Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(11,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.l (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.116304318664704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-1.41362 + 0.0408194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.11 |
Dual form | 370.2.l.c.101.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.671462 | + | 1.16301i | −0.387669 | + | 0.671462i | −0.992135 | − | 0.125169i | \(-0.960053\pi\) |
0.604467 | + | 0.796630i | \(0.293386\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | − | 1.34292i | − | 0.548246i | ||||||
\(7\) | −0.461662 | + | 0.799622i | −0.174492 | + | 0.302229i | −0.939985 | − | 0.341215i | \(-0.889162\pi\) |
0.765493 | + | 0.643444i | \(0.222495\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.598279 | + | 1.03625i | 0.199426 | + | 0.345416i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.56596 | −0.773667 | −0.386834 | − | 0.922149i | \(-0.626431\pi\) | ||||
−0.386834 | + | 0.922149i | \(0.626431\pi\) | |||||||
\(12\) | 0.671462 | + | 1.16301i | 0.193834 | + | 0.335731i | ||||
\(13\) | −1.66565 | − | 0.961662i | −0.461968 | − | 0.266717i | 0.250904 | − | 0.968012i | \(-0.419272\pi\) |
−0.712871 | + | 0.701295i | \(0.752606\pi\) | |||||||
\(14\) | − | 0.923324i | − | 0.246769i | ||||||
\(15\) | 1.16301 | − | 0.671462i | 0.300287 | − | 0.173371i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.77990 | + | 1.02763i | −0.431689 | + | 0.249236i | −0.700066 | − | 0.714078i | \(-0.746846\pi\) |
0.268377 | + | 0.963314i | \(0.413513\pi\) | |||||||
\(18\) | −1.03625 | − | 0.598279i | −0.244246 | − | 0.141016i | ||||
\(19\) | −6.29199 | − | 3.63268i | −1.44348 | − | 0.833395i | −0.445402 | − | 0.895330i | \(-0.646939\pi\) |
−0.998080 | + | 0.0619354i | \(0.980273\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | −0.619977 | − | 1.07383i | −0.135290 | − | 0.234329i | ||||
\(22\) | 2.22219 | − | 1.28298i | 0.473773 | − | 0.273533i | ||||
\(23\) | 8.22046i | 1.71408i | 0.515246 | + | 0.857042i | \(0.327701\pi\) | ||||
−0.515246 | + | 0.857042i | \(0.672299\pi\) | |||||||
\(24\) | −1.16301 | − | 0.671462i | −0.237398 | − | 0.137062i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 1.92332 | 0.377195 | ||||||||
\(27\) | −5.63565 | −1.08458 | ||||||||
\(28\) | 0.461662 | + | 0.799622i | 0.0872459 | + | 0.151114i | ||||
\(29\) | − | 5.75683i | − | 1.06902i | −0.845163 | − | 0.534508i | \(-0.820497\pi\) | ||
0.845163 | − | 0.534508i | \(-0.179503\pi\) | |||||||
\(30\) | −0.671462 | + | 1.16301i | −0.122592 | + | 0.212335i | ||||
\(31\) | − | 10.5357i | − | 1.89227i | −0.323770 | − | 0.946136i | \(-0.604950\pi\) | ||
0.323770 | − | 0.946136i | \(-0.395050\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 1.72295 | − | 2.98423i | 0.299926 | − | 0.519488i | ||||
\(34\) | 1.02763 | − | 1.77990i | 0.176236 | − | 0.305251i | ||||
\(35\) | 0.799622 | − | 0.461662i | 0.135161 | − | 0.0780351i | ||||
\(36\) | 1.19656 | 0.199426 | ||||||||
\(37\) | −3.95342 | − | 4.62282i | −0.649938 | − | 0.759988i | ||||
\(38\) | 7.26537 | 1.17860 | ||||||||
\(39\) | 2.23684 | − | 1.29144i | 0.358181 | − | 0.206796i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −1.50097 | + | 2.59975i | −0.234411 | + | 0.406013i | −0.959101 | − | 0.283062i | \(-0.908650\pi\) |
0.724690 | + | 0.689075i | \(0.241983\pi\) | |||||||
\(42\) | 1.07383 | + | 0.619977i | 0.165696 | + | 0.0956645i | ||||
\(43\) | 6.95091i | 1.06000i | 0.847996 | + | 0.530002i | \(0.177809\pi\) | ||||
−0.847996 | + | 0.530002i | \(0.822191\pi\) | |||||||
\(44\) | −1.28298 | + | 2.22219i | −0.193417 | + | 0.335008i | ||||
\(45\) | − | 1.19656i | − | 0.178372i | ||||||
\(46\) | −4.11023 | − | 7.11913i | −0.606020 | − | 1.04966i | ||||
\(47\) | −10.5209 | −1.53463 | −0.767313 | − | 0.641273i | \(-0.778407\pi\) | ||||
−0.767313 | + | 0.641273i | \(0.778407\pi\) | |||||||
\(48\) | 1.34292 | 0.193834 | ||||||||
\(49\) | 3.07374 | + | 5.32387i | 0.439105 | + | 0.760552i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | − | 2.76005i | − | 0.386484i | ||||||
\(52\) | −1.66565 | + | 0.961662i | −0.230984 | + | 0.133359i | ||||
\(53\) | 2.61745 | + | 4.53356i | 0.359534 | + | 0.622732i | 0.987883 | − | 0.155200i | \(-0.0496022\pi\) |
−0.628349 | + | 0.777932i | \(0.716269\pi\) | |||||||
\(54\) | 4.88062 | − | 2.81783i | 0.664168 | − | 0.383458i | ||||
\(55\) | 2.22219 | + | 1.28298i | 0.299640 | + | 0.172997i | ||||
\(56\) | −0.799622 | − | 0.461662i | −0.106854 | − | 0.0616922i | ||||
\(57\) | 8.44966 | − | 4.87842i | 1.11919 | − | 0.646162i | ||||
\(58\) | 2.87842 | + | 4.98556i | 0.377955 | + | 0.654637i | ||||
\(59\) | −3.68685 | + | 2.12860i | −0.479987 | + | 0.277120i | −0.720411 | − | 0.693547i | \(-0.756047\pi\) |
0.240424 | + | 0.970668i | \(0.422713\pi\) | |||||||
\(60\) | − | 1.34292i | − | 0.173371i | ||||||
\(61\) | 3.49339 | + | 2.01691i | 0.447283 | + | 0.258239i | 0.706682 | − | 0.707531i | \(-0.250191\pi\) |
−0.259399 | + | 0.965770i | \(0.583524\pi\) | |||||||
\(62\) | 5.26786 | + | 9.12420i | 0.669019 | + | 1.15877i | ||||
\(63\) | −1.10481 | −0.139193 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.961662 | + | 1.66565i | 0.119280 | + | 0.206598i | ||||
\(66\) | 3.44589i | 0.424160i | ||||||||
\(67\) | 1.66204 | − | 2.87874i | 0.203050 | − | 0.351694i | −0.746459 | − | 0.665431i | \(-0.768248\pi\) |
0.949510 | + | 0.313737i | \(0.101581\pi\) | |||||||
\(68\) | 2.05525i | 0.249236i | ||||||||
\(69\) | −9.56044 | − | 5.51972i | −1.15094 | − | 0.664497i | ||||
\(70\) | −0.461662 | + | 0.799622i | −0.0551792 | + | 0.0955731i | ||||
\(71\) | −7.86679 | + | 13.6257i | −0.933616 | + | 1.61707i | −0.156533 | + | 0.987673i | \(0.550032\pi\) |
−0.777083 | + | 0.629398i | \(0.783302\pi\) | |||||||
\(72\) | −1.03625 | + | 0.598279i | −0.122123 | + | 0.0705078i | ||||
\(73\) | 7.08485 | 0.829219 | 0.414609 | − | 0.910000i | \(-0.363918\pi\) | ||||
0.414609 | + | 0.910000i | \(0.363918\pi\) | |||||||
\(74\) | 5.73517 | + | 2.02678i | 0.666700 | + | 0.235608i | ||||
\(75\) | −1.34292 | −0.155067 | ||||||||
\(76\) | −6.29199 | + | 3.63268i | −0.721741 | + | 0.416698i | ||||
\(77\) | 1.18461 | − | 2.05180i | 0.134999 | − | 0.233825i | ||||
\(78\) | −1.29144 | + | 2.23684i | −0.146227 | + | 0.253272i | ||||
\(79\) | 12.0757 | + | 6.97191i | 1.35862 | + | 0.784401i | 0.989438 | − | 0.144955i | \(-0.0463036\pi\) |
0.369185 | + | 0.929356i | \(0.379637\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.98929 | − | 3.44555i | 0.221032 | − | 0.382839i | ||||
\(82\) | − | 3.00193i | − | 0.331508i | ||||||
\(83\) | 2.86398 | + | 4.96056i | 0.314363 | + | 0.544492i | 0.979302 | − | 0.202405i | \(-0.0648759\pi\) |
−0.664939 | + | 0.746897i | \(0.731543\pi\) | |||||||
\(84\) | −1.23995 | −0.135290 | ||||||||
\(85\) | 2.05525 | 0.222923 | ||||||||
\(86\) | −3.47546 | − | 6.01967i | −0.374768 | − | 0.649118i | ||||
\(87\) | 6.69523 | + | 3.86549i | 0.717804 | + | 0.414424i | ||||
\(88\) | − | 2.56596i | − | 0.273533i | ||||||
\(89\) | −3.60036 | + | 2.07867i | −0.381638 | + | 0.220339i | −0.678530 | − | 0.734572i | \(-0.737383\pi\) |
0.296893 | + | 0.954911i | \(0.404050\pi\) | |||||||
\(90\) | 0.598279 | + | 1.03625i | 0.0630641 | + | 0.109230i | ||||
\(91\) | 1.53793 | − | 0.887926i | 0.161219 | − | 0.0930799i | ||||
\(92\) | 7.11913 | + | 4.11023i | 0.742220 | + | 0.428521i | ||||
\(93\) | 12.2531 | + | 7.07433i | 1.27059 | + | 0.733574i | ||||
\(94\) | 9.11134 | − | 5.26043i | 0.939763 | − | 0.542572i | ||||
\(95\) | 3.63268 | + | 6.29199i | 0.372706 | + | 0.645545i | ||||
\(96\) | −1.16301 | + | 0.671462i | −0.118699 | + | 0.0685308i | ||||
\(97\) | − | 9.92333i | − | 1.00756i | −0.863832 | − | 0.503781i | \(-0.831942\pi\) | ||
0.863832 | − | 0.503781i | \(-0.168058\pi\) | |||||||
\(98\) | −5.32387 | − | 3.07374i | −0.537792 | − | 0.310494i | ||||
\(99\) | −1.53516 | − | 2.65898i | −0.154290 | − | 0.267237i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 16.4846 | 1.64028 | 0.820140 | − | 0.572163i | \(-0.193896\pi\) | ||||
0.820140 | + | 0.572163i | \(0.193896\pi\) | |||||||
\(102\) | 1.38002 | + | 2.39027i | 0.136643 | + | 0.236672i | ||||
\(103\) | 5.94687i | 0.585963i | 0.956118 | + | 0.292981i | \(0.0946474\pi\) | ||||
−0.956118 | + | 0.292981i | \(0.905353\pi\) | |||||||
\(104\) | 0.961662 | − | 1.66565i | 0.0942987 | − | 0.163330i | ||||
\(105\) | 1.23995i | 0.121007i | ||||||||
\(106\) | −4.53356 | − | 2.61745i | −0.440338 | − | 0.254229i | ||||
\(107\) | 1.86802 | − | 3.23550i | 0.180588 | − | 0.312788i | −0.761493 | − | 0.648173i | \(-0.775533\pi\) |
0.942081 | + | 0.335385i | \(0.108867\pi\) | |||||||
\(108\) | −2.81783 | + | 4.88062i | −0.271146 | + | 0.469638i | ||||
\(109\) | −5.02919 | + | 2.90360i | −0.481709 | + | 0.278115i | −0.721128 | − | 0.692801i | \(-0.756376\pi\) |
0.239419 | + | 0.970916i | \(0.423043\pi\) | |||||||
\(110\) | −2.56596 | −0.244655 | ||||||||
\(111\) | 8.03094 | − | 1.49380i | 0.762263 | − | 0.141785i | ||||
\(112\) | 0.923324 | 0.0872459 | ||||||||
\(113\) | −4.34573 | + | 2.50901i | −0.408812 | + | 0.236028i | −0.690279 | − | 0.723543i | \(-0.742512\pi\) |
0.281467 | + | 0.959571i | \(0.409179\pi\) | |||||||
\(114\) | −4.87842 | + | 8.44966i | −0.456906 | + | 0.791384i | ||||
\(115\) | 4.11023 | − | 7.11913i | 0.383281 | − | 0.663862i | ||||
\(116\) | −4.98556 | − | 2.87842i | −0.462898 | − | 0.267254i | ||||
\(117\) | − | 2.30137i | − | 0.212762i | ||||||
\(118\) | 2.12860 | − | 3.68685i | 0.195954 | − | 0.339402i | ||||
