Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(111,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([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("170.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.k (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: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.121 |
Dual form | 170.2.k.a.111.2 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.52334 | − | 0.630986i | 0.879498 | − | 0.364300i | 0.103196 | − | 0.994661i | \(-0.467093\pi\) |
0.776302 | + | 0.630361i | \(0.217093\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.382683 | + | 0.923880i | 0.171141 | + | 0.413171i | ||||
\(6\) | −1.52334 | − | 0.630986i | −0.621899 | − | 0.257599i | ||||
\(7\) | 1.24830 | − | 3.01367i | 0.471814 | − | 1.13906i | −0.491547 | − | 0.870851i | \(-0.663568\pi\) |
0.963361 | − | 0.268209i | \(-0.0864317\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −0.198912 | + | 0.198912i | −0.0663041 | + | 0.0663041i | ||||
\(10\) | 0.382683 | − | 0.923880i | 0.121015 | − | 0.292156i | ||||
\(11\) | 3.58012 | + | 1.48294i | 1.07945 | + | 0.447122i | 0.850316 | − | 0.526273i | \(-0.176411\pi\) |
0.229133 | + | 0.973395i | \(0.426411\pi\) | |||||||
\(12\) | 0.630986 | + | 1.52334i | 0.182150 | + | 0.439749i | ||||
\(13\) | − | 0.386874i | − | 0.107300i | −0.998560 | − | 0.0536498i | \(-0.982915\pi\) | ||
0.998560 | − | 0.0536498i | \(-0.0170855\pi\) | |||||||
\(14\) | −3.01367 | + | 1.24830i | −0.805437 | + | 0.333623i | ||||
\(15\) | 1.16591 | + | 1.16591i | 0.301037 | + | 0.301037i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.76118 | − | 1.68925i | −0.912219 | − | 0.409702i | ||||
\(18\) | 0.281305 | 0.0663041 | ||||||||
\(19\) | −3.89715 | − | 3.89715i | −0.894067 | − | 0.894067i | 0.100836 | − | 0.994903i | \(-0.467848\pi\) |
−0.994903 | + | 0.100836i | \(0.967848\pi\) | |||||||
\(20\) | −0.923880 | + | 0.382683i | −0.206586 | + | 0.0855706i | ||||
\(21\) | − | 5.37849i | − | 1.17368i | ||||||
\(22\) | −1.48294 | − | 3.58012i | −0.316163 | − | 0.763285i | ||||
\(23\) | 6.91082 | + | 2.86256i | 1.44101 | + | 0.596884i | 0.960042 | − | 0.279857i | \(-0.0902869\pi\) |
0.480964 | + | 0.876741i | \(0.340287\pi\) | |||||||
\(24\) | 0.630986 | − | 1.52334i | 0.128800 | − | 0.310950i | ||||
\(25\) | −0.707107 | + | 0.707107i | −0.141421 | + | 0.141421i | ||||
\(26\) | −0.273561 | + | 0.273561i | −0.0536498 | + | 0.0536498i | ||||
\(27\) | −2.07046 | + | 4.99853i | −0.398460 | + | 0.961967i | ||||
\(28\) | 3.01367 | + | 1.24830i | 0.569530 | + | 0.235907i | ||||
\(29\) | 0.192641 | + | 0.465076i | 0.0357725 | + | 0.0863624i | 0.940756 | − | 0.339084i | \(-0.110117\pi\) |
−0.904984 | + | 0.425446i | \(0.860117\pi\) | |||||||
\(30\) | − | 1.64885i | − | 0.301037i | ||||||
\(31\) | −10.2715 | + | 4.25457i | −1.84481 | + | 0.764144i | −0.900781 | + | 0.434274i | \(0.857005\pi\) |
−0.944026 | + | 0.329871i | \(0.892995\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 6.38944 | 1.11226 | ||||||||
\(34\) | 1.46508 | + | 3.85403i | 0.251258 | + | 0.660961i | ||||
\(35\) | 3.26197 | 0.551374 | ||||||||
\(36\) | −0.198912 | − | 0.198912i | −0.0331521 | − | 0.0331521i | ||||
\(37\) | 1.12132 | − | 0.464466i | 0.184344 | − | 0.0763578i | −0.288602 | − | 0.957449i | \(-0.593191\pi\) |
0.472946 | + | 0.881091i | \(0.343191\pi\) | |||||||
\(38\) | 5.51140i | 0.894067i | ||||||||
\(39\) | −0.244112 | − | 0.589339i | −0.0390892 | − | 0.0943698i | ||||
\(40\) | 0.923880 | + | 0.382683i | 0.146078 | + | 0.0605076i | ||||
\(41\) | −3.32023 | + | 8.01575i | −0.518533 | + | 1.25185i | 0.420271 | + | 0.907399i | \(0.361935\pi\) |
−0.938804 | + | 0.344451i | \(0.888065\pi\) | |||||||
\(42\) | −3.80317 | + | 3.80317i | −0.586842 | + | 0.586842i | ||||
\(43\) | 0.190043 | − | 0.190043i | 0.0289813 | − | 0.0289813i | −0.692468 | − | 0.721449i | \(-0.743476\pi\) |
0.721449 | + | 0.692468i | \(0.243476\pi\) | |||||||
\(44\) | −1.48294 | + | 3.58012i | −0.223561 | + | 0.539724i | ||||
\(45\) | −0.259892 | − | 0.107651i | −0.0387423 | − | 0.0160476i | ||||
\(46\) | −2.86256 | − | 6.91082i | −0.422061 | − | 1.01894i | ||||
\(47\) | 5.12906i | 0.748151i | 0.927398 | + | 0.374075i | \(0.122040\pi\) | ||||
−0.927398 | + | 0.374075i | \(0.877960\pi\) | |||||||
\(48\) | −1.52334 | + | 0.630986i | −0.219875 | + | 0.0910750i | ||||
\(49\) | −2.57420 | − | 2.57420i | −0.367743 | − | 0.367743i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.79543 | − | 0.200039i | −0.951550 | − | 0.0280110i | ||||
\(52\) | 0.386874 | 0.0536498 | ||||||||
\(53\) | −0.609919 | − | 0.609919i | −0.0837788 | − | 0.0837788i | 0.663976 | − | 0.747754i | \(-0.268868\pi\) |
−0.747754 | + | 0.663976i | \(0.768868\pi\) | |||||||
\(54\) | 4.99853 | − | 2.07046i | 0.680214 | − | 0.281754i | ||||
\(55\) | 3.87510i | 0.522518i | ||||||||
\(56\) | −1.24830 | − | 3.01367i | −0.166811 | − | 0.402719i | ||||
\(57\) | −8.39572 | − | 3.47762i | −1.11204 | − | 0.460622i | ||||
\(58\) | 0.192641 | − | 0.465076i | 0.0252950 | − | 0.0610674i | ||||
\(59\) | −6.03300 | + | 6.03300i | −0.785430 | + | 0.785430i | −0.980741 | − | 0.195311i | \(-0.937428\pi\) |
0.195311 | + | 0.980741i | \(0.437428\pi\) | |||||||
\(60\) | −1.16591 | + | 1.16591i | −0.150518 | + | 0.150518i | ||||
\(61\) | 2.59120 | − | 6.25570i | 0.331769 | − | 0.800960i | −0.666683 | − | 0.745341i | \(-0.732287\pi\) |
0.998452 | − | 0.0556194i | \(-0.0177133\pi\) | |||||||
\(62\) | 10.2715 | + | 4.25457i | 1.30448 | + | 0.540332i | ||||
\(63\) | 0.351153 | + | 0.847759i | 0.0442412 | + | 0.106808i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0.357425 | − | 0.148050i | 0.0443331 | − | 0.0183634i | ||||
\(66\) | −4.51802 | − | 4.51802i | −0.556130 | − | 0.556130i | ||||
\(67\) | −2.38009 | −0.290774 | −0.145387 | − | 0.989375i | \(-0.546443\pi\) | ||||
−0.145387 | + | 0.989375i | \(0.546443\pi\) | |||||||
\(68\) | 1.68925 | − | 3.76118i | 0.204851 | − | 0.456110i | ||||
\(69\) | 12.3337 | 1.48481 | ||||||||
\(70\) | −2.30656 | − | 2.30656i | −0.275687 | − | 0.275687i | ||||
\(71\) | 8.21885 | − | 3.40436i | 0.975398 | − | 0.404023i | 0.162679 | − | 0.986679i | \(-0.447986\pi\) |
0.812719 | + | 0.582656i | \(0.197986\pi\) | |||||||
\(72\) | 0.281305i | 0.0331521i | ||||||||
\(73\) | −2.69971 | − | 6.51767i | −0.315977 | − | 0.762836i | −0.999460 | − | 0.0328692i | \(-0.989536\pi\) |
0.683483 | − | 0.729967i | \(-0.260464\pi\) | |||||||
\(74\) | −1.12132 | − | 0.464466i | −0.130351 | − | 0.0539931i | ||||
\(75\) | −0.630986 | + | 1.52334i | −0.0728600 | + | 0.175900i | ||||
\(76\) | 3.89715 | − | 3.89715i | 0.447034 | − | 0.447034i | ||||
\(77\) | 8.93816 | − | 8.93816i | 1.01860 | − | 1.01860i | ||||
\(78\) | −0.244112 | + | 0.589339i | −0.0276403 | + | 0.0667295i | ||||
\(79\) | 4.55215 | + | 1.88556i | 0.512157 | + | 0.212142i | 0.623768 | − | 0.781610i | \(-0.285601\pi\) |
−0.111611 | + | 0.993752i | \(0.535601\pi\) | |||||||
\(80\) | −0.382683 | − | 0.923880i | −0.0427853 | − | 0.103293i | ||||
\(81\) | 8.07695i | 0.897439i | ||||||||
\(82\) | 8.01575 | − | 3.32023i | 0.885192 | − | 0.366658i | ||||
\(83\) | −4.21738 | − | 4.21738i | −0.462918 | − | 0.462918i | 0.436693 | − | 0.899611i | \(-0.356150\pi\) |
−0.899611 | + | 0.436693i | \(0.856150\pi\) | |||||||
\(84\) | 5.37849 | 0.586842 | ||||||||
\(85\) | 0.121320 | − | 4.12132i | 0.0131590 | − | 0.447020i | ||||
\(86\) | −0.268761 | −0.0289813 | ||||||||
\(87\) | 0.586913 | + | 0.586913i | 0.0629236 | + | 0.0629236i | ||||
\(88\) | 3.58012 | − | 1.48294i | 0.381643 | − | 0.158082i | ||||
\(89\) | − | 12.0479i | − | 1.27707i | −0.769591 | − | 0.638537i | \(-0.779540\pi\) | ||
0.769591 | − | 0.638537i | \(-0.220460\pi\) | |||||||
\(90\) | 0.107651 | + | 0.259892i | 0.0113474 | + | 0.0273950i | ||||
\(91\) | −1.16591 | − | 0.482936i | −0.122221 | − | 0.0506255i | ||||
\(92\) | −2.86256 | + | 6.91082i | −0.298442 | + | 0.720503i | ||||
\(93\) | −12.9623 | + | 12.9623i | −1.34413 | + | 1.34413i | ||||
\(94\) | 3.62680 | − | 3.62680i | 0.374075 | − | 0.374075i | ||||
\(95\) | 2.10912 | − | 5.09187i | 0.216391 | − | 0.522415i | ||||
\(96\) | 1.52334 | + | 0.630986i | 0.155475 | + | 0.0643998i | ||||
\(97\) | −4.46961 | − | 10.7906i | −0.453820 | − | 1.09562i | −0.970858 | − | 0.239656i | \(-0.922965\pi\) |
0.517037 | − | 0.855963i | \(-0.327035\pi\) | |||||||
\(98\) | 3.64047i | 0.367743i | ||||||||
\(99\) | −1.00711 | + | 0.417157i | −0.101218 | + | 0.0419258i | ||||
\(100\) | −0.707107 | − | 0.707107i | −0.0707107 | − | 0.0707107i | ||||
\(101\) | −5.24718 | −0.522114 | −0.261057 | − | 0.965323i | \(-0.584071\pi\) | ||||
−0.261057 | + | 0.965323i | \(0.584071\pi\) | |||||||
\(102\) | 4.66364 | + | 4.94654i | 0.461769 | + | 0.489780i | ||||
\(103\) | 16.8149 | 1.65682 | 0.828408 | − | 0.560125i | \(-0.189247\pi\) | ||||
0.828408 | + | 0.560125i | \(0.189247\pi\) | |||||||
\(104\) | −0.273561 | − | 0.273561i | −0.0268249 | − | 0.0268249i | ||||
\(105\) | 4.96908 | − | 2.05826i | 0.484932 | − | 0.200866i | ||||
\(106\) | 0.862555i | 0.0837788i | ||||||||
\(107\) | −3.91601 | − | 9.45410i | −0.378575 | − | 0.913962i | −0.992233 | − | 0.124390i | \(-0.960303\pi\) |
0.613658 | − | 0.789572i | \(-0.289697\pi\) | |||||||
\(108\) | −4.99853 | − | 2.07046i | −0.480984 | − | 0.199230i | ||||
\(109\) | 4.07387 | − | 9.83519i | 0.390206 | − | 0.942040i | −0.599689 | − | 0.800233i | \(-0.704709\pi\) |
0.989894 | − | 0.141807i | \(-0.0452911\pi\) | |||||||
\(110\) | 2.74011 | − | 2.74011i | 0.261259 | − | 0.261259i | ||||
\(111\) | 1.41508 | − | 1.41508i | 0.134313 | − | 0.134313i | ||||
\(112\) | −1.24830 | + | 3.01367i | −0.117954 | + | 0.284765i | ||||
\(113\) | −10.9369 | − | 4.53022i | −1.02886 | − | 0.426167i | −0.196558 | − | 0.980492i | \(-0.562976\pi\) |
−0.832300 | + | 0.554325i | \(0.812976\pi\) | |||||||
\(114\) | 3.47762 | + | 8.39572i | 0.325709 | + | 0.786331i | ||||
\(115\) | 7.48022i | 0.697534i | ||||||||
\(116\) | −0.465076 | + | 0.192641i | −0.0431812 | + | 0.0178862i | ||||
