(-0.926923\pi\) |
0.683961 | + | 0.729519i | \(0.260256\pi\) | |||||||
\(458\) | 0.881649 | + | 1.52706i | 0.0411967 | + | 0.0713549i | ||||
\(459\) | 5.96700 | + | 10.3352i | 0.278516 | + | 0.482404i | ||||
\(460\) | −1.72665 | + | 2.99065i | −0.0805055 | + | 0.139440i | ||||
\(461\) | −36.7587 | −1.71202 | −0.856011 | − | 0.516957i | \(-0.827065\pi\) | ||||
−0.856011 | + | 0.516957i | \(0.827065\pi\) | |||||||
\(462\) | 3.38678 | + | 7.98439i | 0.157567 | + | 0.371467i | ||||
\(463\) | 18.1518 | 0.843585 | 0.421793 | − | 0.906692i | \(-0.361401\pi\) | ||||
0.421793 | + | 0.906692i | \(0.361401\pi\) | |||||||
\(464\) | −3.06911 | + | 5.31585i | −0.142480 | + | 0.246782i | ||||
\(465\) | −0.500573 | − | 0.867017i | −0.0232135 | − | 0.0402070i | ||||
\(466\) | −1.11421 | − | 1.92986i | −0.0516146 | − | 0.0893992i | ||||
\(467\) | −16.8338 | + | 29.1571i | −0.778977 | + | 1.34923i | 0.153554 | + | 0.988140i | \(0.450928\pi\) |
−0.932532 | + | 0.361088i | \(0.882405\pi\) | |||||||
\(468\) | −11.4948 | −0.531349 | ||||||||
\(469\) | 11.1137 | + | 26.2008i | 0.513184 | + | 1.20984i | ||||
\(470\) | 1.12330 | 0.0518142 | ||||||||
\(471\) | 29.7529 | − | 51.5336i | 1.37094 | − | 2.37454i | ||||
\(472\) | 21.1692 | + | 36.6661i | 0.974392 | + | 1.68770i | ||||
\(473\) | 6.04190 | + | 10.4649i | 0.277807 | + | 0.481176i | ||||
\(474\) | −12.1942 | + | 21.1210i | −0.560098 | + | 0.970118i | ||||
\(475\) | 8.47065 | 0.388660 | ||||||||
\(476\) | 1.54494 | − | 2.04912i | 0.0708121 | − | 0.0939211i | ||||
\(477\) | −5.70913 | −0.261403 | ||||||||
\(478\) | 6.98596 | − | 12.1000i | 0.319530 | − | 0.553443i | ||||
\(479\) | −10.9735 | − | 19.0067i | −0.501393 | − | 0.868439i | −0.999999 | − | 0.00160973i | \(-0.999488\pi\) |
0.498605 | − | 0.866829i | \(-0.333846\pi\) | |||||||
\(480\) | 6.88323 | + | 11.9221i | 0.314175 | + | 0.544167i | ||||
\(481\) | −5.57765 | + | 9.66078i | −0.254319 | + | 0.440494i | ||||
\(482\) | 6.31801 | 0.287778 | ||||||||
\(483\) | −32.2922 | − | 3.97332i | −1.46935 | − | 0.180792i | ||||
\(484\) | −0.863486 | −0.0392493 | ||||||||
\(485\) | −8.41270 | + | 14.5712i | −0.382001 | + | 0.661645i | ||||
\(486\) | −4.81468 | − | 8.33928i | −0.218398 | − | 0.378277i | ||||
\(487\) | −9.72600 | − | 16.8459i | −0.440727 | − | 0.763362i | 0.557017 | − | 0.830501i | \(-0.311946\pi\) |
−0.997744 | + | 0.0671397i | \(0.978613\pi\) | |||||||
\(488\) | 2.50117 | − | 4.33216i | 0.113223 | − | 0.196108i | ||||
\(489\) | 49.5633 | 2.24133 | ||||||||
\(490\) | 2.05330 | + | 7.17448i | 0.0927587 | + | 0.324110i | ||||
\(491\) | 6.22618 | 0.280984 | 0.140492 | − | 0.990082i | \(-0.455132\pi\) | ||||
0.140492 | + | 0.990082i | \(0.455132\pi\) | |||||||
\(492\) | 1.63619 | − | 2.83397i | 0.0737653 | − | 0.127765i | ||||
\(493\) | −2.25710 | − | 3.90941i | −0.101655 | − | 0.176071i | ||||
\(494\) | −9.31153 | − | 16.1280i | −0.418945 | − | 0.725635i | ||||
\(495\) | 3.22753 | − | 5.59025i | 0.145067 | − | 0.251263i | ||||
\(496\) | 0.497306 | 0.0223297 | ||||||||
\(497\) | −21.4982 | − | 2.64519i | −0.964325 | − | 0.118653i | ||||
\(498\) | 13.7730 | 0.617183 | ||||||||
\(499\) | −5.18213 | + | 8.97571i | −0.231984 | + | 0.401808i | −0.958392 | − | 0.285456i | \(-0.907855\pi\) |
0.726408 | + | 0.687264i | \(0.241188\pi\) | |||||||
\(500\) | −0.431743 | − | 0.747801i | −0.0193081 | − | 0.0334427i | ||||
\(501\) | 14.2561 | + | 24.6923i | 0.636915 | + | 1.10317i | ||||
\(502\) | −4.32862 | + | 7.49738i | −0.193196 | + | 0.334625i | ||||
\(503\) | −4.68935 | −0.209088 | −0.104544 | − | 0.994520i | \(-0.533338\pi\) | ||||
−0.104544 | + | 0.994520i | \(0.533338\pi\) | |||||||
\(504\) | −31.3864 | + | 41.6292i | −1.39806 | + | 1.85431i | ||||
\(505\) | −14.2529 | −0.634246 | ||||||||
\(506\) | −2.13175 | + | 3.69230i | −0.0947679 | + | 0.164143i | ||||
\(507\) | 13.4481 | + | 23.2929i | 0.597253 | + | 1.03447i | ||||
\(508\) | −2.93089 | − | 5.07646i | −0.130037 | − | 0.225231i | ||||
\(509\) | −15.1957 | + | 26.3196i | −0.673535 | + | 1.16660i | 0.303359 | + | 0.952876i | \(0.401892\pi\) |
−0.976895 | + | 0.213721i | \(0.931442\pi\) | |||||||
\(510\) | 3.68228 | 0.163054 | ||||||||
\(511\) | −13.3910 | − | 31.5696i | −0.592383 | − | 1.39656i | ||||
\(512\) | −16.1638 | −0.714346 | ||||||||
\(513\) | −44.9962 | + | 77.9357i | −1.98663 | + | 3.44094i | ||||
\(514\) | −14.0624 | − | 24.3567i | −0.620264 | − | 1.07433i | ||||
\(515\) | −8.12911 | − | 14.0800i | −0.358212 | − | 0.620441i | ||||
\(516\) | −16.0421 | + | 27.7857i | −0.706214 | + | 1.22320i | ||||
\(517\) | −1.05368 | −0.0463409 | ||||||||
\(518\) | 5.95784 | + | 14.0457i | 0.261772 | + | 0.617134i | ||||
\(519\) | −59.1656 | −2.59708 | ||||||||
\(520\) | −3.14774 | + | 5.45205i | −0.138038 | + | 0.239088i | ||||
\(521\) | −10.1908 | − | 17.6509i | −0.446466 | − | 0.773301i | 0.551687 | − | 0.834051i | \(-0.313984\pi\) |
−0.998153 | + | 0.0607496i | \(0.980651\pi\) | |||||||
\(522\) | 13.8274 | + | 23.9498i | 0.605211 | + | 1.04826i | ||||
\(523\) | −1.02964 | + | 1.78338i | −0.0450229 | + | 0.0779820i | −0.887659 | − | 0.460502i | \(-0.847669\pi\) |
0.842636 | + | 0.538484i | \(0.181003\pi\) | |||||||
