Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(87,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.87");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.m (of order \(8\), degree \(4\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 689.19 | ||
Character | \(\chi\) | \(=\) | 731.689 |
Dual form | 731.2.m.c.87.19 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.639626 | − | 0.639626i | 0.452284 | − | 0.452284i | −0.443828 | − | 0.896112i | \(-0.646380\pi\) |
0.896112 | + | 0.443828i | \(0.146380\pi\) | |||||||
\(3\) | −0.916759 | − | 0.379734i | −0.529291 | − | 0.219239i | 0.102002 | − | 0.994784i | \(-0.467475\pi\) |
−0.631293 | + | 0.775545i | \(0.717475\pi\) | |||||||
\(4\) | 1.18176i | 0.590879i | ||||||||
\(5\) | 0.199818 | − | 0.482403i | 0.0893612 | − | 0.215737i | −0.872880 | − | 0.487935i | \(-0.837750\pi\) |
0.962241 | + | 0.272198i | \(0.0877504\pi\) | |||||||
\(6\) | −0.829270 | + | 0.343495i | −0.338548 | + | 0.140231i | ||||
\(7\) | 0.462611 | + | 1.11684i | 0.174851 | + | 0.422127i | 0.986873 | − | 0.161500i | \(-0.0516332\pi\) |
−0.812022 | + | 0.583627i | \(0.801633\pi\) | |||||||
\(8\) | 2.03513 | + | 2.03513i | 0.719529 | + | 0.719529i | ||||
\(9\) | −1.42507 | − | 1.42507i | −0.475024 | − | 0.475024i | ||||
\(10\) | −0.180749 | − | 0.436366i | −0.0571577 | − | 0.137991i | ||||
\(11\) | 1.30474 | − | 0.540439i | 0.393392 | − | 0.162948i | −0.177214 | − | 0.984172i | \(-0.556708\pi\) |
0.570606 | + | 0.821224i | \(0.306708\pi\) | |||||||
\(12\) | 0.448753 | − | 1.08339i | 0.129544 | − | 0.312747i | ||||
\(13\) | 6.44237i | 1.78679i | 0.449270 | + | 0.893396i | \(0.351684\pi\) | ||||
−0.449270 | + | 0.893396i | \(0.648316\pi\) | |||||||
\(14\) | 1.01026 | + | 0.418463i | 0.270003 | + | 0.111839i | ||||
\(15\) | −0.366369 | + | 0.366369i | −0.0945962 | + | 0.0945962i | ||||
\(16\) | 0.239934 | 0.0599835 | ||||||||
\(17\) | −2.99591 | + | 2.83276i | −0.726615 | + | 0.687045i | ||||
\(18\) | −1.82303 | −0.429691 | ||||||||
\(19\) | 3.13514 | − | 3.13514i | 0.719251 | − | 0.719251i | −0.249201 | − | 0.968452i | \(-0.580168\pi\) |
0.968452 | + | 0.249201i | \(0.0801678\pi\) | |||||||
\(20\) | 0.570083 | + | 0.236136i | 0.127474 | + | 0.0528016i | ||||
\(21\) | − | 1.19954i | − | 0.261762i | ||||||
\(22\) | 0.488864 | − | 1.18022i | 0.104226 | − | 0.251624i | ||||
\(23\) | −5.39622 | + | 2.23519i | −1.12519 | + | 0.466069i | −0.866143 | − | 0.499796i | \(-0.833408\pi\) |
−0.259047 | + | 0.965865i | \(0.583408\pi\) | |||||||
\(24\) | −1.09292 | − | 2.63854i | −0.223091 | − | 0.538589i | ||||
\(25\) | 3.34275 | + | 3.34275i | 0.668550 | + | 0.668550i | ||||
\(26\) | 4.12071 | + | 4.12071i | 0.808137 | + | 0.808137i | ||||
\(27\) | 1.90450 | + | 4.59787i | 0.366521 | + | 0.884861i | ||||
\(28\) | −1.31984 | + | 0.546694i | −0.249426 | + | 0.103315i | ||||
\(29\) | 1.18499 | − | 2.86083i | 0.220048 | − | 0.531242i | −0.774848 | − | 0.632147i | \(-0.782174\pi\) |
0.994896 | + | 0.100905i | \(0.0321738\pi\) | |||||||
\(30\) | 0.468679i | 0.0855686i | ||||||||
\(31\) | 5.43572 | + | 2.25155i | 0.976285 | + | 0.404390i | 0.813048 | − | 0.582197i | \(-0.197807\pi\) |
0.163237 | + | 0.986587i | \(0.447807\pi\) | |||||||
\(32\) | −3.91680 | + | 3.91680i | −0.692399 | + | 0.692399i | ||||
\(33\) | −1.40135 | −0.243944 | ||||||||
\(34\) | −0.104355 | + | 3.72817i | −0.0178967 | + | 0.639375i | ||||
\(35\) | 0.631205 | 0.106693 | ||||||||
\(36\) | 1.68409 | − | 1.68409i | 0.280681 | − | 0.280681i | ||||
\(37\) | 6.99643 | + | 2.89802i | 1.15021 | + | 0.476431i | 0.874603 | − | 0.484840i | \(-0.161122\pi\) |
0.275603 | + | 0.961271i | \(0.411122\pi\) | |||||||
\(38\) | − | 4.01064i | − | 0.650611i | ||||||
\(39\) | 2.44639 | − | 5.90610i | 0.391735 | − | 0.945733i | ||||
\(40\) | 1.38841 | − | 0.575098i | 0.219527 | − | 0.0909310i | ||||
\(41\) | 1.27061 | + | 3.06752i | 0.198436 | + | 0.479066i | 0.991506 | − | 0.130064i | \(-0.0415184\pi\) |
−0.793070 | + | 0.609131i | \(0.791518\pi\) | |||||||
\(42\) | −0.767259 | − | 0.767259i | −0.118391 | − | 0.118391i | ||||
\(43\) | −0.707107 | − | 0.707107i | −0.107833 | − | 0.107833i | ||||
\(44\) | 0.638668 | + | 1.54188i | 0.0962828 | + | 0.232447i | ||||
\(45\) | −0.972213 | + | 0.402704i | −0.144929 | + | 0.0600315i | ||||
\(46\) | −2.02188 | + | 4.88125i | −0.298110 | + | 0.719701i | ||||
\(47\) | 5.93360i | 0.865504i | 0.901513 | + | 0.432752i | \(0.142457\pi\) | ||||
−0.901513 | + | 0.432752i | \(0.857543\pi\) | |||||||
\(48\) | −0.219962 | − | 0.0911111i | −0.0317487 | − | 0.0131508i | ||||
\(49\) | 3.91642 | − | 3.91642i | 0.559489 | − | 0.559489i | ||||
\(50\) | 4.27622 | 0.604748 | ||||||||
\(51\) | 3.82222 | − | 1.45931i | 0.535218 | − | 0.204344i | ||||
\(52\) | −7.61332 | −1.05578 | ||||||||
\(53\) | −7.37026 | + | 7.37026i | −1.01238 | + | 1.01238i | −0.0124602 | + | 0.999922i | \(0.503966\pi\) |
−0.999922 | + | 0.0124602i | \(0.996034\pi\) | |||||||
\(54\) | 4.15909 | + | 1.72275i | 0.565980 | + | 0.234437i | ||||
\(55\) | − | 0.737397i | − | 0.0994306i | ||||||
\(56\) | −1.33145 | + | 3.21440i | −0.177922 | + | 0.429542i | ||||
\(57\) | −4.06469 | + | 1.68365i | −0.538382 | + | 0.223005i | ||||
\(58\) | −1.07191 | − | 2.58781i | −0.140748 | − | 0.339796i | ||||
\(59\) | 3.01122 | + | 3.01122i | 0.392028 | + | 0.392028i | 0.875410 | − | 0.483382i | \(-0.160592\pi\) |
−0.483382 | + | 0.875410i | \(0.660592\pi\) | |||||||
\(60\) | −0.432960 | − | 0.432960i | −0.0558949 | − | 0.0558949i | ||||
\(61\) | −5.47181 | − | 13.2101i | −0.700593 | − | 1.69138i | −0.722265 | − | 0.691616i | \(-0.756899\pi\) |
0.0216720 | − | 0.999765i | \(-0.493101\pi\) | |||||||
\(62\) | 4.91698 | − | 2.03668i | 0.624457 | − | 0.258659i | ||||
\(63\) | 0.932326 | − | 2.25083i | 0.117462 | − | 0.283578i | ||||
\(64\) | 5.49044i | 0.686305i | ||||||||
\(65\) | 3.10782 | + | 1.28730i | 0.385477 | + | 0.159670i | ||||
\(66\) | −0.896340 | + | 0.896340i | −0.110332 | + | 0.110332i | ||||
\(67\) | 8.65354 | 1.05720 | 0.528599 | − | 0.848872i | \(-0.322718\pi\) | ||||
0.528599 | + | 0.848872i | \(0.322718\pi\) | |||||||
\(68\) | −3.34764 | − | 3.54044i | −0.405960 | − | 0.429341i | ||||
\(69\) | 5.79581 | 0.697734 | ||||||||
\(70\) | 0.403735 | − | 0.403735i | 0.0482556 | − | 0.0482556i | ||||
\(71\) | −7.66813 | − | 3.17625i | −0.910040 | − | 0.376951i | −0.121968 | − | 0.992534i | \(-0.538921\pi\) |
−0.788072 | + | 0.615583i | \(0.788921\pi\) | |||||||
\(72\) | − | 5.80042i | − | 0.683587i | ||||||
\(73\) | 3.55138 | − | 8.57380i | 0.415658 | − | 1.00349i | −0.567933 | − | 0.823075i | \(-0.692257\pi\) |
0.983591 | − | 0.180412i | \(-0.0577432\pi\) | |||||||
\(74\) | 6.32874 | − | 2.62145i | 0.735702 | − | 0.304738i | ||||
\(75\) | −1.79514 | − | 4.33385i | −0.207285 | − | 0.500430i | ||||
\(76\) | 3.70498 | + | 3.70498i | 0.424990 | + | 0.424990i | ||||
\(77\) | 1.20717 | + | 1.20717i | 0.137570 | + | 0.137570i | ||||
\(78\) | −2.21292 | − | 5.34247i | −0.250564 | − | 0.604915i | ||||
\(79\) | 2.04936 | − | 0.848873i | 0.230571 | − | 0.0955057i | −0.264407 | − | 0.964411i | \(-0.585176\pi\) |
0.494978 | + | 0.868906i | \(0.335176\pi\) | |||||||
\(80\) | 0.0479431 | − | 0.115745i | 0.00536020 | − | 0.0129407i | ||||
\(81\) | 1.10772i | 0.123080i | ||||||||
\(82\) | 2.77478 | + | 1.14935i | 0.306423 | + | 0.126925i | ||||
\(83\) | −1.34503 | + | 1.34503i | −0.147636 | + | 0.147636i | −0.777061 | − | 0.629425i | \(-0.783290\pi\) |
0.629425 | + | 0.777061i | \(0.283290\pi\) | |||||||
\(84\) | 1.41757 | 0.154670 | ||||||||
\(85\) | 0.767895 | + | 2.01127i | 0.0832899 | + | 0.218153i | ||||
\(86\) | −0.904568 | −0.0975420 | ||||||||
\(87\) | −2.17271 | + | 2.17271i | −0.232939 | + | 0.232939i | ||||
\(88\) | 3.75518 | + | 1.55545i | 0.400303 | + | 0.165811i | ||||
\(89\) | − | 5.67384i | − | 0.601426i | −0.953715 | − | 0.300713i | \(-0.902775\pi\) | ||
0.953715 | − | 0.300713i | \(-0.0972247\pi\) | |||||||
\(90\) | −0.364273 | + | 0.879432i | −0.0383977 | + | 0.0927003i | ||||
\(91\) | −7.19511 | + | 2.98031i | −0.754252 | + | 0.312421i | ||||
\(92\) | −2.64145 | − | 6.37703i | −0.275390 | − | 0.664851i | ||||
\(93\) | −4.12826 | − | 4.12826i | −0.428080 | − | 0.428080i | ||||
\(94\) | 3.79528 | + | 3.79528i | 0.391454 | + | 0.391454i | ||||
\(95\) | −0.885945 | − | 2.13886i | −0.0908960 | − | 0.219442i | ||||
\(96\) | 5.07810 | − | 2.10342i | 0.518282 | − | 0.214679i | ||||
\(97\) | −0.981607 | + | 2.36981i | −0.0996671 | + | 0.240618i | −0.965846 | − | 0.259116i | \(-0.916569\pi\) |
0.866179 | + | 0.499734i | \(0.166569\pi\) | |||||||
\(98\) | − | 5.01009i | − | 0.506095i | ||||||
\(99\) | −2.62950 | − | 1.08918i | −0.264275 | − | 0.109466i | ||||
\(100\) | −3.95032 | + | 3.95032i | −0.395032 | + | 0.395032i | ||||
\(101\) | −14.6890 | −1.46161 | −0.730805 | − | 0.682587i | \(-0.760855\pi\) | ||||
−0.730805 | + | 0.682587i | \(0.760855\pi\) | |||||||
\(102\) | 1.51138 | − | 3.37820i | 0.149649 | − | 0.334492i | ||||
\(103\) | 3.13315 | 0.308718 | 0.154359 | − | 0.988015i | \(-0.450669\pi\) | ||||
0.154359 | + | 0.988015i | \(0.450669\pi\) | |||||||
\(104\) | −13.1111 | + | 13.1111i | −1.28565 | + | 1.28565i | ||||
\(105\) | −0.578663 | − | 0.239690i | −0.0564717 | − | 0.0233914i | ||||
\(106\) | 9.42841i | 0.915768i | ||||||||
\(107\) | 1.88230 | − | 4.54428i | 0.181969 | − | 0.439312i | −0.806403 | − | 0.591366i | \(-0.798589\pi\) |
0.988372 | + | 0.152054i | \(0.0485888\pi\) | |||||||
\(108\) | −5.43357 | + | 2.25066i | −0.522845 | + | 0.216570i | ||||
\(109\) | −4.86895 | − | 11.7547i | −0.466361 | − | 1.12589i | −0.965740 | − | 0.259511i | \(-0.916439\pi\) |
0.499379 | − | 0.866383i | \(-0.333561\pi\) | |||||||
\(110\) | −0.471658 | − | 0.471658i | −0.0449708 | − | 0.0449708i | ||||
\(111\) | −5.31356 | − | 5.31356i | −0.504341 | − | 0.504341i | ||||
\(112\) | 0.110996 | + | 0.267968i | 0.0104881 | + | 0.0253206i | ||||
