Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [833,2,Mod(48,833)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(833, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([8, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("833.48");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 833 = 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 833.t (of order \(16\), degree \(8\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.65153848837\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{16})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Character | \(\chi\) | \(=\) | 833.97 |
Dual form | 833.2.t.d.146.2 |
$q$-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 \(\left(\mathbb{Z}/833\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{13}{16}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.684321 | − | 1.65210i | −0.483888 | − | 1.16821i | −0.957748 | − | 0.287609i | \(-0.907140\pi\) |
0.473859 | − | 0.880601i | \(-0.342860\pi\) | |||||||
\(3\) | 0.302826 | + | 0.453212i | 0.174837 | + | 0.261662i | 0.908530 | − | 0.417819i | \(-0.137205\pi\) |
−0.733694 | + | 0.679481i | \(0.762205\pi\) | |||||||
\(4\) | −0.846919 | + | 0.846919i | −0.423460 | + | 0.423460i | ||||
\(5\) | 0.523006 | − | 2.62933i | 0.233895 | − | 1.17587i | −0.668082 | − | 0.744088i | \(-0.732884\pi\) |
0.901977 | − | 0.431784i | \(-0.142116\pi\) | |||||||
\(6\) | 0.541520 | − | 0.810442i | 0.221075 | − | 0.330861i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.32544 | − | 0.549014i | −0.468613 | − | 0.194106i | ||||
\(9\) | 1.03435 | − | 2.49715i | 0.344784 | − | 0.832383i | ||||
\(10\) | −4.70181 | + | 0.935249i | −1.48684 | + | 0.295752i | ||||
\(11\) | −2.78572 | + | 4.16913i | −0.839927 | + | 1.25704i | 0.124375 | + | 0.992235i | \(0.460307\pi\) |
−0.964302 | + | 0.264805i | \(0.914693\pi\) | |||||||
\(12\) | −0.640303 | − | 0.127364i | −0.184840 | − | 0.0367669i | ||||
\(13\) | −4.70535 | + | 4.70535i | −1.30503 | + | 1.30503i | −0.380072 | + | 0.924957i | \(0.624101\pi\) |
−0.924957 | + | 0.380072i | \(0.875899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.35002 | − | 0.559198i | 0.348574 | − | 0.144384i | ||||
\(16\) | 4.96091i | 1.24023i | ||||||||
\(17\) | −2.09362 | − | 3.55201i | −0.507778 | − | 0.861488i | ||||
\(18\) | −4.83337 | −1.13924 | ||||||||
\(19\) | −4.91367 | + | 2.03531i | −1.12727 | + | 0.466932i | −0.866853 | − | 0.498564i | \(-0.833861\pi\) |
−0.260420 | + | 0.965495i | \(0.583861\pi\) | |||||||
\(20\) | 1.78388 | + | 2.66977i | 0.398889 | + | 0.596979i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.79414 | + | 1.74926i | 1.87492 | + | 0.372944i | ||||
\(23\) | −3.40111 | − | 2.27255i | −0.709180 | − | 0.473859i | 0.147926 | − | 0.988998i | \(-0.452740\pi\) |
−0.857107 | + | 0.515139i | \(0.827740\pi\) | |||||||
\(24\) | −0.152558 | − | 0.766960i | −0.0311407 | − | 0.156555i | ||||
\(25\) | −2.02043 | − | 0.836891i | −0.404087 | − | 0.167378i | ||||
\(26\) | 10.9937 | + | 4.55373i | 2.15604 | + | 0.893059i | ||||
\(27\) | 3.04877 | − | 0.606437i | 0.586735 | − | 0.116709i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.90098 | − | 9.55688i | 0.353004 | − | 1.77467i | −0.241323 | − | 0.970445i | \(-0.577581\pi\) |
0.594327 | − | 0.804224i | \(-0.297419\pi\) | |||||||
\(30\) | −1.84770 | − | 1.84770i | −0.337342 | − | 0.337342i | ||||
\(31\) | −0.638820 | + | 0.426846i | −0.114735 | + | 0.0766638i | −0.611614 | − | 0.791156i | \(-0.709479\pi\) |
0.496879 | + | 0.867820i | \(0.334479\pi\) | |||||||
\(32\) | 5.54503 | − | 2.29683i | 0.980231 | − | 0.406025i | ||||
\(33\) | −2.73309 | −0.475770 | ||||||||
\(34\) | −4.43555 | + | 5.88958i | −0.760691 | + | 1.01006i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.23887 | + | 2.99090i | 0.206478 | + | 0.498483i | ||||
\(37\) | 4.93349 | − | 3.29645i | 0.811061 | − | 0.541934i | −0.0794800 | − | 0.996836i | \(-0.525326\pi\) |
0.890541 | + | 0.454903i | \(0.150326\pi\) | |||||||
\(38\) | 6.72506 | + | 6.72506i | 1.09095 | + | 1.09095i | ||||
\(39\) | −3.55742 | − | 0.707616i | −0.569644 | − | 0.113309i | ||||
\(40\) | −2.13675 | + | 3.19787i | −0.337850 | + | 0.505628i | ||||
\(41\) | 0.0510695 | + | 0.256744i | 0.00797571 | + | 0.0400966i | 0.984568 | − | 0.175001i | \(-0.0559930\pi\) |
−0.976593 | + | 0.215098i | \(0.930993\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.397620 | − | 0.959941i | 0.0606365 | − | 0.146390i | −0.890657 | − | 0.454675i | \(-0.849755\pi\) |
0.951294 | + | 0.308286i | \(0.0997553\pi\) | |||||||
\(44\) | −1.17163 | − | 5.89020i | −0.176630 | − | 0.887981i | ||||
\(45\) | −6.02485 | − | 4.02568i | −0.898132 | − | 0.600113i | ||||
\(46\) | −1.42702 | + | 7.17412i | −0.210403 | + | 1.05777i | ||||
\(47\) | −6.07130 | + | 6.07130i | −0.885590 | + | 0.885590i | −0.994096 | − | 0.108506i | \(-0.965393\pi\) |
0.108506 | + | 0.994096i | \(0.465393\pi\) | |||||||
\(48\) | −2.24834 | + | 1.50229i | −0.324520 | + | 0.216837i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.91066i | 0.553050i | ||||||||