\(524\) | 3.55919 | 0.155484 | ||||||||
\(525\) | 4.89769 | − | 6.49601i | 0.213753 | − | 0.283509i | ||||
\(526\) | −22.1413 | −0.965408 | ||||||||
\(527\) | −0.182866 | + | 0.316733i | −0.00796575 | + | 0.0137971i | ||||
\(528\) | 2.34834 | + | 4.06745i | 0.102198 | + | 0.177013i | ||||
\(529\) | 3.50297 | + | 6.06733i | 0.152303 | + | 0.263797i | ||||
\(530\) | −0.471440 | + | 0.816559i | −0.0204781 | + | 0.0354690i | ||||
\(531\) | 89.5268 | 3.88513 | ||||||||
\(532\) | 19.2069 | + | 2.36327i | 0.832726 | + | 0.102461i | ||||
\(533\) | 2.54170 | 0.110093 | ||||||||
\(534\) | 23.0968 | − | 40.0048i | 0.999496 | − | 1.73118i | ||||
\(535\) | 4.29016 | + | 7.43078i | 0.185480 | + | 0.321260i | ||||
\(536\) | 16.4189 | + | 28.4385i | 0.709191 | + | 1.22835i | ||||
\(537\) | 12.8273 | − | 22.2176i | 0.553540 | − | 0.958759i | ||||
\(538\) | −11.3777 | −0.490529 | ||||||||
\(539\) | −1.92604 | − | 6.72981i | −0.0829604 | − | 0.289874i | ||||
\(540\) | 9.17369 | 0.394773 | ||||||||
\(541\) | −1.30838 | + | 2.26618i | −0.0562516 | + | 0.0974305i | −0.892780 | − | 0.450493i | \(-0.851248\pi\) |
0.836528 | + | 0.547924i | \(0.184582\pi\) | |||||||
\(542\) | 2.79504 | + | 4.84115i | 0.120057 | + | 0.207945i | ||||
\(543\) | 29.0781 | + | 50.3648i | 1.24786 | + | 2.16136i | ||||
\(544\) | 2.51453 | − | 4.35530i | 0.107810 | − | 0.186732i | ||||
\(545\) | −4.14170 | −0.177411 | ||||||||
\(546\) | −17.7522 | − | 2.18428i | −0.759725 | − | 0.0934786i | ||||
\(547\) | 44.6670 | 1.90982 | 0.954910 | − | 0.296894i | \(-0.0959507\pi\) | ||||
0.954910 | + | 0.296894i | \(0.0959507\pi\) | |||||||
\(548\) | 4.96846 | − | 8.60563i | 0.212242 | − | 0.367614i | ||||
\(549\) | −5.28886 | − | 9.16058i | −0.225723 | − | 0.390964i | ||||
\(550\) | −0.533037 | − | 0.923247i | −0.0227288 | − | 0.0393674i | ||||
\(551\) | 17.0204 | − | 29.4802i | 0.725094 | − | 1.25590i | ||||
\(552\) | −37.5400 | −1.59781 | ||||||||
\(553\) | 11.8501 | − | 15.7173i | 0.503917 | − | 0.668367i | ||||
\(554\) | −19.5908 | −0.832335 | ||||||||
\(555\) | 8.31643 | − | 14.4045i | 0.353013 | − | 0.611436i | ||||
\(556\) | −0.338162 | − | 0.585714i | −0.0143413 | − | 0.0248398i | ||||
\(557\) | −13.8418 | − | 23.9747i | −0.586497 | − | 1.01584i | −0.994687 | − | 0.102945i | \(-0.967173\pi\) |
0.408190 | − | 0.912897i | \(-0.366160\pi\) | |||||||
\(558\) | 1.12027 | − | 1.94037i | 0.0474248 | − | 0.0821422i | ||||
\(559\) | −24.9201 | −1.05401 | ||||||||
\(560\) | 1.57807 | + | 3.72032i | 0.0666855 | + | 0.157212i | ||||
\(561\) | −3.45406 | −0.145830 | ||||||||
\(562\) | 1.54376 | − | 2.67386i | 0.0651194 | − | 0.112790i | ||||
\(563\) | 8.93166 | + | 15.4701i | 0.376425 | + | 0.651987i | 0.990539 | − | 0.137230i | \(-0.0438200\pi\) |
−0.614114 | + | 0.789217i | \(0.710487\pi\) | |||||||
\(564\) | −1.39884 | − | 2.42286i | −0.0589017 | − | 0.102021i | ||||
\(565\) | 1.47760 | − | 2.55928i | 0.0621631 | − | 0.107670i | ||||
\(566\) | 4.68232 | 0.196813 | ||||||||
\(567\) | 13.7438 | + | 32.4013i | 0.577185 | + | 1.36073i | ||||
\(568\) | −24.9918 | −1.04863 | ||||||||
\(569\) | −13.5471 | + | 23.4643i | −0.567925 | + | 0.983675i | 0.428846 | + | 0.903378i | \(0.358920\pi\) |
−0.996771 | + | 0.0802974i | \(0.974413\pi\) | |||||||
\(570\) | 13.8837 | + | 24.0473i | 0.581526 | + | 1.00723i | ||||
\(571\) | −16.8092 | − | 29.1144i | −0.703443 | − | 1.21840i | −0.967251 | − | 0.253824i | \(-0.918312\pi\) |
0.263808 | − | 0.964575i | \(-0.415022\pi\) | |||||||
\(572\) | 0.890373 | − | 1.54217i | 0.0372284 | − | 0.0644814i | ||||
\(573\) | 3.67154 | 0.153381 | ||||||||
\(574\) | 2.09278 | − | 2.77574i | 0.0873509 | − | 0.115857i | ||||
\(575\) | 3.99926 | 0.166781 | ||||||||
\(576\) | −25.2641 | + | 43.7588i | −1.05267 | + | 1.82328i | ||||
\(577\) | −0.255512 | − | 0.442560i | −0.0106371 | − | 0.0184240i | 0.860658 | − | 0.509184i | \(-0.170053\pi\) |
−0.871295 | + | 0.490760i | \(0.836719\pi\) | |||||||
\(578\) | 8.38904 | + | 14.5302i | 0.348938 | + | 0.604378i | ||||
\(579\) | 34.1453 | − | 59.1414i | 1.41903 | − | 2.45783i | ||||
\(580\) | −3.47007 | −0.144087 | ||||||||
\(581\) | −11.0330 | − | 1.35753i | −0.457727 | − | 0.0563200i | ||||
\(582\) | −55.1550 | −2.28625 | ||||||||
\(583\) | 0.442221 | − | 0.765949i | 0.0183149 | − | 0.0317224i | ||||
\(584\) | −19.7833 | − | 34.2657i | −0.818639 | − | 1.41792i | ||||
\(585\) | 6.65607 | + | 11.5286i | 0.275195 | + | 0.476651i | ||||
\(586\) | 11.2120 | − | 19.4198i | 0.463165 | − | 0.802226i | ||||
\(587\) | 24.8042 | 1.02378 | 0.511889 | − | 0.859052i | \(-0.328946\pi\) | ||||
0.511889 | + | 0.859052i | \(0.328946\pi\) | |||||||
\(588\) | 12.9177 | − | 13.3631i | 0.532717 | − | 0.551084i | ||||
\(589\) | −2.75792 | −0.113638 | ||||||||
\(590\) | 7.39281 | − | 12.8047i | 0.304357 | − | 0.527162i | ||||
\(591\) | 8.22673 | + | 14.2491i | 0.338402 | + | 0.586130i | ||||
\(592\) | 4.13108 | + | 7.15524i | 0.169786 | + | 0.294078i | ||||
\(593\) | 14.6406 | − | 25.3583i | 0.601219 | − | 1.04134i | −0.391417 | − | 0.920213i | \(-0.628015\pi\) |
0.992637 | − | 0.121129i | \(-0.0386515\pi\) | |||||||