\(113\) | 5.99660 | − | 2.48387i | 0.564113 | − | 0.233663i | −0.0823567 | − | 0.996603i | \(-0.526245\pi\) |
0.646470 | + | 0.762940i | \(0.276245\pi\) | |||||||
\(114\) | −1.52298 | + | 3.67679i | −0.142640 | + | 0.344363i | ||||
\(115\) | 3.04978i | 0.284394i | ||||||||
\(116\) | 3.38080 | + | 1.40038i | 0.313900 | + | 0.130022i | ||||
\(117\) | 9.18084 | − | 9.18084i | 0.848769 | − | 0.848769i | ||||
\(118\) | 3.85211 | 0.354616 | ||||||||
\(119\) | −4.54969 | − | 2.03549i | −0.417069 | − | 0.186593i | ||||
\(120\) | −1.49122 | −0.136129 | ||||||||
\(121\) | −6.36792 | + | 6.36792i | −0.578901 | + | 0.578901i | ||||
\(122\) | −11.9494 | − | 4.94962i | −1.08185 | − | 0.448117i | ||||
\(123\) | − | 3.29467i | − | 0.297070i | ||||||
\(124\) | −2.66079 | + | 6.42371i | −0.238946 | + | 0.576866i | ||||
\(125\) | 4.69251 | − | 1.94370i | 0.419710 | − | 0.173850i | ||||
\(126\) | −0.843352 | − | 2.03603i | −0.0751317 | − | 0.181384i | ||||
\(127\) | −6.44963 | − | 6.44963i | −0.572312 | − | 0.572312i | 0.360462 | − | 0.932774i | \(-0.382619\pi\) |
−0.932774 | + | 0.360462i | \(0.882619\pi\) | |||||||
\(128\) | −4.32177 | − | 4.32177i | −0.381994 | − | 0.381994i | ||||
\(129\) | 0.379734 | + | 0.916759i | 0.0334337 | + | 0.0807161i | ||||
\(130\) | 2.81123 | − | 1.16445i | 0.246561 | − | 0.102129i | ||||
\(131\) | −0.335160 | + | 0.809148i | −0.0292831 | + | 0.0706956i | −0.937845 | − | 0.347055i | \(-0.887182\pi\) |
0.908562 | + | 0.417751i | \(0.137182\pi\) | |||||||
\(132\) | − | 1.65606i | − | 0.144141i | ||||||
\(133\) | 4.95181 | + | 2.05111i | 0.429377 | + | 0.177854i | ||||
\(134\) | 5.53503 | − | 5.53503i | 0.478153 | − | 0.478153i | ||||
\(135\) | 2.59858 | 0.223650 | ||||||||
\(136\) | −11.8621 | − | 0.332031i | −1.01717 | − | 0.0284714i | ||||
\(137\) | −12.9262 | −1.10436 | −0.552181 | − | 0.833724i | \(-0.686204\pi\) | ||||
−0.552181 | + | 0.833724i | \(0.686204\pi\) | |||||||
\(138\) | 3.70715 | − | 3.70715i | 0.315574 | − | 0.315574i | ||||
\(139\) | 18.2574 | + | 7.56245i | 1.54857 | + | 0.641439i | 0.983057 | − | 0.183300i | \(-0.0586779\pi\) |
0.565514 | + | 0.824739i | \(0.308678\pi\) | |||||||
\(140\) | 0.745932i | 0.0630427i | ||||||||
\(141\) | 2.25319 | − | 5.43968i | 0.189753 | − | 0.458104i | ||||
\(142\) | −6.93635 | + | 2.87313i | −0.582085 | + | 0.241108i | ||||
\(143\) | 3.48171 | + | 8.40558i | 0.291155 | + | 0.702910i | ||||
\(144\) | −0.341923 | − | 0.341923i | −0.0284936 | − | 0.0284936i | ||||
\(145\) | −1.14329 | − | 1.14329i | −0.0949449 | − | 0.0949449i | ||||
\(146\) | −3.21247 | − | 7.75558i | −0.265866 | − | 0.641856i | ||||
\(147\) | −5.07761 | + | 2.10322i | −0.418794 | + | 0.173470i | ||||
\(148\) | −3.42475 | + | 8.26808i | −0.281513 | + | 0.679632i | ||||
\(149\) | − | 21.9825i | − | 1.80088i | −0.434984 | − | 0.900438i | \(-0.643246\pi\) | ||
0.434984 | − | 0.900438i | \(-0.356754\pi\) | |||||||
\(150\) | −3.92026 | − | 1.62382i | −0.320088 | − | 0.132585i | ||||
\(151\) | −4.42564 | + | 4.42564i | −0.360153 | + | 0.360153i | −0.863869 | − | 0.503716i | \(-0.831966\pi\) |
0.503716 | + | 0.863869i | \(0.331966\pi\) | |||||||
\(152\) | 12.7609 | 1.03504 | ||||||||
\(153\) | 8.30627 | + | 0.232500i | 0.671522 | + | 0.0187965i | ||||
\(154\) | 1.54427 | 0.124441 | ||||||||
\(155\) | 2.17231 | − | 2.17231i | 0.174484 | − | 0.174484i | ||||
\(156\) | 6.97958 | + | 2.89104i | 0.558813 | + | 0.231468i | ||||
\(157\) | − | 6.68135i | − | 0.533230i | −0.963803 | − | 0.266615i | \(-0.914095\pi\) | ||
0.963803 | − | 0.266615i | \(-0.0859051\pi\) | |||||||
\(158\) | 0.767863 | − | 1.85379i | 0.0610879 | − | 0.147479i | ||||
\(159\) | 9.55548 | − | 3.95801i | 0.757799 | − | 0.313891i | ||||
\(160\) | 1.10683 | + | 2.67212i | 0.0875025 | + | 0.211250i | ||||
\(161\) | −4.99270 | − | 4.99270i | −0.393480 | − | 0.393480i | ||||
\(162\) | 0.708529 | + | 0.708529i | 0.0556673 | + | 0.0556673i | ||||
\(163\) | −4.17338 | − | 10.0754i | −0.326885 | − | 0.789169i | −0.998820 | − | 0.0485597i | \(-0.984537\pi\) |
0.671936 | − | 0.740609i | \(-0.265463\pi\) | |||||||
\(164\) | −3.62507 | + | 1.50155i | −0.283070 | + | 0.117251i | ||||
\(165\) | −0.280015 | + | 0.676015i | −0.0217991 | + | 0.0526277i | ||||
\(166\) | 1.72063i | 0.133547i | ||||||||
\(167\) | −4.19006 | − | 1.73558i | −0.324237 | − | 0.134303i | 0.214627 | − | 0.976696i | \(-0.431146\pi\) |
−0.538864 | + | 0.842393i | \(0.681146\pi\) | |||||||
\(168\) | 2.44123 | − | 2.44123i | 0.188345 | − | 0.188345i | ||||
\(169\) | −28.5041 | −2.19262 | ||||||||
\(170\) | 1.77763 | + | 0.795295i | 0.136338 | + | 0.0609963i | ||||
\(171\) | −8.93561 | −0.683323 | ||||||||
\(172\) | 0.835629 | − | 0.835629i | 0.0637161 | − | 0.0637161i | ||||
\(173\) | 6.44678 | + | 2.67035i | 0.490140 | + | 0.203023i | 0.614044 | − | 0.789272i | \(-0.289542\pi\) |
−0.123904 | + | 0.992294i | \(0.539542\pi\) | |||||||
\(174\) | 2.77944i | 0.210709i | ||||||||
\(175\) | −2.18693 | + | 5.27971i | −0.165316 | + | 0.399109i | ||||
\(176\) | 0.313050 | − | 0.129670i | 0.0235971 | − | 0.00977422i | ||||
\(177\) | −1.61710 | − | 3.90403i | −0.121549 | − | 0.293445i | ||||
\(178\) | −3.62914 | − | 3.62914i | −0.272015 | − | 0.272015i | ||||
\(179\) | 17.0397 | + | 17.0397i | 1.27360 | + | 1.27360i | 0.944183 | + | 0.329422i | \(0.106854\pi\) |
0.329422 | + | 0.944183i | \(0.393146\pi\) | |||||||
\(180\) | −0.475898 | − | 1.14892i | −0.0354714 | − | 0.0856354i | ||||
\(181\) | 4.07779 | − | 1.68908i | 0.303100 | − | 0.125548i | −0.225950 | − | 0.974139i | \(-0.572549\pi\) |
0.529050 | + | 0.848591i | \(0.322549\pi\) | |||||||
\(182\) | −2.69589 | + | 6.50846i | −0.199833 | + | 0.482439i | ||||
\(183\) | 14.1883i | 1.04883i | ||||||||
\(184\) | −15.5309 | − | 6.43313i | −1.14496 | − | 0.474257i | ||||
\(185\) | 2.79602 | − | 2.79602i | 0.205568 | − | 0.205568i | ||||
\(186\) | −5.28108 | −0.387228 | ||||||||
\(187\) | −2.37793 | + | 5.31511i | −0.173892 | + | 0.388679i | ||||
\(188\) | −7.01207 | −0.511408 | ||||||||
\(189\) | −4.25405 | + | 4.25405i | −0.309437 | + | 0.309437i | ||||
\(190\) | −1.93474 | − | 0.801397i | −0.140361 | − | 0.0581394i | ||||
\(191\) | − | 9.30167i | − | 0.673045i | −0.941675 | − | 0.336523i | \(-0.890749\pi\) | ||
0.941675 | − | 0.336523i | \(-0.109251\pi\) | |||||||
\(192\) | 2.08491 | − | 5.03341i | 0.150465 | − | 0.363255i | ||||
\(193\) | 7.03237 | − | 2.91290i | 0.506201 | − | 0.209675i | −0.114942 | − | 0.993372i | \(-0.536668\pi\) |
0.621144 | + | 0.783697i | \(0.286668\pi\) | |||||||
\(194\) | 0.887930 | + | 2.14365i | 0.0637496 | + | 0.153905i | ||||
\(195\) | −2.36029 | − | 2.36029i | −0.169024 | − | 0.169024i | ||||
\(196\) | 4.62826 | + | 4.62826i | 0.330590 | + | 0.330590i | ||||
\(197\) | 2.13815 | + | 5.16195i | 0.152337 | + | 0.367773i | 0.981563 | − | 0.191140i | \(-0.0612184\pi\) |
−0.829226 | + | 0.558913i | \(0.811218\pi\) | |||||||
\(198\) | −2.37856 | + | 0.985234i | −0.169037 | + | 0.0700175i | ||||
\(199\) | −0.0345027 | + | 0.0832969i | −0.00244583 | + | 0.00590476i | −0.925098 | − | 0.379729i | \(-0.876017\pi\) |
0.922652 | + | 0.385634i | \(0.126017\pi\) | |||||||
\(200\) | 13.6059i | 0.962081i | ||||||||
\(201\) | −7.93321 | − | 3.28604i | −0.559565 | − | 0.231779i | ||||
\(202\) | −9.39546 | + | 9.39546i | −0.661062 | + | 0.661062i | ||||
\(203\) | 3.74328 | 0.262727 | ||||||||
\(204\) | 1.72455 | + | 4.51694i | 0.120743 | + | 0.316249i | ||||
\(205\) | 1.73367 | 0.121085 | ||||||||
\(206\) | 2.00404 | − | 2.00404i | 0.139628 | − | 0.139628i | ||||
\(207\) | 10.8753 | + | 4.50470i | 0.755886 | + | 0.313098i | ||||
\(208\) | 1.54574i | 0.107178i | ||||||||
\(209\) | 2.39618 | − | 5.78489i | 0.165747 | − | 0.400149i | ||||
\(210\) | −0.523440 | + | 0.216816i | −0.0361208 | + | 0.0149617i | ||||
\(211\) | 10.5831 | + | 25.5499i | 0.728572 | + | 1.75893i | 0.647297 | + | 0.762238i | \(0.275899\pi\) |
0.0812751 | + | 0.996692i | \(0.474101\pi\) | |||||||
\(212\) | −8.70986 | − | 8.70986i | −0.598195 | − | 0.598195i | ||||
\(213\) | 5.82370 | + | 5.82370i | 0.399033 | + | 0.399033i | ||||
\(214\) | −1.70267 | − | 4.11061i | −0.116392 | − | 0.280995i | ||||
\(215\) | −0.482403 | + | 0.199818i | −0.0328996 | + | 0.0136275i | ||||
\(216\) | −5.48137 | + | 13.2332i | −0.372960 | + | 0.900405i | ||||
\(217\) | 7.11243i | 0.482824i | ||||||||
\(218\) | −10.6329 | − | 4.40429i | −0.720151 | − | 0.298296i | ||||
\(219\) | −6.51152 | + | 6.51152i | −0.440008 | + | 0.440008i | ||||
\(220\) | 0.871425 | 0.0587514 | ||||||||
\(221\) | −18.2497 | − | 19.3008i | −1.22761 | − | 1.29831i | ||||
\(222\) | −6.79739 | −0.456211 | ||||||||
\(223\) | 4.91058 | − | 4.91058i | 0.328837 | − | 0.328837i | −0.523307 | − | 0.852144i | \(-0.675302\pi\) |
0.852144 | + | 0.523307i | \(0.175302\pi\) | |||||||
\(224\) | −6.18640 | − | 2.56249i | −0.413346 | − | 0.171214i | ||||
\(225\) | − | 9.52731i | − | 0.635154i | ||||||
\(226\) | 2.24683 | − | 5.42433i | 0.149457 | − | 0.360821i | ||||
\(227\) | 5.63411 | − | 2.33372i | 0.373949 | − | 0.154895i | −0.187790 | − | 0.982209i | \(-0.560133\pi\) |
0.561739 | + | 0.827314i | \(0.310133\pi\) | |||||||
\(228\) | −1.98967 | − | 4.80348i | −0.131769 | − | 0.318118i | ||||
\(229\) | −10.5862 | − | 10.5862i | −0.699556 | − | 0.699556i | 0.264759 | − | 0.964315i | \(-0.414708\pi\) |
−0.964315 | + | 0.264759i | \(0.914708\pi\) | |||||||
\(230\) | 1.95072 | + | 1.95072i | 0.128627 | + | 0.128627i | ||||
\(231\) | −0.648280 | − | 1.56509i | −0.0426537 | − | 0.102975i | ||||
\(232\) | 8.23379 | − | 3.41055i | 0.540575 | − | 0.223913i | ||||
\(233\) | 6.28407 | − | 15.1711i | 0.411683 | − | 0.993892i | −0.573002 | − | 0.819554i | \(-0.694221\pi\) |
0.984686 | − | 0.174338i | \(-0.0557786\pi\) | |||||||
\(234\) | − | 11.7446i | − | 0.767769i | ||||||
\(235\) | 2.86238 | + | 1.18564i | 0.186721 | + | 0.0773425i | ||||
\(236\) | −3.55854 | + | 3.55854i | −0.231641 | + | 0.231641i | ||||