\(51\) | 0.975807 | − | 2.02450i | 0.136640 | − | 0.283486i | ||||
\(52\) | − | 7.97010i | − | 1.10525i | ||||||
\(53\) | −0.700266 | − | 1.69059i | −0.0961890 | − | 0.232221i | 0.868460 | − | 0.495760i | \(-0.165110\pi\) |
−0.964649 | + | 0.263539i | \(0.915110\pi\) | |||||||
\(54\) | −3.08823 | − | 4.62186i | −0.420255 | − | 0.628956i | ||||
\(55\) | 9.50506 | + | 9.50506i | 1.28166 | + | 1.28166i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.41041 | − | 1.61059i | −0.319267 | − | 0.213327i | ||||
\(58\) | −17.0898 | + | 3.39937i | −2.24400 | + | 0.446359i | ||||
\(59\) | −2.28490 | + | 5.51623i | −0.297468 | + | 0.718151i | 0.702511 | + | 0.711673i | \(0.252062\pi\) |
−0.999979 | + | 0.00647849i | \(0.997938\pi\) | |||||||
\(60\) | −0.669765 | + | 1.61696i | −0.0864663 | + | 0.208748i | ||||
\(61\) | 1.48687 | − | 0.295757i | 0.190374 | − | 0.0378677i | −0.0989824 | − | 0.995089i | \(-0.531559\pi\) |
0.289356 | + | 0.957221i | \(0.406559\pi\) | |||||||
\(62\) | 1.14235 | + | 0.763294i | 0.145079 | + | 0.0969384i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.573383 | − | 0.573383i | −0.0716728 | − | 0.0716728i | ||||
\(65\) | 9.91098 | + | 14.8328i | 1.22931 | + | 1.83979i | ||||
\(66\) | 1.87031 | + | 4.51533i | 0.230219 | + | 0.555799i | ||||
\(67\) | − | 12.3675i | − | 1.51093i | −0.655186 | − | 0.755467i | \(-0.727410\pi\) | ||
0.655186 | − | 0.755467i | \(-0.272590\pi\) | |||||||
\(68\) | 4.78139 | + | 1.23513i | 0.579829 | + | 0.149782i | ||||
\(69\) | − | 2.22961i | − | 0.268414i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.95416 | + | 2.64209i | −0.469273 | + | 0.313558i | −0.767627 | − | 0.640897i | \(-0.778562\pi\) |
0.298354 | + | 0.954455i | \(0.403562\pi\) | |||||||
\(72\) | −2.74194 | + | 2.74194i | −0.323141 | + | 0.323141i | ||||
\(73\) | −0.221196 | + | 1.11203i | −0.0258890 | + | 0.130153i | −0.991568 | − | 0.129584i | \(-0.958636\pi\) |
0.965679 | + | 0.259737i | \(0.0836358\pi\) | |||||||
\(74\) | −8.82216 | − | 5.89478i | −1.02556 | − | 0.685254i | ||||
\(75\) | −0.232552 | − | 1.16912i | −0.0268528 | − | 0.134998i | ||||
\(76\) | 2.43774 | − | 5.88522i | 0.279628 | − | 0.675081i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.26537 | + | 6.36145i | 0.143275 | + | 0.720292i | ||||
\(79\) | −6.72273 | + | 10.0613i | −0.756367 | + | 1.13198i | 0.230911 | + | 0.972975i | \(0.425829\pi\) |
−0.987277 | + | 0.159008i | \(0.949171\pi\) | |||||||
\(80\) | 13.0438 | + | 2.59458i | 1.45835 | + | 0.290083i | ||||
\(81\) | −4.53561 | − | 4.53561i | −0.503957 | − | 0.503957i | ||||
\(82\) | 0.389218 | − | 0.260067i | 0.0429819 | − | 0.0287196i | ||||
\(83\) | −5.11069 | − | 12.3383i | −0.560971 | − | 1.35430i | −0.908990 | − | 0.416817i | \(-0.863146\pi\) |
0.348019 | − | 0.937488i | \(-0.386854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4344 | + | 3.64710i | −1.13177 | + | 0.395583i | ||||
\(86\) | −1.85802 | −0.200355 | ||||||||
\(87\) | 4.90696 | − | 2.03253i | 0.526081 | − | 0.217910i | ||||
\(88\) | 5.98122 | − | 3.99652i | 0.637600 | − | 0.426031i | ||||
\(89\) | −1.38538 | − | 1.38538i | −0.146849 | − | 0.146849i | 0.629860 | − | 0.776709i | \(-0.283112\pi\) |
−0.776709 | + | 0.629860i | \(0.783112\pi\) | |||||||
\(90\) | −2.52788 | + | 12.7085i | −0.266462 | + | 1.33959i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.80513 | − | 0.955800i | 0.500969 | − | 0.0996490i | ||||
\(93\) | −0.386903 | − | 0.160261i | −0.0401200 | − | 0.0166182i | ||||
\(94\) | 14.1851 | + | 5.87566i | 1.46308 | + | 0.606028i | ||||
\(95\) | 2.78161 | + | 13.9841i | 0.285388 | + | 1.43474i | ||||
\(96\) | 2.72013 | + | 1.81753i | 0.277622 | + | 0.185501i | ||||
\(97\) | −9.84825 | − | 1.95894i | −0.999938 | − | 0.198900i | −0.332130 | − | 0.943234i | \(-0.607767\pi\) |
−0.667808 | + | 0.744334i | \(0.732767\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.52952 | + | 11.2687i | 0.756745 | + | 1.13255i | ||||
\(100\) | 2.41992 | − | 1.00236i | 0.241992 | − | 0.100236i | ||||
\(101\) | 5.20889 | 0.518304 | 0.259152 | − | 0.965837i | \(-0.416557\pi\) | ||||
0.259152 | + | 0.965837i | \(0.416557\pi\) | |||||||
\(102\) | −4.01243 | − | 0.226723i | −0.397290 | − | 0.0224489i | ||||
\(103\) | − | 6.41077i | − | 0.631672i | −0.948814 | − | 0.315836i | \(-0.897715\pi\) | ||
0.948814 | − | 0.315836i | \(-0.102285\pi\) | |||||||
\(104\) | 8.81995 | − | 3.65334i | 0.864867 | − | 0.358240i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.31382 | + | 2.31382i | −0.224738 | + | 0.224738i | ||||
\(107\) | 5.31426 | + | 1.05707i | 0.513749 | + | 0.102191i | 0.445155 | − | 0.895454i | \(-0.353149\pi\) |
0.0685944 | + | 0.997645i | \(0.478149\pi\) | |||||||
\(108\) | −2.06846 | + | 3.09566i | −0.199037 | + | 0.297880i | ||||
\(109\) | 2.29235 | − | 0.455976i | 0.219567 | − | 0.0436746i | −0.0840808 | − | 0.996459i | \(-0.526795\pi\) |
0.303648 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(110\) | 9.19878 | − | 22.2078i | 0.877069 | − | 2.11743i | ||||
