Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(43,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.195105024.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(-1.58726 + 0.693255i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.127 |
Dual form | 546.2.s.e.43.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 3.05596i | 1.36667i | 0.730106 | + | 0.683334i | \(0.239471\pi\) | ||||
−0.730106 | + | 0.683334i | \(0.760529\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.52798 | + | 2.64654i | 0.483190 | + | 0.836910i | ||||
\(11\) | −2.98127 | + | 1.72124i | −0.898886 | + | 0.518972i | −0.876839 | − | 0.480785i | \(-0.840352\pi\) |
−0.0220475 | + | 0.999757i | \(0.507018\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.25253 | − | 1.55596i | 0.902091 | − | 0.431546i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.64654 | + | 1.52798i | −0.683334 | + | 0.394523i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.41449 | + | 2.44997i | −0.343064 | + | 0.594205i | −0.985000 | − | 0.172554i | \(-0.944798\pi\) |
0.641936 | + | 0.766758i | \(0.278132\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.49425 | + | 0.862708i | 0.342805 | + | 0.197919i | 0.661512 | − | 0.749935i | \(-0.269915\pi\) |
−0.318707 | + | 0.947853i | \(0.603248\pi\) | |||||||
\(20\) | 2.64654 | + | 1.52798i | 0.591785 | + | 0.341667i | ||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | −1.72124 | + | 2.98127i | −0.366969 | + | 0.635608i | ||||
\(23\) | 1.53130 | + | 2.65229i | 0.319298 | + | 0.553040i | 0.980342 | − | 0.197307i | \(-0.0632196\pi\) |
−0.661044 | + | 0.750347i | \(0.729886\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | −4.33891 | −0.867781 | ||||||||
\(26\) | 2.03880 | − | 2.97377i | 0.399841 | − | 0.583204i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.866025 | − | 0.500000i | 0.163663 | − | 0.0944911i | ||||
\(29\) | −1.92531 | − | 3.33473i | −0.357520 | − | 0.619243i | 0.630026 | − | 0.776574i | \(-0.283044\pi\) |
−0.987546 | + | 0.157331i | \(0.949711\pi\) | |||||||
\(30\) | −1.52798 | + | 2.64654i | −0.278970 | + | 0.483190i | ||||
\(31\) | 0.978370i | 0.175720i | 0.996133 | + | 0.0878602i | \(0.0280029\pi\) | ||||
−0.996133 | + | 0.0878602i | \(0.971997\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −2.98127 | − | 1.72124i | −0.518972 | − | 0.299629i | ||||
\(34\) | 2.82898i | 0.485166i | ||||||||
\(35\) | −1.52798 | + | 2.64654i | −0.258276 | + | 0.447347i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 4.58394 | − | 2.64654i | 0.753596 | − | 0.435089i | −0.0733959 | − | 0.997303i | \(-0.523384\pi\) |
0.826992 | + | 0.562214i | \(0.190050\pi\) | |||||||
\(38\) | 1.72542 | 0.279899 | ||||||||
\(39\) | 2.97377 | + | 2.03880i | 0.476184 | + | 0.326469i | ||||
\(40\) | 3.05596 | 0.483190 | ||||||||
\(41\) | 8.62781 | − | 4.98127i | 1.34744 | − | 0.777943i | 0.359551 | − | 0.933125i | \(-0.382930\pi\) |
0.987886 | + | 0.155182i | \(0.0495964\pi\) | |||||||
\(42\) | 0.500000 | + | 0.866025i | 0.0771517 | + | 0.133631i | ||||
\(43\) | −1.51082 | + | 2.61681i | −0.230397 | + | 0.399060i | −0.957925 | − | 0.287019i | \(-0.907336\pi\) |
0.727528 | + | 0.686078i | \(0.240669\pi\) | |||||||
\(44\) | 3.44247i | 0.518972i | ||||||||
\(45\) | −2.64654 | − | 1.52798i | −0.394523 | − | 0.227778i | ||||
\(46\) | 2.65229 | + | 1.53130i | 0.391058 | + | 0.225778i | ||||
\(47\) | − | 8.04447i | − | 1.17341i | −0.809802 | − | 0.586703i | \(-0.800425\pi\) | ||
0.809802 | − | 0.586703i | \(-0.199575\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | −3.75760 | + | 2.16945i | −0.531405 | + | 0.306807i | ||||
\(51\) | −2.82898 | −0.396137 | ||||||||
\(52\) | 0.278764 | − | 3.59476i | 0.0386576 | − | 0.498503i | ||||
\(53\) | −8.33405 | −1.14477 | −0.572385 | − | 0.819985i | \(-0.693982\pi\) | ||||
−0.572385 | + | 0.819985i | \(0.693982\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | −5.26003 | − | 9.11064i | −0.709263 | − | 1.22848i | ||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 1.72542i | 0.228537i | ||||||||
\(58\) | −3.33473 | − | 1.92531i | −0.437871 | − | 0.252805i | ||||
\(59\) | 8.64080 | + | 4.98877i | 1.12494 | + | 0.649482i | 0.942656 | − | 0.333765i | \(-0.108319\pi\) |
0.182279 | + | 0.983247i | \(0.441652\pi\) | |||||||
\(60\) | 3.05596i | 0.394523i | ||||||||
\(61\) | 5.77260 | − | 9.99843i | 0.739106 | − | 1.28017i | −0.213793 | − | 0.976879i | \(-0.568582\pi\) |
0.952899 | − | 0.303289i | \(-0.0980849\pi\) | |||||||
\(62\) | 0.489185 | + | 0.847293i | 0.0621266 | + | 0.107606i | ||||
\(63\) | −0.866025 | + | 0.500000i | −0.109109 | + | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.75496 | + | 9.93962i | 0.589781 | + | 1.23286i | ||||
\(66\) | −3.44247 | −0.423739 | ||||||||
\(67\) | 4.11410 | − | 2.37527i | 0.502617 | − | 0.290186i | −0.227177 | − | 0.973854i | \(-0.572950\pi\) |
0.729794 | + | 0.683668i | \(0.239616\pi\) | |||||||
\(68\) | 1.41449 | + | 2.44997i | 0.171532 | + | 0.297102i | ||||
\(69\) | −1.53130 | + | 2.65229i | −0.184347 | + | 0.319298i | ||||
\(70\) | 3.05596i | 0.365257i | ||||||||
\(71\) | −3.17784 | − | 1.83473i | −0.377140 | − | 0.217742i | 0.299433 | − | 0.954117i | \(-0.403202\pi\) |
−0.676573 | + | 0.736375i | \(0.736536\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | − | 10.1119i | − | 1.18351i | −0.806117 | − | 0.591756i | \(-0.798435\pi\) | ||
0.806117 | − | 0.591756i | \(-0.201565\pi\) | |||||||
\(74\) | 2.64654 | − | 4.58394i | 0.307654 | − | 0.532873i | ||||
\(75\) | −2.16945 | − | 3.75760i | −0.250507 | − | 0.433891i | ||||
\(76\) | 1.49425 | − | 0.862708i | 0.171403 | − | 0.0989594i | ||||
\(77\) | −3.44247 | −0.392306 | ||||||||
\(78\) | 3.59476 | + | 0.278764i | 0.407026 | + | 0.0315638i | ||||
\(79\) | −4.49843 | −0.506113 | −0.253057 | − | 0.967451i | \(-0.581436\pi\) | ||||
−0.253057 | + | 0.967451i | \(0.581436\pi\) | |||||||
\(80\) | 2.64654 | − | 1.52798i | 0.295892 | − | 0.170833i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.98127 | − | 8.62781i | 0.550089 | − | 0.952782i | ||||
\(83\) | − | 7.15869i | − | 0.785768i | −0.919588 | − | 0.392884i | \(-0.871477\pi\) | ||
0.919588 | − | 0.392884i | \(-0.128523\pi\) | |||||||
\(84\) | 0.866025 | + | 0.500000i | 0.0944911 | + | 0.0545545i | ||||
\(85\) | −7.48701 | − | 4.32263i | −0.812081 | − | 0.468855i | ||||
\(86\) | 3.02163i | 0.325831i | ||||||||
\(87\) | 1.92531 | − | 3.33473i | 0.206414 | − | 0.357520i | ||||
\(88\) | 1.72124 | + | 2.98127i | 0.183484 | + | 0.317804i | ||||
\(89\) | −6.84426 | + | 3.95154i | −0.725490 | + | 0.418862i | −0.816770 | − | 0.576963i | \(-0.804238\pi\) |
0.0912800 | + | 0.995825i | \(0.470904\pi\) | |||||||
\(90\) | −3.05596 | −0.322127 | ||||||||
\(91\) | 3.59476 | + | 0.278764i | 0.376833 | + | 0.0292224i | ||||
\(92\) | 3.06260 | 0.319298 | ||||||||
\(93\) | −0.847293 | + | 0.489185i | −0.0878602 | + | 0.0507261i | ||||
\(94\) | −4.02224 | − | 6.96672i | −0.414862 | − | 0.718562i | ||||
\(95\) | −2.63640 | + | 4.56638i | −0.270489 | + | 0.468501i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −7.88016 | − | 4.54961i | −0.800109 | − | 0.461943i | 0.0434004 | − | 0.999058i | \(-0.486181\pi\) |
−0.843509 | + | 0.537115i | \(0.819514\pi\) | |||||||
\(98\) | 0.866025 | + | 0.500000i | 0.0874818 | + | 0.0505076i | ||||
\(99\) | − | 3.44247i | − | 0.345981i | ||||||
\(100\) | −2.16945 | + | 3.75760i | −0.216945 | + | 0.375760i | ||||
\(101\) | 9.42664 | + | 16.3274i | 0.937985 | + | 1.62464i | 0.769222 | + | 0.638982i | \(0.220644\pi\) |
0.168764 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(102\) | −2.44997 | + | 1.41449i | −0.242583 | + | 0.140055i | ||||
\(103\) | −13.7079 | −1.35068 | −0.675338 | − | 0.737509i | \(-0.736002\pi\) | ||||
−0.675338 | + | 0.737509i | \(0.736002\pi\) | |||||||
\(104\) | −1.55596 | − | 3.25253i | −0.152575 | − | 0.318937i | ||||
\(105\) | −3.05596 | −0.298231 | ||||||||
\(106\) | −7.21750 | + | 4.16702i | −0.701025 | + | 0.404737i | ||||
\(107\) | 1.65736 | + | 2.87063i | 0.160223 | + | 0.277514i | 0.934948 | − | 0.354784i | \(-0.115445\pi\) |
−0.774726 | + | 0.632297i | \(0.782112\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | − | 8.67525i | − | 0.830938i | −0.909607 | − | 0.415469i | \(-0.863617\pi\) | ||
0.909607 | − | 0.415469i | \(-0.136383\pi\) | |||||||
\(110\) | −9.11064 | − | 5.26003i | −0.868666 | − | 0.501524i | ||||
\(111\) | 4.58394 | + | 2.64654i | 0.435089 | + | 0.251199i | ||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 5.60557 | − | 9.70914i | 0.527328 | − | 0.913359i | −0.472165 | − | 0.881510i | \(-0.656527\pi\) |
0.999493 | − | 0.0318486i | \(-0.0101394\pi\) | |||||||
\(114\) | 0.862708 | + | 1.49425i | 0.0808000 | + | 0.139950i | ||||
\(115\) | −8.10529 | + | 4.67959i | −0.755822 | + | 0.436374i | ||||
\(116\) | −3.85061 | −0.357520 | ||||||||
\(117\) | −0.278764 | + | 3.59476i | −0.0257718 | + | 0.332336i | ||||
\(118\) | 9.97753 | 0.918506 | ||||||||
\(119\) | −2.44997 | + | 1.41449i | −0.224588 | + | 0.129666i | ||||
\(120\) | 1.52798 | + | 2.64654i | 0.139485 | + | 0.241595i | ||||
\(121\) | 0.425305 | − | 0.736650i | 0.0386641 | − | 0.0669682i | ||||
\(122\) | − | 11.5452i | − | 1.04525i | ||||||
\(123\) | 8.62781 | + | 4.98127i | 0.777943 | + | 0.449146i | ||||
\(124\) | 0.847293 | + | 0.489185i | 0.0760892 | + | 0.0439301i | ||||
\(125\) | 2.02028i | 0.180699i | ||||||||
\(126\) | −0.500000 | + | 0.866025i | −0.0445435 | + | 0.0771517i | ||||