\(594\) | 11.3260 | 0.464711 | ||||||||
\(595\) | −2.94974 | − | 0.362944i | −0.120927 | − | 0.0148792i | ||||
\(596\) | −9.47581 | −0.388144 | ||||||||
\(597\) | 16.9472 | − | 29.3535i | 0.693604 | − | 1.20136i | ||||
\(598\) | −4.39626 | − | 7.61455i | −0.179777 | − | 0.311382i | ||||
\(599\) | 7.91654 | + | 13.7119i | 0.323461 | + | 0.560251i | 0.981200 | − | 0.192995i | \(-0.0618202\pi\) |
−0.657739 | + | 0.753246i | \(0.728487\pi\) | |||||||
\(600\) | 4.69337 | − | 8.12916i | 0.191606 | − | 0.331871i | ||||
\(601\) | 16.8302 | 0.686516 | 0.343258 | − | 0.939241i | \(-0.388469\pi\) | ||||
0.343258 | + | 0.939241i | \(0.388469\pi\) | |||||||
\(602\) | −20.5187 | + | 27.2148i | −0.836279 | + | 1.10919i | ||||
\(603\) | 69.4374 | 2.82771 | ||||||||
\(604\) | −4.15611 | + | 7.19859i | −0.169110 | + | 0.292906i | ||||
\(605\) | 0.500000 | + | 0.866025i | 0.0203279 | + | 0.0352089i | ||||
\(606\) | −23.3611 | − | 40.4626i | −0.948980 | − | 1.64368i | ||||
\(607\) | −4.86376 | + | 8.42427i | −0.197414 | + | 0.341931i | −0.947689 | − | 0.319195i | \(-0.896588\pi\) |
0.750275 | + | 0.661126i | \(0.229921\pi\) | |||||||
\(608\) | 37.9234 | 1.53800 | ||||||||
\(609\) | −12.7668 | − | 30.0980i | −0.517338 | − | 1.21963i | ||||
\(610\) | −1.74694 | −0.0707317 | ||||||||
\(611\) | 1.08649 | − | 1.88186i | 0.0439548 | − | 0.0761319i | ||||
\(612\) | −3.13057 | − | 5.42231i | −0.126546 | − | 0.219184i | ||||
\(613\) | −5.37652 | − | 9.31241i | −0.217156 | − | 0.376125i | 0.736782 | − | 0.676131i | \(-0.236345\pi\) |
−0.953937 | + | 0.300006i | \(0.903011\pi\) | |||||||
\(614\) | −13.2556 | + | 22.9594i | −0.534953 | + | 0.926566i | ||||
\(615\) | −3.78974 | −0.152817 | ||||||||
\(616\) | −3.15391 | − | 7.43540i | −0.127075 | − | 0.299581i | ||||
\(617\) | −18.5288 | −0.745942 | −0.372971 | − | 0.927843i | \(-0.621661\pi\) | ||||
−0.372971 | + | 0.927843i | \(0.621661\pi\) | |||||||
\(618\) | 26.6479 | − | 46.1555i | 1.07194 | − | 1.85665i | ||||
\(619\) | 12.2292 | + | 21.1817i | 0.491535 | + | 0.851364i | 0.999952 | − | 0.00974711i | \(-0.00310265\pi\) |
−0.508417 | + | 0.861111i | \(0.669769\pi\) | |||||||
\(620\) | 0.140569 | + | 0.243473i | 0.00564539 | + | 0.00977810i | ||||
\(621\) | −21.2441 | + | 36.7959i | −0.852496 | + | 1.47657i | ||||
\(622\) | −25.9572 | −1.04079 | ||||||||
\(623\) | −22.4450 | + | 29.7698i | −0.899242 | + | 1.19270i | ||||
\(624\) | −9.68586 | −0.387745 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −0.612469 | − | 1.06083i | −0.0244792 | − | 0.0423992i | ||||
\(627\) | −13.0232 | − | 22.5569i | −0.520098 | − | 0.900836i | ||||
\(628\) | −8.35512 | + | 14.4715i | −0.333405 | + | 0.577475i | ||||
\(629\) | −6.07620 | −0.242274 | ||||||||
\(630\) | 18.0707 | + | 2.22347i | 0.719953 | + | 0.0885850i | ||||
\(631\) | −38.3589 | −1.52704 | −0.763522 | − | 0.645782i | \(-0.776532\pi\) | ||||
−0.763522 | + | 0.645782i | \(0.776532\pi\) | |||||||
\(632\) | 11.3557 | − | 19.6687i | 0.451707 | − | 0.782380i | ||||
\(633\) | −7.44576 | − | 12.8964i | −0.295942 | − | 0.512587i | ||||
\(634\) | −10.3168 | − | 17.8692i | −0.409731 | − | 0.709675i | ||||
\(635\) | −3.39426 | + | 5.87903i | −0.134697 | + | 0.233302i | ||||
\(636\) | 2.34832 | 0.0931168 | ||||||||
\(637\) | 14.0053 | + | 3.49949i | 0.554912 | + | 0.138655i | ||||
\(638\) | −4.28421 | −0.169614 | ||||||||
\(639\) | −26.4233 | + | 45.7664i | −1.04529 | + | 1.81049i | ||||
\(640\) | −0.304582 | − | 0.527552i | −0.0120397 | − | 0.0208533i | ||||
\(641\) | 16.0912 | + | 27.8707i | 0.635563 | + | 1.10083i | 0.986396 | + | 0.164389i | \(0.0525654\pi\) |
−0.350832 | + | 0.936438i | \(0.614101\pi\) | |||||||
\(642\) | −14.0635 | + | 24.3587i | −0.555042 | + | 0.961361i | ||||
\(643\) | −12.1417 | −0.478821 | −0.239410 | − | 0.970918i | \(-0.576954\pi\) | ||||
−0.239410 | + | 0.970918i | \(0.576954\pi\) | |||||||
\(644\) | 9.06819 | + | 1.11577i | 0.357337 | + | 0.0439677i | ||||
\(645\) | 37.1566 | 1.46304 | ||||||||
\(646\) | 5.07191 | − | 8.78480i | 0.199552 | − | 0.345634i | ||||
\(647\) | −11.1058 | − | 19.2358i | −0.436615 | − | 0.756239i | 0.560811 | − | 0.827944i | \(-0.310489\pi\) |
−0.997426 | + | 0.0717050i | \(0.977156\pi\) | |||||||
\(648\) | 20.3045 | + | 35.1684i | 0.797636 | + | 1.38155i | ||||
\(649\) | −6.93461 | + | 12.0111i | −0.272207 | + | 0.471477i | ||||
\(650\) | 2.19854 | 0.0862338 | ||||||||
\(651\) | −1.59461 | + | 2.11501i | −0.0624979 | + | 0.0828936i | ||||
\(652\) | −13.9182 | −0.545079 | ||||||||
\(653\) | −20.8939 | + | 36.1892i | −0.817640 | + | 1.41619i | 0.0897767 | + | 0.995962i | \(0.471385\pi\) |
−0.907417 | + | 0.420232i | \(0.861949\pi\) | |||||||
\(654\) | −6.78841 | − | 11.7579i | −0.265448 | − | 0.459769i | ||||
\(655\) | −2.06094 | − | 3.56966i | −0.0805277 | − | 0.139478i | ||||
\(656\) | 0.941252 | − | 1.63030i | 0.0367497 | − | 0.0636524i | ||||
\(657\) | −83.6657 | −3.26411 | ||||||||
\(658\) | −1.16055 | − | 2.73602i | −0.0452430 | − | 0.106661i | ||||
\(659\) | −11.0308 | −0.429700 | −0.214850 | − | 0.976647i | \(-0.568926\pi\) | ||||
−0.214850 | + | 0.976647i | \(0.568926\pi\) | |||||||
\(660\) | −1.32757 | + | 2.29942i | −0.0516756 | + | 0.0895048i | ||||
