Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(4,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.t (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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 205.4 | ||
Root | \(1.21245 + 0.727987i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.205 |
Dual form | 273.2.t.c.4.3 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.45597i | 1.02953i | 0.857331 | + | 0.514765i | \(0.172121\pi\) | ||||
−0.857331 | + | 0.514765i | \(0.827879\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.119863 | −0.0599314 | ||||||||
\(5\) | −3.67267 | − | 2.12042i | −1.64247 | − | 0.948279i | −0.979952 | − | 0.199231i | \(-0.936155\pi\) |
−0.662516 | − | 0.749048i | \(-0.730511\pi\) | |||||||
\(6\) | −1.26091 | − | 0.727987i | −0.514765 | − | 0.297200i | ||||
\(7\) | −0.357777 | + | 2.62145i | −0.135227 | + | 0.990815i | ||||
\(8\) | 2.73743i | 0.967829i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 3.08727 | − | 5.34732i | 0.976282 | − | 1.69097i | ||||
\(11\) | −3.49469 | − | 2.01766i | −1.05369 | − | 0.608347i | −0.130008 | − | 0.991513i | \(-0.541500\pi\) |
−0.923680 | + | 0.383166i | \(0.874834\pi\) | |||||||
\(12\) | 0.0599314 | − | 0.103804i | 0.0173007 | − | 0.0299657i | ||||
\(13\) | −3.50498 | + | 0.845633i | −0.972107 | + | 0.234536i | ||||
\(14\) | −3.81676 | − | 0.520915i | −1.02007 | − | 0.139220i | ||||
\(15\) | 3.67267 | − | 2.12042i | 0.948279 | − | 0.547489i | ||||
\(16\) | −4.22536 | −1.05634 | ||||||||
\(17\) | −0.0484615 | −0.0117536 | −0.00587682 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587682 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(18\) | 1.26091 | − | 0.727987i | 0.297200 | − | 0.171588i | ||||
\(19\) | −1.10977 | + | 0.640729i | −0.254600 | + | 0.146993i | −0.621869 | − | 0.783122i | \(-0.713626\pi\) |
0.367269 | + | 0.930115i | \(0.380293\pi\) | |||||||
\(20\) | 0.440217 | + | 0.254159i | 0.0984354 | + | 0.0568317i | ||||
\(21\) | −2.09135 | − | 1.62057i | −0.456371 | − | 0.353637i | ||||
\(22\) | 2.93766 | − | 5.08818i | 0.626311 | − | 1.08480i | ||||
\(23\) | 3.59569 | 0.749754 | 0.374877 | − | 0.927075i | \(-0.377685\pi\) | ||||
0.374877 | + | 0.927075i | \(0.377685\pi\) | |||||||
\(24\) | −2.37069 | − | 1.36872i | −0.483914 | − | 0.279388i | ||||
\(25\) | 6.49234 | + | 11.2451i | 1.29847 | + | 2.24901i | ||||
\(26\) | −1.23122 | − | 5.10317i | −0.241462 | − | 1.00081i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.0428842 | − | 0.314214i | 0.00810435 | − | 0.0593809i | ||||
\(29\) | 1.08299 | + | 1.87579i | 0.201106 | + | 0.348325i | 0.948885 | − | 0.315622i | \(-0.102213\pi\) |
−0.747779 | + | 0.663947i | \(0.768880\pi\) | |||||||
\(30\) | 3.08727 | + | 5.34732i | 0.563657 | + | 0.976282i | ||||
\(31\) | 4.50804 | − | 2.60272i | 0.809667 | − | 0.467461i | −0.0371732 | − | 0.999309i | \(-0.511835\pi\) |
0.846840 | + | 0.531847i | \(0.178502\pi\) | |||||||
\(32\) | − | 0.677151i | − | 0.119704i | ||||||
\(33\) | 3.49469 | − | 2.01766i | 0.608347 | − | 0.351229i | ||||
\(34\) | − | 0.0705587i | − | 0.0121007i | ||||||
\(35\) | 6.87256 | − | 8.86908i | 1.16168 | − | 1.49915i | ||||
\(36\) | 0.0599314 | + | 0.103804i | 0.00998857 | + | 0.0173007i | ||||
\(37\) | 4.30401i | 0.707574i | 0.935326 | + | 0.353787i | \(0.115106\pi\) | ||||
−0.935326 | + | 0.353787i | \(0.884894\pi\) | |||||||
\(38\) | −0.932885 | − | 1.61580i | −0.151334 | − | 0.262118i | ||||
\(39\) | 1.02015 | − | 3.45822i | 0.163355 | − | 0.553758i | ||||
\(40\) | 5.80450 | − | 10.0537i | 0.917772 | − | 1.58963i | ||||
\(41\) | −10.5963 | + | 6.11775i | −1.65486 | + | 0.955432i | −0.679823 | + | 0.733376i | \(0.737943\pi\) |
−0.975034 | + | 0.222056i | \(0.928723\pi\) | |||||||
\(42\) | 2.35951 | − | 3.04496i | 0.364080 | − | 0.469847i | ||||
\(43\) | −2.51030 | + | 4.34796i | −0.382816 | + | 0.663058i | −0.991464 | − | 0.130383i | \(-0.958379\pi\) |
0.608647 | + | 0.793441i | \(0.291713\pi\) | |||||||
\(44\) | 0.418883 | + | 0.241842i | 0.0631490 | + | 0.0364591i | ||||
\(45\) | 4.24083i | 0.632186i | ||||||||
\(46\) | 5.23524i | 0.771894i | ||||||||
\(47\) | 0.819767 | + | 0.473293i | 0.119575 | + | 0.0690368i | 0.558595 | − | 0.829441i | \(-0.311341\pi\) |
−0.439019 | + | 0.898478i | \(0.644674\pi\) | |||||||
\(48\) | 2.11268 | − | 3.65927i | 0.304939 | − | 0.528170i | ||||
\(49\) | −6.74399 | − | 1.87579i | −0.963427 | − | 0.267970i | ||||
\(50\) | −16.3725 | + | 9.45268i | −2.31542 | + | 1.33681i | ||||
\(51\) | 0.0242308 | − | 0.0419689i | 0.00339298 | − | 0.00587682i | ||||
\(52\) | 0.420117 | − | 0.101360i | 0.0582598 | − | 0.0140561i | ||||
\(53\) | 2.66425 | + | 4.61461i | 0.365962 | + | 0.633865i | 0.988930 | − | 0.148382i | \(-0.0474066\pi\) |
−0.622968 | + | 0.782247i | \(0.714073\pi\) | |||||||
\(54\) | 1.45597i | 0.198133i | ||||||||
\(55\) | 8.55656 | + | 14.8204i | 1.15377 | + | 1.99838i | ||||
\(56\) | −7.17604 | − | 0.979391i | −0.958939 | − | 0.130877i | ||||
\(57\) | − | 1.28146i | − | 0.169733i | ||||||
\(58\) | −2.73110 | + | 1.57680i | −0.358611 | + | 0.207044i | ||||
\(59\) | 3.17187i | 0.412943i | 0.978453 | + | 0.206471i | \(0.0661980\pi\) | ||||
−0.978453 | + | 0.206471i | \(0.933802\pi\) | |||||||
\(60\) | −0.440217 | + | 0.254159i | −0.0568317 | + | 0.0328118i | ||||
\(61\) | −1.90786 | − | 3.30451i | −0.244276 | − | 0.423099i | 0.717652 | − | 0.696402i | \(-0.245217\pi\) |
−0.961928 | + | 0.273303i | \(0.911884\pi\) | |||||||
\(62\) | 3.78949 | + | 6.56359i | 0.481265 | + | 0.833576i | ||||
\(63\) | 2.44913 | − | 1.00088i | 0.308561 | − | 0.126099i | ||||
\(64\) | −7.46480 | −0.933100 | ||||||||
\(65\) | 14.6657 | + | 4.32630i | 1.81906 | + | 0.536611i | ||||
\(66\) | 2.93766 | + | 5.08818i | 0.361601 | + | 0.626311i | ||||
\(67\) | −10.5072 | − | 6.06634i | −1.28366 | − | 0.741121i | −0.306144 | − | 0.951985i | \(-0.599039\pi\) |
−0.977515 | + | 0.210864i | \(0.932372\pi\) | |||||||
\(68\) | 0.00580873 | 0.000704412 | ||||||||
\(69\) | −1.79785 | + | 3.11396i | −0.216435 | + | 0.374877i | ||||
\(70\) | 12.9132 | + | 10.0063i | 1.54342 | + | 1.19598i | ||||
\(71\) | 5.69604 | + | 3.28861i | 0.675996 | + | 0.390287i | 0.798345 | − | 0.602201i | \(-0.205709\pi\) |
−0.122349 | + | 0.992487i | \(0.539043\pi\) | |||||||
\(72\) | 2.37069 | − | 1.36872i | 0.279388 | − | 0.161305i | ||||
\(73\) | 12.1155 | − | 6.99486i | 1.41801 | − | 0.818687i | 0.421883 | − | 0.906650i | \(-0.361369\pi\) |
0.996124 | + | 0.0879632i | \(0.0280358\pi\) | |||||||
\(74\) | −6.26653 | −0.728469 | ||||||||
\(75\) | −12.9847 | −1.49934 | ||||||||
\(76\) | 0.133021 | − | 0.0767995i | 0.0152585 | − | 0.00880951i | ||||
\(77\) | 6.53951 | − | 8.43927i | 0.745246 | − | 0.961744i | ||||
\(78\) | 5.03508 | + | 1.48532i | 0.570111 | + | 0.168179i | ||||
\(79\) | 6.29441 | − | 10.9022i | 0.708177 | − | 1.22660i | −0.257356 | − | 0.966317i | \(-0.582851\pi\) |
0.965533 | − | 0.260281i | \(-0.0838153\pi\) | |||||||
\(80\) | 15.5183 | + | 8.95952i | 1.73500 | + | 1.00171i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −8.90729 | − | 15.4279i | −0.983646 | − | 1.70372i | ||||
\(83\) | 3.47006i | 0.380889i | 0.981698 | + | 0.190444i | \(0.0609929\pi\) | ||||
−0.981698 | + | 0.190444i | \(0.939007\pi\) | |||||||
\(84\) | 0.250675 | + | 0.194246i | 0.0273509 | + | 0.0211940i | ||||
\(85\) | 0.177983 | + | 0.102759i | 0.0193050 | + | 0.0111457i | ||||
\(86\) | −6.33052 | − | 3.65493i | −0.682638 | − | 0.394121i | ||||
\(87\) | −2.16598 | −0.232217 | ||||||||
\(88\) | 5.52320 | − | 9.56647i | 0.588776 | − | 1.01979i | ||||
\(89\) | 7.47988i | 0.792866i | 0.918064 | + | 0.396433i | \(0.129752\pi\) | ||||
−0.918064 | + | 0.396433i | \(0.870248\pi\) | |||||||
\(90\) | −6.17455 | −0.650855 | ||||||||
\(91\) | −0.962780 | − | 9.49068i | −0.100927 | − | 0.994894i | ||||
\(92\) | −0.430990 | −0.0449338 | ||||||||
\(93\) | 5.20543i | 0.539778i | ||||||||
\(94\) | −0.689102 | + | 1.19356i | −0.0710754 | + | 0.123106i | ||||
\(95\) | 5.43445 | 0.557563 | ||||||||
\(96\) | 0.586430 | + | 0.338575i | 0.0598522 | + | 0.0345557i | ||||
\(97\) | 3.63599 | + | 2.09924i | 0.369179 | + | 0.213145i | 0.673100 | − | 0.739552i | \(-0.264963\pi\) |
−0.303921 | + | 0.952697i | \(0.598296\pi\) | |||||||
\(98\) | 2.73110 | − | 9.81908i | 0.275883 | − | 0.991877i | ||||
\(99\) | 4.03532i | 0.405565i | ||||||||
\(100\) | −0.778190 | − | 1.34786i | −0.0778190 | − | 0.134786i | ||||
\(101\) | −7.94673 | + | 13.7641i | −0.790729 | + | 1.36958i | 0.134787 | + | 0.990875i | \(0.456965\pi\) |
−0.925516 | + | 0.378708i | \(0.876368\pi\) | |||||||
\(102\) | 0.0611057 | + | 0.0352794i | 0.00605036 | + | 0.00349318i | ||||
\(103\) | −3.27155 | + | 5.66650i | −0.322356 | + | 0.558336i | −0.980974 | − | 0.194141i | \(-0.937808\pi\) |
0.658618 | + | 0.752477i | \(0.271141\pi\) | |||||||
\(104\) | −2.31486 | − | 9.59465i | −0.226991 | − | 0.940833i | ||||
\(105\) | 4.24457 | + | 10.3864i | 0.414227 | + | 1.01360i | ||||
\(106\) | −6.71875 | + | 3.87907i | −0.652583 | + | 0.376769i | ||||
\(107\) | −7.15958 | −0.692143 | −0.346072 | − | 0.938208i | \(-0.612485\pi\) | ||||
−0.346072 | + | 0.938208i | \(0.612485\pi\) | |||||||
\(108\) | −0.119863 | −0.0115338 | ||||||||
\(109\) | 0.693532 | − | 0.400411i | 0.0664283 | − | 0.0383524i | −0.466418 | − | 0.884564i | \(-0.654456\pi\) |
0.532846 | + | 0.846212i | \(0.321122\pi\) | |||||||
\(110\) | −21.5781 | + | 12.4581i | −2.05739 | + | 1.18784i | ||||
\(111\) | −3.72738 | − | 2.15200i | −0.353787 | − | 0.204259i | ||||
\(112\) | 1.51174 | − | 11.0766i | 0.142846 | − | 1.04664i | ||||
\(113\) | −0.289689 | + | 0.501755i | −0.0272516 | + | 0.0472012i | −0.879330 | − | 0.476214i | \(-0.842009\pi\) |
0.852078 | + | 0.523415i | \(0.175342\pi\) | |||||||
\(114\) | 1.86577 | 0.174745 | ||||||||
\(115\) | −13.2058 | − | 7.62437i | −1.23145 | − | 0.710976i | ||||
\(116\) | −0.129810 | − | 0.224837i | −0.0120526 | − | 0.0208756i | ||||