\(127\) | 2.55753 | + | 4.42977i | 0.226944 | + | 0.393078i | 0.956901 | − | 0.290415i | \(-0.0937932\pi\) |
−0.729957 | + | 0.683493i | \(0.760460\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −3.02163 | −0.266040 | ||||||||
\(130\) | 9.08773 | + | 6.23048i | 0.797047 | + | 0.546450i | ||||
\(131\) | −18.7757 | −1.64044 | −0.820219 | − | 0.572049i | \(-0.806149\pi\) | ||||
−0.820219 | + | 0.572049i | \(0.806149\pi\) | |||||||
\(132\) | −2.98127 | + | 1.72124i | −0.259486 | + | 0.149814i | ||||
\(133\) | 0.862708 | + | 1.49425i | 0.0748063 | + | 0.129568i | ||||
\(134\) | 2.37527 | − | 4.11410i | 0.205192 | − | 0.355404i | ||||
\(135\) | − | 3.05596i | − | 0.263015i | ||||||
\(136\) | 2.44997 | + | 1.41449i | 0.210083 | + | 0.121292i | ||||
\(137\) | 2.30457 | + | 1.33055i | 0.196893 | + | 0.113676i | 0.595205 | − | 0.803574i | \(-0.297071\pi\) |
−0.398312 | + | 0.917250i | \(0.630404\pi\) | |||||||
\(138\) | 3.06260i | 0.260706i | ||||||||
\(139\) | 8.35322 | − | 14.4682i | 0.708511 | − | 1.22718i | −0.256898 | − | 0.966439i | \(-0.582700\pi\) |
0.965409 | − | 0.260739i | \(-0.0839662\pi\) | |||||||
\(140\) | 1.52798 | + | 2.64654i | 0.129138 | + | 0.223674i | ||||
\(141\) | 6.96672 | − | 4.02224i | 0.586703 | − | 0.338733i | ||||
\(142\) | −3.66945 | −0.307934 | ||||||||
\(143\) | −7.01850 | + | 10.2371i | −0.586916 | + | 0.856071i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.1908 | − | 5.88366i | 0.846300 | − | 0.488611i | ||||
\(146\) | −5.05596 | − | 8.75718i | −0.418434 | − | 0.724750i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | − | 5.29308i | − | 0.435089i | ||||||
\(149\) | 2.16642 | + | 1.25078i | 0.177480 | + | 0.102468i | 0.586108 | − | 0.810233i | \(-0.300659\pi\) |
−0.408628 | + | 0.912701i | \(0.633993\pi\) | |||||||
\(150\) | −3.75760 | − | 2.16945i | −0.306807 | − | 0.177135i | ||||
\(151\) | 12.6465i | 1.02916i | 0.857444 | + | 0.514578i | \(0.172051\pi\) | ||||
−0.857444 | + | 0.514578i | \(0.827949\pi\) | |||||||
\(152\) | 0.862708 | − | 1.49425i | 0.0699749 | − | 0.121200i | ||||
\(153\) | −1.41449 | − | 2.44997i | −0.114355 | − | 0.198068i | ||||
\(154\) | −2.98127 | + | 1.72124i | −0.240237 | + | 0.138701i | ||||
\(155\) | −2.98986 | −0.240151 | ||||||||
\(156\) | 3.25253 | − | 1.55596i | 0.260411 | − | 0.124577i | ||||
\(157\) | 17.8131 | 1.42164 | 0.710822 | − | 0.703372i | \(-0.248323\pi\) | ||||
0.710822 | + | 0.703372i | \(0.248323\pi\) | |||||||
\(158\) | −3.89576 | + | 2.24922i | −0.309930 | + | 0.178938i | ||||
\(159\) | −4.16702 | − | 7.21750i | −0.330467 | − | 0.572385i | ||||
\(160\) | 1.52798 | − | 2.64654i | 0.120798 | − | 0.209227i | ||||
\(161\) | 3.06260i | 0.241366i | ||||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | −7.68884 | − | 4.43915i | −0.602236 | − | 0.347701i | 0.167684 | − | 0.985841i | \(-0.446371\pi\) |
−0.769921 | + | 0.638139i | \(0.779704\pi\) | |||||||
\(164\) | − | 9.96254i | − | 0.777943i | ||||||
\(165\) | 5.26003 | − | 9.11064i | 0.409493 | − | 0.709263i | ||||
\(166\) | −3.57934 | − | 6.19961i | −0.277811 | − | 0.481183i | ||||
\(167\) | −8.46097 | + | 4.88494i | −0.654730 | + | 0.378008i | −0.790266 | − | 0.612764i | \(-0.790058\pi\) |
0.135536 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 8.15796 | − | 10.1216i | 0.627535 | − | 0.778588i | ||||
\(170\) | −8.64526 | −0.663061 | ||||||||
\(171\) | −1.49425 | + | 0.862708i | −0.114268 | + | 0.0659729i | ||||
\(172\) | 1.51082 | + | 2.61681i | 0.115199 | + | 0.199530i | ||||
\(173\) | 4.33762 | − | 7.51299i | 0.329783 | − | 0.571202i | −0.652685 | − | 0.757629i | \(-0.726358\pi\) |
0.982469 | + | 0.186427i | \(0.0596909\pi\) | |||||||
\(174\) | − | 3.85061i | − | 0.291914i | ||||||
\(175\) | −3.75760 | − | 2.16945i | −0.284048 | − | 0.163995i | ||||
\(176\) | 2.98127 | + | 1.72124i | 0.224722 | + | 0.129743i | ||||
\(177\) | 9.97753i | 0.749957i | ||||||||
\(178\) | −3.95154 | + | 6.84426i | −0.296180 | + | 0.512999i | ||||
\(179\) | −11.7139 | − | 20.2891i | −0.875540 | − | 1.51648i | −0.856187 | − | 0.516667i | \(-0.827173\pi\) |
−0.0193531 | − | 0.999813i | \(-0.506161\pi\) | |||||||
\(180\) | −2.64654 | + | 1.52798i | −0.197262 | + | 0.113889i | ||||
\(181\) | 7.66632 | 0.569833 | 0.284917 | − | 0.958552i | \(-0.408034\pi\) | ||||
0.284917 | + | 0.958552i | \(0.408034\pi\) | |||||||
\(182\) | 3.25253 | − | 1.55596i | 0.241094 | − | 0.115336i | ||||
\(183\) | 11.5452 | 0.853446 | ||||||||
\(184\) | 2.65229 | − | 1.53130i | 0.195529 | − | 0.112889i | ||||
\(185\) | 8.08773 | + | 14.0084i | 0.594622 | + | 1.02992i | ||||
\(186\) | −0.489185 | + | 0.847293i | −0.0358688 | + | 0.0621266i | ||||
\(187\) | − | 9.73869i | − | 0.712163i | ||||||
\(188\) | −6.96672 | − | 4.02224i | −0.508100 | − | 0.293352i | ||||
\(189\) | −0.866025 | − | 0.500000i | −0.0629941 | − | 0.0363696i | ||||
\(190\) | 5.27281i | 0.382530i | ||||||||
\(191\) | −12.7472 | + | 22.0789i | −0.922357 | + | 1.59757i | −0.126600 | + | 0.991954i | \(0.540407\pi\) |
−0.795757 | + | 0.605616i | \(0.792927\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −7.38361 | + | 4.26293i | −0.531484 | + | 0.306852i | −0.741621 | − | 0.670820i | \(-0.765942\pi\) |
0.210137 | + | 0.977672i | \(0.432609\pi\) | |||||||
\(194\) | −9.09922 | −0.653286 | ||||||||
\(195\) | −6.23048 | + | 9.08773i | −0.446174 | + | 0.650786i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 20.5094 | − | 11.8411i | 1.46124 | − | 0.843645i | 0.462168 | − | 0.886792i | \(-0.347072\pi\) |
0.999069 | + | 0.0431470i | \(0.0137384\pi\) | |||||||
\(198\) | −1.72124 | − | 2.98127i | −0.122323 | − | 0.211869i | ||||
\(199\) | −12.4233 | + | 21.5178i | −0.880666 | + | 1.52536i | −0.0300637 | + | 0.999548i | \(0.509571\pi\) |
−0.850602 | + | 0.525810i | \(0.823762\pi\) | |||||||
\(200\) | 4.33891i | 0.306807i | ||||||||
\(201\) | 4.11410 | + | 2.37527i | 0.290186 | + | 0.167539i | ||||
\(202\) | 16.3274 | + | 9.42664i | 1.14879 | + | 0.663256i | ||||
\(203\) | − | 3.85061i | − | 0.270260i | ||||||
\(204\) | −1.41449 | + | 2.44997i | −0.0990341 | + | 0.171532i | ||||
\(205\) | 15.2226 | + | 26.3663i | 1.06319 | + | 1.84150i | ||||
\(206\) | −11.8714 | + | 6.85393i | −0.827116 | + | 0.477536i | ||||
\(207\) | −3.06260 | −0.212865 | ||||||||
\(208\) | −2.97377 | − | 2.03880i | −0.206194 | − | 0.141365i | ||||
\(209\) | −5.93970 | −0.410857 | ||||||||
\(210\) | −2.64654 | + | 1.52798i | −0.182629 | + | 0.105441i | ||||
\(211\) | −0.386509 | − | 0.669453i | −0.0266084 | − | 0.0460871i | 0.852415 | − | 0.522867i | \(-0.175137\pi\) |
−0.879023 | + | 0.476779i | \(0.841804\pi\) | |||||||
\(212\) | −4.16702 | + | 7.21750i | −0.286192 | + | 0.495700i | ||||
\(213\) | − | 3.66945i | − | 0.251427i | ||||||
\(214\) | 2.87063 | + | 1.65736i | 0.196232 | + | 0.113295i | ||||
\(215\) | −7.99687 | − | 4.61699i | −0.545382 | − | 0.314876i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −0.489185 | + | 0.847293i | −0.0332080 | + | 0.0575180i | ||||
\(218\) | −4.33762 | − | 7.51299i | −0.293781 | − | 0.508844i | ||||
\(219\) | 8.75718 | − | 5.05596i | 0.591756 | − | 0.341650i | ||||
\(220\) | −10.5201 | −0.709263 | ||||||||
\(221\) | −0.788619 | + | 10.1695i | −0.0530482 | + | 0.684075i | ||||
\(222\) | 5.29308 | 0.355248 | ||||||||
\(223\) | −18.6502 | + | 10.7677i | −1.24891 | + | 0.721060i | −0.970892 | − | 0.239516i | \(-0.923011\pi\) |
−0.278019 | + | 0.960575i | \(0.589678\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | 2.16945 | − | 3.75760i | 0.144630 | − | 0.250507i | ||||
\(226\) | − | 11.2111i | − | 0.745754i | ||||||
\(227\) | 15.1939 | + | 8.77218i | 1.00845 | + | 0.582230i | 0.910738 | − | 0.412985i | \(-0.135514\pi\) |
0.0977139 | + | 0.995215i | \(0.468847\pi\) | |||||||
\(228\) | 1.49425 | + | 0.862708i | 0.0989594 | + | 0.0571342i | ||||
\(229\) | − | 10.3222i | − | 0.682109i | −0.940043 | − | 0.341055i | \(-0.889216\pi\) | ||
0.940043 | − | 0.341055i | \(-0.110784\pi\) | |||||||
\(230\) | −4.67959 | + | 8.10529i | −0.308563 | + | 0.534447i | ||||
\(231\) | −1.72124 | − | 2.98127i | −0.113249 | − | 0.196153i | ||||
\(232\) | −3.33473 | + | 1.92531i | −0.218936 | + | 0.126402i | ||||
\(233\) | −17.8290 | −1.16802 | −0.584008 | − | 0.811748i | \(-0.698516\pi\) | ||||
−0.584008 | + | 0.811748i | \(0.698516\pi\) | |||||||
\(234\) | 1.55596 | + | 3.25253i | 0.101716 | + | 0.212625i | ||||
\(235\) | 24.5836 | 1.60366 | ||||||||
\(236\) | 8.64080 | − | 4.98877i | 0.562468 | − | 0.324741i | ||||
\(237\) | −2.24922 | − | 3.89576i | −0.146102 | − | 0.253057i | ||||
\(238\) | −1.41449 | + | 2.44997i | −0.0916878 | + | 0.158808i | ||||
\(239\) | − | 5.71271i | − | 0.369525i | −0.982783 | − | 0.184762i | \(-0.940848\pi\) | ||
0.982783 | − | 0.184762i | \(-0.0591515\pi\) | |||||||
\(240\) | 2.64654 | + | 1.52798i | 0.170833 | + | 0.0986308i | ||||
\(241\) | 0.868738 | + | 0.501566i | 0.0559603 | + | 0.0323087i | 0.527719 | − | 0.849419i | \(-0.323047\pi\) |
−0.471759 | + | 0.881728i | \(0.656381\pi\) | |||||||
\(242\) | − | 0.850611i | − | 0.0546793i | ||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −5.77260 | − | 9.99843i | −0.369553 | − | 0.640084i | ||||
\(245\) | −2.64654 | + | 1.52798i | −0.169081 | + | 0.0976191i | ||||
\(246\) | 9.96254 | 0.635188 | ||||||||
\(247\) | 6.20245 | + | 0.480984i | 0.394653 | + | 0.0306043i | ||||
\(248\) | 0.978370 | 0.0621266 | ||||||||
\(249\) | 6.19961 | − | 3.57934i | 0.392884 | − | 0.226832i | ||||
\(250\) | 1.01014 | + | 1.74961i | 0.0638867 | + | 0.110655i | ||||