\(661\) | −20.3416 | − | 35.2327i | −0.791196 | − | 1.37039i | −0.925227 | − | 0.379415i | \(-0.876125\pi\) |
0.134030 | − | 0.990977i | \(-0.457208\pi\) | |||||||
\(662\) | 1.73756 | + | 3.00954i | 0.0675322 | + | 0.116969i | ||||
\(663\) | 3.56161 | − | 6.16889i | 0.138322 | − | 0.239580i | ||||
\(664\) | −12.8260 | −0.497745 | ||||||||
\(665\) | −8.75152 | − | 20.6319i | −0.339369 | − | 0.800070i | ||||
\(666\) | 37.2240 | 1.44240 | ||||||||
\(667\) | 8.03587 | − | 13.9185i | 0.311150 | − | 0.538928i | ||||
\(668\) | −4.00335 | − | 6.93400i | −0.154894 | − | 0.268285i | ||||
\(669\) | 16.5400 | + | 28.6482i | 0.639474 | + | 1.10760i | ||||
\(670\) | 5.73390 | − | 9.93141i | 0.221520 | − | 0.383684i | ||||
\(671\) | 1.63867 | 0.0632601 | ||||||||
\(672\) | 21.9271 | − | 29.0828i | 0.845856 | − | 1.12190i | ||||
\(673\) | −9.01027 | −0.347320 | −0.173660 | − | 0.984806i | \(-0.555559\pi\) | ||||
−0.173660 | + | 0.984806i | \(0.555559\pi\) | |||||||
\(674\) | 0.230000 | − | 0.398371i | 0.00885925 | − | 0.0153447i | ||||
\(675\) | −5.31201 | − | 9.20067i | −0.204459 | − | 0.354134i | ||||
\(676\) | −3.77646 | − | 6.54102i | −0.145249 | − | 0.251578i | ||||
\(677\) | 24.3179 | − | 42.1198i | 0.934612 | − | 1.61880i | 0.159287 | − | 0.987232i | \(-0.449080\pi\) |
0.775325 | − | 0.631563i | \(-0.217586\pi\) | |||||||
\(678\) | 9.68738 | 0.372042 | ||||||||
\(679\) | 44.1826 | + | 5.43635i | 1.69557 | + | 0.208628i | ||||
\(680\) | −3.42910 | −0.131500 | ||||||||
\(681\) | −7.10992 | + | 12.3147i | −0.272453 | + | 0.471902i | ||||
\(682\) | 0.173549 | + | 0.300596i | 0.00664554 | + | 0.0115104i | ||||
\(683\) | 5.24405 | + | 9.08296i | 0.200658 | + | 0.347550i | 0.948741 | − | 0.316056i | \(-0.102359\pi\) |
−0.748083 | + | 0.663606i | \(0.769025\pi\) | |||||||
\(684\) | 23.6071 | − | 40.8887i | 0.902640 | − | 1.56342i | ||||
\(685\) | −11.5079 | −0.439695 | ||||||||
\(686\) | 15.3534 | − | 12.4136i | 0.586196 | − | 0.473952i | ||||
\(687\) | −5.08593 | −0.194040 | ||||||||
\(688\) | −9.22853 | + | 15.9843i | −0.351834 | + | 0.609395i | ||||
\(689\) | 0.911982 | + | 1.57960i | 0.0347437 | + | 0.0601779i | ||||
\(690\) | 6.55495 | + | 11.3535i | 0.249543 | + | 0.432220i | ||||
\(691\) | −11.2768 | + | 19.5320i | −0.428989 | + | 0.743031i | −0.996784 | − | 0.0801393i | \(-0.974463\pi\) |
0.567795 | + | 0.823170i | \(0.307797\pi\) | |||||||
\(692\) | 16.6147 | 0.631595 | ||||||||
\(693\) | −16.9507 | − | 2.08566i | −0.643903 | − | 0.0792276i | ||||
\(694\) | −2.76647 | −0.105014 | ||||||||
\(695\) | −0.391625 | + | 0.678314i | −0.0148552 | + | 0.0257299i | ||||
\(696\) | −18.8612 | − | 32.6685i | −0.714930 | − | 1.23830i | ||||
\(697\) | 0.692220 | + | 1.19896i | 0.0262197 | + | 0.0454139i | ||||
\(698\) | 6.28686 | − | 10.8892i | 0.237961 | − | 0.412161i | ||||
\(699\) | 6.42748 | 0.243110 | ||||||||
\(700\) | −1.37535 | + | 1.82419i | −0.0519834 | + | 0.0689478i | ||||
\(701\) | −25.9143 | −0.978769 | −0.489385 | − | 0.872068i | \(-0.662779\pi\) | ||||
−0.489385 | + | 0.872068i | \(0.662779\pi\) | |||||||
\(702\) | −11.6787 | + | 20.2280i | −0.440783 | + | 0.763458i | ||||
\(703\) | −22.9098 | − | 39.6809i | −0.864060 | − | 1.49660i | ||||
\(704\) | −3.91385 | − | 6.77898i | −0.147509 | − | 0.255492i | ||||
\(705\) | −1.61999 | + | 2.80590i | −0.0610123 | + | 0.105676i | ||||
\(706\) | −2.21002 | −0.0831751 | ||||||||
\(707\) | 14.7255 | + | 34.7157i | 0.553810 | + | 1.30562i | ||||
\(708\) | −36.8247 | −1.38396 | ||||||||
\(709\) | 26.0328 | − | 45.0901i | 0.977682 | − | 1.69340i | 0.306899 | − | 0.951742i | \(-0.400709\pi\) |
0.670783 | − | 0.741653i | \(-0.265958\pi\) | |||||||
\(710\) | 4.36388 | + | 7.55846i | 0.163774 | + | 0.283664i | ||||
\(711\) | −24.0123 | − | 41.5906i | −0.900532 | − | 1.55977i | ||||
\(712\) | −21.5087 | + | 37.2542i | −0.806073 | + | 1.39616i | ||||
\(713\) | −1.30210 | −0.0487640 | ||||||||
\(714\) | −3.80438 | − | 8.96890i | −0.142375 | − | 0.335653i | ||||
\(715\) | −2.06228 | −0.0771248 | ||||||||
\(716\) | −3.60212 | + | 6.23906i | −0.134618 | + | 0.233165i | ||||
\(717\) | 20.1498 | + | 34.9005i | 0.752509 | + | 1.30338i | ||||
\(718\) | 16.1380 | + | 27.9519i | 0.602266 | + | 1.04316i | ||||
\(719\) | −16.5697 | + | 28.6995i | −0.617944 | + | 1.07031i | 0.371917 | + | 0.928266i | \(0.378701\pi\) |
−0.989860 | + | 0.142044i | \(0.954633\pi\) | |||||||
\(720\) | 9.85961 | 0.367446 | ||||||||
\(721\) | −25.8959 | + | 34.3469i | −0.964415 | + | 1.27915i | ||||
\(722\) | 56.2374 | 2.09294 | ||||||||
\(723\) | −9.11162 | + | 15.7818i | −0.338865 | + | 0.586931i | ||||
\(724\) | −8.16562 | − | 14.1433i | −0.303473 | − | 0.525631i | ||||
\(725\) | 2.00934 | + | 3.48028i | 0.0746250 | + | 0.129254i | ||||
\(726\) | −1.63904 | + | 2.83890i | −0.0608305 | + | 0.105362i | ||||
\(727\) | 2.62195 | 0.0972428 | 0.0486214 | − | 0.998817i | \(-0.484517\pi\) | ||||
0.0486214 | + | 0.998817i | \(0.484517\pi\) | |||||||
\(728\) | 16.5316 | + | 2.03410i | 0.612703 | + | 0.0753886i | ||||
\(729\) | −12.1339 | −0.449402 | ||||||||
\(730\) | −6.90882 | + | 11.9664i | −0.255707 | + | 0.442897i | ||||