\(237\) | −2.20112 | −0.142978 | ||||||||
\(238\) | −4.21205 | + | 1.60814i | −0.273027 | + | 0.104240i | ||||
\(239\) | −20.4604 | −1.32348 | −0.661738 | − | 0.749735i | \(-0.730181\pi\) | ||||
−0.661738 | + | 0.749735i | \(0.730181\pi\) | |||||||
\(240\) | −0.0879045 | + | 0.0879045i | −0.00567421 | + | 0.00567421i | ||||
\(241\) | 11.4902 | + | 4.75940i | 0.740149 | + | 0.306580i | 0.720715 | − | 0.693231i | \(-0.243814\pi\) |
0.0194338 | + | 0.999811i | \(0.493814\pi\) | |||||||
\(242\) | 8.14617i | 0.523655i | ||||||||
\(243\) | 6.13414 | − | 14.8091i | 0.393505 | − | 0.950006i | ||||
\(244\) | 15.6111 | − | 6.46635i | 0.999401 | − | 0.413966i | ||||
\(245\) | −1.10672 | − | 2.67186i | −0.0707059 | − | 0.170699i | ||||
\(246\) | −2.10736 | − | 2.10736i | −0.134360 | − | 0.134360i | ||||
\(247\) | 20.1978 | + | 20.1978i | 1.28515 | + | 1.28515i | ||||
\(248\) | 6.48022 | + | 15.6446i | 0.411494 | + | 0.993435i | ||||
\(249\) | 1.74382 | − | 0.722313i | 0.110510 | − | 0.0457747i | ||||
\(250\) | 1.75821 | − | 4.24469i | 0.111199 | − | 0.268458i | ||||
\(251\) | 20.9555i | 1.32270i | 0.750078 | + | 0.661349i | \(0.230016\pi\) | ||||
−0.750078 | + | 0.661349i | \(0.769984\pi\) | |||||||
\(252\) | 2.65994 | + | 1.10178i | 0.167560 | + | 0.0694058i | ||||
\(253\) | −5.83266 | + | 5.83266i | −0.366696 | + | 0.366696i | ||||
\(254\) | −8.25070 | −0.517695 | ||||||||
\(255\) | 0.0597730 | − | 2.13545i | 0.00374313 | − | 0.133727i | ||||
\(256\) | −16.5095 | −1.03184 | ||||||||
\(257\) | 12.9891 | − | 12.9891i | 0.810238 | − | 0.810238i | −0.174431 | − | 0.984669i | \(-0.555809\pi\) |
0.984669 | + | 0.174431i | \(0.0558086\pi\) | |||||||
\(258\) | 0.829270 | + | 0.343495i | 0.0516281 | + | 0.0213851i | ||||
\(259\) | 9.15456i | 0.568837i | ||||||||
\(260\) | −1.52128 | + | 3.67269i | −0.0943455 | + | 0.227770i | ||||
\(261\) | −5.76558 | + | 2.38818i | −0.356881 | + | 0.147825i | ||||
\(262\) | 0.303175 | + | 0.731929i | 0.0187302 | + | 0.0452187i | ||||
\(263\) | −2.96775 | − | 2.96775i | −0.182999 | − | 0.182999i | 0.609662 | − | 0.792661i | \(-0.291305\pi\) |
−0.792661 | + | 0.609662i | \(0.791305\pi\) | |||||||
\(264\) | −2.85194 | − | 2.85194i | −0.175525 | − | 0.175525i | ||||
\(265\) | 2.08272 | + | 5.02814i | 0.127941 | + | 0.308876i | ||||
\(266\) | 4.47925 | − | 1.85537i | 0.274640 | − | 0.113760i | ||||
\(267\) | −2.15455 | + | 5.20155i | −0.131856 | + | 0.318330i | ||||
\(268\) | 10.2264i | 0.624676i | ||||||||
\(269\) | 12.4325 | + | 5.14970i | 0.758022 | + | 0.313983i | 0.728010 | − | 0.685567i | \(-0.240446\pi\) |
0.0300118 | + | 0.999550i | \(0.490446\pi\) | |||||||
\(270\) | 1.66212 | − | 1.66212i | 0.101153 | − | 0.101153i | ||||
\(271\) | 22.2794 | 1.35338 | 0.676688 | − | 0.736270i | \(-0.263415\pi\) | ||||
0.676688 | + | 0.736270i | \(0.263415\pi\) | |||||||
\(272\) | −0.718821 | + | 0.679675i | −0.0435849 | + | 0.0412114i | ||||
\(273\) | 7.72790 | 0.467714 | ||||||||
\(274\) | −8.26794 | + | 8.26794i | −0.499485 | + | 0.499485i | ||||
\(275\) | 6.16795 | + | 2.55485i | 0.371942 | + | 0.154063i | ||||
\(276\) | 6.84924i | 0.412276i | ||||||||
\(277\) | −0.323712 | + | 0.781511i | −0.0194500 | + | 0.0469564i | −0.933306 | − | 0.359082i | \(-0.883090\pi\) |
0.913856 | + | 0.406038i | \(0.133090\pi\) | |||||||
\(278\) | 16.5150 | − | 6.84075i | 0.990506 | − | 0.410281i | ||||
\(279\) | −4.53767 | − | 10.9549i | −0.271663 | − | 0.655854i | ||||
\(280\) | 1.28459 | + | 1.28459i | 0.0767688 | + | 0.0767688i | ||||
\(281\) | 14.0553 | + | 14.0553i | 0.838466 | + | 0.838466i | 0.988657 | − | 0.150191i | \(-0.0479888\pi\) |
−0.150191 | + | 0.988657i | \(0.547989\pi\) | |||||||
\(282\) | −2.03816 | − | 4.92056i | −0.121371 | − | 0.293015i | ||||
\(283\) | 26.6533 | − | 11.0402i | 1.58437 | − | 0.656270i | 0.595276 | − | 0.803521i | \(-0.297043\pi\) |
0.989099 | + | 0.147252i | \(0.0470428\pi\) | |||||||
\(284\) | 3.75355 | − | 9.06188i | 0.222732 | − | 0.537723i | ||||
\(285\) | 2.29724i | 0.136077i | ||||||||
\(286\) | 7.60342 | + | 3.14944i | 0.449600 | + | 0.186230i | ||||
\(287\) | −2.83814 | + | 2.83814i | −0.167530 | + | 0.167530i | ||||
\(288\) | 11.1634 | 0.657812 | ||||||||
\(289\) | 0.950945 | − | 16.9734i | 0.0559379 | − | 0.998434i | ||||
\(290\) | −1.46255 | −0.0858841 | ||||||||
\(291\) | 1.79979 | − | 1.79979i | 0.105506 | − | 0.105506i | ||||
\(292\) | 10.1321 | + | 4.19687i | 0.592939 | + | 0.245603i | ||||
\(293\) | − | 19.4741i | − | 1.13769i | −0.822444 | − | 0.568845i | \(-0.807390\pi\) | ||
0.822444 | − | 0.568845i | \(-0.192610\pi\) | |||||||
\(294\) | −1.90250 | + | 4.59304i | −0.110956 | + | 0.267872i | ||||
\(295\) | 2.05432 | − | 0.850927i | 0.119607 | − | 0.0495429i | ||||
\(296\) | 8.34082 | + | 20.1365i | 0.484801 | + | 1.17041i | ||||
\(297\) | 4.96974 | + | 4.96974i | 0.288373 | + | 0.288373i | ||||
\(298\) | −14.0606 | − | 14.0606i | −0.814507 | − | 0.814507i | ||||
\(299\) | −14.3999 | − | 34.7645i | −0.832768 | − | 2.01048i | ||||
\(300\) | 5.12156 | − | 2.12142i | 0.295693 | − | 0.122480i | ||||
\(301\) | 0.462611 | − | 1.11684i | 0.0266645 | − | 0.0643737i | ||||
\(302\) | 5.66151i | 0.325783i | ||||||||
\(303\) | 13.4663 | + | 5.57791i | 0.773617 | + | 0.320443i | ||||
\(304\) | 0.752228 | − | 0.752228i | 0.0431432 | − | 0.0431432i | ||||
\(305\) | −7.46596 | −0.427500 | ||||||||
\(306\) | 5.46162 | − | 5.16419i | 0.312220 | − | 0.295217i | ||||
\(307\) | 13.6342 | 0.778145 | 0.389073 | − | 0.921207i | \(-0.372796\pi\) | ||||
0.389073 | + | 0.921207i | \(0.372796\pi\) | |||||||
\(308\) | −1.42658 | + | 1.42658i | −0.0812870 | + | 0.0812870i | ||||
\(309\) | −2.87234 | − | 1.18976i | −0.163402 | − | 0.0676832i | ||||
\(310\) | − | 2.77893i | − | 0.157833i | ||||||
\(311\) | 6.91817 | − | 16.7019i | 0.392293 | − | 0.947080i | −0.597146 | − | 0.802133i | \(-0.703699\pi\) |
0.989439 | − | 0.144947i | \(-0.0463013\pi\) | |||||||
\(312\) | 16.9984 | − | 7.04098i | 0.962347 | − | 0.398617i | ||||
\(313\) | −2.54624 | − | 6.14718i | −0.143922 | − | 0.347459i | 0.835437 | − | 0.549586i | \(-0.185215\pi\) |
−0.979359 | + | 0.202127i | \(0.935215\pi\) | |||||||
\(314\) | −4.27356 | − | 4.27356i | −0.241171 | − | 0.241171i | ||||
\(315\) | −0.899513 | − | 0.899513i | −0.0506818 | − | 0.0506818i | ||||
\(316\) | 1.00316 | + | 2.42185i | 0.0564323 | + | 0.136240i | ||||
\(317\) | −14.5390 | + | 6.02226i | −0.816593 | + | 0.338244i | −0.751581 | − | 0.659641i | \(-0.770709\pi\) |
−0.0650118 | + | 0.997884i | \(0.520709\pi\) | |||||||
\(318\) | 3.58029 | − | 8.64358i | 0.200773 | − | 0.484708i | ||||
\(319\) | − | 4.37304i | − | 0.244843i | ||||||
\(320\) | 2.64860 | + | 1.09709i | 0.148061 | + | 0.0613291i | ||||
\(321\) | −3.45123 | + | 3.45123i | −0.192629 | + | 0.192629i | ||||
\(322\) | −6.38693 | −0.355929 | ||||||||
\(323\) | −0.511497 | + | 18.2737i | −0.0284605 | + | 1.01678i | ||||
\(324\) | −1.30906 | −0.0727256 | ||||||||
\(325\) | −21.5352 | + | 21.5352i | −1.19456 | + | 1.19456i | ||||
\(326\) | −9.11391 | − | 3.77511i | −0.504773 | − | 0.209084i | ||||
\(327\) | 12.6251i | 0.698170i | ||||||||
\(328\) | −3.65696 | + | 8.82868i | −0.201922 | + | 0.487482i | ||||
\(329\) | −6.62689 | + | 2.74495i | −0.365352 | + | 0.151334i | ||||
\(330\) | 0.253292 | + | 0.611501i | 0.0139433 | + | 0.0336620i | ||||
\(331\) | −1.07157 | − | 1.07157i | −0.0588989 | − | 0.0588989i | 0.677044 | − | 0.735943i | \(-0.263261\pi\) |
−0.735943 | + | 0.677044i | \(0.763261\pi\) | |||||||
\(332\) | −1.58950 | − | 1.58950i | −0.0872349 | − | 0.0872349i | ||||
\(333\) | −5.84053 | − | 14.1003i | −0.320059 | − | 0.772691i | ||||
\(334\) | −3.79020 | + | 1.56995i | −0.207390 | + | 0.0859039i | ||||
\(335\) | 1.72913 | − | 4.17449i | 0.0944725 | − | 0.228077i | ||||
\(336\) | − | 0.287811i | − | 0.0157014i | ||||||
\(337\) | 1.33511 | + | 0.553022i | 0.0727283 | + | 0.0301250i | 0.418751 | − | 0.908101i | \(-0.362468\pi\) |
−0.346023 | + | 0.938226i | \(0.612468\pi\) | |||||||
\(338\) | −18.2320 | + | 18.2320i | −0.991689 | + | 0.991689i | ||||
\(339\) | −6.44065 | −0.349808 | ||||||||
\(340\) | −2.37683 | + | 0.907466i | −0.128902 | + | 0.0492143i | ||||
\(341\) | 8.30900 | 0.449958 | ||||||||
\(342\) | −5.71545 | + | 5.71545i | −0.309056 | + | 0.309056i | ||||
\(343\) | 14.0037 | + | 5.80052i | 0.756128 | + | 0.313199i | ||||
\(344\) | − | 2.87811i | − | 0.155178i | ||||||
\(345\) | 1.15811 | − | 2.79592i | 0.0623503 | − | 0.150527i | ||||
\(346\) | 5.83155 | − | 2.41551i | 0.313506 | − | 0.129859i | ||||
\(347\) | −1.58723 | − | 3.83192i | −0.0852071 | − | 0.205708i | 0.875533 | − | 0.483159i | \(-0.160511\pi\) |
−0.960740 | + | 0.277451i | \(0.910511\pi\) | |||||||
\(348\) | −2.56761 | − | 2.56761i | −0.137638 | − | 0.137638i | ||||
\(349\) | −14.4784 | − | 14.4784i | −0.775011 | − | 0.775011i | 0.203967 | − | 0.978978i | \(-0.434617\pi\) |
−0.978978 | + | 0.203967i | \(0.934617\pi\) | |||||||
\(350\) | 1.97823 | + | 4.77586i | 0.105741 | + | 0.255280i | ||||
\(351\) | −29.6212 | + | 12.2695i | −1.58106 | + | 0.654897i | ||||
\(352\) | −2.99360 | + | 7.22718i | −0.159559 | + | 0.385210i | ||||
\(353\) | 26.2626i | 1.39782i | 0.715210 | + | 0.698909i | \(0.246331\pi\) | ||||
−0.715210 | + | 0.698909i | \(0.753669\pi\) | |||||||
\(354\) | −3.53146 | − | 1.46278i | −0.187695 | − | 0.0777458i | ||||
\(355\) | −3.06446 | + | 3.06446i | −0.162645 | + | 0.162645i | ||||
\(356\) | 6.70511 | 0.355370 | ||||||||
\(357\) | 3.39802 | + | 3.59372i | 0.179842 | + | 0.190200i | ||||
\(358\) | 21.7980 | 1.15206 | ||||||||
\(359\) | 19.5669 | − | 19.5669i | 1.03270 | − | 1.03270i | 0.0332557 | − | 0.999447i | \(-0.489412\pi\) |
0.999447 | − | 0.0332557i | \(-0.0105876\pi\) | |||||||
\(360\) | −2.79814 | − | 1.15903i | −0.147475 | − | 0.0610861i | ||||
\(361\) | − | 0.658257i | − | 0.0346451i | ||||||
\(362\) | 1.52788 | − | 3.68864i | 0.0803038 | − | 0.193871i | ||||
\(363\) | 8.25596 | − | 3.41973i | 0.433325 | − | 0.179489i | ||||