\(117\) | 0.0769540 | + | 0.0769540i | 0.00711440 | + | 0.00711440i | ||||
\(118\) | 8.53195 | 0.785430 | ||||||||
\(119\) | −9.78592 | + | 9.22625i | −0.897074 | + | 0.845769i | ||||
\(120\) | 1.64885 | 0.150518 | ||||||||
\(121\) | 2.84002 | + | 2.84002i | 0.258183 | + | 0.258183i | ||||
\(122\) | −6.25570 | + | 2.59120i | −0.566365 | + | 0.234596i | ||||
\(123\) | 14.3057i | 1.28990i | ||||||||
\(124\) | −4.25457 | − | 10.2715i | −0.382072 | − | 0.922404i | ||||
\(125\) | −0.923880 | − | 0.382683i | −0.0826343 | − | 0.0342282i | ||||
\(126\) | 0.351153 | − | 0.847759i | 0.0312832 | − | 0.0755244i | ||||
\(127\) | −2.97116 | + | 2.97116i | −0.263648 | + | 0.263648i | −0.826534 | − | 0.562886i | \(-0.809691\pi\) |
0.562886 | + | 0.826534i | \(0.309691\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0.169585 | − | 0.409413i | 0.0149311 | − | 0.0360468i | ||||
\(130\) | −0.357425 | − | 0.148050i | −0.0313482 | − | 0.0129849i | ||||
\(131\) | 7.73878 | + | 18.6831i | 0.676140 | + | 1.63235i | 0.770984 | + | 0.636855i | \(0.219765\pi\) |
−0.0948433 | + | 0.995492i | \(0.530235\pi\) | |||||||
\(132\) | 6.38944i | 0.556130i | ||||||||
\(133\) | −16.6095 | + | 6.87990i | −1.44023 | + | 0.596563i | ||||
\(134\) | 1.68297 | + | 1.68297i | 0.145387 | + | 0.145387i | ||||
\(135\) | −5.41037 | −0.465650 | ||||||||
\(136\) | −3.85403 | + | 1.46508i | −0.330480 | + | 0.125629i | ||||
\(137\) | 9.83591 | 0.840338 | 0.420169 | − | 0.907446i | \(-0.361971\pi\) | ||||
0.420169 | + | 0.907446i | \(0.361971\pi\) | |||||||
\(138\) | −8.72126 | − | 8.72126i | −0.742403 | − | 0.742403i | ||||
\(139\) | −1.15496 | + | 0.478400i | −0.0979624 | + | 0.0405774i | −0.431126 | − | 0.902292i | \(-0.641884\pi\) |
0.333164 | + | 0.942869i | \(0.391884\pi\) | |||||||
\(140\) | 3.26197i | 0.275687i | ||||||||
\(141\) | 3.23637 | + | 7.81329i | 0.272551 | + | 0.657997i | ||||
\(142\) | −8.21885 | − | 3.40436i | −0.689711 | − | 0.285688i | ||||
\(143\) | 0.573709 | − | 1.38506i | 0.0479760 | − | 0.115824i | ||||
\(144\) | 0.198912 | − | 0.198912i | 0.0165760 | − | 0.0165760i | ||||
\(145\) | −0.355953 | + | 0.355953i | −0.0295603 | + | 0.0295603i | ||||
\(146\) | −2.69971 | + | 6.51767i | −0.223429 | + | 0.539406i | ||||
\(147\) | −5.54565 | − | 2.29708i | −0.457398 | − | 0.189460i | ||||
\(148\) | 0.464466 | + | 1.12132i | 0.0381789 | + | 0.0921720i | ||||
\(149\) | 9.68125i | 0.793119i | 0.918009 | + | 0.396559i | \(0.129796\pi\) | ||||
−0.918009 | + | 0.396559i | \(0.870204\pi\) | |||||||
\(150\) | 1.52334 | − | 0.630986i | 0.124380 | − | 0.0515198i | ||||
\(151\) | 7.70193 | + | 7.70193i | 0.626774 | + | 0.626774i | 0.947255 | − | 0.320481i | \(-0.103844\pi\) |
−0.320481 | + | 0.947255i | \(0.603844\pi\) | |||||||
\(152\) | −5.51140 | −0.447034 | ||||||||
\(153\) | 1.08416 | − | 0.412132i | 0.0876489 | − | 0.0333189i | ||||
\(154\) | −12.6405 | −1.01860 | ||||||||
\(155\) | −7.86143 | − | 7.86143i | −0.631445 | − | 0.631445i | ||||
\(156\) | 0.589339 | − | 0.244112i | 0.0471849 | − | 0.0195446i | ||||
\(157\) | 7.93497i | 0.633280i | 0.948546 | + | 0.316640i | \(0.102555\pi\) | ||||
−0.948546 | + | 0.316640i | \(0.897445\pi\) | |||||||
\(158\) | −1.88556 | − | 4.55215i | −0.150007 | − | 0.362149i | ||||
\(159\) | −1.31396 | − | 0.544260i | −0.104204 | − | 0.0431627i | ||||
\(160\) | −0.382683 | + | 0.923880i | −0.0302538 | + | 0.0730391i | ||||
\(161\) | 17.2536 | − | 17.2536i | 1.35977 | − | 1.35977i | ||||
\(162\) | 5.71127 | − | 5.71127i | 0.448720 | − | 0.448720i | ||||
\(163\) | 8.35691 | − | 20.1754i | 0.654564 | − | 1.58026i | −0.151520 | − | 0.988454i | \(-0.548417\pi\) |
0.806083 | − | 0.591802i | \(-0.201583\pi\) | |||||||
\(164\) | −8.01575 | − | 3.32023i | −0.625925 | − | 0.259267i | ||||
\(165\) | 2.44513 | + | 5.90308i | 0.190353 | + | 0.459554i | ||||
\(166\) | 5.96428i | 0.462918i | ||||||||
\(167\) | 17.9066 | − | 7.41716i | 1.38565 | − | 0.573957i | 0.439667 | − | 0.898161i | \(-0.355096\pi\) |
0.945987 | + | 0.324204i | \(0.105096\pi\) | |||||||
\(168\) | −3.80317 | − | 3.80317i | −0.293421 | − | 0.293421i | ||||
\(169\) | 12.8503 | 0.988487 | ||||||||
\(170\) | −3.00000 | + | 2.82843i | −0.230089 | + | 0.216930i | ||||
\(171\) | 1.55038 | 0.118561 | ||||||||
\(172\) | 0.190043 | + | 0.190043i | 0.0144906 | + | 0.0144906i | ||||
\(173\) | −11.5551 | + | 4.78629i | −0.878520 | + | 0.363895i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
−0.102598 | + | 0.994723i | \(0.532715\pi\) | |||||||
\(174\) | − | 0.830020i | − | 0.0629236i | ||||||
\(175\) | 1.24830 | + | 3.01367i | 0.0943628 | + | 0.227812i | ||||
\(176\) | −3.58012 | − | 1.48294i | −0.269862 | − | 0.111781i | ||||
\(177\) | −5.38355 | + | 12.9970i | −0.404652 | + | 0.976916i | ||||
\(178\) | −8.51915 | + | 8.51915i | −0.638537 | + | 0.638537i | ||||
\(179\) | −12.1689 | + | 12.1689i | −0.909550 | + | 0.909550i | −0.996236 | − | 0.0866859i | \(-0.972372\pi\) |
0.0866859 | + | 0.996236i | \(0.472372\pi\) | |||||||
\(180\) | 0.107651 | − | 0.259892i | 0.00802380 | − | 0.0193712i | ||||
\(181\) | 19.4600 | + | 8.06061i | 1.44645 | + | 0.599140i | 0.961353 | − | 0.275319i | \(-0.0887835\pi\) |
0.485099 | + | 0.874459i | \(0.338783\pi\) | |||||||
\(182\) | 0.482936 | + | 1.16591i | 0.0357976 | + | 0.0864230i | ||||
\(183\) | − | 11.1645i | − | 0.825307i | ||||||
\(184\) | 6.91082 | − | 2.86256i | 0.509472 | − | 0.211030i | ||||
\(185\) | 0.858221 | + | 0.858221i | 0.0630977 | + | 0.0630977i | ||||
\(186\) | 18.3314 | 1.34413 | ||||||||
\(187\) | −10.9604 | − | 11.6253i | −0.801506 | − | 0.850126i | ||||
\(188\) | −5.12906 | −0.374075 | ||||||||
\(189\) | 12.4794 | + | 12.4794i | 0.907740 | + | 0.907740i | ||||
\(190\) | −5.09187 | + | 2.10912i | −0.369403 | + | 0.153012i | ||||
\(191\) | − | 14.2761i | − | 1.03298i | −0.856292 | − | 0.516491i | \(-0.827238\pi\) | ||
0.856292 | − | 0.516491i | \(-0.172762\pi\) | |||||||
\(192\) | −0.630986 | − | 1.52334i | −0.0455375 | − | 0.109937i | ||||
\(193\) | −19.1829 | − | 7.94581i | −1.38081 | − | 0.571952i | −0.436115 | − | 0.899891i | \(-0.643646\pi\) |
−0.944699 | + | 0.327939i | \(0.893646\pi\) | |||||||
\(194\) | −4.46961 | + | 10.7906i | −0.320899 | + | 0.774720i | ||||
\(195\) | 0.451061 | − | 0.451061i | 0.0323011 | − | 0.0323011i | ||||
\(196\) | 2.57420 | − | 2.57420i | 0.183871 | − | 0.183871i | ||||
\(197\) | 5.95147 | − | 14.3681i | 0.424025 | − | 1.02369i | −0.557123 | − | 0.830430i | \(-0.688095\pi\) |
0.981148 | − | 0.193257i | \(-0.0619050\pi\) | |||||||
\(198\) | 1.00711 | + | 0.417157i | 0.0715719 | + | 0.0296460i | ||||
\(199\) | 0.959134 | + | 2.31555i | 0.0679912 | + | 0.164145i | 0.954222 | − | 0.299098i | \(-0.0966857\pi\) |
−0.886231 | + | 0.463243i | \(0.846686\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −3.62567 | + | 1.50180i | −0.255735 | + | 0.105929i | ||||
\(202\) | 3.71031 | + | 3.71031i | 0.261057 | + | 0.261057i | ||||
\(203\) | 1.64206 | 0.115250 | ||||||||
\(204\) | 0.200039 | − | 6.79543i | 0.0140055 | − | 0.475775i | ||||
\(205\) | −8.67619 | −0.605971 | ||||||||
\(206\) | −11.8899 | − | 11.8899i | −0.828408 | − | 0.828408i | ||||
\(207\) | −1.94405 | + | 0.805250i | −0.135120 | + | 0.0559687i | ||||
\(208\) | 0.386874i | 0.0268249i | ||||||||
\(209\) | −8.17306 | − | 19.7315i | −0.565342 | − | 1.36486i | ||||
\(210\) | −4.96908 | − | 2.05826i | −0.342899 | − | 0.142033i | ||||
\(211\) | −4.86897 | + | 11.7547i | −0.335194 | + | 0.809229i | 0.662969 | + | 0.748646i | \(0.269296\pi\) |
−0.998163 | + | 0.0605828i | \(0.980704\pi\) | |||||||
\(212\) | 0.609919 | − | 0.609919i | 0.0418894 | − | 0.0418894i | ||||
\(213\) | 10.3720 | − | 10.3720i | 0.710676 | − | 0.710676i | ||||
\(214\) | −3.91601 | + | 9.45410i | −0.267693 | + | 0.646269i | ||||
\(215\) | 0.248303 | + | 0.102850i | 0.0169341 | + | 0.00701434i | ||||
\(216\) | 2.07046 | + | 4.99853i | 0.140877 | + | 0.340107i | ||||
\(217\) | 36.2658i | 2.46188i | ||||||||
\(218\) | −9.83519 | + | 4.07387i | −0.666123 | + | 0.275917i | ||||
\(219\) | −8.22513 | − | 8.22513i | −0.555802 | − | 0.555802i | ||||
\(220\) | −3.87510 | −0.261259 | ||||||||
\(221\) | −0.653526 | + | 1.45510i | −0.0439609 | + | 0.0978807i | ||||
\(222\) | −2.00122 | −0.134313 | ||||||||
\(223\) | −0.243767 | − | 0.243767i | −0.0163238 | − | 0.0163238i | 0.698898 | − | 0.715222i | \(-0.253674\pi\) |
−0.715222 | + | 0.698898i | \(0.753674\pi\) | |||||||
\(224\) | 3.01367 | − | 1.24830i | 0.201359 | − | 0.0834057i | ||||
\(225\) | − | 0.281305i | − | 0.0187536i | ||||||
\(226\) | 4.53022 | + | 10.9369i | 0.301346 | + | 0.727513i | ||||
\(227\) | 14.2037 | + | 5.88336i | 0.942732 | + | 0.390492i | 0.800494 | − | 0.599340i | \(-0.204570\pi\) |
0.142237 | + | 0.989833i | \(0.454570\pi\) | |||||||
\(228\) | 3.47762 | − | 8.39572i | 0.230311 | − | 0.556020i | ||||
\(229\) | 4.74517 | − | 4.74517i | 0.313570 | − | 0.313570i | −0.532721 | − | 0.846291i | \(-0.678831\pi\) |
0.846291 | + | 0.532721i | \(0.178831\pi\) | |||||||
\(230\) | 5.28931 | − | 5.28931i | 0.348767 | − | 0.348767i | ||||
\(231\) | 7.97596 | − | 19.2557i | 0.524780 | − | 1.26693i | ||||
\(232\) | 0.465076 | + | 0.192641i | 0.0305337 | + | 0.0126475i | ||||
\(233\) | 0.594799 | + | 1.43597i | 0.0389666 | + | 0.0940736i | 0.942165 | − | 0.335150i | \(-0.108787\pi\) |
−0.903198 | + | 0.429224i | \(0.858787\pi\) | |||||||
\(234\) | − | 0.108829i | − | 0.00711440i | ||||||
\(235\) | −4.73864 | + | 1.96281i | −0.309115 | + | 0.128039i | ||||
\(236\) | −6.03300 | − | 6.03300i | −0.392715 | − | 0.392715i | ||||
\(237\) | 8.12421 | 0.527724 | ||||||||
\(238\) | 13.4436 | + | 0.395744i | 0.871421 | + | 0.0256523i | ||||
\(239\) | 11.7012 | 0.756890 | 0.378445 | − | 0.925624i | \(-0.376459\pi\) | ||||
0.378445 | + | 0.925624i | \(0.376459\pi\) | |||||||
\(240\) | −1.16591 | − | 1.16591i | −0.0752592 | − | 0.0752592i | ||||
\(241\) | −25.2129 | + | 10.4435i | −1.62411 | + | 0.672728i | −0.994553 | − | 0.104228i | \(-0.966763\pi\) |
−0.629555 | + | 0.776956i | \(0.716763\pi\) | |||||||