\(731\) | −6.78689 | − | 11.7552i | −0.251022 | − | 0.434783i | ||||
\(732\) | 2.17545 | + | 3.76799i | 0.0804069 | + | 0.139269i | ||||
\(733\) | 6.86540 | − | 11.8912i | 0.253579 | − | 0.439212i | −0.710929 | − | 0.703263i | \(-0.751725\pi\) |
0.964509 | + | 0.264051i | \(0.0850588\pi\) | |||||||
\(734\) | 8.57072 | 0.316351 | ||||||||
\(735\) | −20.8824 | − | 5.21784i | −0.770257 | − | 0.192463i | ||||
\(736\) | 17.9048 | 0.659980 | ||||||||
\(737\) | −5.37852 | + | 9.31587i | −0.198120 | + | 0.343155i | ||||
\(738\) | −4.24068 | − | 7.34507i | −0.156102 | − | 0.270376i | ||||
\(739\) | −2.27029 | − | 3.93225i | −0.0835138 | − | 0.144650i | 0.821243 | − | 0.570578i | \(-0.193281\pi\) |
−0.904757 | + | 0.425928i | \(0.859948\pi\) | |||||||
\(740\) | −2.33539 | + | 4.04502i | −0.0858507 | + | 0.148698i | ||||
\(741\) | 53.7150 | 1.97327 | ||||||||
\(742\) | 2.47596 | + | 0.304648i | 0.0908952 | + | 0.0111840i | ||||
\(743\) | 23.7757 | 0.872245 | 0.436123 | − | 0.899887i | \(-0.356351\pi\) | ||||
0.436123 | + | 0.899887i | \(0.356351\pi\) | |||||||
\(744\) | −1.52809 | + | 2.64673i | −0.0560226 | + | 0.0970339i | ||||
\(745\) | 5.48695 | + | 9.50368i | 0.201026 | + | 0.348188i | ||||
\(746\) | 15.9728 | + | 27.6657i | 0.584805 | + | 1.01291i | ||||
\(747\) | −13.5606 | + | 23.4877i | −0.496157 | + | 0.859370i | ||||
\(748\) | 0.969957 | 0.0354651 | ||||||||
\(749\) | 13.6667 | − | 18.1267i | 0.499369 | − | 0.662334i | ||||
\(750\) | −3.27808 | −0.119699 | ||||||||
\(751\) | −17.6055 | + | 30.4935i | −0.642432 | + | 1.11273i | 0.342456 | + | 0.939534i | \(0.388741\pi\) |
−0.984888 | + | 0.173191i | \(0.944592\pi\) | |||||||
\(752\) | −0.804709 | − | 1.39380i | −0.0293447 | − | 0.0508265i | ||||
\(753\) | −12.4852 | − | 21.6249i | −0.454984 | − | 0.788056i | ||||
\(754\) | 4.41761 | − | 7.65153i | 0.160880 | − | 0.278652i | ||||
\(755\) | 9.62635 | 0.350339 | ||||||||
\(756\) | −9.47787 | − | 22.3443i | −0.344707 | − | 0.812653i | ||||
\(757\) | 5.66097 | 0.205752 | 0.102876 | − | 0.994694i | \(-0.467196\pi\) | ||||
0.102876 | + | 0.994694i | \(0.467196\pi\) | |||||||
\(758\) | −10.3052 | + | 17.8491i | −0.374301 | + | 0.648309i | ||||
\(759\) | −6.14868 | − | 10.6498i | −0.223183 | − | 0.386564i | ||||
\(760\) | −12.9291 | − | 22.3939i | −0.468989 | − | 0.812312i | ||||
\(761\) | 7.78513 | − | 13.4842i | 0.282211 | − | 0.488803i | −0.689718 | − | 0.724078i | \(-0.742266\pi\) |
0.971929 | + | 0.235274i | \(0.0755989\pi\) | |||||||
\(762\) | −22.2533 | −0.806152 | ||||||||
\(763\) | 4.27903 | + | 10.0879i | 0.154911 | + | 0.365206i | ||||
\(764\) | −1.03103 | −0.0373014 | ||||||||
\(765\) | −3.62550 | + | 6.27955i | −0.131080 | + | 0.227038i | ||||
\(766\) | 5.37957 | + | 9.31770i | 0.194372 | + | 0.336662i | ||||
\(767\) | −14.3011 | − | 24.7702i | −0.516382 | − | 0.894400i | ||||
\(768\) | 25.0679 | − | 43.4189i | 0.904559 | − | 1.56674i | ||||
\(769\) | −11.4329 | −0.412281 | −0.206140 | − | 0.978522i | \(-0.566090\pi\) | ||||
−0.206140 | + | 0.978522i | \(0.566090\pi\) | |||||||
\(770\) | −1.69803 | + | 2.25217i | −0.0611928 | + | 0.0811627i | ||||
\(771\) | 81.1209 | 2.92150 | ||||||||
\(772\) | −9.58857 | + | 16.6079i | −0.345100 | + | 0.597731i | ||||
\(773\) | −4.16584 | − | 7.21545i | −0.149835 | − | 0.259522i | 0.781331 | − | 0.624116i | \(-0.214541\pi\) |
−0.931166 | + | 0.364595i | \(0.881208\pi\) | |||||||
\(774\) | 41.5778 | + | 72.0149i | 1.49448 | + | 2.58852i | ||||
\(775\) | 0.162793 | − | 0.281965i | 0.00584768 | − | 0.0101285i | ||||
\(776\) | 51.3627 | 1.84381 | ||||||||
\(777\) | −43.6770 | − | 5.37414i | −1.56690 | − | 0.192796i | ||||
\(778\) | 29.0884 | 1.04287 | ||||||||
\(779\) | −5.21992 | + | 9.04116i | −0.187023 | + | 0.323933i | ||||
\(780\) | −2.73782 | − | 4.74204i | −0.0980296 | − | 0.169792i | ||||
\(781\) | −4.09341 | − | 7.09000i | −0.146474 | − | 0.253700i | ||||
\(782\) | 2.39461 | − | 4.14758i | 0.0856309 | − | 0.148317i | ||||
\(783\) | −42.6946 | −1.52578 | ||||||||
\(784\) | 7.43116 | − | 7.68737i | 0.265399 | − | 0.274549i | ||||
\(785\) | 19.3521 | 0.690705 | ||||||||
\(786\) | 6.75594 | − | 11.7016i | 0.240976 | − | 0.417384i | ||||
\(787\) | 10.1759 | + | 17.6252i | 0.362731 | + | 0.628269i | 0.988409 | − | 0.151812i | \(-0.0485109\pi\) |
−0.625678 | + | 0.780082i | \(0.715178\pi\) | |||||||
\(788\) | −2.31020 | − | 4.00139i | −0.0822975 | − | 0.142543i | ||||
\(789\) | 31.9315 | − | 55.3069i | 1.13679 | − | 1.96898i | ||||
\(790\) | −7.93142 | −0.282187 | ||||||||
\(791\) | −7.76020 | − | 0.954836i | −0.275921 | − | 0.0339501i | ||||
\(792\) | −19.7053 | −0.700198 | ||||||||
\(793\) | −1.68969 | + | 2.92664i | −0.0600028 | + | 0.103928i | ||||
\(794\) | 13.4643 | + | 23.3208i | 0.477829 | + | 0.827624i | ||||
\(795\) | −1.35979 | − | 2.35522i | −0.0482268 | − | 0.0835312i | ||||
\(796\) | −4.75907 | + | 8.24294i | −0.168681 | + | 0.292163i | ||||
\(797\) | −11.4434 | −0.405345 | −0.202672 | − | 0.979247i | \(-0.564963\pi\) | ||||
−0.202672 | + | 0.979247i | \(0.564963\pi\) | |||||||
\(798\) | 44.2278 | − | 58.6612i | 1.56565 | − | 2.07658i | ||||
\(799\) | 1.18361 | 0.0418730 | ||||||||