\(364\) | −3.52201 | − | 8.50287i | −0.184603 | − | 0.445672i | ||||
\(365\) | −3.42639 | − | 3.42639i | −0.179346 | − | 0.179346i | ||||
\(366\) | 9.07521 | + | 9.07521i | 0.474369 | + | 0.474369i | ||||
\(367\) | −6.48867 | − | 15.6650i | −0.338706 | − | 0.817708i | −0.997841 | − | 0.0656835i | \(-0.979077\pi\) |
0.659135 | − | 0.752025i | \(-0.270923\pi\) | |||||||
\(368\) | −1.29474 | + | 0.536298i | −0.0674929 | + | 0.0279565i | ||||
\(369\) | 2.56073 | − | 6.18215i | 0.133306 | − | 0.321830i | ||||
\(370\) | − | 3.57682i | − | 0.185950i | ||||||
\(371\) | −11.6410 | − | 4.82185i | −0.604369 | − | 0.250338i | ||||
\(372\) | 4.87860 | − | 4.87860i | 0.252944 | − | 0.252944i | ||||
\(373\) | −15.0546 | −0.779499 | −0.389750 | − | 0.920921i | \(-0.627438\pi\) | ||||
−0.389750 | + | 0.920921i | \(0.627438\pi\) | |||||||
\(374\) | 1.87869 | + | 4.92067i | 0.0971448 | + | 0.254442i | ||||
\(375\) | −5.03998 | −0.260264 | ||||||||
\(376\) | −12.0757 | + | 12.0757i | −0.622755 | + | 0.622755i | ||||
\(377\) | 18.4305 | + | 7.63417i | 0.949219 | + | 0.393180i | ||||
\(378\) | 5.44200i | 0.279906i | ||||||||
\(379\) | −4.85909 | + | 11.7309i | −0.249595 | + | 0.602575i | −0.998170 | − | 0.0604753i | \(-0.980738\pi\) |
0.748575 | + | 0.663050i | \(0.230738\pi\) | |||||||
\(380\) | 2.52761 | − | 1.04697i | 0.129664 | − | 0.0537085i | ||||
\(381\) | 3.46361 | + | 8.36190i | 0.177446 | + | 0.428393i | ||||
\(382\) | −5.94959 | − | 5.94959i | −0.304408 | − | 0.304408i | ||||
\(383\) | 9.58132 | + | 9.58132i | 0.489583 | + | 0.489583i | 0.908174 | − | 0.418592i | \(-0.137476\pi\) |
−0.418592 | + | 0.908174i | \(0.637476\pi\) | |||||||
\(384\) | 2.32090 | + | 5.60315i | 0.118438 | + | 0.285934i | ||||
\(385\) | 0.823556 | − | 0.341128i | 0.0419723 | − | 0.0173855i | ||||
\(386\) | 2.63492 | − | 6.36125i | 0.134114 | − | 0.323779i | ||||
\(387\) | 2.01536i | 0.102446i | ||||||||
\(388\) | −2.80054 | − | 1.16002i | −0.142176 | − | 0.0588912i | ||||
\(389\) | −10.3817 | + | 10.3817i | −0.526371 | + | 0.526371i | −0.919488 | − | 0.393117i | \(-0.871397\pi\) |
0.393117 | + | 0.919488i | \(0.371397\pi\) | |||||||
\(390\) | −3.01940 | −0.152893 | ||||||||
\(391\) | 9.83484 | − | 21.9826i | 0.497369 | − | 1.11171i | ||||
\(392\) | 15.9409 | 0.805136 | ||||||||
\(393\) | 0.614522 | − | 0.614522i | 0.0309985 | − | 0.0309985i | ||||
\(394\) | 4.66933 | + | 1.93410i | 0.235237 | + | 0.0974385i | ||||
\(395\) | − | 1.15824i | − | 0.0582772i | ||||||
\(396\) | 1.28714 | − | 3.10744i | 0.0646814 | − | 0.156155i | ||||
\(397\) | −23.6051 | + | 9.77757i | −1.18471 | + | 0.490722i | −0.886028 | − | 0.463631i | \(-0.846546\pi\) |
−0.298680 | + | 0.954353i | \(0.596546\pi\) | |||||||
\(398\) | 0.0312100 | + | 0.0753477i | 0.00156442 | + | 0.00377684i | ||||
\(399\) | −3.76074 | − | 3.76074i | −0.188273 | − | 0.188273i | ||||
\(400\) | 0.802039 | + | 0.802039i | 0.0401020 | + | 0.0401020i | ||||
\(401\) | 11.9956 | + | 28.9600i | 0.599033 | + | 1.44619i | 0.874568 | + | 0.484903i | \(0.161145\pi\) |
−0.275534 | + | 0.961291i | \(0.588855\pi\) | |||||||
\(402\) | −7.17612 | + | 2.97245i | −0.357912 | + | 0.148252i | ||||
\(403\) | −14.5053 | + | 35.0189i | −0.722561 | + | 1.74442i | ||||
\(404\) | − | 17.3588i | − | 0.863634i | ||||||
\(405\) | 0.534369 | + | 0.221343i | 0.0265530 | + | 0.0109986i | ||||
\(406\) | 2.39430 | − | 2.39430i | 0.118827 | − | 0.118827i | ||||
\(407\) | 10.6947 | 0.530116 | ||||||||
\(408\) | 10.7486 | + | 4.80884i | 0.532136 | + | 0.238073i | ||||
\(409\) | −5.10090 | −0.252223 | −0.126112 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126112 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(410\) | 1.10890 | − | 1.10890i | 0.0547647 | − | 0.0547647i | ||||
\(411\) | 11.8502 | + | 4.90852i | 0.584528 | + | 0.242120i | ||||
\(412\) | 3.70262i | 0.182415i | ||||||||
\(413\) | −1.97004 | + | 4.75609i | −0.0969391 | + | 0.234032i | ||||
\(414\) | 9.83745 | − | 4.07480i | 0.483484 | − | 0.200266i | ||||
\(415\) | 0.380084 | + | 0.917605i | 0.0186576 | + | 0.0450434i | ||||
\(416\) | −25.2335 | − | 25.2335i | −1.23717 | − | 1.23717i | ||||
\(417\) | −13.8659 | − | 13.8659i | −0.679016 | − | 0.679016i | ||||
\(418\) | −2.16751 | − | 5.23282i | −0.106016 | − | 0.255946i | ||||
\(419\) | 28.3031 | − | 11.7235i | 1.38270 | − | 0.572732i | 0.437496 | − | 0.899220i | \(-0.355865\pi\) |
0.945201 | + | 0.326488i | \(0.105865\pi\) | |||||||
\(420\) | 0.283256 | − | 0.683840i | 0.0138215 | − | 0.0333680i | ||||
\(421\) | 0.721867i | 0.0351817i | 0.999845 | + | 0.0175908i | \(0.00559962\pi\) | ||||
−0.999845 | + | 0.0175908i | \(0.994400\pi\) | |||||||
\(422\) | 23.1116 | + | 9.57315i | 1.12506 | + | 0.466014i | ||||
\(423\) | 8.45580 | − | 8.45580i | 0.411135 | − | 0.411135i | ||||
\(424\) | −29.9989 | −1.45688 | ||||||||
\(425\) | −19.4838 | − | 0.545368i | −0.945102 | − | 0.0264542i | ||||
\(426\) | 7.44998 | 0.360953 | ||||||||
\(427\) | 12.2223 | − | 12.2223i | 0.591478 | − | 0.591478i | ||||
\(428\) | 5.37023 | + | 2.22442i | 0.259580 | + | 0.107522i | ||||
\(429\) | − | 9.02802i | − | 0.435877i | ||||||
\(430\) | −0.180749 | + | 0.436366i | −0.00871647 | + | 0.0210434i | ||||
\(431\) | −5.79080 | + | 2.39863i | −0.278933 | + | 0.115538i | −0.517765 | − | 0.855523i | \(-0.673236\pi\) |
0.238831 | + | 0.971061i | \(0.423236\pi\) | |||||||
\(432\) | 0.456955 | + | 1.10319i | 0.0219852 | + | 0.0530770i | ||||
\(433\) | 16.4151 | + | 16.4151i | 0.788859 | + | 0.788859i | 0.981307 | − | 0.192448i | \(-0.0616428\pi\) |
−0.192448 | + | 0.981307i | \(0.561643\pi\) | |||||||
\(434\) | 4.54930 | + | 4.54930i | 0.218373 | + | 0.218373i | ||||
\(435\) | 0.613974 | + | 1.48227i | 0.0294378 | + | 0.0710692i | ||||
\(436\) | 13.8912 | − | 5.75392i | 0.665267 | − | 0.275563i | ||||
\(437\) | −9.91030 | + | 23.9256i | −0.474074 | + | 1.14452i | ||||
\(438\) | 8.32988i | 0.398017i | ||||||||
\(439\) | 34.9630 | + | 14.4822i | 1.66869 | + | 0.691196i | 0.998690 | − | 0.0511616i | \(-0.0162924\pi\) |
0.670004 | + | 0.742357i | \(0.266292\pi\) | |||||||
\(440\) | 1.50070 | − | 1.50070i | 0.0715432 | − | 0.0715432i | ||||
\(441\) | −11.1624 | −0.531541 | ||||||||
\(442\) | −24.0182 | − | 0.672291i | −1.14243 | − | 0.0319776i | ||||
\(443\) | 24.5839 | 1.16802 | 0.584008 | − | 0.811748i | \(-0.301484\pi\) | ||||
0.584008 | + | 0.811748i | \(0.301484\pi\) | |||||||
\(444\) | 6.27934 | − | 6.27934i | 0.298005 | − | 0.298005i | ||||
\(445\) | −2.73708 | − | 1.13373i | −0.129750 | − | 0.0537442i | ||||
\(446\) | − | 6.28187i | − | 0.297455i | ||||||
\(447\) | −8.34750 | + | 20.1526i | −0.394823 | + | 0.953188i | ||||
\(448\) | −6.13196 | + | 2.53994i | −0.289708 | + | 0.120001i | ||||
\(449\) | −13.8243 | − | 33.3748i | −0.652408 | − | 1.57505i | −0.809273 | − | 0.587432i | \(-0.800139\pi\) |
0.156865 | − | 0.987620i | \(-0.449861\pi\) | |||||||
\(450\) | −6.09391 | − | 6.09391i | −0.287270 | − | 0.287270i | ||||
\(451\) | 3.31562 | + | 3.31562i | 0.156126 | + | 0.156126i | ||||
\(452\) | 2.93534 | + | 7.08653i | 0.138067 | + | 0.333322i | ||||
\(453\) | 5.73781 | − | 2.37668i | 0.269586 | − | 0.111666i | ||||
\(454\) | 2.11101 | − | 5.09643i | 0.0990746 | − | 0.239187i | ||||
\(455\) | 4.06646i | 0.190639i | ||||||||
\(456\) | −11.6986 | − | 4.84574i | −0.547839 | − | 0.226923i | ||||
\(457\) | −10.9019 | + | 10.9019i | −0.509970 | + | 0.509970i | −0.914517 | − | 0.404547i | \(-0.867429\pi\) |
0.404547 | + | 0.914517i | \(0.367429\pi\) | |||||||
\(458\) | −13.5424 | −0.632795 | ||||||||
\(459\) | −18.7304 | − | 8.37981i | −0.874259 | − | 0.391136i | ||||
\(460\) | −3.60410 | −0.168042 | ||||||||
\(461\) | 7.08350 | − | 7.08350i | 0.329911 | − | 0.329911i | −0.522641 | − | 0.852553i | \(-0.675053\pi\) |
0.852553 | + | 0.522641i | \(0.175053\pi\) | |||||||
\(462\) | −1.41573 | − | 0.586413i | −0.0658656 | − | 0.0272824i | ||||
\(463\) | − | 1.65429i | − | 0.0768813i | −0.999261 | − | 0.0384406i | \(-0.987761\pi\) | ||
0.999261 | − | 0.0384406i | \(-0.0122391\pi\) | |||||||
\(464\) | 0.284320 | − | 0.686410i | 0.0131992 | − | 0.0318658i | ||||
\(465\) | −2.81638 | + | 1.16658i | −0.130607 | + | 0.0540990i | ||||
\(466\) | −5.68437 | − | 13.7233i | −0.263323 | − | 0.635719i | ||||
\(467\) | 10.5504 | + | 10.5504i | 0.488214 | + | 0.488214i | 0.907742 | − | 0.419528i | \(-0.137804\pi\) |
−0.419528 | + | 0.907742i | \(0.637804\pi\) | |||||||
\(468\) | 10.8495 | + | 10.8495i | 0.501519 | + | 0.501519i | ||||
\(469\) | 4.00322 | + | 9.66463i | 0.184852 | + | 0.446271i | ||||
\(470\) | 2.58922 | − | 1.07249i | 0.119432 | − | 0.0494703i | ||||
\(471\) | −2.53713 | + | 6.12518i | −0.116905 | + | 0.282234i | ||||
\(472\) | 12.2565i | 0.564151i | ||||||||
\(473\) | −1.30474 | − | 0.540439i | −0.0599918 | − | 0.0248494i | ||||
\(474\) | −1.40789 | + | 1.40789i | −0.0646665 | + | 0.0646665i | ||||
\(475\) | 20.9600 | 0.961711 | ||||||||
\(476\) | 2.40546 | − | 5.37662i | 0.110254 | − | 0.246437i | ||||
\(477\) | 21.0063 | 0.961812 | ||||||||
\(478\) | −13.0870 | + | 13.0870i | −0.598587 | + | 0.598587i | ||||
\(479\) | 37.9080 | + | 15.7020i | 1.73206 | + | 0.717443i | 0.999318 | + | 0.0369366i | \(0.0117600\pi\) |
0.732742 | + | 0.680506i | \(0.238240\pi\) | |||||||
\(480\) | − | 2.86999i | − | 0.130997i | ||||||
\(481\) | −18.6701 | + | 45.0736i | −0.851283 | + | 2.05518i | ||||
\(482\) | 10.3937 | − | 4.30520i | 0.473418 | − | 0.196096i | ||||
\(483\) | 2.68121 | + | 6.47300i | 0.121999 | + | 0.294532i | ||||
\(484\) | −7.52533 | − | 7.52533i | −0.342061 | − | 0.342061i | ||||
\(485\) | 0.947060 | + | 0.947060i | 0.0430038 | + | 0.0430038i | ||||
\(486\) | −5.54875 | − | 13.3959i | −0.251696 | − | 0.607648i | ||||
\(487\) | 7.86097 | − | 3.25612i | 0.356214 | − | 0.147549i | −0.197398 | − | 0.980323i | \(-0.563249\pi\) |
0.553612 | + | 0.832775i | \(0.313249\pi\) | |||||||
