Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [798,2,Mod(457,798)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(798, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("798.457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 798.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.37206208130\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 457.3 | ||
Root | \(-2.06288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 798.457 |
Dual form | 798.2.j.l.571.3 |
$q$-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 \(\left(\mathbb{Z}/798\mathbb{Z}\right)^\times\).
\(n\) | \(115\) | \(211\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.574618 | − | 0.995268i | 0.256977 | − | 0.445098i | −0.708453 | − | 0.705758i | \(-0.750607\pi\) |
0.965431 | + | 0.260660i | \(0.0839401\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.00953166 | + | 2.64573i | 0.00360263 | + | 0.999994i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.574618 | − | 0.995268i | −0.181710 | − | 0.314732i | ||||
\(11\) | 1.08415 | + | 1.87780i | 0.326884 | + | 0.566179i | 0.981892 | − | 0.189443i | \(-0.0606682\pi\) |
−0.655008 | + | 0.755622i | \(0.727335\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 2.29847 | 0.637482 | 0.318741 | − | 0.947842i | \(-0.396740\pi\) | ||||
0.318741 | + | 0.947842i | \(0.396740\pi\) | |||||||
\(14\) | 2.29604 | + | 1.31461i | 0.613642 | + | 0.351345i | ||||
\(15\) | 1.14924 | 0.296732 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.49840 | + | 4.32735i | 0.605950 | + | 1.04954i | 0.991901 | + | 0.127017i | \(0.0405402\pi\) |
−0.385951 | + | 0.922519i | \(0.626126\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | ||||
\(20\) | −1.14924 | −0.256977 | ||||||||
\(21\) | −2.28651 | + | 1.33112i | −0.498957 | + | 0.290475i | ||||
\(22\) | 2.16830 | 0.462283 | ||||||||
\(23\) | 3.45783 | − | 5.98914i | 0.721008 | − | 1.24882i | −0.239588 | − | 0.970875i | \(-0.577012\pi\) |
0.960596 | − | 0.277948i | \(-0.0896544\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 1.83963 | + | 3.18633i | 0.367925 | + | 0.637266i | ||||
\(26\) | 1.14924 | − | 1.99054i | 0.225384 | − | 0.390376i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.28651 | − | 1.33112i | 0.432109 | − | 0.251558i | ||||
\(29\) | 3.76643 | 0.699409 | 0.349704 | − | 0.936860i | \(-0.386282\pi\) | ||||
0.349704 | + | 0.936860i | \(0.386282\pi\) | |||||||
\(30\) | 0.574618 | − | 0.995268i | 0.104911 | − | 0.181710i | ||||
\(31\) | −2.19283 | − | 3.79808i | −0.393843 | − | 0.682156i | 0.599110 | − | 0.800667i | \(-0.295521\pi\) |
−0.992953 | + | 0.118511i | \(0.962188\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −1.08415 | + | 1.87780i | −0.188726 | + | 0.326884i | ||||
\(34\) | 4.99679 | 0.856943 | ||||||||
\(35\) | 2.63869 | + | 1.51080i | 0.446020 | + | 0.255372i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.330096 | + | 0.571742i | −0.0542674 | + | 0.0939938i | −0.891883 | − | 0.452266i | \(-0.850616\pi\) |
0.837616 | + | 0.546260i | \(0.183949\pi\) | |||||||
\(38\) | 0.500000 | + | 0.866025i | 0.0811107 | + | 0.140488i | ||||
\(39\) | 1.14924 | + | 1.99054i | 0.184025 | + | 0.318741i | ||||
\(40\) | −0.574618 | + | 0.995268i | −0.0908552 | + | 0.157366i | ||||
\(41\) | 0.806583 | 0.125967 | 0.0629836 | − | 0.998015i | \(-0.479938\pi\) | ||||
0.0629836 | + | 0.998015i | \(0.479938\pi\) | |||||||
\(42\) | 0.00953166 | + | 2.64573i | 0.00147077 | + | 0.408246i | ||||
\(43\) | −2.08397 | −0.317802 | −0.158901 | − | 0.987295i | \(-0.550795\pi\) | ||||
−0.158901 | + | 0.987295i | \(0.550795\pi\) | |||||||
\(44\) | 1.08415 | − | 1.87780i | 0.163442 | − | 0.283089i | ||||
\(45\) | 0.574618 | + | 0.995268i | 0.0856591 | + | 0.148366i | ||||
\(46\) | −3.45783 | − | 5.98914i | −0.509830 | − | 0.883051i | ||||
\(47\) | 1.86113 | − | 3.22356i | 0.271473 | − | 0.470205i | −0.697766 | − | 0.716326i | \(-0.745823\pi\) |
0.969239 | + | 0.246120i | \(0.0791559\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.99982 | + | 0.0504365i | −0.999974 | + | 0.00720521i | ||||
\(50\) | 3.67925 | 0.520325 | ||||||||
\(51\) | −2.49840 | + | 4.32735i | −0.349845 | + | 0.605950i | ||||
\(52\) | −1.14924 | − | 1.99054i | −0.159370 | − | 0.276038i | ||||
\(53\) | 5.63567 | + | 9.76126i | 0.774118 | + | 1.34081i | 0.935289 | + | 0.353886i | \(0.115140\pi\) |
−0.161170 | + | 0.986927i | \(0.551527\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 2.49189 | 0.336006 | ||||||||
\(56\) | −0.00953166 | − | 2.64573i | −0.00127372 | − | 0.353551i | ||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 1.88322 | − | 3.26183i | 0.247278 | − | 0.428299i | ||||
\(59\) | −5.21331 | − | 9.02972i | −0.678715 | − | 1.17557i | −0.975368 | − | 0.220584i | \(-0.929204\pi\) |
0.296653 | − | 0.954985i | \(-0.404130\pi\) | |||||||
\(60\) | −0.574618 | − | 0.995268i | −0.0741829 | − | 0.128489i | ||||
\(61\) | −1.28811 | + | 2.23107i | −0.164926 | + | 0.285660i | −0.936629 | − | 0.350323i | \(-0.886072\pi\) |
0.771703 | + | 0.635983i | \(0.219405\pi\) | |||||||
\(62\) | −4.38565 | −0.556978 | ||||||||
\(63\) | −2.29604 | − | 1.31461i | −0.289274 | − | 0.165626i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.32075 | − | 2.28760i | 0.163818 | − | 0.283742i | ||||
\(66\) | 1.08415 | + | 1.87780i | 0.133450 | + | 0.231142i | ||||
\(67\) | −4.44284 | − | 7.69523i | −0.542779 | − | 0.940121i | −0.998743 | − | 0.0501231i | \(-0.984039\pi\) |
0.455964 | − | 0.889998i | \(-0.349295\pi\) | |||||||
\(68\) | 2.49840 | − | 4.32735i | 0.302975 | − | 0.524768i | ||||
\(69\) | 6.91567 | 0.832549 | ||||||||
\(70\) | 2.62774 | − | 1.52977i | 0.314075 | − | 0.182843i | ||||
\(71\) | −0.323591 | −0.0384031 | −0.0192016 | − | 0.999816i | \(-0.506112\pi\) | ||||
−0.0192016 | + | 0.999816i | \(0.506112\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 2.36415 | + | 4.09483i | 0.276703 | + | 0.479264i | 0.970563 | − | 0.240846i | \(-0.0774248\pi\) |
−0.693860 | + | 0.720110i | \(0.744091\pi\) | |||||||
\(74\) | 0.330096 | + | 0.571742i | 0.0383728 | + | 0.0664637i | ||||
\(75\) | −1.83963 | + | 3.18633i | −0.212422 | + | 0.367925i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −4.95783 | + | 2.88627i | −0.564998 | + | 0.328921i | ||||
\(78\) | 2.29847 | 0.260251 | ||||||||
\(79\) | 3.79604 | − | 6.57493i | 0.427088 | − | 0.739738i | −0.569525 | − | 0.821974i | \(-0.692873\pi\) |
0.996613 | + | 0.0822363i | \(0.0262062\pi\) | |||||||
\(80\) | 0.574618 | + | 0.995268i | 0.0642443 | + | 0.111274i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.403292 | − | 0.698521i | 0.0445361 | − | 0.0771388i | ||||
\(83\) | 3.17435 | 0.348431 | 0.174215 | − | 0.984708i | \(-0.444261\pi\) | ||||
0.174215 | + | 0.984708i | \(0.444261\pi\) | |||||||
\(84\) | 2.29604 | + | 1.31461i | 0.250518 | + | 0.143436i | ||||
\(85\) | 5.74250 | 0.622861 | ||||||||
\(86\) | −1.04198 | + | 1.80477i | −0.112360 | + | 0.194613i | ||||
\(87\) | 1.88322 | + | 3.26183i | 0.201902 | + | 0.349704i | ||||
\(88\) | −1.08415 | − | 1.87780i | −0.115571 | − | 0.200174i | ||||
\(89\) | −6.18879 | + | 10.7193i | −0.656010 | + | 1.13624i | 0.325630 | + | 0.945497i | \(0.394424\pi\) |
−0.981640 | + | 0.190745i | \(0.938910\pi\) | |||||||
\(90\) | 1.14924 | 0.121140 | ||||||||
\(91\) | 0.0219083 | + | 6.08115i | 0.00229661 | + | 0.637478i | ||||
\(92\) | −6.91567 | −0.721008 | ||||||||
\(93\) | 2.19283 | − | 3.79808i | 0.227385 | − | 0.393843i | ||||
\(94\) | −1.86113 | − | 3.22356i | −0.191960 | − | 0.332485i | ||||
\(95\) | 0.574618 | + | 0.995268i | 0.0589546 | + | 0.102112i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −5.91567 | −0.600645 | −0.300323 | − | 0.953838i | \(-0.597094\pi\) | ||||
−0.300323 | + | 0.953838i | \(0.597094\pi\) | |||||||
\(98\) | −3.45623 | + | 6.08724i | −0.349132 | + | 0.614904i | ||||
\(99\) | −2.16830 | −0.217922 | ||||||||
\(100\) | 1.83963 | − | 3.18633i | 0.183963 | − | 0.318633i | ||||
\(101\) | 6.43414 | + | 11.1443i | 0.640221 | + | 1.10890i | 0.985383 | + | 0.170352i | \(0.0544905\pi\) |
−0.345162 | + | 0.938543i | \(0.612176\pi\) | |||||||
\(102\) | 2.49840 | + | 4.32735i | 0.247378 | + | 0.428471i | ||||
\(103\) | −3.47791 | + | 6.02392i | −0.342689 | + | 0.593554i | −0.984931 | − | 0.172947i | \(-0.944671\pi\) |
0.642242 | + | 0.766502i | \(0.278004\pi\) | |||||||
\(104\) | −2.29847 | −0.225384 | ||||||||
\(105\) | 0.0109541 | + | 3.04058i | 0.00106901 | + | 0.296730i | ||||
\(106\) | 11.2713 | 1.09477 | ||||||||
\(107\) | 6.19933 | − | 10.7376i | 0.599312 | − | 1.03804i | −0.393611 | − | 0.919277i | \(-0.628774\pi\) |
0.992923 | − | 0.118762i | \(-0.0378924\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −9.02841 | − | 15.6377i | −0.864765 | − | 1.49782i | −0.867280 | − | 0.497820i | \(-0.834134\pi\) |
0.00251502 | − | 0.999997i | \(-0.499199\pi\) | |||||||
\(110\) | 1.24595 | − | 2.15804i | 0.118796 | − | 0.205761i | ||||
\(111\) | −0.660191 | −0.0626626 | ||||||||
\(112\) | −2.29604 | − | 1.31461i | −0.216955 | − | 0.124219i | ||||
\(113\) | −8.63792 | −0.812587 | −0.406294 | − | 0.913743i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913743i | \(0.633179\pi\) | |||||||
\(114\) | −0.500000 | + | 0.866025i | −0.0468293 | + | 0.0811107i | ||||
\(115\) | −3.97387 | − | 6.88295i | −0.370565 | − | 0.641838i | ||||
\(116\) | −1.88322 | − | 3.26183i | −0.174852 | − | 0.302853i | ||||
\(117\) | −1.14924 | + | 1.99054i | −0.106247 | + | 0.184025i | ||||
\(118\) | −10.4266 | −0.959848 | ||||||||
\(119\) | −11.4252 | + | 6.65134i | −1.04735 | + | 0.609727i | ||||