\(117\) | 2.48483 | + | 2.61259i | 0.229723 | + | 0.241534i | ||||
\(118\) | −4.61817 | −0.425137 | ||||||||
\(119\) | 0.0173384 | − | 0.127039i | 0.00158941 | − | 0.0116457i | ||||
\(120\) | 5.80450 | + | 10.0537i | 0.529876 | + | 0.917772i | ||||
\(121\) | 2.64189 | + | 4.57589i | 0.240172 | + | 0.415990i | ||||
\(122\) | 4.81128 | − | 2.77780i | 0.435593 | − | 0.251490i | ||||
\(123\) | − | 12.2355i | − | 1.10324i | ||||||
\(124\) | −0.540346 | + | 0.311969i | −0.0485245 | + | 0.0280156i | ||||
\(125\) | − | 33.8617i | − | 3.02868i | ||||||
\(126\) | 1.45726 | + | 3.56587i | 0.129823 | + | 0.317673i | ||||
\(127\) | 0.797934 | + | 1.38206i | 0.0708052 | + | 0.122638i | 0.899254 | − | 0.437426i | \(-0.144110\pi\) |
−0.828449 | + | 0.560064i | \(0.810776\pi\) | |||||||
\(128\) | − | 12.2229i | − | 1.08036i | ||||||
\(129\) | −2.51030 | − | 4.34796i | −0.221019 | − | 0.382816i | ||||
\(130\) | −6.29898 | + | 21.3530i | −0.552457 | + | 1.87278i | ||||
\(131\) | 2.97143 | − | 5.14667i | 0.259615 | − | 0.449666i | −0.706524 | − | 0.707689i | \(-0.749738\pi\) |
0.966139 | + | 0.258023i | \(0.0830710\pi\) | |||||||
\(132\) | −0.418883 | + | 0.241842i | −0.0364591 | + | 0.0210497i | ||||
\(133\) | −1.28259 | − | 3.13846i | −0.111214 | − | 0.272139i | ||||
\(134\) | 8.83244 | − | 15.2982i | 0.763006 | − | 1.32157i | ||||
\(135\) | −3.67267 | − | 2.12042i | −0.316093 | − | 0.182496i | ||||
\(136\) | − | 0.132660i | − | 0.0113755i | ||||||
\(137\) | − | 16.0660i | − | 1.37261i | −0.727315 | − | 0.686304i | \(-0.759232\pi\) | ||
0.727315 | − | 0.686304i | \(-0.240768\pi\) | |||||||
\(138\) | −4.53385 | − | 2.61762i | −0.385947 | − | 0.222826i | ||||
\(139\) | 5.62726 | − | 9.74671i | 0.477298 | − | 0.826705i | −0.522363 | − | 0.852723i | \(-0.674949\pi\) |
0.999661 | + | 0.0260182i | \(0.00828280\pi\) | |||||||
\(140\) | −0.823765 | + | 1.06307i | −0.0696208 | + | 0.0898461i | ||||
\(141\) | −0.819767 | + | 0.473293i | −0.0690368 | + | 0.0398584i | ||||
\(142\) | −4.78814 | + | 8.29330i | −0.401812 | + | 0.695958i | ||||
\(143\) | 13.9550 | + | 4.11664i | 1.16698 | + | 0.344251i | ||||
\(144\) | 2.11268 | + | 3.65927i | 0.176057 | + | 0.304939i | ||||
\(145\) | − | 9.18554i | − | 0.762818i | ||||||
\(146\) | 10.1843 | + | 17.6398i | 0.842862 | + | 1.45988i | ||||
\(147\) | 4.99648 | − | 4.90257i | 0.412102 | − | 0.404357i | ||||
\(148\) | − | 0.515890i | − | 0.0424059i | ||||||
\(149\) | 4.83224 | − | 2.78990i | 0.395873 | − | 0.228557i | −0.288829 | − | 0.957381i | \(-0.593266\pi\) |
0.684702 | + | 0.728823i | \(0.259933\pi\) | |||||||
\(150\) | − | 18.9054i | − | 1.54362i | ||||||
\(151\) | −11.1069 | + | 6.41258i | −0.903868 | + | 0.521849i | −0.878453 | − | 0.477828i | \(-0.841424\pi\) |
−0.0254151 | + | 0.999677i | \(0.508091\pi\) | |||||||
\(152\) | −1.75395 | − | 3.03793i | −0.142264 | − | 0.246409i | ||||
\(153\) | 0.0242308 | + | 0.0419689i | 0.00195894 | + | 0.00339298i | ||||
\(154\) | 12.2874 | + | 9.52136i | 0.990144 | + | 0.767253i | ||||
\(155\) | −22.0754 | −1.77314 | ||||||||
\(156\) | −0.122278 | + | 0.414512i | −0.00979010 | + | 0.0331875i | ||||
\(157\) | 1.87821 | + | 3.25315i | 0.149897 | + | 0.259630i | 0.931189 | − | 0.364536i | \(-0.118772\pi\) |
−0.781292 | + | 0.624166i | \(0.785439\pi\) | |||||||
\(158\) | 15.8734 | + | 9.16450i | 1.26282 | + | 0.729089i | ||||
\(159\) | −5.32849 | −0.422577 | ||||||||
\(160\) | −1.43584 | + | 2.48695i | −0.113513 | + | 0.196611i | ||||
\(161\) | −1.28646 | + | 9.42592i | −0.101387 | + | 0.742867i | ||||
\(162\) | −1.26091 | − | 0.727987i | −0.0990665 | − | 0.0571961i | ||||
\(163\) | −16.2233 | + | 9.36652i | −1.27071 | + | 0.733642i | −0.975121 | − | 0.221674i | \(-0.928848\pi\) |
−0.295585 | + | 0.955316i | \(0.595515\pi\) | |||||||
\(164\) | 1.27010 | − | 0.733291i | 0.0991779 | − | 0.0572604i | ||||
\(165\) | −17.1131 | −1.33225 | ||||||||
\(166\) | −5.05232 | −0.392136 | ||||||||
\(167\) | 8.22069 | − | 4.74622i | 0.636136 | − | 0.367273i | −0.146989 | − | 0.989138i | \(-0.546958\pi\) |
0.783124 | + | 0.621865i | \(0.213625\pi\) | |||||||
\(168\) | 4.43620 | − | 5.72494i | 0.342260 | − | 0.441689i | ||||
\(169\) | 11.5698 | − | 5.92786i | 0.889985 | − | 0.455989i | ||||
\(170\) | −0.149614 | + | 0.259139i | −0.0114749 | + | 0.0198751i | ||||
\(171\) | 1.10977 | + | 0.640729i | 0.0848666 | + | 0.0489978i | ||||
\(172\) | 0.300891 | − | 0.521159i | 0.0229427 | − | 0.0397380i | ||||
\(173\) | 8.79700 | + | 15.2368i | 0.668823 | + | 1.15844i | 0.978233 | + | 0.207507i | \(0.0665350\pi\) |
−0.309410 | + | 0.950929i | \(0.600132\pi\) | |||||||
\(174\) | − | 3.15361i | − | 0.239074i | ||||||
\(175\) | −31.8012 | + | 12.9961i | −2.40394 | + | 0.982413i | ||||
\(176\) | 14.7663 | + | 8.52533i | 1.11305 | + | 0.642621i | ||||
\(177\) | −2.74692 | − | 1.58594i | −0.206471 | − | 0.119206i | ||||
\(178\) | −10.8905 | −0.816279 | ||||||||
\(179\) | 8.98969 | − | 15.5706i | 0.671921 | − | 1.16380i | −0.305437 | − | 0.952212i | \(-0.598803\pi\) |
0.977359 | − | 0.211590i | \(-0.0678640\pi\) | |||||||
\(180\) | − | 0.508318i | − | 0.0378878i | ||||||
\(181\) | 9.08741 | 0.675462 | 0.337731 | − | 0.941243i | \(-0.390341\pi\) | ||||
0.337731 | + | 0.941243i | \(0.390341\pi\) | |||||||
\(182\) | 13.8182 | − | 1.40178i | 1.02427 | − | 0.103907i | ||||
\(183\) | 3.81572 | 0.282066 | ||||||||
\(184\) | 9.84296i | 0.725633i | ||||||||
\(185\) | 9.12629 | − | 15.8072i | 0.670978 | − | 1.16217i | ||||
\(186\) | −7.57898 | −0.555717 | ||||||||
\(187\) | 0.169358 | + | 0.0977788i | 0.0123847 | + | 0.00715029i | ||||
\(188\) | −0.0982595 | − | 0.0567302i | −0.00716631 | − | 0.00413747i | ||||
\(189\) | −0.357777 | + | 2.62145i | −0.0260245 | + | 0.190682i | ||||
\(190\) | 7.91242i | 0.574027i | ||||||||
\(191\) | −10.0660 | − | 17.4349i | −0.728352 | − | 1.26154i | −0.957579 | − | 0.288170i | \(-0.906953\pi\) |
0.229227 | − | 0.973373i | \(-0.426380\pi\) | |||||||
\(192\) | 3.73240 | − | 6.46471i | 0.269363 | − | 0.466550i | ||||
\(193\) | −2.76578 | − | 1.59682i | −0.199085 | − | 0.114942i | 0.397144 | − | 0.917756i | \(-0.370001\pi\) |
−0.596229 | + | 0.802815i | \(0.703335\pi\) | |||||||
\(194\) | −3.05644 | + | 5.29391i | −0.219440 | + | 0.380080i | ||||
\(195\) | −11.0796 | + | 10.5378i | −0.793423 | + | 0.754624i | ||||
\(196\) | 0.808354 | + | 0.224837i | 0.0577395 | + | 0.0160598i | ||||
\(197\) | −12.7261 | + | 7.34744i | −0.906700 | + | 0.523483i | −0.879368 | − | 0.476143i | \(-0.842034\pi\) |
−0.0273321 | + | 0.999626i | \(0.508701\pi\) | |||||||
\(198\) | −5.87532 | −0.417541 | ||||||||
\(199\) | −23.1495 | −1.64102 | −0.820511 | − | 0.571630i | \(-0.806311\pi\) | ||||
−0.820511 | + | 0.571630i | \(0.806311\pi\) | |||||||
\(200\) | −30.7826 | + | 17.7723i | −2.17666 | + | 1.25669i | ||||
\(201\) | 10.5072 | − | 6.06634i | 0.741121 | − | 0.427887i | ||||
\(202\) | −20.0402 | − | 11.5702i | −1.41003 | − | 0.814079i | ||||
\(203\) | −5.30476 | + | 2.16788i | −0.372321 | + | 0.152156i | ||||
\(204\) | −0.00290437 | + | 0.00503051i | −0.000203346 | + | 0.000352206i | ||||
\(205\) | 51.8887 | 3.62407 | ||||||||
\(206\) | −8.25027 | − | 4.76330i | −0.574824 | − | 0.331875i | ||||
\(207\) | −1.79785 | − | 3.11396i | −0.124959 | − | 0.216435i | ||||
\(208\) | 14.8098 | − | 3.57310i | 1.02688 | − | 0.247750i | ||||
\(209\) | 5.17109 | 0.357692 | ||||||||
\(210\) | −15.1223 | + | 6.17998i | −1.04354 | + | 0.426459i | ||||
\(211\) | 4.58765 | + | 7.94604i | 0.315827 | + | 0.547028i | 0.979613 | − | 0.200894i | \(-0.0643848\pi\) |
−0.663786 | + | 0.747923i | \(0.731051\pi\) | |||||||
\(212\) | −0.319344 | − | 0.553120i | −0.0219326 | − | 0.0379884i | ||||
\(213\) | −5.69604 | + | 3.28861i | −0.390287 | + | 0.225332i | ||||
\(214\) | − | 10.4242i | − | 0.712582i | ||||||
\(215\) | 18.4390 | − | 10.6457i | 1.25753 | − | 0.726034i | ||||
\(216\) | 2.73743i | 0.186259i | ||||||||
\(217\) | 5.21001 | + | 12.7488i | 0.353679 | + | 0.865443i | ||||
\(218\) | 0.582988 | + | 1.00976i | 0.0394849 | + | 0.0683899i | ||||
\(219\) | 13.9897i | 0.945338i | ||||||||
\(220\) | −1.02561 | − | 1.77641i | −0.0691468 | − | 0.119766i | ||||
\(221\) | 0.169857 | − | 0.0409806i | 0.0114258 | − | 0.00275666i | ||||
\(222\) | 3.13326 | − | 5.42697i | 0.210291 | − | 0.364234i | ||||
\(223\) | 1.96256 | − | 1.13309i | 0.131423 | − | 0.0758770i | −0.432847 | − | 0.901467i | \(-0.642491\pi\) |
0.564270 | + | 0.825590i | \(0.309158\pi\) | |||||||
\(224\) | 1.77512 | + | 0.242269i | 0.118605 | + | 0.0161873i | ||||
\(225\) | 6.49234 | − | 11.2451i | 0.432823 | − | 0.749671i | ||||
\(226\) | −0.730543 | − | 0.421779i | −0.0485950 | − | 0.0280563i | ||||
\(227\) | − | 8.35130i | − | 0.554295i | −0.960827 | − | 0.277148i | \(-0.910611\pi\) | ||
0.960827 | − | 0.277148i | \(-0.0893891\pi\) | |||||||
\(228\) | 0.153599i | 0.0101723i | ||||||||
\(229\) | −6.05361 | − | 3.49506i | −0.400034 | − | 0.230960i | 0.286465 | − | 0.958091i | \(-0.407520\pi\) |
−0.686499 | + | 0.727131i | \(0.740853\pi\) | |||||||
\(230\) | 11.1009 | − | 19.2273i | 0.731971 | − | 1.26781i | ||||
\(231\) | 4.03887 | + | 9.88302i | 0.265738 | + | 0.650255i | ||||
\(232\) | −5.13485 | + | 2.96461i | −0.337119 | + | 0.194636i | ||||
\(233\) | −11.1643 | + | 19.3371i | −0.731395 | + | 1.26681i | 0.224892 | + | 0.974384i | \(0.427797\pi\) |
−0.956287 | + | 0.292429i | \(0.905536\pi\) | |||||||
\(234\) | −3.80386 | + | 3.61785i | −0.248666 | + | 0.236506i | ||||
\(235\) | −2.00716 | − | 3.47649i | −0.130932 | − | 0.226782i | ||||
\(236\) | − | 0.380190i | − | 0.0247482i | ||||||
\(237\) | 6.29441 | + | 10.9022i | 0.408866 | + | 0.708177i | ||||
\(238\) | 0.184966 | + | 0.0252443i | 0.0119896 | + | 0.00163635i | ||||
\(239\) | 12.8510i | 0.831264i | 0.909533 | + | 0.415632i | \(0.136440\pi\) | ||||
−0.909533 | + | 0.415632i | \(0.863560\pi\) | |||||||