\(242\) | − | 4.01639i | − | 0.258183i | ||||||
\(243\) | −1.11493 | − | 2.69167i | −0.0715226 | − | 0.172671i | ||||
\(244\) | 6.25570 | + | 2.59120i | 0.400480 | + | 0.165884i | ||||
\(245\) | 1.39315 | − | 3.36335i | 0.0890048 | − | 0.214877i | ||||
\(246\) | 10.1157 | − | 10.1157i | 0.644951 | − | 0.644951i | ||||
\(247\) | −1.50771 | + | 1.50771i | −0.0959330 | + | 0.0959330i | ||||
\(248\) | −4.25457 | + | 10.2715i | −0.270166 | + | 0.652238i | ||||
\(249\) | −9.08560 | − | 3.76338i | −0.575776 | − | 0.238494i | ||||
\(250\) | 0.382683 | + | 0.923880i | 0.0242030 | + | 0.0584313i | ||||
\(251\) | − | 15.8596i | − | 1.00105i | −0.865723 | − | 0.500523i | \(-0.833141\pi\) | ||
0.865723 | − | 0.500523i | \(-0.166859\pi\) | |||||||
\(252\) | −0.847759 | + | 0.351153i | −0.0534038 | + | 0.0221206i | ||||
\(253\) | 20.4966 | + | 20.4966i | 1.28861 | + | 1.28861i | ||||
\(254\) | 4.20186 | 0.263648 | ||||||||
\(255\) | −2.41569 | − | 6.35471i | −0.151276 | − | 0.397947i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.9077 | + | 20.9077i | 1.30419 | + | 1.30419i | 0.925542 | + | 0.378645i | \(0.123610\pi\) |
0.378645 | + | 0.925542i | \(0.376390\pi\) | |||||||
\(258\) | −0.409413 | + | 0.169585i | −0.0254890 | + | 0.0105579i | ||||
\(259\) | − | 3.95908i | − | 0.246005i | ||||||
\(260\) | 0.148050 | + | 0.357425i | 0.00918169 | + | 0.0221666i | ||||
\(261\) | −0.130828 | − | 0.0541907i | −0.00809804 | − | 0.00335432i | ||||
\(262\) | 7.73878 | − | 18.6831i | 0.478103 | − | 1.15424i | ||||
\(263\) | 15.1865 | − | 15.1865i | 0.936437 | − | 0.936437i | −0.0616599 | − | 0.998097i | \(-0.519639\pi\) |
0.998097 | + | 0.0616599i | \(0.0196394\pi\) | |||||||
\(264\) | 4.51802 | − | 4.51802i | 0.278065 | − | 0.278065i | ||||
\(265\) | 0.330086 | − | 0.796897i | 0.0202770 | − | 0.0489530i | ||||
\(266\) | 16.6095 | + | 6.87990i | 1.01840 | + | 0.421834i | ||||
\(267\) | −7.60205 | − | 18.3530i | −0.465238 | − | 1.12318i | ||||
\(268\) | − | 2.38009i | − | 0.145387i | ||||||
\(269\) | −27.8132 | + | 11.5206i | −1.69580 | + | 0.702424i | −0.999877 | − | 0.0156895i | \(-0.995006\pi\) |
−0.695926 | + | 0.718114i | \(0.745006\pi\) | |||||||
\(270\) | 3.82571 | + | 3.82571i | 0.232825 | + | 0.232825i | ||||
\(271\) | 19.4876 | 1.18379 | 0.591893 | − | 0.806017i | \(-0.298381\pi\) | ||||
0.591893 | + | 0.806017i | \(0.298381\pi\) | |||||||
\(272\) | 3.76118 | + | 1.68925i | 0.228055 | + | 0.102426i | ||||
\(273\) | −2.08080 | −0.125936 | ||||||||
\(274\) | −6.95504 | − | 6.95504i | −0.420169 | − | 0.420169i | ||||
\(275\) | −3.58012 | + | 1.48294i | −0.215890 | + | 0.0894244i | ||||
\(276\) | 12.3337i | 0.742403i | ||||||||
\(277\) | −4.02214 | − | 9.71031i | −0.241667 | − | 0.583436i | 0.755781 | − | 0.654824i | \(-0.227257\pi\) |
−0.997449 | + | 0.0713877i | \(0.977257\pi\) | |||||||
\(278\) | 1.15496 | + | 0.478400i | 0.0692699 | + | 0.0286925i | ||||
\(279\) | 1.19683 | − | 2.88941i | 0.0716524 | − | 0.172984i | ||||
\(280\) | 2.30656 | − | 2.30656i | 0.137844 | − | 0.137844i | ||||
\(281\) | −1.46953 | + | 1.46953i | −0.0876648 | + | 0.0876648i | −0.749579 | − | 0.661915i | \(-0.769744\pi\) |
0.661915 | + | 0.749579i | \(0.269744\pi\) | |||||||
\(282\) | 3.23637 | − | 7.81329i | 0.192723 | − | 0.465274i | ||||
\(283\) | −21.5603 | − | 8.93056i | −1.28163 | − | 0.530867i | −0.365147 | − | 0.930950i | \(-0.618981\pi\) |
−0.916479 | + | 0.400083i | \(0.868981\pi\) | |||||||
\(284\) | 3.40436 | + | 8.21885i | 0.202012 | + | 0.487699i | ||||
\(285\) | − | 9.08746i | − | 0.538294i | ||||||
\(286\) | −1.38506 | + | 0.573709i | −0.0819002 | + | 0.0339242i | ||||
\(287\) | 20.0122 | + | 20.0122i | 1.18128 | + | 1.18128i | ||||
\(288\) | −0.281305 | −0.0165760 | ||||||||
\(289\) | 11.2929 | + | 12.7071i | 0.664288 | + | 0.747477i | ||||
\(290\) | 0.503394 | 0.0295603 | ||||||||
\(291\) | −13.6174 | − | 13.6174i | −0.798268 | − | 0.798268i | ||||
\(292\) | 6.51767 | − | 2.69971i | 0.381418 | − | 0.157989i | ||||
\(293\) | − | 3.46701i | − | 0.202545i | −0.994859 | − | 0.101273i | \(-0.967709\pi\) | ||
0.994859 | − | 0.101273i | \(-0.0322914\pi\) | |||||||
\(294\) | 2.29708 | + | 5.54565i | 0.133969 | + | 0.323429i | ||||
\(295\) | −7.88250 | − | 3.26504i | −0.458937 | − | 0.190098i | ||||
\(296\) | 0.464466 | − | 1.12132i | 0.0269965 | − | 0.0651754i | ||||
\(297\) | −14.8250 | + | 14.8250i | −0.860234 | + | 0.860234i | ||||
\(298\) | 6.84568 | − | 6.84568i | 0.396559 | − | 0.396559i | ||||
\(299\) | 1.10745 | − | 2.67362i | 0.0640454 | − | 0.154619i | ||||
\(300\) | −1.52334 | − | 0.630986i | −0.0879498 | − | 0.0364300i | ||||
\(301\) | −0.335495 | − | 0.809957i | −0.0193376 | − | 0.0466852i | ||||
\(302\) | − | 10.8922i | − | 0.626774i | ||||||
\(303\) | −7.99321 | + | 3.31090i | −0.459198 | + | 0.190206i | ||||
\(304\) | 3.89715 | + | 3.89715i | 0.223517 | + | 0.223517i | ||||
\(305\) | 6.77112 | 0.387713 | ||||||||
\(306\) | −1.05804 | − | 0.475193i | −0.0604839 | − | 0.0271650i | ||||
\(307\) | 0.0492977 | 0.00281357 | 0.00140678 | − | 0.999999i | \(-0.499552\pi\) | ||||
0.00140678 | + | 0.999999i | \(0.499552\pi\) | |||||||
\(308\) | 8.93816 | + | 8.93816i | 0.509299 | + | 0.509299i | ||||
\(309\) | 25.6147 | − | 10.6099i | 1.45717 | − | 0.603578i | ||||
\(310\) | 11.1177i | 0.631445i | ||||||||
\(311\) | −6.55093 | − | 15.8153i | −0.371469 | − | 0.896806i | −0.993502 | − | 0.113815i | \(-0.963693\pi\) |
0.622033 | − | 0.782991i | \(-0.286307\pi\) | |||||||
\(312\) | −0.589339 | − | 0.244112i | −0.0333648 | − | 0.0138201i | ||||
\(313\) | −5.89235 | + | 14.2254i | −0.333055 | + | 0.804067i | 0.665291 | + | 0.746584i | \(0.268307\pi\) |
−0.998347 | + | 0.0574826i | \(0.981693\pi\) | |||||||
\(314\) | 5.61087 | − | 5.61087i | 0.316640 | − | 0.316640i | ||||
\(315\) | −0.648847 | + | 0.648847i | −0.0365584 | + | 0.0365584i | ||||
\(316\) | −1.88556 | + | 4.55215i | −0.106071 | + | 0.256078i | ||||
\(317\) | −25.4894 | − | 10.5581i | −1.43163 | − | 0.593000i | −0.473876 | − | 0.880591i | \(-0.657146\pi\) |
−0.957753 | + | 0.287591i | \(0.907146\pi\) | |||||||
\(318\) | 0.544260 | + | 1.31396i | 0.0305206 | + | 0.0736833i | ||||
\(319\) | 1.95070i | 0.109218i | ||||||||
\(320\) | 0.923880 | − | 0.382683i | 0.0516464 | − | 0.0213927i | ||||
\(321\) | −11.9308 | − | 11.9308i | −0.665913 | − | 0.665913i | ||||
\(322\) | −24.4003 | −1.35977 | ||||||||
\(323\) | 8.07462 | + | 21.2411i | 0.449284 | + | 1.18189i | ||||
\(324\) | −8.07695 | −0.448720 | ||||||||
\(325\) | 0.273561 | + | 0.273561i | 0.0151744 | + | 0.0151744i | ||||
\(326\) | −20.1754 | + | 8.35691i | −1.11741 | + | 0.462846i | ||||
\(327\) | − | 17.5528i | − | 0.970675i | ||||||
\(328\) | 3.32023 | + | 8.01575i | 0.183329 | + | 0.442596i | ||||
\(329\) | 15.4573 | + | 6.40262i | 0.852189 | + | 0.352988i | ||||
\(330\) | 2.44513 | − | 5.90308i | 0.134600 | − | 0.324954i | ||||
\(331\) | −0.548939 | + | 0.548939i | −0.0301724 | + | 0.0301724i | −0.722032 | − | 0.691860i | \(-0.756792\pi\) |
0.691860 | + | 0.722032i | \(0.256792\pi\) | |||||||
\(332\) | 4.21738 | − | 4.21738i | 0.231459 | − | 0.231459i | ||||
\(333\) | −0.130656 | + | 0.315433i | −0.00715993 | + | 0.0172856i | ||||
\(334\) | −17.9066 | − | 7.41716i | −0.979806 | − | 0.405849i | ||||
\(335\) | −0.910819 | − | 2.19891i | −0.0497634 | − | 0.120139i | ||||
\(336\) | 5.37849i | 0.293421i | ||||||||
\(337\) | 25.0517 | − | 10.3768i | 1.36465 | − | 0.565258i | 0.424320 | − | 0.905512i | \(-0.360513\pi\) |
0.940333 | + | 0.340254i | \(0.110513\pi\) | |||||||
\(338\) | −9.08655 | − | 9.08655i | −0.494243 | − | 0.494243i | ||||
\(339\) | −19.5191 | −1.06013 | ||||||||
\(340\) | 4.12132 | + | 0.121320i | 0.223510 | + | 0.00657952i | ||||
\(341\) | −43.0823 | −2.33304 | ||||||||
\(342\) | −1.09629 | − | 1.09629i | −0.0592804 | − | 0.0592804i | ||||
\(343\) | 10.1245 | − | 4.19372i | 0.546673 | − | 0.226439i | ||||
\(344\) | − | 0.268761i | − | 0.0144906i | ||||||
\(345\) | 4.71991 | + | 11.3949i | 0.254112 | + | 0.613480i | ||||
\(346\) | 11.5551 | + | 4.78629i | 0.621208 | + | 0.257313i | ||||
\(347\) | −8.07218 | + | 19.4880i | −0.433337 | + | 1.04617i | 0.544867 | + | 0.838523i | \(0.316580\pi\) |
−0.978204 | + | 0.207646i | \(0.933420\pi\) | |||||||
\(348\) | −0.586913 | + | 0.586913i | −0.0314618 | + | 0.0314618i | ||||
\(349\) | −9.17504 | + | 9.17504i | −0.491129 | + | 0.491129i | −0.908662 | − | 0.417533i | \(-0.862895\pi\) |
0.417533 | + | 0.908662i | \(0.362895\pi\) | |||||||
\(350\) | 1.24830 | − | 3.01367i | 0.0667246 | − | 0.161087i | ||||
\(351\) | 1.93380 | + | 0.801007i | 0.103219 | + | 0.0427546i | ||||
\(352\) | 1.48294 | + | 3.58012i | 0.0790408 | + | 0.190821i | ||||
\(353\) | − | 15.7415i | − | 0.837837i | −0.908024 | − | 0.418919i | \(-0.862409\pi\) | ||
0.908024 | − | 0.418919i | \(-0.137591\pi\) | |||||||
\(354\) | 12.9970 | − | 5.38355i | 0.690784 | − | 0.286132i | ||||
\(355\) | 6.29044 | + | 6.29044i | 0.333862 | + | 0.333862i | ||||
\(356\) | 12.0479 | 0.638537 | ||||||||
\(357\) | −9.08560 | + | 20.2295i | −0.480861 | + | 1.07066i | ||||
\(358\) | 17.2095 | 0.909550 | ||||||||
\(359\) | −3.09805 | − | 3.09805i | −0.163509 | − | 0.163509i | 0.620610 | − | 0.784119i | \(-0.286885\pi\) |
−0.784119 | + | 0.620610i | \(0.786885\pi\) | |||||||
\(360\) | −0.259892 | + | 0.107651i | −0.0136975 | + | 0.00567368i | ||||
\(361\) | 11.3755i | 0.598713i | ||||||||
\(362\) | −8.06061 | − | 19.4600i | −0.423656 | − | 1.02280i | ||||
\(363\) | 6.11831 | + | 2.53429i | 0.321128 | + | 0.133016i | ||||
\(364\) | 0.482936 | − | 1.16591i | 0.0253127 | − | 0.0611103i | ||||
\(365\) | 4.98841 | − | 4.98841i | 0.261105 | − | 0.261105i | ||||
\(366\) | −7.89452 | + | 7.89452i | −0.412653 | + | 0.412653i | ||||
\(367\) | −8.40289 | + | 20.2864i | −0.438627 | + | 1.05894i | 0.537796 | + | 0.843075i | \(0.319257\pi\) |
−0.976423 | + | 0.215865i | \(0.930743\pi\) | |||||||
\(368\) | −6.91082 | − | 2.86256i | −0.360251 | − | 0.149221i | ||||
\(369\) | −0.933997 | − | 2.25487i | −0.0486219 | − | 0.117384i | ||||