\(120\) | −1.14924 | −0.104911 | ||||||||
\(121\) | 3.14924 | − | 5.45464i | 0.286294 | − | 0.495876i | ||||
\(122\) | 1.28811 | + | 2.23107i | 0.116620 | + | 0.201992i | ||||
\(123\) | 0.403292 | + | 0.698521i | 0.0363636 | + | 0.0629836i | ||||
\(124\) | −2.19283 | + | 3.79808i | −0.196922 | + | 0.341078i | ||||
\(125\) | 9.97452 | 0.892148 | ||||||||
\(126\) | −2.28651 | + | 1.33112i | −0.203698 | + | 0.118586i | ||||
\(127\) | −13.8683 | −1.23061 | −0.615305 | − | 0.788289i | \(-0.710967\pi\) | ||||
−0.615305 | + | 0.788289i | \(0.710967\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −1.04198 | − | 1.80477i | −0.0917416 | − | 0.158901i | ||||
\(130\) | −1.32075 | − | 2.28760i | −0.115837 | − | 0.200636i | ||||
\(131\) | −6.10565 | + | 10.5753i | −0.533453 | + | 0.923968i | 0.465784 | + | 0.884899i | \(0.345773\pi\) |
−0.999237 | + | 0.0390690i | \(0.987561\pi\) | |||||||
\(132\) | 2.16830 | 0.188726 | ||||||||
\(133\) | −2.29604 | − | 1.31461i | −0.199092 | − | 0.113991i | ||||
\(134\) | −8.88568 | −0.767606 | ||||||||
\(135\) | −0.574618 | + | 0.995268i | −0.0494553 | + | 0.0856591i | ||||
\(136\) | −2.49840 | − | 4.32735i | −0.214236 | − | 0.371067i | ||||
\(137\) | −5.54038 | − | 9.59622i | −0.473347 | − | 0.819860i | 0.526188 | − | 0.850368i | \(-0.323621\pi\) |
−0.999535 | + | 0.0305079i | \(0.990288\pi\) | |||||||
\(138\) | 3.45783 | − | 5.98914i | 0.294350 | − | 0.509830i | ||||
\(139\) | −11.0175 | −0.934494 | −0.467247 | − | 0.884127i | \(-0.654754\pi\) | ||||
−0.467247 | + | 0.884127i | \(0.654754\pi\) | |||||||
\(140\) | −0.0109541 | − | 3.04058i | −0.000925793 | − | 0.256976i | ||||
\(141\) | 3.72225 | 0.313470 | ||||||||
\(142\) | −0.161795 | + | 0.280238i | −0.0135776 | + | 0.0235170i | ||||
\(143\) | 2.49189 | + | 4.31608i | 0.208382 | + | 0.360929i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 2.16426 | − | 3.74861i | 0.179732 | − | 0.311305i | ||||
\(146\) | 4.72830 | 0.391317 | ||||||||
\(147\) | −3.54359 | − | 6.03680i | −0.292270 | − | 0.497907i | ||||
\(148\) | 0.660191 | 0.0542674 | ||||||||
\(149\) | 10.6085 | − | 18.3744i | 0.869082 | − | 1.50529i | 0.00614520 | − | 0.999981i | \(-0.498044\pi\) |
0.862936 | − | 0.505312i | \(-0.168623\pi\) | |||||||
\(150\) | 1.83963 | + | 3.18633i | 0.150205 | + | 0.260163i | ||||
\(151\) | −4.70093 | − | 8.14226i | −0.382557 | − | 0.662608i | 0.608870 | − | 0.793270i | \(-0.291623\pi\) |
−0.991427 | + | 0.130662i | \(0.958290\pi\) | |||||||
\(152\) | 0.500000 | − | 0.866025i | 0.0405554 | − | 0.0702439i | ||||
\(153\) | −4.99679 | −0.403967 | ||||||||
\(154\) | 0.0206675 | + | 5.73675i | 0.00166543 | + | 0.462280i | ||||
\(155\) | −5.04015 | −0.404835 | ||||||||
\(156\) | 1.14924 | − | 1.99054i | 0.0920126 | − | 0.159370i | ||||
\(157\) | −3.07361 | − | 5.32364i | −0.245300 | − | 0.424873i | 0.716916 | − | 0.697160i | \(-0.245553\pi\) |
−0.962216 | + | 0.272287i | \(0.912220\pi\) | |||||||
\(158\) | −3.79604 | − | 6.57493i | −0.301997 | − | 0.523074i | ||||
\(159\) | −5.63567 | + | 9.76126i | −0.446937 | + | 0.774118i | ||||
\(160\) | 1.14924 | 0.0908552 | ||||||||
\(161\) | 15.8786 | + | 9.09142i | 1.25141 | + | 0.716505i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.30397 | − | 7.45469i | 0.337113 | − | 0.583896i | −0.646776 | − | 0.762680i | \(-0.723883\pi\) |
0.983888 | + | 0.178784i | \(0.0572163\pi\) | |||||||
\(164\) | −0.403292 | − | 0.698521i | −0.0314918 | − | 0.0545454i | ||||
\(165\) | 1.24595 | + | 2.15804i | 0.0969967 | + | 0.168003i | ||||
\(166\) | 1.58718 | − | 2.74907i | 0.123189 | − | 0.213369i | ||||
\(167\) | 11.9749 | 0.926644 | 0.463322 | − | 0.886190i | \(-0.346657\pi\) | ||||
0.463322 | + | 0.886190i | \(0.346657\pi\) | |||||||
\(168\) | 2.28651 | − | 1.33112i | 0.176408 | − | 0.102698i | ||||
\(169\) | −7.71702 | −0.593617 | ||||||||
\(170\) | 2.87125 | − | 4.97315i | 0.220215 | − | 0.381423i | ||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 1.04198 | + | 1.80477i | 0.0794506 | + | 0.137612i | ||||
\(173\) | −4.05092 | + | 7.01641i | −0.307986 | + | 0.533448i | −0.977922 | − | 0.208972i | \(-0.932988\pi\) |
0.669936 | + | 0.742419i | \(0.266322\pi\) | |||||||
\(174\) | 3.76643 | 0.285532 | ||||||||
\(175\) | −8.41264 | + | 4.89754i | −0.635936 | + | 0.370219i | ||||
\(176\) | −2.16830 | −0.163442 | ||||||||
\(177\) | 5.21331 | − | 9.02972i | 0.391856 | − | 0.678715i | ||||
\(178\) | 6.18879 | + | 10.7193i | 0.463869 | + | 0.803445i | ||||
\(179\) | 3.42378 | + | 5.93016i | 0.255905 | + | 0.443241i | 0.965141 | − | 0.261731i | \(-0.0842932\pi\) |
−0.709236 | + | 0.704971i | \(0.750960\pi\) | |||||||
\(180\) | 0.574618 | − | 0.995268i | 0.0428295 | − | 0.0741829i | ||||
\(181\) | −16.5905 | −1.23316 | −0.616582 | − | 0.787291i | \(-0.711483\pi\) | ||||
−0.616582 | + | 0.787291i | \(0.711483\pi\) | |||||||
\(182\) | 5.27739 | + | 3.02160i | 0.391186 | + | 0.223976i | ||||
\(183\) | −2.57622 | −0.190440 | ||||||||
\(184\) | −3.45783 | + | 5.98914i | −0.254915 | + | 0.441526i | ||||
\(185\) | 0.379358 | + | 0.657067i | 0.0278910 | + | 0.0483086i | ||||
\(186\) | −2.19283 | − | 3.79808i | −0.160786 | − | 0.278489i | ||||
\(187\) | −5.41727 | + | 9.38299i | −0.396150 | + | 0.686152i | ||||
\(188\) | −3.72225 | −0.271473 | ||||||||
\(189\) | −0.00953166 | − | 2.64573i | −0.000693326 | − | 0.192449i | ||||
\(190\) | 1.14924 | 0.0833744 | ||||||||
\(191\) | −7.94509 | + | 13.7613i | −0.574887 | + | 0.995733i | 0.421167 | + | 0.906983i | \(0.361621\pi\) |
−0.996054 | + | 0.0887501i | \(0.971713\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −3.24838 | − | 5.62636i | −0.233824 | − | 0.404994i | 0.725107 | − | 0.688637i | \(-0.241790\pi\) |
−0.958930 | + | 0.283642i | \(0.908457\pi\) | |||||||
\(194\) | −2.95783 | + | 5.12312i | −0.212360 | + | 0.367819i | ||||
\(195\) | 2.64149 | 0.189161 | ||||||||
\(196\) | 3.54359 | + | 6.03680i | 0.253113 | + | 0.431200i | ||||
\(197\) | 1.06491 | 0.0758713 | 0.0379357 | − | 0.999280i | \(-0.487922\pi\) | ||||
0.0379357 | + | 0.999280i | \(0.487922\pi\) | |||||||
\(198\) | −1.08415 | + | 1.87780i | −0.0770472 | + | 0.133450i | ||||
\(199\) | −11.7959 | − | 20.4310i | −0.836186 | − | 1.44832i | −0.893061 | − | 0.449936i | \(-0.851447\pi\) |
0.0568749 | − | 0.998381i | \(-0.481886\pi\) | |||||||
\(200\) | −1.83963 | − | 3.18633i | −0.130081 | − | 0.225307i | ||||
\(201\) | 4.44284 | − | 7.69523i | 0.313374 | − | 0.542779i | ||||
\(202\) | 12.8683 | 0.905409 | ||||||||
\(203\) | 0.0359003 | + | 9.96498i | 0.00251971 | + | 0.699404i | ||||
\(204\) | 4.99679 | 0.349845 | ||||||||
\(205\) | 0.463478 | − | 0.802767i | 0.0323707 | − | 0.0560677i | ||||
\(206\) | 3.47791 | + | 6.02392i | 0.242317 | + | 0.419706i | ||||
\(207\) | 3.45783 | + | 5.98914i | 0.240336 | + | 0.416274i | ||||
\(208\) | −1.14924 | + | 1.99054i | −0.0796852 | + | 0.138019i | ||||
\(209\) | −2.16830 | −0.149984 | ||||||||
\(210\) | 2.63869 | + | 1.51080i | 0.182087 | + | 0.104255i | ||||
\(211\) | 17.8699 | 1.23022 | 0.615109 | − | 0.788442i | \(-0.289112\pi\) | ||||
0.615109 | + | 0.788442i | \(0.289112\pi\) | |||||||
\(212\) | 5.63567 | − | 9.76126i | 0.387059 | − | 0.670406i | ||||
\(213\) | −0.161795 | − | 0.280238i | −0.0110860 | − | 0.0192016i | ||||
\(214\) | −6.19933 | − | 10.7376i | −0.423777 | − | 0.734004i | ||||
\(215\) | −1.19749 | + | 2.07411i | −0.0816679 | + | 0.141453i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 10.0278 | − | 5.83783i | 0.680733 | − | 0.396298i | ||||
\(218\) | −18.0568 | −1.22296 | ||||||||
\(219\) | −2.36415 | + | 4.09483i | −0.159755 | + | 0.276703i | ||||
\(220\) | −1.24595 | − | 2.15804i | −0.0840016 | − | 0.145495i | ||||
\(221\) | 5.74250 | + | 9.94630i | 0.386282 | + | 0.669060i | ||||
\(222\) | −0.330096 | + | 0.571742i | −0.0221546 | + | 0.0383728i | ||||
\(223\) | 4.44605 | 0.297729 | 0.148865 | − | 0.988858i | \(-0.452438\pi\) | ||||
0.148865 | + | 0.988858i | \(0.452438\pi\) | |||||||
\(224\) | −2.28651 | + | 1.33112i | −0.152774 | + | 0.0889393i | ||||
\(225\) | −3.67925 | −0.245284 | ||||||||
\(226\) | −4.31896 | + | 7.48066i | −0.287293 | + | 0.497606i | ||||
\(227\) | −10.0469 | − | 17.4017i | −0.666835 | − | 1.15499i | −0.978784 | − | 0.204894i | \(-0.934315\pi\) |
0.311949 | − | 0.950099i | \(-0.399018\pi\) | |||||||
\(228\) | 0.500000 | + | 0.866025i | 0.0331133 | + | 0.0573539i | ||||
\(229\) | −8.97773 | + | 15.5499i | −0.593265 | + | 1.02757i | 0.400524 | + | 0.916286i | \(0.368828\pi\) |
−0.993789 | + | 0.111279i | \(0.964505\pi\) | |||||||
\(230\) | −7.94774 | −0.524059 | ||||||||
\(231\) | −4.97850 | − | 2.85047i | −0.327561 | − | 0.187547i | ||||
\(232\) | −3.76643 | −0.247278 | ||||||||
\(233\) | −5.12697 | + | 8.88016i | −0.335879 | + | 0.581759i | −0.983653 | − | 0.180073i | \(-0.942367\pi\) |
0.647775 | + | 0.761832i | \(0.275700\pi\) | |||||||
\(234\) | 1.14924 | + | 1.99054i | 0.0751280 | + | 0.130125i | ||||
\(235\) | −2.13887 | − | 3.70464i | −0.139525 | − | 0.241664i | ||||
\(236\) | −5.21331 | + | 9.02972i | −0.339358 | + | 0.587785i | ||||
\(237\) | 7.59208 | 0.493158 | ||||||||
\(238\) | 0.0476277 | + | 13.2202i | 0.00308724 | + | 0.856937i | ||||
\(239\) | 1.73965 | 0.112529 | 0.0562644 | − | 0.998416i | \(-0.482081\pi\) | ||||
0.0562644 | + | 0.998416i | \(0.482081\pi\) | |||||||
\(240\) | −0.574618 | + | 0.995268i | −0.0370915 | + | 0.0642443i | ||||
\(241\) | 10.4246 | + | 18.0560i | 0.671508 | + | 1.16309i | 0.977476 | + | 0.211044i | \(0.0676865\pi\) |
−0.305968 | + | 0.952042i | \(0.598980\pi\) | |||||||