\(111\) | 2.98798 | + | 1.23766i | 0.283607 | + | 0.117474i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3160 | − | 15.4390i | 0.970451 | − | 1.45238i | 0.0802713 | − | 0.996773i | \(-0.474421\pi\) |
0.890180 | − | 0.455610i | \(-0.150579\pi\) | |||||||
\(114\) | −1.01135 | + | 5.08440i | −0.0947216 | + | 0.476198i | ||||
\(115\) | −7.75408 | + | 7.75408i | −0.723071 | + | 0.723071i | ||||
\(116\) | 6.48393 | + | 9.70388i | 0.602018 | + | 0.900983i | ||||
\(117\) | 6.88297 | + | 16.6170i | 0.636331 | + | 1.53624i | ||||
\(118\) | 10.6769 | 0.982893 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.09638 | −0.191372 | ||||||||
\(121\) | −5.41187 | − | 13.0654i | −0.491988 | − | 1.18776i | ||||
\(122\) | −1.50611 | − | 2.25406i | −0.136357 | − | 0.204073i | ||||
\(123\) | −0.100894 | + | 0.100894i | −0.00909731 | + | 0.00909731i | ||||
\(124\) | 0.179525 | − | 0.902533i | 0.0161218 | − | 0.0810498i | ||||
\(125\) | 4.18982 | − | 6.27050i | 0.374748 | − | 0.560851i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.38122 | + | 0.572121i | 0.122564 | + | 0.0507675i | 0.443122 | − | 0.896461i | \(-0.353871\pi\) |
−0.320559 | + | 0.947229i | \(0.603871\pi\) | |||||||
\(128\) | 4.03874 | − | 9.75039i | 0.356978 | − | 0.861821i | ||||
\(129\) | 0.555466 | − | 0.110489i | 0.0489061 | − | 0.00972803i | ||||
\(130\) | 17.7230 | − | 26.5243i | 1.55441 | − | 2.32634i | ||||
\(131\) | 3.52084 | + | 0.700339i | 0.307617 | + | 0.0611889i | 0.346485 | − | 0.938055i | \(-0.387375\pi\) |
−0.0388678 | + | 0.999244i | \(0.512375\pi\) | |||||||
\(132\) | 2.31471 | − | 2.31471i | 0.201469 | − | 0.201469i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.4324 | + | 8.46337i | −1.76509 | + | 0.731124i | ||||
\(135\) | − | 8.33338i | − | 0.717223i | ||||||
\(136\) | 0.824863 | + | 5.85739i | 0.0707315 | + | 0.502267i | ||||
\(137\) | 4.88115 | 0.417025 | 0.208512 | − | 0.978020i | \(-0.433138\pi\) | ||||
0.208512 | + | 0.978020i | \(0.433138\pi\) | |||||||
\(138\) | −3.68354 | + | 1.52577i | −0.313563 | + | 0.129882i | ||||
\(139\) | −2.96540 | − | 4.43803i | −0.251522 | − | 0.376429i | 0.684126 | − | 0.729364i | \(-0.260184\pi\) |
−0.935648 | + | 0.352935i | \(0.885184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.59013 | − | 0.913034i | −0.386559 | − | 0.0768914i | ||||
\(142\) | 7.07091 | + | 4.72463i | 0.593377 | + | 0.396482i | ||||
\(143\) | −6.50941 | − | 32.7250i | −0.544344 | − | 2.73660i | ||||
\(144\) | 12.3881 | + | 5.13133i | 1.03234 | + | 0.427611i | ||||
\(145\) | −24.1340 | − | 9.99661i | −2.00422 | − | 0.830173i | ||||
\(146\) | 1.98854 | − | 0.395546i | 0.164573 | − | 0.0327356i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.38644 | + | 6.97010i | −0.113965 | + | 0.572939i | ||||
\(149\) | 5.31090 | + | 5.31090i | 0.435086 | + | 0.435086i | 0.890354 | − | 0.455268i | \(-0.150457\pi\) |
−0.455268 | + | 0.890354i | \(0.650457\pi\) | |||||||
\(150\) | −1.77236 | + | 1.18425i | −0.144712 | + | 0.0966936i | ||||
\(151\) | −5.31362 | + | 2.20097i | −0.432416 | + | 0.179113i | −0.588265 | − | 0.808668i | \(-0.700189\pi\) |
0.155849 | + | 0.987781i | \(0.450189\pi\) | |||||||
\(152\) | 7.63017 | 0.618889 | ||||||||
\(153\) | −11.0354 | + | 1.55406i | −0.892162 | + | 0.125638i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.788211 | + | 1.90291i | 0.0633107 | + | 0.152845i | ||||
\(156\) | 3.61214 | − | 2.41356i | 0.289203 | − | 0.193239i | ||||
\(157\) | −4.89744 | − | 4.89744i | −0.390858 | − | 0.390858i | 0.484135 | − | 0.874993i | \(-0.339134\pi\) |
−0.874993 | + | 0.484135i | \(0.839134\pi\) | |||||||
\(158\) | 21.2227 | + | 4.22146i | 1.68839 | + | 0.335842i | ||||
\(159\) | 0.554137 | − | 0.829325i | 0.0439459 | − | 0.0657697i | ||||
\(160\) | −3.13903 | − | 15.7809i | −0.248162 | − | 1.24759i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.38946 | + | 10.5971i | −0.344869 | + | 0.832587i | ||||
\(163\) | 2.46110 | + | 12.3728i | 0.192769 | + | 0.969113i | 0.949112 | + | 0.314938i | \(0.101984\pi\) |
−0.756344 | + | 0.654175i | \(0.773016\pi\) | |||||||
\(164\) | −0.260693 | − | 0.174189i | −0.0203567 | − | 0.0136019i | ||||
\(165\) | −1.42942 | + | 7.18619i | −0.111280 | + | 0.559444i | ||||
\(166\) | −16.8867 | + | 16.8867i | −1.31066 | + | 1.31066i | ||||
\(167\) | −11.1181 | + | 7.42888i | −0.860345 | + | 0.574864i | −0.905610 | − | 0.424111i | \(-0.860587\pi\) |
0.0452651 | + | 0.998975i | \(0.485587\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 31.2806i | − | 2.40620i | ||||||
\(170\) | 13.1658 | + | 14.7428i | 1.00977 | + | 1.13072i | ||||
\(171\) | 14.3754i | 1.09931i | ||||||||
\(172\) | 0.476240 | + | 1.14974i | 0.0363129 | + | 0.0876672i | ||||
\(173\) | 1.97005 | + | 2.94838i | 0.149780 | + | 0.224161i | 0.898771 | − | 0.438419i | \(-0.144461\pi\) |
−0.748991 | + | 0.662580i | \(0.769461\pi\) | |||||||
\(174\) | −6.71588 | − | 6.71588i | −0.509129 | − | 0.509129i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.6827 | − | 13.8197i | −1.55901 | − | 1.04170i | ||||
\(177\) | −3.19195 | + | 0.634917i | −0.239921 | + | 0.0477233i | ||||
\(178\) | −1.34073 | + | 3.23682i | −0.100492 | + | 0.242610i | ||||