\(119\) | − | 1.89766i | − | 0.173959i | ||||||
\(120\) | 0.671462 | + | 1.16301i | 0.0612958 | + | 0.106167i | ||||
\(121\) | −4.41583 | −0.401439 | ||||||||
\(122\) | −4.03382 | −0.365205 | ||||||||
\(123\) | −2.01568 | − | 3.49126i | −0.181748 | − | 0.314797i | ||||
\(124\) | −9.12420 | − | 5.26786i | −0.819378 | − | 0.473068i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0.956794 | − | 0.552405i | 0.0852380 | − | 0.0492122i | ||||
\(127\) | −2.85853 | − | 4.95113i | −0.253654 | − | 0.439342i | 0.710875 | − | 0.703318i | \(-0.248299\pi\) |
−0.964529 | + | 0.263977i | \(0.914966\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −8.08395 | − | 4.66727i | −0.711752 | − | 0.410930i | ||||
\(130\) | −1.66565 | − | 0.961662i | −0.146087 | − | 0.0843433i | ||||
\(131\) | −5.09112 | + | 2.93936i | −0.444813 | + | 0.256813i | −0.705637 | − | 0.708573i | \(-0.749339\pi\) |
0.260824 | + | 0.965386i | \(0.416006\pi\) | |||||||
\(132\) | −1.72295 | − | 2.98423i | −0.149963 | − | 0.259744i | ||||
\(133\) | 5.80955 | − | 3.35415i | 0.503752 | − | 0.290841i | ||||
\(134\) | 3.32408i | 0.287157i | ||||||||
\(135\) | 4.88062 | + | 2.81783i | 0.420057 | + | 0.242520i | ||||
\(136\) | −1.02763 | − | 1.77990i | −0.0881182 | − | 0.152625i | ||||
\(137\) | −10.4012 | −0.888636 | −0.444318 | − | 0.895869i | \(-0.646554\pi\) | ||||
−0.444318 | + | 0.895869i | \(0.646554\pi\) | |||||||
\(138\) | 11.0394 | 0.939740 | ||||||||
\(139\) | 7.32003 | + | 12.6787i | 0.620877 | + | 1.07539i | 0.989323 | + | 0.145741i | \(0.0465565\pi\) |
−0.368446 | + | 0.929649i | \(0.620110\pi\) | |||||||
\(140\) | − | 0.923324i | − | 0.0780351i | ||||||
\(141\) | 7.06436 | − | 12.2358i | 0.594926 | − | 1.03044i | ||||
\(142\) | − | 15.7336i | − | 1.32033i | ||||||
\(143\) | 4.27399 | + | 2.46759i | 0.357409 | + | 0.206350i | ||||
\(144\) | 0.598279 | − | 1.03625i | 0.0498566 | − | 0.0863541i | ||||
\(145\) | −2.87842 | + | 4.98556i | −0.239039 | + | 0.414028i | ||||
\(146\) | −6.13566 | + | 3.54242i | −0.507791 | + | 0.293173i | ||||
\(147\) | −8.25558 | −0.680909 | ||||||||
\(148\) | −5.98019 | + | 1.11235i | −0.491569 | + | 0.0914343i | ||||
\(149\) | 19.9932 | 1.63791 | 0.818953 | − | 0.573860i | \(-0.194555\pi\) | ||||
0.818953 | + | 0.573860i | \(0.194555\pi\) | |||||||
\(150\) | 1.16301 | − | 0.671462i | 0.0949590 | − | 0.0548246i | ||||
\(151\) | −7.15059 | + | 12.3852i | −0.581907 | + | 1.00789i | 0.413347 | + | 0.910574i | \(0.364360\pi\) |
−0.995253 | + | 0.0973182i | \(0.968974\pi\) | |||||||
\(152\) | 3.63268 | − | 6.29199i | 0.294650 | − | 0.510348i | ||||
\(153\) | −2.12975 | − | 1.22961i | −0.172180 | − | 0.0994084i | ||||
\(154\) | 2.36922i | 0.190917i | ||||||||
\(155\) | −5.26786 | + | 9.12420i | −0.423125 | + | 0.732874i | ||||
\(156\) | − | 2.58288i | − | 0.206796i | ||||||
\(157\) | −4.54457 | − | 7.87142i | −0.362696 | − | 0.628208i | 0.625708 | − | 0.780058i | \(-0.284810\pi\) |
−0.988404 | + | 0.151850i | \(0.951477\pi\) | |||||||
\(158\) | −13.9438 | −1.10931 | ||||||||
\(159\) | −7.03007 | −0.557520 | ||||||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −6.57326 | − | 3.79508i | −0.518046 | − | 0.299094i | ||||
\(162\) | 3.97858i | 0.312587i | ||||||||
\(163\) | −7.21054 | + | 4.16301i | −0.564773 | + | 0.326072i | −0.755059 | − | 0.655657i | \(-0.772392\pi\) |
0.190286 | + | 0.981729i | \(0.439058\pi\) | |||||||
\(164\) | 1.50097 | + | 2.59975i | 0.117206 | + | 0.203006i | ||||
\(165\) | −2.98423 | + | 1.72295i | −0.232322 | + | 0.134131i | ||||
\(166\) | −4.96056 | − | 2.86398i | −0.385014 | − | 0.222288i | ||||
\(167\) | 6.46115 | + | 3.73035i | 0.499979 | + | 0.288663i | 0.728705 | − | 0.684828i | \(-0.240123\pi\) |
−0.228726 | + | 0.973491i | \(0.573456\pi\) | |||||||
\(168\) | 1.07383 | − | 0.619977i | 0.0828479 | − | 0.0478322i | ||||
\(169\) | −4.65041 | − | 8.05475i | −0.357724 | − | 0.619596i | ||||
\(170\) | −1.77990 | + | 1.02763i | −0.136512 | + | 0.0788154i | ||||
\(171\) | − | 8.69343i | − | 0.664803i | ||||||
\(172\) | 6.01967 | + | 3.47546i | 0.458995 | + | 0.265001i | ||||
\(173\) | −1.76710 | − | 3.06071i | −0.134350 | − | 0.232701i | 0.790999 | − | 0.611818i | \(-0.209561\pi\) |
−0.925349 | + | 0.379116i | \(0.876228\pi\) | |||||||
\(174\) | −7.73098 | −0.586084 | ||||||||
\(175\) | −0.923324 | −0.0697967 | ||||||||
\(176\) | 1.28298 | + | 2.22219i | 0.0967084 | + | 0.167504i | ||||
\(177\) | − | 5.71710i | − | 0.429723i | ||||||
\(178\) | 2.07867 | − | 3.60036i | 0.155803 | − | 0.269858i | ||||
\(179\) | − | 17.0164i | − | 1.27187i | −0.771743 | − | 0.635934i | \(-0.780615\pi\) | ||
0.771743 | − | 0.635934i | \(-0.219385\pi\) | |||||||
\(180\) | −1.03625 | − | 0.598279i | −0.0772375 | − | 0.0445931i | ||||
\(181\) | 4.13726 | − | 7.16595i | 0.307520 | − | 0.532641i | −0.670299 | − | 0.742091i | \(-0.733834\pi\) |
0.977819 | + | 0.209450i | \(0.0671675\pi\) | |||||||
\(182\) | −0.887926 | + | 1.53793i | −0.0658174 | + | 0.113999i | ||||
\(183\) | −4.69136 | + | 2.70856i | −0.346795 | + | 0.200222i | ||||
\(184\) | −8.22046 | −0.606020 | ||||||||
\(185\) | 1.11235 | + | 5.98019i | 0.0817813 | + | 0.439672i | ||||
\(186\) | −14.1487 | −1.03743 | ||||||||
\(187\) | 4.56716 | − | 2.63685i | 0.333984 | − | 0.192826i | ||||
\(188\) | −5.26043 | + | 9.11134i | −0.383657 | + | 0.664513i | ||||
\(189\) | 2.60177 | − | 4.50639i | 0.189251 | − | 0.327792i | ||||
\(190\) | −6.29199 | − | 3.63268i | −0.456469 | − | 0.263543i | ||||
\(191\) | 9.40975i | 0.680866i | 0.940269 | + | 0.340433i | \(0.110574\pi\) | ||||
−0.940269 | + | 0.340433i | \(0.889426\pi\) | |||||||
\(192\) | 0.671462 | − | 1.16301i | 0.0484586 | − | 0.0839327i | ||||
\(193\) | − | 14.4344i | − | 1.03901i | −0.854467 | − | 0.519505i | \(-0.826116\pi\) | ||
0.854467 | − | 0.519505i | \(-0.173884\pi\) | |||||||
\(194\) | 4.96167 | + | 8.59386i | 0.356227 | + | 0.617003i | ||||
\(195\) | −2.58288 | −0.184964 | ||||||||
\(196\) | 6.14747 | 0.439105 | ||||||||
\(197\) | 0.351202 | + | 0.608300i | 0.0250221 | + | 0.0433396i | 0.878265 | − | 0.478174i | \(-0.158701\pi\) |
−0.853243 | + | 0.521513i | \(0.825368\pi\) | |||||||
\(198\) | 2.65898 | + | 1.53516i | 0.188965 | + | 0.109099i | ||||
\(199\) | − | 14.3972i | − | 1.02059i | −0.859998 | − | 0.510297i | \(-0.829536\pi\) | ||
0.859998 | − | 0.510297i | \(-0.170464\pi\) | |||||||
\(200\) | −0.866025 | + | 0.500000i | −0.0612372 | + | 0.0353553i | ||||
\(201\) | 2.23199 | + | 3.86592i | 0.157433 | + | 0.272681i | ||||
\(202\) | −14.2761 | + | 8.24230i | −1.00446 | + | 0.579926i | ||||
\(203\) | 4.60329 | + | 2.65771i | 0.323088 | + | 0.186535i | ||||
\(204\) | −2.39027 | − | 1.38002i | −0.167352 | − | 0.0966210i | ||||
\(205\) | 2.59975 | − | 1.50097i | 0.181574 | − | 0.104832i | ||||
\(206\) | −2.97344 | − | 5.15014i | −0.207169 | − | 0.358828i | ||||
\(207\) | −8.51845 | + | 4.91813i | −0.592073 | + | 0.341834i | ||||
\(208\) | 1.92332i | 0.133359i | ||||||||
\(209\) | 16.1450 | + | 9.32134i | 1.11678 | + | 0.644771i | ||||
\(210\) | −0.619977 | − | 1.07383i | −0.0427825 | − | 0.0741014i | ||||
\(211\) | −11.5889 | −0.797810 | −0.398905 | − | 0.916992i | \(-0.630610\pi\) | ||||
−0.398905 | + | 0.916992i | \(0.630610\pi\) | |||||||
\(212\) | 5.23490 | 0.359534 | ||||||||
\(213\) | −10.5645 | − | 18.2982i | −0.723867 | − | 1.25377i | ||||
\(214\) | 3.73604i | 0.255390i | ||||||||
\(215\) | 3.47546 | − | 6.01967i | 0.237024 | − | 0.410538i | ||||
\(216\) | − | 5.63565i | − | 0.383458i | ||||||
\(217\) | 8.42460 | + | 4.86394i | 0.571899 | + | 0.330186i | ||||
\(218\) | 2.90360 | − | 5.02919i | 0.196657 | − | 0.340620i | ||||
\(219\) | −4.75720 | + | 8.23972i | −0.321462 | + | 0.556788i | ||||
\(220\) | 2.22219 | − | 1.28298i | 0.149820 | − | 0.0864986i | ||||
\(221\) | 3.95292 | 0.265902 | ||||||||
\(222\) | −6.20810 | + | 5.30913i | −0.416660 | + | 0.356326i | ||||
\(223\) | 9.39729 | 0.629289 | 0.314645 | − | 0.949210i | \(-0.398115\pi\) | ||||
0.314645 | + | 0.949210i | \(0.398115\pi\) | |||||||
\(224\) | −0.799622 | + | 0.461662i | −0.0534270 | + | 0.0308461i | ||||
\(225\) | −0.598279 | + | 1.03625i | −0.0398853 | + | 0.0690833i | ||||
\(226\) | 2.50901 | − | 4.34573i | 0.166897 | − | 0.289074i | ||||
\(227\) | −4.32885 | − | 2.49926i | −0.287316 | − | 0.165882i | 0.349415 | − | 0.936968i | \(-0.386380\pi\) |
−0.636731 | + | 0.771086i | \(0.719714\pi\) | |||||||
\(228\) | − | 9.75683i | − | 0.646162i | ||||||
\(229\) | −13.2423 | + | 22.9363i | −0.875076 | + | 1.51568i | −0.0183940 | + | 0.999831i | \(0.505855\pi\) |
−0.856682 | + | 0.515845i | \(0.827478\pi\) | |||||||
\(230\) | 8.22046i | 0.542041i | ||||||||
\(231\) | 1.59084 | + | 2.75541i | 0.104669 | + | 0.181293i | ||||
\(232\) | 5.75683 | 0.377955 | ||||||||
\(233\) | −19.9818 | −1.30905 | −0.654525 | − | 0.756040i | \(-0.727131\pi\) | ||||
−0.654525 | + | 0.756040i | \(0.727131\pi\) | |||||||
\(234\) | 1.15068 | + | 1.99304i | 0.0752226 | + | 0.130289i | ||||
\(235\) | 9.11134 | + | 5.26043i | 0.594358 | + | 0.343153i | ||||
\(236\) | 4.25720i | 0.277120i | ||||||||
\(237\) | −16.2167 | + | 9.36274i | −1.05339 | + | 0.608175i | ||||
\(238\) | 0.948832 | + | 1.64343i | 0.0615037 | + | 0.106527i | ||||
\(239\) | −6.87303 | + | 3.96815i | −0.444580 | + | 0.256678i | −0.705538 | − | 0.708672i | \(-0.749295\pi\) |
0.260959 | + | 0.965350i | \(0.415961\pi\) | |||||||
\(240\) | −1.16301 | − | 0.671462i | −0.0750717 | − | 0.0433427i | ||||
\(241\) | 6.39989 | + | 3.69498i | 0.412253 | + | 0.238014i | 0.691757 | − | 0.722130i | \(-0.256837\pi\) |