\(370\) | − | 1.21371i | − | 0.0630977i | ||||||
\(371\) | −2.59946 | + | 1.07673i | −0.134957 | + | 0.0559010i | ||||
\(372\) | −12.9623 | − | 12.9623i | −0.672063 | − | 0.672063i | ||||
\(373\) | −34.7421 | −1.79888 | −0.899440 | − | 0.437045i | \(-0.856025\pi\) | ||||
−0.899440 | + | 0.437045i | \(0.856025\pi\) | |||||||
\(374\) | −0.470128 | + | 15.9705i | −0.0243098 | + | 0.825816i | ||||
\(375\) | −1.64885 | −0.0851461 | ||||||||
\(376\) | 3.62680 | + | 3.62680i | 0.187038 | + | 0.187038i | ||||
\(377\) | 0.179926 | − | 0.0745277i | 0.00926665 | − | 0.00383837i | ||||
\(378\) | − | 17.6485i | − | 0.907740i | ||||||
\(379\) | 4.06600 | + | 9.81620i | 0.208857 | + | 0.504224i | 0.993244 | − | 0.116047i | \(-0.0370224\pi\) |
−0.784387 | + | 0.620272i | \(0.787022\pi\) | |||||||
\(380\) | 5.09187 | + | 2.10912i | 0.261207 | + | 0.108196i | ||||
\(381\) | −2.65131 | + | 6.40084i | −0.135831 | + | 0.327925i | ||||
\(382\) | −10.0947 | + | 10.0947i | −0.516491 | + | 0.516491i | ||||
\(383\) | −3.92646 | + | 3.92646i | −0.200633 | + | 0.200633i | −0.800271 | − | 0.599638i | \(-0.795311\pi\) |
0.599638 | + | 0.800271i | \(0.295311\pi\) | |||||||
\(384\) | −0.630986 | + | 1.52334i | −0.0321999 | + | 0.0777374i | ||||
\(385\) | 11.6783 | + | 4.83730i | 0.595180 | + | 0.246531i | ||||
\(386\) | 7.94581 | + | 19.1829i | 0.404431 | + | 0.976383i | ||||
\(387\) | 0.0756037i | 0.00384315i | ||||||||
\(388\) | 10.7906 | − | 4.46961i | 0.547810 | − | 0.226910i | ||||
\(389\) | −6.26679 | − | 6.26679i | −0.317739 | − | 0.317739i | 0.530159 | − | 0.847898i | \(-0.322132\pi\) |
−0.847898 | + | 0.530159i | \(0.822132\pi\) | |||||||
\(390\) | −0.637896 | −0.0323011 | ||||||||
\(391\) | −21.1572 | − | 22.4407i | −1.06997 | − | 1.13487i | ||||
\(392\) | −3.64047 | −0.183871 | ||||||||
\(393\) | 23.5775 | + | 23.5775i | 1.18933 | + | 1.18933i | ||||
\(394\) | −14.3681 | + | 5.95147i | −0.723856 | + | 0.299831i | ||||
\(395\) | 4.92721i | 0.247915i | ||||||||
\(396\) | −0.417157 | − | 1.00711i | −0.0209629 | − | 0.0506089i | ||||
\(397\) | 4.68003 | + | 1.93853i | 0.234884 | + | 0.0972922i | 0.497021 | − | 0.867739i | \(-0.334427\pi\) |
−0.262137 | + | 0.965031i | \(0.584427\pi\) | |||||||
\(398\) | 0.959134 | − | 2.31555i | 0.0480770 | − | 0.116068i | ||||
\(399\) | −20.9608 | + | 20.9608i | −1.04935 | + | 1.04935i | ||||
\(400\) | 0.707107 | − | 0.707107i | 0.0353553 | − | 0.0353553i | ||||
\(401\) | −1.49473 | + | 3.60859i | −0.0746431 | + | 0.180204i | −0.956797 | − | 0.290757i | \(-0.906093\pi\) |
0.882154 | + | 0.470961i | \(0.156093\pi\) | |||||||
\(402\) | 3.62567 | + | 1.50180i | 0.180832 | + | 0.0749030i | ||||
\(403\) | 1.64598 | + | 3.97376i | 0.0819923 | + | 0.197947i | ||||
\(404\) | − | 5.24718i | − | 0.261057i | ||||||
\(405\) | −7.46213 | + | 3.09092i | −0.370796 | + | 0.153589i | ||||
\(406\) | −1.16111 | − | 1.16111i | −0.0576249 | − | 0.0576249i | ||||
\(407\) | 4.70324 | 0.233131 | ||||||||
\(408\) | −4.94654 | + | 4.66364i | −0.244890 | + | 0.230885i | ||||
\(409\) | 35.1203 | 1.73659 | 0.868295 | − | 0.496049i | \(-0.165216\pi\) | ||||
0.868295 | + | 0.496049i | \(0.165216\pi\) | |||||||
\(410\) | 6.13499 | + | 6.13499i | 0.302986 | + | 0.302986i | ||||
\(411\) | 14.9834 | − | 6.20632i | 0.739076 | − | 0.306135i | ||||
\(412\) | 16.8149i | 0.828408i | ||||||||
\(413\) | 10.6505 | + | 25.7125i | 0.524075 | + | 1.26523i | ||||
\(414\) | 1.94405 | + | 0.805250i | 0.0955446 | + | 0.0395759i | ||||
\(415\) | 2.28243 | − | 5.51028i | 0.112040 | − | 0.270489i | ||||
\(416\) | 0.273561 | − | 0.273561i | 0.0134124 | − | 0.0134124i | ||||
\(417\) | −1.45753 | + | 1.45753i | −0.0713754 | + | 0.0713754i | ||||
\(418\) | −8.17306 | + | 19.7315i | −0.399757 | + | 0.965099i | ||||
\(419\) | −21.1715 | − | 8.76953i | −1.03430 | − | 0.428420i | −0.200035 | − | 0.979789i | \(-0.564106\pi\) |
−0.834261 | + | 0.551369i | \(0.814106\pi\) | |||||||
\(420\) | 2.05826 | + | 4.96908i | 0.100433 | + | 0.242466i | ||||
\(421\) | − | 28.3500i | − | 1.38170i | −0.723000 | − | 0.690848i | \(-0.757237\pi\) | ||
0.723000 | − | 0.690848i | \(-0.242763\pi\) | |||||||
\(422\) | 11.7547 | − | 4.86897i | 0.572211 | − | 0.237018i | ||||
\(423\) | −1.02023 | − | 1.02023i | −0.0496055 | − | 0.0496055i | ||||
\(424\) | −0.862555 | −0.0418894 | ||||||||
\(425\) | 3.85403 | − | 1.46508i | 0.186948 | − | 0.0710666i | ||||
\(426\) | −14.6682 | −0.710676 | ||||||||
\(427\) | −15.6180 | − | 15.6180i | −0.755809 | − | 0.755809i | ||||
\(428\) | 9.45410 | − | 3.91601i | 0.456981 | − | 0.189288i | ||||
\(429\) | − | 2.47191i | − | 0.119345i | ||||||
\(430\) | −0.102850 | − | 0.248303i | −0.00495989 | − | 0.0119742i | ||||
\(431\) | 17.1728 | + | 7.11320i | 0.827184 | + | 0.342631i | 0.755787 | − | 0.654817i | \(-0.227254\pi\) |
0.0713968 | + | 0.997448i | \(0.477254\pi\) | |||||||
\(432\) | 2.07046 | − | 4.99853i | 0.0996150 | − | 0.240492i | ||||
\(433\) | 7.09542 | − | 7.09542i | 0.340984 | − | 0.340984i | −0.515753 | − | 0.856737i | \(-0.672488\pi\) |
0.856737 | + | 0.515753i | \(0.172488\pi\) | |||||||
\(434\) | 25.6438 | − | 25.6438i | 1.23094 | − | 1.23094i | ||||
\(435\) | −0.317635 | + | 0.766838i | −0.0152294 | + | 0.0367671i | ||||
\(436\) | 9.83519 | + | 4.07387i | 0.471020 | + | 0.195103i | ||||
\(437\) | −15.7767 | − | 38.0883i | −0.754701 | − | 1.82201i | ||||
\(438\) | 11.6321i | 0.555802i | ||||||||
\(439\) | 33.3356 | − | 13.8081i | 1.59102 | − | 0.659023i | 0.600912 | − | 0.799315i | \(-0.294804\pi\) |
0.990110 | + | 0.140293i | \(0.0448043\pi\) | |||||||
\(440\) | 2.74011 | + | 2.74011i | 0.130630 | + | 0.130630i | ||||
\(441\) | 1.02408 | 0.0487657 | ||||||||
\(442\) | 1.49102 | − | 0.566800i | 0.0709208 | − | 0.0269599i | ||||
\(443\) | −1.26810 | −0.0602493 | −0.0301247 | − | 0.999546i | \(-0.509590\pi\) | ||||
−0.0301247 | + | 0.999546i | \(0.509590\pi\) | |||||||
\(444\) | 1.41508 | + | 1.41508i | 0.0671565 | + | 0.0671565i | ||||
\(445\) | 11.1308 | − | 4.61053i | 0.527650 | − | 0.218560i | ||||
\(446\) | 0.344739i | 0.0163238i | ||||||||
\(447\) | 6.10874 | + | 14.7478i | 0.288933 | + | 0.697547i | ||||
\(448\) | −3.01367 | − | 1.24830i | −0.142383 | − | 0.0589768i | ||||
\(449\) | 1.76923 | − | 4.27131i | 0.0834953 | − | 0.201576i | −0.876618 | − | 0.481187i | \(-0.840206\pi\) |
0.960113 | + | 0.279612i | \(0.0902057\pi\) | |||||||
\(450\) | −0.198912 | + | 0.198912i | −0.00937682 | + | 0.00937682i | ||||
\(451\) | −23.7737 | + | 23.7737i | −1.11946 | + | 1.11946i | ||||
\(452\) | 4.53022 | − | 10.9369i | 0.213083 | − | 0.514429i | ||||
\(453\) | 16.5924 | + | 6.87282i | 0.779581 | + | 0.322913i | ||||
\(454\) | −5.88336 | − | 14.2037i | −0.276120 | − | 0.666612i | ||||
\(455\) | − | 1.26197i | − | 0.0591622i | ||||||
\(456\) | −8.39572 | + | 3.47762i | −0.393165 | + | 0.162854i | ||||
\(457\) | −3.84756 | − | 3.84756i | −0.179981 | − | 0.179981i | 0.611366 | − | 0.791348i | \(-0.290620\pi\) |
−0.791348 | + | 0.611366i | \(0.790620\pi\) | |||||||
\(458\) | −6.71069 | −0.313570 | ||||||||
\(459\) | 16.2311 | − | 15.3028i | 0.757603 | − | 0.714275i | ||||
\(460\) | −7.48022 | −0.348767 | ||||||||
\(461\) | −0.930680 | − | 0.930680i | −0.0433461 | − | 0.0433461i | 0.685102 | − | 0.728448i | \(-0.259758\pi\) |
−0.728448 | + | 0.685102i | \(0.759758\pi\) | |||||||
\(462\) | −19.2557 | + | 7.97596i | −0.895855 | + | 0.371075i | ||||
\(463\) | 11.2825i | 0.524343i | 0.965021 | + | 0.262172i | \(0.0844387\pi\) | ||||
−0.965021 | + | 0.262172i | \(0.915561\pi\) | |||||||
\(464\) | −0.192641 | − | 0.465076i | −0.00894312 | − | 0.0215906i | ||||
\(465\) | −16.9360 | − | 7.01514i | −0.785390 | − | 0.325319i | ||||
\(466\) | 0.594799 | − | 1.43597i | 0.0275535 | − | 0.0665201i | ||||
\(467\) | −15.4555 | + | 15.4555i | −0.715195 | + | 0.715195i | −0.967617 | − | 0.252422i | \(-0.918773\pi\) |
0.252422 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(468\) | −0.0769540 | + | 0.0769540i | −0.00355720 | + | 0.00355720i | ||||
\(469\) | −2.97107 | + | 7.17279i | −0.137191 | + | 0.331209i | ||||
\(470\) | 4.73864 | + | 1.96281i | 0.218577 | + | 0.0905376i | ||||
\(471\) | 5.00686 | + | 12.0876i | 0.230704 | + | 0.556969i | ||||
\(472\) | 8.53195i | 0.392715i | ||||||||
\(473\) | 0.962198 | − | 0.398556i | 0.0442419 | − | 0.0183256i | ||||
\(474\) | −5.74468 | − | 5.74468i | −0.263862 | − | 0.263862i | ||||
\(475\) | 5.51140 | 0.252880 | ||||||||
\(476\) | −9.22625 | − | 9.78592i | −0.422885 | − | 0.448537i | ||||
\(477\) | 0.242641 | 0.0111098 | ||||||||
\(478\) | −8.27403 | − | 8.27403i | −0.378445 | − | 0.378445i | ||||
\(479\) | −4.04430 | + | 1.67520i | −0.184789 | + | 0.0765420i | −0.473159 | − | 0.880977i | \(-0.656886\pi\) |
0.288371 | + | 0.957519i | \(0.406886\pi\) | |||||||
\(480\) | 1.64885i | 0.0752592i | ||||||||
\(481\) | −0.179690 | − | 0.433810i | −0.00819315 | − | 0.0197800i | ||||
\(482\) | 25.2129 | + | 10.4435i | 1.14842 | + | 0.475690i | ||||
\(483\) | 15.3962 | − | 37.1698i | 0.700553 | − | 1.69128i | ||||
\(484\) | −2.84002 | + | 2.84002i | −0.129092 | + | 0.129092i | ||||
\(485\) | 8.25877 | − | 8.25877i | 0.375011 | − | 0.375011i | ||||
\(486\) | −1.11493 | + | 2.69167i | −0.0505741 | + | 0.122097i | ||||
\(487\) | −18.3854 | − | 7.61547i | −0.833121 | − | 0.345090i | −0.0749834 | − | 0.997185i | \(-0.523890\pi\) |
−0.758137 | + | 0.652095i | \(0.773890\pi\) | |||||||
\(488\) | −2.59120 | − | 6.25570i | −0.117298 | − | 0.283182i | ||||
\(489\) | − | 36.0069i | − | 1.62829i | ||||||
\(490\) | −3.36335 | + | 1.39315i | −0.151941 | + | 0.0629359i | ||||
\(491\) | 18.4660 | + | 18.4660i | 0.833361 | + | 0.833361i | 0.987975 | − | 0.154614i | \(-0.0494134\pi\) |
−0.154614 | + | 0.987975i | \(0.549413\pi\) | |||||||
\(492\) | −14.3057 | −0.644951 | ||||||||
\(493\) | 0.0610720 | − | 2.07465i | 0.00275054 | − | 0.0934375i | ||||
\(494\) | 2.13222 | 0.0959330 | ||||||||
\(495\) | −0.770805 | − | 0.770805i | −0.0346451 | − | 0.0346451i | ||||