\(179\) | −3.28072 | + | 7.92036i | −0.245213 | + | 0.591996i | −0.997786 | − | 0.0665132i | \(-0.978813\pi\) |
0.752573 | + | 0.658509i | \(0.228813\pi\) | |||||||
\(180\) | 8.51199 | − | 1.69314i | 0.634446 | − | 0.126199i | ||||
\(181\) | 4.23355 | + | 2.82877i | 0.314677 | + | 0.210261i | 0.702871 | − | 0.711317i | \(-0.251901\pi\) |
−0.388194 | + | 0.921578i | \(0.626901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.584303 | + | 0.584303i | 0.0431930 | + | 0.0431930i | ||||
\(184\) | 3.26030 | + | 4.87938i | 0.240352 | + | 0.359713i | ||||
\(185\) | −6.08721 | − | 14.6958i | −0.447541 | − | 1.08046i | ||||
\(186\) | 0.748872i | 0.0549100i | ||||||||
\(187\) | 20.6410 | + | 1.16633i | 1.50942 | + | 0.0852902i | ||||
\(188\) | − | 10.2838i | − | 0.750023i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.1996 | − | 14.1651i | 1.53798 | − | 1.02765i | ||||
\(191\) | 17.4411 | − | 17.4411i | 1.26200 | − | 1.26200i | 0.311872 | − | 0.950124i | \(-0.399044\pi\) |
0.950124 | − | 0.311872i | \(-0.100956\pi\) | |||||||
\(192\) | 0.0862284 | − | 0.433499i | 0.00622300 | − | 0.0312851i | ||||
\(193\) | −16.9790 | − | 11.3450i | −1.22218 | − | 0.816633i | −0.234345 | − | 0.972153i | \(-0.575295\pi\) |
−0.987833 | + | 0.155520i | \(0.950295\pi\) | |||||||
\(194\) | 3.50301 | + | 17.6108i | 0.251501 | + | 1.26438i | ||||
\(195\) | −3.72111 | + | 8.98355i | −0.266474 | + | 0.643325i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.66733 | + | 8.38222i | 0.118792 | + | 0.597208i | 0.993621 | + | 0.112775i | \(0.0359740\pi\) |
−0.874828 | + | 0.484433i | \(0.839026\pi\) | |||||||
\(198\) | 13.4644 | − | 20.1509i | 0.956875 | − | 1.43206i | ||||
\(199\) | −15.9403 | − | 3.17072i | −1.12998 | − | 0.224766i | −0.405519 | − | 0.914087i | \(-0.632909\pi\) |
−0.724457 | + | 0.689320i | \(0.757909\pi\) | |||||||
\(200\) | 2.21849 | + | 2.21849i | 0.156871 | + | 0.156871i | ||||
\(201\) | 5.60511 | − | 3.74522i | 0.395354 | − | 0.264167i | ||||
\(202\) | −3.56456 | − | 8.60560i | −0.250801 | − | 0.605488i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.888154 | + | 2.54101i | 0.0621832 | + | 0.177907i | ||||
\(205\) | 0.701772 | 0.0490139 | ||||||||
\(206\) | −10.5912 | + | 4.38703i | −0.737925 | + | 0.305659i | ||||
\(207\) | −9.19284 | + | 6.14246i | −0.638947 | + | 0.426931i | ||||
\(208\) | −23.3428 | − | 23.3428i | −1.61853 | − | 1.61853i | ||||
\(209\) | 5.20266 | − | 26.1555i | 0.359875 | − | 1.80922i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.74454 | + | 1.93831i | −0.670842 | + | 0.133439i | −0.518748 | − | 0.854927i | \(-0.673602\pi\) |
−0.152094 | + | 0.988366i | \(0.548602\pi\) | |||||||
\(212\) | 2.02486 | + | 0.838726i | 0.139068 | + | 0.0576039i | ||||
\(213\) | −2.39485 | − | 0.991979i | −0.164092 | − | 0.0679693i | ||||
\(214\) | −1.89028 | − | 9.50307i | −0.129217 | − | 0.649616i | ||||
\(215\) | −2.31604 | − | 1.54753i | −0.157953 | − | 0.105541i | ||||
\(216\) | −4.37389 | − | 0.870022i | −0.297606 | − | 0.0591975i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.32202 | − | 3.47515i | −0.157267 | − | 0.235367i | ||||
\(219\) | −0.570967 | + | 0.236502i | −0.0385824 | + | 0.0159813i | ||||
\(220\) | −16.1000 | −1.08546 | ||||||||
\(221\) | 26.5646 | + | 6.86221i | 1.78693 | + | 0.461602i | ||||
\(222\) | − | 5.78340i | − | 0.388157i | ||||||
\(223\) | −1.88077 | + | 0.779040i | −0.125946 | + | 0.0521684i | −0.444766 | − | 0.895647i | \(-0.646713\pi\) |
0.318821 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.17968 | + | 4.17968i | −0.278645 | + | 0.278645i | ||||
\(226\) | −32.5663 | − | 6.47784i | −2.16628 | − | 0.430899i | ||||
\(227\) | 0.793816 | − | 1.18803i | 0.0526874 | − | 0.0788523i | −0.804191 | − | 0.594371i | \(-0.797401\pi\) |
0.856878 | + | 0.515519i | \(0.172401\pi\) | |||||||
\(228\) | 3.40546 | − | 0.677389i | 0.225532 | − | 0.0448612i | ||||
\(229\) | 3.45831 | − | 8.34911i | 0.228532 | − | 0.551724i | −0.767467 | − | 0.641088i | \(-0.778483\pi\) |
0.995999 | + | 0.0893636i | \(0.0284833\pi\) | |||||||
\(230\) | 18.1168 | + | 7.50422i | 1.19459 | + | 0.494813i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.76650 | + | 11.6234i | −0.509896 | + | 0.763113i | ||||
\(233\) | −0.354571 | + | 1.78255i | −0.0232287 | + | 0.116779i | −0.990660 | − | 0.136355i | \(-0.956461\pi\) |
0.967431 | + | 0.253134i | \(0.0814612\pi\) | |||||||
\(234\) | 22.7427 | − | 22.7427i | 1.48674 | − | 1.48674i | ||||
\(235\) | 12.7881 | + | 19.1388i | 0.834204 | + | 1.24848i | ||||
\(236\) | −2.73668 | − | 6.60692i | −0.178142 | − | 0.430074i | ||||
\(237\) | −6.59571 | −0.428438 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.77316 | −0.308750 | −0.154375 | − | 0.988012i | \(-0.549336\pi\) | ||||
−0.154375 | + | 0.988012i | \(0.549336\pi\) | |||||||
\(240\) | 2.77413 | + | 6.69733i | 0.179069 | + | 0.432311i | ||||
\(241\) | 8.03495 | + | 12.0252i | 0.517577 | + | 0.774608i | 0.994545 | − | 0.104313i | \(-0.0332642\pi\) |
−0.476968 | + | 0.878921i | \(0.658264\pi\) | |||||||