\(242\) | −3.14924 | − | 5.45464i | −0.202441 | − | 0.350637i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 2.57622 | 0.164926 | ||||||||
\(245\) | −3.97203 | + | 6.99568i | −0.253764 | + | 0.446938i | ||||
\(246\) | 0.806583 | 0.0514259 | ||||||||
\(247\) | −1.14924 | + | 1.99054i | −0.0731242 | + | 0.126655i | ||||
\(248\) | 2.19283 | + | 3.79808i | 0.139245 | + | 0.241179i | ||||
\(249\) | 1.58718 | + | 2.74907i | 0.100583 | + | 0.174215i | ||||
\(250\) | 4.98726 | − | 8.63819i | 0.315422 | − | 0.546327i | ||||
\(251\) | 3.19663 | 0.201769 | 0.100885 | − | 0.994898i | \(-0.467833\pi\) | ||||
0.100885 | + | 0.994898i | \(0.467833\pi\) | |||||||
\(252\) | 0.00953166 | + | 2.64573i | 0.000600438 | + | 0.166666i | ||||
\(253\) | 14.9952 | 0.942743 | ||||||||
\(254\) | −6.93414 | + | 12.0103i | −0.435087 | + | 0.753592i | ||||
\(255\) | 2.87125 | + | 4.97315i | 0.179805 | + | 0.311431i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.51095 | − | 13.0094i | 0.468520 | − | 0.811501i | −0.530832 | − | 0.847477i | \(-0.678121\pi\) |
0.999353 | + | 0.0359757i | \(0.0114539\pi\) | |||||||
\(258\) | −2.08397 | −0.129742 | ||||||||
\(259\) | −1.51582 | − | 0.867895i | −0.0941887 | − | 0.0539284i | ||||
\(260\) | −2.64149 | −0.163818 | ||||||||
\(261\) | −1.88322 | + | 3.26183i | −0.116568 | + | 0.201902i | ||||
\(262\) | 6.10565 | + | 10.5753i | 0.377208 | + | 0.653344i | ||||
\(263\) | −5.33802 | − | 9.24573i | −0.329157 | − | 0.570116i | 0.653188 | − | 0.757196i | \(-0.273431\pi\) |
−0.982345 | + | 0.187080i | \(0.940098\pi\) | |||||||
\(264\) | 1.08415 | − | 1.87780i | 0.0667248 | − | 0.115571i | ||||
\(265\) | 12.9534 | 0.795723 | ||||||||
\(266\) | −2.28651 | + | 1.33112i | −0.140195 | + | 0.0816163i | ||||
\(267\) | −12.3776 | −0.757495 | ||||||||
\(268\) | −4.44284 | + | 7.69523i | −0.271390 | + | 0.470061i | ||||
\(269\) | 1.62453 | + | 2.81377i | 0.0990494 | + | 0.171559i | 0.911291 | − | 0.411762i | \(-0.135086\pi\) |
−0.812242 | + | 0.583321i | \(0.801753\pi\) | |||||||
\(270\) | 0.574618 | + | 0.995268i | 0.0349702 | + | 0.0605701i | ||||
\(271\) | −9.01746 | + | 15.6187i | −0.547772 | + | 0.948768i | 0.450655 | + | 0.892698i | \(0.351190\pi\) |
−0.998427 | + | 0.0560702i | \(0.982143\pi\) | |||||||
\(272\) | −4.99679 | −0.302975 | ||||||||
\(273\) | −5.25548 | + | 3.05955i | −0.318076 | + | 0.185172i | ||||
\(274\) | −11.0808 | −0.669413 | ||||||||
\(275\) | −3.98886 | + | 6.90892i | −0.240538 | + | 0.416623i | ||||
\(276\) | −3.45783 | − | 5.98914i | −0.208137 | − | 0.360504i | ||||
\(277\) | −11.1420 | − | 19.2984i | −0.669455 | − | 1.15953i | −0.978057 | − | 0.208339i | \(-0.933194\pi\) |
0.308601 | − | 0.951192i | \(-0.400139\pi\) | |||||||
\(278\) | −5.50876 | + | 9.54145i | −0.330393 | + | 0.572258i | ||||
\(279\) | 4.38565 | 0.262562 | ||||||||
\(280\) | −2.63869 | − | 1.51080i | −0.157692 | − | 0.0902876i | ||||
\(281\) | 7.10790 | 0.424022 | 0.212011 | − | 0.977267i | \(-0.431999\pi\) | ||||
0.212011 | + | 0.977267i | \(0.431999\pi\) | |||||||
\(282\) | 1.86113 | − | 3.22356i | 0.110828 | − | 0.191960i | ||||
\(283\) | 7.87368 | + | 13.6376i | 0.468042 | + | 0.810672i | 0.999333 | − | 0.0365169i | \(-0.0116263\pi\) |
−0.531291 | + | 0.847189i | \(0.678293\pi\) | |||||||
\(284\) | 0.161795 | + | 0.280238i | 0.00960078 | + | 0.0166290i | ||||
\(285\) | −0.574618 | + | 0.995268i | −0.0340375 | + | 0.0589546i | ||||
\(286\) | 4.98378 | 0.294697 | ||||||||
\(287\) | 0.00768807 | + | 2.13400i | 0.000453813 | + | 0.125966i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −3.98396 | + | 6.90043i | −0.234351 | + | 0.405907i | ||||
\(290\) | −2.16426 | − | 3.74861i | −0.127090 | − | 0.220126i | ||||
\(291\) | −2.95783 | − | 5.12312i | −0.173391 | − | 0.300323i | ||||
\(292\) | 2.36415 | − | 4.09483i | 0.138352 | − | 0.239632i | ||||
\(293\) | 22.0139 | 1.28607 | 0.643034 | − | 0.765837i | \(-0.277675\pi\) | ||||
0.643034 | + | 0.765837i | \(0.277675\pi\) | |||||||
\(294\) | −6.99982 | + | 0.0504365i | −0.408238 | + | 0.00294151i | ||||
\(295\) | −11.9827 | −0.697657 | ||||||||
\(296\) | 0.330096 | − | 0.571742i | 0.0191864 | − | 0.0332318i | ||||
\(297\) | −1.08415 | − | 1.87780i | −0.0629088 | − | 0.108961i | ||||
\(298\) | −10.6085 | − | 18.3744i | −0.614534 | − | 1.06440i | ||||
\(299\) | 7.94774 | − | 13.7659i | 0.459630 | − | 0.796102i | ||||
\(300\) | 3.67925 | 0.212422 | ||||||||
\(301\) | −0.0198637 | − | 5.51363i | −0.00114492 | − | 0.317800i | ||||
\(302\) | −9.40187 | −0.541017 | ||||||||
\(303\) | −6.43414 | + | 11.1443i | −0.369632 | + | 0.640221i | ||||
\(304\) | −0.500000 | − | 0.866025i | −0.0286770 | − | 0.0496700i | ||||
\(305\) | 1.48035 | + | 2.56403i | 0.0847643 | + | 0.146816i | ||||
\(306\) | −2.49840 | + | 4.32735i | −0.142824 | + | 0.247378i | ||||
\(307\) | 14.3776 | 0.820571 | 0.410286 | − | 0.911957i | \(-0.365429\pi\) | ||||
0.410286 | + | 0.911957i | \(0.365429\pi\) | |||||||
\(308\) | 4.97850 | + | 2.85047i | 0.283676 | + | 0.162421i | ||||
\(309\) | −6.95582 | −0.395703 | ||||||||
\(310\) | −2.52008 | + | 4.36490i | −0.143131 | + | 0.247910i | ||||
\(311\) | 1.48726 | + | 2.57601i | 0.0843348 | + | 0.146072i | 0.905108 | − | 0.425183i | \(-0.139790\pi\) |
−0.820773 | + | 0.571255i | \(0.806457\pi\) | |||||||
\(312\) | −1.14924 | − | 1.99054i | −0.0650627 | − | 0.112692i | ||||
\(313\) | 8.37942 | − | 14.5136i | 0.473633 | − | 0.820356i | −0.525912 | − | 0.850539i | \(-0.676276\pi\) |
0.999544 | + | 0.0301834i | \(0.00960914\pi\) | |||||||
\(314\) | −6.14721 | −0.346907 | ||||||||
\(315\) | −2.62774 | + | 1.52977i | −0.148056 | + | 0.0861930i | ||||
\(316\) | −7.59208 | −0.427088 | ||||||||
\(317\) | 1.40531 | − | 2.43406i | 0.0789298 | − | 0.136710i | −0.823859 | − | 0.566795i | \(-0.808183\pi\) |
0.902788 | + | 0.430085i | \(0.141516\pi\) | |||||||
\(318\) | 5.63567 | + | 9.76126i | 0.316032 | + | 0.547384i | ||||
\(319\) | 4.08338 | + | 7.07262i | 0.228625 | + | 0.395990i | ||||
\(320\) | 0.574618 | − | 0.995268i | 0.0321221 | − | 0.0556372i | ||||
\(321\) | 12.3987 | 0.692026 | ||||||||
\(322\) | 15.8127 | − | 9.20560i | 0.881209 | − | 0.513008i | ||||
\(323\) | −4.99679 | −0.278029 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 4.22834 | + | 7.32369i | 0.234546 | + | 0.406245i | ||||
\(326\) | −4.30397 | − | 7.45469i | −0.238375 | − | 0.412877i | ||||
\(327\) | 9.02841 | − | 15.6377i | 0.499272 | − | 0.864765i | ||||
\(328\) | −0.806583 | −0.0445361 | ||||||||
\(329\) | 8.54643 | + | 4.89332i | 0.471180 | + | 0.269777i | ||||
\(330\) | 2.49189 | 0.137174 | ||||||||
\(331\) | 5.06954 | − | 8.78069i | 0.278647 | − | 0.482631i | −0.692402 | − | 0.721512i | \(-0.743447\pi\) |
0.971049 | + | 0.238882i | \(0.0767808\pi\) | |||||||
\(332\) | −1.58718 | − | 2.74907i | −0.0871076 | − | 0.150875i | ||||
\(333\) | −0.330096 | − | 0.571742i | −0.0180891 | − | 0.0313313i | ||||
\(334\) | 5.98744 | − | 10.3706i | 0.327618 | − | 0.567451i | ||||
\(335\) | −10.2118 | −0.557928 | ||||||||
\(336\) | −0.00953166 | − | 2.64573i | −0.000519994 | − | 0.144337i | ||||
\(337\) | 21.4364 | 1.16772 | 0.583858 | − | 0.811856i | \(-0.301542\pi\) | ||||
0.583858 | + | 0.811856i | \(0.301542\pi\) | |||||||
\(338\) | −3.85851 | + | 6.68313i | −0.209875 | + | 0.363515i | ||||
\(339\) | −4.31896 | − | 7.48066i | −0.234574 | − | 0.406294i | ||||
\(340\) | −2.87125 | − | 4.97315i | −0.155715 | − | 0.269707i | ||||
\(341\) | 4.75470 | − | 8.23539i | 0.257482 | − | 0.445971i | ||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −0.200161 | − | 18.5192i | −0.0108077 | − | 0.999942i | ||||
\(344\) | 2.08397 | 0.112360 | ||||||||
\(345\) | 3.97387 | − | 6.88295i | 0.213946 | − | 0.370565i | ||||
\(346\) | 4.05092 | + | 7.01641i | 0.217779 | + | 0.377204i | ||||
\(347\) | −14.5913 | − | 25.2729i | −0.783302 | − | 1.35672i | −0.930008 | − | 0.367539i | \(-0.880200\pi\) |
0.146706 | − | 0.989180i | \(-0.453133\pi\) | |||||||
\(348\) | 1.88322 | − | 3.26183i | 0.100951 | − | 0.174852i | ||||
\(349\) | 9.36208 | 0.501141 | 0.250570 | − | 0.968098i | \(-0.419382\pi\) | ||||
0.250570 | + | 0.968098i | \(0.419382\pi\) | |||||||
\(350\) | 0.0350694 | + | 9.73433i | 0.00187454 | + | 0.520322i | ||||
\(351\) | −2.29847 | −0.122683 | ||||||||
\(352\) | −1.08415 | + | 1.87780i | −0.0577854 | + | 0.100087i | ||||
\(353\) | −16.7997 | − | 29.0980i | −0.894159 | − | 1.54873i | −0.834843 | − | 0.550489i | \(-0.814441\pi\) |
−0.0593161 | − | 0.998239i | \(-0.518892\pi\) | |||||||
\(354\) | −5.21331 | − | 9.02972i | −0.277084 | − | 0.479924i | ||||
\(355\) | −0.185941 | + | 0.322059i | −0.00986873 | + | 0.0170931i | ||||
\(356\) | 12.3776 | 0.656010 | ||||||||
\(357\) | −11.4728 | − | 6.56884i | −0.607206 | − | 0.347660i | ||||
\(358\) | 6.84755 | 0.361905 | ||||||||
\(359\) | 12.1815 | − | 21.0990i | 0.642915 | − | 1.11356i | −0.341863 | − | 0.939750i | \(-0.611058\pi\) |
0.984779 | − | 0.173812i | \(-0.0556087\pi\) | |||||||
\(360\) | −0.574618 | − | 0.995268i | −0.0302851 | − | 0.0524553i | ||||
\(361\) | −0.500000 | − | 0.866025i | −0.0263158 | − | 0.0455803i | ||||
\(362\) | −8.29527 | + | 14.3678i | −0.435989 | + | 0.755156i | ||||
\(363\) | 6.29847 | 0.330584 | ||||||||
\(364\) | 5.25548 | − | 3.05955i | 0.275462 | − | 0.160364i | ||||
\(365\) | 5.43394 | 0.284426 | ||||||||
\(366\) | −1.28811 | + | 2.23107i | −0.0673307 | + | 0.116620i | ||||
\(367\) | 16.5786 | + | 28.7149i | 0.865394 | + | 1.49891i | 0.866655 | + | 0.498907i | \(0.166265\pi\) |
−0.00126140 | + | 0.999999i | \(0.500402\pi\) | |||||||
\(368\) | 3.45783 | + | 5.98914i | 0.180252 | + | 0.312206i | ||||
\(369\) | −0.403292 | + | 0.698521i | −0.0209945 | + | 0.0363636i | ||||