\(251\) | −0.336293 | + | 0.582476i | −0.0212266 | + | 0.0367656i | −0.876444 | − | 0.481505i | \(-0.840090\pi\) |
0.855217 | + | 0.518270i | \(0.173424\pi\) | |||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | −9.13042 | − | 5.27145i | −0.574025 | − | 0.331413i | ||||
\(254\) | 4.42977 | + | 2.55753i | 0.277948 | + | 0.160474i | ||||
\(255\) | − | 8.64526i | − | 0.541387i | ||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 12.1717 | + | 21.0820i | 0.759248 | + | 1.31506i | 0.943234 | + | 0.332128i | \(0.107766\pi\) |
−0.183986 | + | 0.982929i | \(0.558900\pi\) | |||||||
\(258\) | −2.61681 | + | 1.51082i | −0.162915 | + | 0.0940592i | ||||
\(259\) | 5.29308 | 0.328896 | ||||||||
\(260\) | 10.9854 | + | 0.851893i | 0.681289 | + | 0.0528322i | ||||
\(261\) | 3.85061 | 0.238347 | ||||||||
\(262\) | −16.2602 | + | 9.38784i | −1.00456 | + | 0.579983i | ||||
\(263\) | 8.54648 | + | 14.8029i | 0.526999 | + | 0.912788i | 0.999505 | + | 0.0314610i | \(0.0100160\pi\) |
−0.472506 | + | 0.881327i | \(0.656651\pi\) | |||||||
\(264\) | −1.72124 | + | 2.98127i | −0.105935 | + | 0.183484i | ||||
\(265\) | − | 25.4685i | − | 1.56452i | ||||||
\(266\) | 1.49425 | + | 0.862708i | 0.0916186 | + | 0.0528960i | ||||
\(267\) | −6.84426 | − | 3.95154i | −0.418862 | − | 0.241830i | ||||
\(268\) | − | 4.75055i | − | 0.290186i | ||||||
\(269\) | 13.3297 | − | 23.0877i | 0.812727 | − | 1.40768i | −0.0982223 | − | 0.995165i | \(-0.531316\pi\) |
0.910949 | − | 0.412519i | \(-0.135351\pi\) | |||||||
\(270\) | −1.52798 | − | 2.64654i | −0.0929900 | − | 0.161063i | ||||
\(271\) | 21.1739 | − | 12.2247i | 1.28622 | − | 0.742600i | 0.308243 | − | 0.951308i | \(-0.400259\pi\) |
0.977978 | + | 0.208708i | \(0.0669257\pi\) | |||||||
\(272\) | 2.82898 | 0.171532 | ||||||||
\(273\) | 1.55596 | + | 3.25253i | 0.0941711 | + | 0.196852i | ||||
\(274\) | 2.66109 | 0.160763 | ||||||||
\(275\) | 12.9354 | − | 7.46828i | 0.780037 | − | 0.450354i | ||||
\(276\) | 1.53130 | + | 2.65229i | 0.0921734 | + | 0.159649i | ||||
\(277\) | −14.2406 | + | 24.6655i | −0.855636 | + | 1.48201i | 0.0204175 | + | 0.999792i | \(0.493500\pi\) |
−0.876054 | + | 0.482214i | \(0.839833\pi\) | |||||||
\(278\) | − | 16.7064i | − | 1.00199i | ||||||
\(279\) | −0.847293 | − | 0.489185i | −0.0507261 | − | 0.0292867i | ||||
\(280\) | 2.64654 | + | 1.52798i | 0.158161 | + | 0.0913143i | ||||
\(281\) | − | 9.76032i | − | 0.582252i | −0.956685 | − | 0.291126i | \(-0.905970\pi\) | ||
0.956685 | − | 0.291126i | \(-0.0940298\pi\) | |||||||
\(282\) | 4.02224 | − | 6.96672i | 0.239521 | − | 0.414862i | ||||
\(283\) | 5.83562 | + | 10.1076i | 0.346891 | + | 0.600833i | 0.985696 | − | 0.168536i | \(-0.0539039\pi\) |
−0.638804 | + | 0.769369i | \(0.720571\pi\) | |||||||
\(284\) | −3.17784 | + | 1.83473i | −0.188570 | + | 0.108871i | ||||
\(285\) | −5.27281 | −0.312334 | ||||||||
\(286\) | −0.959638 | + | 12.3749i | −0.0567446 | + | 0.731741i | ||||
\(287\) | 9.96254 | 0.588070 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 4.49843 | + | 7.79152i | 0.264614 | + | 0.458324i | ||||
\(290\) | 5.88366 | − | 10.1908i | 0.345500 | − | 0.598424i | ||||
\(291\) | − | 9.09922i | − | 0.533406i | ||||||
\(292\) | −8.75718 | − | 5.05596i | −0.512475 | − | 0.295878i | ||||
\(293\) | 18.8968 | + | 10.9101i | 1.10396 | + | 0.637373i | 0.937259 | − | 0.348634i | \(-0.113354\pi\) |
0.166704 | + | 0.986007i | \(0.446688\pi\) | |||||||
\(294\) | 1.00000i | 0.0583212i | ||||||||
\(295\) | −15.2455 | + | 26.4059i | −0.887626 | + | 1.53741i | ||||
\(296\) | −2.64654 | − | 4.58394i | −0.153827 | − | 0.266436i | ||||
\(297\) | 2.98127 | − | 1.72124i | 0.172991 | − | 0.0998762i | ||||
\(298\) | 2.50157 | 0.144912 | ||||||||
\(299\) | 9.10746 | + | 6.24401i | 0.526698 | + | 0.361101i | ||||
\(300\) | −4.33891 | −0.250507 | ||||||||
\(301\) | −2.61681 | + | 1.51082i | −0.150830 | + | 0.0870819i | ||||
\(302\) | 6.32323 | + | 10.9522i | 0.363861 | + | 0.630226i | ||||
\(303\) | −9.42664 | + | 16.3274i | −0.541546 | + | 0.937985i | ||||
\(304\) | − | 1.72542i | − | 0.0989594i | ||||||
\(305\) | 30.5548 | + | 17.6408i | 1.74957 | + | 1.01011i | ||||
\(306\) | −2.44997 | − | 1.41449i | −0.140055 | − | 0.0808610i | ||||
\(307\) | 4.87046i | 0.277972i | 0.990294 | + | 0.138986i | \(0.0443843\pi\) | ||||
−0.990294 | + | 0.138986i | \(0.955616\pi\) | |||||||
\(308\) | −1.72124 | + | 2.98127i | −0.0980765 | + | 0.169874i | ||||
\(309\) | −6.85393 | − | 11.8714i | −0.389906 | − | 0.675338i | ||||
\(310\) | −2.58930 | + | 1.49493i | −0.147062 | + | 0.0849064i | ||||
\(311\) | −3.90344 | −0.221344 | −0.110672 | − | 0.993857i | \(-0.535300\pi\) | ||||
−0.110672 | + | 0.993857i | \(0.535300\pi\) | |||||||
\(312\) | 2.03880 | − | 2.97377i | 0.115424 | − | 0.168357i | ||||
\(313\) | 26.0528 | 1.47259 | 0.736297 | − | 0.676659i | \(-0.236573\pi\) | ||||
0.736297 | + | 0.676659i | \(0.236573\pi\) | |||||||
\(314\) | 15.4266 | − | 8.90657i | 0.870576 | − | 0.502627i | ||||
\(315\) | −1.52798 | − | 2.64654i | −0.0860920 | − | 0.149116i | ||||
\(316\) | −2.24922 | + | 3.89576i | −0.126528 | + | 0.219154i | ||||
\(317\) | − | 11.1107i | − | 0.624040i | −0.950076 | − | 0.312020i | \(-0.898994\pi\) | ||
0.950076 | − | 0.312020i | \(-0.101006\pi\) | |||||||
\(318\) | −7.21750 | − | 4.16702i | −0.404737 | − | 0.233675i | ||||
\(319\) | 11.4797 | + | 6.62781i | 0.642740 | + | 0.371086i | ||||
\(320\) | − | 3.05596i | − | 0.170833i | ||||||
\(321\) | −1.65736 | + | 2.87063i | −0.0925046 | + | 0.160223i | ||||
\(322\) | 1.53130 | + | 2.65229i | 0.0853359 | + | 0.147806i | ||||
\(323\) | −4.22722 | + | 2.44058i | −0.235209 | + | 0.135798i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −14.1124 | + | 6.75118i | −0.782818 | + | 0.374488i | ||||
\(326\) | −8.87831 | −0.491724 | ||||||||
\(327\) | 7.51299 | − | 4.33762i | 0.415469 | − | 0.239871i | ||||
\(328\) | −4.98127 | − | 8.62781i | −0.275045 | − | 0.476391i | ||||
\(329\) | 4.02224 | − | 6.96672i | 0.221753 | − | 0.384087i | ||||
\(330\) | − | 10.5201i | − | 0.579110i | ||||||
\(331\) | 12.6854 | + | 7.32391i | 0.697252 | + | 0.402559i | 0.806323 | − | 0.591475i | \(-0.201454\pi\) |
−0.109071 | + | 0.994034i | \(0.534788\pi\) | |||||||
\(332\) | −6.19961 | − | 3.57934i | −0.340248 | − | 0.196442i | ||||
\(333\) | 5.29308i | 0.290059i | ||||||||
\(334\) | −4.88494 | + | 8.46097i | −0.267292 | + | 0.462964i | ||||
\(335\) | 7.25875 | + | 12.5725i | 0.396588 | + | 0.686910i | ||||
\(336\) | 0.866025 | − | 0.500000i | 0.0472456 | − | 0.0272772i | ||||
\(337\) | −27.5456 | −1.50050 | −0.750251 | − | 0.661153i | \(-0.770068\pi\) | ||||
−0.750251 | + | 0.661153i | \(0.770068\pi\) | |||||||
\(338\) | 2.00418 | − | 12.8446i | 0.109013 | − | 0.698653i | ||||
\(339\) | 11.2111 | 0.608906 | ||||||||
\(340\) | −7.48701 | + | 4.32263i | −0.406040 | + | 0.234427i | ||||
\(341\) | −1.68401 | − | 2.91678i | −0.0911940 | − | 0.157953i | ||||
\(342\) | −0.862708 | + | 1.49425i | −0.0466499 | + | 0.0808000i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 2.61681 | + | 1.51082i | 0.141089 | + | 0.0814577i | ||||
\(345\) | −8.10529 | − | 4.67959i | −0.436374 | − | 0.251941i | ||||
\(346\) | − | 8.67525i | − | 0.466384i | ||||||
\(347\) | −2.62073 | + | 4.53924i | −0.140688 | + | 0.243679i | −0.927756 | − | 0.373187i | \(-0.878265\pi\) |
0.787068 | + | 0.616867i | \(0.211598\pi\) | |||||||
\(348\) | −1.92531 | − | 3.33473i | −0.103207 | − | 0.178760i | ||||
\(349\) | −4.52901 | + | 2.61482i | −0.242432 | + | 0.139968i | −0.616294 | − | 0.787516i | \(-0.711367\pi\) |
0.373862 | + | 0.927484i | \(0.378033\pi\) | |||||||
\(350\) | −4.33891 | −0.231924 | ||||||||
\(351\) | −3.25253 | + | 1.55596i | −0.173607 | + | 0.0830511i | ||||
\(352\) | 3.44247 | 0.183484 | ||||||||
\(353\) | 3.26227 | − | 1.88348i | 0.173633 | − | 0.100247i | −0.410665 | − | 0.911786i | \(-0.634703\pi\) |
0.584298 | + | 0.811539i | \(0.301370\pi\) | |||||||
\(354\) | 4.98877 | + | 8.64080i | 0.265150 | + | 0.459253i | ||||
\(355\) | 5.60686 | − | 9.71136i | 0.297581 | − | 0.515425i | ||||
\(356\) | 7.90307i | 0.418862i | ||||||||
\(357\) | −2.44997 | − | 1.41449i | −0.129666 | − | 0.0748628i | ||||
\(358\) | −20.2891 | − | 11.7139i | −1.07231 | − | 0.619100i | ||||
\(359\) | − | 20.6003i | − | 1.08724i | −0.839330 | − | 0.543622i | \(-0.817053\pi\) | ||
0.839330 | − | 0.543622i | \(-0.182947\pi\) | |||||||
\(360\) | −1.52798 | + | 2.64654i | −0.0805317 | + | 0.139485i | ||||
\(361\) | −8.01147 | − | 13.8763i | −0.421656 | − | 0.730330i | ||||
\(362\) | 6.63923 | − | 3.83316i | 0.348950 | − | 0.201466i | ||||
\(363\) | 0.850611 | 0.0446455 | ||||||||
\(364\) | 2.03880 | − | 2.97377i | 0.106862 | − | 0.155868i | ||||
\(365\) | 30.9017 | 1.61747 | ||||||||
\(366\) | 9.99843 | − | 5.77260i | 0.522627 | − | 0.301739i | ||||
\(367\) | 13.9579 | + | 24.1759i | 0.728598 | + | 1.26197i | 0.957476 | + | 0.288514i | \(0.0931612\pi\) |
−0.228877 | + | 0.973455i | \(0.573505\pi\) | |||||||
\(368\) | 1.53130 | − | 2.65229i | 0.0798245 | − | 0.138260i | ||||
\(369\) | 9.96254i | 0.518629i | ||||||||
\(370\) | 14.0084 | + | 8.08773i | 0.728260 | + | 0.420461i | ||||
\(371\) | −7.21750 | − | 4.16702i | −0.374714 | − | 0.216341i | ||||
\(372\) | 0.978370i | 0.0507261i | ||||||||
\(373\) | −15.7091 | + | 27.2090i | −0.813388 | + | 1.40883i | 0.0970910 | + | 0.995276i | \(0.469046\pi\) |
−0.910479 | + | 0.413554i | \(0.864287\pi\) | |||||||
\(374\) | −4.86934 | − | 8.43395i | −0.251788 | − | 0.436109i | ||||