\(488\) | 15.7485 | − | 38.0202i | 0.712901 | − | 1.72109i | ||||
\(489\) | 10.8215i | 0.489366i | ||||||||
\(490\) | −2.41688 | − | 1.00110i | −0.109184 | − | 0.0452253i | ||||
\(491\) | −19.5906 | + | 19.5906i | −0.884110 | + | 0.884110i | −0.993949 | − | 0.109839i | \(-0.964966\pi\) |
0.109839 | + | 0.993949i | \(0.464966\pi\) | |||||||
\(492\) | 3.89350 | 0.175533 | ||||||||
\(493\) | 4.55390 | + | 11.9276i | 0.205098 | + | 0.537191i | ||||
\(494\) | 25.8380 | 1.16251 | ||||||||
\(495\) | −1.05084 | + | 1.05084i | −0.0472319 | + | 0.0472319i | ||||
\(496\) | 1.30421 | + | 0.540223i | 0.0585610 | + | 0.0242568i | ||||
\(497\) | − | 10.0335i | − | 0.450062i | ||||||
\(498\) | 0.653381 | − | 1.57740i | 0.0292787 | − | 0.0706850i | ||||
\(499\) | −17.2890 | + | 7.16136i | −0.773964 | + | 0.320586i | −0.734477 | − | 0.678634i | \(-0.762572\pi\) |
−0.0394870 | + | 0.999220i | \(0.512572\pi\) | |||||||
\(500\) | 2.29698 | + | 5.54540i | 0.102724 | + | 0.247998i | ||||
\(501\) | 3.18222 | + | 3.18222i | 0.142171 | + | 0.142171i | ||||
\(502\) | 13.4037 | + | 13.4037i | 0.598235 | + | 0.598235i | ||||
\(503\) | −10.1322 | − | 24.4613i | −0.451773 | − | 1.09068i | −0.971648 | − | 0.236434i | \(-0.924021\pi\) |
0.519875 | − | 0.854243i | \(-0.325979\pi\) | |||||||
\(504\) | 6.47816 | − | 2.68334i | 0.288560 | − | 0.119525i | ||||
\(505\) | −2.93512 | + | 7.08601i | −0.130611 | + | 0.315323i | ||||
\(506\) | 7.46144i | 0.331701i | ||||||||
\(507\) | 26.1314 | + | 10.8240i | 1.16054 | + | 0.480710i | ||||
\(508\) | 7.62190 | − | 7.62190i | 0.338167 | − | 0.338167i | ||||
\(509\) | 11.7714 | 0.521759 | 0.260880 | − | 0.965371i | \(-0.415987\pi\) | ||||
0.260880 | + | 0.965371i | \(0.415987\pi\) | |||||||
\(510\) | −1.32765 | − | 1.40412i | −0.0587895 | − | 0.0621754i | ||||
\(511\) | 11.2185 | 0.496276 | ||||||||
\(512\) | −1.91637 | + | 1.91637i | −0.0846924 | + | 0.0846924i | ||||
\(513\) | 20.3859 | + | 8.44411i | 0.900058 | + | 0.372816i | ||||
\(514\) | − | 16.6163i | − | 0.732915i | ||||||
\(515\) | 0.626059 | − | 1.51144i | 0.0275874 | − | 0.0666020i | ||||
\(516\) | −1.08339 | + | 0.448753i | −0.0476934 | + | 0.0197553i | ||||
\(517\) | 3.20675 | + | 7.74177i | 0.141033 | + | 0.340483i | ||||
\(518\) | 5.85549 | + | 5.85549i | 0.257276 | + | 0.257276i | ||||
\(519\) | −4.89613 | − | 4.89613i | −0.214916 | − | 0.214916i | ||||
\(520\) | 3.70500 | + | 8.94465i | 0.162475 | + | 0.392249i | ||||
\(521\) | −7.41863 | + | 3.07290i | −0.325016 | + | 0.134626i | −0.539225 | − | 0.842162i | \(-0.681283\pi\) |
0.214209 | + | 0.976788i | \(0.431283\pi\) | |||||||
\(522\) | −2.16027 | + | 5.21536i | −0.0945526 | + | 0.228270i | ||||
\(523\) | 43.9153i | 1.92028i | 0.279513 | + | 0.960142i | \(0.409827\pi\) | ||||
−0.279513 | + | 0.960142i | \(0.590173\pi\) | |||||||
\(524\) | −0.956217 | − | 0.396078i | −0.0417725 | − | 0.0173028i | ||||
\(525\) | 4.00977 | − | 4.00977i | 0.175001 | − | 0.175001i | ||||
\(526\) | −3.79650 | −0.165535 | ||||||||
\(527\) | −22.6630 | + | 8.65266i | −0.987217 | + | 0.376916i | ||||
\(528\) | −0.336232 | −0.0146326 | ||||||||
\(529\) | 7.85969 | − | 7.85969i | 0.341726 | − | 0.341726i | ||||
\(530\) | 4.54829 | + | 1.88396i | 0.197565 | + | 0.0818342i | ||||
\(531\) | − | 8.58242i | − | 0.372445i | ||||||
\(532\) | −2.42391 | + | 5.85184i | −0.105090 | + | 0.253710i | ||||
\(533\) | −19.7621 | + | 8.18573i | −0.855992 | + | 0.354563i | ||||
\(534\) | 1.94894 | + | 4.70515i | 0.0843388 | + | 0.203612i | ||||
\(535\) | −1.81605 | − | 1.81605i | −0.0785149 | − | 0.0785149i | ||||
\(536\) | 17.6111 | + | 17.6111i | 0.760684 | + | 0.760684i | ||||
\(537\) | −9.15073 | − | 22.0918i | −0.394883 | − | 0.953332i | ||||
\(538\) | 11.2460 | − | 4.65825i | 0.484850 | − | 0.200832i | ||||
\(539\) | 2.99331 | − | 7.22648i | 0.128931 | − | 0.311266i | ||||
\(540\) | 3.07089i | 0.132150i | ||||||||
\(541\) | −27.4936 | − | 11.3882i | −1.18204 | − | 0.489619i | −0.296887 | − | 0.954912i | \(-0.595949\pi\) |
−0.885156 | + | 0.465294i | \(0.845949\pi\) | |||||||
\(542\) | 14.2505 | − | 14.2505i | 0.612110 | − | 0.612110i | ||||
\(543\) | −4.37975 | −0.187953 | ||||||||
\(544\) | 0.639024 | − | 22.8297i | 0.0273979 | − | 0.978817i | ||||
\(545\) | −6.64339 | −0.284572 | ||||||||
\(546\) | 4.94297 | − | 4.94297i | 0.211539 | − | 0.211539i | ||||
\(547\) | −41.5771 | − | 17.2218i | −1.77771 | − | 0.736350i | −0.993226 | − | 0.116196i | \(-0.962930\pi\) |
−0.784480 | − | 0.620154i | \(-0.787070\pi\) | |||||||
\(548\) | − | 15.2757i | − | 0.652544i | ||||||
\(549\) | −11.0276 | + | 26.6231i | −0.470648 | + | 1.13624i | ||||
\(550\) | 5.57933 | − | 2.31103i | 0.237903 | − | 0.0985428i | ||||
\(551\) | −5.25398 | − | 12.6842i | −0.223827 | − | 0.540367i | ||||
\(552\) | 11.7953 | + | 11.7953i | 0.502039 | + | 0.502039i | ||||
\(553\) | 1.89611 | + | 1.89611i | 0.0806310 | + | 0.0806310i | ||||
\(554\) | 0.292820 | + | 0.706929i | 0.0124407 | + | 0.0300345i | ||||
\(555\) | −3.62502 | + | 1.50153i | −0.153874 | + | 0.0637365i | ||||
\(556\) | −8.93699 | + | 21.5758i | −0.379013 | + | 0.915018i | ||||
\(557\) | 13.9798i | 0.592342i | 0.955135 | + | 0.296171i | \(0.0957098\pi\) | ||||
−0.955135 | + | 0.296171i | \(0.904290\pi\) | |||||||
\(558\) | −9.90946 | − | 4.10463i | −0.419501 | − | 0.173763i | ||||
\(559\) | 4.55544 | − | 4.55544i | 0.192675 | − | 0.192675i | ||||
\(560\) | 0.151448 | 0.00639983 | ||||||||
\(561\) | 4.19832 | − | 3.96969i | 0.177253 | − | 0.167600i | ||||
\(562\) | 17.9802 | 0.758449 | ||||||||
\(563\) | −24.2319 | + | 24.2319i | −1.02125 | + | 1.02125i | −0.0214825 | + | 0.999769i | \(0.506839\pi\) |
−0.999769 | + | 0.0214825i | \(0.993161\pi\) | |||||||
\(564\) | 6.42838 | + | 2.66272i | 0.270684 | + | 0.112121i | ||||
\(565\) | − | 3.38910i | − | 0.142580i | ||||||
\(566\) | 9.98657 | − | 24.1097i | 0.419767 | − | 1.01341i | ||||
\(567\) | −1.23715 | + | 0.512445i | −0.0519555 | + | 0.0215207i | ||||
\(568\) | −9.14160 | − | 22.0698i | −0.383573 | − | 0.926027i | ||||
\(569\) | −18.9485 | − | 18.9485i | −0.794362 | − | 0.794362i | 0.187838 | − | 0.982200i | \(-0.439852\pi\) |
−0.982200 | + | 0.187838i | \(0.939852\pi\) | |||||||
\(570\) | 1.46938 | + | 1.46938i | 0.0615454 | + | 0.0615454i | ||||
\(571\) | −0.240236 | − | 0.579981i | −0.0100536 | − | 0.0242715i | 0.918773 | − | 0.394786i | \(-0.129181\pi\) |
−0.928827 | + | 0.370515i | \(0.879181\pi\) | |||||||
\(572\) | −9.93336 | + | 4.11453i | −0.415335 | + | 0.172037i | ||||
\(573\) | −3.53216 | + | 8.52739i | −0.147558 | + | 0.356237i | ||||
\(574\) | 3.63069i | 0.151542i | ||||||||
\(575\) | −25.5099 | − | 10.5665i | −1.06384 | − | 0.440655i | ||||
\(576\) | 7.82427 | − | 7.82427i | 0.326011 | − | 0.326011i | ||||
\(577\) | 5.83950 | 0.243101 | 0.121551 | − | 0.992585i | \(-0.461213\pi\) | ||||
0.121551 | + | 0.992585i | \(0.461213\pi\) | |||||||
\(578\) | −10.2484 | − | 11.4649i | −0.426276 | − | 0.476875i | ||||
\(579\) | −7.55312 | −0.313897 | ||||||||
\(580\) | 1.35109 | − | 1.35109i | 0.0561009 | − | 0.0561009i | ||||
\(581\) | −2.12441 | − | 0.879958i | −0.0881352 | − | 0.0365068i | ||||
\(582\) | − | 2.30239i | − | 0.0954371i | ||||||
\(583\) | −5.63306 | + | 13.5994i | −0.233297 | + | 0.563230i | ||||
\(584\) | 24.6764 | − | 10.2213i | 1.02112 | − | 0.422960i | ||||
\(585\) | −2.59437 | − | 6.26335i | −0.107264 | − | 0.258958i | ||||
\(586\) | −12.4562 | − | 12.4562i | −0.514559 | − | 0.514559i | ||||
\(587\) | −10.5807 | − | 10.5807i | −0.436710 | − | 0.436710i | 0.454193 | − | 0.890903i | \(-0.349928\pi\) |
−0.890903 | + | 0.454193i | \(0.849928\pi\) | |||||||
\(588\) | −2.48549 | − | 6.00051i | −0.102500 | − | 0.247457i | ||||
\(589\) | 24.1007 | − | 9.98284i | 0.993052 | − | 0.411336i | ||||
\(590\) | 0.769721 | − | 1.85827i | 0.0316889 | − | 0.0765038i | ||||
\(591\) | − | 5.54419i | − | 0.228057i | ||||||
\(592\) | 1.67868 | + | 0.695333i | 0.0689934 | + | 0.0285780i | ||||
\(593\) | 23.4782 | − | 23.4782i | 0.964132 | − | 0.964132i | −0.0352463 | − | 0.999379i | \(-0.511222\pi\) |
0.999379 | + | 0.0352463i | \(0.0112216\pi\) | |||||||
\(594\) | 6.35755 | 0.260853 | ||||||||
\(595\) | −1.89103 | + | 1.78805i | −0.0775248 | + | 0.0733030i | ||||
\(596\) | 25.9780 | 1.06410 | ||||||||
\(597\) | 0.0632613 | − | 0.0632613i | 0.00258911 | − | 0.00258911i | ||||
\(598\) | −31.4468 | − | 13.0257i | −1.28596 | − | 0.532660i | ||||
\(599\) | − | 14.8261i | − | 0.605777i | −0.953026 | − | 0.302888i | \(-0.902049\pi\) | ||
0.953026 | − | 0.302888i | \(-0.0979509\pi\) | |||||||
\(600\) | 5.16662 | − | 12.4733i | 0.210926 | − | 0.509221i | ||||
\(601\) | 36.2753 | − | 15.0257i | 1.47970 | − | 0.612912i | 0.510653 | − | 0.859787i | \(-0.329404\pi\) |
0.969047 | + | 0.246875i | \(0.0794036\pi\) | |||||||
\(602\) | −0.418463 | − | 1.01026i | −0.0170553 | − | 0.0411751i | ||||
\(603\) | −12.3319 | − | 12.3319i | −0.502194 | − | 0.502194i | ||||
\(604\) | −5.23003 | − | 5.23003i | −0.212807 | − | 0.212807i | ||||
\(605\) | 1.79948 | + | 4.34432i | 0.0731592 | + | 0.176622i | ||||
\(606\) | 12.1811 | − | 5.04560i | 0.494825 | − | 0.204963i | ||||
\(607\) | −12.0379 | + | 29.0621i | −0.488605 | + | 1.17960i | 0.466818 | + | 0.884353i | \(0.345400\pi\) |
−0.955422 | + | 0.295242i | \(0.904600\pi\) | |||||||
\(608\) | 24.5595i | 0.996018i | ||||||||
\(609\) | −3.43169 | − | 1.42145i | −0.139059 | − | 0.0576001i | ||||
\(610\) | −4.77542 | + | 4.77542i | −0.193351 | + | 0.193351i | ||||
\(611\) | −38.2264 | −1.54648 | ||||||||
\(612\) | −0.274758 | + | 9.81600i | −0.0111064 | + | 0.396788i | ||||
\(613\) | −36.1297 | −1.45927 | −0.729633 | − | 0.683839i | \(-0.760309\pi\) | ||||
−0.729633 | + | 0.683839i | \(0.760309\pi\) | |||||||
\(614\) | 8.72079 | − | 8.72079i | 0.351942 | − | 0.351942i | ||||
\(615\) | −1.58936 | − | 0.658334i | −0.0640891 | − | 0.0265466i | ||||
\(616\) | 4.91351i | 0.197971i | ||||||||