\(370\) | 0.758716 | 0.0394438 | ||||||||
\(371\) | −25.7720 | + | 15.0035i | −1.33801 | + | 0.778944i | ||||
\(372\) | −4.38565 | −0.227385 | ||||||||
\(373\) | 11.2730 | − | 19.5254i | 0.583693 | − | 1.01099i | −0.411343 | − | 0.911480i | \(-0.634940\pi\) |
0.995037 | − | 0.0995064i | \(-0.0317264\pi\) | |||||||
\(374\) | 5.41727 | + | 9.38299i | 0.280120 | + | 0.485183i | ||||
\(375\) | 4.98726 | + | 8.63819i | 0.257541 | + | 0.446074i | ||||
\(376\) | −1.86113 | + | 3.22356i | −0.0959802 | + | 0.166243i | ||||
\(377\) | 8.65704 | 0.445860 | ||||||||
\(378\) | −2.29604 | − | 1.31461i | −0.118095 | − | 0.0676164i | ||||
\(379\) | 18.7616 | 0.963717 | 0.481858 | − | 0.876249i | \(-0.339962\pi\) | ||||
0.481858 | + | 0.876249i | \(0.339962\pi\) | |||||||
\(380\) | 0.574618 | − | 0.995268i | 0.0294773 | − | 0.0510562i | ||||
\(381\) | −6.93414 | − | 12.0103i | −0.355247 | − | 0.615305i | ||||
\(382\) | 7.94509 | + | 13.7613i | 0.406506 | + | 0.704090i | ||||
\(383\) | 4.05885 | − | 7.03014i | 0.207398 | − | 0.359223i | −0.743496 | − | 0.668740i | \(-0.766834\pi\) |
0.950894 | + | 0.309517i | \(0.100167\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.0237518 | + | 6.59288i | 0.00121051 | + | 0.336004i | ||||
\(386\) | −6.49676 | −0.330676 | ||||||||
\(387\) | 1.04198 | − | 1.80477i | 0.0529670 | − | 0.0917416i | ||||
\(388\) | 2.95783 | + | 5.12312i | 0.150161 | + | 0.260087i | ||||
\(389\) | 17.5017 | + | 30.3138i | 0.887371 | + | 1.53697i | 0.842972 | + | 0.537958i | \(0.180804\pi\) |
0.0443993 | + | 0.999014i | \(0.485863\pi\) | |||||||
\(390\) | 1.32075 | − | 2.28760i | 0.0668786 | − | 0.115837i | ||||
\(391\) | 34.5562 | 1.74758 | ||||||||
\(392\) | 6.99982 | − | 0.0504365i | 0.353544 | − | 0.00254743i | ||||
\(393\) | −12.2113 | −0.615978 | ||||||||
\(394\) | 0.532453 | − | 0.922235i | 0.0268246 | − | 0.0464615i | ||||
\(395\) | −4.36255 | − | 7.55615i | −0.219504 | − | 0.380191i | ||||
\(396\) | 1.08415 | + | 1.87780i | 0.0544806 | + | 0.0943632i | ||||
\(397\) | −7.51095 | + | 13.0094i | −0.376964 | + | 0.652921i | −0.990619 | − | 0.136654i | \(-0.956365\pi\) |
0.613655 | + | 0.789574i | \(0.289699\pi\) | |||||||
\(398\) | −23.5917 | −1.18255 | ||||||||
\(399\) | −0.00953166 | − | 2.64573i | −0.000477180 | − | 0.132452i | ||||
\(400\) | −3.67925 | −0.183963 | ||||||||
\(401\) | 13.3143 | − | 23.0611i | 0.664886 | − | 1.15162i | −0.314430 | − | 0.949281i | \(-0.601814\pi\) |
0.979316 | − | 0.202336i | \(-0.0648532\pi\) | |||||||
\(402\) | −4.44284 | − | 7.69523i | −0.221589 | − | 0.383803i | ||||
\(403\) | −5.04015 | − | 8.72980i | −0.251068 | − | 0.434862i | ||||
\(404\) | 6.43414 | − | 11.1443i | 0.320110 | − | 0.554448i | ||||
\(405\) | −1.14924 | −0.0571060 | ||||||||
\(406\) | 8.64787 | + | 4.95140i | 0.429187 | + | 0.245734i | ||||
\(407\) | −1.43149 | −0.0709565 | ||||||||
\(408\) | 2.49840 | − | 4.32735i | 0.123689 | − | 0.214236i | ||||
\(409\) | −13.8245 | − | 23.9447i | −0.683575 | − | 1.18399i | −0.973882 | − | 0.227053i | \(-0.927091\pi\) |
0.290307 | − | 0.956934i | \(-0.406243\pi\) | |||||||
\(410\) | −0.463478 | − | 0.802767i | −0.0228895 | − | 0.0396458i | ||||
\(411\) | 5.54038 | − | 9.59622i | 0.273287 | − | 0.473347i | ||||
\(412\) | 6.95582 | 0.342689 | ||||||||
\(413\) | 23.8405 | − | 13.8791i | 1.17312 | − | 0.682946i | ||||
\(414\) | 6.91567 | 0.339887 | ||||||||
\(415\) | 1.82404 | − | 3.15933i | 0.0895387 | − | 0.155086i | ||||
\(416\) | 1.14924 | + | 1.99054i | 0.0563460 | + | 0.0975941i | ||||
\(417\) | −5.50876 | − | 9.54145i | −0.269765 | − | 0.467247i | ||||
\(418\) | −1.08415 | + | 1.87780i | −0.0530275 | + | 0.0918464i | ||||
\(419\) | 1.91888 | 0.0937433 | 0.0468716 | − | 0.998901i | \(-0.485075\pi\) | ||||
0.0468716 | + | 0.998901i | \(0.485075\pi\) | |||||||
\(420\) | 2.62774 | − | 1.52977i | 0.128221 | − | 0.0746453i | ||||
\(421\) | 25.9815 | 1.26626 | 0.633130 | − | 0.774046i | \(-0.281770\pi\) | ||||
0.633130 | + | 0.774046i | \(0.281770\pi\) | |||||||
\(422\) | 8.93497 | − | 15.4758i | 0.434948 | − | 0.753351i | ||||
\(423\) | 1.86113 | + | 3.22356i | 0.0904910 | + | 0.156735i | ||||
\(424\) | −5.63567 | − | 9.76126i | −0.273692 | − | 0.474049i | ||||
\(425\) | −9.19223 | + | 15.9214i | −0.445889 | + | 0.772302i | ||||
\(426\) | −0.323591 | −0.0156780 | ||||||||
\(427\) | −5.91511 | − | 3.38673i | −0.286252 | − | 0.163896i | ||||
\(428\) | −12.3987 | −0.599312 | ||||||||
\(429\) | −2.49189 | + | 4.31608i | −0.120310 | + | 0.208382i | ||||
\(430\) | 1.19749 | + | 2.07411i | 0.0577479 | + | 0.100022i | ||||
\(431\) | −0.482541 | − | 0.835785i | −0.0232432 | − | 0.0402584i | 0.854170 | − | 0.519994i | \(-0.174066\pi\) |
−0.877413 | + | 0.479736i | \(0.840733\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −5.93960 | −0.285439 | −0.142720 | − | 0.989763i | \(-0.545585\pi\) | ||||
−0.142720 | + | 0.989763i | \(0.545585\pi\) | |||||||
\(434\) | −0.0418025 | − | 11.6033i | −0.00200658 | − | 0.556975i | ||||
\(435\) | 4.32852 | 0.207537 | ||||||||
\(436\) | −9.02841 | + | 15.6377i | −0.432383 | + | 0.748909i | ||||
\(437\) | 3.45783 | + | 5.98914i | 0.165411 | + | 0.286500i | ||||
\(438\) | 2.36415 | + | 4.09483i | 0.112964 | + | 0.195659i | ||||
\(439\) | −10.7960 | + | 18.6993i | −0.515267 | + | 0.892468i | 0.484576 | + | 0.874749i | \(0.338974\pi\) |
−0.999843 | + | 0.0177192i | \(0.994359\pi\) | |||||||
\(440\) | −2.49189 | −0.118796 | ||||||||
\(441\) | 3.45623 | − | 6.08724i | 0.164582 | − | 0.289869i | ||||
\(442\) | 11.4850 | 0.546286 | ||||||||
\(443\) | −6.96718 | + | 12.0675i | −0.331021 | + | 0.573345i | −0.982712 | − | 0.185139i | \(-0.940726\pi\) |
0.651691 | + | 0.758484i | \(0.274060\pi\) | |||||||
\(444\) | 0.330096 | + | 0.571742i | 0.0156656 | + | 0.0271337i | ||||
\(445\) | 7.11238 | + | 12.3190i | 0.337159 | + | 0.583977i | ||||
\(446\) | 2.22302 | − | 3.85039i | 0.105263 | − | 0.182321i | ||||
\(447\) | 21.2170 | 1.00353 | ||||||||
\(448\) | 0.00953166 | + | 2.64573i | 0.000450328 | + | 0.124999i | ||||
\(449\) | 14.3273 | 0.676149 | 0.338074 | − | 0.941119i | \(-0.390224\pi\) | ||||
0.338074 | + | 0.941119i | \(0.390224\pi\) | |||||||
\(450\) | −1.83963 | + | 3.18633i | −0.0867209 | + | 0.150205i | ||||
\(451\) | 0.874457 | + | 1.51460i | 0.0411766 | + | 0.0713199i | ||||
\(452\) | 4.31896 | + | 7.48066i | 0.203147 | + | 0.351861i | ||||
\(453\) | 4.70093 | − | 8.14226i | 0.220869 | − | 0.382557i | ||||
\(454\) | −20.0938 | −0.943047 | ||||||||
\(455\) | 6.06497 | + | 3.47254i | 0.284330 | + | 0.162795i | ||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −16.1491 | + | 27.9710i | −0.755421 | + | 1.30843i | 0.189744 | + | 0.981834i | \(0.439234\pi\) |
−0.945165 | + | 0.326594i | \(0.894099\pi\) | |||||||
\(458\) | 8.97773 | + | 15.5499i | 0.419502 | + | 0.726598i | ||||
\(459\) | −2.49840 | − | 4.32735i | −0.116615 | − | 0.201983i | ||||
\(460\) | −3.97387 | + | 6.88295i | −0.185283 | + | 0.320919i | ||||
\(461\) | 0.375849 | 0.0175050 | 0.00875252 | − | 0.999962i | \(-0.497214\pi\) | ||||
0.00875252 | + | 0.999962i | \(0.497214\pi\) | |||||||
\(462\) | −4.95783 | + | 2.88627i | −0.230659 | + | 0.134282i | ||||
\(463\) | 7.80824 | 0.362880 | 0.181440 | − | 0.983402i | \(-0.441924\pi\) | ||||
0.181440 | + | 0.983402i | \(0.441924\pi\) | |||||||
\(464\) | −1.88322 | + | 3.26183i | −0.0874261 | + | 0.151426i | ||||
\(465\) | −2.52008 | − | 4.36490i | −0.116866 | − | 0.202417i | ||||
\(466\) | 5.12697 | + | 8.88016i | 0.237502 | + | 0.411366i | ||||
\(467\) | 6.12774 | − | 10.6136i | 0.283558 | − | 0.491137i | −0.688701 | − | 0.725046i | \(-0.741819\pi\) |
0.972258 | + | 0.233909i | \(0.0751518\pi\) | |||||||
\(468\) | 2.29847 | 0.106247 | ||||||||
\(469\) | 20.3172 | − | 11.8279i | 0.938160 | − | 0.546163i | ||||
\(470\) | −4.27775 | −0.197318 | ||||||||
\(471\) | 3.07361 | − | 5.32364i | 0.141624 | − | 0.245300i | ||||
\(472\) | 5.21331 | + | 9.02972i | 0.239962 | + | 0.415627i | ||||
\(473\) | −2.25933 | − | 3.91328i | −0.103884 | − | 0.179933i | ||||
\(474\) | 3.79604 | − | 6.57493i | 0.174358 | − | 0.301997i | ||||
\(475\) | −3.67925 | −0.168816 | ||||||||
\(476\) | 11.4728 | + | 6.56884i | 0.525856 | + | 0.301082i | ||||
\(477\) | −11.2713 | −0.516079 | ||||||||
\(478\) | 0.869826 | − | 1.50658i | 0.0397849 | − | 0.0689095i | ||||
\(479\) | −13.5375 | − | 23.4477i | −0.618546 | − | 1.07135i | −0.989751 | − | 0.142802i | \(-0.954389\pi\) |
0.371206 | − | 0.928551i | \(-0.378945\pi\) | |||||||
\(480\) | 0.574618 | + | 0.995268i | 0.0262276 | + | 0.0454276i | ||||
\(481\) | −0.758716 | + | 1.31413i | −0.0345945 | + | 0.0599194i | ||||
\(482\) | 20.8492 | 0.949656 | ||||||||
\(483\) | 0.0659178 | + | 18.2970i | 0.00299936 | + | 0.832543i | ||||
\(484\) | −6.29847 | −0.286294 | ||||||||
\(485\) | −3.39925 | + | 5.88768i | −0.154352 | + | 0.267346i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −14.8749 | − | 25.7641i | −0.674047 | − | 1.16748i | −0.976746 | − | 0.214398i | \(-0.931221\pi\) |
0.302699 | − | 0.953086i | \(-0.402112\pi\) | |||||||
\(488\) | 1.28811 | − | 2.23107i | 0.0583101 | − | 0.100996i | ||||
\(489\) | 8.60793 | 0.389264 | ||||||||
\(490\) | 4.07242 | + | 6.93772i | 0.183973 | + | 0.313414i | ||||
\(491\) | 18.4381 | 0.832099 | 0.416050 | − | 0.909342i | \(-0.363414\pi\) | ||||
0.416050 | + | 0.909342i | \(0.363414\pi\) | |||||||
\(492\) | 0.403292 | − | 0.698521i | 0.0181818 | − | 0.0314918i | ||||
\(493\) | 9.41004 | + | 16.2987i | 0.423807 | + | 0.734055i | ||||
\(494\) | 1.14924 | + | 1.99054i | 0.0517066 | + | 0.0895585i | ||||