\(242\) | −17.8819 | + | 17.8819i | −1.14949 | + | 1.14949i | ||||
\(243\) | 2.50140 | − | 12.5754i | 0.160465 | − | 0.806712i | ||||
\(244\) | −1.00878 | + | 1.50974i | −0.0645802 | + | 0.0966512i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.235731 | + | 0.0976429i | 0.0150296 | + | 0.00622548i | ||||
\(247\) | 13.5437 | − | 32.6974i | 0.861764 | − | 2.08048i | ||||
\(248\) | 1.08106 | − | 0.215036i | 0.0686474 | − | 0.0136548i | ||||
\(249\) | 4.04421 | − | 6.05259i | 0.256292 | − | 0.383567i | ||||
\(250\) | −13.2267 | − | 2.63095i | −0.836528 | − | 0.166396i | ||||
\(251\) | 22.0951 | − | 22.0951i | 1.39463 | − | 1.39463i | 0.580038 | − | 0.814589i | \(-0.303037\pi\) |
0.814589 | − | 0.580038i | \(-0.196963\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.9491 | − | 7.84898i | 1.19132 | − | 0.493461i | ||||
\(254\) | − | 2.67343i | − | 0.167746i | ||||||
\(255\) | −4.81271 | − | 3.62454i | −0.301384 | − | 0.226977i | ||||
\(256\) | −20.4942 | −1.28089 | ||||||||
\(257\) | −20.6564 | + | 8.55615i | −1.28851 | + | 0.533718i | −0.918541 | − | 0.395326i | \(-0.870632\pi\) |
−0.369969 | + | 0.929044i | \(0.620632\pi\) | |||||||
\(258\) | −0.562657 | − | 0.842075i | −0.0350295 | − | 0.0524253i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −20.9560 | − | 4.16841i | −1.29964 | − | 0.258514i | ||||
\(261\) | −21.8987 | − | 14.6322i | −1.35549 | − | 0.905712i | ||||
\(262\) | −1.25236 | − | 6.29603i | −0.0773710 | − | 0.388970i | ||||
\(263\) | −6.50189 | − | 2.69317i | −0.400924 | − | 0.166068i | 0.173105 | − | 0.984903i | \(-0.444620\pi\) |
−0.574028 | + | 0.818835i | \(0.694620\pi\) | |||||||
\(264\) | 3.62254 | + | 1.50051i | 0.222952 | + | 0.0923497i | ||||
\(265\) | −4.81136 | + | 0.957040i | −0.295560 | + | 0.0587905i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.208340 | − | 1.04740i | 0.0127502 | − | 0.0640996i | ||||
\(268\) | 10.4743 | + | 10.4743i | 0.639820 | + | 0.639820i | ||||
\(269\) | −3.49544 | + | 2.33558i | −0.213121 | + | 0.142403i | −0.657549 | − | 0.753412i | \(-0.728407\pi\) |
0.444429 | + | 0.895814i | \(0.353407\pi\) | |||||||
\(270\) | −13.7676 | + | 5.70271i | −0.837867 | + | 0.347056i | ||||
\(271\) | 4.29597 | 0.260961 | 0.130481 | − | 0.991451i | \(-0.458348\pi\) | ||||
0.130481 | + | 0.991451i | \(0.458348\pi\) | |||||||
\(272\) | 17.6212 | − | 10.3863i | 1.06844 | − | 0.629759i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.34027 | − | 8.06414i | −0.201793 | − | 0.487172i | ||||
\(275\) | 9.11747 | − | 6.09210i | 0.549804 | − | 0.367367i | ||||
\(276\) | 1.88830 | + | 1.88830i | 0.113662 | + | 0.113662i | ||||
\(277\) | −12.2433 | − | 2.43534i | −0.735627 | − | 0.146325i | −0.186962 | − | 0.982367i | \(-0.559864\pi\) |
−0.548666 | + | 0.836042i | \(0.684864\pi\) | |||||||
\(278\) | −5.30278 | + | 7.93617i | −0.318040 | + | 0.475980i | ||||
\(279\) | 0.405133 | + | 2.03674i | 0.0242546 | + | 0.121936i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.91965 | + | 7.04865i | −0.174172 | + | 0.420487i | −0.986725 | − | 0.162399i | \(-0.948077\pi\) |
0.812554 | + | 0.582887i | \(0.198077\pi\) | |||||||
\(282\) | 1.63270 | + | 8.20816i | 0.0972262 | + | 0.488789i | ||||
\(283\) | −5.96002 | − | 3.98236i | −0.354286 | − | 0.236727i | 0.365672 | − | 0.930744i | \(-0.380839\pi\) |
−0.719958 | + | 0.694017i | \(0.755839\pi\) | |||||||
\(284\) | 1.11122 | − | 5.58649i | 0.0659389 | − | 0.331497i | ||||
\(285\) | −5.49542 | + | 5.49542i | −0.325521 | + | 0.325521i | ||||
\(286\) | −49.6104 | + | 33.1486i | −2.93352 | + | 1.96012i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 16.2225i | − | 0.955919i | ||||||
\(289\) | −8.23349 | + | 14.8731i | −0.484323 | + | 0.874889i | ||||
\(290\) | 46.7126i | 2.74306i | ||||||||
\(291\) | −2.09450 | − | 5.05656i | −0.122782 | − | 0.296421i | ||||
\(292\) | −0.754461 | − | 1.12913i | −0.0441515 | − | 0.0660774i | ||||
\(293\) | 4.15110 | + | 4.15110i | 0.242510 | + | 0.242510i | 0.817888 | − | 0.575378i | \(-0.195145\pi\) |
−0.575378 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.3090 | + | 8.89276i | 0.774877 | + | 0.517756i | ||||
\(296\) | −8.34884 | + | 1.66069i | −0.485266 | + | 0.0965255i | ||||
\(297\) | −5.96470 | + | 14.4001i | −0.346107 | + | 0.835577i | ||||
\(298\) | 5.13976 | − | 12.4085i | 0.297739 | − | 0.718804i | ||||
\(299\) | 26.6965 | − | 5.31027i | 1.54390 | − | 0.307101i | ||||
\(300\) | 1.18710 | + | 0.793195i | 0.0685372 | + | 0.0457951i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.27245 | + | 7.27245i | 0.418482 | + | 0.418482i | ||||
\(303\) | 1.57739 | + | 2.36073i | 0.0906187 | + | 0.135620i | ||||
\(304\) | −10.0970 | − | 24.3762i | −0.579101 | − | 1.39807i | ||||
\(305\) | − | 4.06415i | − | 0.232712i | ||||||
\(306\) | 10.1192 | + | 17.1681i | 0.578479 | + | 0.981438i | ||||
\(307\) | − | 24.0844i | − | 1.37457i | −0.726387 | − | 0.687286i | \(-0.758802\pi\) | ||
0.726387 | − | 0.687286i | \(-0.241198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.90544 | − | 1.94135i | 0.165284 | − | 0.110440i | ||||