\(800\) | −2.23852 | + | 3.87722i | −0.0791435 | + | 0.137081i | ||||
\(801\) | 45.4813 | + | 78.7759i | 1.60700 | + | 2.78341i | ||||
\(802\) | −2.83113 | − | 4.90367i | −0.0999708 | − | 0.173154i | ||||
\(803\) | 6.48062 | − | 11.2248i | 0.228696 | − | 0.396113i | ||||
\(804\) | −28.5615 | −1.00728 | ||||||||
\(805\) | −4.13186 | − | 9.74095i | −0.145629 | − | 0.343323i | ||||
\(806\) | −0.715812 | −0.0252134 | ||||||||
\(807\) | 16.4086 | − | 28.4205i | 0.577609 | − | 1.00045i | ||||
\(808\) | 21.7548 | + | 37.6805i | 0.765333 | + | 1.32560i | ||||
\(809\) | 20.6469 | + | 35.7616i | 0.725908 | + | 1.25731i | 0.958599 | + | 0.284759i | \(0.0919134\pi\) |
−0.232691 | + | 0.972551i | \(0.574753\pi\) | |||||||
\(810\) | 7.09084 | − | 12.2817i | 0.249147 | − | 0.431535i | ||||
\(811\) | −7.63142 | −0.267976 | −0.133988 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133988 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(812\) | 3.58513 | + | 8.45202i | 0.125814 | + | 0.296608i | ||||
\(813\) | −16.1236 | −0.565480 | ||||||||
\(814\) | −2.88332 | + | 4.99405i | −0.101060 | + | 0.175041i | ||||
\(815\) | 8.05931 | + | 13.9591i | 0.282305 | + | 0.488967i | ||||
\(816\) | −2.63790 | − | 4.56898i | −0.0923450 | − | 0.159946i | ||||
\(817\) | 51.1788 | − | 88.6443i | 1.79052 | − | 3.10127i | ||||
\(818\) | −32.0547 | −1.12077 | ||||||||
\(819\) | 21.2034 | − | 28.1230i | 0.740908 | − | 0.982698i | ||||
\(820\) | 1.06422 | 0.0371642 | ||||||||
\(821\) | −27.7710 | + | 48.1008i | −0.969216 | + | 1.67873i | −0.271381 | + | 0.962472i | \(0.587480\pi\) |
−0.697835 | + | 0.716259i | \(0.745853\pi\) | |||||||
\(822\) | −18.8619 | − | 32.6698i | −0.657886 | − | 1.13949i | ||||
\(823\) | 2.22654 | + | 3.85648i | 0.0776122 | + | 0.134428i | 0.902219 | − | 0.431278i | \(-0.141937\pi\) |
−0.824607 | + | 0.565706i | \(0.808604\pi\) | |||||||
\(824\) | −24.8156 | + | 42.9820i | −0.864494 | + | 1.49735i | ||||
\(825\) | 3.07491 | 0.107055 | ||||||||
\(826\) | −38.8263 | − | 4.77729i | −1.35094 | − | 0.166223i | ||||
\(827\) | −3.60111 | −0.125223 | −0.0626114 | − | 0.998038i | \(-0.519943\pi\) | ||||
−0.0626114 | + | 0.998038i | \(0.519943\pi\) | |||||||
\(828\) | 11.1456 | − | 19.3048i | 0.387338 | − | 0.670889i | ||||
\(829\) | 8.04361 | + | 13.9319i | 0.279366 | + | 0.483876i | 0.971227 | − | 0.238154i | \(-0.0765424\pi\) |
−0.691861 | + | 0.722030i | \(0.743209\pi\) | |||||||
\(830\) | 2.23958 | + | 3.87906i | 0.0777369 | + | 0.134644i | ||||
\(831\) | 28.2532 | − | 48.9360i | 0.980093 | − | 1.69757i | ||||
\(832\) | 16.1429 | 0.559653 | ||||||||
\(833\) | 2.16353 | + | 7.55963i | 0.0749618 | + | 0.261926i | ||||
\(834\) | −2.56755 | −0.0889071 | ||||||||
\(835\) | −4.63626 | + | 8.03025i | −0.160445 | + | 0.277898i | ||||
\(836\) | 3.65714 | + | 6.33436i | 0.126485 | + | 0.219078i | ||||
\(837\) | 1.72951 | + | 2.99560i | 0.0597807 | + | 0.103543i | ||||
\(838\) | −6.92781 | + | 11.9993i | −0.239317 | + | 0.414509i | ||||
\(839\) | −14.6263 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581246\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581246\pi\) | |||||||
\(840\) | −24.6491 | − | 3.03289i | −0.850475 | − | 0.104645i | ||||
\(841\) | −12.8502 | −0.443110 | ||||||||
\(842\) | 1.36499 | − | 2.36423i | 0.0470407 | − | 0.0814768i | ||||
\(843\) | 4.45270 | + | 7.71230i | 0.153359 | + | 0.265626i | ||||
\(844\) | 2.09089 | + | 3.62153i | 0.0719715 | + | 0.124658i | ||||
\(845\) | −4.37351 | + | 7.57514i | −0.150453 | + | 0.260593i | ||||
\(846\) | −7.25101 | −0.249295 | ||||||||
\(847\) | 1.59279 | − | 2.11259i | 0.0547289 | − | 0.0725893i | ||||
\(848\) | 1.35092 | 0.0463906 | ||||||||
\(849\) | −6.75268 | + | 11.6960i | −0.231751 | + | 0.401405i | ||||
\(850\) | 0.598763 | + | 1.03709i | 0.0205374 | + | 0.0355718i | ||||
\(851\) | −10.8164 | − | 18.7346i | −0.370782 | − | 0.642214i | ||||
\(852\) | 10.8686 | − | 18.8249i | 0.372351 | − | 0.644932i | ||||
\(853\) | −44.9908 | −1.54046 | −0.770228 | − | 0.637769i | \(-0.779857\pi\) | ||||
−0.770228 | + | 0.637769i | \(0.779857\pi\) | |||||||
\(854\) | 1.80487 | + | 4.25501i | 0.0617613 | + | 0.145603i | ||||
\(855\) | −54.6786 | −1.86997 | ||||||||
\(856\) | 13.0965 | − | 22.6838i | 0.447630 | − | 0.775318i | ||||
\(857\) | 19.4907 | + | 33.7588i | 0.665789 | + | 1.15318i | 0.979071 | + | 0.203520i | \(0.0652380\pi\) |
−0.313282 | + | 0.949660i | \(0.601429\pi\) | |||||||
\(858\) | −3.38016 | − | 5.85460i | −0.115397 | − | 0.199873i | ||||
\(859\) | −13.7589 | + | 23.8312i | −0.469449 | + | 0.813109i | −0.999390 | − | 0.0349252i | \(-0.988881\pi\) |
0.529941 | + | 0.848034i | \(0.322214\pi\) | |||||||
\(860\) | −10.4342 | −0.355803 | ||||||||
\(861\) | 3.91540 | + | 9.23063i | 0.133436 | + | 0.314579i | ||||
\(862\) | 1.05527 | 0.0359427 | ||||||||
\(863\) | 10.8383 | − | 18.7725i | 0.368941 | − | 0.639025i | −0.620459 | − | 0.784239i | \(-0.713054\pi\) |
0.989400 | + | 0.145214i | \(0.0463870\pi\) | |||||||
\(864\) | −23.7820 | − | 41.1917i | −0.809082 | − | 1.40137i | ||||
\(865\) | −9.62070 | − | 16.6635i | −0.327114 | − | 0.566578i | ||||