\(375\) | −1.74961 | + | 1.01014i | −0.0903495 | + | 0.0521633i | ||||
\(376\) | −8.04447 | −0.414862 | ||||||||
\(377\) | −11.4508 | − | 7.85061i | −0.589748 | − | 0.404327i | ||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −27.5747 | + | 15.9203i | −1.41642 | + | 0.817770i | −0.995982 | − | 0.0895514i | \(-0.971457\pi\) |
−0.420437 | + | 0.907322i | \(0.638123\pi\) | |||||||
\(380\) | 2.63640 | + | 4.56638i | 0.135245 | + | 0.234251i | ||||
\(381\) | −2.55753 | + | 4.42977i | −0.131026 | + | 0.226944i | ||||
\(382\) | 25.4945i | 1.30441i | ||||||||
\(383\) | −4.08962 | − | 2.36114i | −0.208970 | − | 0.120649i | 0.391863 | − | 0.920024i | \(-0.371831\pi\) |
−0.600832 | + | 0.799375i | \(0.705164\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | − | 10.5201i | − | 0.536152i | ||||||
\(386\) | −4.26293 | + | 7.38361i | −0.216977 | + | 0.375816i | ||||
\(387\) | −1.51082 | − | 2.61681i | −0.0767990 | − | 0.133020i | ||||
\(388\) | −7.88016 | + | 4.54961i | −0.400054 | + | 0.230972i | ||||
\(389\) | −30.5902 | −1.55099 | −0.775493 | − | 0.631356i | \(-0.782499\pi\) | ||||
−0.775493 | + | 0.631356i | \(0.782499\pi\) | |||||||
\(390\) | −0.851893 | + | 10.9854i | −0.0431373 | + | 0.556270i | ||||
\(391\) | −8.66403 | −0.438159 | ||||||||
\(392\) | 0.866025 | − | 0.500000i | 0.0437409 | − | 0.0252538i | ||||
\(393\) | −9.38784 | − | 16.2602i | −0.473554 | − | 0.820219i | ||||
\(394\) | 11.8411 | − | 20.5094i | 0.596547 | − | 1.03325i | ||||
\(395\) | − | 13.7470i | − | 0.691689i | ||||||
\(396\) | −2.98127 | − | 1.72124i | −0.149814 | − | 0.0864954i | ||||
\(397\) | 10.1133 | + | 5.83891i | 0.507571 | + | 0.293046i | 0.731835 | − | 0.681482i | \(-0.238664\pi\) |
−0.224264 | + | 0.974529i | \(0.571998\pi\) | |||||||
\(398\) | 24.8466i | 1.24545i | ||||||||
\(399\) | −0.862708 | + | 1.49425i | −0.0431894 | + | 0.0748063i | ||||
\(400\) | 2.16945 | + | 3.75760i | 0.108473 | + | 0.187880i | ||||
\(401\) | 8.01677 | − | 4.62849i | 0.400339 | − | 0.231136i | −0.286292 | − | 0.958143i | \(-0.592423\pi\) |
0.686630 | + | 0.727007i | \(0.259089\pi\) | |||||||
\(402\) | 4.75055 | 0.236936 | ||||||||
\(403\) | 1.52231 | + | 3.18218i | 0.0758315 | + | 0.158516i | ||||
\(404\) | 18.8533 | 0.937985 | ||||||||
\(405\) | 2.64654 | − | 1.52798i | 0.131508 | − | 0.0759260i | ||||
\(406\) | −1.92531 | − | 3.33473i | −0.0955513 | − | 0.165500i | ||||
\(407\) | −9.11064 | + | 15.7801i | −0.451598 | + | 0.782190i | ||||
\(408\) | 2.82898i | 0.140055i | ||||||||
\(409\) | −22.1693 | − | 12.7994i | −1.09620 | − | 0.632891i | −0.160980 | − | 0.986958i | \(-0.551465\pi\) |
−0.935220 | + | 0.354066i | \(0.884799\pi\) | |||||||
\(410\) | 26.3663 | + | 15.2226i | 1.30214 | + | 0.751789i | ||||
\(411\) | 2.66109i | 0.131262i | ||||||||
\(412\) | −6.85393 | + | 11.8714i | −0.337669 | + | 0.584860i | ||||
\(413\) | 4.98877 | + | 8.64080i | 0.245481 | + | 0.425186i | ||||
\(414\) | −2.65229 | + | 1.53130i | −0.130353 | + | 0.0752592i | ||||
\(415\) | 21.8767 | 1.07388 | ||||||||
\(416\) | −3.59476 | − | 0.278764i | −0.176248 | − | 0.0136675i | ||||
\(417\) | 16.7064 | 0.818118 | ||||||||
\(418\) | −5.14393 | + | 2.96985i | −0.251598 | + | 0.145260i | ||||
\(419\) | −14.1018 | − | 24.4251i | −0.688920 | − | 1.19324i | −0.972188 | − | 0.234203i | \(-0.924752\pi\) |
0.283268 | − | 0.959041i | \(-0.408581\pi\) | |||||||
\(420\) | −1.52798 | + | 2.64654i | −0.0745579 | + | 0.129138i | ||||
\(421\) | − | 5.07012i | − | 0.247102i | −0.992338 | − | 0.123551i | \(-0.960572\pi\) | ||
0.992338 | − | 0.123551i | \(-0.0394283\pi\) | |||||||
\(422\) | −0.669453 | − | 0.386509i | −0.0325885 | − | 0.0188150i | ||||
\(423\) | 6.96672 | + | 4.02224i | 0.338733 | + | 0.195568i | ||||
\(424\) | 8.33405i | 0.404737i | ||||||||
\(425\) | 6.13734 | − | 10.6302i | 0.297705 | − | 0.515640i | ||||
\(426\) | −1.83473 | − | 3.17784i | −0.0888928 | − | 0.153967i | ||||
\(427\) | 9.99843 | − | 5.77260i | 0.483858 | − | 0.279356i | ||||
\(428\) | 3.31471 | 0.160223 | ||||||||
\(429\) | −12.3749 | − | 0.959638i | −0.597464 | − | 0.0463318i | ||||
\(430\) | −9.23399 | −0.445302 | ||||||||
\(431\) | −13.9808 | + | 8.07185i | −0.673434 | + | 0.388807i | −0.797376 | − | 0.603482i | \(-0.793779\pi\) |
0.123943 | + | 0.992289i | \(0.460446\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −11.3014 | + | 19.5747i | −0.543113 | + | 0.940699i | 0.455610 | + | 0.890179i | \(0.349421\pi\) |
−0.998723 | + | 0.0505195i | \(0.983912\pi\) | |||||||
\(434\) | 0.978370i | 0.0469633i | ||||||||
\(435\) | 10.1908 | + | 5.88366i | 0.488611 | + | 0.282100i | ||||
\(436\) | −7.51299 | − | 4.33762i | −0.359807 | − | 0.207735i | ||||
\(437\) | 5.28425i | 0.252780i | ||||||||
\(438\) | 5.05596 | − | 8.75718i | 0.241583 | − | 0.418434i | ||||
\(439\) | 14.1486 | + | 24.5060i | 0.675273 | + | 1.16961i | 0.976389 | + | 0.216020i | \(0.0693077\pi\) |
−0.301115 | + | 0.953588i | \(0.597359\pi\) | |||||||
\(440\) | −9.11064 | + | 5.26003i | −0.434333 | + | 0.250762i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 4.40179 | + | 9.20136i | 0.209372 | + | 0.437664i | ||||
\(443\) | −1.38096 | −0.0656112 | −0.0328056 | − | 0.999462i | \(-0.510444\pi\) | ||||
−0.0328056 | + | 0.999462i | \(0.510444\pi\) | |||||||
\(444\) | 4.58394 | − | 2.64654i | 0.217544 | − | 0.125599i | ||||
\(445\) | −12.0757 | − | 20.9158i | −0.572445 | − | 0.991504i | ||||
\(446\) | −10.7677 | + | 18.6502i | −0.509866 | + | 0.883114i | ||||
\(447\) | 2.50157i | 0.118320i | ||||||||
\(448\) | −0.866025 | − | 0.500000i | −0.0409159 | − | 0.0236228i | ||||
\(449\) | −32.0480 | − | 18.5029i | −1.51244 | − | 0.873208i | −0.999894 | − | 0.0145487i | \(-0.995369\pi\) |
−0.512547 | − | 0.858659i | \(-0.671298\pi\) | |||||||
\(450\) | − | 4.33891i | − | 0.204538i | ||||||
\(451\) | −17.1479 | + | 29.7010i | −0.807462 | + | 1.39856i | ||||
\(452\) | −5.60557 | − | 9.70914i | −0.263664 | − | 0.456679i | ||||
\(453\) | −10.9522 | + | 6.32323i | −0.514578 | + | 0.297091i | ||||
\(454\) | 17.5444 | 0.823398 | ||||||||
\(455\) | −0.851893 | + | 10.9854i | −0.0399374 | + | 0.515006i | ||||
\(456\) | 1.72542 | 0.0808000 | ||||||||
\(457\) | 12.0530 | − | 6.95878i | 0.563813 | − | 0.325518i | −0.190861 | − | 0.981617i | \(-0.561128\pi\) |
0.754675 | + | 0.656099i | \(0.227795\pi\) | |||||||
\(458\) | −5.16109 | − | 8.93928i | −0.241162 | − | 0.417705i | ||||
\(459\) | 1.41449 | − | 2.44997i | 0.0660228 | − | 0.114355i | ||||
\(460\) | 9.35918i | 0.436374i | ||||||||
\(461\) | 4.19845 | + | 2.42397i | 0.195541 | + | 0.112896i | 0.594574 | − | 0.804041i | \(-0.297321\pi\) |
−0.399033 | + | 0.916937i | \(0.630654\pi\) | |||||||
\(462\) | −2.98127 | − | 1.72124i | −0.138701 | − | 0.0800791i | ||||
\(463\) | − | 24.4377i | − | 1.13571i | −0.823127 | − | 0.567857i | \(-0.807773\pi\) | ||
0.823127 | − | 0.567857i | \(-0.192227\pi\) | |||||||
\(464\) | −1.92531 | + | 3.33473i | −0.0893801 | + | 0.154811i | ||||
\(465\) | −1.49493 | − | 2.58930i | −0.0693258 | − | 0.120076i | ||||
\(466\) | −15.4404 | + | 8.91449i | −0.715260 | + | 0.412956i | ||||
\(467\) | −36.0027 | −1.66600 | −0.833002 | − | 0.553270i | \(-0.813380\pi\) | ||||
−0.833002 | + | 0.553270i | \(0.813380\pi\) | |||||||
\(468\) | 2.97377 | + | 2.03880i | 0.137463 | + | 0.0942434i | ||||
\(469\) | 4.75055 | 0.219360 | ||||||||
\(470\) | 21.2900 | − | 12.2918i | 0.982035 | − | 0.566978i | ||||
\(471\) | 8.90657 | + | 15.4266i | 0.410393 | + | 0.710822i | ||||
\(472\) | 4.98877 | − | 8.64080i | 0.229627 | − | 0.397725i | ||||
\(473\) | − | 10.4019i | − | 0.478279i | ||||||
\(474\) | −3.89576 | − | 2.24922i | −0.178938 | − | 0.103310i | ||||
\(475\) | −6.48343 | − | 3.74321i | −0.297480 | − | 0.171750i | ||||
\(476\) | 2.82898i | 0.129666i | ||||||||
\(477\) | 4.16702 | − | 7.21750i | 0.190795 | − | 0.330467i | ||||
\(478\) | −2.85636 | − | 4.94735i | −0.130647 | − | 0.226287i | ||||
\(479\) | −8.22108 | + | 4.74644i | −0.375631 | + | 0.216870i | −0.675915 | − | 0.736979i | \(-0.736252\pi\) |
0.300285 | + | 0.953850i | \(0.402918\pi\) | |||||||
\(480\) | 3.05596 | 0.139485 | ||||||||
\(481\) | 10.7915 | − | 15.7404i | 0.492051 | − | 0.717701i | ||||
\(482\) | 1.00313 | 0.0456914 | ||||||||
\(483\) | −2.65229 | + | 1.53130i | −0.120683 | + | 0.0696765i | ||||
\(484\) | −0.425305 | − | 0.736650i | −0.0193321 | − | 0.0334841i | ||||
\(485\) | 13.9034 | − | 24.0815i | 0.631323 | − | 1.09348i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −35.4383 | − | 20.4603i | −1.60586 | − | 0.927144i | −0.990283 | − | 0.139069i | \(-0.955589\pi\) |
−0.615578 | − | 0.788076i | \(-0.711078\pi\) | |||||||
\(488\) | −9.99843 | − | 5.77260i | −0.452608 | − | 0.261313i | ||||
\(489\) | − | 8.87831i | − | 0.401491i | ||||||
\(490\) | −1.52798 | + | 2.64654i | −0.0690272 | + | 0.119559i | ||||
\(491\) | −2.55753 | − | 4.42977i | −0.115420 | − | 0.199913i | 0.802528 | − | 0.596615i | \(-0.203488\pi\) |
−0.917947 | + | 0.396702i | \(0.870155\pi\) | |||||||
\(492\) | 8.62781 | − | 4.98127i | 0.388972 | − | 0.224573i | ||||
\(493\) | 10.8933 | 0.490610 | ||||||||
\(494\) | 5.61197 | − | 2.68468i | 0.252495 | − | 0.120790i | ||||
\(495\) | 10.5201 | 0.472842 | ||||||||
\(496\) | 0.847293 | − | 0.489185i | 0.0380446 | − | 0.0219651i | ||||
\(497\) | −1.83473 | − | 3.17784i | −0.0822987 | − | 0.142546i | ||||
\(498\) | 3.57934 | − | 6.19961i | 0.160394 | − | 0.277811i | ||||
\(499\) | − | 19.5827i | − | 0.876640i | −0.898819 | − | 0.438320i | \(-0.855574\pi\) | ||