\(617\) | 10.8485 | − | 26.1907i | 0.436746 | − | 1.05440i | −0.540320 | − | 0.841460i | \(-0.681697\pi\) |
0.977066 | − | 0.212938i | \(-0.0683033\pi\) | |||||||
\(618\) | −2.59823 | + | 1.07622i | −0.104516 | + | 0.0432920i | ||||
\(619\) | −15.7017 | − | 37.9072i | −0.631104 | − | 1.52362i | −0.838236 | − | 0.545308i | \(-0.816413\pi\) |
0.207131 | − | 0.978313i | \(-0.433587\pi\) | |||||||
\(620\) | 2.56714 | + | 2.56714i | 0.103099 | + | 0.103099i | ||||
\(621\) | −20.5542 | − | 20.5542i | −0.824812 | − | 0.824812i | ||||
\(622\) | −6.25795 | − | 15.1080i | −0.250921 | − | 0.605777i | ||||
\(623\) | 6.33679 | − | 2.62478i | 0.253878 | − | 0.105160i | ||||
\(624\) | 0.586971 | − | 1.41707i | 0.0234977 | − | 0.0567284i | ||||
\(625\) | 20.9847i | 0.839390i | ||||||||
\(626\) | −5.56054 | − | 2.30325i | −0.222244 | − | 0.0920564i | ||||
\(627\) | −4.39344 | + | 4.39344i | −0.175457 | + | 0.175457i | ||||
\(628\) | 7.89573 | 0.315074 | ||||||||
\(629\) | −29.1701 | + | 11.1370i | −1.16309 | + | 0.444062i | ||||
\(630\) | −1.15070 | −0.0458451 | ||||||||
\(631\) | 0.683703 | − | 0.683703i | 0.0272178 | − | 0.0272178i | −0.693367 | − | 0.720585i | \(-0.743873\pi\) |
0.720585 | + | 0.693367i | \(0.243873\pi\) | |||||||
\(632\) | 5.89829 | + | 2.44315i | 0.234622 | + | 0.0971834i | ||||
\(633\) | − | 27.4419i | − | 1.09072i | ||||||
\(634\) | −5.44754 | + | 13.1515i | −0.216350 | + | 0.522314i | ||||
\(635\) | −4.40007 | + | 1.82257i | −0.174611 | + | 0.0723264i | ||||
\(636\) | 4.67741 | + | 11.2923i | 0.185471 | + | 0.447767i | ||||
\(637\) | 25.2310 | + | 25.2310i | 0.999690 | + | 0.999690i | ||||
\(638\) | −2.79711 | − | 2.79711i | −0.110739 | − | 0.110739i | ||||
\(639\) | 6.40126 | + | 15.4540i | 0.253230 | + | 0.611351i | ||||
\(640\) | −2.94840 | + | 1.22127i | −0.116546 | + | 0.0482749i | ||||
\(641\) | 9.27939 | − | 22.4024i | 0.366514 | − | 0.884843i | −0.627802 | − | 0.778373i | \(-0.716045\pi\) |
0.994316 | − | 0.106470i | \(-0.0339547\pi\) | |||||||
\(642\) | 4.41499i | 0.174246i | ||||||||
\(643\) | −9.12200 | − | 3.77846i | −0.359737 | − | 0.149008i | 0.195492 | − | 0.980705i | \(-0.437369\pi\) |
−0.555229 | + | 0.831697i | \(0.687369\pi\) | |||||||
\(644\) | 5.90017 | − | 5.90017i | 0.232499 | − | 0.232499i | ||||
\(645\) | 0.518125 | 0.0204011 | ||||||||
\(646\) | 11.3612 | + | 12.0155i | 0.446999 | + | 0.472744i | ||||
\(647\) | 0.0624048 | 0.00245338 | 0.00122669 | − | 0.999999i | \(-0.499610\pi\) | ||||
0.00122669 | + | 0.999999i | \(0.499610\pi\) | |||||||
\(648\) | −2.25437 | + | 2.25437i | −0.0885599 | + | 0.0885599i | ||||
\(649\) | 5.55623 | + | 2.30147i | 0.218101 | + | 0.0903405i | ||||
\(650\) | 27.5490i | 1.08056i | ||||||||
\(651\) | 2.70083 | − | 6.52039i | 0.105854 | − | 0.255554i | ||||
\(652\) | 11.9067 | − | 4.93193i | 0.466303 | − | 0.193149i | ||||
\(653\) | 10.1017 | + | 24.3876i | 0.395309 | + | 0.954360i | 0.988763 | + | 0.149492i | \(0.0477639\pi\) |
−0.593454 | + | 0.804868i | \(0.702236\pi\) | |||||||
\(654\) | 8.07535 | + | 8.07535i | 0.315771 | + | 0.315771i | ||||
\(655\) | 0.323364 | + | 0.323364i | 0.0126349 | + | 0.0126349i | ||||
\(656\) | 0.304862 | + | 0.736003i | 0.0119029 | + | 0.0287361i | ||||
\(657\) | −17.2792 | + | 7.15730i | −0.674128 | + | 0.279233i | ||||
\(658\) | −2.48299 | + | 5.99447i | −0.0967971 | + | 0.233689i | ||||
\(659\) | 33.6076i | 1.30917i | 0.755990 | + | 0.654583i | \(0.227156\pi\) | ||||
−0.755990 | + | 0.654583i | \(0.772844\pi\) | |||||||
\(660\) | −0.798886 | − | 0.330909i | −0.0310966 | − | 0.0128806i | ||||
\(661\) | 8.46905 | − | 8.46905i | 0.329408 | − | 0.329408i | −0.522953 | − | 0.852361i | \(-0.675170\pi\) |
0.852361 | + | 0.522953i | \(0.175170\pi\) | |||||||
\(662\) | −1.37081 | −0.0532781 | ||||||||
\(663\) | 9.40141 | + | 24.6242i | 0.365120 | + | 0.956323i | ||||
\(664\) | −5.47462 | −0.212456 | ||||||||
\(665\) | 1.97892 | − | 1.97892i | 0.0767392 | − | 0.0767392i | ||||
\(666\) | −12.7547 | − | 5.28316i | −0.494233 | − | 0.204718i | ||||
\(667\) | 18.0863i | 0.700306i | ||||||||
\(668\) | 2.05104 | − | 4.95164i | 0.0793570 | − | 0.191585i | ||||
\(669\) | −6.36653 | + | 2.63710i | −0.246144 | + | 0.101956i | ||||
\(670\) | −1.56411 | − | 3.77611i | −0.0604270 | − | 0.145884i | ||||
\(671\) | −14.2785 | − | 14.2785i | −0.551216 | − | 0.551216i | ||||
\(672\) | 4.69837 | + | 4.69837i | 0.181244 | + | 0.181244i | ||||
\(673\) | 8.37785 | + | 20.2259i | 0.322943 | + | 0.779652i | 0.999080 | + | 0.0428771i | \(0.0136524\pi\) |
−0.676138 | + | 0.736775i | \(0.736348\pi\) | |||||||
\(674\) | 1.20770 | − | 0.500246i | 0.0465189 | − | 0.0192688i | ||||
\(675\) | −9.00326 | + | 21.7358i | −0.346536 | + | 0.836611i | ||||
\(676\) | − | 33.6850i | − | 1.29558i | ||||||
\(677\) | −13.8298 | − | 5.72847i | −0.531521 | − | 0.220163i | 0.100748 | − | 0.994912i | \(-0.467876\pi\) |
−0.632269 | + | 0.774749i | \(0.717876\pi\) | |||||||
\(678\) | −4.11961 | + | 4.11961i | −0.158213 | + | 0.158213i | ||||
\(679\) | −3.10080 | −0.118998 | ||||||||
\(680\) | −2.53044 | + | 5.65598i | −0.0970378 | + | 0.216897i | ||||
\(681\) | −6.05131 | −0.231887 | ||||||||
\(682\) | 5.31465 | − | 5.31465i | 0.203509 | − | 0.203509i | ||||
\(683\) | −18.6315 | − | 7.71743i | −0.712915 | − | 0.295299i | −0.00340503 | − | 0.999994i | \(-0.501084\pi\) |
−0.709510 | + | 0.704695i | \(0.751084\pi\) | |||||||
\(684\) | − | 10.5597i | − | 0.403761i | ||||||
\(685\) | −2.58289 | + | 6.23564i | −0.0986871 | + | 0.238252i | ||||
\(686\) | 12.6673 | − | 5.24696i | 0.483639 | − | 0.200330i | ||||
\(687\) | 5.68505 | + | 13.7249i | 0.216898 | + | 0.523639i | ||||
\(688\) | −0.169659 | − | 0.169659i | −0.00646819 | − | 0.00646819i | ||||
\(689\) | −47.4819 | − | 47.4819i | −1.80892 | − | 1.80892i | ||||
\(690\) | −1.04759 | − | 2.52909i | −0.0398809 | − | 0.0962810i | ||||
\(691\) | −47.4912 | + | 19.6715i | −1.80665 | + | 0.748339i | −0.823052 | + | 0.567966i | \(0.807730\pi\) |
−0.983598 | + | 0.180373i | \(0.942270\pi\) | |||||||
\(692\) | −3.15570 | + | 7.61854i | −0.119962 | + | 0.289613i | ||||
\(693\) | − | 3.44061i | − | 0.130698i | ||||||
\(694\) | −3.46623 | − | 1.43576i | −0.131576 | − | 0.0545006i | ||||
\(695\) | 7.29630 | − | 7.29630i | 0.276764 | − | 0.276764i | ||||
\(696\) | −8.84350 | −0.335212 | ||||||||
\(697\) | −12.4962 | − | 5.59069i | −0.473327 | − | 0.211762i | ||||
\(698\) | −18.5215 | −0.701050 | ||||||||
\(699\) | −11.5220 | + | 11.5220i | −0.435801 | + | 0.435801i | ||||
\(700\) | −6.23934 | − | 2.58442i | −0.235825 | − | 0.0976819i | ||||
\(701\) | − | 3.32047i | − | 0.125412i | −0.998032 | − | 0.0627062i | \(-0.980027\pi\) | ||
0.998032 | − | 0.0627062i | \(-0.0199731\pi\) | |||||||
\(702\) | −11.0986 | + | 26.7944i | −0.418889 | + | 1.01129i | ||||
\(703\) | 31.0205 | − | 12.8491i | 1.16996 | − | 0.484614i | ||||
\(704\) | 2.96725 | + | 7.16357i | 0.111832 | + | 0.269987i | ||||
\(705\) | −2.17389 | − | 2.17389i | −0.0818734 | − | 0.0818734i | ||||
\(706\) | 16.7983 | + | 16.7983i | 0.632211 | + | 0.632211i | ||||
\(707\) | −6.79529 | − | 16.4053i | −0.255563 | − | 0.616984i | ||||
\(708\) | 4.61362 | − | 1.91102i | 0.173390 | − | 0.0718207i | ||||
\(709\) | 16.6060 | − | 40.0904i | 0.623651 | − | 1.50563i | −0.223736 | − | 0.974650i | \(-0.571825\pi\) |
0.847387 | − | 0.530976i | \(-0.178175\pi\) | |||||||
\(710\) | 3.92021i | 0.147123i | ||||||||
\(711\) | −4.13019 | − | 1.71078i | −0.154894 | − | 0.0641593i | ||||
\(712\) | 11.5470 | − | 11.5470i | 0.432743 | − | 0.432743i | ||||
\(713\) | −34.3650 | −1.28698 | ||||||||
\(714\) | 4.47210 | + | 0.125178i | 0.167364 | + | 0.00468467i | ||||
\(715\) | 4.75058 | 0.177662 | ||||||||
\(716\) | −20.1368 | + | 20.1368i | −0.752546 | + | 0.752546i | ||||
\(717\) | 18.7573 | + | 7.76953i | 0.700504 | + | 0.290158i | ||||
\(718\) | − | 25.0310i | − | 0.934149i | ||||||
\(719\) | 1.99490 | − | 4.81611i | 0.0743972 | − | 0.179611i | −0.882306 | − | 0.470677i | \(-0.844010\pi\) |
0.956703 | + | 0.291066i | \(0.0940099\pi\) | |||||||
\(720\) | −0.233267 | + | 0.0966223i | −0.00869335 | + | 0.00360090i | ||||
\(721\) | 1.44943 | + | 3.49923i | 0.0539796 | + | 0.130318i | ||||
\(722\) | −0.421038 | − | 0.421038i | −0.0156694 | − | 0.0156694i | ||||
\(723\) | −8.72644 | − | 8.72644i | −0.324540 | − | 0.324540i | ||||
\(724\) | 1.99608 | + | 4.81896i | 0.0741837 | + | 0.179095i | ||||
\(725\) | 13.5242 | − | 5.60189i | 0.502275 | − | 0.208049i | ||||
\(726\) | 3.09338 | − | 7.46807i | 0.114806 | − | 0.277166i | ||||
\(727\) | − | 20.9921i | − | 0.778552i | −0.921121 | − | 0.389276i | \(-0.872725\pi\) | ||
0.921121 | − | 0.389276i | \(-0.127275\pi\) | |||||||
\(728\) | −20.7083 | − | 8.57768i | −0.767502 | − | 0.317910i | ||||
\(729\) | −8.89722 | + | 8.89722i | −0.329527 | + | 0.329527i | ||||
\(730\) | −4.38322 | −0.162230 | ||||||||
\(731\) | 4.12149 | + | 0.115364i | 0.152439 | + | 0.00426690i | ||||
\(732\) | −16.7672 | −0.619732 | ||||||||
\(733\) | 5.33284 | − | 5.33284i | 0.196973 | − | 0.196973i | −0.601728 | − | 0.798701i | \(-0.705521\pi\) |
0.798701 | + | 0.601728i | \(0.205521\pi\) | |||||||
\(734\) | −14.1701 | − | 5.86944i | −0.523027 | − | 0.216645i | ||||
\(735\) | 2.86971i | 0.105851i | ||||||||
\(736\) | 12.3811 | − | 29.8907i | 0.456375 | − | 1.10179i | ||||
\(737\) | 11.2906 | − | 4.67671i | 0.415894 | − | 0.172269i | ||||
\(738\) | −2.31635 | − | 5.59217i | −0.0852661 | − | 0.205851i | ||||
\(739\) | 36.9764 | + | 36.9764i | 1.36020 | + | 1.36020i | 0.873657 | + | 0.486543i | \(0.161742\pi\) |
0.486543 | + | 0.873657i | \(0.338258\pi\) | |||||||
\(740\) | 3.30422 | + | 3.30422i | 0.121466 | + | 0.121466i | ||||
\(741\) | −10.8467 | − | 26.1862i | −0.398463 | − | 0.961976i | ||||
\(742\) | −10.5300 | + | 4.36169i | −0.386570 | + | 0.160123i | ||||
\(743\) | 16.8760 | − | 40.7424i | 0.619122 | − | 1.49469i | −0.233603 | − | 0.972332i | \(-0.575052\pi\) |
0.852725 | − | 0.522360i | \(-0.174948\pi\) | |||||||