\(866\) | −17.3139 | + | 29.9885i | −0.588349 | + | 1.01905i | ||||
\(867\) | −48.3935 | −1.64353 | ||||||||
\(868\) | 0.447794 | − | 0.593929i | 0.0151991 | − | 0.0201592i | ||||
\(869\) | 7.43983 | 0.252379 | ||||||||
\(870\) | −6.58678 | + | 11.4086i | −0.223313 | + | 0.386789i | ||||
\(871\) | −11.0920 | − | 19.2119i | −0.375838 | − | 0.650970i | ||||
\(872\) | 6.32165 | + | 10.9494i | 0.214078 | + | 0.370794i | ||||
\(873\) | 54.3045 | − | 94.0582i | 1.83793 | − | 3.18339i | ||||
\(874\) | 36.1146 | 1.22160 | ||||||||
\(875\) | 2.62595 | + | 0.323104i | 0.0887733 | + | 0.0109229i | ||||
\(876\) | 34.4139 | 1.16274 | ||||||||
\(877\) | 10.5589 | − | 18.2885i | 0.356549 | − | 0.617560i | −0.630833 | − | 0.775918i | \(-0.717287\pi\) |
0.987382 | + | 0.158358i | \(0.0506201\pi\) | |||||||
\(878\) | −1.30110 | − | 2.25358i | −0.0439101 | − | 0.0760546i | ||||
\(879\) | 32.3392 | + | 56.0132i | 1.09078 | + | 1.88928i | ||||
\(880\) | −0.763711 | + | 1.32279i | −0.0257447 | + | 0.0445911i | ||||
\(881\) | 12.4701 | 0.420128 | 0.210064 | − | 0.977688i | \(-0.432633\pi\) | ||||
0.210064 | + | 0.977688i | \(0.432633\pi\) | |||||||
\(882\) | −13.2542 | − | 46.3118i | −0.446292 | − | 1.55940i | ||||
\(883\) | 29.8363 | 1.00407 | 0.502035 | − | 0.864847i | \(-0.332585\pi\) | ||||
0.502035 | + | 0.864847i | \(0.332585\pi\) | |||||||
\(884\) | −1.00016 | + | 1.73233i | −0.0336390 | + | 0.0582645i | ||||
\(885\) | 21.3233 | + | 36.9330i | 0.716775 | + | 1.24149i | ||||
\(886\) | −15.8806 | − | 27.5060i | −0.533519 | − | 0.924082i | ||||
\(887\) | −14.2285 | + | 24.6446i | −0.477748 | + | 0.827483i | −0.999675 | − | 0.0255070i | \(-0.991880\pi\) |
0.521927 | + | 0.852990i | \(0.325213\pi\) | |||||||
\(888\) | −50.7749 | −1.70390 | ||||||||
\(889\) | 17.8263 | + | 2.19340i | 0.597875 | + | 0.0735641i | ||||
\(890\) | 15.0227 | 0.503564 | ||||||||
\(891\) | −6.65135 | + | 11.5205i | −0.222829 | + | 0.385951i | ||||
\(892\) | −4.64471 | − | 8.04488i | −0.155516 | − | 0.269362i | ||||
\(893\) | 4.46269 | + | 7.72960i | 0.149338 | + | 0.258661i | ||||
\(894\) | −17.9867 | + | 31.1538i | −0.601565 | + | 1.04194i | ||||
\(895\) | 8.34322 | 0.278883 | ||||||||
\(896\) | −0.970271 | + | 1.28691i | −0.0324145 | + | 0.0429927i | ||||
\(897\) | 25.3605 | 0.846764 | ||||||||
\(898\) | −17.4284 | + | 30.1869i | −0.581595 | + | 1.00735i | ||||
\(899\) | −0.654212 | − | 1.13313i | −0.0218192 | − | 0.0377919i | ||||
\(900\) | 2.78693 | + | 4.82710i | 0.0928977 | + | 0.160903i | ||||
\(901\) | −0.496749 | + | 0.860394i | −0.0165491 | + | 0.0286639i | ||||
\(902\) | 1.31391 | 0.0437483 | ||||||||
\(903\) | −38.3886 | − | 90.5019i | −1.27749 | − | 3.01172i | ||||
\(904\) | −9.02130 | −0.300044 | ||||||||
\(905\) | −9.45658 | + | 16.3793i | −0.314347 | + | 0.544466i | ||||
\(906\) | 15.7780 | + | 27.3283i | 0.524188 | + | 0.907921i | ||||
\(907\) | 5.46525 | + | 9.46609i | 0.181471 | + | 0.314316i | 0.942382 | − | 0.334540i | \(-0.108581\pi\) |
−0.760911 | + | 0.648856i | \(0.775248\pi\) | |||||||
\(908\) | 1.99658 | − | 3.45818i | 0.0662589 | − | 0.114764i | ||||
\(909\) | 92.0035 | 3.05156 | ||||||||
\(910\) | −2.27144 | − | 5.35496i | −0.0752975 | − | 0.177515i | ||||
\(911\) | 4.19124 | 0.138862 | 0.0694310 | − | 0.997587i | \(-0.477882\pi\) | ||||
0.0694310 | + | 0.997587i | \(0.477882\pi\) | |||||||
\(912\) | 19.8920 | − | 34.4539i | 0.658689 | − | 1.14088i | ||||
\(913\) | −2.10077 | − | 3.63864i | −0.0695254 | − | 0.120422i | ||||
\(914\) | −6.60459 | − | 11.4395i | −0.218461 | − | 0.378385i | ||||
\(915\) | 2.51938 | − | 4.36369i | 0.0832881 | − | 0.144259i | ||||
\(916\) | 1.42821 | 0.0471895 | ||||||||
\(917\) | −6.56530 | + | 8.70784i | −0.216805 | + | 0.287558i | ||||
\(918\) | −12.7225 | −0.419906 | ||||||||
\(919\) | −14.9232 | + | 25.8478i | −0.492272 | + | 0.852641i | −0.999960 | − | 0.00890030i | \(-0.997167\pi\) |
0.507688 | + | 0.861541i | \(0.330500\pi\) | |||||||
\(920\) | −6.10424 | − | 10.5729i | −0.201251 | − | 0.348577i | ||||
\(921\) | −38.2336 | − | 66.2225i | −1.25984 | − | 2.18210i | ||||
\(922\) | 19.5937 | − | 33.9374i | 0.645286 | − | 1.11767i | ||||
\(923\) | 16.8835 | 0.555727 | ||||||||
\(924\) | 6.97226 | + | 0.857886i | 0.229371 | + | 0.0282224i | ||||
\(925\) | 5.40922 | 0.177854 | ||||||||
\(926\) | −9.67558 | + | 16.7586i | −0.317959 | + | 0.550721i | ||||
\(927\) | 52.4740 | + | 90.8876i | 1.72347 | + | 2.98514i | ||||
\(928\) | 8.99588 | + | 15.5813i | 0.295304 | + | 0.511482i | ||||
\(929\) | 8.32722 | − | 14.4232i | 0.273207 | − | 0.473209i | −0.696474 | − | 0.717582i | \(-0.745249\pi\) |
0.969681 | + | 0.244373i | \(0.0785822\pi\) | |||||||
\(930\) | 1.06730 | 0.0349980 | ||||||||
\(931\) | −41.2111 | + | 42.6320i | −1.35064 | + | 1.39721i | ||||
\(932\) | −1.80494 | −0.0591229 | ||||||||
\(933\) | 37.4346 | − | 64.8386i | 1.22555 | − | 2.12272i | ||||
\(934\) | −17.9461 | − | 31.0836i | −0.587215 | − | 1.01709i | ||||
\(935\) | −0.561652 | − | 0.972810i | −0.0183680 | − | 0.0318143i | ||||
\(936\) | 20.3189 | − | 35.1934i | 0.664144 | − | 1.15033i | ||||
\(937\) | 8.35998 | 0.273109 | 0.136554 | − | 0.990633i | \(-0.456397\pi\) | ||||