0.898819 | − | 0.438320i | \(-0.144426\pi\) | |||||||
\(500\) | 1.74961 | + | 1.01014i | 0.0782450 | + | 0.0451747i | ||||
\(501\) | −8.46097 | − | 4.88494i | −0.378008 | − | 0.218243i | ||||
\(502\) | 0.672585i | 0.0300189i | ||||||||
\(503\) | 14.5429 | − | 25.1890i | 0.648436 | − | 1.12312i | −0.335060 | − | 0.942197i | \(-0.608757\pi\) |
0.983496 | − | 0.180928i | \(-0.0579100\pi\) | |||||||
\(504\) | 0.500000 | + | 0.866025i | 0.0222718 | + | 0.0385758i | ||||
\(505\) | −49.8960 | + | 28.8075i | −2.22034 | + | 1.28191i | ||||
\(506\) | −10.5429 | −0.468689 | ||||||||
\(507\) | 12.8446 | + | 2.00418i | 0.570448 | + | 0.0890088i | ||||
\(508\) | 5.11506 | 0.226944 | ||||||||
\(509\) | −4.52051 | + | 2.60992i | −0.200368 | + | 0.115682i | −0.596827 | − | 0.802370i | \(-0.703572\pi\) |
0.396459 | + | 0.918052i | \(0.370239\pi\) | |||||||
\(510\) | −4.32263 | − | 7.48701i | −0.191409 | − | 0.331531i | ||||
\(511\) | 5.05596 | − | 8.75718i | 0.223663 | − | 0.387395i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.49425 | − | 0.862708i | −0.0659729 | − | 0.0380895i | ||||
\(514\) | 21.0820 | + | 12.1717i | 0.929885 | + | 0.536870i | ||||
\(515\) | − | 41.8907i | − | 1.84592i | ||||||
\(516\) | −1.51082 | + | 2.61681i | −0.0665099 | + | 0.115199i | ||||
\(517\) | 13.8464 | + | 23.9827i | 0.608965 | + | 1.05476i | ||||
\(518\) | 4.58394 | − | 2.64654i | 0.201407 | − | 0.116282i | ||||
\(519\) | 8.67525 | 0.380801 | ||||||||
\(520\) | 9.93962 | − | 4.75496i | 0.435881 | − | 0.208519i | ||||
\(521\) | −14.5259 | −0.636389 | −0.318195 | − | 0.948025i | \(-0.603077\pi\) | ||||
−0.318195 | + | 0.948025i | \(0.603077\pi\) | |||||||
\(522\) | 3.33473 | − | 1.92531i | 0.145957 | − | 0.0842683i | ||||
\(523\) | −13.9367 | − | 24.1391i | −0.609410 | − | 1.05553i | −0.991338 | − | 0.131337i | \(-0.958073\pi\) |
0.381927 | − | 0.924192i | \(-0.375260\pi\) | |||||||
\(524\) | −9.38784 | + | 16.2602i | −0.410110 | + | 0.710331i | ||||
\(525\) | − | 4.33891i | − | 0.189365i | ||||||
\(526\) | 14.8029 | + | 8.54648i | 0.645439 | + | 0.372644i | ||||
\(527\) | −2.39698 | − | 1.38389i | −0.104414 | − | 0.0602834i | ||||
\(528\) | 3.44247i | 0.149814i | ||||||||
\(529\) | 6.81025 | − | 11.7957i | 0.296098 | − | 0.512856i | ||||
\(530\) | −12.7343 | − | 22.0564i | −0.553141 | − | 0.958069i | ||||
\(531\) | −8.64080 | + | 4.98877i | −0.374979 | + | 0.216494i | ||||
\(532\) | 1.72542 | 0.0748063 | ||||||||
\(533\) | 20.3116 | − | 29.6263i | 0.879792 | − | 1.28326i | ||||
\(534\) | −7.90307 | −0.341999 | ||||||||
\(535\) | −8.77252 | + | 5.06482i | −0.379269 | + | 0.218971i | ||||
\(536\) | −2.37527 | − | 4.11410i | −0.102596 | − | 0.177702i | ||||
\(537\) | 11.7139 | − | 20.2891i | 0.505493 | − | 0.875540i | ||||
\(538\) | − | 26.6594i | − | 1.14937i | ||||||
\(539\) | −2.98127 | − | 1.72124i | −0.128412 | − | 0.0741389i | ||||
\(540\) | −2.64654 | − | 1.52798i | −0.113889 | − | 0.0657538i | ||||
\(541\) | 1.42341i | 0.0611970i | 0.999532 | + | 0.0305985i | \(0.00974133\pi\) | ||||
−0.999532 | + | 0.0305985i | \(0.990259\pi\) | |||||||
\(542\) | 12.2247 | − | 21.1739i | 0.525097 | − | 0.909496i | ||||
\(543\) | 3.83316 | + | 6.63923i | 0.164497 | + | 0.284917i | ||||
\(544\) | 2.44997 | − | 1.41449i | 0.105042 | − | 0.0606458i | ||||
\(545\) | 26.5112 | 1.13562 | ||||||||
\(546\) | 2.97377 | + | 2.03880i | 0.127266 | + | 0.0872524i | ||||
\(547\) | −9.33008 | −0.398925 | −0.199463 | − | 0.979905i | \(-0.563920\pi\) | ||||
−0.199463 | + | 0.979905i | \(0.563920\pi\) | |||||||
\(548\) | 2.30457 | − | 1.33055i | 0.0984465 | − | 0.0568381i | ||||
\(549\) | 5.77260 | + | 9.99843i | 0.246369 | + | 0.426723i | ||||
\(550\) | 7.46828 | − | 12.9354i | 0.318449 | − | 0.551569i | ||||
\(551\) | − | 6.64390i | − | 0.283040i | ||||||
\(552\) | 2.65229 | + | 1.53130i | 0.112889 | + | 0.0651764i | ||||
\(553\) | −3.89576 | − | 2.24922i | −0.165664 | − | 0.0956464i | ||||
\(554\) | 28.4812i | 1.21005i | ||||||||
\(555\) | −8.08773 | + | 14.0084i | −0.343305 | + | 0.594622i | ||||
\(556\) | −8.35322 | − | 14.4682i | −0.354256 | − | 0.613589i | ||||
\(557\) | 9.34071 | − | 5.39286i | 0.395779 | − | 0.228503i | −0.288882 | − | 0.957365i | \(-0.593284\pi\) |
0.684661 | + | 0.728862i | \(0.259950\pi\) | |||||||
\(558\) | −0.978370 | −0.0414177 | ||||||||
\(559\) | −0.842322 | + | 10.8620i | −0.0356264 | + | 0.459415i | ||||
\(560\) | 3.05596 | 0.129138 | ||||||||
\(561\) | 8.43395 | − | 4.86934i | 0.356082 | − | 0.205584i | ||||
\(562\) | −4.88016 | − | 8.45268i | −0.205857 | − | 0.356555i | ||||
\(563\) | 12.7541 | − | 22.0908i | 0.537522 | − | 0.931016i | −0.461514 | − | 0.887133i | \(-0.652694\pi\) |
0.999037 | − | 0.0438831i | \(-0.0139729\pi\) | |||||||
\(564\) | − | 8.04447i | − | 0.338733i | ||||||
\(565\) | 29.6708 | + | 17.1304i | 1.24826 | + | 0.720682i | ||||
\(566\) | 10.1076 | + | 5.83562i | 0.424853 | + | 0.245289i | ||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | −1.83473 | + | 3.17784i | −0.0769834 | + | 0.133339i | ||||
\(569\) | −4.10835 | − | 7.11587i | −0.172231 | − | 0.298313i | 0.766969 | − | 0.641685i | \(-0.221764\pi\) |
−0.939200 | + | 0.343372i | \(0.888431\pi\) | |||||||
\(570\) | −4.56638 | + | 2.63640i | −0.191265 | + | 0.110427i | ||||
\(571\) | 2.70500 | 0.113201 | 0.0566003 | − | 0.998397i | \(-0.481974\pi\) | ||||
0.0566003 | + | 0.998397i | \(0.481974\pi\) | |||||||
\(572\) | 5.35636 | + | 11.1968i | 0.223961 | + | 0.468160i | ||||
\(573\) | −25.4945 | −1.06505 | ||||||||
\(574\) | 8.62781 | − | 4.98127i | 0.360118 | − | 0.207914i | ||||
\(575\) | −6.64416 | − | 11.5080i | −0.277081 | − | 0.479918i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 21.4253i | − | 0.891946i | −0.895046 | − | 0.445973i | \(-0.852858\pi\) | ||
0.895046 | − | 0.445973i | \(-0.147142\pi\) | |||||||
\(578\) | 7.79152 | + | 4.49843i | 0.324084 | + | 0.187110i | ||||
\(579\) | −7.38361 | − | 4.26293i | −0.306852 | − | 0.177161i | ||||
\(580\) | − | 11.7673i | − | 0.488611i | ||||||
\(581\) | 3.57934 | − | 6.19961i | 0.148496 | − | 0.257203i | ||||
\(582\) | −4.54961 | − | 7.88016i | −0.188587 | − | 0.326643i | ||||
\(583\) | 24.8460 | − | 14.3449i | 1.02902 | − | 0.594104i | ||||
\(584\) | −10.1119 | −0.418434 | ||||||||
\(585\) | −10.9854 | − | 0.851893i | −0.454192 | − | 0.0352214i | ||||
\(586\) | 21.8202 | 0.901382 | ||||||||
\(587\) | −4.96515 | + | 2.86663i | −0.204934 | + | 0.118319i | −0.598955 | − | 0.800783i | \(-0.704417\pi\) |
0.394021 | + | 0.919101i | \(0.371084\pi\) | |||||||
\(588\) | 0.500000 | + | 0.866025i | 0.0206197 | + | 0.0357143i | ||||
\(589\) | −0.844048 | + | 1.46193i | −0.0347784 | + | 0.0602379i | ||||
\(590\) | 30.4910i | 1.25529i | ||||||||
\(591\) | 20.5094 | + | 11.8411i | 0.843645 | + | 0.487079i | ||||
\(592\) | −4.58394 | − | 2.64654i | −0.188399 | − | 0.108772i | ||||
\(593\) | 17.3442i | 0.712240i | 0.934440 | + | 0.356120i | \(0.115901\pi\) | ||||
−0.934440 | + | 0.356120i | \(0.884099\pi\) | |||||||
\(594\) | 1.72124 | − | 2.98127i | 0.0706232 | − | 0.122323i | ||||
\(595\) | −4.32263 | − | 7.48701i | −0.177211 | − | 0.306938i | ||||
\(596\) | 2.16642 | − | 1.25078i | 0.0887400 | − | 0.0512341i | ||||
\(597\) | −24.8466 | −1.01691 | ||||||||
\(598\) | 11.0093 | + | 0.853743i | 0.450204 | + | 0.0349121i | ||||
\(599\) | −31.5835 | −1.29047 | −0.645234 | − | 0.763985i | \(-0.723240\pi\) | ||||
−0.645234 | + | 0.763985i | \(0.723240\pi\) | |||||||
\(600\) | −3.75760 | + | 2.16945i | −0.153404 | + | 0.0885676i | ||||
\(601\) | −12.4478 | − | 21.5603i | −0.507757 | − | 0.879462i | −0.999960 | − | 0.00898069i | \(-0.997141\pi\) |
0.492202 | − | 0.870481i | \(-0.336192\pi\) | |||||||
\(602\) | −1.51082 | + | 2.61681i | −0.0615762 | + | 0.106653i | ||||
\(603\) | 4.75055i | 0.193457i | ||||||||
\(604\) | 10.9522 | + | 6.32323i | 0.445637 | + | 0.257289i | ||||
\(605\) | 2.25118 | + | 1.29972i | 0.0915233 | + | 0.0528410i | ||||
\(606\) | 18.8533i | 0.765862i | ||||||||
\(607\) | −7.62951 | + | 13.2147i | −0.309672 | + | 0.536368i | −0.978291 | − | 0.207238i | \(-0.933553\pi\) |
0.668618 | + | 0.743606i | \(0.266886\pi\) | |||||||
\(608\) | −0.862708 | − | 1.49425i | −0.0349874 | − | 0.0606000i | ||||
\(609\) | 3.33473 | − | 1.92531i | 0.135130 | − | 0.0780173i | ||||
\(610\) | 35.2817 | 1.42851 | ||||||||
\(611\) | −12.5169 | − | 26.1649i | −0.506379 | − | 1.05852i | ||||
\(612\) | −2.82898 | −0.114355 | ||||||||
\(613\) | −39.6220 | + | 22.8757i | −1.60032 | + | 0.923943i | −0.608892 | + | 0.793253i | \(0.708386\pi\) |
−0.991423 | + | 0.130690i | \(0.958281\pi\) | |||||||
\(614\) | 2.43523 | + | 4.21794i | 0.0982779 | + | 0.170222i | ||||
\(615\) | −15.2226 | + | 26.3663i | −0.613833 | + | 1.06319i | ||||
\(616\) | 3.44247i | 0.138701i | ||||||||
\(617\) | 36.6167 | + | 21.1406i | 1.47413 | + | 0.851090i | 0.999575 | − | 0.0291358i | \(-0.00927553\pi\) |
0.474555 | + | 0.880226i | \(0.342609\pi\) | |||||||
\(618\) | −11.8714 | − | 6.85393i | −0.477536 | − | 0.275705i | ||||
\(619\) | − | 22.0261i | − | 0.885303i | −0.896694 | − | 0.442651i | \(-0.854038\pi\) | ||
0.896694 | − | 0.442651i | \(-0.145962\pi\) | |||||||
\(620\) | −1.49493 | + | 2.58930i | −0.0600379 | + | 0.103989i | ||||
\(621\) | −1.53130 | − | 2.65229i | −0.0614489 | − | 0.106433i | ||||
\(622\) | −3.38048 | + | 1.95172i | −0.135545 | + | 0.0782569i | ||||
\(623\) | −7.90307 | −0.316630 | ||||||||
\(624\) | 0.278764 | − | 3.59476i | 0.0111595 | − | 0.143906i | ||||
\(625\) | −27.8684 | −1.11474 | ||||||||