−0.279504 | + | 0.960144i | \(0.590170\pi\) | |||||||
\(242\) | 3.82422 | − | 2.20791i | 0.245830 | − | 0.141930i | ||||
\(243\) | −5.78202 | − | 10.0148i | −0.370917 | − | 0.642447i | ||||
\(244\) | 3.49339 | − | 2.01691i | 0.223642 | − | 0.129120i | ||||
\(245\) | − | 6.14747i | − | 0.392748i | ||||||
\(246\) | 3.49126 | + | 2.01568i | 0.222595 | + | 0.128515i | ||||
\(247\) | 6.98683 | + | 12.1015i | 0.444561 | + | 0.770003i | ||||
\(248\) | 10.5357 | 0.669019 | ||||||||
\(249\) | −7.69221 | −0.487474 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | − | 15.1646i | − | 0.957182i | −0.878038 | − | 0.478591i | \(-0.841148\pi\) | ||
0.878038 | − | 0.478591i | \(-0.158852\pi\) | |||||||
\(252\) | −0.552405 | + | 0.956794i | −0.0347983 | + | 0.0602724i | ||||
\(253\) | − | 21.0934i | − | 1.32613i | ||||||
\(254\) | 4.95113 | + | 2.85853i | 0.310661 | + | 0.179360i | ||||
\(255\) | −1.38002 | + | 2.39027i | −0.0864204 | + | 0.149685i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.38654 | + | 3.10992i | −0.336003 | + | 0.193991i | −0.658503 | − | 0.752578i | \(-0.728810\pi\) |
0.322500 | + | 0.946569i | \(0.395477\pi\) | |||||||
\(258\) | 9.33454 | 0.581143 | ||||||||
\(259\) | 5.52166 | − | 1.02706i | 0.343099 | − | 0.0638182i | ||||
\(260\) | 1.92332 | 0.119280 | ||||||||
\(261\) | 5.96551 | − | 3.44419i | 0.369256 | − | 0.213190i | ||||
\(262\) | 2.93936 | − | 5.09112i | 0.181594 | − | 0.314530i | ||||
\(263\) | 13.9347 | − | 24.1355i | 0.859247 | − | 1.48826i | −0.0134004 | − | 0.999910i | \(-0.504266\pi\) |
0.872648 | − | 0.488350i | \(-0.162401\pi\) | |||||||
\(264\) | 2.98423 | + | 1.72295i | 0.183667 | + | 0.106040i | ||||
\(265\) | − | 5.23490i | − | 0.321577i | ||||||
\(266\) | −3.35415 | + | 5.80955i | −0.205656 | + | 0.356206i | ||||
\(267\) | − | 5.58299i | − | 0.341673i | ||||||
\(268\) | −1.66204 | − | 2.87874i | −0.101525 | − | 0.175847i | ||||
\(269\) | −10.8811 | −0.663434 | −0.331717 | − | 0.943379i | \(-0.607628\pi\) | ||||
−0.331717 | + | 0.943379i | \(0.607628\pi\) | |||||||
\(270\) | −5.63565 | −0.342975 | ||||||||
\(271\) | 12.0081 | + | 20.7986i | 0.729439 | + | 1.26343i | 0.957120 | + | 0.289690i | \(0.0935523\pi\) |
−0.227681 | + | 0.973736i | \(0.573114\pi\) | |||||||
\(272\) | 1.77990 | + | 1.02763i | 0.107922 | + | 0.0623090i | ||||
\(273\) | 2.38483i | 0.144337i | ||||||||
\(274\) | 9.00772 | − | 5.20061i | 0.544176 | − | 0.314180i | ||||
\(275\) | −1.28298 | − | 2.22219i | −0.0773667 | − | 0.134003i | ||||
\(276\) | −9.56044 | + | 5.51972i | −0.575471 | + | 0.332248i | ||||
\(277\) | 4.54885 | + | 2.62628i | 0.273314 | + | 0.157798i | 0.630393 | − | 0.776277i | \(-0.282894\pi\) |
−0.357079 | + | 0.934074i | \(0.616227\pi\) | |||||||
\(278\) | −12.6787 | − | 7.32003i | −0.760415 | − | 0.439026i | ||||
\(279\) | 10.9176 | − | 6.30330i | 0.653622 | − | 0.377369i | ||||
\(280\) | 0.461662 | + | 0.799622i | 0.0275896 | + | 0.0477866i | ||||
\(281\) | 16.7463 | − | 9.66850i | 0.999002 | − | 0.576774i | 0.0910494 | − | 0.995846i | \(-0.470978\pi\) |
0.907953 | + | 0.419072i | \(0.137645\pi\) | |||||||
\(282\) | 14.1287i | 0.841353i | ||||||||
\(283\) | −0.882827 | − | 0.509701i | −0.0524786 | − | 0.0302986i | 0.473531 | − | 0.880777i | \(-0.342979\pi\) |
−0.526010 | + | 0.850479i | \(0.676312\pi\) | |||||||
\(284\) | 7.86679 | + | 13.6257i | 0.466808 | + | 0.808535i | ||||
\(285\) | −9.75683 | −0.577945 | ||||||||
\(286\) | −4.93518 | −0.291823 | ||||||||
\(287\) | −1.38588 | − | 2.40041i | −0.0818058 | − | 0.141692i | ||||
\(288\) | 1.19656i | 0.0705078i | ||||||||
\(289\) | −6.38797 | + | 11.0643i | −0.375763 | + | 0.650840i | ||||
\(290\) | − | 5.75683i | − | 0.338053i | ||||||
\(291\) | 11.5409 | + | 6.66313i | 0.676539 | + | 0.390600i | ||||
\(292\) | 3.54242 | − | 6.13566i | 0.207305 | − | 0.359062i | ||||
\(293\) | −6.44390 | + | 11.1612i | −0.376457 | + | 0.652042i | −0.990544 | − | 0.137196i | \(-0.956191\pi\) |
0.614087 | + | 0.789238i | \(0.289524\pi\) | |||||||
\(294\) | 7.14954 | − | 4.12779i | 0.416970 | − | 0.240738i | ||||
\(295\) | 4.25720 | 0.247864 | ||||||||
\(296\) | 4.62282 | − | 3.95342i | 0.268696 | − | 0.229788i | ||||
\(297\) | 14.4609 | 0.839106 | ||||||||
\(298\) | −17.3146 | + | 9.99660i | −1.00301 | + | 0.579087i | ||||
\(299\) | 7.90531 | − | 13.6924i | 0.457176 | − | 0.791852i | ||||
\(300\) | −0.671462 | + | 1.16301i | −0.0387669 | + | 0.0671462i | ||||
\(301\) | −5.55811 | − | 3.20897i | −0.320364 | − | 0.184962i | ||||
\(302\) | − | 14.3012i | − | 0.822940i | ||||||
\(303\) | −11.0688 | + | 19.1717i | −0.635885 | + | 1.10138i | ||||
\(304\) | 7.26537i | 0.416698i | ||||||||
\(305\) | −2.01691 | − | 3.49339i | −0.115488 | − | 0.200031i | ||||
\(306\) | 2.45923 | 0.140585 | ||||||||
\(307\) | −24.3287 | −1.38851 | −0.694255 | − | 0.719729i | \(-0.744266\pi\) | ||||
−0.694255 | + | 0.719729i | \(0.744266\pi\) | |||||||
\(308\) | −1.18461 | − | 2.05180i | −0.0674993 | − | 0.116912i | ||||
\(309\) | −6.91625 | − | 3.99310i | −0.393452 | − | 0.227159i | ||||
\(310\) | − | 10.5357i | − | 0.598389i | ||||||
\(311\) | −5.48120 | + | 3.16457i | −0.310810 | + | 0.179446i | −0.647289 | − | 0.762245i | \(-0.724097\pi\) |
0.336479 | + | 0.941691i | \(0.390764\pi\) | |||||||
\(312\) | 1.29144 | + | 2.23684i | 0.0731133 | + | 0.126636i | ||||
\(313\) | 10.7348 | − | 6.19774i | 0.606766 | − | 0.350317i | −0.164932 | − | 0.986305i | \(-0.552741\pi\) |
0.771699 | + | 0.635988i | \(0.219407\pi\) | |||||||
\(314\) | 7.87142 | + | 4.54457i | 0.444210 | + | 0.256465i | ||||
\(315\) | 0.956794 | + | 0.552405i | 0.0539092 | + | 0.0311245i | ||||
\(316\) | 12.0757 | − | 6.97191i | 0.679312 | − | 0.392201i | ||||
\(317\) | 15.4949 | + | 26.8379i | 0.870280 | + | 1.50737i | 0.861708 | + | 0.507405i | \(0.169395\pi\) |
0.00857192 | + | 0.999963i | \(0.497271\pi\) | |||||||
\(318\) | 6.08822 | − | 3.51503i | 0.341410 | − | 0.197113i | ||||
\(319\) | 14.7718i | 0.827064i | ||||||||
\(320\) | 0.866025 | + | 0.500000i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | 2.50861 | + | 4.34503i | 0.140017 | + | 0.242516i | ||||
\(322\) | 7.59015 | 0.422983 | ||||||||
\(323\) | 14.9322 | 0.830848 | ||||||||
\(324\) | −1.98929 | − | 3.44555i | −0.110516 | − | 0.191419i | ||||
\(325\) | − | 1.92332i | − | 0.106687i | ||||||
\(326\) | 4.16301 | − | 7.21054i | 0.230568 | − | 0.399355i | ||||
\(327\) | − | 7.79863i | − | 0.431265i | ||||||
\(328\) | −2.59975 | − | 1.50097i | −0.143547 | − | 0.0828770i | ||||
\(329\) | 4.85709 | − | 8.41272i | 0.267780 | − | 0.463808i | ||||
\(330\) | 1.72295 | − | 2.98423i | 0.0948451 | − | 0.164276i | ||||
\(331\) | 2.81641 | − | 1.62606i | 0.154804 | − | 0.0893761i | −0.420597 | − | 0.907248i | \(-0.638179\pi\) |
0.575401 | + | 0.817871i | \(0.304846\pi\) | |||||||
\(332\) | 5.72796 | 0.314363 | ||||||||
\(333\) | 2.42515 | − | 6.86246i | 0.132898 | − | 0.376061i | ||||
\(334\) | −7.46070 | −0.408231 | ||||||||
\(335\) | −2.87874 | + | 1.66204i | −0.157282 | + | 0.0908069i | ||||
\(336\) | −0.619977 | + | 1.07383i | −0.0338225 | + | 0.0585823i | ||||
\(337\) | −15.2430 | + | 26.4016i | −0.830339 | + | 1.43819i | 0.0674306 | + | 0.997724i | \(0.478520\pi\) |
−0.897770 | + | 0.440465i | \(0.854813\pi\) | |||||||
\(338\) | 8.05475 | + | 4.65041i | 0.438121 | + | 0.252949i | ||||
\(339\) | − | 6.73881i | − | 0.366002i | ||||||
\(340\) | 1.02763 | − | 1.77990i | 0.0557309 | − | 0.0965287i | ||||
\(341\) | 27.0343i | 1.46399i | ||||||||
\(342\) | 4.34672 | + | 7.52873i | 0.235044 | + | 0.407107i | ||||
\(343\) | −12.1394 | −0.655465 | ||||||||
\(344\) | −6.95091 | −0.374768 | ||||||||
\(345\) | 5.51972 | + | 9.56044i | 0.297172 | + | 0.514717i | ||||
\(346\) | 3.06071 | + | 1.76710i | 0.164545 | + | 0.0949999i | ||||
\(347\) | 15.8277i | 0.849676i | 0.905270 | + | 0.424838i | \(0.139669\pi\) | ||||
−0.905270 | + | 0.424838i | \(0.860331\pi\) | |||||||
\(348\) | 6.69523 | − | 3.86549i | 0.358902 | − | 0.207212i | ||||
\(349\) | −1.51935 | − | 2.63159i | −0.0813289 | − | 0.140866i | 0.822492 | − | 0.568777i | \(-0.192583\pi\) |
−0.903821 | + | 0.427911i | \(0.859250\pi\) | |||||||
\(350\) | 0.799622 | − | 0.461662i | 0.0427416 | − | 0.0246769i | ||||
\(351\) | 9.38701 | + | 5.41959i | 0.501042 | + | 0.289277i | ||||
\(352\) | −2.22219 | − | 1.28298i | −0.118443 | − | 0.0683832i | ||||
\(353\) | 19.1232 | − | 11.0408i | 1.01782 | − | 0.587641i | 0.104352 | − | 0.994540i | \(-0.466723\pi\) |
0.913473 | + | 0.406899i | \(0.133390\pi\) | |||||||
\(354\) | 2.85855 | + | 4.95115i | 0.151930 | + | 0.263151i | ||||
\(355\) | 13.6257 | − | 7.86679i | 0.723176 | − | 0.417526i | ||||
\(356\) | 4.15734i | 0.220339i | ||||||||
\(357\) | 2.20699 | + | 1.27421i | 0.116807 | + | 0.0674383i | ||||
\(358\) | 8.50822 | + | 14.7367i | 0.449673 | + | 0.778857i | ||||
\(359\) | −10.5058 | −0.554477 | −0.277239 | − | 0.960801i | \(-0.589419\pi\) | ||||
−0.277239 | + | 0.960801i | \(0.589419\pi\) | |||||||
\(360\) | 1.19656 | 0.0630641 | ||||||||
\(361\) | 16.8928 | + | 29.2592i | 0.889095 | + | 1.53996i | ||||
\(362\) | 8.27452i | 0.434899i | ||||||||
\(363\) | 2.96506 | − | 5.13563i | 0.155625 | − | 0.269551i | ||||
\(364\) | − | 1.77585i | − | 0.0930799i | ||||||
\(365\) | −6.13566 | − | 3.54242i | −0.321155 | − | 0.185419i | ||||
\(366\) | 2.70856 | − | 4.69136i | 0.141579 | − | 0.245221i | ||||
\(367\) | 6.16031 | − | 10.6700i | 0.321566 | − | 0.556968i | −0.659246 | − | 0.751928i | \(-0.729124\pi\) |