\(240\) | −15.5183 | + | 8.95952i | −1.00171 | + | 0.578335i | ||||
\(241\) | 14.9262i | 0.961483i | 0.876862 | + | 0.480742i | \(0.159633\pi\) | ||||
−0.876862 | + | 0.480742i | \(0.840367\pi\) | |||||||
\(242\) | −6.66238 | + | 3.84653i | −0.428274 | + | 0.247264i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0.228681 | + | 0.396088i | 0.0146398 | + | 0.0253569i | ||||
\(245\) | 20.7910 | + | 21.1892i | 1.32829 | + | 1.35373i | ||||
\(246\) | 17.8146 | 1.13582 | ||||||||
\(247\) | 3.34792 | − | 3.18421i | 0.213023 | − | 0.202606i | ||||
\(248\) | 7.12476 | + | 12.3404i | 0.452423 | + | 0.783619i | ||||
\(249\) | −3.00516 | − | 1.73503i | −0.190444 | − | 0.109953i | ||||
\(250\) | 49.3018 | 3.11812 | ||||||||
\(251\) | −5.86990 | + | 10.1670i | −0.370505 | + | 0.641733i | −0.989643 | − | 0.143549i | \(-0.954149\pi\) |
0.619138 | + | 0.785282i | \(0.287482\pi\) | |||||||
\(252\) | −0.293560 | + | 0.119968i | −0.0184925 | + | 0.00755729i | ||||
\(253\) | −12.5658 | − | 7.25488i | −0.790006 | − | 0.456110i | ||||
\(254\) | −2.01225 | + | 1.16177i | −0.126260 | + | 0.0728961i | ||||
\(255\) | −0.177983 | + | 0.102759i | −0.0111457 | + | 0.00643499i | ||||
\(256\) | 2.86658 | 0.179161 | ||||||||
\(257\) | −30.6013 | −1.90885 | −0.954427 | − | 0.298445i | \(-0.903532\pi\) | ||||
−0.954427 | + | 0.298445i | \(0.903532\pi\) | |||||||
\(258\) | 6.33052 | − | 3.65493i | 0.394121 | − | 0.227546i | ||||
\(259\) | −11.2827 | − | 1.53988i | −0.701075 | − | 0.0956833i | ||||
\(260\) | −1.75788 | − | 0.518562i | −0.109019 | − | 0.0321598i | ||||
\(261\) | 1.08299 | − | 1.87579i | 0.0670353 | − | 0.116108i | ||||
\(262\) | 7.49342 | + | 4.32633i | 0.462945 | + | 0.267281i | ||||
\(263\) | 9.08377 | − | 15.7336i | 0.560129 | − | 0.970173i | −0.437355 | − | 0.899289i | \(-0.644085\pi\) |
0.997485 | − | 0.0708837i | \(-0.0225819\pi\) | |||||||
\(264\) | 5.52320 | + | 9.56647i | 0.339930 | + | 0.588776i | ||||
\(265\) | − | 22.5973i | − | 1.38814i | ||||||
\(266\) | 4.56951 | − | 1.86741i | 0.280175 | − | 0.114498i | ||||
\(267\) | −6.47777 | − | 3.73994i | −0.396433 | − | 0.228881i | ||||
\(268\) | 1.25942 | + | 0.727128i | 0.0769315 | + | 0.0444164i | ||||
\(269\) | 10.1222 | 0.617163 | 0.308581 | − | 0.951198i | \(-0.400146\pi\) | ||||
0.308581 | + | 0.951198i | \(0.400146\pi\) | |||||||
\(270\) | 3.08727 | − | 5.34732i | 0.187886 | − | 0.325427i | ||||
\(271\) | 26.5527i | 1.61296i | 0.591260 | + | 0.806481i | \(0.298631\pi\) | ||||
−0.591260 | + | 0.806481i | \(0.701369\pi\) | |||||||
\(272\) | 0.204767 | 0.0124158 | ||||||||
\(273\) | 8.70056 | + | 3.91155i | 0.526582 | + | 0.236738i | ||||
\(274\) | 23.3916 | 1.41314 | ||||||||
\(275\) | − | 52.3973i | − | 3.15968i | ||||||
\(276\) | 0.215495 | − | 0.373248i | 0.0129713 | − | 0.0224669i | ||||
\(277\) | 29.3101 | 1.76107 | 0.880537 | − | 0.473977i | \(-0.157182\pi\) | ||||
0.880537 | + | 0.473977i | \(0.157182\pi\) | |||||||
\(278\) | 14.1910 | + | 8.19315i | 0.851117 | + | 0.491393i | ||||
\(279\) | −4.50804 | − | 2.60272i | −0.269889 | − | 0.155820i | ||||
\(280\) | 24.2785 | + | 18.8132i | 1.45092 | + | 1.12430i | ||||
\(281\) | 6.74332i | 0.402273i | 0.979563 | + | 0.201136i | \(0.0644635\pi\) | ||||
−0.979563 | + | 0.201136i | \(0.935537\pi\) | |||||||
\(282\) | −0.689102 | − | 1.19356i | −0.0410354 | − | 0.0710754i | ||||
\(283\) | −8.69346 | + | 15.0575i | −0.516772 | + | 0.895076i | 0.483038 | + | 0.875599i | \(0.339533\pi\) |
−0.999810 | + | 0.0194766i | \(0.993800\pi\) | |||||||
\(284\) | −0.682744 | − | 0.394182i | −0.0405134 | − | 0.0233904i | ||||
\(285\) | −2.71722 | + | 4.70637i | −0.160955 | + | 0.278781i | ||||
\(286\) | −5.99372 | + | 20.3182i | −0.354416 | + | 1.20144i | ||||
\(287\) | −12.2463 | − | 29.9663i | −0.722875 | − | 1.76886i | ||||
\(288\) | −0.586430 | + | 0.338575i | −0.0345557 | + | 0.0199507i | ||||
\(289\) | −16.9977 | −0.999862 | ||||||||
\(290\) | 13.3739 | 0.785344 | ||||||||
\(291\) | −3.63599 | + | 2.09924i | −0.213145 | + | 0.123060i | ||||
\(292\) | −1.45219 | + | 0.838424i | −0.0849831 | + | 0.0490650i | ||||
\(293\) | 15.2346 | + | 8.79572i | 0.890017 | + | 0.513852i | 0.873948 | − | 0.486019i | \(-0.161552\pi\) |
0.0160689 | + | 0.999871i | \(0.494885\pi\) | |||||||
\(294\) | 7.13802 | + | 7.27475i | 0.416298 | + | 0.424272i | ||||
\(295\) | 6.72570 | − | 11.6492i | 0.391585 | − | 0.678245i | ||||
\(296\) | −11.7819 | −0.684811 | ||||||||
\(297\) | −3.49469 | − | 2.01766i | −0.202782 | − | 0.117076i | ||||
\(298\) | 4.06202 | + | 7.03562i | 0.235306 | + | 0.407563i | ||||
\(299\) | −12.6028 | + | 3.04063i | −0.728841 | + | 0.175844i | ||||
\(300\) | 1.55638 | 0.0898576 | ||||||||
\(301\) | −10.4998 | − | 8.13621i | −0.605200 | − | 0.468964i | ||||
\(302\) | −9.33656 | − | 16.1714i | −0.537259 | − | 0.930559i | ||||
\(303\) | −7.94673 | − | 13.7641i | −0.456528 | − | 0.790729i | ||||
\(304\) | 4.68920 | − | 2.70731i | 0.268944 | − | 0.155275i | ||||
\(305\) | 16.1818i | 0.926569i | ||||||||
\(306\) | −0.0611057 | + | 0.0352794i | −0.00349318 | + | 0.00201679i | ||||
\(307\) | 0.0778605i | 0.00444373i | 0.999998 | + | 0.00222187i | \(0.000707243\pi\) | ||||
−0.999998 | + | 0.00222187i | \(0.999293\pi\) | |||||||
\(308\) | −0.783844 | + | 1.01155i | −0.0446636 | + | 0.0576387i | ||||
\(309\) | −3.27155 | − | 5.66650i | −0.186112 | − | 0.322356i | ||||
\(310\) | − | 32.1412i | − | 1.82550i | ||||||
\(311\) | 15.0689 | + | 26.1002i | 0.854482 | + | 1.48001i | 0.877125 | + | 0.480262i | \(0.159458\pi\) |
−0.0226436 | + | 0.999744i | \(0.507208\pi\) | |||||||
\(312\) | 9.46665 | + | 2.79260i | 0.535943 | + | 0.158100i | ||||
\(313\) | −10.0024 | + | 17.3247i | −0.565371 | + | 0.979252i | 0.431644 | + | 0.902044i | \(0.357934\pi\) |
−0.997015 | + | 0.0772078i | \(0.975400\pi\) | |||||||
\(314\) | −4.73650 | + | 2.73462i | −0.267296 | + | 0.154324i | ||||
\(315\) | −11.1171 | − | 1.51727i | −0.626379 | − | 0.0854887i | ||||
\(316\) | −0.754466 | + | 1.30677i | −0.0424420 | + | 0.0735117i | ||||
\(317\) | 20.7932 | + | 12.0050i | 1.16786 | + | 0.674266i | 0.953176 | − | 0.302416i | \(-0.0977933\pi\) |
0.214688 | + | 0.976683i | \(0.431127\pi\) | |||||||
\(318\) | − | 7.75815i | − | 0.435055i | ||||||
\(319\) | − | 8.74040i | − | 0.489368i | ||||||
\(320\) | 27.4158 | + | 15.8285i | 1.53259 | + | 0.884840i | ||||
\(321\) | 3.57979 | − | 6.20038i | 0.199805 | − | 0.346072i | ||||
\(322\) | −13.7239 | − | 1.87305i | −0.764803 | − | 0.104381i | ||||
\(323\) | 0.0537814 | − | 0.0310507i | 0.00299247 | − | 0.00172771i | ||||
\(324\) | 0.0599314 | − | 0.103804i | 0.00332952 | − | 0.00576690i | ||||
\(325\) | −32.2647 | − | 33.9236i | −1.78973 | − | 1.88174i | ||||
\(326\) | −13.6374 | − | 23.6207i | −0.755306 | − | 1.30823i | ||||
\(327\) | 0.800821i | 0.0442855i | ||||||||
\(328\) | −16.7469 | − | 29.0065i | −0.924694 | − | 1.60162i | ||||
\(329\) | −1.53401 | + | 1.97964i | −0.0845725 | + | 0.109141i | ||||
\(330\) | − | 24.9163i | − | 1.37160i | ||||||
\(331\) | −7.74452 | + | 4.47130i | −0.425677 | + | 0.245765i | −0.697503 | − | 0.716582i | \(-0.745706\pi\) |
0.271826 | + | 0.962346i | \(0.412372\pi\) | |||||||
\(332\) | − | 0.415931i | − | 0.0228272i | ||||||
\(333\) | 3.72738 | − | 2.15200i | 0.204259 | − | 0.117929i | ||||
\(334\) | 6.91037 | + | 11.9691i | 0.378119 | + | 0.654921i | ||||
\(335\) | 25.7263 | + | 44.5593i | 1.40558 | + | 2.43454i | ||||
\(336\) | 8.83672 | + | 6.84748i | 0.482082 | + | 0.373561i | ||||
\(337\) | −6.95546 | −0.378888 | −0.189444 | − | 0.981892i | \(-0.560669\pi\) | ||||
−0.189444 | + | 0.981892i | \(0.560669\pi\) | |||||||
\(338\) | 8.63081 | + | 16.8454i | 0.469454 | + | 0.916266i | ||||
\(339\) | −0.289689 | − | 0.501755i | −0.0157337 | − | 0.0272516i | ||||
\(340\) | −0.0213336 | − | 0.0123169i | −0.00115697 | − | 0.000667980i | ||||
\(341\) | −21.0056 | −1.13752 | ||||||||
\(342\) | −0.932885 | + | 1.61580i | −0.0504446 | + | 0.0873727i | ||||
\(343\) | 7.33014 | − | 17.0079i | 0.395790 | − | 0.918341i | ||||
\(344\) | −11.9022 | − | 6.87176i | −0.641726 | − | 0.370501i | ||||
\(345\) | 13.2058 | − | 7.62437i | 0.710976 | − | 0.410482i | ||||
\(346\) | −22.1845 | + | 12.8082i | −1.19264 | + | 0.688573i | ||||
\(347\) | 14.6491 | 0.786407 | 0.393204 | − | 0.919451i | \(-0.371367\pi\) | ||||
0.393204 | + | 0.919451i | \(0.371367\pi\) | |||||||
\(348\) | 0.259620 | 0.0139171 | ||||||||
\(349\) | 9.58341 | − | 5.53298i | 0.512988 | − | 0.296174i | −0.221073 | − | 0.975257i | \(-0.570956\pi\) |
0.734061 | + | 0.679083i | \(0.237623\pi\) | |||||||
\(350\) | −18.9220 | − | 46.3017i | −1.01142 | − | 2.47493i | ||||
\(351\) | −3.50498 | + | 0.845633i | −0.187082 | + | 0.0451365i | ||||
\(352\) | −1.36626 | + | 2.36643i | −0.0728218 | + | 0.126131i | ||||
\(353\) | −2.71822 | − | 1.56937i | −0.144676 | − | 0.0835290i | 0.425914 | − | 0.904763i | \(-0.359952\pi\) |
−0.570591 | + | 0.821234i | \(0.693286\pi\) | |||||||
\(354\) | 2.30908 | − | 3.99945i | 0.122726 | − | 0.212568i | ||||
\(355\) | −13.9465 | − | 24.1560i | −0.740201 | − | 1.28207i | ||||
\(356\) | − | 0.896559i | − | 0.0475176i | ||||||
\(357\) | 0.101350 | + | 0.0785352i | 0.00536402 | + | 0.00415652i | ||||
\(358\) | 22.6704 | + | 13.0888i | 1.19817 | + | 0.691763i | ||||
\(359\) | 11.4388 | + | 6.60421i | 0.603719 | + | 0.348557i | 0.770503 | − | 0.637436i | \(-0.220005\pi\) |
−0.166785 | + | 0.985993i | \(0.553338\pi\) | |||||||
\(360\) | −11.6090 | −0.611848 | ||||||||
\(361\) | −8.67893 | + | 15.0324i | −0.456786 | + | 0.791176i | ||||
\(362\) | 13.2310i | 0.695408i | ||||||||
\(363\) | −5.28379 | −0.277327 | ||||||||
\(364\) | 0.115401 | + | 1.13758i | 0.00604868 | + | 0.0596254i | ||||
\(365\) | −59.3281 | −3.10538 | ||||||||
\(366\) | 5.55559i | 0.290395i | ||||||||
\(367\) | 2.82967 | − | 4.90112i | 0.147707 | − | 0.255837i | −0.782672 | − | 0.622434i | \(-0.786144\pi\) |
0.930380 | + | 0.366597i | \(0.119477\pi\) | |||||||