\(626\) | 22.5624 | − | 13.0264i | 0.901775 | − | 0.520640i | ||||
\(627\) | −2.96985 | − | 5.14393i | −0.118604 | − | 0.205429i | ||||
\(628\) | 8.90657 | − | 15.4266i | 0.355411 | − | 0.615590i | ||||
\(629\) | 14.9740i | 0.597054i | ||||||||
\(630\) | −2.64654 | − | 1.52798i | −0.105441 | − | 0.0608762i | ||||
\(631\) | 18.0721 | + | 10.4339i | 0.719440 | + | 0.415369i | 0.814547 | − | 0.580098i | \(-0.196986\pi\) |
−0.0951064 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(632\) | 4.49843i | 0.178938i | ||||||||
\(633\) | 0.386509 | − | 0.669453i | 0.0153624 | − | 0.0266084i | ||||
\(634\) | −5.55536 | − | 9.62216i | −0.220631 | − | 0.382145i | ||||
\(635\) | −13.5372 | + | 7.81571i | −0.537208 | + | 0.310157i | ||||
\(636\) | −8.33405 | −0.330467 | ||||||||
\(637\) | 2.97377 | + | 2.03880i | 0.117825 | + | 0.0807800i | ||||
\(638\) | 13.2556 | 0.524795 | ||||||||
\(639\) | 3.17784 | − | 1.83473i | 0.125713 | − | 0.0725807i | ||||
\(640\) | −1.52798 | − | 2.64654i | −0.0603988 | − | 0.104614i | ||||
\(641\) | −10.4526 | + | 18.1045i | −0.412853 | + | 0.715083i | −0.995200 | − | 0.0978574i | \(-0.968801\pi\) |
0.582347 | + | 0.812940i | \(0.302134\pi\) | |||||||
\(642\) | 3.31471i | 0.130821i | ||||||||
\(643\) | 33.8703 | + | 19.5550i | 1.33571 | + | 0.771174i | 0.986168 | − | 0.165746i | \(-0.0530032\pi\) |
0.349544 | + | 0.936920i | \(0.386337\pi\) | |||||||
\(644\) | 2.65229 | + | 1.53130i | 0.104515 | + | 0.0603416i | ||||
\(645\) | − | 9.23399i | − | 0.363588i | ||||||
\(646\) | −2.44058 | + | 4.22722i | −0.0960235 | + | 0.166318i | ||||
\(647\) | −3.96755 | − | 6.87201i | −0.155981 | − | 0.270166i | 0.777435 | − | 0.628963i | \(-0.216520\pi\) |
−0.933416 | + | 0.358797i | \(0.883187\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −34.3474 | −1.34825 | ||||||||
\(650\) | −8.84615 | + | 12.9029i | −0.346974 | + | 0.506094i | ||||
\(651\) | −0.978370 | −0.0383453 | ||||||||
\(652\) | −7.68884 | + | 4.43915i | −0.301118 | + | 0.173851i | ||||
\(653\) | −21.3998 | − | 37.0655i | −0.837439 | − | 1.45049i | −0.892029 | − | 0.451978i | \(-0.850719\pi\) |
0.0545901 | − | 0.998509i | \(-0.482615\pi\) | |||||||
\(654\) | 4.33762 | − | 7.51299i | 0.169615 | − | 0.293781i | ||||
\(655\) | − | 57.3778i | − | 2.24194i | ||||||
\(656\) | −8.62781 | − | 4.98127i | −0.336859 | − | 0.194486i | ||||
\(657\) | 8.75718 | + | 5.05596i | 0.341650 | + | 0.197252i | ||||
\(658\) | − | 8.04447i | − | 0.313606i | ||||||
\(659\) | −0.364274 | + | 0.630941i | −0.0141901 | + | 0.0245780i | −0.873033 | − | 0.487661i | \(-0.837850\pi\) |
0.858843 | + | 0.512239i | \(0.171184\pi\) | |||||||
\(660\) | −5.26003 | − | 9.11064i | −0.204746 | − | 0.354631i | ||||
\(661\) | −2.04352 | + | 1.17983i | −0.0794836 | + | 0.0458899i | −0.539215 | − | 0.842168i | \(-0.681279\pi\) |
0.459731 | + | 0.888058i | \(0.347946\pi\) | |||||||
\(662\) | 14.6478 | 0.569304 | ||||||||
\(663\) | −9.20136 | + | 4.40179i | −0.357351 | + | 0.170951i | ||||
\(664\) | −7.15869 | −0.277811 | ||||||||
\(665\) | −4.56638 | + | 2.63640i | −0.177077 | + | 0.102235i | ||||
\(666\) | 2.64654 | + | 4.58394i | 0.102551 | + | 0.177624i | ||||
\(667\) | 5.89644 | − | 10.2129i | 0.228311 | − | 0.395446i | ||||
\(668\) | 9.76989i | 0.378008i | ||||||||
\(669\) | −18.6502 | − | 10.7677i | −0.721060 | − | 0.416304i | ||||
\(670\) | 12.5725 | + | 7.25875i | 0.485719 | + | 0.280430i | ||||
\(671\) | 39.7440i | 1.53430i | ||||||||
\(672\) | 0.500000 | − | 0.866025i | 0.0192879 | − | 0.0334077i | ||||
\(673\) | 15.6279 | + | 27.0682i | 0.602410 | + | 1.04340i | 0.992455 | + | 0.122609i | \(0.0391260\pi\) |
−0.390045 | + | 0.920796i | \(0.627541\pi\) | |||||||
\(674\) | −23.8552 | + | 13.7728i | −0.918867 | + | 0.530508i | ||||
\(675\) | 4.33891 | 0.167005 | ||||||||
\(676\) | −4.68662 | − | 12.1258i | −0.180255 | − | 0.466378i | ||||
\(677\) | −41.7294 | −1.60379 | −0.801895 | − | 0.597464i | \(-0.796175\pi\) | ||||
−0.801895 | + | 0.597464i | \(0.796175\pi\) | |||||||
\(678\) | 9.70914 | − | 5.60557i | 0.372877 | − | 0.215281i | ||||
\(679\) | −4.54961 | − | 7.88016i | −0.174598 | − | 0.302413i | ||||
\(680\) | −4.32263 | + | 7.48701i | −0.165765 | + | 0.287114i | ||||
\(681\) | 17.5444i | 0.672301i | ||||||||
\(682\) | −2.91678 | − | 1.68401i | −0.111689 | − | 0.0644839i | ||||
\(683\) | −7.98473 | − | 4.60999i | −0.305527 | − | 0.176396i | 0.339396 | − | 0.940644i | \(-0.389777\pi\) |
−0.644923 | + | 0.764247i | \(0.723111\pi\) | |||||||
\(684\) | 1.72542i | 0.0659729i | ||||||||
\(685\) | −4.06610 | + | 7.04269i | −0.155358 | + | 0.269087i | ||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | 8.93928 | − | 5.16109i | 0.341055 | − | 0.196908i | ||||
\(688\) | 3.02163 | 0.115199 | ||||||||
\(689\) | −27.1068 | + | 12.9675i | −1.03269 | + | 0.494021i | ||||
\(690\) | −9.35918 | −0.356298 | ||||||||
\(691\) | −7.97487 | + | 4.60429i | −0.303378 | + | 0.175156i | −0.643960 | − | 0.765060i | \(-0.722709\pi\) |
0.340581 | + | 0.940215i | \(0.389376\pi\) | |||||||
\(692\) | −4.33762 | − | 7.51299i | −0.164892 | − | 0.285601i | ||||
\(693\) | 1.72124 | − | 2.98127i | 0.0653843 | − | 0.113249i | ||||
\(694\) | 5.24146i | 0.198963i | ||||||||
\(695\) | 44.2143 | + | 25.5271i | 1.67714 | + | 0.968300i | ||||
\(696\) | −3.33473 | − | 1.92531i | −0.126402 | − | 0.0729785i | ||||
\(697\) | 28.1838i | 1.06754i | ||||||||
\(698\) | −2.61482 | + | 4.52901i | −0.0989725 | + | 0.171425i | ||||
\(699\) | −8.91449 | − | 15.4404i | −0.337177 | − | 0.584008i | ||||
\(700\) | −3.75760 | + | 2.16945i | −0.142024 | + | 0.0819976i | ||||
\(701\) | 20.8683 | 0.788184 | 0.394092 | − | 0.919071i | \(-0.371059\pi\) | ||||
0.394092 | + | 0.919071i | \(0.371059\pi\) | |||||||
\(702\) | −2.03880 | + | 2.97377i | −0.0769494 | + | 0.112238i | ||||
\(703\) | 9.13277 | 0.344449 | ||||||||
\(704\) | 2.98127 | − | 1.72124i | 0.112361 | − | 0.0648715i | ||||
\(705\) | 12.2918 | + | 21.2900i | 0.462936 | + | 0.801829i | ||||
\(706\) | 1.88348 | − | 3.26227i | 0.0708855 | − | 0.122777i | ||||
\(707\) | 18.8533i | 0.709050i | ||||||||
\(708\) | 8.64080 | + | 4.98877i | 0.324741 | + | 0.187489i | ||||
\(709\) | −12.8731 | − | 7.43226i | −0.483458 | − | 0.279124i | 0.238399 | − | 0.971167i | \(-0.423378\pi\) |
−0.721856 | + | 0.692043i | \(0.756711\pi\) | |||||||
\(710\) | − | 11.2137i | − | 0.420843i | ||||||
\(711\) | 2.24922 | − | 3.89576i | 0.0843522 | − | 0.146102i | ||||
\(712\) | 3.95154 | + | 6.84426i | 0.148090 | + | 0.256499i | ||||
\(713\) | −2.59492 | + | 1.49818i | −0.0971804 | + | 0.0561072i | ||||
\(714\) | −2.82898 | −0.105872 | ||||||||
\(715\) | −31.2843 | − | 21.4483i | −1.16996 | − | 0.802120i | ||||
\(716\) | −23.4278 | −0.875540 | ||||||||
\(717\) | 4.94735 | − | 2.85636i | 0.184762 | − | 0.106673i | ||||
\(718\) | −10.3002 | − | 17.8404i | −0.384399 | − | 0.665798i | ||||
\(719\) | −12.8265 | + | 22.2162i | −0.478349 | + | 0.828524i | −0.999692 | − | 0.0248229i | \(-0.992098\pi\) |
0.521343 | + | 0.853347i | \(0.325431\pi\) | |||||||
\(720\) | 3.05596i | 0.113889i | ||||||||
\(721\) | −11.8714 | − | 6.85393i | −0.442112 | − | 0.255254i | ||||
\(722\) | −13.8763 | − | 8.01147i | −0.516421 | − | 0.298156i | ||||
\(723\) | 1.00313i | 0.0373069i | ||||||||
\(724\) | 3.83316 | − | 6.63923i | 0.142458 | − | 0.246745i | ||||
\(725\) | 8.35372 | + | 14.4691i | 0.310249 | + | 0.537368i | ||||
\(726\) | 0.736650 | − | 0.425305i | 0.0273397 | − | 0.0157846i | ||||
\(727\) | 41.6568 | 1.54497 | 0.772483 | − | 0.635036i | \(-0.219015\pi\) | ||||
0.772483 | + | 0.635036i | \(0.219015\pi\) | |||||||
\(728\) | 0.278764 | − | 3.59476i | 0.0103317 | − | 0.133231i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 26.7616 | − | 15.4508i | 0.990492 | − | 0.571861i | ||||
\(731\) | −4.27407 | − | 7.40290i | −0.158082 | − | 0.273806i | ||||
\(732\) | 5.77260 | − | 9.99843i | 0.213361 | − | 0.369553i | ||||
\(733\) | 26.4965i | 0.978671i | 0.872096 | + | 0.489336i | \(0.162761\pi\) | ||||
−0.872096 | + | 0.489336i | \(0.837239\pi\) | |||||||
\(734\) | 24.1759 | + | 13.9579i | 0.892347 | + | 0.515197i | ||||
\(735\) | −2.64654 | − | 1.52798i | −0.0976191 | − | 0.0563604i | ||||
\(736\) | − | 3.06260i | − | 0.112889i | ||||||
\(737\) | −8.17682 | + | 14.1627i | −0.301197 | + | 0.521688i | ||||
\(738\) | 4.98127 | + | 8.62781i | 0.183363 | + | 0.317594i | ||||
\(739\) | 18.1009 | − | 10.4506i | 0.665853 | − | 0.384431i | −0.128650 | − | 0.991690i | \(-0.541064\pi\) |
0.794504 | + | 0.607259i | \(0.207731\pi\) | |||||||
\(740\) | 16.1755 | 0.594622 | ||||||||
\(741\) | 2.68468 | + | 5.61197i | 0.0986243 | + | 0.206161i | ||||
\(742\) | −8.33405 | −0.305953 | ||||||||
\(743\) | 4.88999 | − | 2.82323i | 0.179396 | − | 0.103574i | −0.407613 | − | 0.913155i | \(-0.633639\pi\) |
0.587009 | + | 0.809580i | \(0.300305\pi\) | |||||||
\(744\) | 0.489185 | + | 0.847293i | 0.0179344 | + | 0.0310633i | ||||
\(745\) | −3.82235 | + | 6.62050i | −0.140040 | + | 0.242556i | ||||
\(746\) | 31.4183i | 1.15030i | ||||||||
\(747\) | 6.19961 | + | 3.57934i | 0.226832 | + | 0.130961i | ||||
\(748\) | −8.43395 | − | 4.86934i | −0.308376 | − | 0.178041i | ||||
\(749\) | 3.31471i | 0.121117i | ||||||||
\(750\) | −1.01014 | + | 1.74961i | −0.0368850 | + | 0.0638867i | ||||
\(751\) | 7.70439 | + | 13.3444i | 0.281137 | + | 0.486944i | 0.971665 | − | 0.236362i | \(-0.0759551\pi\) |
−0.690528 | + | 0.723306i | \(0.742622\pi\) | |||||||
\(752\) | −6.96672 | + | 4.02224i | −0.254050 | + | 0.146676i | ||||