\(495\) | −1.24595 | + | 2.15804i | −0.0560011 | + | 0.0969967i | ||||
\(496\) | 4.38565 | 0.196922 | ||||||||
\(497\) | −0.00308435 | − | 0.856135i | −0.000138352 | − | 0.0384029i | ||||
\(498\) | 3.17435 | 0.142246 | ||||||||
\(499\) | −16.5785 | + | 28.7148i | −0.742156 | + | 1.28545i | 0.209356 | + | 0.977840i | \(0.432863\pi\) |
−0.951512 | + | 0.307612i | \(0.900470\pi\) | |||||||
\(500\) | −4.98726 | − | 8.63819i | −0.223037 | − | 0.386311i | ||||
\(501\) | 5.98744 | + | 10.3706i | 0.267499 | + | 0.463322i | ||||
\(502\) | 1.59831 | − | 2.76836i | 0.0713362 | − | 0.123558i | ||||
\(503\) | 12.8678 | 0.573747 | 0.286873 | − | 0.957968i | \(-0.407384\pi\) | ||||
0.286873 | + | 0.957968i | \(0.407384\pi\) | |||||||
\(504\) | 2.29604 | + | 1.31461i | 0.102274 | + | 0.0585575i | ||||
\(505\) | 14.7887 | 0.658089 | ||||||||
\(506\) | 7.49762 | − | 12.9863i | 0.333310 | − | 0.577310i | ||||
\(507\) | −3.85851 | − | 6.68313i | −0.171362 | − | 0.296808i | ||||
\(508\) | 6.93414 | + | 12.0103i | 0.307653 | + | 0.532870i | ||||
\(509\) | −4.35117 | + | 7.53645i | −0.192862 | + | 0.334047i | −0.946198 | − | 0.323589i | \(-0.895110\pi\) |
0.753335 | + | 0.657637i | \(0.228444\pi\) | |||||||
\(510\) | 5.74250 | 0.254282 | ||||||||
\(511\) | −10.8113 | + | 6.29395i | −0.478264 | + | 0.278428i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.500000 | − | 0.866025i | 0.0220755 | − | 0.0382360i | ||||
\(514\) | −7.51095 | − | 13.0094i | −0.331294 | − | 0.573818i | ||||
\(515\) | 3.99694 | + | 6.92291i | 0.176126 | + | 0.305060i | ||||
\(516\) | −1.04198 | + | 1.80477i | −0.0458708 | + | 0.0794506i | ||||
\(517\) | 8.07096 | 0.354960 | ||||||||
\(518\) | −1.50953 | + | 0.878795i | −0.0663250 | + | 0.0386120i | ||||
\(519\) | −8.10185 | −0.355632 | ||||||||
\(520\) | −1.32075 | + | 2.28760i | −0.0579185 | + | 0.100318i | ||||
\(521\) | −18.8983 | − | 32.7328i | −0.827948 | − | 1.43405i | −0.899645 | − | 0.436622i | \(-0.856175\pi\) |
0.0716971 | − | 0.997426i | \(-0.477159\pi\) | |||||||
\(522\) | 1.88322 | + | 3.26183i | 0.0824261 | + | 0.142766i | ||||
\(523\) | −21.1682 | + | 36.6644i | −0.925620 | + | 1.60322i | −0.135058 | + | 0.990838i | \(0.543122\pi\) |
−0.790561 | + | 0.612383i | \(0.790211\pi\) | |||||||
\(524\) | 12.2113 | 0.533453 | ||||||||
\(525\) | −8.44771 | − | 4.83679i | −0.368688 | − | 0.211095i | ||||
\(526\) | −10.6760 | −0.465498 | ||||||||
\(527\) | 10.9571 | − | 18.9782i | 0.477298 | − | 0.826705i | ||||
\(528\) | −1.08415 | − | 1.87780i | −0.0471816 | − | 0.0817209i | ||||
\(529\) | −12.4132 | − | 21.5004i | −0.539706 | − | 0.934798i | ||||
\(530\) | 6.47672 | − | 11.2180i | 0.281331 | − | 0.487279i | ||||
\(531\) | 10.4266 | 0.452477 | ||||||||
\(532\) | 0.00953166 | + | 2.64573i | 0.000413250 | + | 0.114707i | ||||
\(533\) | 1.85391 | 0.0803018 | ||||||||
\(534\) | −6.18879 | + | 10.7193i | −0.267815 | + | 0.463869i | ||||
\(535\) | −7.12450 | − | 12.3400i | −0.308019 | − | 0.533505i | ||||
\(536\) | 4.44284 | + | 7.69523i | 0.191901 | + | 0.332383i | ||||
\(537\) | −3.42378 | + | 5.93016i | −0.147747 | + | 0.255905i | ||||
\(538\) | 3.24906 | 0.140077 | ||||||||
\(539\) | −7.68356 | − | 13.0896i | −0.330955 | − | 0.563809i | ||||
\(540\) | 1.14924 | 0.0494553 | ||||||||
\(541\) | −4.00573 | + | 6.93813i | −0.172220 | + | 0.298294i | −0.939196 | − | 0.343382i | \(-0.888427\pi\) |
0.766976 | + | 0.641676i | \(0.221761\pi\) | |||||||
\(542\) | 9.01746 | + | 15.6187i | 0.387333 | + | 0.670880i | ||||
\(543\) | −8.29527 | − | 14.3678i | −0.355984 | − | 0.616582i | ||||
\(544\) | −2.49840 | + | 4.32735i | −0.107118 | + | 0.185534i | ||||
\(545\) | −20.7516 | −0.888900 | ||||||||
\(546\) | 0.0219083 | + | 6.08115i | 0.000937587 | + | 0.260249i | ||||
\(547\) | −34.1587 | −1.46052 | −0.730260 | − | 0.683170i | \(-0.760601\pi\) | ||||
−0.730260 | + | 0.683170i | \(0.760601\pi\) | |||||||
\(548\) | −5.54038 | + | 9.59622i | −0.236673 | + | 0.409930i | ||||
\(549\) | −1.28811 | − | 2.23107i | −0.0549753 | − | 0.0952199i | ||||
\(550\) | 3.98886 | + | 6.90892i | 0.170086 | + | 0.294597i | ||||
\(551\) | −1.88322 | + | 3.26183i | −0.0802277 | + | 0.138958i | ||||
\(552\) | −6.91567 | −0.294350 | ||||||||
\(553\) | 17.4317 | + | 9.98064i | 0.741271 | + | 0.424420i | ||||
\(554\) | −22.2839 | −0.946753 | ||||||||
\(555\) | −0.379358 | + | 0.657067i | −0.0161029 | + | 0.0278910i | ||||
\(556\) | 5.50876 | + | 9.54145i | 0.233623 | + | 0.404648i | ||||
\(557\) | 20.2395 | + | 35.0559i | 0.857576 | + | 1.48537i | 0.874234 | + | 0.485505i | \(0.161364\pi\) |
−0.0166578 | + | 0.999861i | \(0.505303\pi\) | |||||||
\(558\) | 2.19283 | − | 3.79808i | 0.0928297 | − | 0.160786i | ||||
\(559\) | −4.78995 | −0.202593 | ||||||||
\(560\) | −2.62774 | + | 1.52977i | −0.111042 | + | 0.0646448i | ||||
\(561\) | −10.8345 | −0.457435 | ||||||||
\(562\) | 3.55395 | − | 6.15562i | 0.149914 | − | 0.259659i | ||||
\(563\) | −9.10220 | − | 15.7655i | −0.383612 | − | 0.664436i | 0.607964 | − | 0.793965i | \(-0.291987\pi\) |
−0.991576 | + | 0.129529i | \(0.958653\pi\) | |||||||
\(564\) | −1.86113 | − | 3.22356i | −0.0783675 | − | 0.135737i | ||||
\(565\) | −4.96351 | + | 8.59705i | −0.208816 | + | 0.361681i | ||||
\(566\) | 15.7474 | 0.661911 | ||||||||
\(567\) | 2.28651 | − | 1.33112i | 0.0960243 | − | 0.0559019i | ||||
\(568\) | 0.323591 | 0.0135776 | ||||||||
\(569\) | 8.01265 | − | 13.8783i | 0.335908 | − | 0.581809i | −0.647751 | − | 0.761852i | \(-0.724290\pi\) |
0.983659 | + | 0.180043i | \(0.0576237\pi\) | |||||||
\(570\) | 0.574618 | + | 0.995268i | 0.0240681 | + | 0.0416872i | ||||
\(571\) | −3.51315 | − | 6.08495i | −0.147021 | − | 0.254647i | 0.783104 | − | 0.621890i | \(-0.213635\pi\) |
−0.930125 | + | 0.367243i | \(0.880302\pi\) | |||||||
\(572\) | 2.49189 | − | 4.31608i | 0.104191 | − | 0.180464i | ||||
\(573\) | −15.8902 | −0.663822 | ||||||||
\(574\) | 1.85195 | + | 1.06034i | 0.0772987 | + | 0.0442579i | ||||
\(575\) | 25.4445 | 1.06111 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −11.4555 | − | 19.8414i | −0.476897 | − | 0.826010i | 0.522753 | − | 0.852484i | \(-0.324905\pi\) |
−0.999649 | + | 0.0264748i | \(0.991572\pi\) | |||||||
\(578\) | 3.98396 | + | 6.90043i | 0.165711 | + | 0.287020i | ||||
\(579\) | 3.24838 | − | 5.62636i | 0.134998 | − | 0.233824i | ||||
\(580\) | −4.32852 | −0.179732 | ||||||||
\(581\) | 0.0302568 | + | 8.39850i | 0.00125527 | + | 0.348428i | ||||
\(582\) | −5.91567 | −0.245212 | ||||||||
\(583\) | −12.2198 | + | 21.1653i | −0.506093 | + | 0.876579i | ||||
\(584\) | −2.36415 | − | 4.09483i | −0.0978293 | − | 0.169445i | ||||
\(585\) | 1.32075 | + | 2.28760i | 0.0546061 | + | 0.0945806i | ||||
\(586\) | 11.0070 | − | 19.0646i | 0.454694 | − | 0.787553i | ||||
\(587\) | −9.55395 | −0.394334 | −0.197167 | − | 0.980370i | \(-0.563174\pi\) | ||||
−0.197167 | + | 0.980370i | \(0.563174\pi\) | |||||||
\(588\) | −3.45623 | + | 6.08724i | −0.142533 | + | 0.251033i | ||||
\(589\) | 4.38565 | 0.180708 | ||||||||
\(590\) | −5.99133 | + | 10.3773i | −0.246659 | + | 0.427226i | ||||
\(591\) | 0.532453 | + | 0.922235i | 0.0219022 | + | 0.0379357i | ||||
\(592\) | −0.330096 | − | 0.571742i | −0.0135668 | − | 0.0234985i | ||||
\(593\) | −4.05336 | + | 7.02062i | −0.166452 | + | 0.288302i | −0.937170 | − | 0.348874i | \(-0.886564\pi\) |
0.770718 | + | 0.637176i | \(0.219898\pi\) | |||||||
\(594\) | −2.16830 | −0.0889664 | ||||||||
\(595\) | 0.0547355 | + | 15.1931i | 0.00224394 | + | 0.622857i | ||||
\(596\) | −21.2170 | −0.869082 | ||||||||
\(597\) | 11.7959 | − | 20.4310i | 0.482772 | − | 0.836186i | ||||
\(598\) | −7.94774 | − | 13.7659i | −0.325007 | − | 0.562929i | ||||
\(599\) | 9.15859 | + | 15.8631i | 0.374210 | + | 0.648150i | 0.990208 | − | 0.139597i | \(-0.0445807\pi\) |
−0.615999 | + | 0.787747i | \(0.711247\pi\) | |||||||
\(600\) | 1.83963 | − | 3.18633i | 0.0751025 | − | 0.130081i | ||||
\(601\) | 15.5629 | 0.634824 | 0.317412 | − | 0.948288i | \(-0.397186\pi\) | ||||
0.317412 | + | 0.948288i | \(0.397186\pi\) | |||||||
\(602\) | −4.78487 | − | 2.73961i | −0.195017 | − | 0.111658i | ||||
\(603\) | 8.88568 | 0.361853 | ||||||||
\(604\) | −4.70093 | + | 8.14226i | −0.191278 | + | 0.331304i | ||||
\(605\) | −3.61922 | − | 6.26867i | −0.147142 | − | 0.254858i | ||||
\(606\) | 6.43414 | + | 11.1443i | 0.261369 | + | 0.452705i | ||||
\(607\) | −14.1959 | + | 24.5880i | −0.576193 | + | 0.997996i | 0.419718 | + | 0.907655i | \(0.362129\pi\) |
−0.995911 | + | 0.0903411i | \(0.971204\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −8.61197 | + | 5.01358i | −0.348975 | + | 0.203160i | ||||
\(610\) | 2.96069 | 0.119875 | ||||||||
\(611\) | 4.27775 | − | 7.40928i | 0.173059 | − | 0.299747i | ||||
\(612\) | 2.49840 | + | 4.32735i | 0.100992 | + | 0.174923i | ||||
\(613\) | 17.7205 | + | 30.6927i | 0.715723 | + | 1.23967i | 0.962680 | + | 0.270642i | \(0.0872360\pi\) |
−0.246957 | + | 0.969026i | \(0.579431\pi\) | |||||||
\(614\) | 7.18879 | − | 12.4513i | 0.290116 | − | 0.502495i | ||||
\(615\) | 0.926955 | 0.0373784 | ||||||||
\(616\) | 4.95783 | − | 2.88627i | 0.199757 | − | 0.116291i | ||||
\(617\) | 27.6964 | 1.11502 | 0.557508 | − | 0.830172i | \(-0.311758\pi\) | ||||
0.557508 | + | 0.830172i | \(0.311758\pi\) | |||||||
\(618\) | −3.47791 | + | 6.02392i | −0.139902 | + | 0.242317i | ||||
\(619\) | 13.1957 | + | 22.8556i | 0.530380 | + | 0.918645i | 0.999372 | + | 0.0354425i | \(0.0112841\pi\) |
−0.468992 | + | 0.883203i | \(0.655383\pi\) | |||||||
\(620\) | 2.52008 | + | 4.36490i | 0.101209 | + | 0.175299i | ||||