\(368\) | −15.1931 | −0.791994 | ||||||||
\(369\) | 10.5963 | + | 6.11775i | 0.551619 | + | 0.318477i | ||||
\(370\) | 23.0149 | + | 13.2877i | 1.19649 | + | 0.690792i | ||||
\(371\) | −13.0502 | + | 5.33318i | −0.677531 | + | 0.276885i | ||||
\(372\) | − | 0.623937i | − | 0.0323496i | ||||||
\(373\) | 5.56866 | + | 9.64521i | 0.288334 | + | 0.499410i | 0.973412 | − | 0.229060i | \(-0.0735652\pi\) |
−0.685078 | + | 0.728470i | \(0.740232\pi\) | |||||||
\(374\) | −0.142363 | + | 0.246581i | −0.00736144 | + | 0.0127504i | ||||
\(375\) | 29.3251 | + | 16.9308i | 1.51434 | + | 0.874305i | ||||
\(376\) | −1.29561 | + | 2.24406i | −0.0668158 | + | 0.115728i | ||||
\(377\) | −5.38208 | − | 5.65880i | −0.277191 | − | 0.291443i | ||||
\(378\) | −3.81676 | − | 0.520915i | −0.196313 | − | 0.0267930i | ||||
\(379\) | 3.15893 | − | 1.82381i | 0.162263 | − | 0.0936828i | −0.416669 | − | 0.909058i | \(-0.636803\pi\) |
0.578933 | + | 0.815375i | \(0.303469\pi\) | |||||||
\(380\) | −0.651388 | −0.0334155 | ||||||||
\(381\) | −1.59587 | −0.0817588 | ||||||||
\(382\) | 25.3847 | − | 14.6559i | 1.29880 | − | 0.749860i | ||||
\(383\) | 17.5134 | − | 10.1114i | 0.894895 | − | 0.516668i | 0.0193546 | − | 0.999813i | \(-0.493839\pi\) |
0.875540 | + | 0.483145i | \(0.160506\pi\) | |||||||
\(384\) | 10.5853 | + | 6.11143i | 0.540179 | + | 0.311873i | ||||
\(385\) | −41.9122 | + | 17.1282i | −2.13605 | + | 0.872933i | ||||
\(386\) | 2.32493 | − | 4.02690i | 0.118336 | − | 0.204964i | ||||
\(387\) | 5.02059 | 0.255211 | ||||||||
\(388\) | −0.435820 | − | 0.251621i | −0.0221254 | − | 0.0127741i | ||||
\(389\) | −2.17109 | − | 3.76044i | −0.110079 | − | 0.190662i | 0.805723 | − | 0.592292i | \(-0.201777\pi\) |
−0.915802 | + | 0.401631i | \(0.868444\pi\) | |||||||
\(390\) | −15.3427 | − | 16.1316i | −0.776908 | − | 0.816853i | ||||
\(391\) | −0.174253 | −0.00881233 | ||||||||
\(392\) | 5.13485 | − | 18.4612i | 0.259349 | − | 0.932432i | ||||
\(393\) | 2.97143 | + | 5.14667i | 0.149889 | + | 0.259615i | ||||
\(394\) | −10.6977 | − | 18.5289i | −0.538942 | − | 0.933475i | ||||
\(395\) | −46.2346 | + | 26.6936i | −2.32632 | + | 1.34310i | ||||
\(396\) | − | 0.483684i | − | 0.0243061i | ||||||
\(397\) | 0.739259 | − | 0.426812i | 0.0371024 | − | 0.0214211i | −0.481334 | − | 0.876537i | \(-0.659848\pi\) |
0.518436 | + | 0.855116i | \(0.326514\pi\) | |||||||
\(398\) | − | 33.7051i | − | 1.68948i | ||||||
\(399\) | 3.35928 | + | 0.458476i | 0.168174 | + | 0.0229525i | ||||
\(400\) | −27.4325 | − | 47.5144i | −1.37162 | − | 2.37572i | ||||
\(401\) | − | 14.2417i | − | 0.711199i | −0.934638 | − | 0.355600i | \(-0.884277\pi\) | ||
0.934638 | − | 0.355600i | \(-0.115723\pi\) | |||||||
\(402\) | 8.83244 | + | 15.2982i | 0.440522 | + | 0.763006i | ||||
\(403\) | −13.5996 | + | 12.9346i | −0.677447 | + | 0.644319i | ||||
\(404\) | 0.952517 | − | 1.64981i | 0.0473895 | − | 0.0820810i | ||||
\(405\) | 3.67267 | − | 2.12042i | 0.182496 | − | 0.105364i | ||||
\(406\) | −3.15638 | − | 7.72359i | −0.156649 | − | 0.383315i | ||||
\(407\) | 8.68402 | − | 15.0412i | 0.430451 | − | 0.745563i | ||||
\(408\) | 0.114887 | + | 0.0663300i | 0.00568775 | + | 0.00328383i | ||||
\(409\) | − | 9.05933i | − | 0.447955i | −0.974594 | − | 0.223978i | \(-0.928096\pi\) | ||
0.974594 | − | 0.223978i | \(-0.0719042\pi\) | |||||||
\(410\) | 75.5487i | 3.73108i | ||||||||
\(411\) | 13.9135 | + | 8.03298i | 0.686304 | + | 0.396238i | ||||
\(412\) | 0.392137 | − | 0.679202i | 0.0193192 | − | 0.0334619i | ||||
\(413\) | −8.31491 | − | 1.13482i | −0.409150 | − | 0.0558411i | ||||
\(414\) | 4.53385 | − | 2.61762i | 0.222826 | − | 0.128649i | ||||
\(415\) | 7.35798 | − | 12.7444i | 0.361189 | − | 0.625598i | ||||
\(416\) | 0.572621 | + | 2.37340i | 0.0280750 | + | 0.116366i | ||||
\(417\) | 5.62726 | + | 9.74671i | 0.275568 | + | 0.477298i | ||||
\(418\) | 7.52897i | 0.368254i | ||||||||
\(419\) | −10.9547 | − | 18.9741i | −0.535171 | − | 0.926944i | −0.999155 | − | 0.0411002i | \(-0.986914\pi\) |
0.463984 | − | 0.885844i | \(-0.346420\pi\) | |||||||
\(420\) | −0.508766 | − | 1.24494i | −0.0248252 | − | 0.0607467i | ||||
\(421\) | − | 6.13705i | − | 0.299102i | −0.988754 | − | 0.149551i | \(-0.952217\pi\) | ||
0.988754 | − | 0.149551i | \(-0.0477827\pi\) | |||||||
\(422\) | −11.5692 | + | 6.67950i | −0.563182 | + | 0.325153i | ||||
\(423\) | − | 0.946585i | − | 0.0460245i | ||||||
\(424\) | −12.6322 | + | 7.29319i | −0.613473 | + | 0.354189i | ||||
\(425\) | −0.314628 | − | 0.544953i | −0.0152617 | − | 0.0264341i | ||||
\(426\) | −4.78814 | − | 8.29330i | −0.231986 | − | 0.401812i | ||||
\(427\) | 9.34519 | − | 3.81908i | 0.452246 | − | 0.184818i | ||||
\(428\) | 0.858168 | 0.0414811 | ||||||||
\(429\) | −10.5426 | + | 10.0271i | −0.509003 | + | 0.484112i | ||||
\(430\) | 15.4999 | + | 26.8467i | 0.747474 | + | 1.29466i | ||||
\(431\) | 22.2097 | + | 12.8228i | 1.06980 | + | 0.617651i | 0.928128 | − | 0.372262i | \(-0.121418\pi\) |
0.141675 | + | 0.989913i | \(0.454751\pi\) | |||||||
\(432\) | −4.22536 | −0.203293 | ||||||||
\(433\) | −9.98231 | + | 17.2899i | −0.479719 | + | 0.830898i | −0.999729 | − | 0.0232619i | \(-0.992595\pi\) |
0.520010 | + | 0.854160i | \(0.325928\pi\) | |||||||
\(434\) | −18.5619 | + | 7.58565i | −0.891000 | + | 0.364123i | ||||
\(435\) | 7.95492 | + | 4.59277i | 0.381409 | + | 0.220207i | ||||
\(436\) | −0.0831286 | + | 0.0479943i | −0.00398114 | + | 0.00229851i | ||||
\(437\) | −3.99041 | + | 2.30386i | −0.190887 | + | 0.110209i | ||||
\(438\) | −20.3687 | −0.973254 | ||||||||
\(439\) | 23.2057 | 1.10755 | 0.553774 | − | 0.832667i | \(-0.313187\pi\) | ||||
0.553774 | + | 0.832667i | \(0.313187\pi\) | |||||||
\(440\) | −40.5698 | + | 23.4230i | −1.93409 | + | 1.11665i | ||||
\(441\) | 1.74751 | + | 6.77836i | 0.0832149 | + | 0.322779i | ||||
\(442\) | 0.0596668 | + | 0.247307i | 0.00283806 | + | 0.0117632i | ||||
\(443\) | −1.72662 | + | 2.99059i | −0.0820340 | + | 0.142087i | −0.904124 | − | 0.427271i | \(-0.859475\pi\) |
0.822089 | + | 0.569358i | \(0.192808\pi\) | |||||||
\(444\) | 0.446774 | + | 0.257945i | 0.0212030 | + | 0.0122415i | ||||
\(445\) | 15.8605 | − | 27.4711i | 0.751858 | − | 1.30226i | ||||
\(446\) | 1.64974 | + | 2.85744i | 0.0781176 | + | 0.135304i | ||||
\(447\) | 5.57979i | 0.263915i | ||||||||
\(448\) | 2.67074 | − | 19.5686i | 0.126180 | − | 0.924529i | ||||
\(449\) | −16.9875 | − | 9.80772i | −0.801688 | − | 0.462855i | 0.0423728 | − | 0.999102i | \(-0.486508\pi\) |
−0.844061 | + | 0.536247i | \(0.819842\pi\) | |||||||
\(450\) | 16.3725 | + | 9.45268i | 0.771808 | + | 0.445604i | ||||
\(451\) | 49.3741 | 2.32494 | ||||||||
\(452\) | 0.0347229 | − | 0.0601418i | 0.00163323 | − | 0.00282883i | ||||
\(453\) | − | 12.8252i | − | 0.602579i | ||||||
\(454\) | 12.1593 | 0.570663 | ||||||||
\(455\) | −16.5882 | + | 36.8976i | −0.777668 | + | 1.72979i | ||||
\(456\) | 3.50790 | 0.164273 | ||||||||
\(457\) | 39.1402i | 1.83090i | 0.402428 | + | 0.915452i | \(0.368166\pi\) | ||||
−0.402428 | + | 0.915452i | \(0.631834\pi\) | |||||||
\(458\) | 5.08871 | − | 8.81391i | 0.237780 | − | 0.411847i | ||||
\(459\) | −0.0484615 | −0.00226199 | ||||||||
\(460\) | 1.58288 | + | 0.913878i | 0.0738023 | + | 0.0426098i | ||||
\(461\) | 13.2521 | + | 7.65108i | 0.617210 | + | 0.356346i | 0.775782 | − | 0.631001i | \(-0.217356\pi\) |
−0.158572 | + | 0.987347i | \(0.550689\pi\) | |||||||
\(462\) | −14.3894 | + | 5.88049i | −0.669457 | + | 0.273585i | ||||
\(463\) | 6.98877i | 0.324796i | 0.986725 | + | 0.162398i | \(0.0519228\pi\) | ||||
−0.986725 | + | 0.162398i | \(0.948077\pi\) | |||||||
\(464\) | −4.57601 | − | 7.92589i | −0.212436 | − | 0.367950i | ||||
\(465\) | 11.0377 | − | 19.1178i | 0.511860 | − | 0.886568i | ||||
\(466\) | −28.1543 | − | 16.2549i | −1.30422 | − | 0.752993i | ||||
\(467\) | 7.25825 | − | 12.5716i | 0.335872 | − | 0.581747i | −0.647780 | − | 0.761827i | \(-0.724303\pi\) |
0.983652 | + | 0.180081i | \(0.0576359\pi\) | |||||||
\(468\) | −0.297839 | − | 0.313152i | −0.0137676 | − | 0.0144755i | ||||
\(469\) | 19.6618 | − | 25.3737i | 0.907899 | − | 1.17165i | ||||
\(470\) | 5.06169 | − | 2.92237i | 0.233478 | − | 0.134799i | ||||
\(471\) | −3.75641 | −0.173086 | ||||||||
\(472\) | −8.68279 | −0.399658 | ||||||||
\(473\) | 17.5454 | − | 10.1298i | 0.806738 | − | 0.465771i | ||||
\(474\) | −15.8734 | + | 9.16450i | −0.729089 | + | 0.420940i | ||||
\(475\) | −14.4101 | − | 8.31966i | −0.661179 | − | 0.381732i | ||||
\(476\) | −0.00207823 | + | 0.0152273i | −9.52556e−5 | + | 0.000697942i | ||||
\(477\) | 2.66425 | − | 4.61461i | 0.121987 | − | 0.211288i | ||||
\(478\) | −18.7108 | −0.855811 | ||||||||
\(479\) | −14.6591 | − | 8.46346i | −0.669793 | − | 0.386705i | 0.126205 | − | 0.992004i | \(-0.459720\pi\) |
−0.795998 | + | 0.605299i | \(0.793054\pi\) | |||||||
\(480\) | −1.43584 | − | 2.48695i | −0.0655369 | − | 0.113513i | ||||
\(481\) | −3.63961 | − | 15.0855i | −0.165952 | − | 0.687838i | ||||
\(482\) | −21.7322 | −0.989876 | ||||||||
\(483\) | −7.51986 | − | 5.82707i | −0.342165 | − | 0.265141i | ||||
\(484\) | −0.316665 | − | 0.548479i | −0.0143938 | − | 0.0249309i | ||||
\(485\) | −8.90253 | − | 15.4196i | −0.404243 | − | 0.700169i | ||||
\(486\) | 1.26091 | − | 0.727987i | 0.0571961 | − | 0.0330222i | ||||
\(487\) | − | 25.4528i | − | 1.15338i | −0.816965 | − | 0.576688i | \(-0.804345\pi\) | ||
0.816965 | − | 0.576688i | \(-0.195655\pi\) | |||||||
\(488\) | 9.04587 | − | 5.22264i | 0.409487 | − | 0.236418i | ||||
\(489\) | − | 18.7330i | − | 0.847137i | ||||||
\(490\) | −30.8510 | + | 30.2712i | −1.39371 | + | 1.36751i | ||||
\(491\) | −0.0663605 | − | 0.114940i | −0.00299481 | − | 0.00518716i | 0.864524 | − | 0.502591i | \(-0.167620\pi\) |
−0.867519 | + | 0.497404i | \(0.834287\pi\) | |||||||
\(492\) | 1.46658i | 0.0661186i | ||||||||
\(493\) | −0.0524832 | − | 0.0909036i | −0.00236373 | − | 0.00409409i | ||||