\(496\) | 10.2715 | − | 4.25457i | 0.461202 | − | 0.191036i | ||||
\(497\) | − | 29.0186i | − | 1.30166i | ||||||
\(498\) | 3.76338 | + | 9.08560i | 0.168641 | + | 0.407135i | ||||
\(499\) | 0.991395 | + | 0.410649i | 0.0443809 | + | 0.0183832i | 0.404763 | − | 0.914421i | \(-0.367354\pi\) |
−0.360383 | + | 0.932805i | \(0.617354\pi\) | |||||||
\(500\) | 0.382683 | − | 0.923880i | 0.0171141 | − | 0.0413171i | ||||
\(501\) | 22.5976 | − | 22.5976i | 1.00959 | − | 1.00959i | ||||
\(502\) | −11.2144 | + | 11.2144i | −0.500523 | + | 0.500523i | ||||
\(503\) | −6.48860 | + | 15.6649i | −0.289312 | + | 0.698462i | −0.999987 | − | 0.00505889i | \(-0.998390\pi\) |
0.710675 | + | 0.703521i | \(0.248390\pi\) | |||||||
\(504\) | 0.847759 | + | 0.351153i | 0.0377622 | + | 0.0156416i | ||||
\(505\) | −2.00801 | − | 4.84776i | −0.0893552 | − | 0.215722i | ||||
\(506\) | − | 28.9866i | − | 1.28861i | ||||||
\(507\) | 19.5754 | − | 8.10838i | 0.869372 | − | 0.360106i | ||||
\(508\) | −2.97116 | − | 2.97116i | −0.131824 | − | 0.131824i | ||||
\(509\) | −13.4425 | −0.595830 | −0.297915 | − | 0.954592i | \(-0.596291\pi\) | ||||
−0.297915 | + | 0.954592i | \(0.596291\pi\) | |||||||
\(510\) | −2.78531 | + | 6.20160i | −0.123336 | + | 0.274612i | ||||
\(511\) | −23.0122 | −1.01800 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 27.5489 | − | 11.4111i | 1.21631 | − | 0.503814i | ||||
\(514\) | − | 29.5680i | − | 1.30419i | ||||||
\(515\) | 6.43476 | + | 15.5349i | 0.283550 | + | 0.684549i | ||||
\(516\) | 0.409413 | + | 0.169585i | 0.0180234 | + | 0.00746554i | ||||
\(517\) | −7.60607 | + | 18.3627i | −0.334515 | + | 0.807590i | ||||
\(518\) | −2.79949 | + | 2.79949i | −0.123003 | + | 0.123003i | ||||
\(519\) | −14.5823 | + | 14.5823i | −0.640090 | + | 0.640090i | ||||
\(520\) | 0.148050 | − | 0.357425i | 0.00649244 | − | 0.0156741i | ||||
\(521\) | −4.37555 | − | 1.81241i | −0.191696 | − | 0.0794032i | 0.284770 | − | 0.958596i | \(-0.408083\pi\) |
−0.476467 | + | 0.879193i | \(0.658083\pi\) | |||||||
\(522\) | 0.0541907 | + | 0.130828i | 0.00237186 | + | 0.00572618i | ||||
\(523\) | − | 0.534337i | − | 0.0233649i | −0.999932 | − | 0.0116825i | \(-0.996281\pi\) | ||
0.999932 | − | 0.0116825i | \(-0.00371873\pi\) | |||||||
\(524\) | −18.6831 | + | 7.73878i | −0.816174 | + | 0.338070i | ||||
\(525\) | 3.80317 | + | 3.80317i | 0.165984 | + | 0.165984i | ||||
\(526\) | −21.4769 | −0.936437 | ||||||||
\(527\) | 45.8198 | + | 1.34881i | 1.99594 | + | 0.0587550i | ||||
\(528\) | −6.38944 | −0.278065 | ||||||||
\(529\) | 23.3017 | + | 23.3017i | 1.01312 | + | 1.01312i | ||||
\(530\) | −0.796897 | + | 0.330086i | −0.0346150 | + | 0.0143380i | ||||
\(531\) | − | 2.40008i | − | 0.104154i | ||||||
\(532\) | −6.87990 | − | 16.6095i | −0.298281 | − | 0.720115i | ||||
\(533\) | 3.10109 | + | 1.28451i | 0.134323 | + | 0.0556384i | ||||
\(534\) | −7.60205 | + | 18.3530i | −0.328973 | + | 0.794211i | ||||
\(535\) | 7.23585 | − | 7.23585i | 0.312833 | − | 0.312833i | ||||
\(536\) | −1.68297 | + | 1.68297i | −0.0726934 | + | 0.0726934i | ||||
\(537\) | −10.8590 | + | 26.2158i | −0.468598 | + | 1.13130i | ||||
\(538\) | 27.8132 | + | 11.5206i | 1.19911 | + | 0.496689i | ||||
\(539\) | −5.39858 | − | 13.0333i | −0.232533 | − | 0.561385i | ||||
\(540\) | − | 5.41037i | − | 0.232825i | ||||||
\(541\) | −3.87392 | + | 1.60463i | −0.166553 | + | 0.0689884i | −0.464402 | − | 0.885624i | \(-0.653731\pi\) |
0.297849 | + | 0.954613i | \(0.403731\pi\) | |||||||
\(542\) | −13.7798 | − | 13.7798i | −0.591893 | − | 0.591893i | ||||
\(543\) | 34.7303 | 1.49042 | ||||||||
\(544\) | −1.46508 | − | 3.85403i | −0.0628146 | − | 0.165240i | ||||
\(545\) | 10.6455 | 0.456004 | ||||||||
\(546\) | 1.47135 | + | 1.47135i | 0.0629679 | + | 0.0629679i | ||||
\(547\) | 21.6550 | − | 8.96980i | 0.925901 | − | 0.383521i | 0.131779 | − | 0.991279i | \(-0.457931\pi\) |
0.794122 | + | 0.607758i | \(0.207931\pi\) | |||||||
\(548\) | 9.83591i | 0.420169i | ||||||||
\(549\) | 0.728915 | + | 1.75976i | 0.0311093 | + | 0.0751046i | ||||
\(550\) | 3.58012 | + | 1.48294i | 0.152657 | + | 0.0632326i | ||||
\(551\) | 1.06172 | − | 2.56322i | 0.0452308 | − | 0.109197i | ||||
\(552\) | 8.72126 | − | 8.72126i | 0.371202 | − | 0.371202i | ||||
\(553\) | 11.3649 | − | 11.3649i | 0.483285 | − | 0.483285i | ||||
\(554\) | −4.02214 | + | 9.71031i | −0.170885 | + | 0.412552i | ||||
\(555\) | 1.84889 | + | 0.765833i | 0.0784808 | + | 0.0325078i | ||||
\(556\) | −0.478400 | − | 1.15496i | −0.0202887 | − | 0.0489812i | ||||
\(557\) | − | 28.1590i | − | 1.19313i | −0.802563 | − | 0.596567i | \(-0.796531\pi\) | ||
0.802563 | − | 0.596567i | \(-0.203469\pi\) | |||||||
\(558\) | −2.88941 | + | 1.19683i | −0.122318 | + | 0.0506659i | ||||
\(559\) | −0.0735226 | − | 0.0735226i | −0.00310968 | − | 0.00310968i | ||||
\(560\) | −3.26197 | −0.137844 | ||||||||
\(561\) | −24.0318 | − | 10.7933i | −1.01462 | − | 0.455695i | ||||
\(562\) | 2.07823 | 0.0876648 | ||||||||
\(563\) | 9.54033 | + | 9.54033i | 0.402077 | + | 0.402077i | 0.878964 | − | 0.476887i | \(-0.158235\pi\) |
−0.476887 | + | 0.878964i | \(0.658235\pi\) | |||||||
\(564\) | −7.81329 | + | 3.23637i | −0.328999 | + | 0.136276i | ||||
\(565\) | − | 11.8380i | − | 0.498030i | ||||||
\(566\) | 8.93056 | + | 21.5603i | 0.375379 | + | 0.906246i | ||||
\(567\) | 24.3413 | + | 10.0825i | 1.02224 | + | 0.423425i | ||||
\(568\) | 3.40436 | − | 8.21885i | 0.142844 | − | 0.344855i | ||||
\(569\) | −2.03477 | + | 2.03477i | −0.0853018 | + | 0.0853018i | −0.748470 | − | 0.663168i | \(-0.769211\pi\) |
0.663168 | + | 0.748470i | \(0.269211\pi\) | |||||||
\(570\) | −6.42580 | + | 6.42580i | −0.269147 | + | 0.269147i | ||||
\(571\) | 14.5080 | − | 35.0255i | 0.607142 | − | 1.46577i | −0.258953 | − | 0.965890i | \(-0.583377\pi\) |
0.866095 | − | 0.499880i | \(-0.166623\pi\) | |||||||
\(572\) | 1.38506 | + | 0.573709i | 0.0579122 | + | 0.0239880i | ||||
\(573\) | −9.00803 | − | 21.7473i | −0.376316 | − | 0.908507i | ||||
\(574\) | − | 28.3015i | − | 1.18128i | ||||||
\(575\) | −6.91082 | + | 2.86256i | −0.288201 | + | 0.119377i | ||||
\(576\) | 0.198912 | + | 0.198912i | 0.00828802 | + | 0.00828802i | ||||
\(577\) | −32.0749 | −1.33529 | −0.667647 | − | 0.744478i | \(-0.732698\pi\) | ||||
−0.667647 | + | 0.744478i | \(0.732698\pi\) | |||||||
\(578\) | 1.00000 | − | 16.9706i | 0.0415945 | − | 0.705882i | ||||
\(579\) | −34.2357 | −1.42279 | ||||||||
\(580\) | −0.355953 | − | 0.355953i | −0.0147802 | − | 0.0147802i | ||||
\(581\) | −17.9744 | + | 7.44523i | −0.745702 | + | 0.308880i | ||||
\(582\) | 19.2580i | 0.798268i | ||||||||
\(583\) | −1.27911 | − | 3.08805i | −0.0529755 | − | 0.127894i | ||||
\(584\) | −6.51767 | − | 2.69971i | −0.269703 | − | 0.111715i | ||||
\(585\) | −0.0416472 | + | 0.100545i | −0.00172190 | + | 0.00415704i | ||||
\(586\) | −2.45155 | + | 2.45155i | −0.101273 | + | 0.101273i | ||||
\(587\) | 15.5504 | − | 15.5504i | 0.641833 | − | 0.641833i | −0.309173 | − | 0.951006i | \(-0.600052\pi\) |
0.951006 | + | 0.309173i | \(0.100052\pi\) | |||||||
\(588\) | 2.29708 | − | 5.54565i | 0.0947301 | − | 0.228699i | ||||
\(589\) | 56.6101 | + | 23.4487i | 2.33258 | + | 0.966186i | ||||
\(590\) | 3.26504 | + | 7.88250i | 0.134419 | + | 0.324517i | ||||
\(591\) | − | 25.6428i | − | 1.05480i | ||||||
\(592\) | −1.12132 | + | 0.464466i | −0.0460860 | + | 0.0190894i | ||||
\(593\) | 15.0634 | + | 15.0634i | 0.618579 | + | 0.618579i | 0.945167 | − | 0.326588i | \(-0.105899\pi\) |
−0.326588 | + | 0.945167i | \(0.605899\pi\) | |||||||
\(594\) | 20.9657 | 0.860234 | ||||||||
\(595\) | −12.2689 | − | 5.51028i | −0.502974 | − | 0.225899i | ||||
\(596\) | −9.68125 | −0.396559 | ||||||||
\(597\) | 2.92217 | + | 2.92217i | 0.119596 | + | 0.119596i | ||||
\(598\) | −2.67362 | + | 1.10745i | −0.109332 | + | 0.0452869i | ||||
\(599\) | 46.7012i | 1.90816i | 0.299552 | + | 0.954080i | \(0.403163\pi\) | ||||
−0.299552 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(600\) | 0.630986 | + | 1.52334i | 0.0257599 | + | 0.0621899i | ||||
\(601\) | −25.2665 | − | 10.4657i | −1.03064 | − | 0.426905i | −0.197697 | − | 0.980263i | \(-0.563346\pi\) |
−0.832943 | + | 0.553358i | \(0.813346\pi\) | |||||||
\(602\) | −0.335495 | + | 0.809957i | −0.0136738 | + | 0.0330114i | ||||
\(603\) | 0.473428 | − | 0.473428i | 0.0192795 | − | 0.0192795i | ||||
\(604\) | −7.70193 | + | 7.70193i | −0.313387 | + | 0.313387i | ||||
\(605\) | −1.53701 | + | 3.71066i | −0.0624882 | + | 0.150860i | ||||
\(606\) | 7.99321 | + | 3.31090i | 0.324702 | + | 0.134496i | ||||
\(607\) | 7.51669 | + | 18.1469i | 0.305093 | + | 0.736560i | 0.999850 | + | 0.0173153i | \(0.00551189\pi\) |
−0.694757 | + | 0.719245i | \(0.744488\pi\) | |||||||
\(608\) | − | 5.51140i | − | 0.223517i | ||||||
\(609\) | 2.50141 | − | 1.03612i | 0.101362 | − | 0.0419855i | ||||
\(610\) | −4.78791 | − | 4.78791i | −0.193857 | − | 0.193857i | ||||
\(611\) | 1.98430 | 0.0802763 | ||||||||
\(612\) | 0.412132 | + | 1.08416i | 0.0166595 | + | 0.0438244i | ||||
\(613\) | 4.06372 | 0.164132 | 0.0820661 | − | 0.996627i | \(-0.473848\pi\) | ||||
0.0820661 | + | 0.996627i | \(0.473848\pi\) | |||||||
\(614\) | −0.0348588 | − | 0.0348588i | −0.00140678 | − | 0.00140678i | ||||
\(615\) | −13.2167 | + | 5.47455i | −0.532951 | + | 0.220755i | ||||
\(616\) | − | 12.6405i | − | 0.509299i | ||||||
\(617\) | 10.2233 | + | 24.6812i | 0.411574 | + | 0.993629i | 0.984715 | + | 0.174172i | \(0.0557248\pi\) |
−0.573141 | + | 0.819457i | \(0.694275\pi\) | |||||||
\(618\) | −25.6147 | − | 10.6099i | −1.03037 | − | 0.426794i | ||||
\(619\) | −3.79149 | + | 9.15346i | −0.152393 | + | 0.367909i | −0.981577 | − | 0.191067i | \(-0.938805\pi\) |
0.829184 | + | 0.558975i | \(0.188805\pi\) | |||||||
\(620\) | 7.86143 | − | 7.86143i | 0.315723 | − | 0.315723i | ||||
\(621\) | −28.6171 | + | 28.6171i | −1.14837 | + | 1.14837i | ||||
\(622\) | −6.55093 | + | 15.8153i | −0.262668 | + | 0.634137i | ||||
\(623\) | −36.3084 | − | 15.0394i | −1.45466 | − | 0.602541i | ||||