\(621\) | −3.45783 | + | 5.98914i | −0.138758 | + | 0.240336i | ||||
\(622\) | 2.97452 | 0.119267 | ||||||||
\(623\) | −28.4194 | − | 16.2717i | −1.13860 | − | 0.651912i | ||||
\(624\) | −2.29847 | −0.0920126 | ||||||||
\(625\) | −3.46659 | + | 6.00431i | −0.138664 | + | 0.240173i | ||||
\(626\) | −8.37942 | − | 14.5136i | −0.334909 | − | 0.580079i | ||||
\(627\) | −1.08415 | − | 1.87780i | −0.0432968 | − | 0.0749922i | ||||
\(628\) | −3.07361 | + | 5.32364i | −0.122650 | + | 0.212436i | ||||
\(629\) | −3.29884 | −0.131533 | ||||||||
\(630\) | 0.0109541 | + | 3.04058i | 0.000436423 | + | 0.121139i | ||||
\(631\) | 21.3293 | 0.849105 | 0.424553 | − | 0.905403i | \(-0.360431\pi\) | ||||
0.424553 | + | 0.905403i | \(0.360431\pi\) | |||||||
\(632\) | −3.79604 | + | 6.57493i | −0.150998 | + | 0.261537i | ||||
\(633\) | 8.93497 | + | 15.4758i | 0.355133 | + | 0.615109i | ||||
\(634\) | −1.40531 | − | 2.43406i | −0.0558118 | − | 0.0966689i | ||||
\(635\) | −7.96897 | + | 13.8027i | −0.316239 | + | 0.547742i | ||||
\(636\) | 11.2713 | 0.446937 | ||||||||
\(637\) | −16.0889 | + | 0.115927i | −0.637465 | + | 0.00459319i | ||||
\(638\) | 8.16675 | 0.323325 | ||||||||
\(639\) | 0.161795 | − | 0.280238i | 0.00640052 | − | 0.0110860i | ||||
\(640\) | −0.574618 | − | 0.995268i | −0.0227138 | − | 0.0393414i | ||||
\(641\) | −9.50348 | − | 16.4605i | −0.375365 | − | 0.650151i | 0.615017 | − | 0.788514i | \(-0.289149\pi\) |
−0.990382 | + | 0.138363i | \(0.955816\pi\) | |||||||
\(642\) | 6.19933 | − | 10.7376i | 0.244668 | − | 0.423777i | ||||
\(643\) | 3.46630 | 0.136697 | 0.0683487 | − | 0.997661i | \(-0.478227\pi\) | ||||
0.0683487 | + | 0.997661i | \(0.478227\pi\) | |||||||
\(644\) | −0.0659178 | − | 18.2970i | −0.00259752 | − | 0.721004i | ||||
\(645\) | −2.39497 | −0.0943020 | ||||||||
\(646\) | −2.49840 | + | 4.32735i | −0.0982981 | + | 0.170257i | ||||
\(647\) | −6.18045 | − | 10.7049i | −0.242979 | − | 0.420851i | 0.718583 | − | 0.695441i | \(-0.244791\pi\) |
−0.961561 | + | 0.274590i | \(0.911458\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 11.3040 | − | 19.5791i | 0.443722 | − | 0.768549i | ||||
\(650\) | 8.45667 | 0.331698 | ||||||||
\(651\) | 10.0696 | + | 5.76543i | 0.394660 | + | 0.225965i | ||||
\(652\) | −8.60793 | −0.337113 | ||||||||
\(653\) | −25.3561 | + | 43.9181i | −0.992262 | + | 1.71865i | −0.388605 | + | 0.921405i | \(0.627043\pi\) |
−0.603658 | + | 0.797244i | \(0.706291\pi\) | |||||||
\(654\) | −9.02841 | − | 15.6377i | −0.353039 | − | 0.611481i | ||||
\(655\) | 7.01684 | + | 12.1535i | 0.274171 | + | 0.474877i | ||||
\(656\) | −0.403292 | + | 0.698521i | −0.0157459 | + | 0.0272727i | ||||
\(657\) | −4.72830 | −0.184469 | ||||||||
\(658\) | 8.51095 | − | 4.95477i | 0.331792 | − | 0.193157i | ||||
\(659\) | −29.4985 | −1.14910 | −0.574549 | − | 0.818470i | \(-0.694822\pi\) | ||||
−0.574549 | + | 0.818470i | \(0.694822\pi\) | |||||||
\(660\) | 1.24595 | − | 2.15804i | 0.0484984 | − | 0.0840016i | ||||
\(661\) | 18.9490 | + | 32.8205i | 0.737029 | + | 1.27657i | 0.953827 | + | 0.300355i | \(0.0971051\pi\) |
−0.216799 | + | 0.976216i | \(0.569562\pi\) | |||||||
\(662\) | −5.06954 | − | 8.78069i | −0.197033 | − | 0.341271i | ||||
\(663\) | −5.74250 | + | 9.94630i | −0.223020 | + | 0.386282i | ||||
\(664\) | −3.17435 | −0.123189 | ||||||||
\(665\) | −2.62774 | + | 1.52977i | −0.101899 | + | 0.0593221i | ||||
\(666\) | −0.660191 | −0.0255819 | ||||||||
\(667\) | 13.0237 | − | 22.5577i | 0.504279 | − | 0.873438i | ||||
\(668\) | −5.98744 | − | 10.3706i | −0.231661 | − | 0.401249i | ||||
\(669\) | 2.22302 | + | 3.85039i | 0.0859471 | + | 0.148865i | ||||
\(670\) | −5.10588 | + | 8.84364i | −0.197257 | + | 0.341660i | ||||
\(671\) | −5.58602 | −0.215646 | ||||||||
\(672\) | −2.29604 | − | 1.31461i | −0.0885716 | − | 0.0507123i | ||||
\(673\) | −0.234048 | −0.00902187 | −0.00451094 | − | 0.999990i | \(-0.501436\pi\) | ||||
−0.00451094 | + | 0.999990i | \(0.501436\pi\) | |||||||
\(674\) | 10.7182 | − | 18.5645i | 0.412850 | − | 0.715077i | ||||
\(675\) | −1.83963 | − | 3.18633i | −0.0708073 | − | 0.122642i | ||||
\(676\) | 3.85851 | + | 6.68313i | 0.148404 | + | 0.257044i | ||||
\(677\) | 5.61173 | − | 9.71981i | 0.215676 | − | 0.373562i | −0.737805 | − | 0.675014i | \(-0.764138\pi\) |
0.953482 | + | 0.301451i | \(0.0974710\pi\) | |||||||
\(678\) | −8.63792 | −0.331737 | ||||||||
\(679\) | −0.0563861 | − | 15.6513i | −0.00216390 | − | 0.600641i | ||||
\(680\) | −5.74250 | −0.220215 | ||||||||
\(681\) | 10.0469 | − | 17.4017i | 0.384997 | − | 0.666835i | ||||
\(682\) | −4.75470 | − | 8.23539i | −0.182067 | − | 0.315349i | ||||
\(683\) | −8.25937 | − | 14.3056i | −0.316036 | − | 0.547390i | 0.663621 | − | 0.748069i | \(-0.269019\pi\) |
−0.979657 | + | 0.200679i | \(0.935685\pi\) | |||||||
\(684\) | −0.500000 | + | 0.866025i | −0.0191180 | + | 0.0331133i | ||||
\(685\) | −12.7344 | −0.486557 | ||||||||
\(686\) | −16.1382 | − | 9.08624i | −0.616158 | − | 0.346914i | ||||
\(687\) | −17.9555 | −0.685043 | ||||||||
\(688\) | 1.04198 | − | 1.80477i | 0.0397253 | − | 0.0688062i | ||||
\(689\) | 12.9534 | + | 22.4360i | 0.493486 | + | 0.854744i | ||||
\(690\) | −3.97387 | − | 6.88295i | −0.151283 | − | 0.262029i | ||||
\(691\) | −20.7288 | + | 35.9033i | −0.788559 | + | 1.36582i | 0.138291 | + | 0.990392i | \(0.455839\pi\) |
−0.926850 | + | 0.375433i | \(0.877494\pi\) | |||||||
\(692\) | 8.10185 | 0.307986 | ||||||||
\(693\) | −0.0206675 | − | 5.73675i | −0.000785093 | − | 0.217921i | ||||
\(694\) | −29.1826 | −1.10776 | ||||||||
\(695\) | −6.33087 | + | 10.9654i | −0.240144 | + | 0.415941i | ||||
\(696\) | −1.88322 | − | 3.26183i | −0.0713831 | − | 0.123639i | ||||
\(697\) | 2.01516 | + | 3.49037i | 0.0763298 | + | 0.132207i | ||||
\(698\) | 4.68104 | − | 8.10780i | 0.177180 | − | 0.306885i | ||||
\(699\) | −10.2539 | −0.387839 | ||||||||
\(700\) | 8.44771 | + | 4.83679i | 0.319293 | + | 0.182814i | ||||
\(701\) | 26.9202 | 1.01676 | 0.508380 | − | 0.861133i | \(-0.330244\pi\) | ||||
0.508380 | + | 0.861133i | \(0.330244\pi\) | |||||||
\(702\) | −1.14924 | + | 1.99054i | −0.0433752 | + | 0.0751280i | ||||
\(703\) | −0.330096 | − | 0.571742i | −0.0124498 | − | 0.0215637i | ||||
\(704\) | 1.08415 | + | 1.87780i | 0.0408604 | + | 0.0707724i | ||||
\(705\) | 2.13887 | − | 3.70464i | 0.0805547 | − | 0.139525i | ||||
\(706\) | −33.5994 | −1.26453 | ||||||||
\(707\) | −29.4234 | + | 17.1292i | −1.10658 | + | 0.644212i | ||||
\(708\) | −10.4266 | −0.391856 | ||||||||
\(709\) | −14.8103 | + | 25.6522i | −0.556212 | + | 0.963388i | 0.441596 | + | 0.897214i | \(0.354412\pi\) |
−0.997808 | + | 0.0661736i | \(0.978921\pi\) | |||||||
\(710\) | 0.185941 | + | 0.322059i | 0.00697825 | + | 0.0120867i | ||||
\(711\) | 3.79604 | + | 6.57493i | 0.142363 | + | 0.246579i | ||||
\(712\) | 6.18879 | − | 10.7193i | 0.231935 | − | 0.401722i | ||||
\(713\) | −30.3297 | −1.13586 | ||||||||
\(714\) | −11.4252 | + | 6.65134i | −0.427577 | + | 0.248920i | ||||
\(715\) | 5.72755 | 0.214198 | ||||||||
\(716\) | 3.42378 | − | 5.93016i | 0.127953 | − | 0.221620i | ||||
\(717\) | 0.869826 | + | 1.50658i | 0.0324843 | + | 0.0562644i | ||||
\(718\) | −12.1815 | − | 21.0990i | −0.454610 | − | 0.787407i | ||||
\(719\) | 13.2519 | − | 22.9530i | 0.494213 | − | 0.856001i | −0.505765 | − | 0.862671i | \(-0.668790\pi\) |
0.999978 | + | 0.00666979i | \(0.00212307\pi\) | |||||||
\(720\) | −1.14924 | −0.0428295 | ||||||||
\(721\) | −15.9708 | − | 9.14421i | −0.594785 | − | 0.340548i | ||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −10.4246 | + | 18.0560i | −0.387695 | + | 0.671508i | ||||
\(724\) | 8.29527 | + | 14.3678i | 0.308291 | + | 0.533976i | ||||
\(725\) | 6.92883 | + | 12.0011i | 0.257330 | + | 0.445709i | ||||
\(726\) | 3.14924 | − | 5.45464i | 0.116879 | − | 0.202441i | ||||
\(727\) | 27.4510 | 1.01810 | 0.509051 | − | 0.860736i | \(-0.329996\pi\) | ||||
0.509051 | + | 0.860736i | \(0.329996\pi\) | |||||||
\(728\) | −0.0219083 | − | 6.08115i | −0.000811974 | − | 0.225382i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.71697 | − | 4.70593i | 0.100560 | − | 0.174174i | ||||
\(731\) | −5.20658 | − | 9.01806i | −0.192572 | − | 0.333545i | ||||
\(732\) | 1.28811 | + | 2.23107i | 0.0476100 | + | 0.0824629i | ||||
\(733\) | 7.08255 | − | 12.2673i | 0.261600 | − | 0.453104i | −0.705067 | − | 0.709140i | \(-0.749083\pi\) |
0.966667 | + | 0.256036i | \(0.0824166\pi\) | |||||||
\(734\) | 33.1571 | 1.22385 | ||||||||
\(735\) | −8.04445 | + | 0.0579634i | −0.296724 | + | 0.00213801i | ||||
\(736\) | 6.91567 | 0.254915 | ||||||||
\(737\) | 9.63341 | − | 16.6856i | 0.354851 | − | 0.614621i | ||||
\(738\) | 0.403292 | + | 0.698521i | 0.0148454 | + | 0.0257129i | ||||
\(739\) | −3.77009 | − | 6.52999i | −0.138685 | − | 0.240210i | 0.788314 | − | 0.615273i | \(-0.210954\pi\) |
−0.926999 | + | 0.375063i | \(0.877621\pi\) | |||||||
\(740\) | 0.379358 | − | 0.657067i | 0.0139455 | − | 0.0241543i | ||||
\(741\) | −2.29847 | −0.0844365 | ||||||||
\(742\) | 0.107434 | + | 29.8209i | 0.00394404 | + | 1.09476i | ||||
\(743\) | −53.8226 | −1.97456 | −0.987279 | − | 0.158997i | \(-0.949174\pi\) | ||||
−0.987279 | + | 0.158997i | \(0.949174\pi\) | |||||||
\(744\) | −2.19283 | + | 3.79808i | −0.0803929 | + | 0.139245i | ||||
\(745\) | −12.1917 | − | 21.1166i | −0.446668 | − | 0.773652i | ||||
\(746\) | −11.2730 | − | 19.5254i | −0.412734 | − | 0.714876i | ||||
\(747\) | −1.58718 | + | 2.74907i | −0.0580718 | + | 0.100583i | ||||
\(748\) | 10.8345 | 0.396150 | ||||||||
\(749\) | 28.4678 | + | 16.2994i | 1.04019 | + | 0.595568i | ||||