0.980811 | + | 0.194959i | \(0.0624575\pi\) | |||||||
\(368\) | 7.11913 | − | 4.11023i | 0.371110 | − | 0.214261i | ||||
\(369\) | −3.59198 | −0.186991 | ||||||||
\(370\) | −3.95342 | − | 4.62282i | −0.205528 | − | 0.240329i | ||||
\(371\) | −4.83351 | −0.250943 | ||||||||
\(372\) | 12.2531 | − | 7.07433i | 0.635294 | − | 0.366787i | ||||
\(373\) | −13.2072 | + | 22.8755i | −0.683841 | + | 1.18445i | 0.289959 | + | 0.957039i | \(0.406358\pi\) |
−0.973800 | + | 0.227408i | \(0.926975\pi\) | |||||||
\(374\) | −2.63685 | + | 4.56716i | −0.136348 | + | 0.236162i | ||||
\(375\) | 1.16301 | + | 0.671462i | 0.0600573 | + | 0.0346741i | ||||
\(376\) | − | 10.5209i | − | 0.542572i | ||||||
\(377\) | −5.53613 | + | 9.58885i | −0.285125 | + | 0.493851i | ||||
\(378\) | 5.20354i | 0.267641i | ||||||||
\(379\) | 1.42044 | + | 2.46028i | 0.0729631 | + | 0.126376i | 0.900199 | − | 0.435479i | \(-0.143421\pi\) |
−0.827236 | + | 0.561855i | \(0.810088\pi\) | |||||||
\(380\) | 7.26537 | 0.372706 | ||||||||
\(381\) | 7.67759 | 0.393335 | ||||||||
\(382\) | −4.70488 | − | 8.14908i | −0.240722 | − | 0.416943i | ||||
\(383\) | −19.1202 | − | 11.0391i | −0.976998 | − | 0.564070i | −0.0756355 | − | 0.997136i | \(-0.524099\pi\) |
−0.901362 | + | 0.433065i | \(0.857432\pi\) | |||||||
\(384\) | 1.34292i | 0.0685308i | ||||||||
\(385\) | −2.05180 | + | 1.18461i | −0.104570 | + | 0.0603732i | ||||
\(386\) | 7.21720 | + | 12.5006i | 0.367346 | + | 0.636261i | ||||
\(387\) | −7.20288 | + | 4.15858i | −0.366143 | + | 0.211393i | ||||
\(388\) | −8.59386 | − | 4.96167i | −0.436287 | − | 0.251890i | ||||
\(389\) | −2.65801 | − | 1.53460i | −0.134766 | − | 0.0778074i | 0.431101 | − | 0.902304i | \(-0.358125\pi\) |
−0.565867 | + | 0.824496i | \(0.691459\pi\) | |||||||
\(390\) | 2.23684 | − | 1.29144i | 0.113267 | − | 0.0653945i | ||||
\(391\) | −8.44756 | − | 14.6316i | −0.427212 | − | 0.739952i | ||||
\(392\) | −5.32387 | + | 3.07374i | −0.268896 | + | 0.155247i | ||||
\(393\) | − | 7.89467i | − | 0.398233i | ||||||
\(394\) | −0.608300 | − | 0.351202i | −0.0306457 | − | 0.0176933i | ||||
\(395\) | −6.97191 | − | 12.0757i | −0.350795 | − | 0.607595i | ||||
\(396\) | −3.07032 | −0.154290 | ||||||||
\(397\) | 31.2700 | 1.56940 | 0.784698 | − | 0.619878i | \(-0.212818\pi\) | ||||
0.784698 | + | 0.619878i | \(0.212818\pi\) | |||||||
\(398\) | 7.19862 | + | 12.4684i | 0.360834 | + | 0.624984i | ||||
\(399\) | 9.00872i | 0.451000i | ||||||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | 3.17832i | 0.158717i | 0.996846 | + | 0.0793587i | \(0.0252873\pi\) | ||||
−0.996846 | + | 0.0793587i | \(0.974713\pi\) | |||||||
\(402\) | −3.86592 | − | 2.23199i | −0.192815 | − | 0.111322i | ||||
\(403\) | −10.1318 | + | 17.5488i | −0.504701 | + | 0.874168i | ||||
\(404\) | 8.24230 | − | 14.2761i | 0.410070 | − | 0.710262i | ||||
\(405\) | −3.44555 | + | 1.98929i | −0.171211 | + | 0.0988485i | ||||
\(406\) | −5.31542 | −0.263800 | ||||||||
\(407\) | 10.1443 | + | 11.8620i | 0.502835 | + | 0.587978i | ||||
\(408\) | 2.76005 | 0.136643 | ||||||||
\(409\) | −0.0108400 | + | 0.00625847i | −0.000536003 | + | 0.000309461i | −0.500268 | − | 0.865871i | \(-0.666765\pi\) |
0.499732 | + | 0.866180i | \(0.333432\pi\) | |||||||
\(410\) | −1.50097 | + | 2.59975i | −0.0741274 | + | 0.128392i | ||||
\(411\) | 6.98402 | − | 12.0967i | 0.344496 | − | 0.596685i | ||||
\(412\) | 5.15014 | + | 2.97344i | 0.253729 | + | 0.146491i | ||||
\(413\) | − | 3.93078i | − | 0.193421i | ||||||
\(414\) | 4.91813 | − | 8.51845i | 0.241713 | − | 0.418659i | ||||
\(415\) | − | 5.72796i | − | 0.281174i | ||||||
\(416\) | −0.961662 | − | 1.66565i | −0.0471494 | − | 0.0816651i | ||||
\(417\) | −19.6605 | −0.962777 | ||||||||
\(418\) | −18.6427 | −0.911843 | ||||||||
\(419\) | −1.64658 | − | 2.85196i | −0.0804408 | − | 0.139327i | 0.822999 | − | 0.568043i | \(-0.192299\pi\) |
−0.903439 | + | 0.428716i | \(0.858966\pi\) | |||||||
\(420\) | 1.07383 | + | 0.619977i | 0.0523976 | + | 0.0302518i | ||||
\(421\) | − | 19.3554i | − | 0.943326i | −0.881779 | − | 0.471663i | \(-0.843654\pi\) | ||
0.881779 | − | 0.471663i | \(-0.156346\pi\) | |||||||
\(422\) | 10.0362 | − | 5.79443i | 0.488557 | − | 0.282068i | ||||
\(423\) | −6.29441 | − | 10.9022i | −0.306045 | − | 0.530085i | ||||
\(424\) | −4.53356 | + | 2.61745i | −0.220169 | + | 0.127115i | ||||
\(425\) | −1.77990 | − | 1.02763i | −0.0863379 | − | 0.0498472i | ||||
\(426\) | 18.2982 | + | 10.5645i | 0.886552 | + | 0.511851i | ||||
\(427\) | −3.22554 | + | 1.86226i | −0.156095 | + | 0.0901213i | ||||
\(428\) | −1.86802 | − | 3.23550i | −0.0902941 | − | 0.156394i | ||||
\(429\) | −5.73964 | + | 3.31378i | −0.277113 | + | 0.159991i | ||||
\(430\) | 6.95091i | 0.335203i | ||||||||
\(431\) | 3.15630 | + | 1.82229i | 0.152034 | + | 0.0877766i | 0.574087 | − | 0.818794i | \(-0.305357\pi\) |
−0.422053 | + | 0.906571i | \(0.638691\pi\) | |||||||
\(432\) | 2.81783 | + | 4.88062i | 0.135573 | + | 0.234819i | ||||
\(433\) | −23.7592 | −1.14179 | −0.570897 | − | 0.821022i | \(-0.693404\pi\) | ||||
−0.570897 | + | 0.821022i | \(0.693404\pi\) | |||||||
\(434\) | −9.72789 | −0.466954 | ||||||||
\(435\) | −3.86549 | − | 6.69523i | −0.185336 | − | 0.321012i | ||||
\(436\) | 5.80721i | 0.278115i | ||||||||
\(437\) | 29.8623 | − | 51.7231i | 1.42851 | − | 2.47425i | ||||
\(438\) | − | 9.51440i | − | 0.454616i | ||||||
\(439\) | 20.3096 | + | 11.7258i | 0.969324 | + | 0.559640i | 0.899030 | − | 0.437887i | \(-0.144273\pi\) |
0.0702940 | + | 0.997526i | \(0.477606\pi\) | |||||||
\(440\) | −1.28298 | + | 2.22219i | −0.0611638 | + | 0.105939i | ||||
\(441\) | −3.67790 | + | 6.37031i | −0.175138 | + | 0.303348i | ||||
\(442\) | −3.42333 | + | 1.97646i | −0.162831 | + | 0.0940106i | ||||
\(443\) | −38.9584 | −1.85097 | −0.925486 | − | 0.378783i | \(-0.876343\pi\) | ||||
−0.925486 | + | 0.378783i | \(0.876343\pi\) | |||||||
\(444\) | 2.72180 | − | 7.70189i | 0.129171 | − | 0.365516i | ||||
\(445\) | 4.15734 | 0.197077 | ||||||||
\(446\) | −8.13829 | + | 4.69865i | −0.385359 | + | 0.222487i | ||||
\(447\) | −13.4247 | + | 23.2522i | −0.634965 | + | 1.09979i | ||||
\(448\) | 0.461662 | − | 0.799622i | 0.0218115 | − | 0.0377786i | ||||
\(449\) | 12.2385 | + | 7.06587i | 0.577568 | + | 0.333459i | 0.760166 | − | 0.649728i | \(-0.225117\pi\) |
−0.182598 | + | 0.983188i | \(0.558451\pi\) | |||||||
\(450\) | − | 1.19656i | − | 0.0564063i | ||||||
\(451\) | 3.85142 | − | 6.67086i | 0.181356 | − | 0.314119i | ||||
\(452\) | 5.01802i | 0.236028i | ||||||||
\(453\) | −9.60269 | − | 16.6323i | −0.451174 | − | 0.781456i | ||||
\(454\) | 4.99853 | 0.234593 | ||||||||
\(455\) | −1.77585 | −0.0832532 | ||||||||
\(456\) | 4.87842 | + | 8.44966i | 0.228453 | + | 0.395692i | ||||
\(457\) | −25.4320 | − | 14.6832i | −1.18966 | − | 0.686851i | −0.231431 | − | 0.972851i | \(-0.574341\pi\) |
−0.958229 | + | 0.286000i | \(0.907674\pi\) | |||||||
\(458\) | − | 26.4846i | − | 1.23754i | ||||||
\(459\) | 10.0309 | − | 5.79135i | 0.468203 | − | 0.270317i | ||||
\(460\) | −4.11023 | − | 7.11913i | −0.191641 | − | 0.331931i | ||||
\(461\) | −25.1231 | + | 14.5048i | −1.17010 | + | 0.675558i | −0.953704 | − | 0.300747i | \(-0.902764\pi\) |
−0.216397 | + | 0.976305i | \(0.569431\pi\) | |||||||
\(462\) | −2.75541 | − | 1.59084i | −0.128193 | − | 0.0740125i | ||||
\(463\) | 28.0943 | + | 16.2203i | 1.30566 | + | 0.753820i | 0.981368 | − | 0.192138i | \(-0.0615422\pi\) |
0.324287 | + | 0.945959i | \(0.394876\pi\) | |||||||
\(464\) | −4.98556 | + | 2.87842i | −0.231449 | + | 0.133627i | ||||
\(465\) | −7.07433 | − | 12.2531i | −0.328064 | − | 0.568224i | ||||
\(466\) | 17.3047 | − | 9.99090i | 0.801627 | − | 0.462819i | ||||
\(467\) | − | 0.495692i | − | 0.0229379i | −0.999934 | − | 0.0114689i | \(-0.996349\pi\) | ||
0.999934 | − | 0.0114689i | \(-0.00365076\pi\) | |||||||
\(468\) | −1.99304 | − | 1.15068i | −0.0921285 | − | 0.0531904i | ||||
\(469\) | 1.53460 | + | 2.65801i | 0.0708613 | + | 0.122735i | ||||
\(470\) | −10.5209 | −0.485291 | ||||||||
\(471\) | 12.2060 | 0.562423 | ||||||||
\(472\) | −2.12860 | − | 3.68685i | −0.0979769 | − | 0.169701i | ||||
\(473\) | − | 17.8358i | − | 0.820091i | ||||||
\(474\) | 9.36274 | − | 16.2167i | 0.430045 | − | 0.744860i | ||||
\(475\) | − | 7.26537i | − | 0.333358i | ||||||
\(476\) | −1.64343 | − | 0.948832i | −0.0753263 | − | 0.0434897i | ||||
\(477\) | −3.13193 | + | 5.42466i | −0.143401 | + | 0.248378i | ||||
\(478\) | 3.96815 | − | 6.87303i | 0.181499 | − | 0.314365i | ||||
\(479\) | 25.6937 | − | 14.8343i | 1.17398 | − | 0.677795i | 0.219363 | − | 0.975643i | \(-0.429602\pi\) |
0.954613 | + | 0.297848i | \(0.0962688\pi\) | |||||||
\(480\) | 1.34292 | 0.0612958 | ||||||||
\(481\) | 2.13940 | + | 11.5018i | 0.0975483 | + | 0.524439i | ||||
\(482\) | −7.38995 | −0.336603 | ||||||||
\(483\) | 8.82739 | − | 5.09649i | 0.401660 | − | 0.231899i | ||||
\(484\) | −2.20791 | + | 3.82422i | −0.100360 | + | 0.173828i | ||||
\(485\) | −4.96167 | + | 8.59386i | −0.225298 | + | 0.390227i | ||||
\(486\) | 10.0148 | + | 5.78202i | 0.454278 | + | 0.262278i | ||||
\(487\) | − | 34.7629i | − | 1.57526i | −0.616151 | − | 0.787628i | \(-0.711309\pi\) | ||
0.616151 | − | 0.787628i | \(-0.288691\pi\) | |||||||
\(488\) | −2.01691 | + | 3.49339i | −0.0913013 | + | 0.158139i | ||||
\(489\) | − | 11.1812i | − | 0.505631i | ||||||
\(490\) | 3.07374 | + | 5.32387i | 0.138857 | + | 0.240508i | ||||
\(491\) | −33.6299 | −1.51770 | −0.758848 | − | 0.651268i | \(-0.774237\pi\) | ||||
−0.758848 | + | 0.651268i | \(0.774237\pi\) | |||||||