\(494\) | 4.63612 | + | 4.87449i | 0.208589 | + | 0.219314i | ||||
\(495\) | 8.55656 | − | 14.8204i | 0.384589 | − | 0.666127i | ||||
\(496\) | −19.0481 | + | 10.9974i | −0.855283 | + | 0.493798i | ||||
\(497\) | −10.6588 | + | 13.7553i | −0.478115 | + | 0.617009i | ||||
\(498\) | 2.52616 | − | 4.37544i | 0.113200 | − | 0.196068i | ||||
\(499\) | −3.97198 | − | 2.29323i | −0.177810 | − | 0.102659i | 0.408453 | − | 0.912779i | \(-0.366068\pi\) |
−0.586264 | + | 0.810120i | \(0.699402\pi\) | |||||||
\(500\) | 4.05876i | 0.181513i | ||||||||
\(501\) | 9.49243i | 0.424091i | ||||||||
\(502\) | −14.8028 | − | 8.54643i | −0.660683 | − | 0.381446i | ||||
\(503\) | −10.9290 | + | 18.9296i | −0.487301 | + | 0.844029i | −0.999893 | − | 0.0146024i | \(-0.995352\pi\) |
0.512593 | + | 0.858632i | \(0.328685\pi\) | |||||||
\(504\) | 2.73984 | + | 6.70433i | 0.122042 | + | 0.298635i | ||||
\(505\) | 58.3714 | − | 33.7008i | 2.59749 | − | 1.49966i | ||||
\(506\) | 10.5629 | − | 18.2955i | 0.469579 | − | 0.813335i | ||||
\(507\) | −0.651232 | + | 12.9837i | −0.0289222 | + | 0.576625i | ||||
\(508\) | −0.0956426 | − | 0.165658i | −0.00424345 | − | 0.00734988i | ||||
\(509\) | 35.1753i | 1.55912i | 0.626329 | + | 0.779559i | \(0.284557\pi\) | ||||
−0.626329 | + | 0.779559i | \(0.715443\pi\) | |||||||
\(510\) | −0.149614 | − | 0.259139i | −0.00662502 | − | 0.0114749i | ||||
\(511\) | 14.0020 | + | 34.2627i | 0.619414 | + | 1.51569i | ||||
\(512\) | − | 20.2721i | − | 0.895907i | ||||||
\(513\) | −1.10977 | + | 0.640729i | −0.0489978 | + | 0.0282889i | ||||
\(514\) | − | 44.5547i | − | 1.96522i | ||||||
\(515\) | 24.0307 | − | 13.8741i | 1.05892 | − | 0.611366i | ||||
\(516\) | 0.300891 | + | 0.521159i | 0.0132460 | + | 0.0229427i | ||||
\(517\) | −1.90989 | − | 3.30802i | −0.0839967 | − | 0.145486i | ||||
\(518\) | 2.24202 | − | 16.4274i | 0.0985088 | − | 0.721778i | ||||
\(519\) | −17.5940 | −0.772291 | ||||||||
\(520\) | −11.8429 | + | 40.1465i | −0.519347 | + | 1.76054i | ||||
\(521\) | −9.16197 | − | 15.8690i | −0.401393 | − | 0.695233i | 0.592501 | − | 0.805570i | \(-0.298141\pi\) |
−0.993894 | + | 0.110336i | \(0.964807\pi\) | |||||||
\(522\) | 2.73110 | + | 1.57680i | 0.119537 | + | 0.0690148i | ||||
\(523\) | −8.29587 | −0.362753 | −0.181376 | − | 0.983414i | \(-0.558055\pi\) | ||||
−0.181376 | + | 0.983414i | \(0.558055\pi\) | |||||||
\(524\) | −0.356164 | + | 0.616894i | −0.0155591 | + | 0.0269491i | ||||
\(525\) | 4.64562 | − | 34.0387i | 0.202752 | − | 1.48557i | ||||
\(526\) | 22.9077 | + | 13.2257i | 0.998822 | + | 0.576670i | ||||
\(527\) | −0.218466 | + | 0.126131i | −0.00951654 | + | 0.00549437i | ||||
\(528\) | −14.7663 | + | 8.52533i | −0.642621 | + | 0.371017i | ||||
\(529\) | −10.0710 | −0.437870 | ||||||||
\(530\) | 32.9010 | 1.42913 | ||||||||
\(531\) | 2.74692 | − | 1.58594i | 0.119206 | − | 0.0688238i | ||||
\(532\) | 0.153734 | + | 0.376184i | 0.00666523 | + | 0.0163097i | ||||
\(533\) | 31.9663 | − | 30.4032i | 1.38462 | − | 1.31691i | ||||
\(534\) | 5.44526 | − | 9.43147i | 0.235639 | − | 0.408139i | ||||
\(535\) | 26.2948 | + | 15.1813i | 1.13682 | + | 0.656345i | ||||
\(536\) | 16.6062 | − | 28.7628i | 0.717278 | − | 1.24236i | ||||
\(537\) | 8.98969 | + | 15.5706i | 0.387934 | + | 0.671921i | ||||
\(538\) | 14.7377i | 0.635388i | ||||||||
\(539\) | 19.7834 | + | 20.1624i | 0.852133 | + | 0.868455i | ||||
\(540\) | 0.440217 | + | 0.254159i | 0.0189439 | + | 0.0109373i | ||||
\(541\) | −15.6366 | − | 9.02781i | −0.672271 | − | 0.388136i | 0.124665 | − | 0.992199i | \(-0.460214\pi\) |
−0.796937 | + | 0.604063i | \(0.793548\pi\) | |||||||
\(542\) | −38.6601 | −1.66059 | ||||||||
\(543\) | −4.54370 | + | 7.86993i | −0.194989 | + | 0.337731i | ||||
\(544\) | 0.0328157i | 0.00140696i | ||||||||
\(545\) | −3.39615 | −0.145475 | ||||||||
\(546\) | −5.69512 | + | 12.6678i | −0.243729 | + | 0.542132i | ||||
\(547\) | 39.4973 | 1.68878 | 0.844391 | − | 0.535727i | \(-0.179962\pi\) | ||||
0.844391 | + | 0.535727i | \(0.179962\pi\) | |||||||
\(548\) | 1.92571i | 0.0822623i | ||||||||
\(549\) | −1.90786 | + | 3.30451i | −0.0814255 | + | 0.141033i | ||||
\(550\) | 76.2891 | 3.25298 | ||||||||
\(551\) | −2.40375 | − | 1.38780i | −0.102403 | − | 0.0591224i | ||||
\(552\) | −8.52426 | − | 4.92148i | −0.362816 | − | 0.209472i | ||||
\(553\) | 26.3277 | + | 20.4011i | 1.11957 | + | 0.867541i | ||||
\(554\) | 42.6748i | 1.81308i | ||||||||
\(555\) | 9.12629 | + | 15.8072i | 0.387390 | + | 0.670978i | ||||
\(556\) | −0.674500 | + | 1.16827i | −0.0286052 | + | 0.0495456i | ||||
\(557\) | 21.9234 | + | 12.6575i | 0.928925 | + | 0.536315i | 0.886471 | − | 0.462783i | \(-0.153149\pi\) |
0.0424534 | + | 0.999098i | \(0.486483\pi\) | |||||||
\(558\) | 3.78949 | − | 6.56359i | 0.160422 | − | 0.277859i | ||||
\(559\) | 5.12177 | − | 17.3623i | 0.216628 | − | 0.734348i | ||||
\(560\) | −29.0390 | + | 37.4750i | −1.22712 | + | 1.58361i | ||||
\(561\) | −0.169358 | + | 0.0977788i | −0.00715029 | + | 0.00412822i | ||||
\(562\) | −9.81811 | −0.414152 | ||||||||
\(563\) | 13.5622 | 0.571577 | 0.285789 | − | 0.958293i | \(-0.407744\pi\) | ||||
0.285789 | + | 0.958293i | \(0.407744\pi\) | |||||||
\(564\) | 0.0982595 | − | 0.0567302i | 0.00413747 | − | 0.00238877i | ||||
\(565\) | 2.12786 | − | 1.22852i | 0.0895198 | − | 0.0516843i | ||||
\(566\) | −21.9234 | − | 12.6575i | −0.921507 | − | 0.532032i | ||||
\(567\) | −2.09135 | − | 1.62057i | −0.0878286 | − | 0.0680575i | ||||
\(568\) | −9.00236 | + | 15.5925i | −0.377730 | + | 0.654248i | ||||
\(569\) | 12.5214 | 0.524922 | 0.262461 | − | 0.964943i | \(-0.415466\pi\) | ||||
0.262461 | + | 0.964943i | \(0.415466\pi\) | |||||||
\(570\) | −6.85236 | − | 3.95621i | −0.287014 | − | 0.165707i | ||||
\(571\) | −4.44524 | − | 7.69938i | −0.186028 | − | 0.322209i | 0.757895 | − | 0.652377i | \(-0.226228\pi\) |
−0.943922 | + | 0.330168i | \(0.892895\pi\) | |||||||
\(572\) | −1.67269 | − | 0.493432i | −0.0699386 | − | 0.0206314i | ||||
\(573\) | 20.1321 | 0.841029 | ||||||||
\(574\) | 43.6302 | − | 17.8303i | 1.82109 | − | 0.744221i | ||||
\(575\) | 23.3444 | + | 40.4338i | 0.973531 | + | 1.68620i | ||||
\(576\) | 3.73240 | + | 6.46471i | 0.155517 | + | 0.269363i | ||||
\(577\) | −24.6718 | + | 14.2443i | −1.02710 | + | 0.592997i | −0.916153 | − | 0.400829i | \(-0.868722\pi\) |
−0.110948 | + | 0.993826i | \(0.535389\pi\) | |||||||
\(578\) | − | 24.7482i | − | 1.02939i | ||||||
\(579\) | 2.76578 | − | 1.59682i | 0.114942 | − | 0.0663616i | ||||
\(580\) | 1.10101i | 0.0457167i | ||||||||
\(581\) | −9.09659 | − | 1.24151i | −0.377390 | − | 0.0515065i | ||||
\(582\) | −3.05644 | − | 5.29391i | −0.126693 | − | 0.219440i | ||||
\(583\) | − | 21.5022i | − | 0.890528i | ||||||
\(584\) | 19.1480 | + | 33.1653i | 0.792348 | + | 1.37239i | ||||
\(585\) | −3.58619 | − | 14.8641i | −0.148271 | − | 0.614553i | ||||
\(586\) | −12.8063 | + | 22.1812i | −0.529025 | + | 0.916299i | ||||
\(587\) | 13.5984 | − | 7.85103i | 0.561266 | − | 0.324047i | −0.192388 | − | 0.981319i | \(-0.561623\pi\) |
0.753653 | + | 0.657272i | \(0.228290\pi\) | |||||||
\(588\) | −0.598892 | + | 0.587636i | −0.0246979 | + | 0.0242337i | ||||
\(589\) | −3.33527 | + | 5.77686i | −0.137427 | + | 0.238031i | ||||
\(590\) | 16.9610 | + | 9.79244i | 0.698274 | + | 0.403149i | ||||
\(591\) | − | 14.6949i | − | 0.604467i | ||||||
\(592\) | − | 18.1860i | − | 0.747439i | ||||||
\(593\) | −14.8094 | − | 8.55019i | −0.608148 | − | 0.351114i | 0.164092 | − | 0.986445i | \(-0.447530\pi\) |
−0.772240 | + | 0.635331i | \(0.780864\pi\) | |||||||
\(594\) | 2.93766 | − | 5.08818i | 0.120534 | − | 0.208770i | ||||
\(595\) | −0.333055 | + | 0.429809i | −0.0136539 | + | 0.0176205i | ||||
\(596\) | −0.579206 | + | 0.334405i | −0.0237252 | + | 0.0136978i | ||||
\(597\) | 11.5747 | − | 20.0480i | 0.473722 | − | 0.820511i | ||||
\(598\) | −4.42709 | − | 18.3494i | −0.181037 | − | 0.750363i | ||||
\(599\) | −21.8381 | − | 37.8247i | −0.892280 | − | 1.54547i | −0.837135 | − | 0.546996i | \(-0.815771\pi\) |
−0.0551452 | − | 0.998478i | \(-0.517562\pi\) | |||||||
\(600\) | − | 35.5447i | − | 1.45111i | ||||||
\(601\) | 14.9028 | + | 25.8124i | 0.607898 | + | 1.05291i | 0.991586 | + | 0.129448i | \(0.0413205\pi\) |
−0.383688 | + | 0.923463i | \(0.625346\pi\) | |||||||
\(602\) | 11.8461 | − | 15.2875i | 0.482812 | − | 0.623071i | ||||
\(603\) | 12.1327i | 0.494081i | ||||||||
\(604\) | 1.33131 | − | 0.768630i | 0.0541701 | − | 0.0312751i | ||||
\(605\) | − | 22.4077i | − | 0.911001i | ||||||
\(606\) | 20.0402 | − | 11.5702i | 0.814079 | − | 0.470009i | ||||
\(607\) | −0.375968 | − | 0.651196i | −0.0152601 | − | 0.0264312i | 0.858295 | − | 0.513157i | \(-0.171524\pi\) |
−0.873555 | + | 0.486726i | \(0.838191\pi\) | |||||||
\(608\) | 0.433870 | + | 0.751485i | 0.0175958 | + | 0.0304767i | ||||
\(609\) | 0.774937 | − | 5.67800i | 0.0314020 | − | 0.230084i | ||||
\(610\) | −23.5603 | −0.953930 | ||||||||
\(611\) | −3.27350 | − | 0.965661i | −0.132432 | − | 0.0390665i | ||||
\(612\) | −0.00290437 | − | 0.00503051i | −0.000117402 | − | 0.000203346i | ||||
\(613\) | −23.5664 | − | 13.6061i | −0.951837 | − | 0.549543i | −0.0581859 | − | 0.998306i | \(-0.518532\pi\) |
−0.893651 | + | 0.448762i | \(0.851865\pi\) | |||||||
\(614\) | −0.113363 | −0.00457495 | ||||||||
\(615\) | −25.9444 | + | 44.9370i | −1.04618 | + | 1.81203i | ||||
\(616\) | 23.1019 | + | 17.9015i | 0.930804 | + | 0.721271i | ||||
\(617\) | 13.3489 | + | 7.70701i | 0.537408 | + | 0.310272i | 0.744028 | − | 0.668149i | \(-0.232913\pi\) |
−0.206620 | + | 0.978421i | \(0.566246\pi\) | |||||||
\(618\) | 8.25027 | − | 4.76330i | 0.331875 | − | 0.191608i | ||||
\(619\) | 37.4700 | − | 21.6333i | 1.50605 | − | 0.869516i | 0.506070 | − | 0.862493i | \(-0.331098\pi\) |
0.999975 | − | 0.00702301i | \(-0.00223551\pi\) | |||||||
\(620\) | 2.64602 | 0.106267 | ||||||||