\(753\) | −0.672585 | −0.0245104 | ||||||||
\(754\) | −13.8420 | − | 1.07341i | −0.504097 | − | 0.0390914i | ||||
\(755\) | −38.6471 | −1.40651 | ||||||||
\(756\) | −0.866025 | + | 0.500000i | −0.0314970 | + | 0.0181848i | ||||
\(757\) | 17.7686 | + | 30.7761i | 0.645811 | + | 1.11858i | 0.984114 | + | 0.177540i | \(0.0568139\pi\) |
−0.338303 | + | 0.941037i | \(0.609853\pi\) | |||||||
\(758\) | −15.9203 | + | 27.5747i | −0.578251 | + | 1.00156i | ||||
\(759\) | − | 10.5429i | − | 0.382683i | ||||||
\(760\) | 4.56638 | + | 2.63640i | 0.165640 | + | 0.0956324i | ||||
\(761\) | 36.2213 | + | 20.9124i | 1.31302 | + | 0.758073i | 0.982595 | − | 0.185759i | \(-0.0594745\pi\) |
0.330425 | + | 0.943832i | \(0.392808\pi\) | |||||||
\(762\) | 5.11506i | 0.185299i | ||||||||
\(763\) | 4.33762 | − | 7.51299i | 0.157033 | − | 0.271988i | ||||
\(764\) | 12.7472 | + | 22.0789i | 0.461179 | + | 0.798785i | ||||
\(765\) | 7.48701 | − | 4.32263i | 0.270694 | − | 0.156285i | ||||
\(766\) | −4.72228 | −0.170623 | ||||||||
\(767\) | 35.8668 | + | 2.78138i | 1.29508 | + | 0.100430i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 15.4609 | − | 8.92635i | 0.557534 | − | 0.321893i | −0.194621 | − | 0.980879i | \(-0.562348\pi\) |
0.752155 | + | 0.658986i | \(0.229014\pi\) | |||||||
\(770\) | −5.26003 | − | 9.11064i | −0.189558 | − | 0.328325i | ||||
\(771\) | −12.1717 | + | 21.0820i | −0.438352 | + | 0.759248i | ||||
\(772\) | 8.52586i | 0.306852i | ||||||||
\(773\) | 10.4892 | + | 6.05596i | 0.377272 | + | 0.217818i | 0.676630 | − | 0.736323i | \(-0.263439\pi\) |
−0.299359 | + | 0.954141i | \(0.596773\pi\) | |||||||
\(774\) | −2.61681 | − | 1.51082i | −0.0940592 | − | 0.0543051i | ||||
\(775\) | − | 4.24506i | − | 0.152487i | ||||||
\(776\) | −4.54961 | + | 7.88016i | −0.163322 | + | 0.282881i | ||||
\(777\) | 2.64654 | + | 4.58394i | 0.0949441 | + | 0.164448i | ||||
\(778\) | −26.4919 | + | 15.2951i | −0.949781 | + | 0.548357i | ||||
\(779\) | 17.1895 | 0.615878 | ||||||||
\(780\) | 4.75496 | + | 9.93962i | 0.170255 | + | 0.355896i | ||||
\(781\) | 12.6320 | 0.452008 | ||||||||
\(782\) | −7.50327 | + | 4.33201i | −0.268316 | + | 0.154913i | ||||
\(783\) | 1.92531 | + | 3.33473i | 0.0688048 | + | 0.119173i | ||||
\(784\) | 0.500000 | − | 0.866025i | 0.0178571 | − | 0.0309295i | ||||
\(785\) | 54.4363i | 1.94292i | ||||||||
\(786\) | −16.2602 | − | 9.38784i | −0.579983 | − | 0.334853i | ||||
\(787\) | 27.7604 | + | 16.0275i | 0.989551 | + | 0.571317i | 0.905140 | − | 0.425114i | \(-0.139766\pi\) |
0.0844108 | + | 0.996431i | \(0.473099\pi\) | |||||||
\(788\) | − | 23.6823i | − | 0.843645i | ||||||
\(789\) | −8.54648 | + | 14.8029i | −0.304263 | + | 0.526999i | ||||
\(790\) | −6.87352 | − | 11.9053i | −0.244549 | − | 0.423571i | ||||
\(791\) | 9.70914 | − | 5.60557i | 0.345217 | − | 0.199311i | ||||
\(792\) | −3.44247 | −0.122323 | ||||||||
\(793\) | 3.21839 | − | 41.5022i | 0.114288 | − | 1.47379i | ||||
\(794\) | 11.6778 | 0.414430 | ||||||||
\(795\) | 22.0564 | − | 12.7343i | 0.782260 | − | 0.451638i | ||||
\(796\) | 12.4233 | + | 21.5178i | 0.440333 | + | 0.762679i | ||||
\(797\) | 4.56545 | − | 7.90758i | 0.161716 | − | 0.280101i | −0.773768 | − | 0.633469i | \(-0.781630\pi\) |
0.935484 | + | 0.353368i | \(0.114964\pi\) | |||||||
\(798\) | 1.72542i | 0.0610791i | ||||||||
\(799\) | 19.7087 | + | 11.3788i | 0.697244 | + | 0.402554i | ||||
\(800\) | 3.75760 | + | 2.16945i | 0.132851 | + | 0.0767018i | ||||
\(801\) | − | 7.90307i | − | 0.279241i | ||||||
\(802\) | 4.62849 | − | 8.01677i | 0.163438 | − | 0.283082i | ||||
\(803\) | 17.4050 | + | 30.1464i | 0.614209 | + | 1.06384i | ||||
\(804\) | 4.11410 | − | 2.37527i | 0.145093 | − | 0.0837695i | ||||
\(805\) | −9.35918 | −0.329868 | ||||||||
\(806\) | 2.90945 | + | 1.99470i | 0.102481 | + | 0.0702602i | ||||
\(807\) | 26.6594 | 0.938456 | ||||||||
\(808\) | 16.3274 | − | 9.42664i | 0.574396 | − | 0.331628i | ||||
\(809\) | −10.7311 | − | 18.5869i | −0.377287 | − | 0.653480i | 0.613380 | − | 0.789788i | \(-0.289810\pi\) |
−0.990666 | + | 0.136308i | \(0.956476\pi\) | |||||||
\(810\) | 1.52798 | − | 2.64654i | 0.0536878 | − | 0.0929900i | ||||
\(811\) | − | 44.2671i | − | 1.55443i | −0.629236 | − | 0.777214i | \(-0.716632\pi\) | ||
0.629236 | − | 0.777214i | \(-0.283368\pi\) | |||||||
\(812\) | −3.33473 | − | 1.92531i | −0.117026 | − | 0.0675650i | ||||
\(813\) | 21.1739 | + | 12.2247i | 0.742600 | + | 0.428740i | ||||
\(814\) | 18.2213i | 0.638656i | ||||||||
\(815\) | 13.5659 | − | 23.4968i | 0.475192 | − | 0.823057i | ||||
\(816\) | 1.41449 | + | 2.44997i | 0.0495171 | + | 0.0857661i | ||||
\(817\) | −4.51508 | + | 2.60678i | −0.157963 | + | 0.0911998i | ||||
\(818\) | −25.5989 | −0.895043 | ||||||||
\(819\) | −2.03880 | + | 2.97377i | −0.0712413 | + | 0.103912i | ||||
\(820\) | 30.4451 | 1.06319 | ||||||||
\(821\) | −8.07131 | + | 4.65997i | −0.281691 | + | 0.162634i | −0.634188 | − | 0.773178i | \(-0.718666\pi\) |
0.352498 | + | 0.935813i | \(0.385332\pi\) | |||||||
\(822\) | 1.33055 | + | 2.30457i | 0.0464081 | + | 0.0803813i | ||||
\(823\) | 14.8426 | − | 25.7082i | 0.517381 | − | 0.896131i | −0.482415 | − | 0.875943i | \(-0.660240\pi\) |
0.999796 | − | 0.0201878i | \(-0.00642642\pi\) | |||||||
\(824\) | 13.7079i | 0.477536i | ||||||||
\(825\) | 12.9354 | + | 7.46828i | 0.450354 | + | 0.260012i | ||||
\(826\) | 8.64080 | + | 4.98877i | 0.300652 | + | 0.173581i | ||||
\(827\) | − | 22.6364i | − | 0.787146i | −0.919293 | − | 0.393573i | \(-0.871239\pi\) | ||
0.919293 | − | 0.393573i | \(-0.128761\pi\) | |||||||
\(828\) | −1.53130 | + | 2.65229i | −0.0532163 | + | 0.0921734i | ||||
\(829\) | −4.82167 | − | 8.35138i | −0.167463 | − | 0.290055i | 0.770064 | − | 0.637967i | \(-0.220224\pi\) |
−0.937527 | + | 0.347912i | \(0.886891\pi\) | |||||||
\(830\) | 18.9458 | − | 10.9383i | 0.657617 | − | 0.379675i | ||||
\(831\) | −28.4812 | −0.988003 | ||||||||
\(832\) | −3.25253 | + | 1.55596i | −0.112761 | + | 0.0539433i | ||||
\(833\) | −2.82898 | −0.0980184 | ||||||||
\(834\) | 14.4682 | − | 8.35322i | 0.500993 | − | 0.289249i | ||||
\(835\) | −14.9282 | − | 25.8564i | −0.516612 | − | 0.894798i | ||||
\(836\) | −2.96985 | + | 5.14393i | −0.102714 | + | 0.177906i | ||||
\(837\) | − | 0.978370i | − | 0.0338174i | ||||||
\(838\) | −24.4251 | − | 14.1018i | −0.843751 | − | 0.487140i | ||||
\(839\) | −28.9983 | − | 16.7422i | −1.00113 | − | 0.578005i | −0.0925499 | − | 0.995708i | \(-0.529502\pi\) |
−0.908583 | + | 0.417704i | \(0.862835\pi\) | |||||||
\(840\) | 3.05596i | 0.105441i | ||||||||
\(841\) | 7.08640 | − | 12.2740i | 0.244359 | − | 0.423241i | ||||
\(842\) | −2.53506 | − | 4.39085i | −0.0873639 | − | 0.151319i | ||||
\(843\) | 8.45268 | − | 4.88016i | 0.291126 | − | 0.168082i | ||||
\(844\) | −0.773018 | −0.0266084 | ||||||||
\(845\) | 30.9314 | + | 24.9304i | 1.06407 | + | 0.857633i | ||||
\(846\) | 8.04447 | 0.276575 | ||||||||
\(847\) | 0.736650 | − | 0.425305i | 0.0253116 | − | 0.0146137i | ||||
\(848\) | 4.16702 | + | 7.21750i | 0.143096 | + | 0.247850i | ||||
\(849\) | −5.83562 | + | 10.1076i | −0.200278 | + | 0.346891i | ||||
\(850\) | − | 12.2747i | − | 0.421018i | ||||||
\(851\) | 14.0388 | + | 8.10529i | 0.481243 | + | 0.277846i | ||||
\(852\) | −3.17784 | − | 1.83473i | −0.108871 | − | 0.0628567i | ||||
\(853\) | 23.7246i | 0.812316i | 0.913803 | + | 0.406158i | \(0.133132\pi\) | ||||
−0.913803 | + | 0.406158i | \(0.866868\pi\) | |||||||
\(854\) | 5.77260 | − | 9.99843i | 0.197534 | − | 0.342139i | ||||
\(855\) | −2.63640 | − | 4.56638i | −0.0901631 | − | 0.156167i | ||||
\(856\) | 2.87063 | − | 1.65736i | 0.0981159 | − | 0.0566473i | ||||
\(857\) | −24.4823 | −0.836299 | −0.418149 | − | 0.908378i | \(-0.637321\pi\) | ||||
−0.418149 | + | 0.908378i | \(0.637321\pi\) | |||||||
\(858\) | −11.1968 | + | 5.35636i | −0.382251 | + | 0.182863i | ||||
\(859\) | −26.7787 | −0.913676 | −0.456838 | − | 0.889550i | \(-0.651018\pi\) | ||||
−0.456838 | + | 0.889550i | \(0.651018\pi\) | |||||||
\(860\) | −7.99687 | + | 4.61699i | −0.272691 | + | 0.157438i | ||||
\(861\) | 4.98127 | + | 8.62781i | 0.169761 | + | 0.294035i | ||||
\(862\) | −8.07185 | + | 13.9808i | −0.274928 | + | 0.476190i | ||||
\(863\) | − | 54.8533i | − | 1.86723i | −0.358282 | − | 0.933614i | \(-0.616637\pi\) | ||
0.358282 | − | 0.933614i | \(-0.383363\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 22.9594 | + | 13.2556i | 0.780643 | + | 0.450705i | ||||
\(866\) | 22.6029i | 0.768077i | ||||||||
\(867\) | −4.49843 | + | 7.79152i | −0.152775 | + | 0.264614i | ||||
\(868\) | 0.489185 | + | 0.847293i | 0.0166040 | + | 0.0287590i | ||||
\(869\) | 13.4110 | − | 7.74287i | 0.454938 | − | 0.262659i | ||||
\(870\) | 11.7673 | 0.398950 | ||||||||
\(871\) | 9.68540 | − | 14.1270i | 0.328177 | − | 0.478677i | ||||
\(872\) | −8.67525 | −0.293781 | ||||||||
\(873\) | 7.88016 | − | 4.54961i | 0.266703 | − | 0.153981i | ||||
\(874\) | 2.64213 | + | 4.57630i | 0.0893713 | + | 0.154796i | ||||
\(875\) | −1.01014 | + | 1.74961i | −0.0341489 | + | 0.0591476i | ||||
\(876\) | − | 10.1119i | − | 0.341650i | ||||||
\(877\) | 4.67626 | + | 2.69984i | 0.157906 | + | 0.0911671i | 0.576871 | − | 0.816835i | \(-0.304274\pi\) |
−0.418965 | + | 0.908002i | \(0.637607\pi\) | |||||||
\(878\) | 24.5060 | + | 14.1486i | 0.827038 | + | 0.477490i | ||||
\(879\) | 21.8202i | 0.735975i | ||||||||
\(880\) | −5.26003 | + | 9.11064i | −0.177316 | + | 0.307120i | ||||