\(492\) | −4.03136 | −0.181748 | ||||||||
\(493\) | 5.91587 | + | 10.2466i | 0.266438 | + | 0.461483i | ||||
\(494\) | −12.1015 | − | 6.98683i | −0.544474 | − | 0.314352i | ||||
\(495\) | 3.07032i | 0.138001i | ||||||||
\(496\) | −9.12420 | + | 5.26786i | −0.409689 | + | 0.236534i | ||||
\(497\) | −7.26360 | − | 12.5809i | −0.325817 | − | 0.564331i | ||||
\(498\) | 6.66165 | − | 3.84610i | 0.298516 | − | 0.172348i | ||||
\(499\) | −5.78065 | − | 3.33746i | −0.258777 | − | 0.149405i | 0.364999 | − | 0.931008i | \(-0.381069\pi\) |
−0.623777 | + | 0.781603i | \(0.714403\pi\) | |||||||
\(500\) | −0.866025 | − | 0.500000i | −0.0387298 | − | 0.0223607i | ||||
\(501\) | −8.67683 | + | 5.00957i | −0.387652 | + | 0.223811i | ||||
\(502\) | 7.58231 | + | 13.1329i | 0.338415 | + | 0.586152i | ||||
\(503\) | −30.6980 | + | 17.7235i | −1.36876 | + | 0.790252i | −0.990769 | − | 0.135559i | \(-0.956717\pi\) |
−0.377987 | + | 0.925811i | \(0.623384\pi\) | |||||||
\(504\) | − | 1.10481i | − | 0.0492122i | ||||||
\(505\) | −14.2761 | − | 8.24230i | −0.635277 | − | 0.366778i | ||||
\(506\) | 10.5467 | + | 18.2674i | 0.468858 | + | 0.812086i | ||||
\(507\) | 12.4903 | 0.554713 | ||||||||
\(508\) | −5.71707 | −0.253654 | ||||||||
\(509\) | −17.0193 | − | 29.4782i | −0.754366 | − | 1.30660i | −0.945689 | − | 0.325073i | \(-0.894611\pi\) |
0.191323 | − | 0.981527i | \(-0.438722\pi\) | |||||||
\(510\) | − | 2.76005i | − | 0.122217i | ||||||
\(511\) | −3.27081 | + | 5.66520i | −0.144692 | + | 0.250614i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 35.4595 | + | 20.4726i | 1.56558 | + | 0.903885i | ||||
\(514\) | 3.10992 | − | 5.38654i | 0.137173 | − | 0.237590i | ||||
\(515\) | 2.97344 | − | 5.15014i | 0.131025 | − | 0.226942i | ||||
\(516\) | −8.08395 | + | 4.66727i | −0.355876 | + | 0.205465i | ||||
\(517\) | 26.9962 | 1.18729 | ||||||||
\(518\) | −4.26837 | + | 3.65028i | −0.187541 | + | 0.160384i | ||||
\(519\) | 4.74616 | 0.208333 | ||||||||
\(520\) | −1.66565 | + | 0.961662i | −0.0730435 | + | 0.0421717i | ||||
\(521\) | 5.22902 | − | 9.05693i | 0.229087 | − | 0.396791i | −0.728450 | − | 0.685099i | \(-0.759759\pi\) |
0.957538 | + | 0.288307i | \(0.0930925\pi\) | |||||||
\(522\) | −3.44419 | + | 5.96551i | −0.150748 | + | 0.261103i | ||||
\(523\) | −8.39138 | − | 4.84477i | −0.366929 | − | 0.211847i | 0.305187 | − | 0.952293i | \(-0.401281\pi\) |
−0.672116 | + | 0.740446i | \(0.734614\pi\) | |||||||
\(524\) | 5.87872i | 0.256813i | ||||||||
\(525\) | 0.619977 | − | 1.07383i | 0.0270580 | − | 0.0468658i | ||||
\(526\) | 27.8693i | 1.21516i | ||||||||
\(527\) | 10.8268 | + | 18.7525i | 0.471622 | + | 0.816874i | ||||
\(528\) | −3.44589 | −0.149963 | ||||||||
\(529\) | −44.5760 | −1.93809 | ||||||||
\(530\) | 2.61745 | + | 4.53356i | 0.113695 | + | 0.196925i | ||||
\(531\) | −4.41153 | − | 2.54700i | −0.191444 | − | 0.110530i | ||||
\(532\) | − | 6.70829i | − | 0.290841i | ||||||
\(533\) | 5.00016 | − | 2.88684i | 0.216581 | − | 0.125043i | ||||
\(534\) | 2.79149 | + | 4.83501i | 0.120800 | + | 0.209231i | ||||
\(535\) | −3.23550 | + | 1.86802i | −0.139883 | + | 0.0807615i | ||||
\(536\) | 2.87874 | + | 1.66204i | 0.124343 | + | 0.0717892i | ||||
\(537\) | 19.7902 | + | 11.4259i | 0.854011 | + | 0.493063i | ||||
\(538\) | 9.42333 | − | 5.44056i | 0.406268 | − | 0.234559i | ||||
\(539\) | −7.88710 | − | 13.6609i | −0.339721 | − | 0.588415i | ||||
\(540\) | 4.88062 | − | 2.81783i | 0.210028 | − | 0.121260i | ||||
\(541\) | 9.38662i | 0.403562i | 0.979431 | + | 0.201781i | \(0.0646730\pi\) | ||||
−0.979431 | + | 0.201781i | \(0.935327\pi\) | |||||||
\(542\) | −20.7986 | − | 12.0081i | −0.893377 | − | 0.515791i | ||||
\(543\) | 5.55602 | + | 9.62331i | 0.238432 | + | 0.412976i | ||||
\(544\) | −2.05525 | −0.0881182 | ||||||||
\(545\) | 5.80721 | 0.248753 | ||||||||
\(546\) | −1.19242 | − | 2.06533i | −0.0510307 | − | 0.0883878i | ||||
\(547\) | − | 24.0289i | − | 1.02740i | −0.857970 | − | 0.513700i | \(-0.828274\pi\) | ||
0.857970 | − | 0.513700i | \(-0.171726\pi\) | |||||||
\(548\) | −5.20061 | + | 9.00772i | −0.222159 | + | 0.384791i | ||||
\(549\) | 4.82670i | 0.205999i | ||||||||
\(550\) | 2.22219 | + | 1.28298i | 0.0947545 | + | 0.0547065i | ||||
\(551\) | −20.9128 | + | 36.2220i | −0.890913 | + | 1.54311i | ||||
\(552\) | 5.51972 | − | 9.56044i | 0.234935 | − | 0.406919i | ||||
\(553\) | −11.1498 | + | 6.43734i | −0.474137 | + | 0.273743i | ||||
\(554\) | −5.25256 | −0.223160 | ||||||||
\(555\) | −7.70189 | − | 2.72180i | −0.326927 | − | 0.115534i | ||||
\(556\) | 14.6401 | 0.620877 | ||||||||
\(557\) | 15.7183 | − | 9.07495i | 0.666005 | − | 0.384518i | −0.128556 | − | 0.991702i | \(-0.541034\pi\) |
0.794561 | + | 0.607184i | \(0.207701\pi\) | |||||||
\(558\) | −6.30330 | + | 10.9176i | −0.266840 | + | 0.462180i | ||||
\(559\) | 6.68443 | − | 11.5778i | 0.282721 | − | 0.489688i | ||||
\(560\) | −0.799622 | − | 0.461662i | −0.0337902 | − | 0.0195088i | ||||
\(561\) | 7.08218i | 0.299010i | ||||||||
\(562\) | −9.66850 | + | 16.7463i | −0.407841 | + | 0.706401i | ||||
\(563\) | − | 19.4195i | − | 0.818436i | −0.912437 | − | 0.409218i | \(-0.865802\pi\) | ||
0.912437 | − | 0.409218i | \(-0.134198\pi\) | |||||||
\(564\) | −7.06436 | − | 12.2358i | −0.297463 | − | 0.515221i | ||||
\(565\) | 5.01802 | 0.211110 | ||||||||
\(566\) | 1.01940 | 0.0428486 | ||||||||
\(567\) | 1.83676 | + | 3.18136i | 0.0771366 | + | 0.133605i | ||||
\(568\) | −13.6257 | − | 7.86679i | −0.571721 | − | 0.330083i | ||||
\(569\) | 10.1824i | 0.426867i | 0.976958 | + | 0.213433i | \(0.0684646\pi\) | ||||
−0.976958 | + | 0.213433i | \(0.931535\pi\) | |||||||
\(570\) | 8.44966 | − | 4.87842i | 0.353918 | − | 0.204334i | ||||
\(571\) | −7.42714 | − | 12.8642i | −0.310816 | − | 0.538349i | 0.667723 | − | 0.744410i | \(-0.267269\pi\) |
−0.978539 | + | 0.206060i | \(0.933936\pi\) | |||||||
\(572\) | 4.27399 | − | 2.46759i | 0.178705 | − | 0.103175i | ||||
\(573\) | −10.9436 | − | 6.31829i | −0.457175 | − | 0.263950i | ||||
\(574\) | 2.40041 | + | 1.38588i | 0.100191 | + | 0.0578454i | ||||
\(575\) | −7.11913 | + | 4.11023i | −0.296888 | + | 0.171408i | ||||
\(576\) | −0.598279 | − | 1.03625i | −0.0249283 | − | 0.0431771i | ||||
\(577\) | −38.8951 | + | 22.4561i | −1.61922 | + | 0.934859i | −0.632102 | + | 0.774885i | \(0.717808\pi\) |
−0.987121 | + | 0.159974i | \(0.948859\pi\) | |||||||
\(578\) | − | 12.7759i | − | 0.531409i | ||||||
\(579\) | 16.7873 | + | 9.69214i | 0.697656 | + | 0.402792i | ||||
\(580\) | 2.87842 | + | 4.98556i | 0.119520 | + | 0.207014i | ||||
\(581\) | −5.28876 | −0.219415 | ||||||||
\(582\) | −13.3263 | −0.552392 | ||||||||
\(583\) | −6.71628 | − | 11.6329i | −0.278160 | − | 0.481787i | ||||
\(584\) | 7.08485i | 0.293173i | ||||||||
\(585\) | −1.15068 | + | 1.99304i | −0.0475749 | + | 0.0824022i | ||||
\(586\) | − | 12.8878i | − | 0.532390i | ||||||
\(587\) | −4.80132 | − | 2.77204i | −0.198172 | − | 0.114415i | 0.397631 | − | 0.917546i | \(-0.369833\pi\) |
−0.595802 | + | 0.803131i | \(0.703166\pi\) | |||||||
\(588\) | −4.12779 | + | 7.14954i | −0.170227 | + | 0.294842i | ||||
\(589\) | −38.2730 | + | 66.2907i | −1.57701 | + | 2.73146i | ||||
\(590\) | −3.68685 | + | 2.12860i | −0.151785 | + | 0.0876332i | ||||
\(591\) | −0.943274 | −0.0388011 | ||||||||
\(592\) | −2.02678 | + | 5.73517i | −0.0833000 | + | 0.235714i | ||||
\(593\) | 4.98431 | 0.204681 | 0.102340 | − | 0.994749i | \(-0.467367\pi\) | ||||
0.102340 | + | 0.994749i | \(0.467367\pi\) | |||||||
\(594\) | −12.5235 | + | 7.23044i | −0.513845 | + | 0.296669i | ||||
\(595\) | −0.948832 | + | 1.64343i | −0.0388983 | + | 0.0673739i | ||||
\(596\) | 9.99660 | − | 17.3146i | 0.409477 | − | 0.709234i | ||||
\(597\) | 16.7441 | + | 9.66720i | 0.685289 | + | 0.395652i | ||||
\(598\) | 15.8106i | 0.646544i | ||||||||
\(599\) | 21.9749 | − | 38.0617i | 0.897870 | − | 1.55516i | 0.0676592 | − | 0.997708i | \(-0.478447\pi\) |
0.830211 | − | 0.557449i | \(-0.188220\pi\) | |||||||
\(600\) | − | 1.34292i | − | 0.0548246i | ||||||
\(601\) | 23.2651 | + | 40.2964i | 0.949005 | + | 1.64372i | 0.747527 | + | 0.664231i | \(0.231241\pi\) |
0.201477 | + | 0.979493i | \(0.435426\pi\) | |||||||
\(602\) | 6.41795 | 0.261576 | ||||||||
\(603\) | 3.97745 | 0.161974 | ||||||||
\(604\) | 7.15059 | + | 12.3852i | 0.290953 | + | 0.503946i | ||||
\(605\) | 3.82422 | + | 2.20791i | 0.155477 | + | 0.0897644i | ||||
\(606\) | − | 22.1376i | − | 0.899277i | ||||||
\(607\) | 26.3275 | − | 15.2002i | 1.06860 | − | 0.616957i | 0.140803 | − | 0.990038i | \(-0.455032\pi\) |
0.927799 | + | 0.373080i | \(0.121698\pi\) | |||||||
\(608\) | −3.63268 | − | 6.29199i | −0.147325 | − | 0.255174i | ||||
\(609\) | −6.18187 | + | 3.56910i | −0.250502 | + | 0.144627i | ||||
\(610\) | 3.49339 | + | 2.01691i | 0.141443 | + | 0.0816624i | ||||
\(611\) | 17.5241 | + | 10.1175i | 0.708947 | + | 0.409311i | ||||
\(612\) | −2.12975 | + | 1.22961i | −0.0860902 | + | 0.0497042i | ||||
\(613\) | 14.1066 | + | 24.4333i | 0.569759 | + | 0.986852i | 0.996589 | + | 0.0825200i | \(0.0262968\pi\) |
−0.426830 | + | 0.904332i | \(0.640370\pi\) | |||||||
\(614\) | 21.0692 | − | 12.1643i | 0.850285 | − | 0.490913i | ||||
\(615\) | 4.03136i | 0.162560i | ||||||||
\(616\) | 2.05180 | + | 1.18461i | 0.0826695 | + | 0.0477292i | ||||
\(617\) | 11.8816 | + | 20.5796i | 0.478336 | + | 0.828503i | 0.999692 | − | 0.0248368i | \(-0.00790662\pi\) |
−0.521355 | + | 0.853340i | \(0.674573\pi\) | |||||||
\(618\) | 7.98619 | 0.321252 | ||||||||