\(310\) | 2.60440 | − | 2.60440i | 0.147920 | − | 0.147920i | ||||
\(311\) | 0.631126 | − | 3.17289i | 0.0357879 | − | 0.179918i | −0.958757 | − | 0.284227i | \(-0.908263\pi\) |
0.994545 | + | 0.104309i | \(0.0332631\pi\) | |||||||
\(312\) | 4.32665 | + | 2.89098i | 0.244949 | + | 0.163669i | ||||
\(313\) | −1.29305 | − | 6.50060i | −0.0730875 | − | 0.367436i | 0.926881 | − | 0.375355i | \(-0.122479\pi\) |
−0.999969 | + | 0.00791932i | \(0.997479\pi\) | |||||||
\(314\) | −4.73963 | + | 11.4425i | −0.267473 | + | 0.645737i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.82748 | − | 14.2147i | −0.159058 | − | 0.799639i | ||||
\(317\) | 6.30432 | − | 9.43509i | 0.354086 | − | 0.529927i | −0.611079 | − | 0.791570i | \(-0.709264\pi\) |
0.965165 | + | 0.261643i | \(0.0842641\pi\) | |||||||
\(318\) | −1.74933 | − | 0.347964i | −0.0980978 | − | 0.0195129i | ||||
\(319\) | 34.5483 | + | 34.5483i | 1.93433 | + | 1.93433i | ||||
\(320\) | −1.80749 | + | 1.20773i | −0.101042 | + | 0.0675141i | ||||
\(321\) | 1.13022 | + | 2.72860i | 0.0630828 | + | 0.152295i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.5168 | + | 13.1922i | 0.974660 | + | 0.734034i | ||||
\(324\) | 7.68260 | 0.426811 | ||||||||
\(325\) | 13.4447 | − | 5.56898i | 0.745778 | − | 0.308911i | ||||
\(326\) | 18.7569 | − | 12.5330i | 1.03885 | − | 0.694137i | ||||
\(327\) | 0.900837 | + | 0.900837i | 0.0498164 | + | 0.0498164i | ||||
\(328\) | 0.0732665 | − | 0.368335i | 0.00404546 | − | 0.0203379i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 12.8505 | − | 2.55612i | 0.707395 | − | 0.140710i | ||||
\(331\) | 22.6983 | + | 9.40193i | 1.24761 | + | 0.516777i | 0.906085 | − | 0.423096i | \(-0.139057\pi\) |
0.341524 | + | 0.939873i | \(0.389057\pi\) | |||||||
\(332\) | 14.7779 | + | 6.12120i | 0.811042 | + | 0.335945i | ||||
\(333\) | −3.12877 | − | 15.7294i | −0.171455 | − | 0.861964i | ||||
\(334\) | 19.8816 | + | 13.2845i | 1.08787 | + | 0.726894i | ||||
\(335\) | −32.5183 | − | 6.46829i | −1.77666 | − | 0.353401i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.83989 | + | 4.25020i | 0.154699 | + | 0.231523i | 0.900721 | − | 0.434398i | \(-0.143039\pi\) |
−0.746022 | + | 0.665921i | \(0.768039\pi\) | |||||||
\(338\) | −51.6787 | + | 21.4060i | −2.81095 | + | 1.16433i | ||||
\(339\) | 10.1211 | 0.549704 | ||||||||
\(340\) | 5.74827 | − | 11.9259i | 0.311744 | − | 0.646771i | ||||
\(341\) | − | 3.85240i | − | 0.208619i | ||||||
\(342\) | 23.7496 | − | 9.83739i | 1.28423 | − | 0.531945i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.05404 | + | 1.05404i | −0.0568302 | + | 0.0568302i | ||||
\(345\) | −5.86238 | − | 1.16610i | −0.315620 | − | 0.0627807i | ||||
\(346\) | 3.52287 | − | 5.27235i | 0.189391 | − | 0.283443i | ||||
\(347\) | −20.6231 | + | 4.10219i | −1.10711 | + | 0.220217i | −0.714601 | − | 0.699533i | \(-0.753392\pi\) |
−0.392505 | + | 0.919750i | \(0.628392\pi\) | |||||||
\(348\) | −2.43441 | + | 5.87719i | −0.130498 | + | 0.315050i | ||||
\(349\) | 26.1712 | + | 10.8405i | 1.40091 | + | 0.580276i | 0.949988 | − | 0.312287i | \(-0.101095\pi\) |
0.450923 | + | 0.892563i | \(0.351095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.4920 | + | 17.1990i | −0.613398 | + | 0.918015i | ||||
\(352\) | −5.87115 | + | 29.5163i | −0.312933 | + | 1.57322i | ||||
\(353\) | 4.04792 | − | 4.04792i | 0.215449 | − | 0.215449i | −0.591128 | − | 0.806577i | \(-0.701317\pi\) |
0.806577 | + | 0.591128i | \(0.201317\pi\) | |||||||
\(354\) | 3.23326 | + | 4.83892i | 0.171846 | + | 0.257186i | ||||
\(355\) | 4.87886 | + | 11.7786i | 0.258943 | + | 0.625144i | ||||
\(356\) | 2.34660 | 0.124370 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.3303 | 0.810231 | ||||||||
\(359\) | −8.48019 | − | 20.4730i | −0.447567 | − | 1.08052i | −0.973231 | − | 0.229831i | \(-0.926183\pi\) |
0.525663 | − | 0.850693i | \(-0.323817\pi\) | |||||||
\(360\) | 5.77541 | + | 8.64352i | 0.304391 | + | 0.455553i | ||||
\(361\) | 6.56663 | − | 6.56663i | 0.345612 | − | 0.345612i | ||||
\(362\) | 1.77629 | − | 8.93003i | 0.0933599 | − | 0.469352i | ||||
\(363\) | 4.28254 | − | 6.40927i | 0.224775 | − | 0.336400i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.80819 | + | 1.16319i | 0.146988 | + | 0.0608843i | ||||
\(366\) | 0.565475 | − | 1.36518i | 0.0295579 | − | 0.0713590i | ||||
\(367\) | 27.1486 | − | 5.40020i | 1.41715 | − | 0.281888i | 0.573684 | − | 0.819076i | \(-0.305514\pi\) |
0.843462 | + | 0.537188i | \(0.180514\pi\) | |||||||
\(368\) | 11.2739 | − | 16.8726i | 0.587693 | − | 0.879544i | ||||
\(369\) | 0.693951 | + | 0.138035i | 0.0361256 | + | 0.00718584i | ||||
\(370\) | −20.1134 | + | 20.1134i | −1.04564 | + | 1.04564i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.463403 | − | 0.191948i | 0.0240264 | − | 0.00995204i | ||||
\(373\) | 26.1076i | 1.35180i | 0.736994 | + | 0.675899i | \(0.236244\pi\) | ||||
−0.736994 | + | 0.675899i | \(0.763756\pi\) | |||||||
\(374\) | −12.1982 | − | 34.8991i | −0.630755 | − | 1.80459i | ||||
\(375\) | 4.11065 | 0.212273 | ||||||||
\(376\) | 11.3804 | − | 4.71390i | 0.586897 | − | 0.243101i | ||||