\(750\) | 9.97452 | 0.364218 | ||||||||
\(751\) | −10.3881 | + | 17.9927i | −0.379068 | + | 0.656565i | −0.990927 | − | 0.134402i | \(-0.957089\pi\) |
0.611859 | + | 0.790967i | \(0.290422\pi\) | |||||||
\(752\) | 1.86113 | + | 3.22356i | 0.0678683 | + | 0.117551i | ||||
\(753\) | 1.59831 | + | 2.76836i | 0.0582458 | + | 0.100885i | ||||
\(754\) | 4.32852 | − | 7.49722i | 0.157635 | − | 0.273033i | ||||
\(755\) | −10.8050 | −0.393233 | ||||||||
\(756\) | −2.28651 | + | 1.33112i | −0.0831595 | + | 0.0484124i | ||||
\(757\) | −15.9757 | −0.580647 | −0.290323 | − | 0.956929i | \(-0.593763\pi\) | ||||
−0.290323 | + | 0.956929i | \(0.593763\pi\) | |||||||
\(758\) | 9.38078 | − | 16.2480i | 0.340725 | − | 0.590154i | ||||
\(759\) | 7.49762 | + | 12.9863i | 0.272146 | + | 0.471371i | ||||
\(760\) | −0.574618 | − | 0.995268i | −0.0208436 | − | 0.0361022i | ||||
\(761\) | −7.09149 | + | 12.2828i | −0.257066 | + | 0.445252i | −0.965455 | − | 0.260571i | \(-0.916089\pi\) |
0.708388 | + | 0.705823i | \(0.249422\pi\) | |||||||
\(762\) | −13.8683 | −0.502395 | ||||||||
\(763\) | 41.2871 | − | 24.0358i | 1.49469 | − | 0.870156i | ||||
\(764\) | 15.8902 | 0.574887 | ||||||||
\(765\) | −2.87125 | + | 4.97315i | −0.103810 | + | 0.179805i | ||||
\(766\) | −4.05885 | − | 7.03014i | −0.146652 | − | 0.254009i | ||||
\(767\) | −11.9827 | − | 20.7546i | −0.432669 | − | 0.749404i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −39.7426 | −1.43316 | −0.716578 | − | 0.697507i | \(-0.754292\pi\) | ||||
−0.716578 | + | 0.697507i | \(0.754292\pi\) | |||||||
\(770\) | 5.72148 | + | 3.27587i | 0.206188 | + | 0.118054i | ||||
\(771\) | 15.0219 | 0.541001 | ||||||||
\(772\) | −3.24838 | + | 5.62636i | −0.116912 | + | 0.202497i | ||||
\(773\) | −0.0918959 | − | 0.159168i | −0.00330527 | − | 0.00572489i | 0.864368 | − | 0.502860i | \(-0.167719\pi\) |
−0.867673 | + | 0.497135i | \(0.834385\pi\) | |||||||
\(774\) | −1.04198 | − | 1.80477i | −0.0374533 | − | 0.0648711i | ||||
\(775\) | 8.06796 | − | 13.9741i | 0.289810 | − | 0.501965i | ||||
\(776\) | 5.91567 | 0.212360 | ||||||||
\(777\) | −0.00629271 | − | 1.74669i | −0.000225750 | − | 0.0626622i | ||||
\(778\) | 35.0034 | 1.25493 | ||||||||
\(779\) | −0.403292 | + | 0.698521i | −0.0144494 | + | 0.0250271i | ||||
\(780\) | −1.32075 | − | 2.28760i | −0.0472903 | − | 0.0819092i | ||||
\(781\) | −0.350821 | − | 0.607639i | −0.0125534 | − | 0.0217430i | ||||
\(782\) | 17.2781 | − | 29.9265i | 0.617863 | − | 1.07017i | ||||
\(783\) | −3.76643 | −0.134601 | ||||||||
\(784\) | 3.45623 | − | 6.08724i | 0.123437 | − | 0.217401i | ||||
\(785\) | −7.06460 | −0.252146 | ||||||||
\(786\) | −6.10565 | + | 10.5753i | −0.217781 | + | 0.377208i | ||||
\(787\) | 10.1079 | + | 17.5074i | 0.360308 | + | 0.624071i | 0.988011 | − | 0.154381i | \(-0.0493383\pi\) |
−0.627704 | + | 0.778452i | \(0.716005\pi\) | |||||||
\(788\) | −0.532453 | − | 0.922235i | −0.0189678 | − | 0.0328533i | ||||
\(789\) | 5.33802 | − | 9.24573i | 0.190039 | − | 0.329157i | ||||
\(790\) | −8.72510 | −0.310425 | ||||||||
\(791\) | −0.0823337 | − | 22.8536i | −0.00292745 | − | 0.812582i | ||||
\(792\) | 2.16830 | 0.0770472 | ||||||||
\(793\) | −2.96069 | + | 5.12807i | −0.105137 | + | 0.182103i | ||||
\(794\) | 7.51095 | + | 13.0094i | 0.266554 | + | 0.461685i | ||||
\(795\) | 6.47672 | + | 11.2180i | 0.229705 | + | 0.397861i | ||||
\(796\) | −11.7959 | + | 20.4310i | −0.418093 | + | 0.724158i | ||||
\(797\) | −33.9377 | −1.20213 | −0.601067 | − | 0.799198i | \(-0.705258\pi\) | ||||
−0.601067 | + | 0.799198i | \(0.705258\pi\) | |||||||
\(798\) | −2.29604 | − | 1.31461i | −0.0812789 | − | 0.0465368i | ||||
\(799\) | 18.5993 | 0.657996 | ||||||||
\(800\) | −1.83963 | + | 3.18633i | −0.0650406 | + | 0.112654i | ||||
\(801\) | −6.18879 | − | 10.7193i | −0.218670 | − | 0.378748i | ||||
\(802\) | −13.3143 | − | 23.0611i | −0.470145 | − | 0.814316i | ||||
\(803\) | −5.12619 | + | 8.87883i | −0.180899 | + | 0.313327i | ||||
\(804\) | −8.88568 | −0.313374 | ||||||||
\(805\) | 18.1726 | − | 10.5794i | 0.640499 | − | 0.372875i | ||||
\(806\) | −10.0803 | −0.355064 | ||||||||
\(807\) | −1.62453 | + | 2.81377i | −0.0571862 | + | 0.0990494i | ||||
\(808\) | −6.43414 | − | 11.1443i | −0.226352 | − | 0.392054i | ||||
\(809\) | 17.3595 | + | 30.0676i | 0.610328 | + | 1.05712i | 0.991185 | + | 0.132485i | \(0.0422958\pi\) |
−0.380857 | + | 0.924634i | \(0.624371\pi\) | |||||||
\(810\) | −0.574618 | + | 0.995268i | −0.0201900 | + | 0.0349702i | ||||
\(811\) | 44.1620 | 1.55074 | 0.775369 | − | 0.631509i | \(-0.217564\pi\) | ||||
0.775369 | + | 0.631509i | \(0.217564\pi\) | |||||||
\(812\) | 8.61197 | − | 5.01358i | 0.302221 | − | 0.175942i | ||||
\(813\) | −18.0349 | −0.632512 | ||||||||
\(814\) | −0.715746 | + | 1.23971i | −0.0250869 | + | 0.0434518i | ||||
\(815\) | −4.94628 | − | 8.56720i | −0.173261 | − | 0.300096i | ||||
\(816\) | −2.49840 | − | 4.32735i | −0.0874613 | − | 0.151487i | ||||
\(817\) | 1.04198 | − | 1.80477i | 0.0364544 | − | 0.0631409i | ||||
\(818\) | −27.6489 | −0.966721 | ||||||||
\(819\) | −5.27739 | − | 3.02160i | −0.184407 | − | 0.105583i | ||||
\(820\) | −0.926955 | −0.0323707 | ||||||||
\(821\) | −6.05371 | + | 10.4853i | −0.211276 | + | 0.365941i | −0.952114 | − | 0.305743i | \(-0.901095\pi\) |
0.740838 | + | 0.671684i | \(0.234429\pi\) | |||||||
\(822\) | −5.54038 | − | 9.59622i | −0.193243 | − | 0.334707i | ||||
\(823\) | −1.84812 | − | 3.20103i | −0.0644213 | − | 0.111581i | 0.832016 | − | 0.554752i | \(-0.187187\pi\) |
−0.896437 | + | 0.443171i | \(0.853853\pi\) | |||||||
\(824\) | 3.47791 | − | 6.02392i | 0.121159 | − | 0.209853i | ||||
\(825\) | −7.97773 | −0.277749 | ||||||||
\(826\) | −0.0993830 | − | 27.5861i | −0.00345798 | − | 0.959842i | ||||
\(827\) | −11.8614 | −0.412461 | −0.206230 | − | 0.978503i | \(-0.566120\pi\) | ||||
−0.206230 | + | 0.978503i | \(0.566120\pi\) | |||||||
\(828\) | 3.45783 | − | 5.98914i | 0.120168 | − | 0.208137i | ||||
\(829\) | −17.1460 | − | 29.6978i | −0.595506 | − | 1.03145i | −0.993475 | − | 0.114048i | \(-0.963618\pi\) |
0.397969 | − | 0.917399i | \(-0.369715\pi\) | |||||||
\(830\) | −1.82404 | − | 3.15933i | −0.0633134 | − | 0.109662i | ||||
\(831\) | 11.1420 | − | 19.2984i | 0.386510 | − | 0.669455i | ||||
\(832\) | 2.29847 | 0.0796852 | ||||||||
\(833\) | −17.7066 | − | 30.1646i | −0.613496 | − | 1.04514i | ||||
\(834\) | −11.0175 | −0.381505 | ||||||||
\(835\) | 6.88099 | − | 11.9182i | 0.238126 | − | 0.412447i | ||||
\(836\) | 1.08415 | + | 1.87780i | 0.0374961 | + | 0.0649452i | ||||
\(837\) | 2.19283 | + | 3.79808i | 0.0757951 | + | 0.131281i | ||||
\(838\) | 0.959438 | − | 1.66180i | 0.0331432 | − | 0.0574058i | ||||
\(839\) | 23.5395 | 0.812672 | 0.406336 | − | 0.913724i | \(-0.366806\pi\) | ||||
0.406336 | + | 0.913724i | \(0.366806\pi\) | |||||||
\(840\) | −0.0109541 | − | 3.04058i | −0.000377953 | − | 0.104910i | ||||
\(841\) | −14.8140 | −0.510827 | ||||||||
\(842\) | 12.9907 | − | 22.5006i | 0.447690 | − | 0.775423i | ||||
\(843\) | 3.55395 | + | 6.15562i | 0.122405 | + | 0.212011i | ||||
\(844\) | −8.93497 | − | 15.4758i | −0.307554 | − | 0.532700i | ||||
\(845\) | −4.43434 | + | 7.68050i | −0.152546 | + | 0.264217i | ||||
\(846\) | 3.72225 | 0.127974 | ||||||||
\(847\) | 14.4615 | + | 8.28005i | 0.496904 | + | 0.284506i | ||||
\(848\) | −11.2713 | −0.387059 | ||||||||
\(849\) | −7.87368 | + | 13.6376i | −0.270224 | + | 0.468042i | ||||
\(850\) | 9.19223 | + | 15.9214i | 0.315291 | + | 0.546100i | ||||
\(851\) | 2.28283 | + | 3.95398i | 0.0782544 | + | 0.135541i | ||||
\(852\) | −0.161795 | + | 0.280238i | −0.00554301 | + | 0.00960078i | ||||
\(853\) | −54.9855 | −1.88267 | −0.941334 | − | 0.337477i | \(-0.890427\pi\) | ||||
−0.941334 | + | 0.337477i | \(0.890427\pi\) | |||||||
\(854\) | −5.89055 | + | 3.42927i | −0.201571 | + | 0.117347i | ||||
\(855\) | −1.14924 | −0.0393031 | ||||||||
\(856\) | −6.19933 | + | 10.7376i | −0.211889 | + | 0.367002i | ||||
\(857\) | −29.0666 | − | 50.3449i | −0.992897 | − | 1.71975i | −0.599485 | − | 0.800386i | \(-0.704628\pi\) |
−0.393412 | − | 0.919362i | \(-0.628705\pi\) | |||||||
\(858\) | 2.49189 | + | 4.31608i | 0.0850717 | + | 0.147349i | ||||
\(859\) | −5.82584 | + | 10.0907i | −0.198775 | + | 0.344289i | −0.948132 | − | 0.317878i | \(-0.897030\pi\) |
0.749356 | + | 0.662167i | \(0.230363\pi\) | |||||||
\(860\) | 2.39497 | 0.0816679 | ||||||||
\(861\) | −1.84426 | + | 1.07366i | −0.0628521 | + | 0.0365902i | ||||
\(862\) | −0.965082 | −0.0328708 | ||||||||
\(863\) | 4.82235 | − | 8.35255i | 0.164155 | − | 0.284324i | −0.772200 | − | 0.635379i | \(-0.780844\pi\) |
0.936355 | + | 0.351055i | \(0.114177\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 4.65547 | + | 8.06351i | 0.158291 | + | 0.274168i | ||||
\(866\) | −2.96980 | + | 5.14385i | −0.100918 | + | 0.174795i | ||||
\(867\) | −7.96793 | −0.270605 | ||||||||
\(868\) | −10.0696 | − | 5.76543i | −0.341785 | − | 0.195691i | ||||
\(869\) | 16.4619 | 0.558432 | ||||||||
\(870\) | 2.16426 | − | 3.74861i | 0.0733753 | − | 0.127090i | ||||
\(871\) | −10.2118 | − | 17.6873i | −0.346012 | − | 0.599310i | ||||
\(872\) | 9.02841 | + | 15.6377i | 0.305741 | + | 0.529558i | ||||
\(873\) | 2.95783 | − | 5.12312i | 0.100108 | − | 0.173391i | ||||
\(874\) | 6.91567 | 0.233926 | ||||||||
\(875\) | 0.0950737 | + | 26.3899i | 0.00321408 | + | 0.892142i | ||||
\(876\) | 4.72830 | 0.159755 | ||||||||
\(877\) | 25.9599 | − | 44.9639i | 0.876605 | − | 1.51832i | 0.0215614 | − | 0.999768i | \(-0.493136\pi\) |
0.855043 | − | 0.518556i | \(-0.173530\pi\) | |||||||