\(881\) | −8.18333 | − | 14.1739i | −0.275703 | − | 0.477532i | 0.694609 | − | 0.719387i | \(-0.255577\pi\) |
−0.970312 | + | 0.241855i | \(0.922244\pi\) | |||||||
\(882\) | −0.866025 | + | 0.500000i | −0.0291606 | + | 0.0168359i | ||||
\(883\) | 10.8294 | 0.364440 | 0.182220 | − | 0.983258i | \(-0.441672\pi\) | ||||
0.182220 | + | 0.983258i | \(0.441672\pi\) | |||||||
\(884\) | 8.41274 | + | 5.76772i | 0.282951 | + | 0.193989i | ||||
\(885\) | −30.4910 | −1.02494 | ||||||||
\(886\) | −1.19594 | + | 0.690478i | −0.0401785 | + | 0.0231971i | ||||
\(887\) | 16.5776 | + | 28.7133i | 0.556623 | + | 0.964099i | 0.997775 | + | 0.0666668i | \(0.0212364\pi\) |
−0.441153 | + | 0.897432i | \(0.645430\pi\) | |||||||
\(888\) | 2.64654 | − | 4.58394i | 0.0888121 | − | 0.153827i | ||||
\(889\) | 5.11506i | 0.171553i | ||||||||
\(890\) | −20.9158 | − | 12.0757i | −0.701099 | − | 0.404780i | ||||
\(891\) | 2.98127 | + | 1.72124i | 0.0998762 | + | 0.0576636i | ||||
\(892\) | 21.5354i | 0.721060i | ||||||||
\(893\) | 6.94003 | − | 12.0205i | 0.232239 | − | 0.402250i | ||||
\(894\) | 1.25078 | + | 2.16642i | 0.0418324 | + | 0.0724559i | ||||
\(895\) | 62.0028 | − | 35.7973i | 2.07252 | − | 1.19657i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −0.853743 | + | 11.0093i | −0.0285056 | + | 0.367590i | ||||
\(898\) | −37.0059 | −1.23490 | ||||||||
\(899\) | 3.26260 | − | 1.88366i | 0.108814 | − | 0.0628236i | ||||
\(900\) | −2.16945 | − | 3.75760i | −0.0723151 | − | 0.125253i | ||||
\(901\) | 11.7884 | − | 20.4182i | 0.392730 | − | 0.680228i | ||||
\(902\) | 34.2957i | 1.14192i | ||||||||
\(903\) | −2.61681 | − | 1.51082i | −0.0870819 | − | 0.0502768i | ||||
\(904\) | −9.70914 | − | 5.60557i | −0.322921 | − | 0.186439i | ||||
\(905\) | 23.4280i | 0.778773i | ||||||||
\(906\) | −6.32323 | + | 10.9522i | −0.210075 | + | 0.363861i | ||||
\(907\) | 15.5349 | + | 26.9073i | 0.515829 | + | 0.893442i | 0.999831 | + | 0.0183754i | \(0.00584940\pi\) |
−0.484002 | + | 0.875067i | \(0.660817\pi\) | |||||||
\(908\) | 15.1939 | − | 8.77218i | 0.504226 | − | 0.291115i | ||||
\(909\) | −18.8533 | −0.625324 | ||||||||
\(910\) | 4.75496 | + | 9.93962i | 0.157625 | + | 0.329495i | ||||
\(911\) | −7.26309 | −0.240637 | −0.120318 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120318 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(912\) | 1.49425 | − | 0.862708i | 0.0494797 | − | 0.0285671i | ||||
\(913\) | 12.3218 | + | 21.3420i | 0.407792 | + | 0.706316i | ||||
\(914\) | 6.95878 | − | 12.0530i | 0.230176 | − | 0.398676i | ||||
\(915\) | 35.2817i | 1.16638i | ||||||||
\(916\) | −8.93928 | − | 5.16109i | −0.295362 | − | 0.170527i | ||||
\(917\) | −16.2602 | − | 9.38784i | −0.536960 | − | 0.310014i | ||||
\(918\) | − | 2.82898i | − | 0.0933703i | ||||||
\(919\) | −17.0863 | + | 29.5943i | −0.563625 | + | 0.976226i | 0.433552 | + | 0.901129i | \(0.357260\pi\) |
−0.997176 | + | 0.0750977i | \(0.976073\pi\) | |||||||
\(920\) | 4.67959 | + | 8.10529i | 0.154282 | + | 0.267224i | ||||
\(921\) | −4.21794 | + | 2.43523i | −0.138986 | + | 0.0802436i | ||||
\(922\) | 4.84795 | 0.159659 | ||||||||
\(923\) | −13.1908 | − | 1.02291i | −0.434180 | − | 0.0336696i | ||||
\(924\) | −3.44247 | −0.113249 | ||||||||
\(925\) | −19.8893 | + | 11.4831i | −0.653956 | + | 0.377562i | ||||
\(926\) | −12.2188 | − | 21.1636i | −0.401536 | − | 0.695480i | ||||
\(927\) | 6.85393 | − | 11.8714i | 0.225113 | − | 0.389906i | ||||
\(928\) | 3.85061i | 0.126402i | ||||||||
\(929\) | −11.8252 | − | 6.82728i | −0.387972 | − | 0.223996i | 0.293309 | − | 0.956018i | \(-0.405244\pi\) |
−0.681281 | + | 0.732022i | \(0.738577\pi\) | |||||||
\(930\) | −2.58930 | − | 1.49493i | −0.0849064 | − | 0.0490207i | ||||
\(931\) | 1.72542i | 0.0565482i | ||||||||
\(932\) | −8.91449 | + | 15.4404i | −0.292004 | + | 0.505765i | ||||
\(933\) | −1.95172 | − | 3.38048i | −0.0638965 | − | 0.110672i | ||||
\(934\) | −31.1792 | + | 18.0013i | −1.02022 | + | 0.589022i | ||||
\(935\) | 29.7611 | 0.973291 | ||||||||
\(936\) | 3.59476 | + | 0.278764i | 0.117498 | + | 0.00911169i | ||||
\(937\) | 43.5716 | 1.42342 | 0.711712 | − | 0.702472i | \(-0.247920\pi\) | ||||
0.711712 | + | 0.702472i | \(0.247920\pi\) | |||||||
\(938\) | 4.11410 | − | 2.37527i | 0.134330 | − | 0.0775555i | ||||
\(939\) | 13.0264 | + | 22.5624i | 0.425101 | + | 0.736297i | ||||
\(940\) | 12.2918 | − | 21.2900i | 0.400914 | − | 0.694404i | ||||
\(941\) | 55.8282i | 1.81995i | 0.414666 | + | 0.909973i | \(0.363898\pi\) | ||||
−0.414666 | + | 0.909973i | \(0.636102\pi\) | |||||||
\(942\) | 15.4266 | + | 8.90657i | 0.502627 | + | 0.290192i | ||||
\(943\) | 26.4235 | + | 15.2556i | 0.860468 | + | 0.496791i | ||||
\(944\) | − | 9.97753i | − | 0.324741i | ||||||
\(945\) | 1.52798 | − | 2.64654i | 0.0497052 | − | 0.0860920i | ||||
\(946\) | −5.20094 | − | 9.00829i | −0.169097 | − | 0.292885i | ||||
\(947\) | 45.4573 | − | 26.2448i | 1.47716 | − | 0.852842i | 0.477497 | − | 0.878633i | \(-0.341544\pi\) |
0.999667 | + | 0.0257916i | \(0.00821064\pi\) | |||||||
\(948\) | −4.49843 | −0.146102 | ||||||||
\(949\) | −15.7338 | − | 32.8894i | −0.510740 | − | 1.06763i | ||||
\(950\) | −7.48642 | −0.242891 | ||||||||
\(951\) | 9.62216 | − | 5.55536i | 0.312020 | − | 0.180145i | ||||
\(952\) | 1.41449 | + | 2.44997i | 0.0458439 | + | 0.0794040i | ||||
\(953\) | −3.50985 | + | 6.07925i | −0.113695 | + | 0.196926i | −0.917257 | − | 0.398295i | \(-0.869602\pi\) |
0.803562 | + | 0.595221i | \(0.202935\pi\) | |||||||
\(954\) | − | 8.33405i | − | 0.269825i | ||||||
\(955\) | −67.4721 | − | 38.9551i | −2.18335 | − | 1.26056i | ||||
\(956\) | −4.94735 | − | 2.85636i | −0.160009 | − | 0.0923812i | ||||
\(957\) | 13.2556i | 0.428493i | ||||||||
\(958\) | −4.74644 | + | 8.22108i | −0.153351 | + | 0.265611i | ||||
\(959\) | 1.33055 | + | 2.30457i | 0.0429656 | + | 0.0744186i | ||||
\(960\) | 2.64654 | − | 1.52798i | 0.0854167 | − | 0.0493154i | ||||
\(961\) | 30.0428 | 0.969122 | ||||||||
\(962\) | 1.47552 | − | 19.0274i | 0.0475727 | − | 0.613467i | ||||
\(963\) | −3.31471 | −0.106815 | ||||||||
\(964\) | 0.868738 | − | 0.501566i | 0.0279802 | − | 0.0161543i | ||||
\(965\) | −13.0274 | − | 22.5640i | −0.419365 | − | 0.726362i | ||||
\(966\) | −1.53130 | + | 2.65229i | −0.0492687 | + | 0.0853359i | ||||
\(967\) | 36.8770i | 1.18588i | 0.805245 | + | 0.592942i | \(0.202034\pi\) | ||||
−0.805245 | + | 0.592942i | \(0.797966\pi\) | |||||||
\(968\) | −0.736650 | − | 0.425305i | −0.0236768 | − | 0.0136698i | ||||
\(969\) | −4.22722 | − | 2.44058i | −0.135798 | − | 0.0784029i | ||||
\(970\) | − | 27.8069i | − | 0.892825i | ||||||
\(971\) | −13.8202 | + | 23.9372i | −0.443511 | + | 0.768183i | −0.997947 | − | 0.0640432i | \(-0.979600\pi\) |
0.554437 | + | 0.832226i | \(0.312934\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 14.4682 | − | 8.35322i | 0.463830 | − | 0.267792i | ||||
\(974\) | −40.9206 | −1.31118 | ||||||||
\(975\) | −12.9029 | − | 8.84615i | −0.413224 | − | 0.283303i | ||||
\(976\) | −11.5452 | −0.369553 | ||||||||
\(977\) | −48.1904 | + | 27.8227i | −1.54175 | + | 0.890128i | −0.543017 | + | 0.839721i | \(0.682718\pi\) |
−0.998729 | + | 0.0504061i | \(0.983948\pi\) | |||||||
\(978\) | −4.43915 | − | 7.68884i | −0.141948 | − | 0.245862i | ||||
\(979\) | 13.6030 | − | 23.5612i | 0.434755 | − | 0.753018i | ||||
\(980\) | 3.05596i | 0.0976191i | ||||||||
\(981\) | 7.51299 | + | 4.33762i | 0.239871 | + | 0.138490i | ||||
\(982\) | −4.42977 | − | 2.55753i | −0.141360 | − | 0.0816140i | ||||
\(983\) | 25.0022i | 0.797446i | 0.917071 | + | 0.398723i | \(0.130547\pi\) | ||||
−0.917071 | + | 0.398723i | \(0.869453\pi\) | |||||||
\(984\) | 4.98127 | − | 8.62781i | 0.158797 | − | 0.275045i | ||||
\(985\) | 36.1860 | + | 62.6761i | 1.15298 | + | 1.99703i | ||||
\(986\) | 9.43388 | − | 5.44665i | 0.300436 | − | 0.173457i | ||||
\(987\) | 8.04447 | 0.256058 | ||||||||
\(988\) | 3.51777 | − | 5.13099i | 0.111915 | − | 0.163239i | ||||
\(989\) | −9.25404 | −0.294261 | ||||||||
\(990\) | 9.11064 | − | 5.26003i | 0.289555 | − | 0.167175i | ||||
\(991\) | 13.6076 | + | 23.5690i | 0.432258 | + | 0.748694i | 0.997067 | − | 0.0765281i | \(-0.0243835\pi\) |
−0.564809 | + | 0.825222i | \(0.691050\pi\) | |||||||
\(992\) | 0.489185 | − | 0.847293i | 0.0155316 | − | 0.0269016i | ||||
\(993\) | 14.6478i | 0.464835i | ||||||||
\(994\) | −3.17784 | − | 1.83473i | −0.100795 | − | 0.0581940i | ||||
\(995\) | −65.7577 | − | 37.9652i | −2.08466 | − | 1.20358i | ||||
\(996\) | − | 7.15869i | − | 0.226832i | ||||||
\(997\) | 8.42706 | − | 14.5961i | 0.266888 | − | 0.462263i | −0.701169 | − | 0.712995i | \(-0.747338\pi\) |
0.968056 | + | 0.250732i | \(0.0806714\pi\) | |||||||
\(998\) | −9.79133 | − | 16.9591i | −0.309939 | − | 0.536830i | ||||
\(999\) | −4.58394 | + | 2.64654i | −0.145030 | + | 0.0837329i |
(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 | 546.2.s.e.127.4 | yes | 8 | |
3.2 | odd | 2 | 1638.2.bj.f.127.1 | 8 | |||
13.2 | odd | 12 | 7098.2.a.co.1.3 | 4 | |||
13.4 | even | 6 | inner | 546.2.s.e.43.3 | ✓ | 8 | |
13.11 | odd | 12 | 7098.2.a.cn.1.2 | 4 | |||
39.17 | odd | 6 | 1638.2.bj.f.1135.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.e.43.3 | ✓ | 8 | 13.4 | even | 6 | inner | |
546.2.s.e.127.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1638.2.bj.f.127.1 | 8 | 3.2 | odd | 2 | |||
1638.2.bj.f.1135.2 | 8 | 39.17 | odd | 6 | |||
7098.2.a.cn.1.2 | 4 | 13.11 | odd | 12 | |||
7098.2.a.co.1.3 | 4 | 13.2 | odd | 12 |