\(624\) | 0.244112 | + | 0.589339i | 0.00977231 | + | 0.0235924i | ||||
\(625\) | − | 1.00000i | − | 0.0400000i | ||||||
\(626\) | 14.2254 | − | 5.89235i | 0.568561 | − | 0.235506i | ||||
\(627\) | −24.9006 | − | 24.9006i | −0.994435 | − | 0.994435i | ||||
\(628\) | −7.93497 | −0.316640 | ||||||||
\(629\) | −5.00208 | − | 0.147248i | −0.199446 | − | 0.00587114i | ||||
\(630\) | 0.917608 | 0.0365584 | ||||||||
\(631\) | −14.0357 | − | 14.0357i | −0.558753 | − | 0.558753i | 0.370199 | − | 0.928952i | \(-0.379289\pi\) |
−0.928952 | + | 0.370199i | \(0.879289\pi\) | |||||||
\(632\) | 4.55215 | − | 1.88556i | 0.181075 | − | 0.0750036i | ||||
\(633\) | 20.9787i | 0.833827i | ||||||||
\(634\) | 10.5581 | + | 25.4894i | 0.419315 | + | 1.01232i | ||||
\(635\) | −3.88201 | − | 1.60798i | −0.154053 | − | 0.0638108i | ||||
\(636\) | 0.544260 | − | 1.31396i | 0.0215813 | − | 0.0521019i | ||||
\(637\) | −0.995890 | + | 0.995890i | −0.0394586 | + | 0.0394586i | ||||
\(638\) | 1.37935 | − | 1.37935i | 0.0546092 | − | 0.0546092i | ||||
\(639\) | −0.957662 | + | 2.31200i | −0.0378845 | + | 0.0914614i | ||||
\(640\) | −0.923880 | − | 0.382683i | −0.0365195 | − | 0.0151269i | ||||
\(641\) | 6.29557 | + | 15.1989i | 0.248660 | + | 0.600319i | 0.998091 | − | 0.0617642i | \(-0.0196727\pi\) |
−0.749431 | + | 0.662083i | \(0.769673\pi\) | |||||||
\(642\) | 16.8727i | 0.665913i | ||||||||
\(643\) | 5.04875 | − | 2.09126i | 0.199103 | − | 0.0824713i | −0.280904 | − | 0.959736i | \(-0.590634\pi\) |
0.480007 | + | 0.877265i | \(0.340634\pi\) | |||||||
\(644\) | 17.2536 | + | 17.2536i | 0.679887 | + | 0.679887i | ||||
\(645\) | 0.443146 | 0.0174489 | ||||||||
\(646\) | 9.31012 | − | 20.7294i | 0.366302 | − | 0.815586i | ||||
\(647\) | −18.0212 | −0.708488 | −0.354244 | − | 0.935153i | \(-0.615262\pi\) | ||||
−0.354244 | + | 0.935153i | \(0.615262\pi\) | |||||||
\(648\) | 5.71127 | + | 5.71127i | 0.224360 | + | 0.224360i | ||||
\(649\) | −30.5455 | + | 12.6523i | −1.19901 | + | 0.496648i | ||||
\(650\) | − | 0.386874i | − | 0.0151744i | ||||||
\(651\) | 22.8832 | + | 55.2449i | 0.896863 | + | 2.16522i | ||||
\(652\) | 20.1754 | + | 8.35691i | 0.790128 | + | 0.327282i | ||||
\(653\) | 1.07011 | − | 2.58348i | 0.0418768 | − | 0.101099i | −0.901557 | − | 0.432660i | \(-0.857575\pi\) |
0.943434 | + | 0.331560i | \(0.107575\pi\) | |||||||
\(654\) | −12.4117 | + | 12.4117i | −0.485337 | + | 0.485337i | ||||
\(655\) | −14.2994 | + | 14.2994i | −0.558724 | + | 0.558724i | ||||
\(656\) | 3.32023 | − | 8.01575i | 0.129633 | − | 0.312962i | ||||
\(657\) | 1.83345 | + | 0.759440i | 0.0715297 | + | 0.0296286i | ||||
\(658\) | −6.40262 | − | 15.4573i | −0.249600 | − | 0.602588i | ||||
\(659\) | 39.8730i | 1.55323i | 0.629975 | + | 0.776616i | \(0.283065\pi\) | ||||
−0.629975 | + | 0.776616i | \(0.716935\pi\) | |||||||
\(660\) | −5.90308 | + | 2.44513i | −0.229777 | + | 0.0951767i | ||||
\(661\) | 15.0252 | + | 15.0252i | 0.584414 | + | 0.584414i | 0.936113 | − | 0.351699i | \(-0.114396\pi\) |
−0.351699 | + | 0.936113i | \(0.614396\pi\) | |||||||
\(662\) | 0.776318 | 0.0301724 | ||||||||
\(663\) | −0.0773898 | + | 2.62897i | −0.00300557 | + | 0.102101i | ||||
\(664\) | −5.96428 | −0.231459 | ||||||||
\(665\) | −12.7124 | − | 12.7124i | −0.492966 | − | 0.492966i | ||||
\(666\) | 0.315433 | − | 0.130656i | 0.0122228 | − | 0.00506283i | ||||
\(667\) | 3.76550i | 0.145801i | ||||||||
\(668\) | 7.41716 | + | 17.9066i | 0.286978 | + | 0.692827i | ||||
\(669\) | −0.525153 | − | 0.217525i | −0.0203036 | − | 0.00841001i | ||||
\(670\) | −0.910819 | + | 2.19891i | −0.0351880 | + | 0.0849514i | ||||
\(671\) | 18.5536 | − | 18.5536i | 0.716254 | − | 0.716254i | ||||
\(672\) | 3.80317 | − | 3.80317i | 0.146710 | − | 0.146710i | ||||
\(673\) | −3.09140 | + | 7.46331i | −0.119165 | + | 0.287690i | −0.972195 | − | 0.234172i | \(-0.924762\pi\) |
0.853030 | + | 0.521861i | \(0.174762\pi\) | |||||||
\(674\) | −25.0517 | − | 10.3768i | −0.964956 | − | 0.399698i | ||||
\(675\) | −2.07046 | − | 4.99853i | −0.0796920 | − | 0.192393i | ||||
\(676\) | 12.8503i | 0.494243i | ||||||||
\(677\) | −14.9417 | + | 6.18907i | −0.574258 | + | 0.237865i | −0.650862 | − | 0.759196i | \(-0.725592\pi\) |
0.0766041 | + | 0.997062i | \(0.475592\pi\) | |||||||
\(678\) | 13.8021 | + | 13.8021i | 0.530066 | + | 0.530066i | ||||
\(679\) | −38.0987 | −1.46209 | ||||||||
\(680\) | −2.82843 | − | 3.00000i | −0.108465 | − | 0.115045i | ||||
\(681\) | 25.3493 | 0.971387 | ||||||||
\(682\) | 30.4638 | + | 30.4638i | 1.16652 | + | 1.16652i | ||||
\(683\) | −21.6024 | + | 8.94801i | −0.826593 | + | 0.342386i | −0.755553 | − | 0.655087i | \(-0.772632\pi\) |
−0.0710401 | + | 0.997473i | \(0.522632\pi\) | |||||||
\(684\) | 1.55038i | 0.0592804i | ||||||||
\(685\) | 3.76404 | + | 9.08719i | 0.143817 | + | 0.347204i | ||||
\(686\) | −10.1245 | − | 4.19372i | −0.386556 | − | 0.160117i | ||||
\(687\) | 4.23435 | − | 10.2226i | 0.161551 | − | 0.390018i | ||||
\(688\) | −0.190043 | + | 0.190043i | −0.00724531 | + | 0.00724531i | ||||
\(689\) | −0.235962 | + | 0.235962i | −0.00898942 | + | 0.00898942i | ||||
\(690\) | 4.71991 | − | 11.3949i | 0.179684 | − | 0.433796i | ||||
\(691\) | 28.6113 | + | 11.8512i | 1.08842 | + | 0.450840i | 0.853457 | − | 0.521164i | \(-0.174502\pi\) |
0.234967 | + | 0.972003i | \(0.424502\pi\) | |||||||
\(692\) | −4.78629 | − | 11.5551i | −0.181948 | − | 0.439260i | ||||
\(693\) | 3.55582i | 0.135074i | ||||||||
\(694\) | 19.4880 | − | 8.07218i | 0.739753 | − | 0.306416i | ||||
\(695\) | −0.883968 | − | 0.883968i | −0.0335308 | − | 0.0335308i | ||||
\(696\) | 0.830020 | 0.0314618 | ||||||||
\(697\) | 26.0286 | − | 24.5400i | 0.985902 | − | 0.929517i | ||||
\(698\) | 12.9755 | 0.491129 | ||||||||
\(699\) | 1.81216 | + | 1.81216i | 0.0685421 | + | 0.0685421i | ||||
\(700\) | −3.01367 | + | 1.24830i | −0.113906 | + | 0.0471814i | ||||
\(701\) | 14.5668i | 0.550179i | 0.961419 | + | 0.275090i | \(0.0887075\pi\) | ||||
−0.961419 | + | 0.275090i | \(0.911292\pi\) | |||||||
\(702\) | −0.801007 | − | 1.93380i | −0.0302320 | − | 0.0729866i | ||||
\(703\) | −6.18005 | − | 2.55986i | −0.233085 | − | 0.0965469i | ||||
\(704\) | 1.48294 | − | 3.58012i | 0.0558903 | − | 0.134931i | ||||
\(705\) | −5.98003 | + | 5.98003i | −0.225221 | + | 0.225221i | ||||
\(706\) | −11.1309 | + | 11.1309i | −0.418919 | + | 0.418919i | ||||
\(707\) | −6.55007 | + | 15.8133i | −0.246341 | + | 0.594719i | ||||
\(708\) | −12.9970 | − | 5.38355i | −0.488458 | − | 0.202326i | ||||
\(709\) | −16.7641 | − | 40.4722i | −0.629590 | − | 1.51996i | −0.840134 | − | 0.542380i | \(-0.817523\pi\) |
0.210544 | − | 0.977584i | \(-0.432477\pi\) | |||||||
\(710\) | − | 8.89602i | − | 0.333862i | ||||||
\(711\) | −1.28054 | + | 0.530417i | −0.0480240 | + | 0.0198922i | ||||
\(712\) | −8.51915 | − | 8.51915i | −0.319268 | − | 0.319268i | ||||
\(713\) | −83.1631 | −3.11448 | ||||||||
\(714\) | 20.7289 | − | 7.87990i | 0.775759 | − | 0.294898i | ||||
\(715\) | 1.49918 | 0.0560660 | ||||||||
\(716\) | −12.1689 | − | 12.1689i | −0.454775 | − | 0.454775i | ||||
\(717\) | 17.8249 | − | 7.38332i | 0.665684 | − | 0.275735i | ||||
\(718\) | 4.38130i | 0.163509i | ||||||||
\(719\) | −14.5402 | − | 35.1032i | −0.542258 | − | 1.30913i | −0.923126 | − | 0.384498i | \(-0.874375\pi\) |
0.380867 | − | 0.924630i | \(-0.375625\pi\) | |||||||
\(720\) | 0.259892 | + | 0.107651i | 0.00968559 | + | 0.00401190i | ||||
\(721\) | 20.9900 | − | 50.6744i | 0.781709 | − | 1.88721i | ||||
\(722\) | 8.04373 | − | 8.04373i | 0.299357 | − | 0.299357i | ||||
\(723\) | −31.8180 | + | 31.8180i | −1.18333 | + | 1.18333i | ||||
\(724\) | −8.06061 | + | 19.4600i | −0.299570 | + | 0.723226i | ||||
\(725\) | −0.465076 | − | 0.192641i | −0.0172725 | − | 0.00715449i | ||||
\(726\) | −2.53429 | − | 6.11831i | −0.0940562 | − | 0.227072i | ||||
\(727\) | 18.6950i | 0.693360i | 0.937984 | + | 0.346680i | \(0.112691\pi\) | ||||
−0.937984 | + | 0.346680i | \(0.887309\pi\) | |||||||
\(728\) | −1.16591 | + | 0.482936i | −0.0432115 | + | 0.0178988i | ||||
\(729\) | −20.5306 | − | 20.5306i | −0.760393 | − | 0.760393i | ||||
\(730\) | −7.05468 | −0.261105 | ||||||||
\(731\) | −1.03581 | + | 0.393755i | −0.0383109 | + | 0.0145636i | ||||
\(732\) | 11.1645 | 0.412653 | ||||||||
\(733\) | −25.3096 | − | 25.3096i | −0.934832 | − | 0.934832i | 0.0631706 | − | 0.998003i | \(-0.479879\pi\) |
−0.998003 | + | 0.0631706i | \(0.979879\pi\) | |||||||
\(734\) | 20.2864 | − | 8.40289i | 0.748784 | − | 0.310156i | ||||
\(735\) | − | 6.00257i | − | 0.221408i | ||||||
\(736\) | 2.86256 | + | 6.91082i | 0.105515 | + | 0.254736i | ||||
\(737\) | −8.52100 | − | 3.52951i | −0.313875 | − | 0.130011i | ||||
\(738\) | −0.933997 | + | 2.25487i | −0.0343809 | + | 0.0830028i | ||||
\(739\) | 2.72089 | − | 2.72089i | 0.100089 | − | 0.100089i | −0.655289 | − | 0.755378i | \(-0.727453\pi\) |
0.755378 | + | 0.655289i | \(0.227453\pi\) | |||||||
\(740\) | −0.858221 | + | 0.858221i | −0.0315488 | + | 0.0315488i | ||||
\(741\) | −1.34540 | + | 3.24808i | −0.0494245 | + | 0.119321i | ||||
\(742\) | 2.59946 | + | 1.07673i | 0.0954290 | + | 0.0395280i | ||||
\(743\) | 10.2614 | + | 24.7732i | 0.376453 | + | 0.908839i | 0.992625 | + | 0.121227i | \(0.0386828\pi\) |
−0.616172 | + | 0.787612i | \(0.711317\pi\) | |||||||
\(744\) | 18.3314i | 0.672063i | ||||||||
\(745\) | −8.94431 | + | 3.70485i | −0.327694 | + | 0.135735i | ||||
\(746\) | 24.5664 | + | 24.5664i | 0.899440 | + | 0.899440i | ||||
\(747\) | 1.67778 | 0.0613867 | ||||||||
\(748\) | 11.6253 | − | 10.9604i | 0.425063 | − | 0.400753i | ||||
\(749\) | −33.3799 | −1.21967 | ||||||||
\(750\) | 1.16591 | + | 1.16591i | 0.0425730 | + | 0.0425730i | ||||
\(751\) | −8.19609 | + | 3.39493i | −0.299080 | + | 0.123883i | −0.527177 | − | 0.849755i | \(-0.676750\pi\) |
0.228097 | + | 0.973638i | \(0.426750\pi\) | |||||||
\(752\) | − | 5.12906i | − | 0.187038i | ||||||
\(753\) | −10.0072 | − | 24.1594i | −0.364681 | − | 0.880418i | ||||