\(878\) | 10.7960 | + | 18.6993i | 0.364349 | + | 0.631070i | ||||
\(879\) | 11.0070 | + | 19.0646i | 0.371256 | + | 0.643034i | ||||
\(880\) | −1.24595 | + | 2.15804i | −0.0420008 | + | 0.0727475i | ||||
\(881\) | 1.32443 | 0.0446213 | 0.0223106 | − | 0.999751i | \(-0.492898\pi\) | ||||
0.0223106 | + | 0.999751i | \(0.492898\pi\) | |||||||
\(882\) | −3.54359 | − | 6.03680i | −0.119319 | − | 0.203270i | ||||
\(883\) | −45.6432 | −1.53602 | −0.768009 | − | 0.640439i | \(-0.778752\pi\) | ||||
−0.768009 | + | 0.640439i | \(0.778752\pi\) | |||||||
\(884\) | 5.74250 | − | 9.94630i | 0.193141 | − | 0.334530i | ||||
\(885\) | −5.99133 | − | 10.3773i | −0.201396 | − | 0.348829i | ||||
\(886\) | 6.96718 | + | 12.0675i | 0.234067 | + | 0.405416i | ||||
\(887\) | −2.59044 | + | 4.48678i | −0.0869786 | + | 0.150651i | −0.906233 | − | 0.422779i | \(-0.861054\pi\) |
0.819254 | + | 0.573431i | \(0.194388\pi\) | |||||||
\(888\) | 0.660191 | 0.0221546 | ||||||||
\(889\) | −0.132188 | − | 36.6918i | −0.00443343 | − | 1.23060i | ||||
\(890\) | 14.2248 | 0.476815 | ||||||||
\(891\) | 1.08415 | − | 1.87780i | 0.0363204 | − | 0.0629088i | ||||
\(892\) | −2.22302 | − | 3.85039i | −0.0744324 | − | 0.128921i | ||||
\(893\) | 1.86113 | + | 3.22356i | 0.0622802 | + | 0.107872i | ||||
\(894\) | 10.6085 | − | 18.3744i | 0.354801 | − | 0.614534i | ||||
\(895\) | 7.86946 | 0.263047 | ||||||||
\(896\) | 2.29604 | + | 1.31461i | 0.0767053 | + | 0.0439181i | ||||
\(897\) | 15.8955 | 0.530735 | ||||||||
\(898\) | 7.16367 | − | 12.4078i | 0.239055 | − | 0.414055i | ||||
\(899\) | −8.25913 | − | 14.3052i | −0.275457 | − | 0.477106i | ||||
\(900\) | 1.83963 | + | 3.18633i | 0.0613209 | + | 0.106211i | ||||
\(901\) | −28.1602 | + | 48.7750i | −0.938154 | + | 1.62493i | ||||
\(902\) | 1.74891 | 0.0582325 | ||||||||
\(903\) | 4.76501 | − | 2.77402i | 0.158570 | − | 0.0923135i | ||||
\(904\) | 8.63792 | 0.287293 | ||||||||
\(905\) | −9.53323 | + | 16.5120i | −0.316895 | + | 0.548878i | ||||
\(906\) | −4.70093 | − | 8.14226i | −0.156178 | − | 0.270508i | ||||
\(907\) | −29.2508 | − | 50.6640i | −0.971258 | − | 1.68227i | −0.691767 | − | 0.722121i | \(-0.743168\pi\) |
−0.279491 | − | 0.960148i | \(-0.590166\pi\) | |||||||
\(908\) | −10.0469 | + | 17.4017i | −0.333418 | + | 0.577496i | ||||
\(909\) | −12.8683 | −0.426814 | ||||||||
\(910\) | 6.03979 | − | 3.51615i | 0.200217 | − | 0.116559i | ||||
\(911\) | 23.2344 | 0.769790 | 0.384895 | − | 0.922960i | \(-0.374238\pi\) | ||||
0.384895 | + | 0.922960i | \(0.374238\pi\) | |||||||
\(912\) | 0.500000 | − | 0.866025i | 0.0165567 | − | 0.0286770i | ||||
\(913\) | 3.44148 | + | 5.96081i | 0.113896 | + | 0.197274i | ||||
\(914\) | 16.1491 | + | 27.9710i | 0.534163 | + | 0.925198i | ||||
\(915\) | −1.48035 | + | 2.56403i | −0.0489387 | + | 0.0847643i | ||||
\(916\) | 17.9555 | 0.593265 | ||||||||
\(917\) | −28.0376 | − | 16.0531i | −0.925884 | − | 0.530121i | ||||
\(918\) | −4.99679 | −0.164919 | ||||||||
\(919\) | −8.93753 | + | 15.4803i | −0.294822 | + | 0.510647i | −0.974943 | − | 0.222453i | \(-0.928594\pi\) |
0.680122 | + | 0.733099i | \(0.261927\pi\) | |||||||
\(920\) | 3.97387 | + | 6.88295i | 0.131015 | + | 0.226924i | ||||
\(921\) | 7.18879 | + | 12.4513i | 0.236879 | + | 0.410286i | ||||
\(922\) | 0.187925 | − | 0.325495i | 0.00618897 | − | 0.0107196i | ||||
\(923\) | −0.743764 | −0.0244813 | ||||||||
\(924\) | 0.0206675 | + | 5.73675i | 0.000679911 | + | 0.188725i | ||||
\(925\) | −2.42901 | −0.0798654 | ||||||||
\(926\) | 3.90412 | − | 6.76214i | 0.128297 | − | 0.222218i | ||||
\(927\) | −3.47791 | − | 6.02392i | −0.114230 | − | 0.197851i | ||||
\(928\) | 1.88322 | + | 3.26183i | 0.0618196 | + | 0.107075i | ||||
\(929\) | −23.2246 | + | 40.2262i | −0.761974 | + | 1.31978i | 0.179857 | + | 0.983693i | \(0.442436\pi\) |
−0.941832 | + | 0.336085i | \(0.890897\pi\) | |||||||
\(930\) | −5.04015 | −0.165273 | ||||||||
\(931\) | 3.45623 | − | 6.08724i | 0.113273 | − | 0.199501i | ||||
\(932\) | 10.2539 | 0.335879 | ||||||||
\(933\) | −1.48726 | + | 2.57601i | −0.0486907 | + | 0.0843348i | ||||
\(934\) | −6.12774 | − | 10.6136i | −0.200506 | − | 0.347286i | ||||
\(935\) | 6.22573 | + | 10.7833i | 0.203603 | + | 0.352651i | ||||
\(936\) | 1.14924 | − | 1.99054i | 0.0375640 | − | 0.0650627i | ||||
\(937\) | −42.3561 | −1.38371 | −0.691857 | − | 0.722034i | \(-0.743207\pi\) | ||||
−0.691857 | + | 0.722034i | \(0.743207\pi\) | |||||||
\(938\) | −0.0846953 | − | 23.5092i | −0.00276540 | − | 0.767601i | ||||
\(939\) | 16.7588 | 0.546904 | ||||||||
\(940\) | −2.13887 | + | 3.70464i | −0.0697624 | + | 0.120832i | ||||
\(941\) | 23.2485 | + | 40.2675i | 0.757878 | + | 1.31268i | 0.943931 | + | 0.330144i | \(0.107097\pi\) |
−0.186052 | + | 0.982540i | \(0.559569\pi\) | |||||||
\(942\) | −3.07361 | − | 5.32364i | −0.100143 | − | 0.173454i | ||||
\(943\) | 2.78903 | − | 4.83074i | 0.0908233 | − | 0.157311i | ||||
\(944\) | 10.4266 | 0.339358 | ||||||||
\(945\) | −2.63869 | − | 1.51080i | −0.0858367 | − | 0.0491464i | ||||
\(946\) | −4.51867 | −0.146915 | ||||||||
\(947\) | −23.6328 | + | 40.9333i | −0.767964 | + | 1.33015i | 0.170701 | + | 0.985323i | \(0.445397\pi\) |
−0.938665 | + | 0.344830i | \(0.887937\pi\) | |||||||
\(948\) | −3.79604 | − | 6.57493i | −0.123290 | − | 0.213544i | ||||
\(949\) | 5.43394 | + | 9.41186i | 0.176393 | + | 0.305522i | ||||
\(950\) | −1.83963 | + | 3.18633i | −0.0596854 | + | 0.103378i | ||||
\(951\) | 2.81061 | 0.0911403 | ||||||||
\(952\) | 11.4252 | − | 6.65134i | 0.370293 | − | 0.215571i | ||||
\(953\) | −0.673201 | −0.0218071 | −0.0109036 | − | 0.999941i | \(-0.503471\pi\) | ||||
−0.0109036 | + | 0.999941i | \(0.503471\pi\) | |||||||
\(954\) | −5.63567 | + | 9.76126i | −0.182461 | + | 0.316032i | ||||
\(955\) | 9.13080 | + | 15.8150i | 0.295466 | + | 0.511761i | ||||
\(956\) | −0.869826 | − | 1.50658i | −0.0281322 | − | 0.0487264i | ||||
\(957\) | −4.08338 | + | 7.07262i | −0.131997 | + | 0.228625i | ||||
\(958\) | −27.0751 | −0.874756 | ||||||||
\(959\) | 25.3362 | − | 14.7498i | 0.818150 | − | 0.476297i | ||||
\(960\) | 1.14924 | 0.0370915 | ||||||||
\(961\) | 5.88303 | − | 10.1897i | 0.189775 | − | 0.328700i | ||||
\(962\) | 0.758716 | + | 1.31413i | 0.0244620 | + | 0.0423694i | ||||
\(963\) | 6.19933 | + | 10.7376i | 0.199771 | + | 0.346013i | ||||
\(964\) | 10.4246 | − | 18.0560i | 0.335754 | − | 0.581543i | ||||
\(965\) | −7.46632 | −0.240349 | ||||||||
\(966\) | 15.8786 | + | 9.09142i | 0.510887 | + | 0.292512i | ||||
\(967\) | 1.83609 | 0.0590447 | 0.0295224 | − | 0.999564i | \(-0.490601\pi\) | ||||
0.0295224 | + | 0.999564i | \(0.490601\pi\) | |||||||
\(968\) | −3.14924 | + | 5.45464i | −0.101220 | + | 0.175319i | ||||
\(969\) | −2.49840 | − | 4.32735i | −0.0802600 | − | 0.139014i | ||||
\(970\) | 3.39925 | + | 5.88768i | 0.109143 | + | 0.189042i | ||||
\(971\) | −6.32442 | + | 10.9542i | −0.202960 | + | 0.351538i | −0.949481 | − | 0.313825i | \(-0.898390\pi\) |
0.746521 | + | 0.665362i | \(0.231723\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −0.105015 | − | 29.1494i | −0.00336663 | − | 0.934488i | ||||
\(974\) | −29.7498 | −0.953247 | ||||||||
\(975\) | −4.22834 | + | 7.32369i | −0.135415 | + | 0.234546i | ||||
\(976\) | −1.28811 | − | 2.23107i | −0.0412314 | − | 0.0714149i | ||||
\(977\) | −10.6728 | − | 18.4859i | −0.341454 | − | 0.591416i | 0.643249 | − | 0.765657i | \(-0.277586\pi\) |
−0.984703 | + | 0.174241i | \(0.944253\pi\) | |||||||
\(978\) | 4.30397 | − | 7.45469i | 0.137626 | − | 0.238375i | ||||
\(979\) | −26.8383 | −0.857756 | ||||||||
\(980\) | 8.04445 | − | 0.0579634i | 0.256971 | − | 0.00185157i | ||||
\(981\) | 18.0568 | 0.576510 | ||||||||
\(982\) | 9.21904 | − | 15.9679i | 0.294191 | − | 0.509555i | ||||
\(983\) | −12.8634 | − | 22.2801i | −0.410279 | − | 0.710624i | 0.584641 | − | 0.811292i | \(-0.301235\pi\) |
−0.994920 | + | 0.100668i | \(0.967902\pi\) | |||||||
\(984\) | −0.403292 | − | 0.698521i | −0.0128565 | − | 0.0222681i | ||||
\(985\) | 0.611914 | − | 1.05987i | 0.0194972 | − | 0.0337702i | ||||
\(986\) | 18.8201 | 0.599353 | ||||||||
\(987\) | 0.0354792 | + | 9.84809i | 0.00112932 | + | 0.313468i | ||||
\(988\) | 2.29847 | 0.0731242 | ||||||||
\(989\) | −7.20602 | + | 12.4812i | −0.229138 | + | 0.396879i | ||||
\(990\) | 1.24595 | + | 2.15804i | 0.0395987 | + | 0.0685870i | ||||
\(991\) | 29.0912 | + | 50.3874i | 0.924111 | + | 1.60061i | 0.792985 | + | 0.609241i | \(0.208526\pi\) |
0.131126 | + | 0.991366i | \(0.458141\pi\) | |||||||
\(992\) | 2.19283 | − | 3.79808i | 0.0696223 | − | 0.120589i | ||||
\(993\) | 10.1391 | 0.321754 | ||||||||
\(994\) | −0.742976 | − | 0.425396i | −0.0235658 | − | 0.0134927i | ||||
\(995\) | −27.1125 | −0.859523 | ||||||||
\(996\) | 1.58718 | − | 2.74907i | 0.0502916 | − | 0.0871076i | ||||
\(997\) | 25.6396 | + | 44.4091i | 0.812014 | + | 1.40645i | 0.911453 | + | 0.411405i | \(0.134962\pi\) |
−0.0994388 | + | 0.995044i | \(0.531705\pi\) | |||||||
\(998\) | 16.5785 | + | 28.7148i | 0.524783 | + | 0.908952i | ||||
\(999\) | 0.330096 | − | 0.571742i | 0.0104438 | − | 0.0180891i |
(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 | 798.2.j.l.457.3 | ✓ | 8 | |
7.2 | even | 3 | 5586.2.a.bw.1.2 | 4 | |||
7.4 | even | 3 | inner | 798.2.j.l.571.3 | yes | 8 | |
7.5 | odd | 6 | 5586.2.a.bz.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.l.457.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
798.2.j.l.571.3 | yes | 8 | 7.4 | even | 3 | inner | |
5586.2.a.bw.1.2 | 4 | 7.2 | even | 3 | |||
5586.2.a.bz.1.3 | 4 | 7.5 | odd | 6 |