\(619\) | 2.84179 | 0.114221 | 0.0571106 | − | 0.998368i | \(-0.481811\pi\) | ||||
0.0571106 | + | 0.998368i | \(0.481811\pi\) | |||||||
\(620\) | 5.26786 | + | 9.12420i | 0.211562 | + | 0.366437i | ||||
\(621\) | − | 46.3277i | − | 1.85907i | ||||||
\(622\) | 3.16457 | − | 5.48120i | 0.126888 | − | 0.219776i | ||||
\(623\) | − | 3.83857i | − | 0.153789i | ||||||
\(624\) | −2.23684 | − | 1.29144i | −0.0895451 | − | 0.0516989i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −6.19774 | + | 10.7348i | −0.247711 | + | 0.429049i | ||||
\(627\) | −21.6815 | + | 12.5178i | −0.865877 | + | 0.499914i | ||||
\(628\) | −9.08913 | −0.362696 | ||||||||
\(629\) | 11.7872 | + | 4.16554i | 0.469987 | + | 0.166091i | ||||
\(630\) | −1.10481 | −0.0440167 | ||||||||
\(631\) | −0.988858 | + | 0.570917i | −0.0393658 | + | 0.0227279i | −0.519554 | − | 0.854438i | \(-0.673902\pi\) |
0.480188 | + | 0.877166i | \(0.340568\pi\) | |||||||
\(632\) | −6.97191 | + | 12.0757i | −0.277328 | + | 0.480346i | ||||
\(633\) | 7.78148 | − | 13.4779i | 0.309286 | − | 0.535699i | ||||
\(634\) | −26.8379 | − | 15.4949i | −1.06587 | − | 0.615381i | ||||
\(635\) | 5.71707i | 0.226875i | ||||||||
\(636\) | −3.51503 | + | 6.08822i | −0.139380 | + | 0.241413i | ||||
\(637\) | − | 11.8236i | − | 0.468467i | ||||||
\(638\) | −7.38591 | − | 12.7928i | −0.292411 | − | 0.506471i | ||||
\(639\) | −18.8261 | −0.744750 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −19.8079 | − | 34.3082i | −0.782364 | − | 1.35509i | −0.930561 | − | 0.366136i | \(-0.880681\pi\) |
0.148198 | − | 0.988958i | \(-0.452653\pi\) | |||||||
\(642\) | −4.34503 | − | 2.50861i | −0.171485 | − | 0.0990068i | ||||
\(643\) | − | 27.6189i | − | 1.08918i | −0.838702 | − | 0.544591i | \(-0.816685\pi\) | ||
0.838702 | − | 0.544591i | \(-0.183315\pi\) | |||||||
\(644\) | −6.57326 | + | 3.79508i | −0.259023 | + | 0.149547i | ||||
\(645\) | 4.66727 | + | 8.08395i | 0.183774 | + | 0.318305i | ||||
\(646\) | −12.9316 | + | 7.46609i | −0.508789 | + | 0.293749i | ||||
\(647\) | −29.5607 | − | 17.0669i | −1.16215 | − | 0.670969i | −0.210333 | − | 0.977630i | \(-0.567455\pi\) |
−0.951819 | + | 0.306661i | \(0.900788\pi\) | |||||||
\(648\) | 3.44555 | + | 1.98929i | 0.135354 | + | 0.0781466i | ||||
\(649\) | 9.46032 | − | 5.46192i | 0.371350 | − | 0.214399i | ||||
\(650\) | 0.961662 | + | 1.66565i | 0.0377195 | + | 0.0653321i | ||||
\(651\) | −11.3136 | + | 6.53190i | −0.443414 | + | 0.256005i | ||||
\(652\) | 8.32601i | 0.326072i | ||||||||
\(653\) | −2.94777 | − | 1.70190i | −0.115355 | − | 0.0666004i | 0.441212 | − | 0.897403i | \(-0.354549\pi\) |
−0.556568 | + | 0.830802i | \(0.687882\pi\) | |||||||
\(654\) | 3.89932 | + | 6.75381i | 0.152475 | + | 0.264095i | ||||
\(655\) | 5.87872 | 0.229700 | ||||||||
\(656\) | 3.00193 | 0.117206 | ||||||||
\(657\) | 4.23871 | + | 7.34167i | 0.165368 | + | 0.286426i | ||||
\(658\) | 9.71417i | 0.378698i | ||||||||
\(659\) | 18.4772 | − | 32.0035i | 0.719771 | − | 1.24668i | −0.241319 | − | 0.970446i | \(-0.577580\pi\) |
0.961090 | − | 0.276235i | \(-0.0890867\pi\) | |||||||
\(660\) | 3.44589i | 0.134131i | ||||||||
\(661\) | −5.34346 | − | 3.08505i | −0.207836 | − | 0.119994i | 0.392469 | − | 0.919765i | \(-0.371621\pi\) |
−0.600305 | + | 0.799771i | \(0.704954\pi\) | |||||||
\(662\) | −1.62606 | + | 2.81641i | −0.0631985 | + | 0.109463i | ||||
\(663\) | −2.65423 | + | 4.59727i | −0.103082 | + | 0.178543i | ||||
\(664\) | −4.96056 | + | 2.86398i | −0.192507 | + | 0.111144i | ||||
\(665\) | −6.70829 | −0.260136 | ||||||||
\(666\) | 1.33099 | + | 7.15564i | 0.0515747 | + | 0.277276i | ||||
\(667\) | 47.3238 | 1.83239 | ||||||||
\(668\) | 6.46115 | − | 3.73035i | 0.249990 | − | 0.144332i | ||||
\(669\) | −6.30992 | + | 10.9291i | −0.243956 | + | 0.422544i | ||||
\(670\) | 1.66204 | − | 2.87874i | 0.0642102 | − | 0.111215i | ||||
\(671\) | −8.96393 | − | 5.17532i | −0.346048 | − | 0.199791i | ||||
\(672\) | − | 1.23995i | − | 0.0478322i | ||||||
\(673\) | 9.15112 | − | 15.8502i | 0.352750 | − | 0.610980i | −0.633981 | − | 0.773349i | \(-0.718580\pi\) |
0.986730 | + | 0.162369i | \(0.0519134\pi\) | |||||||
\(674\) | − | 30.4860i | − | 1.17428i | ||||||
\(675\) | −2.81783 | − | 4.88062i | −0.108458 | − | 0.187855i | ||||
\(676\) | −9.30082 | −0.357724 | ||||||||
\(677\) | −12.6160 | −0.484874 | −0.242437 | − | 0.970167i | \(-0.577947\pi\) | ||||
−0.242437 | + | 0.970167i | \(0.577947\pi\) | |||||||
\(678\) | 3.36941 | + | 5.83598i | 0.129401 | + | 0.224130i | ||||
\(679\) | 7.93492 | + | 4.58123i | 0.304514 | + | 0.175811i | ||||
\(680\) | 2.05525i | 0.0788154i | ||||||||
\(681\) | 5.81331 | − | 3.35632i | 0.222767 | − | 0.128614i | ||||
\(682\) | −13.5171 | − | 23.4124i | −0.517598 | − | 0.896506i | ||||
\(683\) | −14.5068 | + | 8.37553i | −0.555089 | + | 0.320481i | −0.751172 | − | 0.660107i | \(-0.770511\pi\) |
0.196083 | + | 0.980587i | \(0.437178\pi\) | |||||||
\(684\) | −7.52873 | − | 4.34672i | −0.287868 | − | 0.166201i | ||||
\(685\) | 9.00772 | + | 5.20061i | 0.344167 | + | 0.198705i | ||||
\(686\) | 10.5130 | − | 6.06969i | 0.401389 | − | 0.231742i | ||||
\(687\) | −17.7834 | − | 30.8017i | −0.678479 | − | 1.17516i | ||||
\(688\) | 6.01967 | − | 3.47546i | 0.229498 | − | 0.132501i | ||||
\(689\) | − | 10.0684i | − | 0.383576i | ||||||
\(690\) | −9.56044 | − | 5.51972i | −0.363960 | − | 0.210132i | ||||
\(691\) | −8.24768 | − | 14.2854i | −0.313756 | − | 0.543442i | 0.665416 | − | 0.746473i | \(-0.268254\pi\) |
−0.979172 | + | 0.203031i | \(0.934921\pi\) | |||||||
\(692\) | −3.53420 | −0.134350 | ||||||||
\(693\) | 2.83490 | 0.107689 | ||||||||
\(694\) | −7.91385 | − | 13.7072i | −0.300406 | − | 0.520318i | ||||
\(695\) | − | 14.6401i | − | 0.555329i | ||||||
\(696\) | −3.86549 | + | 6.69523i | −0.146521 | + | 0.253782i | ||||
\(697\) | − | 6.16973i | − | 0.233695i | ||||||
\(698\) | 2.63159 | + | 1.51935i | 0.0996071 | + | 0.0575082i | ||||
\(699\) | 13.4170 | − | 23.2389i | 0.507478 | − | 0.878977i | ||||
\(700\) | −0.461662 | + | 0.799622i | −0.0174492 | + | 0.0302229i | ||||
\(701\) | −8.87777 | + | 5.12559i | −0.335309 | + | 0.193591i | −0.658196 | − | 0.752847i | \(-0.728680\pi\) |
0.322887 | + | 0.946438i | \(0.395347\pi\) | |||||||
\(702\) | −10.8392 | −0.409099 | ||||||||
\(703\) | 8.08161 | + | 43.4483i | 0.304804 | + | 1.63868i | ||||
\(704\) | 2.56596 | 0.0967084 | ||||||||
\(705\) | −12.2358 | + | 7.06436i | −0.460828 | + | 0.266059i | ||||
\(706\) | −11.0408 | + | 19.1232i | −0.415525 | + | 0.719711i | ||||
\(707\) | −7.61032 | + | 13.1815i | −0.286215 | + | 0.495740i | ||||
\(708\) | −4.95115 | − | 2.85855i | −0.186076 | − | 0.107431i | ||||
\(709\) | 49.6789i | 1.86573i | 0.360225 | + | 0.932865i | \(0.382700\pi\) | ||||
−0.360225 | + | 0.932865i | \(0.617300\pi\) | |||||||
\(710\) | −7.86679 | + | 13.6257i | −0.295235 | + | 0.511363i | ||||
\(711\) | 16.6846i | 0.625721i | ||||||||
\(712\) | −2.07867 | − | 3.60036i | −0.0779014 | − | 0.134929i | ||||
\(713\) | 86.6085 | 3.24351 | ||||||||
\(714\) | −2.54842 | −0.0953721 | ||||||||
\(715\) | −2.46759 | − | 4.27399i | −0.0922827 | − | 0.159838i | ||||
\(716\) | −14.7367 | − | 8.50822i | −0.550735 | − | 0.317967i | ||||
\(717\) | − | 10.6578i | − | 0.398024i | ||||||
\(718\) | 9.09833 | − | 5.25292i | 0.339547 | − | 0.196037i | ||||
\(719\) | 4.45385 | + | 7.71430i | 0.166101 | + | 0.287695i | 0.937046 | − | 0.349207i | \(-0.113549\pi\) |
−0.770945 | + | 0.636902i | \(0.780216\pi\) | |||||||
\(720\) | −1.03625 | + | 0.598279i | −0.0386187 | + | 0.0222965i | ||||
\(721\) | −4.75525 | − | 2.74545i | −0.177095 | − | 0.102246i | ||||
\(722\) | −29.2592 | − | 16.8928i | −1.08891 | − | 0.628685i | ||||
\(723\) | −8.59456 | + | 4.96207i | −0.319635 | + | 0.184541i | ||||
\(724\) | −4.13726 | − | 7.16595i | −0.153760 | − | 0.266320i | ||||
\(725\) | 4.98556 | − | 2.87842i | 0.185159 | − | 0.106902i | ||||
\(726\) | 5.93012i | 0.220087i | ||||||||
\(727\) | 33.3490 | + | 19.2541i | 1.23685 | + | 0.714094i | 0.968448 | − | 0.249214i | \(-0.0801722\pi\) |
0.268399 | + | 0.963308i | \(0.413506\pi\) | |||||||
\(728\) | 0.887926 | + | 1.53793i | 0.0329087 | + | 0.0569996i | ||||
\(729\) | 27.4653 | 1.01724 | ||||||||
\(730\) | 7.08485 | 0.262222 | ||||||||
\(731\) | −7.14294 | − | 12.3719i | −0.264191 | − | 0.457593i | ||||
\(732\) | 5.41712i | 0.200222i | ||||||||
\(733\) | −5.24691 | + | 9.08791i | −0.193799 | + | 0.335670i | −0.946506 | − | 0.322686i | \(-0.895414\pi\) |
0.752707 | + | 0.658356i | \(0.228748\pi\) | |||||||
\(734\) | 12.3206i | 0.454763i | ||||||||
\(735\) | 7.14954 | + | 4.12779i | 0.263715 | + | 0.152256i | ||||
\(736\) | −4.11023 | + | 7.11913i | −0.151505 | + | 0.262415i | ||||
\(737\) | −4.26474 | + | 7.38674i | −0.157094 | + | 0.272094i | ||||
\(738\) | 3.11075 | − | 1.79599i | 0.114508 | − | 0.0661114i | ||||
\(739\) | 0.0900634 | 0.00331304 | 0.00165652 | − | 0.999999i | \(-0.499473\pi\) | ||||
0.00165652 | + | 0.999999i | \(0.499473\pi\) | |||||||
\(740\) | 5.73517 | + | 2.02678i | 0.210829 | + | 0.0745057i | ||||
\(741\) | −18.7656 | −0.689370 | ||||||||
\(742\) | 4.18594 | − | 2.41675i | 0.153671 | − | 0.0887218i | ||||
\(743\) | 14.8898 | − | 25.7899i | 0.546255 | − | 0.946141i | −0.452272 | − | 0.891880i | \(-0.649386\pi\) |
0.998527 | − | 0.0542607i | \(-0.0172802\pi\) | |||||||
\(744\) | −7.07433 | + | 12.2531i | −0.259358 | + | 0.449221i | ||||
\(745\) | −17.3146 | − | 9.99660i | −0.634358 | − | 0.366247i | ||||
\(746\) | − | 26.4143i | − | 0.967097i | ||||||