\(621\) | 3.59569 | 0.144290 | ||||||||
\(622\) | −38.0012 | + | 21.9400i | −1.52371 | + | 0.879714i | ||||
\(623\) | −19.6081 | − | 2.67613i | −0.785583 | − | 0.107217i | ||||
\(624\) | −4.31051 | + | 14.6122i | −0.172558 | + | 0.584957i | ||||
\(625\) | −39.3392 | + | 68.1375i | −1.57357 | + | 2.72550i | ||||
\(626\) | −25.2244 | − | 14.5633i | −1.00817 | − | 0.582067i | ||||
\(627\) | −2.58554 | + | 4.47829i | −0.103257 | + | 0.178846i | ||||
\(628\) | −0.225127 | − | 0.389932i | −0.00898355 | − | 0.0155600i | ||||
\(629\) | − | 0.208579i | − | 0.00831658i | ||||||
\(630\) | 2.20911 | − | 16.1863i | 0.0880132 | − | 0.644876i | ||||
\(631\) | −13.6641 | − | 7.88896i | −0.543958 | − | 0.314054i | 0.202723 | − | 0.979236i | \(-0.435021\pi\) |
−0.746682 | + | 0.665182i | \(0.768354\pi\) | |||||||
\(632\) | 29.8441 | + | 17.2305i | 1.18714 | + | 0.685394i | ||||
\(633\) | −9.17530 | −0.364685 | ||||||||
\(634\) | −17.4789 | + | 30.2744i | −0.694177 | + | 1.20235i | ||||
\(635\) | − | 6.76781i | − | 0.268572i | ||||||
\(636\) | 0.638688 | 0.0253256 | ||||||||
\(637\) | 25.2238 | + | 0.871673i | 0.999403 | + | 0.0345370i | ||||
\(638\) | 12.7258 | 0.503819 | ||||||||
\(639\) | − | 6.57723i | − | 0.260191i | ||||||
\(640\) | −25.9176 | + | 44.8906i | −1.02448 | + | 1.77446i | ||||
\(641\) | −16.1808 | −0.639104 | −0.319552 | − | 0.947569i | \(-0.603532\pi\) | ||||
−0.319552 | + | 0.947569i | \(0.603532\pi\) | |||||||
\(642\) | 9.02760 | + | 5.21209i | 0.356291 | + | 0.205705i | ||||
\(643\) | 10.1953 | + | 5.88625i | 0.402063 | + | 0.232131i | 0.687374 | − | 0.726304i | \(-0.258763\pi\) |
−0.285311 | + | 0.958435i | \(0.592097\pi\) | |||||||
\(644\) | 0.154198 | − | 1.12982i | 0.00607627 | − | 0.0445210i | ||||
\(645\) | 21.2915i | 0.838352i | ||||||||
\(646\) | 0.0452090 | + | 0.0783043i | 0.00177872 | + | 0.00308084i | ||||
\(647\) | −8.77908 | + | 15.2058i | −0.345141 | + | 0.597802i | −0.985379 | − | 0.170374i | \(-0.945502\pi\) |
0.640238 | + | 0.768176i | \(0.278836\pi\) | |||||||
\(648\) | −2.37069 | − | 1.36872i | −0.0931293 | − | 0.0537683i | ||||
\(649\) | 6.39976 | − | 11.0847i | 0.251213 | − | 0.435113i | ||||
\(650\) | 49.3919 | − | 46.9766i | 1.93731 | − | 1.84258i | ||||
\(651\) | −13.6458 | − | 1.86239i | −0.534820 | − | 0.0729926i | ||||
\(652\) | 1.94457 | − | 1.12270i | 0.0761552 | − | 0.0439682i | ||||
\(653\) | −30.9961 | −1.21297 | −0.606485 | − | 0.795095i | \(-0.707421\pi\) | ||||
−0.606485 | + | 0.795095i | \(0.707421\pi\) | |||||||
\(654\) | −1.16598 | −0.0455933 | ||||||||
\(655\) | −21.8262 | + | 12.6013i | −0.852819 | + | 0.492375i | ||||
\(656\) | 44.7730 | − | 25.8497i | 1.74809 | − | 1.00926i | ||||
\(657\) | −12.1155 | − | 6.99486i | −0.472669 | − | 0.272896i | ||||
\(658\) | −2.88231 | − | 2.23347i | −0.112364 | − | 0.0870699i | ||||
\(659\) | 3.05016 | − | 5.28303i | 0.118817 | − | 0.205797i | −0.800482 | − | 0.599357i | \(-0.795423\pi\) |
0.919299 | + | 0.393559i | \(0.128756\pi\) | |||||||
\(660\) | 2.05123 | 0.0798438 | ||||||||
\(661\) | 32.8669 | + | 18.9757i | 1.27837 | + | 0.738070i | 0.976549 | − | 0.215293i | \(-0.0690708\pi\) |
0.301825 | + | 0.953363i | \(0.402404\pi\) | |||||||
\(662\) | −6.51010 | − | 11.2758i | −0.253022 | − | 0.438247i | ||||
\(663\) | −0.0494381 | + | 0.167591i | −0.00192002 | + | 0.00650868i | ||||
\(664\) | −9.49906 | −0.368635 | ||||||||
\(665\) | −1.94432 | + | 14.2461i | −0.0753976 | + | 0.552441i | ||||
\(666\) | 3.13326 | + | 5.42697i | 0.121411 | + | 0.210291i | ||||
\(667\) | 3.89409 | + | 6.74476i | 0.150780 | + | 0.261158i | ||||
\(668\) | −0.985354 | + | 0.568895i | −0.0381245 | + | 0.0220112i | ||||
\(669\) | 2.26617i | 0.0876152i | ||||||||
\(670\) | −64.8773 | + | 37.4569i | −2.50643 | + | 1.44709i | ||||
\(671\) | 15.3976i | 0.594419i | ||||||||
\(672\) | −1.09737 | + | 1.41616i | −0.0423319 | + | 0.0546296i | ||||
\(673\) | 8.90401 | + | 15.4222i | 0.343225 | + | 0.594482i | 0.985030 | − | 0.172386i | \(-0.0551475\pi\) |
−0.641805 | + | 0.766868i | \(0.721814\pi\) | |||||||
\(674\) | − | 10.1270i | − | 0.390077i | ||||||
\(675\) | 6.49234 | + | 11.2451i | 0.249890 | + | 0.432823i | ||||
\(676\) | −1.38679 | + | 0.710529i | −0.0533381 | + | 0.0273281i | ||||
\(677\) | −2.24699 | + | 3.89190i | −0.0863589 | + | 0.149578i | −0.905969 | − | 0.423343i | \(-0.860857\pi\) |
0.819611 | + | 0.572921i | \(0.194190\pi\) | |||||||
\(678\) | 0.730543 | − | 0.421779i | 0.0280563 | − | 0.0161983i | ||||
\(679\) | −6.80392 | + | 8.78050i | −0.261111 | + | 0.336965i | ||||
\(680\) | −0.281295 | + | 0.487217i | −0.0107872 | + | 0.0186839i | ||||
\(681\) | 7.23244 | + | 4.17565i | 0.277148 | + | 0.160011i | ||||
\(682\) | − | 30.5836i | − | 1.17111i | ||||||
\(683\) | 18.8903i | 0.722816i | 0.932408 | + | 0.361408i | \(0.117704\pi\) | ||||
−0.932408 | + | 0.361408i | \(0.882296\pi\) | |||||||
\(684\) | −0.133021 | − | 0.0767995i | −0.00508617 | − | 0.00293650i | ||||
\(685\) | −34.0665 | + | 59.0050i | −1.30162 | + | 2.25446i | ||||
\(686\) | 24.7631 | + | 10.6725i | 0.945459 | + | 0.407478i | ||||
\(687\) | 6.05361 | − | 3.49506i | 0.230960 | − | 0.133345i | ||||
\(688\) | 10.6069 | − | 18.3717i | 0.404384 | − | 0.700414i | ||||
\(689\) | −13.2404 | − | 13.9212i | −0.504419 | − | 0.530354i | ||||
\(690\) | 11.1009 | + | 19.2273i | 0.422604 | + | 0.731971i | ||||
\(691\) | 36.0946i | 1.37310i | 0.727081 | + | 0.686551i | \(0.240876\pi\) | ||||
−0.727081 | + | 0.686551i | \(0.759124\pi\) | |||||||
\(692\) | −1.05443 | − | 1.82633i | −0.0400835 | − | 0.0694267i | ||||
\(693\) | −10.5784 | − | 1.44374i | −0.401839 | − | 0.0548433i | ||||
\(694\) | 21.3288i | 0.809630i | ||||||||
\(695\) | −41.3342 | + | 23.8643i | −1.56789 | + | 0.905224i | ||||
\(696\) | − | 5.92921i | − | 0.224746i | ||||||
\(697\) | 0.513510 | − | 0.296475i | 0.0194506 | − | 0.0112298i | ||||
\(698\) | 8.05588 | + | 13.9532i | 0.304920 | + | 0.528136i | ||||
\(699\) | −11.1643 | − | 19.3371i | −0.422271 | − | 0.731395i | ||||
\(700\) | 3.81178 | − | 1.55775i | 0.144072 | − | 0.0588774i | ||||
\(701\) | 7.46818 | 0.282069 | 0.141035 | − | 0.990005i | \(-0.454957\pi\) | ||||
0.141035 | + | 0.990005i | \(0.454957\pi\) | |||||||
\(702\) | −1.23122 | − | 5.10317i | −0.0464694 | − | 0.192607i | ||||
\(703\) | −2.75770 | − | 4.77648i | −0.104009 | − | 0.180148i | ||||
\(704\) | 26.0872 | + | 15.0614i | 0.983196 | + | 0.567649i | ||||
\(705\) | 4.01431 | 0.151188 | ||||||||
\(706\) | 2.28496 | − | 3.95766i | 0.0859955 | − | 0.148949i | ||||
\(707\) | −33.2388 | − | 25.7564i | −1.25007 | − | 0.968671i | ||||
\(708\) | 0.329254 | + | 0.190095i | 0.0123741 | + | 0.00714420i | ||||
\(709\) | 13.9053 | − | 8.02823i | 0.522225 | − | 0.301506i | −0.215620 | − | 0.976477i | \(-0.569177\pi\) |
0.737844 | + | 0.674971i | \(0.235844\pi\) | |||||||
\(710\) | 35.1705 | − | 20.3057i | 1.31993 | − | 0.762059i | ||||
\(711\) | −12.5888 | −0.472118 | ||||||||
\(712\) | −20.4757 | −0.767358 | ||||||||
\(713\) | 16.2095 | − | 9.35856i | 0.607051 | − | 0.350481i | ||||
\(714\) | −0.114345 | + | 0.147563i | −0.00427926 | + | 0.00552241i | ||||
\(715\) | −42.5232 | − | 44.7095i | −1.59028 | − | 1.67204i | ||||
\(716\) | −1.07753 | + | 1.86634i | −0.0402692 | + | 0.0697483i | ||||
\(717\) | −11.1293 | − | 6.42552i | −0.415632 | − | 0.239965i | ||||
\(718\) | −9.61557 | + | 16.6547i | −0.358850 | + | 0.621546i | ||||
\(719\) | −7.60447 | − | 13.1713i | −0.283599 | − | 0.491208i | 0.688670 | − | 0.725075i | \(-0.258195\pi\) |
−0.972268 | + | 0.233868i | \(0.924862\pi\) | |||||||
\(720\) | − | 17.9190i | − | 0.667803i | ||||||
\(721\) | −13.6839 | − | 10.6036i | −0.509617 | − | 0.394897i | ||||
\(722\) | −21.8867 | − | 12.6363i | −0.814540 | − | 0.470275i | ||||
\(723\) | −12.9265 | − | 7.46312i | −0.480742 | − | 0.277556i | ||||
\(724\) | −1.08924 | −0.0404814 | ||||||||
\(725\) | −14.0622 | + | 24.3565i | −0.522259 | + | 0.904579i | ||||
\(726\) | − | 7.69306i | − | 0.285516i | ||||||
\(727\) | 40.3565 | 1.49674 | 0.748369 | − | 0.663282i | \(-0.230837\pi\) | ||||
0.748369 | + | 0.663282i | \(0.230837\pi\) | |||||||
\(728\) | 25.9801 | − | 2.63554i | 0.962887 | − | 0.0976798i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 86.3802i | − | 3.19708i | ||||||
\(731\) | 0.121653 | − | 0.210709i | 0.00449949 | − | 0.00779334i | ||||
\(732\) | −0.457363 | −0.0169046 | ||||||||
\(733\) | −33.4424 | − | 19.3080i | −1.23522 | − | 0.713156i | −0.267109 | − | 0.963666i | \(-0.586068\pi\) |
−0.968114 | + | 0.250510i | \(0.919402\pi\) | |||||||
\(734\) | 7.13591 | + | 4.11992i | 0.263391 | + | 0.152069i | ||||
\(735\) | −28.7459 | + | 7.41092i | −1.06031 | + | 0.273356i | ||||
\(736\) | − | 2.43483i | − | 0.0897489i | ||||||
\(737\) | 24.4796 | + | 42.3999i | 0.901718 | + | 1.56182i | ||||
\(738\) | −8.90729 | + | 15.4279i | −0.327882 | + | 0.567908i | ||||
\(739\) | 8.88879 | + | 5.13195i | 0.326980 | + | 0.188782i | 0.654499 | − | 0.756063i | \(-0.272879\pi\) |
−0.327520 | + | 0.944844i | \(0.606213\pi\) | |||||||
\(740\) | −1.09390 | + | 1.89470i | −0.0402127 | + | 0.0696504i | ||||
\(741\) | 1.08364 | + | 4.49149i | 0.0398086 | + | 0.164999i | ||||
\(742\) | −7.76498 | − | 19.0007i | −0.285061 | − | 0.697538i | ||||
\(743\) | −1.51273 | + | 0.873374i | −0.0554966 | + | 0.0320410i | −0.527492 | − | 0.849560i | \(-0.676867\pi\) |
0.471995 | + | 0.881601i | \(0.343534\pi\) | |||||||
\(744\) | −14.2495 | −0.522413 | ||||||||
\(745\) | −23.6630 | −0.866945 | ||||||||
\(746\) | −14.0432 | + | 8.10783i | −0.514157 | + | 0.296849i | ||||
\(747\) | 3.00516 | − | 1.73503i | 0.109953 | − | 0.0634815i | ||||
\(748\) | −0.0202997 | − | 0.0117200i | −0.000742230 | − | 0.000428527i | ||||
\(749\) | 2.56154 | − | 18.7685i | 0.0935965 | − | 0.685786i | ||||
\(750\) | −24.6509 | + | 42.6966i | −0.900123 | + | 1.55906i | ||||
\(751\) | 24.6041 | 0.897816 | 0.448908 | − | 0.893578i | \(-0.351813\pi\) | ||||