\(744\) | − | 16.8031i | − | 0.616032i | ||||||
\(745\) | −10.6044 | − | 4.39249i | −0.388516 | − | 0.160929i | ||||
\(746\) | −9.62933 | + | 9.62933i | −0.352555 | + | 0.352555i | ||||
\(747\) | 3.83352 | 0.140261 | ||||||||
\(748\) | −6.28117 | − | 2.81014i | −0.229662 | − | 0.102749i | ||||
\(749\) | 5.94601 | 0.217263 | ||||||||
\(750\) | −3.22370 | + | 3.22370i | −0.117713 | + | 0.117713i | ||||
\(751\) | −5.61679 | − | 2.32655i | −0.204960 | − | 0.0848970i | 0.277842 | − | 0.960627i | \(-0.410381\pi\) |
−0.482802 | + | 0.875730i | \(0.660381\pi\) | |||||||
\(752\) | 1.42367i | 0.0519160i | ||||||||
\(753\) | 7.95751 | − | 19.2111i | 0.289988 | − | 0.700092i | ||||
\(754\) | 16.6716 | − | 6.90562i | 0.607145 | − | 0.251488i | ||||
\(755\) | 1.25062 | + | 3.01926i | 0.0455147 | + | 0.109882i | ||||
\(756\) | −5.02726 | − | 5.02726i | −0.182840 | − | 0.182840i | ||||
\(757\) | −23.6814 | − | 23.6814i | −0.860716 | − | 0.860716i | 0.130706 | − | 0.991421i | \(-0.458276\pi\) |
−0.991421 | + | 0.130706i | \(0.958276\pi\) | |||||||
\(758\) | 4.39537 | + | 10.6114i | 0.159647 | + | 0.385422i | ||||
\(759\) | 7.56200 | − | 3.13228i | 0.274483 | − | 0.113695i | ||||
\(760\) | 2.54985 | − | 6.15588i | 0.0924928 | − | 0.223297i | ||||
\(761\) | 15.2033i | 0.551119i | 0.961284 | + | 0.275560i | \(0.0888631\pi\) | ||||
−0.961284 | + | 0.275560i | \(0.911137\pi\) | |||||||
\(762\) | 7.56390 | + | 3.13307i | 0.274011 | + | 0.113499i | ||||
\(763\) | 10.8757 | − | 10.8757i | 0.393726 | − | 0.393726i | ||||
\(764\) | 10.9923 | 0.397688 | ||||||||
\(765\) | 1.77190 | − | 3.96051i | 0.0640631 | − | 0.143193i | ||||
\(766\) | 12.2569 | 0.442861 | ||||||||
\(767\) | −19.3994 | + | 19.3994i | −0.700473 | + | 0.700473i | ||||
\(768\) | 15.1352 | + | 6.26922i | 0.546146 | + | 0.226221i | ||||
\(769\) | − | 21.0273i | − | 0.758264i | −0.925343 | − | 0.379132i | \(-0.876223\pi\) | ||
0.925343 | − | 0.379132i | \(-0.123777\pi\) | |||||||
\(770\) | 0.308573 | − | 0.744962i | 0.0111202 | − | 0.0268466i | ||||
\(771\) | −16.8403 | + | 6.97547i | −0.606488 | + | 0.251216i | ||||
\(772\) | 3.44235 | + | 8.31056i | 0.123893 | + | 0.299104i | ||||
\(773\) | −8.96396 | − | 8.96396i | −0.322411 | − | 0.322411i | 0.527280 | − | 0.849691i | \(-0.323212\pi\) |
−0.849691 | + | 0.527280i | \(0.823212\pi\) | |||||||
\(774\) | 1.28907 | + | 1.28907i | 0.0463348 | + | 0.0463348i | ||||
\(775\) | 10.6439 | + | 25.6966i | 0.382340 | + | 0.923050i | ||||
\(776\) | −6.82058 | + | 2.82518i | −0.244845 | + | 0.101418i | ||||
\(777\) | 3.47630 | − | 8.39252i | 0.124711 | − | 0.301080i | ||||
\(778\) | 13.2807i | 0.476138i | ||||||||
\(779\) | 13.6007 | + | 5.63358i | 0.487294 | + | 0.201844i | ||||
\(780\) | 2.78929 | − | 2.78929i | 0.0998725 | − | 0.0998725i | ||||
\(781\) | −11.7215 | −0.419426 | ||||||||
\(782\) | −7.77004 | − | 20.3513i | −0.277856 | − | 0.727760i | ||||
\(783\) | 15.4105 | 0.550728 | ||||||||
\(784\) | 0.939683 | − | 0.939683i | 0.0335601 | − | 0.0335601i | ||||
\(785\) | −3.22310 | − | 1.33505i | −0.115037 | − | 0.0476500i | ||||
\(786\) | − | 0.786128i | − | 0.0280403i | ||||||
\(787\) | −2.64948 | + | 6.39640i | −0.0944437 | + | 0.228007i | −0.964041 | − | 0.265755i | \(-0.914379\pi\) |
0.869597 | + | 0.493762i | \(0.164379\pi\) | |||||||
\(788\) | −6.10017 | + | 2.52677i | −0.217310 | + | 0.0900126i | ||||
\(789\) | 1.59375 | + | 3.84766i | 0.0567392 | + | 0.136980i | ||||
\(790\) | −0.740838 | − | 0.740838i | −0.0263578 | − | 0.0263578i | ||||
\(791\) | 5.54819 | + | 5.54819i | 0.197271 | + | 0.197271i | ||||
\(792\) | −3.13478 | − | 7.56802i | −0.111389 | − | 0.268918i | ||||
\(793\) | 85.1044 | − | 35.2514i | 3.02215 | − | 1.25181i | ||||
\(794\) | −8.84447 | + | 21.3524i | −0.313878 | + | 0.757770i | ||||
\(795\) | − | 5.40047i | − | 0.191535i | ||||||
\(796\) | −0.0984368 | − | 0.0407738i | −0.00348900 | − | 0.00144519i | ||||
\(797\) | 4.13731 | − | 4.13731i | 0.146551 | − | 0.146551i | −0.630024 | − | 0.776575i | \(-0.716955\pi\) |
0.776575 | + | 0.630024i | \(0.216955\pi\) | |||||||
\(798\) | −4.81094 | −0.170305 | ||||||||
\(799\) | −16.8085 | − | 17.7765i | −0.594641 | − | 0.628888i | ||||
\(800\) | −26.1858 | −0.925806 | ||||||||
\(801\) | −8.08563 | + | 8.08563i | −0.285692 | + | 0.285692i | ||||
\(802\) | 26.1963 | + | 10.8509i | 0.925023 | + | 0.383157i | ||||
\(803\) | − | 13.1058i | − | 0.462495i | ||||||
\(804\) | 3.88330 | − | 9.37512i | 0.136954 | − | 0.330635i | ||||
\(805\) | −3.40613 | + | 1.41086i | −0.120050 | + | 0.0497264i | ||||
\(806\) | 13.1210 | + | 31.6770i | 0.462169 | + | 1.11577i | ||||
\(807\) | −9.44207 | − | 9.44207i | −0.332377 | − | 0.332377i | ||||
\(808\) | −29.8941 | − | 29.8941i | −1.05167 | − | 1.05167i | ||||
\(809\) | −17.2231 | − | 41.5803i | −0.605533 | − | 1.46189i | −0.867811 | − | 0.496894i | \(-0.834474\pi\) |
0.262278 | − | 0.964992i | \(-0.415526\pi\) | |||||||
\(810\) | 0.483373 | − | 0.200220i | 0.0169840 | − | 0.00703500i | ||||
\(811\) | −11.6605 | + | 28.1509i | −0.409456 | + | 0.988513i | 0.575826 | + | 0.817572i | \(0.304681\pi\) |
−0.985281 | + | 0.170941i | \(0.945319\pi\) | |||||||
\(812\) | 4.42365i | 0.155240i | ||||||||
\(813\) | −20.4248 | − | 8.46024i | −0.716330 | − | 0.296713i | ||||
\(814\) | 6.84060 | − | 6.84060i | 0.239763 | − | 0.239763i | ||||
\(815\) | −5.69433 | −0.199464 | ||||||||
\(816\) | 0.917081 | − | 0.350138i | 0.0321043 | − | 0.0122573i | ||||
\(817\) | −4.43376 | −0.155118 | ||||||||
\(818\) | −3.26267 | + | 3.26267i | −0.114076 | + | 0.114076i | ||||
\(819\) | 14.5007 | + | 6.00639i | 0.506695 | + | 0.209880i | ||||
\(820\) | 2.04878i | 0.0715465i | ||||||||
\(821\) | −13.6322 | + | 32.9109i | −0.475765 | + | 1.14860i | 0.485811 | + | 0.874064i | \(0.338524\pi\) |
−0.961577 | + | 0.274536i | \(0.911476\pi\) | |||||||
\(822\) | 10.7193 | − | 4.44009i | 0.373880 | − | 0.154866i | ||||
\(823\) | −18.9470 | − | 45.7421i | −0.660451 | − | 1.59447i | −0.797097 | − | 0.603851i | \(-0.793632\pi\) |
0.136646 | − | 0.990620i | \(-0.456368\pi\) | |||||||
\(824\) | 6.37638 | + | 6.37638i | 0.222132 | + | 0.222132i | ||||
\(825\) | −4.68436 | − | 4.68436i | −0.163089 | − | 0.163089i | ||||
\(826\) | 1.78203 | + | 4.30220i | 0.0620048 | + | 0.149693i | ||||
\(827\) | 32.8985 | − | 13.6270i | 1.14399 | − | 0.473858i | 0.271479 | − | 0.962444i | \(-0.412487\pi\) |
0.872516 | + | 0.488586i | \(0.162487\pi\) | |||||||
\(828\) | −5.32346 | + | 12.8520i | −0.185003 | + | 0.446637i | ||||
\(829\) | − | 43.4546i | − | 1.50924i | −0.656162 | − | 0.754620i | \(-0.727821\pi\) | ||
0.656162 | − | 0.754620i | \(-0.272179\pi\) | |||||||
\(830\) | 0.830035 | + | 0.343812i | 0.0288110 | + | 0.0119339i | ||||
\(831\) | 0.593532 | − | 0.593532i | 0.0205894 | − | 0.0205894i | ||||
\(832\) | −35.3715 | −1.22628 | ||||||||
\(833\) | −0.638962 | + | 22.8275i | −0.0221387 | + | 0.790927i | ||||
\(834\) | −17.7380 | −0.614216 | ||||||||
\(835\) | −1.67450 | + | 1.67450i | −0.0579484 | + | 0.0579484i | ||||
\(836\) | 6.83633 | + | 2.83170i | 0.236440 | + | 0.0979365i | ||||
\(837\) | 29.2808i | 1.01209i | ||||||||
\(838\) | 10.6047 | − | 25.6021i | 0.366334 | − | 0.884409i | ||||
\(839\) | −0.589198 | + | 0.244054i | −0.0203414 | + | 0.00842568i | −0.392831 | − | 0.919611i | \(-0.628504\pi\) |
0.372490 | + | 0.928036i | \(0.378504\pi\) | |||||||
\(840\) | −0.689856 | − | 1.66546i | −0.0238023 | − | 0.0574638i | ||||
\(841\) | 13.7260 | + | 13.7260i | 0.473309 | + | 0.473309i | ||||
\(842\) | 0.461725 | + | 0.461725i | 0.0159121 | + | 0.0159121i | ||||
\(843\) | −7.54802 | − | 18.2225i | −0.259968 | − | 0.627617i | ||||
\(844\) | −30.1938 | + | 12.5067i | −1.03931 | + | 0.430498i | ||||
\(845\) | −5.69563 | + | 13.7505i | −0.195936 | + | 0.473030i | ||||
\(846\) | − | 10.8171i | − | 0.371900i | ||||||
\(847\) | −10.0578 | − | 4.16609i | −0.345591 | − | 0.143148i | ||||
\(848\) | −1.76838 | + | 1.76838i | −0.0607263 | + | 0.0607263i | ||||
\(849\) | −28.6270 | −0.982475 | ||||||||
\(850\) | −12.8112 | + | 12.1135i | −0.439419 | + | 0.415489i | ||||
\(851\) | −44.2319 | −1.51625 | ||||||||
\(852\) | −6.88220 | + | 6.88220i | −0.235780 | + | 0.235780i | ||||
\(853\) | 6.96863 | + | 2.88650i | 0.238601 | + | 0.0988319i | 0.498780 | − | 0.866729i | \(-0.333782\pi\) |
−0.260179 | + | 0.965560i | \(0.583782\pi\) | |||||||
\(854\) | − | 15.6354i | − | 0.535032i | ||||||
\(855\) | −1.78549 | + | 4.31056i | −0.0610626 | + | 0.147418i | ||||
\(856\) | 13.0789 | − | 5.41748i | 0.447029 | − | 0.185166i | ||||
\(857\) | −10.7346 | − | 25.9156i | −0.366687 | − | 0.885260i | −0.994289 | − | 0.106725i | \(-0.965963\pi\) |
0.627602 | − | 0.778534i | \(-0.284037\pi\) | |||||||
\(858\) | −5.77455 | − | 5.77455i | −0.197140 | − | 0.197140i | ||||
\(859\) | 24.6325 | + | 24.6325i | 0.840449 | + | 0.840449i | 0.988917 | − | 0.148468i | \(-0.0474341\pi\) |
−0.148468 | + | 0.988917i | \(0.547434\pi\) | |||||||
\(860\) | −0.236136 | − | 0.570083i | −0.00805218 | − | 0.0194397i | ||||
\(861\) | 3.67963 | − | 1.52415i | 0.125401 | − | 0.0519429i | ||||
\(862\) | −2.16972 | + | 5.23817i | −0.0739010 | + | 0.178413i | ||||
\(863\) | 0.574219i | 0.0195466i | 0.999952 | + | 0.00977332i | \(0.00311099\pi\) | ||||
−0.999952 | + | 0.00977332i | \(0.996889\pi\) | |||||||
\(864\) | −25.4685 | − | 10.5494i | −0.866456 | − | 0.358898i | ||||
\(865\) | 2.57636 | − | 2.57636i | 0.0875990 | − | 0.0875990i | ||||
\(866\) | 20.9990 | 0.713576 | ||||||||
\(867\) | −7.31716 | + | 15.1994i | −0.248504 | + | 0.516198i | ||||
\(868\) | −8.40517 | −0.285290 | ||||||||
\(869\) | 2.21511 | − | 2.21511i | 0.0751424 | − | 0.0751424i | ||||
\(870\) | 1.34081 | + | 0.555381i | 0.0454577 | + | 0.0188292i | ||||
\(871\) | 55.7493i | 1.88899i | ||||||||
\(872\) | 14.0134 | − | 33.8313i | 0.474553 | − | 1.14567i | ||||
\(873\) | 4.77601 | − | 1.97829i | 0.161643 | − | 0.0669549i | ||||