\(754\) | −0.179926 | − | 0.0745277i | −0.00655251 | − | 0.00271414i | ||||
\(755\) | −4.16826 | + | 10.0631i | −0.151698 | + | 0.366232i | ||||
\(756\) | −12.4794 | + | 12.4794i | −0.453870 | + | 0.453870i | ||||
\(757\) | −1.40238 | + | 1.40238i | −0.0509705 | + | 0.0509705i | −0.732133 | − | 0.681162i | \(-0.761475\pi\) |
0.681162 | + | 0.732133i | \(0.261475\pi\) | |||||||
\(758\) | 4.06600 | − | 9.81620i | 0.147684 | − | 0.356540i | ||||
\(759\) | 44.1563 | + | 18.2901i | 1.60277 | + | 0.663890i | ||||
\(760\) | −2.10912 | − | 5.09187i | −0.0765059 | − | 0.184702i | ||||
\(761\) | 8.91397i | 0.323131i | 0.986862 | + | 0.161566i | \(0.0516544\pi\) | ||||
−0.986862 | + | 0.161566i | \(0.948346\pi\) | |||||||
\(762\) | 6.40084 | − | 2.65131i | 0.231878 | − | 0.0960469i | ||||
\(763\) | −24.5546 | − | 24.5546i | −0.888936 | − | 0.888936i | ||||
\(764\) | 14.2761 | 0.516491 | ||||||||
\(765\) | 0.795649 | + | 0.843914i | 0.0287668 | + | 0.0305118i | ||||
\(766\) | 5.55285 | 0.200633 | ||||||||
\(767\) | 2.33401 | + | 2.33401i | 0.0842763 | + | 0.0842763i | ||||
\(768\) | 1.52334 | − | 0.630986i | 0.0549686 | − | 0.0227688i | ||||
\(769\) | − | 48.4038i | − | 1.74549i | −0.488180 | − | 0.872743i | \(-0.662339\pi\) | ||
0.488180 | − | 0.872743i | \(-0.337661\pi\) | |||||||
\(770\) | −4.83730 | − | 11.6783i | −0.174324 | − | 0.420856i | ||||
\(771\) | 45.0419 | + | 18.6570i | 1.62215 | + | 0.671915i | ||||
\(772\) | 7.94581 | − | 19.1829i | 0.285976 | − | 0.690407i | ||||
\(773\) | 13.5594 | − | 13.5594i | 0.487699 | − | 0.487699i | −0.419881 | − | 0.907579i | \(-0.637928\pi\) |
0.907579 | + | 0.419881i | \(0.137928\pi\) | |||||||
\(774\) | 0.0534599 | − | 0.0534599i | 0.00192158 | − | 0.00192158i | ||||
\(775\) | 4.25457 | − | 10.2715i | 0.152829 | − | 0.368961i | ||||
\(776\) | −10.7906 | − | 4.46961i | −0.387360 | − | 0.160450i | ||||
\(777\) | −2.49813 | − | 6.03101i | −0.0896198 | − | 0.216361i | ||||
\(778\) | 8.86259i | 0.317739i | ||||||||
\(779\) | 44.1780 | − | 18.2991i | 1.58284 | − | 0.655635i | ||||
\(780\) | 0.451061 | + | 0.451061i | 0.0161506 | + | 0.0161506i | ||||
\(781\) | 34.4730 | 1.23354 | ||||||||
\(782\) | −0.907502 | + | 30.8284i | −0.0324522 | + | 1.10242i | ||||
\(783\) | −2.72355 | −0.0973317 | ||||||||
\(784\) | 2.57420 | + | 2.57420i | 0.0919356 | + | 0.0919356i | ||||
\(785\) | −7.33096 | + | 3.03658i | −0.261653 | + | 0.108380i | ||||
\(786\) | − | 33.3436i | − | 1.18933i | ||||||
\(787\) | −13.0796 | − | 31.5770i | −0.466238 | − | 1.12560i | −0.965793 | − | 0.259316i | \(-0.916503\pi\) |
0.499555 | − | 0.866282i | \(-0.333497\pi\) | |||||||
\(788\) | 14.3681 | + | 5.95147i | 0.511843 | + | 0.212012i | ||||
\(789\) | 13.5516 | − | 32.7165i | 0.482451 | − | 1.16474i | ||||
\(790\) | 3.48406 | − | 3.48406i | 0.123957 | − | 0.123957i | ||||
\(791\) | −27.3052 | + | 27.3052i | −0.970860 | + | 0.970860i | ||||
\(792\) | −0.417157 | + | 1.00711i | −0.0148230 | + | 0.0357859i | ||||
\(793\) | −2.42017 | − | 1.00247i | −0.0859427 | − | 0.0355986i | ||||
\(794\) | −1.93853 | − | 4.68003i | −0.0687959 | − | 0.166088i | ||||
\(795\) | − | 1.42222i | − | 0.0504410i | ||||||
\(796\) | −2.31555 | + | 0.959134i | −0.0820726 | + | 0.0339956i | ||||
\(797\) | 12.2144 | + | 12.2144i | 0.432656 | + | 0.432656i | 0.889531 | − | 0.456875i | \(-0.151031\pi\) |
−0.456875 | + | 0.889531i | \(0.651031\pi\) | |||||||
\(798\) | 29.6430 | 1.04935 | ||||||||
\(799\) | 8.66425 | − | 19.2913i | 0.306519 | − | 0.682478i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 2.39647 | + | 2.39647i | 0.0846753 | + | 0.0846753i | ||||
\(802\) | 3.60859 | − | 1.49473i | 0.127424 | − | 0.0527806i | ||||
\(803\) | − | 27.3376i | − | 0.964722i | ||||||
\(804\) | −1.50180 | − | 3.62567i | −0.0529645 | − | 0.127868i | ||||
\(805\) | 22.5429 | + | 9.33758i | 0.794533 | + | 0.329106i | ||||
\(806\) | 1.64598 | − | 3.97376i | 0.0579773 | − | 0.139970i | ||||
\(807\) | −35.0995 | + | 35.0995i | −1.23556 | + | 1.23556i | ||||
\(808\) | −3.71031 | + | 3.71031i | −0.130528 | + | 0.130528i | ||||
\(809\) | 3.34288 | − | 8.07043i | 0.117529 | − | 0.283741i | −0.854157 | − | 0.520015i | \(-0.825926\pi\) |
0.971686 | + | 0.236274i | \(0.0759263\pi\) | |||||||
\(810\) | 7.46213 | + | 3.09092i | 0.262193 | + | 0.108604i | ||||
\(811\) | 7.81129 | + | 18.8581i | 0.274291 | + | 0.662198i | 0.999658 | − | 0.0261652i | \(-0.00832960\pi\) |
−0.725366 | + | 0.688363i | \(0.758330\pi\) | |||||||
\(812\) | 1.64206i | 0.0576249i | ||||||||
\(813\) | 29.6861 | − | 12.2964i | 1.04114 | − | 0.431253i | ||||
\(814\) | −3.32569 | − | 3.32569i | −0.116565 | − | 0.116565i | ||||
\(815\) | 21.8377 | 0.764940 | ||||||||
\(816\) | 6.79543 | + | 0.200039i | 0.237887 | + | 0.00700275i | ||||
\(817\) | −1.48125 | −0.0518224 | ||||||||
\(818\) | −24.8338 | − | 24.8338i | −0.868295 | − | 0.868295i | ||||
\(819\) | 0.327976 | − | 0.135852i | 0.0114604 | − | 0.00474706i | ||||
\(820\) | − | 8.67619i | − | 0.302986i | ||||||
\(821\) | 21.1824 | + | 51.1388i | 0.739270 | + | 1.78475i | 0.608834 | + | 0.793298i | \(0.291638\pi\) |
0.130436 | + | 0.991457i | \(0.458362\pi\) | |||||||
\(822\) | −14.9834 | − | 6.20632i | −0.522606 | − | 0.216470i | ||||
\(823\) | 5.83962 | − | 14.0981i | 0.203556 | − | 0.491429i | −0.788827 | − | 0.614615i | \(-0.789311\pi\) |
0.992384 | + | 0.123187i | \(0.0393114\pi\) | |||||||
\(824\) | 11.8899 | − | 11.8899i | 0.414204 | − | 0.414204i | ||||
\(825\) | −4.51802 | + | 4.51802i | −0.157297 | + | 0.157297i | ||||
\(826\) | 10.6505 | − | 25.7125i | 0.370577 | − | 0.894652i | ||||
\(827\) | −27.8773 | − | 11.5472i | −0.969389 | − | 0.401534i | −0.158904 | − | 0.987294i | \(-0.550796\pi\) |
−0.810484 | + | 0.585760i | \(0.800796\pi\) | |||||||
\(828\) | −0.805250 | − | 1.94405i | −0.0279844 | − | 0.0675602i | ||||
\(829\) | 45.3366i | 1.57460i | 0.616567 | + | 0.787302i | \(0.288523\pi\) | ||||
−0.616567 | + | 0.787302i | \(0.711477\pi\) | |||||||
\(830\) | −5.51028 | + | 2.28243i | −0.191264 | + | 0.0792243i | ||||
\(831\) | −12.2542 | − | 12.2542i | −0.425092 | − | 0.425092i | ||||
\(832\) | −0.386874 | −0.0134124 | ||||||||
\(833\) | 5.33356 | + | 14.0305i | 0.184797 | + | 0.486127i | ||||
\(834\) | 2.06126 | 0.0713754 | ||||||||
\(835\) | 13.7051 | + | 13.7051i | 0.474285 | + | 0.474285i | ||||
\(836\) | 19.7315 | − | 8.17306i | 0.682428 | − | 0.282671i | ||||
\(837\) | − | 60.1511i | − | 2.07912i | ||||||
\(838\) | 8.76953 | + | 21.1715i | 0.302938 | + | 0.731358i | ||||
\(839\) | 13.9838 | + | 5.79230i | 0.482776 | + | 0.199972i | 0.610779 | − | 0.791801i | \(-0.290857\pi\) |
−0.128003 | + | 0.991774i | \(0.540857\pi\) | |||||||
\(840\) | 2.05826 | − | 4.96908i | 0.0710167 | − | 0.171450i | ||||
\(841\) | 20.3269 | − | 20.3269i | 0.700928 | − | 0.700928i | ||||
\(842\) | −20.0465 | + | 20.0465i | −0.690848 | + | 0.690848i | ||||
\(843\) | −1.31133 | + | 3.16584i | −0.0451648 | + | 0.109037i | ||||
\(844\) | −11.7547 | − | 4.86897i | −0.404615 | − | 0.167597i | ||||
\(845\) | 4.91761 | + | 11.8722i | 0.169171 | + | 0.408415i | ||||
\(846\) | 1.44283i | 0.0496055i | ||||||||
\(847\) | 12.1041 | − | 5.01367i | 0.415901 | − | 0.172272i | ||||
\(848\) | 0.609919 | + | 0.609919i | 0.0209447 | + | 0.0209447i | ||||
\(849\) | −38.4786 | −1.32058 | ||||||||
\(850\) | −3.76118 | − | 1.68925i | −0.129007 | − | 0.0579407i | ||||
\(851\) | 9.07880 | 0.311217 | ||||||||
\(852\) | 10.3720 | + | 10.3720i | 0.355338 | + | 0.355338i | ||||
\(853\) | −10.8316 | + | 4.48661i | −0.370868 | + | 0.153619i | −0.560330 | − | 0.828269i | \(-0.689326\pi\) |
0.189462 | + | 0.981888i | \(0.439326\pi\) | |||||||
\(854\) | 22.0872i | 0.755809i | ||||||||
\(855\) | 0.593306 | + | 1.43237i | 0.0202906 | + | 0.0489859i | ||||
\(856\) | −9.45410 | − | 3.91601i | −0.323134 | − | 0.133847i | ||||
\(857\) | 7.16039 | − | 17.2867i | 0.244594 | − | 0.590503i | −0.753134 | − | 0.657867i | \(-0.771459\pi\) |
0.997728 | + | 0.0673641i | \(0.0214589\pi\) | |||||||
\(858\) | −1.74790 | + | 1.74790i | −0.0596725 | + | 0.0596725i | ||||
\(859\) | 24.0468 | − | 24.0468i | 0.820465 | − | 0.820465i | −0.165710 | − | 0.986175i | \(-0.552991\pi\) |
0.986175 | + | 0.165710i | \(0.0529914\pi\) | |||||||
\(860\) | −0.102850 | + | 0.248303i | −0.00350717 | + | 0.00846706i | ||||
\(861\) | 43.1127 | + | 17.8578i | 1.46928 | + | 0.608594i | ||||
\(862\) | −7.11320 | − | 17.1728i | −0.242277 | − | 0.584908i | ||||
\(863\) | − | 4.32882i | − | 0.147355i | −0.997282 | − | 0.0736774i | \(-0.976526\pi\) | ||
0.997282 | − | 0.0736774i | \(-0.0234735\pi\) | |||||||
\(864\) | −4.99853 | + | 2.07046i | −0.170053 | + | 0.0704384i | ||||
\(865\) | −8.84391 | − | 8.84391i | −0.300702 | − | 0.300702i | ||||
\(866\) | −10.0344 | −0.340984 | ||||||||
\(867\) | 25.2209 | + | 12.2315i | 0.856546 | + | 0.415404i | ||||
\(868\) | −36.2658 | −1.23094 | ||||||||
\(869\) | 13.5011 | + | 13.5011i | 0.457993 | + | 0.457993i | ||||
\(870\) | 0.766838 | − | 0.317635i | 0.0259983 | − | 0.0107688i | ||||
\(871\) | 0.920793i | 0.0311999i | ||||||||
\(872\) | −4.07387 | − | 9.83519i | −0.137959 | − | 0.333061i | ||||
\(873\) | 3.03544 | + | 1.25732i | 0.102734 | + | 0.0425539i | ||||
\(874\) | −15.7767 | + | 38.0883i | −0.533655 | + | 1.28836i | ||||
\(875\) | −2.30656 | + | 2.30656i | −0.0779761 | + | 0.0779761i | ||||
\(876\) | 8.22513 | − | 8.22513i | 0.277901 | − | 0.277901i | ||||
\(877\) | −14.0035 | + | 33.8074i | −0.472864 | + | 1.14160i | 0.490027 | + | 0.871707i | \(0.336987\pi\) |
−0.962892 | + | 0.269888i | \(0.913013\pi\) | |||||||
\(878\) | −33.3356 | − | 13.8081i | −1.12502 | − | 0.466000i | ||||
\(879\) | −2.18764 | − | 5.28143i | −0.0737872 | − | 0.178138i | ||||
\(880\) | − | 3.87510i | − | 0.130630i | ||||||
\(881\) | −14.7746 | + | 6.11984i | −0.497769 | + | 0.206183i | −0.617420 | − | 0.786633i | \(-0.711822\pi\) |
0.119652 | + | 0.992816i | \(0.461822\pi\) | |||||||
\(882\) | −0.724134 | − | 0.724134i | −0.0243828 | − | 0.0243828i | ||||
\(883\) | 9.64068 | 0.324435 | 0.162217 | − | 0.986755i | \(-0.448135\pi\) | ||||