0.448908 | + | 0.893578i | \(0.351813\pi\) | |||||||
\(752\) | −3.46381 | − | 1.99983i | −0.126312 | − | 0.0729263i | ||||
\(753\) | −5.86990 | − | 10.1670i | −0.213911 | − | 0.370505i | ||||
\(754\) | 8.23907 | − | 7.83618i | 0.300049 | − | 0.285377i | ||||
\(755\) | 54.3894 | 1.97943 | ||||||||
\(756\) | 0.0428842 | − | 0.314214i | 0.00155968 | − | 0.0114279i | ||||
\(757\) | 6.03229 | + | 10.4482i | 0.219247 | + | 0.379747i | 0.954578 | − | 0.297961i | \(-0.0963065\pi\) |
−0.735331 | + | 0.677708i | \(0.762973\pi\) | |||||||
\(758\) | 2.65542 | + | 4.59932i | 0.0964492 | + | 0.167055i | ||||
\(759\) | 12.5658 | − | 7.25488i | 0.456110 | − | 0.263335i | ||||
\(760\) | 14.8764i | 0.539625i | ||||||||
\(761\) | 8.96051 | − | 5.17335i | 0.324818 | − | 0.187534i | −0.328720 | − | 0.944427i | \(-0.606617\pi\) |
0.653538 | + | 0.756894i | \(0.273284\pi\) | |||||||
\(762\) | − | 2.32354i | − | 0.0841731i | ||||||
\(763\) | 0.801526 | + | 1.96132i | 0.0290172 | + | 0.0710044i | ||||
\(764\) | 1.20654 | + | 2.08979i | 0.0436512 | + | 0.0756060i | ||||
\(765\) | − | 0.205517i | − | 0.00743049i | ||||||
\(766\) | 14.7219 | + | 25.4991i | 0.531925 | + | 0.921321i | ||||
\(767\) | −2.68224 | − | 11.1174i | −0.0968501 | − | 0.401425i | ||||
\(768\) | −1.43329 | + | 2.48253i | −0.0517194 | + | 0.0895807i | ||||
\(769\) | 25.6321 | − | 14.7987i | 0.924316 | − | 0.533654i | 0.0393069 | − | 0.999227i | \(-0.487485\pi\) |
0.885010 | + | 0.465573i | \(0.154152\pi\) | |||||||
\(770\) | −24.9382 | − | 61.0232i | −0.898710 | − | 2.19912i | ||||
\(771\) | 15.3006 | − | 26.5015i | 0.551039 | − | 0.954427i | ||||
\(772\) | 0.331514 | + | 0.191399i | 0.0119314 | + | 0.00688862i | ||||
\(773\) | 33.5754i | 1.20762i | 0.797128 | + | 0.603811i | \(0.206352\pi\) | ||||
−0.797128 | + | 0.603811i | \(0.793648\pi\) | |||||||
\(774\) | 7.30985i | 0.262747i | ||||||||
\(775\) | 58.5354 | + | 33.7954i | 2.10265 | + | 1.21397i | ||||
\(776\) | −5.74653 | + | 9.95327i | −0.206288 | + | 0.357302i | ||||
\(777\) | 6.97494 | − | 9.00120i | 0.250225 | − | 0.322916i | ||||
\(778\) | 5.47510 | − | 3.16105i | 0.196292 | − | 0.113329i | ||||
\(779\) | 7.83964 | − | 13.5787i | 0.280884 | − | 0.486506i | ||||
\(780\) | 1.32803 | − | 1.26308i | 0.0475510 | − | 0.0452257i | ||||
\(781\) | −13.2706 | − | 22.9853i | −0.474859 | − | 0.822480i | ||||
\(782\) | − | 0.253707i | − | 0.00907256i | ||||||
\(783\) | 1.08299 | + | 1.87579i | 0.0387028 | + | 0.0670353i | ||||
\(784\) | 28.4958 | + | 7.92589i | 1.01771 | + | 0.283067i | ||||
\(785\) | − | 15.9303i | − | 0.568578i | ||||||
\(786\) | −7.49342 | + | 4.32633i | −0.267281 | + | 0.154315i | ||||
\(787\) | − | 21.9610i | − | 0.782824i | −0.920216 | − | 0.391412i | \(-0.871987\pi\) | ||
0.920216 | − | 0.391412i | \(-0.128013\pi\) | |||||||
\(788\) | 1.52539 | − | 0.880685i | 0.0543398 | − | 0.0313731i | ||||
\(789\) | 9.08377 | + | 15.7336i | 0.323391 | + | 0.560129i | ||||
\(790\) | −38.8651 | − | 67.3164i | −1.38276 | − | 2.39501i | ||||
\(791\) | −1.21168 | − | 0.938921i | −0.0430825 | − | 0.0333842i | ||||
\(792\) | −11.0464 | −0.392517 | ||||||||
\(793\) | 9.48142 | + | 9.96890i | 0.336695 | + | 0.354006i | ||||
\(794\) | 0.621427 | + | 1.07634i | 0.0220536 | + | 0.0381980i | ||||
\(795\) | 19.5698 | + | 11.2986i | 0.694069 | + | 0.400721i | ||||
\(796\) | 2.77476 | 0.0983488 | ||||||||
\(797\) | 1.40719 | − | 2.43732i | 0.0498451 | − | 0.0863343i | −0.840026 | − | 0.542546i | \(-0.817461\pi\) |
0.889871 | + | 0.456211i | \(0.150794\pi\) | |||||||
\(798\) | −0.667530 | + | 4.89102i | −0.0236303 | + | 0.173140i | ||||
\(799\) | −0.0397271 | − | 0.0229365i | −0.00140544 | − | 0.000811434i | ||||
\(800\) | 7.61460 | − | 4.39629i | 0.269217 | − | 0.155432i | ||||
\(801\) | 6.47777 | − | 3.73994i | 0.228881 | − | 0.132144i | ||||
\(802\) | 20.7356 | 0.732201 | ||||||||
\(803\) | −56.4530 | −1.99218 | ||||||||
\(804\) | −1.25942 | + | 0.727128i | −0.0444164 | + | 0.0256438i | ||||
\(805\) | 24.7116 | − | 31.8905i | 0.870970 | − | 1.12399i | ||||
\(806\) | −18.8325 | − | 19.8007i | −0.663346 | − | 0.697451i | ||||
\(807\) | −5.06111 | + | 8.76610i | −0.178160 | + | 0.308581i | ||||
\(808\) | −37.6784 | − | 21.7536i | −1.32552 | − | 0.765290i | ||||
\(809\) | −19.9724 | + | 34.5932i | −0.702192 | + | 1.21623i | 0.265503 | + | 0.964110i | \(0.414462\pi\) |
−0.967695 | + | 0.252122i | \(0.918871\pi\) | |||||||
\(810\) | 3.08727 | + | 5.34732i | 0.108476 | + | 0.187886i | ||||
\(811\) | − | 45.8322i | − | 1.60939i | −0.593691 | − | 0.804693i | \(-0.702330\pi\) | ||
0.593691 | − | 0.804693i | \(-0.297670\pi\) | |||||||
\(812\) | 0.635843 | − | 0.259848i | 0.0223137 | − | 0.00911889i | ||||
\(813\) | −22.9953 | − | 13.2763i | −0.806481 | − | 0.465622i | ||||
\(814\) | 21.8996 | + | 12.6437i | 0.767579 | + | 0.443162i | ||||
\(815\) | 79.4437 | 2.78279 | ||||||||
\(816\) | −0.102384 | + | 0.177334i | −0.00358414 | + | 0.00620792i | ||||
\(817\) | − | 6.43368i | − | 0.225086i | ||||||
\(818\) | 13.1902 | 0.461183 | ||||||||
\(819\) | −7.73778 | + | 5.57913i | −0.270380 | + | 0.194951i | ||||
\(820\) | −6.21953 | −0.217195 | ||||||||
\(821\) | − | 54.5859i | − | 1.90506i | −0.304443 | − | 0.952531i | \(-0.598470\pi\) | ||
0.304443 | − | 0.952531i | \(-0.401530\pi\) | |||||||
\(822\) | −11.6958 | + | 20.2578i | −0.407938 | + | 0.706570i | ||||
\(823\) | −50.0972 | −1.74628 | −0.873139 | − | 0.487471i | \(-0.837919\pi\) | ||||
−0.873139 | + | 0.487471i | \(0.837919\pi\) | |||||||
\(824\) | −15.5116 | − | 8.95565i | −0.540374 | − | 0.311985i | ||||
\(825\) | 45.3774 | + | 26.1986i | 1.57984 | + | 0.912120i | ||||
\(826\) | 1.65228 | − | 12.1063i | 0.0574900 | − | 0.421232i | ||||
\(827\) | − | 19.4771i | − | 0.677284i | −0.940915 | − | 0.338642i | \(-0.890033\pi\) | ||
0.940915 | − | 0.338642i | \(-0.109967\pi\) | |||||||
\(828\) | 0.215495 | + | 0.373248i | 0.00748896 | + | 0.0129713i | ||||
\(829\) | −7.40473 | + | 12.8254i | −0.257177 | + | 0.445444i | −0.965485 | − | 0.260460i | \(-0.916126\pi\) |
0.708308 | + | 0.705904i | \(0.249459\pi\) | |||||||
\(830\) | 18.5555 | + | 10.7130i | 0.644071 | + | 0.371855i | ||||
\(831\) | −14.6551 | + | 25.3833i | −0.508378 | + | 0.880537i | ||||
\(832\) | 26.1640 | − | 6.31248i | 0.907074 | − | 0.218846i | ||||
\(833\) | 0.326824 | + | 0.0909036i | 0.0113238 | + | 0.00314962i | ||||
\(834\) | −14.1910 | + | 8.19315i | −0.491393 | + | 0.283706i | ||||
\(835\) | −40.2558 | −1.39311 | ||||||||
\(836\) | −0.619821 | −0.0214370 | ||||||||
\(837\) | 4.50804 | − | 2.60272i | 0.155820 | − | 0.0899630i | ||||
\(838\) | 27.6258 | − | 15.9497i | 0.954316 | − | 0.550975i | ||||
\(839\) | −41.3739 | − | 23.8872i | −1.42839 | − | 0.824679i | −0.431393 | − | 0.902164i | \(-0.641978\pi\) |
−0.996994 | + | 0.0774846i | \(0.975311\pi\) | |||||||
\(840\) | −28.4319 | + | 11.6192i | −0.980995 | + | 0.400901i | ||||
\(841\) | 12.1543 | − | 21.0518i | 0.419113 | − | 0.725925i | ||||
\(842\) | 8.93539 | 0.307934 | ||||||||
\(843\) | −5.83989 | − | 3.37166i | −0.201136 | − | 0.116126i | ||||
\(844\) | −0.549889 | − | 0.952435i | −0.0189279 | − | 0.0327842i | ||||
\(845\) | −55.0616 | − | 2.76177i | −1.89418 | − | 0.0950076i | ||||
\(846\) | 1.37820 | 0.0473836 | ||||||||
\(847\) | −12.9407 | + | 5.28844i | −0.444647 | + | 0.181713i | ||||
\(848\) | −11.2574 | − | 19.4984i | −0.386580 | − | 0.669577i | ||||
\(849\) | −8.69346 | − | 15.0575i | −0.298359 | − | 0.516772i | ||||
\(850\) | 0.793437 | − | 0.458091i | 0.0272147 | − | 0.0157124i | ||||
\(851\) | 15.4759i | 0.530506i | ||||||||
\(852\) | 0.682744 | − | 0.394182i | 0.0233904 | − | 0.0135045i | ||||
\(853\) | 20.3132i | 0.695509i | 0.937586 | + | 0.347755i | \(0.113056\pi\) | ||||
−0.937586 | + | 0.347755i | \(0.886944\pi\) | |||||||
\(854\) | 5.56048 | + | 13.6064i | 0.190276 | + | 0.465600i | ||||
\(855\) | −2.71722 | − | 4.70637i | −0.0929271 | − | 0.160955i | ||||
\(856\) | − | 19.5989i | − | 0.669876i | ||||||
\(857\) | −3.72976 | − | 6.46014i | −0.127406 | − | 0.220674i | 0.795265 | − | 0.606262i | \(-0.207332\pi\) |
−0.922671 | + | 0.385588i | \(0.873999\pi\) | |||||||
\(858\) | −14.5992 | − | 15.3498i | −0.498408 | − | 0.524033i | ||||
\(859\) | −3.78123 | + | 6.54929i | −0.129014 | + | 0.223459i | −0.923295 | − | 0.384092i | \(-0.874515\pi\) |
0.794281 | + | 0.607551i | \(0.207848\pi\) | |||||||
\(860\) | −2.21015 | + | 1.27603i | −0.0753654 | + | 0.0435122i | ||||
\(861\) | 32.0747 | + | 4.37758i | 1.09310 | + | 0.149188i | ||||
\(862\) | −18.6696 | + | 32.3367i | −0.635890 | + | 1.10139i | ||||
\(863\) | 17.3688 | + | 10.0279i | 0.591239 | + | 0.341352i | 0.765587 | − | 0.643332i | \(-0.222448\pi\) |
−0.174348 | + | 0.984684i | \(0.555782\pi\) | |||||||
\(864\) | − | 0.677151i | − | 0.0230371i | ||||||
\(865\) | − | 74.6132i | − | 2.53693i | ||||||
\(866\) | −25.1736 | − | 14.5340i | −0.855434 | − | 0.493885i | ||||
\(867\) | 8.49883 | − | 14.7204i | 0.288635 | − | 0.499931i | ||||
\(868\) | −0.624487 | − | 1.52810i | −0.0211965 | − | 0.0518672i | ||||
\(869\) | −43.9940 | + | 25.3999i | −1.49239 | + | 0.861634i | ||||
\(870\) | −6.68696 | + | 11.5822i | −0.226709 | + | 0.392672i | ||||
\(871\) | 41.9575 | + | 12.3772i | 1.42167 | + | 0.419385i | ||||
\(872\) | 1.09610 | + | 1.89850i | 0.0371185 | + | 0.0642912i | ||||
\(873\) | − | 4.19848i | − | 0.142097i | ||||||
\(874\) | −3.35437 | − | 5.80993i | −0.113463 | − | 0.196524i | ||||
\(875\) | 88.7667 | + | 12.1149i | 3.00086 | + | 0.409560i | ||||
\(876\) | − | 1.67685i | − | 0.0566554i | ||||||
\(877\) | 24.4425 | − | 14.1119i | 0.825365 | − | 0.476525i | −0.0268979 | − | 0.999638i | \(-0.508563\pi\) |
0.852263 | + | 0.523113i | \(0.175230\pi\) | |||||||
\(878\) | 33.7870i | 1.14025i | ||||||||
\(879\) | −15.2346 | + | 8.79572i | −0.513852 | + | 0.296672i | ||||
\(880\) | −36.1545 | − | 62.6215i | −1.21877 | − | 2.11097i | ||||