\(874\) | 8.96453 | + | 21.6423i | 0.303230 | + | 0.732062i | ||||
\(875\) | 4.34161 | + | 4.34161i | 0.146773 | + | 0.146773i | ||||
\(876\) | −7.69504 | − | 7.69504i | −0.259991 | − | 0.259991i | ||||
\(877\) | 14.1886 | + | 34.2544i | 0.479116 | + | 1.15669i | 0.960024 | + | 0.279918i | \(0.0903073\pi\) |
−0.480908 | + | 0.876771i | \(0.659693\pi\) | |||||||
\(878\) | 31.6264 | − | 13.1001i | 1.06734 | − | 0.442107i | ||||
\(879\) | −7.39499 | + | 17.8531i | −0.249427 | + | 0.602170i | ||||
\(880\) | − | 0.176927i | − | 0.00596420i | ||||||
\(881\) | −6.32032 | − | 2.61796i | −0.212937 | − | 0.0882014i | 0.273665 | − | 0.961825i | \(-0.411764\pi\) |
−0.486602 | + | 0.873624i | \(0.661764\pi\) | |||||||
\(882\) | −7.13973 | + | 7.13973i | −0.240407 | + | 0.240407i | ||||
\(883\) | −42.4752 | −1.42940 | −0.714702 | − | 0.699430i | \(-0.753437\pi\) | ||||
−0.714702 | + | 0.699430i | \(0.753437\pi\) | |||||||
\(884\) | 22.8088 | − | 21.5667i | 0.767143 | − | 0.725367i | ||||
\(885\) | −2.20644 | −0.0741687 | ||||||||
\(886\) | 15.7245 | − | 15.7245i | 0.528275 | − | 0.528275i | ||||
\(887\) | 18.1556 | + | 7.52028i | 0.609604 | + | 0.252506i | 0.666059 | − | 0.745899i | \(-0.267980\pi\) |
−0.0564552 | + | 0.998405i | \(0.517980\pi\) | |||||||
\(888\) | − | 21.6276i | − | 0.725776i | ||||||
\(889\) | 4.21954 | − | 10.1869i | 0.141519 | − | 0.341657i | ||||
\(890\) | −2.47587 | + | 1.02554i | −0.0829914 | + | 0.0343762i | ||||
\(891\) | 0.598657 | + | 1.44529i | 0.0200558 | + | 0.0484189i | ||||
\(892\) | 5.80312 | + | 5.80312i | 0.194303 | + | 0.194303i | ||||
\(893\) | 18.6027 | + | 18.6027i | 0.622515 | + | 0.622515i | ||||
\(894\) | 7.55088 | + | 18.2294i | 0.252539 | + | 0.609683i | ||||
\(895\) | 11.6248 | − | 4.81515i | 0.388575 | − | 0.160953i | ||||
\(896\) | 2.82744 | − | 6.82604i | 0.0944580 | − | 0.228042i | ||||
\(897\) | 37.3388i | 1.24670i | ||||||||
\(898\) | −30.1897 | − | 12.5050i | −1.00744 | − | 0.417297i | ||||
\(899\) | 12.8826 | − | 12.8826i | 0.429659 | − | 0.429659i | ||||
\(900\) | 11.2590 | 0.375299 | ||||||||
\(901\) | 1.20245 | − | 42.9588i | 0.0400595 | − | 1.43116i | ||||
\(902\) | 4.24151 | 0.141227 | ||||||||
\(903\) | −0.848205 | + | 0.848205i | −0.0282265 | + | 0.0282265i | ||||
\(904\) | 17.2589 | + | 7.14887i | 0.574023 | + | 0.237768i | ||||
\(905\) | − | 2.30465i | − | 0.0766090i | ||||||
\(906\) | 2.14987 | − | 5.19024i | 0.0714245 | − | 0.172434i | ||||
\(907\) | −15.7553 | + | 6.52605i | −0.523146 | + | 0.216694i | −0.628598 | − | 0.777730i | \(-0.716371\pi\) |
0.105453 | + | 0.994424i | \(0.466371\pi\) | |||||||
\(908\) | 2.75790 | + | 6.65815i | 0.0915240 | + | 0.220958i | ||||
\(909\) | 20.9329 | + | 20.9329i | 0.694299 | + | 0.694299i | ||||
\(910\) | 2.60101 | + | 2.60101i | 0.0862227 | + | 0.0862227i | ||||
\(911\) | 4.00855 | + | 9.67751i | 0.132809 | + | 0.320630i | 0.976269 | − | 0.216563i | \(-0.0694847\pi\) |
−0.843459 | + | 0.537193i | \(0.819485\pi\) | |||||||
\(912\) | −0.975258 | + | 0.403965i | −0.0322940 | + | 0.0133766i | ||||
\(913\) | −1.02800 | + | 2.48181i | −0.0340218 | + | 0.0821359i | ||||
\(914\) | 13.9463i | 0.461302i | ||||||||
\(915\) | 6.84448 | + | 2.83508i | 0.226272 | + | 0.0937248i | ||||
\(916\) | 12.5103 | − | 12.5103i | 0.413353 | − | 0.413353i | ||||
\(917\) | −1.05874 | −0.0349627 | ||||||||
\(918\) | −17.3404 | + | 6.62049i | −0.572318 | + | 0.218509i | ||||
\(919\) | 28.8314 | 0.951061 | 0.475531 | − | 0.879699i | \(-0.342256\pi\) | ||||
0.475531 | + | 0.879699i | \(0.342256\pi\) | |||||||
\(920\) | −6.20672 | + | 6.20672i | −0.204629 | + | 0.204629i | ||||
\(921\) | −12.4993 | − | 5.17737i | −0.411865 | − | 0.170600i | ||||
\(922\) | − | 9.06158i | − | 0.298427i | ||||||
\(923\) | 20.4625 | − | 49.4010i | 0.673533 | − | 1.62605i | ||||
\(924\) | 1.84955 | − | 0.766110i | 0.0608458 | − | 0.0252032i | ||||
\(925\) | 13.7000 | + | 33.0746i | 0.450452 | + | 1.08749i | ||||
\(926\) | −1.05813 | − | 1.05813i | −0.0347722 | − | 0.0347722i | ||||
\(927\) | −4.46496 | − | 4.46496i | −0.146649 | − | 0.146649i | ||||
\(928\) | 6.56391 | + | 15.8467i | 0.215471 | + | 0.520193i | ||||
\(929\) | 16.2581 | − | 6.73431i | 0.533410 | − | 0.220946i | −0.0996859 | − | 0.995019i | \(-0.531784\pi\) |
0.633096 | + | 0.774073i | \(0.281784\pi\) | |||||||
\(930\) | −1.05525 | + | 2.54761i | −0.0346031 | + | 0.0835393i | ||||
\(931\) | − | 24.5571i | − | 0.804826i | ||||||
\(932\) | 17.9286 | + | 7.42625i | 0.587270 | + | 0.243255i | ||||
\(933\) | −12.6846 | + | 12.6846i | −0.415275 | + | 0.415275i | ||||
\(934\) | 13.4966 | 0.441623 | ||||||||
\(935\) | 2.08887 | + | 2.20917i | 0.0683133 | + | 0.0722477i | ||||
\(936\) | 37.3685 | 1.22143 | ||||||||
\(937\) | 4.32581 | − | 4.32581i | 0.141318 | − | 0.141318i | −0.632909 | − | 0.774227i | \(-0.718139\pi\) |
0.774227 | + | 0.632909i | \(0.218139\pi\) | |||||||
\(938\) | 8.74231 | + | 3.62118i | 0.285447 | + | 0.118236i | ||||
\(939\) | 6.60238i | 0.215460i | ||||||||
\(940\) | −1.40114 | + | 3.38264i | −0.0457001 | + | 0.110330i | ||||
\(941\) | −17.7542 | + | 7.35404i | −0.578771 | + | 0.239735i | −0.652812 | − | 0.757520i | \(-0.726411\pi\) |
0.0740403 | + | 0.997255i | \(0.476411\pi\) | |||||||
\(942\) | 2.29501 | + | 5.54064i | 0.0747755 | + | 0.180524i | ||||
\(943\) | −13.7130 | − | 13.7130i | −0.446556 | − | 0.446556i | ||||
\(944\) | 0.722495 | + | 0.722495i | 0.0235152 | + | 0.0235152i | ||||
\(945\) | 1.20213 | + | 2.90220i | 0.0391053 | + | 0.0944086i | ||||
\(946\) | −1.18022 | + | 0.488864i | −0.0383723 | + | 0.0158943i | ||||
\(947\) | −15.2897 | + | 36.9126i | −0.496848 | + | 1.19950i | 0.454324 | + | 0.890837i | \(0.349881\pi\) |
−0.951172 | + | 0.308661i | \(0.900119\pi\) | |||||||
\(948\) | − | 2.60118i | − | 0.0844826i | ||||||
\(949\) | 55.2356 | + | 22.8793i | 1.79302 | + | 0.742694i | ||||
\(950\) | 13.4066 | − | 13.4066i | 0.434966 | − | 0.434966i | ||||
\(951\) | 15.6156 | 0.506372 | ||||||||
\(952\) | −5.11672 | − | 13.4017i | −0.165834 | − | 0.434352i | ||||
\(953\) | 14.4242 | 0.467245 | 0.233622 | − | 0.972327i | \(-0.424942\pi\) | ||||
0.233622 | + | 0.972327i | \(0.424942\pi\) | |||||||
\(954\) | 13.4362 | − | 13.4362i | 0.435012 | − | 0.435012i | ||||
\(955\) | −4.48715 | − | 1.85864i | −0.145201 | − | 0.0601442i | ||||
\(956\) | − | 24.1793i | − | 0.782014i | ||||||
\(957\) | −1.66059 | + | 4.00902i | −0.0536793 | + | 0.129593i | ||||
\(958\) | 34.2903 | − | 14.2035i | 1.10787 | − | 0.458895i | ||||
\(959\) | −5.97981 | − | 14.4365i | −0.193098 | − | 0.466180i | ||||
\(960\) | −2.01153 | − | 2.01153i | −0.0649218 | − | 0.0649218i | ||||
\(961\) | 2.55730 | + | 2.55730i | 0.0824934 | + | 0.0824934i | ||||
\(962\) | 16.8884 | + | 40.7721i | 0.544503 | + | 1.31455i | ||||
\(963\) | −9.15833 | + | 3.79351i | −0.295123 | + | 0.122244i | ||||
\(964\) | −5.62445 | + | 13.5786i | −0.181151 | + | 0.437338i | ||||
\(965\) | − | 3.97448i | − | 0.127943i | ||||||
\(966\) | 5.85527 | + | 2.42533i | 0.188390 | + | 0.0780338i | ||||
\(967\) | 12.5538 | − | 12.5538i | 0.403703 | − | 0.403703i | −0.475833 | − | 0.879536i | \(-0.657853\pi\) |
0.879536 | + | 0.475833i | \(0.157853\pi\) | |||||||
\(968\) | −25.9191 | −0.833072 | ||||||||
\(969\) | 7.40807 | − | 16.5584i | 0.237982 | − | 0.531931i | ||||
\(970\) | 1.21153 | 0.0388998 | ||||||||
\(971\) | 31.1335 | − | 31.1335i | 0.999121 | − | 0.999121i | −0.000878135 | − | 1.00000i | \(-0.500280\pi\) |
1.00000 | 0.000878135i | \(0.000279519\pi\) | ||||||||
\(972\) | 17.5008 | + | 7.24907i | 0.561338 | + | 0.232514i | ||||
\(973\) | 23.8891i | 0.765849i | ||||||||
\(974\) | 2.94538 | − | 7.11077i | 0.0943760 | − | 0.227844i | ||||
\(975\) | 27.9203 | − | 11.5649i | 0.894164 | − | 0.370375i | ||||
\(976\) | −1.31287 | − | 3.16956i | −0.0420240 | − | 0.101455i | ||||
\(977\) | −22.3761 | − | 22.3761i | −0.715873 | − | 0.715873i | 0.251884 | − | 0.967757i | \(-0.418950\pi\) |
−0.967757 | + | 0.251884i | \(0.918950\pi\) | |||||||
\(978\) | 6.92172 | + | 6.92172i | 0.221332 | + | 0.221332i | ||||
\(979\) | −3.06637 | − | 7.40286i | −0.0980015 | − | 0.236597i | ||||
\(980\) | 3.15749 | − | 1.30788i | 0.100862 | − | 0.0417786i | ||||
\(981\) | −9.81266 | + | 23.6899i | −0.313294 | + | 0.756359i | ||||
\(982\) | 25.0613i | 0.799737i | ||||||||
\(983\) | −27.6950 | − | 11.4716i | −0.883333 | − | 0.365889i | −0.105545 | − | 0.994415i | \(-0.533659\pi\) |
−0.777789 | + | 0.628526i | \(0.783659\pi\) | |||||||
\(984\) | 6.70510 | − | 6.70510i | 0.213751 | − | 0.213751i | ||||
\(985\) | 2.91738 | 0.0929554 | ||||||||
\(986\) | 10.5420 | + | 4.71640i | 0.335725 | + | 0.150201i | ||||
\(987\) | 7.11761 | 0.226556 | ||||||||
\(988\) | −23.8688 | + | 23.8688i | −0.759369 | + | 0.759369i | ||||
\(989\) | 5.39622 | + | 2.23519i | 0.171590 | + | 0.0710749i | ||||
\(990\) | 1.34429i | 0.0427244i | ||||||||
\(991\) | −3.51438 | + | 8.48447i | −0.111638 | + | 0.269518i | −0.969818 | − | 0.243832i | \(-0.921596\pi\) |
0.858180 | + | 0.513350i | \(0.171596\pi\) | |||||||
\(992\) | −30.1095 | + | 12.4718i | −0.955978 | + | 0.395979i | ||||
\(993\) | 0.575461 | + | 1.38929i | 0.0182617 | + | 0.0440876i | ||||
\(994\) | −6.41766 | − | 6.41766i | −0.203556 | − | 0.203556i | ||||
\(995\) | 0.0332884 | + | 0.0332884i | 0.00105531 | + | 0.00105531i | ||||
\(996\) | 0.853599 | + | 2.06077i | 0.0270473 | + | 0.0652980i | ||||
\(997\) | −5.78837 | + | 2.39762i | −0.183320 | + | 0.0759335i | −0.472455 | − | 0.881355i | \(-0.656632\pi\) |
0.289136 | + | 0.957288i | \(0.406632\pi\) | |||||||
\(998\) | −6.47793 | + | 15.6391i | −0.205055 | + | 0.495047i | ||||
\(999\) | 37.6880i | 1.19239i |
(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 | 731.2.m.c.689.19 | yes | 128 | |
17.2 | even | 8 | inner | 731.2.m.c.87.19 | ✓ | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.m.c.87.19 | ✓ | 128 | 17.2 | even | 8 | inner | |
731.2.m.c.689.19 | yes | 128 | 1.1 | even | 1 | trivial |