\(377\) | 36.0237 | + | 53.9132i | 1.85531 | + | 2.77667i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.55946 | + | 1.30476i | 0.336937 | + | 0.0670209i | 0.360659 | − | 0.932698i | \(-0.382552\pi\) |
−0.0237224 | + | 0.999719i | \(0.507552\pi\) | |||||||
\(380\) | −14.1992 | − | 9.48762i | −0.728405 | − | 0.486705i | ||||
\(381\) | 0.158979 | + | 0.799240i | 0.00814472 | + | 0.0409463i | ||||
\(382\) | −40.7498 | − | 16.8791i | −2.08494 | − | 0.863611i | ||||
\(383\) | −13.4919 | − | 5.58852i | −0.689403 | − | 0.285560i | 0.0103486 | − | 0.999946i | \(-0.496706\pi\) |
−0.699751 | + | 0.714386i | \(0.746706\pi\) | |||||||
\(384\) | 5.64203 | − | 1.12227i | 0.287919 | − | 0.0572706i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.12399 | + | 35.8147i | −0.362601 | + | 1.82292i | ||||
\(387\) | −1.98584 | − | 1.98584i | −0.100946 | − | 0.100946i | ||||
\(388\) | 9.99973 | − | 6.68161i | 0.507660 | − | 0.339207i | ||||
\(389\) | −11.6682 | + | 4.83312i | −0.591601 | + | 0.245049i | −0.658339 | − | 0.752721i | \(-0.728741\pi\) |
0.0667382 | + | 0.997771i | \(0.478741\pi\) | |||||||
\(390\) | 17.3881 | 0.880482 | ||||||||
\(391\) | −0.951470 | + | 16.8386i | −0.0481179 | + | 0.851566i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.748802 | + | 1.80777i | 0.0377721 | + | 0.0911898i | ||||
\(394\) | 12.7073 | − | 8.49072i | 0.640182 | − | 0.427756i | ||||
\(395\) | 22.9384 | + | 22.9384i | 1.15416 | + | 1.15416i | ||||
\(396\) | −15.9206 | − | 3.16680i | −0.800040 | − | 0.159138i | ||||
\(397\) | 2.12684 | − | 3.18304i | 0.106743 | − | 0.159752i | −0.774253 | − | 0.632877i | \(-0.781874\pi\) |
0.880996 | + | 0.473125i | \(0.156874\pi\) | |||||||
\(398\) | 5.66993 | + | 28.5047i | 0.284208 | + | 1.42881i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.15174 | − | 10.0232i | 0.207587 | − | 0.501159i | ||||
\(401\) | 2.31756 | + | 11.6512i | 0.115733 | + | 0.581831i | 0.994514 | + | 0.104605i | \(0.0333577\pi\) |
−0.878781 | + | 0.477226i | \(0.841642\pi\) | |||||||
\(402\) | −10.0232 | − | 6.69726i | −0.499910 | − | 0.334029i | ||||
\(403\) | 0.997412 | − | 5.01433i | 0.0496846 | − | 0.249782i | ||||
\(404\) | −4.41151 | + | 4.41151i | −0.219481 | + | 0.219481i | ||||
\(405\) | −14.2978 | + | 9.55347i | −0.710462 | + | 0.474716i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.7514i | 1.47472i | ||||||||
\(408\) | −2.40485 | + | 2.14761i | −0.119058 | + | 0.106323i | ||||
\(409\) | − | 2.45600i | − | 0.121441i | −0.998155 | − | 0.0607207i | \(-0.980660\pi\) | ||
0.998155 | − | 0.0607207i | \(-0.0193399\pi\) | |||||||
\(410\) | −0.480238 | − | 1.15940i | −0.0237173 | − | 0.0572585i | ||||
\(411\) | 1.47814 | + | 2.21219i | 0.0729113 | + | 0.109119i | ||||
\(412\) | 5.42940 | + | 5.42940i | 0.267487 | + | 0.267487i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.4388 | + | 10.9841i | 0.807924 | + | 0.539837i | ||||
\(415\) | −35.1144 | + | 6.98468i | −1.72370 | + | 0.342865i | ||||
\(416\) | −15.2839 | + | 36.8986i | −0.749356 | + | 1.80911i | ||||
\(417\) | 1.11337 | − | 2.68791i | 0.0545219 | − | 0.131627i | ||||
\(418\) | −46.7718 | + | 9.30349i | −2.28768 | + | 0.455048i | ||||
\(419\) | 28.3283 | + | 18.9283i | 1.38393 | + | 0.924710i | 0.999999 | + | 0.00134678i | \(0.000428695\pi\) |
0.383927 | + | 0.923363i | \(0.374571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.501993 | − | 0.501993i | −0.0244656 | − | 0.0244656i | 0.694768 | − | 0.719234i | \(-0.255507\pi\) |
−0.719234 | + | 0.694768i | \(0.755507\pi\) | |||||||
\(422\) | 9.87067 | + | 14.7725i | 0.480497 | + | 0.719114i | ||||
\(423\) | 8.88107 | + | 21.4408i | 0.431813 | + | 1.04249i | ||||
\(424\) | 2.62523i | 0.127492i | ||||||||
\(425\) | 1.25738 | + | 8.92872i | 0.0609920 | + | 0.433107i | ||||
\(426\) | 4.63536i | 0.224584i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.39601 | + | 3.60550i | −0.260826 | + | 0.174278i | ||||
\(429\) | 12.8601 | − | 12.8601i | 0.620893 | − | 0.620893i | ||||
\(430\) | −0.971754 | + | 4.88533i | −0.0468621 | + | 0.235592i | ||||
\(431\) | −9.35137 | − | 6.24839i | −0.450440 | − | 0.300974i | 0.309581 | − | 0.950873i | \(-0.399811\pi\) |
−0.760021 | + | 0.649899i | \(0.774811\pi\) | |||||||
\(432\) | 3.00848 | + | 15.1246i | 0.144745 | + | 0.727685i | ||||
\(433\) | 2.47687 | − | 5.97968i | 0.119031 | − | 0.287365i | −0.853123 | − | 0.521710i | \(-0.825294\pi\) |
0.972154 | + | 0.234345i | \(0.0752944\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.77782 | − | 13.9650i | −0.133186 | − | 0.669572i | ||||
\(436\) | −1.55526 | + | 2.32761i | −0.0744833 | + | 0.111472i | ||||
\(437\) | 21.3373 | + | 4.24425i | 1.02070 | + | 0.203030i | ||||
\(438\) | 0.781450 | + | 0.781450i | 0.0373391 | + | 0.0373391i | ||||
\(439\) | −17.9030 | + | 11.9624i | −0.854463 | + | 0.570934i | −0.903852 | − | 0.427846i | \(-0.859273\pi\) |
0.0493888 | + | 0.998780i | \(0.484273\pi\) | |||||||
\(440\) | −7.37995 | − | 17.8168i | −0.351825 | − | 0.849382i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.84172 | − | 48.5834i | −0.325427 | − | 2.31088i | ||||