\(881\) | −15.5671 | − | 26.9631i | −0.524470 | − | 0.908409i | −0.999594 | − | 0.0284903i | \(-0.990930\pi\) |
0.475124 | − | 0.879919i | \(-0.342403\pi\) | |||||||
\(882\) | −9.86913 | + | 2.54434i | −0.332311 | + | 0.0856722i | ||||
\(883\) | −48.8522 | −1.64401 | −0.822004 | − | 0.569482i | \(-0.807144\pi\) | ||||
−0.822004 | + | 0.569482i | \(0.807144\pi\) | |||||||
\(884\) | −0.0203595 | + | 0.00491205i | −0.000684764 | + | 0.000165210i | ||||
\(885\) | 6.72570 | + | 11.6492i | 0.226082 | + | 0.391585i | ||||
\(886\) | −4.35422 | − | 2.51391i | −0.146283 | − | 0.0844565i | ||||
\(887\) | 15.6735 | 0.526266 | 0.263133 | − | 0.964760i | \(-0.415244\pi\) | ||||
0.263133 | + | 0.964760i | \(0.415244\pi\) | |||||||
\(888\) | 5.89096 | − | 10.2035i | 0.197688 | − | 0.342405i | ||||
\(889\) | −3.90849 | + | 1.59727i | −0.131087 | + | 0.0535708i | ||||
\(890\) | 39.9973 | + | 23.0924i | 1.34071 | + | 0.774060i | ||||
\(891\) | 3.49469 | − | 2.01766i | 0.117076 | − | 0.0675941i | ||||
\(892\) | −0.235238 | + | 0.135815i | −0.00787635 | + | 0.00454741i | ||||
\(893\) | −1.21301 | −0.0405918 | ||||||||
\(894\) | −8.12404 | −0.271709 | ||||||||
\(895\) | −66.0324 | + | 38.1238i | −2.20722 | + | 1.27434i | ||||
\(896\) | 32.0416 | + | 4.37306i | 1.07044 | + | 0.146094i | ||||
\(897\) | 3.66815 | − | 12.4347i | 0.122476 | − | 0.415182i | ||||
\(898\) | 14.2798 | − | 24.7333i | 0.476523 | − | 0.825362i | ||||
\(899\) | 9.76430 | + | 5.63742i | 0.325657 | + | 0.188018i | ||||
\(900\) | −0.778190 | + | 1.34786i | −0.0259397 | + | 0.0449288i | ||||
\(901\) | −0.129113 | − | 0.223631i | −0.00430139 | − | 0.00745022i | ||||
\(902\) | 71.8875i | 2.39359i | ||||||||
\(903\) | 12.2961 | − | 5.02501i | 0.409188 | − | 0.167222i | ||||
\(904\) | −1.37352 | − | 0.793003i | −0.0456827 | − | 0.0263749i | ||||
\(905\) | −33.3751 | − | 19.2691i | −1.10942 | − | 0.640527i | ||||
\(906\) | 18.6731 | 0.620373 | ||||||||
\(907\) | 1.57527 | − | 2.72845i | 0.0523060 | − | 0.0905967i | −0.838687 | − | 0.544614i | \(-0.816676\pi\) |
0.890993 | + | 0.454017i | \(0.150010\pi\) | |||||||
\(908\) | 1.00101i | 0.0332197i | ||||||||
\(909\) | 15.8935 | 0.527153 | ||||||||
\(910\) | −53.7220 | − | 24.1521i | −1.78087 | − | 0.800633i | ||||
\(911\) | −1.18315 | −0.0391996 | −0.0195998 | − | 0.999808i | \(-0.506239\pi\) | ||||
−0.0195998 | + | 0.999808i | \(0.506239\pi\) | |||||||
\(912\) | 5.41462i | 0.179296i | ||||||||
\(913\) | 7.00140 | − | 12.1268i | 0.231713 | − | 0.401338i | ||||
\(914\) | −56.9872 | −1.88497 | ||||||||
\(915\) | −14.0139 | − | 8.09092i | −0.463285 | − | 0.267477i | ||||
\(916\) | 0.725603 | + | 0.418927i | 0.0239746 | + | 0.0138417i | ||||
\(917\) | 12.4286 | + | 9.63081i | 0.410429 | + | 0.318038i | ||||
\(918\) | − | 0.0705587i | − | 0.00232879i | ||||||
\(919\) | 2.56154 | + | 4.43672i | 0.0844974 | + | 0.146354i | 0.905177 | − | 0.425035i | \(-0.139738\pi\) |
−0.820680 | + | 0.571389i | \(0.806405\pi\) | |||||||
\(920\) | 20.8712 | − | 36.1500i | 0.688103 | − | 1.19183i | ||||
\(921\) | −0.0674292 | − | 0.0389302i | −0.00222187 | − | 0.00128280i | ||||
\(922\) | −11.1398 | + | 19.2947i | −0.366869 | + | 0.635436i | ||||
\(923\) | −22.7455 | − | 6.70977i | −0.748677 | − | 0.220855i | ||||
\(924\) | −0.484110 | − | 1.18461i | −0.0159261 | − | 0.0389707i | ||||
\(925\) | −48.3988 | + | 27.9431i | −1.59134 | + | 0.918763i | ||||
\(926\) | −10.1755 | −0.334387 | ||||||||
\(927\) | 6.54310 | 0.214904 | ||||||||
\(928\) | 1.27019 | − | 0.733346i | 0.0416961 | − | 0.0240733i | ||||
\(929\) | 27.2201 | − | 15.7155i | 0.893063 | − | 0.515610i | 0.0181195 | − | 0.999836i | \(-0.494232\pi\) |
0.874943 | + | 0.484226i | \(0.160899\pi\) | |||||||
\(930\) | 27.8351 | + | 16.0706i | 0.912748 | + | 0.526975i | ||||
\(931\) | 8.68618 | − | 2.23936i | 0.284678 | − | 0.0733922i | ||||
\(932\) | 1.33818 | − | 2.31779i | 0.0438335 | − | 0.0759219i | ||||
\(933\) | −30.1379 | −0.986670 | ||||||||
\(934\) | 18.3040 | + | 10.5678i | 0.598925 | + | 0.345790i | ||||
\(935\) | −0.414664 | − | 0.718218i | −0.0135609 | − | 0.0234883i | ||||
\(936\) | −7.15178 | + | 6.80206i | −0.233763 | + | 0.222332i | ||||
\(937\) | −1.86220 | −0.0608355 | −0.0304178 | − | 0.999537i | \(-0.509684\pi\) | ||||
−0.0304178 | + | 0.999537i | \(0.509684\pi\) | |||||||
\(938\) | 36.9435 | + | 28.6271i | 1.20625 | + | 0.934709i | ||||
\(939\) | −10.0024 | − | 17.3247i | −0.326417 | − | 0.565371i | ||||
\(940\) | 0.240583 | + | 0.416702i | 0.00784696 | + | 0.0135913i | ||||
\(941\) | 43.4248 | − | 25.0713i | 1.41561 | − | 0.817303i | 0.419700 | − | 0.907663i | \(-0.362135\pi\) |
0.995909 | + | 0.0903602i | \(0.0288018\pi\) | |||||||
\(942\) | − | 5.46924i | − | 0.178198i | ||||||
\(943\) | −38.1009 | + | 21.9975i | −1.24073 | + | 0.716339i | ||||
\(944\) | − | 13.4023i | − | 0.436208i | ||||||
\(945\) | 6.87256 | − | 8.86908i | 0.223565 | − | 0.288511i | ||||
\(946\) | 14.7488 | + | 25.5457i | 0.479525 | + | 0.830561i | ||||
\(947\) | 0 | 0.000321344i | 0 | 1.04423e-5i | −1.00000 | 5.22114e-6i | \(-0.999998\pi\) | |||
1.00000 | 5.22114e-6i | \(-1.66194e-6\pi\) | ||||||||
\(948\) | −0.754466 | − | 1.30677i | −0.0245039 | − | 0.0424420i | ||||
\(949\) | −36.5494 | + | 34.7621i | −1.18644 | + | 1.12843i | ||||
\(950\) | 12.1132 | − | 20.9807i | 0.393004 | − | 0.680704i | ||||
\(951\) | −20.7932 | + | 12.0050i | −0.674266 | + | 0.389288i | ||||
\(952\) | 0.347762 | + | 0.0474628i | 0.0112710 | + | 0.00153828i | ||||
\(953\) | −28.6176 | + | 49.5671i | −0.927015 | + | 1.60564i | −0.138727 | + | 0.990331i | \(0.544301\pi\) |
−0.788288 | + | 0.615306i | \(0.789032\pi\) | |||||||
\(954\) | 6.71875 | + | 3.87907i | 0.217528 | + | 0.125590i | ||||
\(955\) | 85.3767i | 2.76273i | ||||||||
\(956\) | − | 1.54036i | − | 0.0498188i | ||||||
\(957\) | 7.56941 | + | 4.37020i | 0.244684 | + | 0.141268i | ||||
\(958\) | 12.3226 | − | 21.3433i | 0.398125 | − | 0.689572i | ||||
\(959\) | 42.1161 | + | 5.74804i | 1.36000 | + | 0.185614i | ||||
\(960\) | −27.4158 | + | 15.8285i | −0.884840 | + | 0.510863i | ||||
\(961\) | −1.95175 | + | 3.38052i | −0.0629595 | + | 0.109049i | ||||
\(962\) | 21.9641 | − | 5.29918i | 0.708150 | − | 0.170852i | ||||
\(963\) | 3.57979 | + | 6.20038i | 0.115357 | + | 0.199805i | ||||
\(964\) | − | 1.78910i | − | 0.0576230i | ||||||
\(965\) | 6.77185 | + | 11.7292i | 0.217994 | + | 0.377576i | ||||
\(966\) | 8.48406 | − | 10.9487i | 0.272970 | − | 0.352270i | ||||
\(967\) | 13.9192i | 0.447610i | 0.974634 | + | 0.223805i | \(0.0718478\pi\) | ||||
−0.974634 | + | 0.223805i | \(0.928152\pi\) | |||||||
\(968\) | −12.5262 | + | 7.23200i | −0.402607 | + | 0.232445i | ||||
\(969\) | 0.0621014i | 0.00199498i | ||||||||
\(970\) | 22.4506 | − | 12.9619i | 0.720845 | − | 0.416180i | ||||
\(971\) | −10.4459 | − | 18.0928i | −0.335224 | − | 0.580625i | 0.648304 | − | 0.761382i | \(-0.275479\pi\) |
−0.983528 | + | 0.180757i | \(0.942145\pi\) | |||||||
\(972\) | 0.0599314 | + | 0.103804i | 0.00192230 | + | 0.00332952i | ||||
\(973\) | 23.5372 | + | 18.2387i | 0.754568 | + | 0.584707i | ||||
\(974\) | 37.0586 | 1.18743 | ||||||||
\(975\) | 45.5111 | − | 10.9803i | 1.45752 | − | 0.351650i | ||||
\(976\) | 8.06139 | + | 13.9627i | 0.258039 | + | 0.446936i | ||||
\(977\) | −7.43409 | − | 4.29208i | −0.237838 | − | 0.137316i | 0.376345 | − | 0.926480i | \(-0.377181\pi\) |
−0.614183 | + | 0.789164i | \(0.710514\pi\) | |||||||
\(978\) | 27.2748 | 0.872153 | ||||||||
\(979\) | 15.0918 | − | 26.1398i | 0.482338 | − | 0.835433i | ||||
\(980\) | −2.49207 | − | 2.53980i | −0.0796062 | − | 0.0811310i | ||||
\(981\) | −0.693532 | − | 0.400411i | −0.0221428 | − | 0.0127841i | ||||
\(982\) | 0.167350 | − | 0.0966193i | 0.00534034 | − | 0.00308325i | ||||
\(983\) | 2.72691 | − | 1.57438i | 0.0869750 | − | 0.0502150i | −0.455882 | − | 0.890040i | \(-0.650676\pi\) |
0.542857 | + | 0.839825i | \(0.317343\pi\) | |||||||
\(984\) | 33.4939 | 1.06775 | ||||||||
\(985\) | 62.3186 | 1.98563 | ||||||||
\(986\) | 0.132353 | − | 0.0764143i | 0.00421499 | − | 0.00243353i | ||||
\(987\) | −0.947418 | − | 2.31831i | −0.0301567 | − | 0.0737926i | ||||
\(988\) | −0.401291 | + | 0.381668i | −0.0127668 | + | 0.0121425i | ||||
\(989\) | −9.02625 | + | 15.6339i | −0.287018 | + | 0.497130i | ||||
\(990\) | 21.5781 | + | 12.4581i | 0.685798 | + | 0.395945i | ||||
\(991\) | −3.10422 | + | 5.37666i | −0.0986088 | + | 0.170795i | −0.911109 | − | 0.412165i | \(-0.864773\pi\) |
0.812500 | + | 0.582961i | \(0.198106\pi\) | |||||||
\(992\) | −1.76243 | − | 3.05262i | −0.0559572 | − | 0.0969208i | ||||
\(993\) | − | 8.94260i | − | 0.283785i | ||||||
\(994\) | −20.0274 | − | 15.5190i | −0.635230 | − | 0.492233i | ||||
\(995\) | 85.0204 | + | 49.0865i | 2.69533 | + | 1.55615i | ||||
\(996\) | 0.360207 | + | 0.207966i | 0.0114136 | + | 0.00658964i | ||||
\(997\) | −22.5169 | −0.713116 | −0.356558 | − | 0.934273i | \(-0.616050\pi\) | ||||
−0.356558 | + | 0.934273i | \(0.616050\pi\) | |||||||
\(998\) | 3.33888 | − | 5.78311i | 0.105690 | − | 0.183061i | ||||
\(999\) | 4.30401i | 0.136173i |
(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 | 273.2.t.c.205.4 | yes | 12 | |
3.2 | odd | 2 | 819.2.bm.e.478.3 | 12 | |||
7.4 | even | 3 | 273.2.bl.c.88.3 | yes | 12 | ||
13.4 | even | 6 | 273.2.bl.c.121.3 | yes | 12 | ||
21.11 | odd | 6 | 819.2.do.f.361.4 | 12 | |||
39.17 | odd | 6 | 819.2.do.f.667.4 | 12 | |||
91.4 | even | 6 | inner | 273.2.t.c.4.3 | ✓ | 12 | |
273.95 | odd | 6 | 819.2.bm.e.550.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.c.4.3 | ✓ | 12 | 91.4 | even | 6 | inner | |
273.2.t.c.205.4 | yes | 12 | 1.1 | even | 1 | trivial | |
273.2.bl.c.88.3 | yes | 12 | 7.4 | even | 3 | ||
273.2.bl.c.121.3 | yes | 12 | 13.4 | even | 6 | ||
819.2.bm.e.478.3 | 12 | 3.2 | odd | 2 | |||
819.2.bm.e.550.4 | 12 | 273.95 | odd | 6 | |||
819.2.do.f.361.4 | 12 | 21.11 | odd | 6 | |||
819.2.do.f.667.4 | 12 | 39.17 | odd | 6 |