0.136554 | + | 0.990633i | \(0.456397\pi\) | |||||||
\(938\) | −30.1139 | − | 3.70529i | −0.983253 | − | 0.120982i | ||||
\(939\) | 3.53313 | 0.115299 | ||||||||
\(940\) | 0.454920 | − | 0.787944i | 0.0148379 | − | 0.0256999i | ||||
\(941\) | −10.6580 | − | 18.4601i | −0.347440 | − | 0.601784i | 0.638354 | − | 0.769743i | \(-0.279616\pi\) |
−0.985794 | + | 0.167959i | \(0.946282\pi\) | |||||||
\(942\) | 31.7188 | + | 54.9386i | 1.03346 | + | 1.79000i | ||||
\(943\) | −2.46449 | + | 4.26861i | −0.0802547 | + | 0.139005i | ||||
\(944\) | −21.1841 | −0.689485 | ||||||||
\(945\) | −16.9218 | + | 22.4442i | −0.550468 | + | 0.730109i | ||||
\(946\) | −12.8822 | −0.418837 | ||||||||
\(947\) | 6.34435 | − | 10.9887i | 0.206164 | − | 0.357086i | −0.744339 | − | 0.667802i | \(-0.767235\pi\) |
0.950503 | + | 0.310716i | \(0.100569\pi\) | |||||||
\(948\) | 9.87690 | + | 17.1073i | 0.320787 | + | 0.555619i | ||||
\(949\) | 13.3648 | + | 23.1486i | 0.433841 | + | 0.751434i | ||||
\(950\) | −4.51517 | + | 7.82050i | −0.146491 | + | 0.253731i | ||||
\(951\) | 59.5139 | 1.92987 | ||||||||
\(952\) | 3.54280 | + | 8.35222i | 0.114823 | + | 0.270697i | ||||
\(953\) | −38.6944 | −1.25343 | −0.626717 | − | 0.779247i | \(-0.715602\pi\) | ||||
−0.626717 | + | 0.779247i | \(0.715602\pi\) | |||||||
\(954\) | 3.04318 | − | 5.27094i | 0.0985266 | − | 0.170653i | ||||
\(955\) | 0.597017 | + | 1.03406i | 0.0193190 | + | 0.0334615i | ||||
\(956\) | −5.65840 | − | 9.80064i | −0.183006 | − | 0.316975i | ||||
\(957\) | 6.17854 | − | 10.7015i | 0.199724 | − | 0.345932i | ||||
\(958\) | 23.3972 | 0.755929 | ||||||||
\(959\) | 11.8895 | + | 28.0297i | 0.383932 | + | 0.905127i | ||||
\(960\) | −24.0694 | −0.776838 | ||||||||
\(961\) | 15.4470 | − | 26.7550i | 0.498290 | − | 0.863064i | ||||
\(962\) | −5.94619 | − | 10.2991i | −0.191713 | − | 0.332057i | ||||
\(963\) | −27.6933 | − | 47.9662i | −0.892404 | − | 1.54569i | ||||
\(964\) | 2.55869 | − | 4.43179i | 0.0824100 | − | 0.142738i | ||||
\(965\) | 22.2090 | 0.714933 | ||||||||
\(966\) | 20.8813 | − | 27.6958i | 0.671845 | − | 0.891097i | ||||
\(967\) | −13.1619 | −0.423259 | −0.211630 | − | 0.977350i | \(-0.567877\pi\) | ||||
−0.211630 | + | 0.977350i | \(0.567877\pi\) | |||||||
\(968\) | 1.52634 | − | 2.64371i | 0.0490586 | − | 0.0849719i | ||||
\(969\) | 14.6291 | + | 25.3383i | 0.469953 | + | 0.813983i | ||||
\(970\) | −8.96856 | − | 15.5340i | −0.287963 | − | 0.498767i | ||||
\(971\) | 17.7976 | − | 30.8264i | 0.571153 | − | 0.989266i | −0.425295 | − | 0.905055i | \(-0.639830\pi\) |
0.996448 | − | 0.0842114i | \(-0.0268371\pi\) | |||||||
\(972\) | −7.79948 | −0.250168 | ||||||||
\(973\) | 2.05677 | + | 0.253071i | 0.0659371 | + | 0.00811307i | ||||
\(974\) | 20.7373 | 0.664465 | ||||||||
\(975\) | −3.17066 | + | 5.49174i | −0.101542 | + | 0.175876i | ||||
\(976\) | 1.25147 | + | 2.16761i | 0.0400585 | + | 0.0693834i | ||||
\(977\) | 9.60016 | + | 16.6280i | 0.307136 | + | 0.531976i | 0.977735 | − | 0.209845i | \(-0.0672959\pi\) |
−0.670598 | + | 0.741821i | \(0.733963\pi\) | |||||||
\(978\) | −26.4191 | + | 45.7592i | −0.844789 | + | 1.46322i | ||||
\(979\) | −14.0917 | −0.450371 | ||||||||
\(980\) | 5.86411 | + | 1.46526i | 0.187322 | + | 0.0468059i | ||||
\(981\) | 26.7349 | 0.853581 | ||||||||
\(982\) | −3.31879 | + | 5.74831i | −0.105907 | + | 0.183436i | ||||
\(983\) | 16.4478 | + | 28.4884i | 0.524603 | + | 0.908639i | 0.999590 | + | 0.0286461i | \(0.00911958\pi\) |
−0.474987 | + | 0.879993i | \(0.657547\pi\) | |||||||
\(984\) | 5.78445 | + | 10.0190i | 0.184401 | + | 0.319393i | ||||
\(985\) | −2.67544 | + | 4.63399i | −0.0852465 | + | 0.147651i | ||||
\(986\) | 4.81247 | 0.153260 | ||||||||
\(987\) | 8.50802 | + | 1.04685i | 0.270813 | + | 0.0333216i | ||||
\(988\) | −15.0841 | −0.479888 | ||||||||
\(989\) | 24.1631 | − | 41.8517i | 0.768342 | − | 1.33081i | ||||
\(990\) | 3.44079 | + | 5.95963i | 0.109356 | + | 0.189409i | ||||
\(991\) | 9.98802 | + | 17.2998i | 0.317280 | + | 0.549545i | 0.979920 | − | 0.199393i | \(-0.0638972\pi\) |
−0.662640 | + | 0.748939i | \(0.730564\pi\) | |||||||
\(992\) | 0.728828 | − | 1.26237i | 0.0231403 | − | 0.0400802i | ||||
\(993\) | −10.0234 | −0.318083 | ||||||||
\(994\) | 13.9015 | − | 18.4381i | 0.440929 | − | 0.584823i | ||||
\(995\) | 11.0229 | 0.349450 | ||||||||
\(996\) | 5.57784 | − | 9.66111i | 0.176741 | − | 0.306124i | ||||
\(997\) | 2.02065 | + | 3.49986i | 0.0639945 | + | 0.110842i | 0.896248 | − | 0.443554i | \(-0.146283\pi\) |
−0.832253 | + | 0.554396i | \(0.812949\pi\) | |||||||
\(998\) | −5.52454 | − | 9.56878i | −0.174876 | − | 0.302894i | ||||
\(999\) | −28.7338 | + | 49.7685i | −0.909099 | + | 1.57460i |
(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 | 385.2.i.d.331.5 | yes | 20 | |
7.2 | even | 3 | 2695.2.a.y.1.6 | 10 | |||
7.4 | even | 3 | inner | 385.2.i.d.221.5 | ✓ | 20 | |
7.5 | odd | 6 | 2695.2.a.z.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.i.d.221.5 | ✓ | 20 | 7.4 | even | 3 | inner | |
385.2.i.d.331.5 | yes | 20 | 1.1 | even | 1 | trivial | |
2695.2.a.y.1.6 | 10 | 7.2 | even | 3 | |||
2695.2.a.z.1.6 | 10 | 7.5 | odd | 6 |