0.162217 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(884\) | −1.45510 | − | 0.653526i | −0.0489404 | − | 0.0219804i | ||||
\(885\) | −14.0679 | −0.472887 | ||||||||
\(886\) | 0.896683 | + | 0.896683i | 0.0301247 | + | 0.0301247i | ||||
\(887\) | −19.4510 | + | 8.05687i | −0.653101 | + | 0.270523i | −0.684532 | − | 0.728983i | \(-0.739993\pi\) |
0.0314313 | + | 0.999506i | \(0.489993\pi\) | |||||||
\(888\) | − | 2.00122i | − | 0.0671565i | ||||||
\(889\) | 5.24519 | + | 12.6630i | 0.175918 | + | 0.424704i | ||||
\(890\) | −11.1308 | − | 4.61053i | −0.373105 | − | 0.154545i | ||||
\(891\) | −11.9776 | + | 28.9165i | −0.401265 | + | 0.968739i | ||||
\(892\) | 0.243767 | − | 0.243767i | 0.00816192 | − | 0.00816192i | ||||
\(893\) | 19.9887 | − | 19.9887i | 0.668897 | − | 0.668897i | ||||
\(894\) | 6.10874 | − | 14.7478i | 0.204307 | − | 0.493240i | ||||
\(895\) | −15.8995 | − | 6.58579i | −0.531462 | − | 0.220139i | ||||
\(896\) | 1.24830 | + | 3.01367i | 0.0417029 | + | 0.100680i | ||||
\(897\) | − | 4.77160i | − | 0.159319i | ||||||
\(898\) | −4.27131 | + | 1.76923i | −0.142535 | + | 0.0590401i | ||||
\(899\) | −3.95740 | − | 3.95740i | −0.131987 | − | 0.131987i | ||||
\(900\) | 0.281305 | 0.00937682 | ||||||||
\(901\) | 1.26371 | + | 3.32431i | 0.0421002 | + | 0.110749i | ||||
\(902\) | 33.6211 | 1.11946 | ||||||||
\(903\) | −1.02214 | − | 1.02214i | −0.0340148 | − | 0.0340148i | ||||
\(904\) | −10.9369 | + | 4.53022i | −0.363756 | + | 0.150673i | ||||
\(905\) | 21.0634i | 0.700170i | ||||||||
\(906\) | −6.87282 | − | 16.5924i | −0.228334 | − | 0.551247i | ||||
\(907\) | −22.9245 | − | 9.49564i | −0.761196 | − | 0.315298i | −0.0318952 | − | 0.999491i | \(-0.510154\pi\) |
−0.729300 | + | 0.684194i | \(0.760154\pi\) | |||||||
\(908\) | −5.88336 | + | 14.2037i | −0.195246 | + | 0.471366i | ||||
\(909\) | 1.04373 | − | 1.04373i | 0.0346183 | − | 0.0346183i | ||||
\(910\) | −0.892349 | + | 0.892349i | −0.0295811 | + | 0.0295811i | ||||
\(911\) | −0.193157 | + | 0.466323i | −0.00639959 | + | 0.0154500i | −0.927047 | − | 0.374945i | \(-0.877662\pi\) |
0.920647 | + | 0.390395i | \(0.127662\pi\) | |||||||
\(912\) | 8.39572 | + | 3.47762i | 0.278010 | + | 0.115155i | ||||
\(913\) | −8.84464 | − | 21.3529i | −0.292715 | − | 0.706677i | ||||
\(914\) | 5.44127i | 0.179981i | ||||||||
\(915\) | 10.3147 | − | 4.27249i | 0.340993 | − | 0.141244i | ||||
\(916\) | 4.74517 | + | 4.74517i | 0.156785 | + | 0.156785i | ||||
\(917\) | 65.9649 | 2.17835 | ||||||||
\(918\) | −22.2979 | − | 0.656388i | −0.735939 | − | 0.0216640i | ||||
\(919\) | 20.9247 | 0.690243 | 0.345121 | − | 0.938558i | \(-0.387838\pi\) | ||||
0.345121 | + | 0.938558i | \(0.387838\pi\) | |||||||
\(920\) | 5.28931 | + | 5.28931i | 0.174383 | + | 0.174383i | ||||
\(921\) | 0.0750970 | − | 0.0311062i | 0.00247453 | − | 0.00102498i | ||||
\(922\) | 1.31618i | 0.0433461i | ||||||||
\(923\) | −1.31706 | − | 3.17966i | −0.0433515 | − | 0.104660i | ||||
\(924\) | 19.2557 | + | 7.97596i | 0.633465 | + | 0.262390i | ||||
\(925\) | −0.464466 | + | 1.12132i | −0.0152716 | + | 0.0368688i | ||||
\(926\) | 7.97795 | − | 7.97795i | 0.262172 | − | 0.262172i | ||||
\(927\) | −3.34468 | + | 3.34468i | −0.109854 | + | 0.109854i | ||||
\(928\) | −0.192641 | + | 0.465076i | −0.00632374 | + | 0.0152669i | ||||
\(929\) | −38.5898 | − | 15.9844i | −1.26609 | − | 0.524432i | −0.354318 | − | 0.935125i | \(-0.615287\pi\) |
−0.911774 | + | 0.410693i | \(0.865287\pi\) | |||||||
\(930\) | 7.01514 | + | 16.9360i | 0.230036 | + | 0.555355i | ||||
\(931\) | 20.0641i | 0.657573i | ||||||||
\(932\) | −1.43597 | + | 0.594799i | −0.0470368 | + | 0.0194833i | ||||
\(933\) | −19.9585 | − | 19.9585i | −0.653413 | − | 0.653413i | ||||
\(934\) | 21.8574 | 0.715195 | ||||||||
\(935\) | 6.54600 | − | 14.5749i | 0.214077 | − | 0.476651i | ||||
\(936\) | 0.108829 | 0.00355720 | ||||||||
\(937\) | 18.9789 | + | 18.9789i | 0.620014 | + | 0.620014i | 0.945535 | − | 0.325521i | \(-0.105540\pi\) |
−0.325521 | + | 0.945535i | \(0.605540\pi\) | |||||||
\(938\) | 7.17279 | − | 2.97107i | 0.234200 | − | 0.0970088i | ||||
\(939\) | 25.3880i | 0.828507i | ||||||||
\(940\) | −1.96281 | − | 4.73864i | −0.0640197 | − | 0.154557i | ||||
\(941\) | −47.1619 | − | 19.5351i | −1.53743 | − | 0.636826i | −0.556445 | − | 0.830885i | \(-0.687835\pi\) |
−0.980990 | + | 0.194058i | \(0.937835\pi\) | |||||||
\(942\) | 5.00686 | − | 12.0876i | 0.163132 | − | 0.393836i | ||||
\(943\) | −45.8911 | + | 45.8911i | −1.49442 | + | 1.49442i | ||||
\(944\) | 6.03300 | − | 6.03300i | 0.196357 | − | 0.196357i | ||||
\(945\) | −6.75378 | + | 16.3051i | −0.219700 | + | 0.530404i | ||||
\(946\) | −0.962198 | − | 0.398556i | −0.0312838 | − | 0.0129582i | ||||
\(947\) | 7.76243 | + | 18.7402i | 0.252245 | + | 0.608974i | 0.998385 | − | 0.0568159i | \(-0.0180948\pi\) |
−0.746139 | + | 0.665790i | \(0.768095\pi\) | |||||||
\(948\) | 8.12421i | 0.263862i | ||||||||
\(949\) | −2.52152 | + | 1.04445i | −0.0818520 | + | 0.0339042i | ||||
\(950\) | −3.89715 | − | 3.89715i | −0.126440 | − | 0.126440i | ||||
\(951\) | −45.4910 | −1.47515 | ||||||||
\(952\) | −0.395744 | + | 13.4436i | −0.0128261 | + | 0.435711i | ||||
\(953\) | −42.9260 | −1.39051 | −0.695254 | − | 0.718764i | \(-0.744708\pi\) | ||||
−0.695254 | + | 0.718764i | \(0.744708\pi\) | |||||||
\(954\) | −0.171573 | − | 0.171573i | −0.00555488 | − | 0.00555488i | ||||
\(955\) | 13.1894 | − | 5.46323i | 0.426799 | − | 0.176786i | ||||
\(956\) | 11.7012i | 0.378445i | ||||||||
\(957\) | 1.23087 | + | 2.97157i | 0.0397883 | + | 0.0960574i | ||||
\(958\) | 4.04430 | + | 1.67520i | 0.130665 | + | 0.0541233i | ||||
\(959\) | 12.2782 | − | 29.6422i | 0.396483 | − | 0.957196i | ||||
\(960\) | 1.16591 | − | 1.16591i | 0.0376296 | − | 0.0376296i | ||||
\(961\) | 65.4810 | − | 65.4810i | 2.11229 | − | 2.11229i | ||||
\(962\) | −0.179690 | + | 0.433810i | −0.00579343 | + | 0.0139866i | ||||
\(963\) | 2.65948 | + | 1.10159i | 0.0857006 | + | 0.0354983i | ||||
\(964\) | −10.4435 | − | 25.2129i | −0.336364 | − | 0.812054i | ||||
\(965\) | − | 20.7634i | − | 0.668398i | ||||||
\(966\) | −37.1698 | + | 15.3962i | −1.19592 | + | 0.495366i | ||||
\(967\) | −25.3012 | − | 25.3012i | −0.813632 | − | 0.813632i | 0.171545 | − | 0.985176i | \(-0.445124\pi\) |
−0.985176 | + | 0.171545i | \(0.945124\pi\) | |||||||
\(968\) | 4.01639 | 0.129092 | ||||||||
\(969\) | 25.7032 | + | 27.2624i | 0.825706 | + | 0.875794i | ||||
\(970\) | −11.6797 | −0.375011 | ||||||||
\(971\) | 34.0013 | + | 34.0013i | 1.09115 | + | 1.09115i | 0.995406 | + | 0.0957464i | \(0.0305238\pi\) |
0.0957464 | + | 0.995406i | \(0.469476\pi\) | |||||||
\(972\) | 2.69167 | − | 1.11493i | 0.0863354 | − | 0.0357613i | ||||
\(973\) | 4.07786i | 0.130730i | ||||||||
\(974\) | 7.61547 | + | 18.3854i | 0.244015 | + | 0.589105i | ||||
\(975\) | 0.589339 | + | 0.244112i | 0.0188740 | + | 0.00781785i | ||||
\(976\) | −2.59120 | + | 6.25570i | −0.0829422 | + | 0.200240i | ||||
\(977\) | −16.9706 | + | 16.9706i | −0.542937 | + | 0.542937i | −0.924389 | − | 0.381452i | \(-0.875424\pi\) |
0.381452 | + | 0.924389i | \(0.375424\pi\) | |||||||
\(978\) | −25.4608 | + | 25.4608i | −0.814145 | + | 0.814145i | ||||
\(979\) | 17.8663 | − | 43.1329i | 0.571008 | − | 1.37853i | ||||
\(980\) | 3.36335 | + | 1.39315i | 0.107438 | + | 0.0445024i | ||||
\(981\) | 1.14600 | + | 2.76668i | 0.0365889 | + | 0.0883334i | ||||
\(982\) | − | 26.1149i | − | 0.833361i | ||||||
\(983\) | 38.9250 | − | 16.1233i | 1.24152 | − | 0.514252i | 0.337327 | − | 0.941387i | \(-0.390477\pi\) |
0.904188 | + | 0.427135i | \(0.140477\pi\) | |||||||
\(984\) | 10.1157 | + | 10.1157i | 0.322475 | + | 0.322475i | ||||
\(985\) | 15.5519 | 0.495526 | ||||||||
\(986\) | −1.51018 | + | 1.42381i | −0.0480940 | + | 0.0453435i | ||||
\(987\) | 27.5866 | 0.878092 | ||||||||
\(988\) | −1.50771 | − | 1.50771i | −0.0479665 | − | 0.0479665i | ||||
\(989\) | 1.85736 | − | 0.769343i | 0.0590606 | − | 0.0244637i | ||||
\(990\) | 1.09008i | 0.0346451i | ||||||||
\(991\) | 6.27811 | + | 15.1567i | 0.199431 | + | 0.481468i | 0.991680 | − | 0.128730i | \(-0.0410899\pi\) |
−0.792249 | + | 0.610198i | \(0.791090\pi\) | |||||||
\(992\) | −10.2715 | − | 4.25457i | −0.326119 | − | 0.135083i | ||||
\(993\) | −0.489846 | + | 1.18259i | −0.0155448 | + | 0.0375284i | ||||
\(994\) | −20.5192 | + | 20.5192i | −0.650831 | + | 0.650831i | ||||
\(995\) | −1.77225 | + | 1.77225i | −0.0561840 | + | 0.0561840i | ||||
\(996\) | 3.76338 | − | 9.08560i | 0.119247 | − | 0.287888i | ||||
\(997\) | −38.1614 | − | 15.8070i | −1.20858 | − | 0.500611i | −0.314820 | − | 0.949151i | \(-0.601944\pi\) |
−0.893763 | + | 0.448540i | \(0.851944\pi\) | |||||||
\(998\) | −0.410649 | − | 0.991395i | −0.0129989 | − | 0.0313821i | ||||
\(999\) | 6.56661i | 0.207758i |
(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 | 170.2.k.a.121.2 | yes | 8 | |
5.2 | odd | 4 | 850.2.o.f.699.1 | 8 | |||
5.3 | odd | 4 | 850.2.o.c.699.2 | 8 | |||
5.4 | even | 2 | 850.2.l.d.801.1 | 8 | |||
17.3 | odd | 16 | 2890.2.a.bf.1.3 | 4 | |||
17.5 | odd | 16 | 2890.2.b.p.2311.6 | 8 | |||
17.9 | even | 8 | inner | 170.2.k.a.111.2 | ✓ | 8 | |
17.12 | odd | 16 | 2890.2.b.p.2311.3 | 8 | |||
17.14 | odd | 16 | 2890.2.a.bc.1.2 | 4 | |||
85.9 | even | 8 | 850.2.l.d.451.1 | 8 | |||
85.43 | odd | 8 | 850.2.o.f.349.1 | 8 | |||
85.77 | odd | 8 | 850.2.o.c.349.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.k.a.111.2 | ✓ | 8 | 17.9 | even | 8 | inner | |
170.2.k.a.121.2 | yes | 8 | 1.1 | even | 1 | trivial | |
850.2.l.d.451.1 | 8 | 85.9 | even | 8 | |||
850.2.l.d.801.1 | 8 | 5.4 | even | 2 | |||
850.2.o.c.349.2 | 8 | 85.77 | odd | 8 | |||
850.2.o.c.699.2 | 8 | 5.3 | odd | 4 | |||
850.2.o.f.349.1 | 8 | 85.43 | odd | 8 | |||
850.2.o.f.699.1 | 8 | 5.2 | odd | 4 | |||
2890.2.a.bc.1.2 | 4 | 17.14 | odd | 16 | |||
2890.2.a.bf.1.3 | 4 | 17.3 | odd | 16 | |||
2890.2.b.p.2311.3 | 8 | 17.12 | odd | 16 | |||
2890.2.b.p.2311.6 | 8 | 17.5 | odd | 16 |