\(747\) | −3.42692 | + | 5.93559i | −0.125384 | + | 0.217172i | ||||
\(748\) | − | 5.27371i | − | 0.192826i | ||||||
\(749\) | 1.72479 | + | 2.98742i | 0.0630224 | + | 0.109158i | ||||
\(750\) | −1.34292 | −0.0490366 | ||||||||
\(751\) | 45.3962 | 1.65653 | 0.828266 | − | 0.560335i | \(-0.189328\pi\) | ||||
0.828266 | + | 0.560335i | \(0.189328\pi\) | |||||||
\(752\) | 5.26043 | + | 9.11134i | 0.191828 | + | 0.332256i | ||||
\(753\) | 17.6365 | + | 10.1825i | 0.642711 | + | 0.371069i | ||||
\(754\) | − | 11.0723i | − | 0.403228i | ||||||
\(755\) | 12.3852 | − | 7.15059i | 0.450743 | − | 0.260237i | ||||
\(756\) | −2.60177 | − | 4.50639i | −0.0946254 | − | 0.163896i | ||||
\(757\) | 9.16026 | − | 5.28868i | 0.332935 | − | 0.192220i | −0.324208 | − | 0.945986i | \(-0.605098\pi\) |
0.657144 | + | 0.753765i | \(0.271765\pi\) | |||||||
\(758\) | −2.46028 | − | 1.42044i | −0.0893612 | − | 0.0515927i | ||||
\(759\) | 24.5318 | + | 14.1634i | 0.890446 | + | 0.514099i | ||||
\(760\) | −6.29199 | + | 3.63268i | −0.228235 | + | 0.131771i | ||||
\(761\) | −16.0028 | − | 27.7176i | −0.580100 | − | 1.00476i | −0.995467 | − | 0.0951083i | \(-0.969680\pi\) |
0.415367 | − | 0.909654i | \(-0.363653\pi\) | |||||||
\(762\) | −6.64898 | + | 3.83879i | −0.240867 | + | 0.139065i | ||||
\(763\) | − | 5.36193i | − | 0.194115i | ||||||
\(764\) | 8.14908 | + | 4.70488i | 0.294823 | + | 0.170216i | ||||
\(765\) | 1.22961 | + | 2.12975i | 0.0444568 | + | 0.0770014i | ||||
\(766\) | 22.0781 | 0.797716 | ||||||||
\(767\) | 8.18799 | 0.295651 | ||||||||
\(768\) | −0.671462 | − | 1.16301i | −0.0242293 | − | 0.0419663i | ||||
\(769\) | − | 18.6714i | − | 0.673309i | −0.941628 | − | 0.336655i | \(-0.890704\pi\) | ||
0.941628 | − | 0.336655i | \(-0.109296\pi\) | |||||||
\(770\) | 1.18461 | − | 2.05180i | 0.0426903 | − | 0.0739418i | ||||
\(771\) | − | 8.35277i | − | 0.300818i | ||||||
\(772\) | −12.5006 | − | 7.21720i | −0.449905 | − | 0.259753i | ||||
\(773\) | −4.24530 | + | 7.35307i | −0.152693 | + | 0.264471i | −0.932216 | − | 0.361901i | \(-0.882128\pi\) |
0.779524 | + | 0.626373i | \(0.215461\pi\) | |||||||
\(774\) | 4.15858 | − | 7.20288i | 0.149477 | − | 0.258902i | ||||
\(775\) | 9.12420 | − | 5.26786i | 0.327751 | − | 0.189227i | ||||
\(776\) | 9.92333 | 0.356227 | ||||||||
\(777\) | −2.51311 | + | 7.11134i | −0.0901572 | + | 0.255118i | ||||
\(778\) | 3.06920 | 0.110036 | ||||||||
\(779\) | 18.8881 | − | 10.9051i | 0.676738 | − | 0.390715i | ||||
\(780\) | −1.29144 | + | 2.23684i | −0.0462409 | + | 0.0800916i | ||||
\(781\) | 20.1859 | − | 34.9630i | 0.722308 | − | 1.25107i | ||||
\(782\) | 14.6316 | + | 8.44756i | 0.523225 | + | 0.302084i | ||||
\(783\) | 32.4435i | 1.15944i | ||||||||
\(784\) | 3.07374 | − | 5.32387i | 0.109776 | − | 0.190138i | ||||
\(785\) | 9.08913i | 0.324405i | ||||||||
\(786\) | 3.94733 | + | 6.83698i | 0.140797 | + | 0.243867i | ||||
\(787\) | 11.6067 | 0.413733 | 0.206867 | − | 0.978369i | \(-0.433673\pi\) | ||||
0.206867 | + | 0.978369i | \(0.433673\pi\) | |||||||
\(788\) | 0.702404 | 0.0250221 | ||||||||
\(789\) | 18.7132 | + | 32.4122i | 0.666206 | + | 1.15390i | ||||
\(790\) | 12.0757 | + | 6.97191i | 0.429634 | + | 0.248050i | ||||
\(791\) | − | 4.63326i | − | 0.164740i | ||||||
\(792\) | 2.65898 | − | 1.53516i | 0.0944827 | − | 0.0545496i | ||||
\(793\) | −3.87918 | − | 6.71893i | −0.137754 | − | 0.238596i | ||||
\(794\) | −27.0806 | + | 15.6350i | −0.961055 | + | 0.554865i | ||||
\(795\) | 6.08822 | + | 3.51503i | 0.215927 | + | 0.124665i | ||||
\(796\) | −12.4684 | − | 7.19862i | −0.441930 | − | 0.255148i | ||||
\(797\) | −32.7557 | + | 18.9115i | −1.16027 | + | 0.669880i | −0.951368 | − | 0.308057i | \(-0.900321\pi\) |
−0.208899 | + | 0.977937i | \(0.566988\pi\) | |||||||
\(798\) | −4.50436 | − | 7.80178i | −0.159453 | − | 0.276180i | ||||
\(799\) | 18.7261 | − | 10.8115i | 0.662482 | − | 0.382484i | ||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | −4.30804 | − | 2.48725i | −0.152217 | − | 0.0878826i | ||||
\(802\) | −1.58916 | − | 2.75250i | −0.0561151 | − | 0.0971942i | ||||
\(803\) | −18.1795 | −0.641539 | ||||||||
\(804\) | 4.46398 | 0.157433 | ||||||||
\(805\) | 3.79508 | + | 6.57326i | 0.133759 | + | 0.231677i | ||||
\(806\) | − | 20.2636i | − | 0.713755i | ||||||
\(807\) | 7.30625 | − | 12.6548i | 0.257192 | − | 0.445470i | ||||
\(808\) | 16.4846i | 0.579926i | ||||||||
\(809\) | 24.0866 | + | 13.9064i | 0.846841 | + | 0.488924i | 0.859584 | − | 0.510995i | \(-0.170723\pi\) |
−0.0127426 | + | 0.999919i | \(0.504056\pi\) | |||||||
\(810\) | 1.98929 | − | 3.44555i | 0.0698965 | − | 0.121064i | ||||
\(811\) | −22.0688 | + | 38.2242i | −0.774940 | + | 1.34223i | 0.159889 | + | 0.987135i | \(0.448886\pi\) |
−0.934828 | + | 0.355100i | \(0.884447\pi\) | |||||||
\(812\) | 4.60329 | − | 2.65771i | 0.161544 | − | 0.0932674i | ||||
\(813\) | −32.2519 | −1.13112 | ||||||||
\(814\) | −14.7162 | − | 5.20063i | −0.515804 | − | 0.182282i | ||||
\(815\) | 8.32601 | 0.291647 | ||||||||
\(816\) | −2.39027 | + | 1.38002i | −0.0836762 | + | 0.0483105i | ||||
\(817\) | 25.2505 | − | 43.7351i | 0.883403 | − | 1.53010i | ||||
\(818\) | 0.00625847 | − | 0.0108400i | 0.000218822 | − | 0.000379011i | ||||
\(819\) | 1.84023 | + | 1.06245i | 0.0643027 | + | 0.0371252i | ||||
\(820\) | − | 3.00193i | − | 0.104832i | ||||||
\(821\) | −1.17267 | + | 2.03112i | −0.0409264 | + | 0.0708866i | −0.885763 | − | 0.464138i | \(-0.846364\pi\) |
0.844837 | + | 0.535024i | \(0.179698\pi\) | |||||||
\(822\) | 13.9680i | 0.487191i | ||||||||
\(823\) | −4.82924 | − | 8.36448i | −0.168337 | − | 0.291568i | 0.769499 | − | 0.638649i | \(-0.220506\pi\) |
−0.937835 | + | 0.347081i | \(0.887173\pi\) | |||||||
\(824\) | −5.94687 | −0.207169 | ||||||||
\(825\) | 3.44589 | 0.119971 | ||||||||
\(826\) | 1.96539 | + | 3.40416i | 0.0683847 | + | 0.118446i | ||||
\(827\) | 9.14985 | + | 5.28267i | 0.318171 | + | 0.183696i | 0.650577 | − | 0.759440i | \(-0.274527\pi\) |
−0.332406 | + | 0.943136i | \(0.607860\pi\) | |||||||
\(828\) | 9.83626i | 0.341834i | ||||||||
\(829\) | −25.8734 | + | 14.9380i | −0.898621 | + | 0.518819i | −0.876753 | − | 0.480942i | \(-0.840295\pi\) |
−0.0218685 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(830\) | 2.86398 | + | 4.96056i | 0.0994102 | + | 0.172183i | ||||
\(831\) | −6.10875 | + | 3.52689i | −0.211910 | + | 0.122346i | ||||
\(832\) | 1.66565 | + | 0.961662i | 0.0577459 | + | 0.0333396i | ||||
\(833\) | −10.9419 | − | 6.31731i | −0.379114 | − | 0.218882i | ||||
\(834\) | 17.0265 | − | 9.83023i | 0.589578 | − | 0.340393i | ||||
\(835\) | −3.73035 | − | 6.46115i | −0.129094 | − | 0.223597i | ||||
\(836\) | 16.1450 | − | 9.32134i | 0.558388 | − | 0.322385i | ||||
\(837\) | 59.3757i | 2.05232i | ||||||||
\(838\) | 2.85196 | + | 1.64658i | 0.0985194 | + | 0.0568802i | ||||
\(839\) | 4.14171 | + | 7.17365i | 0.142988 | + | 0.247662i | 0.928620 | − | 0.371031i | \(-0.120996\pi\) |
−0.785633 | + | 0.618693i | \(0.787662\pi\) | |||||||
\(840\) | −1.23995 | −0.0427825 | ||||||||
\(841\) | −4.14112 | −0.142797 | ||||||||
\(842\) | 9.67772 | + | 16.7623i | 0.333516 | + | 0.577667i | ||||
\(843\) | 25.9681i | 0.894389i | ||||||||
\(844\) | −5.79443 | + | 10.0362i | −0.199453 | + | 0.345462i | ||||
\(845\) | 9.30082i | 0.319958i | ||||||||
\(846\) | 10.9022 | + | 6.29441i | 0.374827 | + | 0.216406i | ||||
\(847\) | 2.03862 | − | 3.53099i | 0.0700478 | − | 0.121326i | ||||
\(848\) | 2.61745 | − | 4.53356i | 0.0898836 | − | 0.155683i | ||||
\(849\) | 1.18557 | − | 0.684489i | 0.0406886 | − | 0.0234916i | ||||
\(850\) | 2.05525 | 0.0704946 | ||||||||
\(851\) | 38.0018 | − | 32.4989i | 1.30268 | − | 1.11405i | ||||
\(852\) | −21.1290 | −0.723867 | ||||||||
\(853\) | 3.05650 | − | 1.76467i | 0.104653 | − | 0.0604213i | −0.446760 | − | 0.894654i | \(-0.647422\pi\) |
0.551413 | + | 0.834233i | \(0.314089\pi\) | |||||||
\(854\) | 1.86226 | − | 3.22554i | 0.0637254 | − | 0.110376i | ||||
\(855\) | −4.34672 | + | 7.52873i | −0.148655 | + | 0.257477i | ||||
\(856\) | 3.23550 | + | 1.86802i | 0.110587 | + | 0.0638476i | ||||
\(857\) | − | 22.4791i | − | 0.767873i | −0.923360 | − | 0.383936i | \(-0.874568\pi\) | ||
0.923360 | − | 0.383936i | \(-0.125432\pi\) | |||||||
\(858\) | 3.31378 | − | 5.73964i | 0.113131 | − | 0.195948i | ||||
\(859\) | 39.4974i | 1.34763i | 0.738898 | + | 0.673817i | \(0.235346\pi\) | ||||
−0.738898 | + | 0.673817i | \(0.764654\pi\) | |||||||
\(860\) | −3.47546 | − | 6.01967i | −0.118512 | − | 0.205269i | ||||
\(861\) | 3.72225 | 0.126854 | ||||||||
\(862\) | −3.64458 | −0.124135 | ||||||||
\(863\) | 10.1444 | + | 17.5705i | 0.345318 | + | 0.598108i | 0.985411 | − | 0.170189i | \(-0.0544378\pi\) |
−0.640094 | + | 0.768297i | \(0.721104\pi\) | |||||||
\(864\) | −4.88062 | − | 2.81783i | −0.166042 | − | 0.0958644i | ||||
\(865\) | 3.53420i | 0.120166i | ||||||||
\(866\) | 20.5761 | − | 11.8796i | 0.699203 | − | 0.403685i | ||||
\(867\) | −8.57855 | − | 14.8585i | −0.291343 | − | 0.504621i | ||||
\(868\) | 8.42460 | − | 4.86394i | 0.285949 | − | 0.165093i | ||||
\(869\) | −30.9858 | − | 17.8897i | −1.05112 | − | 0.606866i | ||||
\(870\) | 6.69523 | + | 3.86549i | 0.226989 | + | 0.131052i | ||||
\(871\) | −5.53675 | + | 3.19664i | −0.187605 | + | 0.108314i | ||||
\(872\) | −2.90360 | − | 5.02919i | −0.0983284 | − | 0.170310i | ||||
\(873\) | 10.2830 | − | 5.93692i | 0.348028 | − | 0.200934i | ||||
\(874\) | 59.7247i | 2.02022i | ||||||||
\(875\) | 0.799622 | + | 0.461662i | 0.0270322 | + | 0.0156070i | ||||
\(876\) | 4.75720 | + | 8.23972i | 0.160731 | + | 0.278394i | ||||
\(877\) | −52.3779 | −1.76868 | −0.884338 | − | 0.466847i | \(-0.845390\pi\) | ||||
−0.884338 | + | 0.466847i | \(0.845390\pi\) | |||||||
\(878\) | −23.4515 | −0.791450 | ||||||||
\(879\) | −8.65367 | − | 14.9886i | −0.291881 | − | 0.505553i | ||||
\(880\) | − | 2.56596i | − | 0.0864986i | ||||||
\(881\) | 7.78882 | − | 13.4906i | 0.262412 | − | 0.454511i | −0.704470 | − | 0.709733i | \(-0.748815\pi\) |
0.966882 | + | 0.255222i | \(0.0821487\pi\) | |||||||
\(882\) | − | 7.35580i | − | 0.247683i | ||||||
\(883\) | 4.49887 | + | 2.59742i | 0.151399 | + | 0.0874102i | 0.573786 | − | 0.819006i | \(-0.305474\pi\) |
−0.422387 | + | 0.906416i | \(0.638808\pi\) | |||||||
\(884\) | 1.97646 | − | 3.42333i | 0.0664755 | − | 0.115139i | ||||
\(885\) | −2.85855 | + | 4.95115i | −0.0960891 | + | 0.166431i | ||||
\(886\) | 33.7390 | − | 19.4792i | 1.13348 | − | 0.654417i | ||||
\(887\) | 31.7194 | 1.06503 | 0.532516 | − | 0.846420i | \(-0.321247\pi\) | ||||
0.532516 | + | 0.846420i | \(0.321247\pi\) | |||||||
\(888\) | 1.49380 | + | 8.03094i | 0.0501285 | + | 0.269501i | ||||
\(889\) | 5.27871 | 0.177042 | ||||||||
\(890\) | −3.60036 | + | 2.07867i | −0.120684 | + | 0.0696772i | ||||
\(891\) | −5.10444 | + | 8.84116i | −0.171005 | + | 0.296190i | ||||
\(892\) | 4.69865 | − | 8.13829i | 0.157322 | − | 0.272490i | ||||
\(893\) | 66.1972 | + | 38.2190i | 2.21521 | + | 1.27895i | ||||
\(894\) | − | 26.8493i | − | 0.897976i | ||||||
\(895\) | −8.50822 | + | 14.7367i | −0.284398 | + | 0.492593i | ||||
\(896\) | 0.923324i | 0.0308461i | ||||||||
\(897\) | 10.6162 | + | 18.3878i | 0.354465 | + | 0.613952i | ||||
\(898\) | −14.1317 | −0.471583 | ||||||||
\(899\) | −60.6524 | −2.02287 | ||||||||
\(900\) | 0.598279 | + | 1.03625i | 0.0199426 | + | 0.0345416i | ||||
\(901\) | −9.31760 | − | 5.37952i | −0.310414 | − | 0.179218i | ||||
\(902\) | 7.70285i | 0.256477i | ||||||||
\(903\) | 7.46411 | − | 4.30941i | 0.248390 | − | 0.143408i | ||||
\(904\) | −2.50901 | − | 4.34573i | −0.0834484 | − | 0.144537i | ||||
\(905\) | −7.16595 | + | 4.13726i | −0.238204 | + | 0.137527i | ||||
\(906\) | 16.6323 | + | 9.60269i | 0.552573 | + | 0.319028i | ||||
\(907\) | 47.4891 | + | 27.4179i | 1.57685 | + | 0.910396i | 0.995295 | + | 0.0968892i | \(0.0308893\pi\) |
0.581556 | + | 0.813506i | \(0.302444\pi\) | |||||||
\(908\) | −4.32885 | + | 2.49926i | −0.143658 | + | 0.0829410i | ||||
\(909\) | 9.86239 | + | 17.0822i | 0.327115 | + | 0.566579i | ||||
\(910\) | 1.53793 | − | 0.887926i | 0.0509820 | − | 0.0294345i | ||||
\(911\) | − | 21.0065i | − | 0.695975i | −0.937499 | − | 0.347987i | \(-0.886865\pi\) | ||
0.937499 | − | 0.347987i | \(-0.113135\pi\) | |||||||
\(912\) | −8.44966 | − | 4.87842i | −0.279796 | − | 0.161541i | ||||
\(913\) | −7.34887 | − | 12.7286i | −0.243212 | − | 0.421256i | ||||
\(914\) | 29.3664 | 0.971354 | ||||||||
\(915\) | 5.41712 | 0.179084 | ||||||||
\(916\) | 13.2423 | + | 22.9363i | 0.437538 | + | 0.757838i | ||||
\(917\) | − | 5.42796i | − | 0.179247i | ||||||
\(918\) | −5.79135 | + | 10.0309i | −0.191143 | + | 0.331069i | ||||
\(919\) | 31.6976i | 1.04561i | 0.852453 | + | 0.522804i | \(0.175114\pi\) | ||||
−0.852453 | + | 0.522804i | \(0.824886\pi\) | |||||||
\(920\) | 7.11913 | + | 4.11023i | 0.234711 | + | 0.135510i | ||||
\(921\) | 16.3358 | − | 28.2944i | 0.538282 | − | 0.932331i | ||||
\(922\) | 14.5048 | − | 25.1231i | 0.477692 | − | 0.827386i | ||||
\(923\) | 26.2066 | − | 15.1304i | 0.862601 | − | 0.498023i | ||||
\(924\) | 3.18168 | 0.104669 | ||||||||
\(925\) | 2.02678 | − | 5.73517i | 0.0666400 | − | 0.188571i | ||||
\(926\) | −32.4406 | −1.06606 | ||||||||
\(927\) | −6.16244 | + | 3.55789i | −0.202401 | + | 0.116856i | ||||
\(928\) | 2.87842 | − | 4.98556i | 0.0944886 | − | 0.163659i | ||||
\(929\) | −0.610310 | + | 1.05709i | −0.0200236 | + | 0.0346819i | −0.875864 | − | 0.482559i | \(-0.839707\pi\) |
0.855840 | + | 0.517241i | \(0.173041\pi\) | |||||||
\(930\) | 12.2531 | + | 7.07433i | 0.401795 | + | 0.231977i | ||||
\(931\) | − | 44.6637i | − | 1.46379i | ||||||
\(932\) | −9.99090 | + | 17.3047i | −0.327263 | + | 0.566836i | ||||
\(933\) | − | 8.49955i | − | 0.278263i | ||||||
\(934\) | 0.247846 | + | 0.429282i | 0.00810977 | + | 0.0140465i | ||||
\(935\) | −5.27371 | −0.172469 | ||||||||
\(936\) | 2.30137 | 0.0752226 | ||||||||
\(937\) | 15.1797 | + | 26.2920i | 0.495900 | + | 0.858923i | 0.999989 | − | 0.00472828i | \(-0.00150506\pi\) |
−0.504089 | + | 0.863652i | \(0.668172\pi\) | |||||||
\(938\) | −2.65801 | − | 1.53460i | −0.0867870 | − | 0.0501065i | ||||
\(939\) | 16.6462i | 0.543227i | ||||||||
\(940\) | 9.11134 | − | 5.26043i | 0.297179 | − | 0.171576i | ||||
\(941\) | 19.5570 | + | 33.8738i | 0.637541 | + | 1.10425i | 0.985971 | + | 0.166918i | \(0.0533816\pi\) |
−0.348430 | + | 0.937335i | \(0.613285\pi\) | |||||||
\(942\) | −10.5707 | + | 6.10300i | −0.344412 | + | 0.198847i | ||||
\(943\) | −21.3711 | − | 12.3386i | −0.695940 | − | 0.401801i | ||||
\(944\) | 3.68685 | + | 2.12860i | 0.119997 | + | 0.0692801i | ||||
\(945\) | −4.50639 | + | 2.60177i | −0.146593 | + | 0.0846355i | ||||
\(946\) | 8.91790 | + | 15.4463i | 0.289946 | + | 0.502201i | ||||
\(947\) | 7.13906 | − | 4.12174i | 0.231988 | − | 0.133938i | −0.379501 | − | 0.925191i | \(-0.623904\pi\) |
0.611489 | + | 0.791253i | \(0.290571\pi\) | |||||||
\(948\) | 18.7255i | 0.608175i | ||||||||
\(949\) | −11.8009 | − | 6.81323i | −0.383072 | − | 0.221167i | ||||
\(950\) | 3.63268 | + | 6.29199i | 0.117860 | + | 0.204139i | ||||
\(951\) | −41.6169 | −1.34952 | ||||||||
\(952\) | 1.89766 | 0.0615037 | ||||||||
\(953\) | 29.6054 | + | 51.2780i | 0.959012 | + | 1.66106i | 0.724908 | + | 0.688845i | \(0.241882\pi\) |
0.234103 | + | 0.972212i | \(0.424785\pi\) | |||||||
\(954\) | − | 6.26386i | − | 0.202800i | ||||||
\(955\) | 4.70488 | − | 8.14908i | 0.152246 | − | 0.263698i | ||||
\(956\) | 7.93630i | 0.256678i | ||||||||
\(957\) | −17.1797 | − | 9.91871i | −0.555341 | − | 0.320626i | ||||
\(958\) | −14.8343 | + | 25.6937i | −0.479274 | + | 0.830127i | ||||
\(959\) | 4.80185 | − | 8.31704i | 0.155060 | − | 0.268571i | ||||
\(960\) | −1.16301 | + | 0.671462i | −0.0375358 | + | 0.0216713i | ||||
\(961\) | −80.0014 | −2.58069 | ||||||||
\(962\) | −7.60370 | − | 8.89119i | −0.245153 | − | 0.286663i | ||||
\(963\) | 4.47038 | 0.144056 | ||||||||
\(964\) | 6.39989 | − | 3.69498i | 0.206127 | − | 0.119007i | ||||
\(965\) | −7.21720 | + | 12.5006i | −0.232330 | + | 0.402407i | ||||
\(966\) | −5.09649 | + | 8.82739i | −0.163977 | + | 0.284017i | ||||
\(967\) | −37.1087 | − | 21.4247i | −1.19333 | − | 0.688972i | −0.234273 | − | 0.972171i | \(-0.575271\pi\) |
−0.959061 | + | 0.283199i | \(0.908604\pi\) | |||||||
\(968\) | − | 4.41583i | − | 0.141930i | ||||||
\(969\) | −10.0264 | + | 17.3662i | −0.322094 | + | 0.557883i | ||||
\(970\) | − | 9.92333i | − | 0.318619i | ||||||
\(971\) | −24.5335 | − | 42.4933i | −0.787318 | − | 1.36367i | −0.927604 | − | 0.373564i | \(-0.878136\pi\) |
0.140286 | − | 0.990111i | \(-0.455198\pi\) | |||||||
\(972\) | −11.5640 | −0.370917 | ||||||||
\(973\) | −13.5175 | −0.433352 | ||||||||
\(974\) | 17.3814 | + | 30.1055i | 0.556937 | + | 0.964644i | ||||
\(975\) | 2.23684 | + | 1.29144i | 0.0716361 | + | 0.0413591i | ||||
\(976\) | − | 4.03382i | − | 0.129120i | ||||||
\(977\) | −27.5869 | + | 15.9273i | −0.882584 | + | 0.509560i | −0.871510 | − | 0.490378i | \(-0.836859\pi\) |
−0.0110747 | + | 0.999939i | \(0.503525\pi\) | |||||||
\(978\) | 5.59060 | + | 9.68320i | 0.178768 | + | 0.309634i | ||||
\(979\) | 9.23840 | − | 5.33379i | 0.295261 | − | 0.170469i | ||||
\(980\) | −5.32387 | − | 3.07374i | −0.170065 | − | 0.0981869i | ||||
\(981\) | −6.01771 | − | 3.47433i | −0.192131 | − | 0.110927i | ||||
\(982\) | 29.1243 | − | 16.8149i | 0.929395 | − | 0.536587i | ||||
\(983\) | 18.3044 | + | 31.7042i | 0.583821 | + | 1.01121i | 0.995021 | + | 0.0996629i | \(0.0317764\pi\) |
−0.411200 | + | 0.911545i | \(0.634890\pi\) | |||||||
\(984\) | 3.49126 | − | 2.01568i | 0.111297 | − | 0.0642576i | ||||
\(985\) | − | 0.702404i | − | 0.0223804i | ||||||
\(986\) | −10.2466 | − | 5.91587i | −0.326318 | − | 0.188400i | ||||
\(987\) | 6.52269 | + | 11.2976i | 0.207620 | + | 0.359608i | ||||
\(988\) | 13.9737 | 0.444561 | ||||||||
\(989\) | −57.1397 | −1.81694 | ||||||||
\(990\) | −1.53516 | − | 2.65898i | −0.0487907 | − | 0.0845079i | ||||
\(991\) | − | 25.6983i | − | 0.816334i | −0.912907 | − | 0.408167i | \(-0.866168\pi\) | ||
0.912907 | − | 0.408167i | \(-0.133832\pi\) | |||||||
\(992\) | 5.26786 | − | 9.12420i | 0.167255 | − | 0.289694i | ||||
\(993\) | 4.36734i | 0.138593i | ||||||||
\(994\) | 12.5809 | + | 7.26360i | 0.399042 | + | 0.230387i | ||||
\(995\) | −7.19862 | + | 12.4684i | −0.228212 | + | 0.395274i | ||||
\(996\) | −3.84610 | + | 6.66165i | −0.121868 | + | 0.211082i | ||||
\(997\) | 26.8778 | − | 15.5179i | 0.851229 | − | 0.491458i | −0.00983602 | − | 0.999952i | \(-0.503131\pi\) |
0.861065 | + | 0.508494i | \(0.169798\pi\) | |||||||
\(998\) | 6.67491 | 0.211291 | ||||||||
\(999\) | 22.2801 | + | 26.0526i | 0.704911 | + | 0.824269i |
(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 | 370.2.l.c.11.1 | ✓ | 12 | |
37.27 | even | 6 | inner | 370.2.l.c.101.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.l.c.11.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
370.2.l.c.101.1 | yes | 12 | 37.27 | even | 6 | inner |