\(443\) | −32.3242 | −1.53577 | −0.767886 | − | 0.640587i | \(-0.778691\pi\) | ||||
−0.767886 | + | 0.640587i | \(0.778691\pi\) | |||||||
\(444\) | −3.57878 | + | 1.48238i | −0.169841 | + | 0.0703506i | ||||
\(445\) | −4.36717 | + | 2.91805i | −0.207023 | + | 0.138329i | ||||
\(446\) | 2.57410 | + | 2.57410i | 0.121887 | + | 0.121887i | ||||
\(447\) | −0.798681 | + | 4.01524i | −0.0377763 | + | 0.189914i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1303 | + | 4.20309i | −0.997203 | + | 0.198356i | −0.666601 | − | 0.745415i | \(-0.732252\pi\) |
−0.330601 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(450\) | 9.76549 | + | 4.04500i | 0.460350 | + | 0.190683i | ||||
\(451\) | −1.21266 | − | 0.502301i | −0.0571020 | − | 0.0236524i | ||||
\(452\) | 4.33877 | + | 21.8125i | 0.204079 | + | 1.02597i | ||||
\(453\) | −2.60661 | − | 1.74168i | −0.122469 | − | 0.0818314i | ||||
\(454\) | −2.50597 | − | 0.498468i | −0.117611 | − | 0.0233943i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.31062 | + | 3.45809i | 0.108205 | + | 0.161940i | ||||
\(457\) | 3.91001 | − | 1.61958i | 0.182903 | − | 0.0757608i | −0.289353 | − | 0.957223i | \(-0.593440\pi\) |
0.472255 | + | 0.881462i | \(0.343440\pi\) | |||||||
\(458\) | −16.1601 | −0.755114 | ||||||||
\(459\) | −8.53703 | − | 9.55959i | −0.398475 | − | 0.446203i | ||||
\(460\) | − | 13.1342i | − | 0.612383i | ||||||
\(461\) | −33.5138 | + | 13.8819i | −1.56089 | + | 0.646544i | −0.985245 | − | 0.171152i | \(-0.945251\pi\) |
−0.575650 | + | 0.817696i | \(0.695251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.81782 | − | 9.81782i | 0.456273 | − | 0.456273i | −0.441157 | − | 0.897430i | \(-0.645432\pi\) |
0.897430 | + | 0.441157i | \(0.145432\pi\) | |||||||
\(464\) | 47.4108 | + | 9.43059i | 2.20099 | + | 0.437804i | ||||
\(465\) | −0.623730 | + | 0.933478i | −0.0289248 | + | 0.0432890i | ||||
\(466\) | 3.18759 | − | 0.634051i | 0.147662 | − | 0.0293718i | ||||
\(467\) | 13.5691 | − | 32.7586i | 0.627901 | − | 1.51589i | −0.214324 | − | 0.976763i | \(-0.568755\pi\) |
0.842225 | − | 0.539125i | \(-0.181245\pi\) | |||||||
\(468\) | −19.9025 | − | 8.24390i | −0.919995 | − | 0.381074i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 22.8679 | − | 34.2243i | 1.05482 | − | 1.57865i | ||||
\(471\) | 0.736504 | − | 3.70265i | 0.0339363 | − | 0.170609i | ||||
\(472\) | 6.05697 | − | 6.05697i | 0.278795 | − | 0.278795i | ||||
\(473\) | 2.89446 | + | 4.33186i | 0.133087 | + | 0.199179i | ||||
\(474\) | 4.51359 | + | 10.8968i | 0.207316 | + | 0.500505i | ||||
\(475\) | 11.6311 | 0.533670 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.94598 | −0.226461 | ||||||||
\(478\) | 3.26637 | + | 7.88572i | 0.149400 | + | 0.360685i | ||||
\(479\) | 6.42831 | + | 9.62065i | 0.293717 | + | 0.439579i | 0.948753 | − | 0.316019i | \(-0.102346\pi\) |
−0.655036 | + | 0.755598i | \(0.727346\pi\) | |||||||
\(480\) | 6.20153 | − | 6.20153i | 0.283060 | − | 0.283060i | ||||
\(481\) | −7.70284 | + | 38.7248i | −0.351219 | + | 1.76570i | ||||
\(482\) | 14.3682 | − | 21.5036i | 0.654456 | − | 0.979462i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.6488 | + | 6.48193i | 0.711307 | + | 0.294633i | ||||
\(485\) | −10.3014 | + | 24.8697i | −0.467762 | + | 1.12928i | ||||
\(486\) | −22.4876 | + | 4.47305i | −1.02006 | + | 0.202902i | ||||
\(487\) | 15.0011 | − | 22.4507i | 0.679765 | − | 1.01734i | −0.317838 | − | 0.948145i | \(-0.602957\pi\) |
0.997603 | − | 0.0691955i | \(-0.0220432\pi\) | |||||||
\(488\) | −2.13313 | − | 0.424305i | −0.0965621 | − | 0.0192074i | ||||
\(489\) | −4.86221 | + | 4.86221i | −0.219877 | + | 0.219877i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.96262 | + | 2.46980i | −0.269089 | + | 0.111460i | −0.513148 | − | 0.858300i | \(-0.671521\pi\) |
0.244059 | + | 0.969760i | \(0.421521\pi\) | |||||||
\(492\) | − | 0.170898i | − | 0.00770468i | ||||||
\(493\) | −37.9260 | + | 13.2562i | −1.70810 | + | 0.597029i | ||||
\(494\) | −63.2875 | −2.84744 | ||||||||
\(495\) | 33.5671 | − | 13.9040i | 1.50873 | − | 0.624937i | ||||
\(496\) | −2.11754 | − | 3.16913i | −0.0950804 | − | 0.142298i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.7670 | − | 2.53952i | −0.572104 | − | 0.113798i | ||||
\(499\) | −26.9971 | − | 18.0389i | −1.20856 | − | 0.807532i | −0.222661 | − | 0.974896i | \(-0.571474\pi\) |
−0.985895 | + | 0.167364i | \(0.946474\pi\) | |||||||
\(500\) | 1.76217 | + | 8.85904i | 0.0788068 | + | 0.396188i | ||||
\(501\) | −6.73372 | − | 2.78920i | −0.300840 | − | 0.124612i | ||||
\(502\) | −51.6233 | − | 21.3831i | −2.30406 | − | 0.954374i | ||||
\(503\) | −27.8736 | + | 5.54441i | −1.24282 | + | 0.247213i | −0.772348 | − | 0.635200i | \(-0.780918\pi\) |
−0.470476 | + | 0.882413i | \(0.655918\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.72428 | − | 13.6959i | 0.121229 | − | 0.609459i | ||||
\(506\) | −25.9346 | − | 25.9346i | −1.15293 | − | 1.15293i | ||||
\(507\) | 14.1767 | − | 9.47260i | 0.629611 | − | 0.420693i | ||||
\(508\) | −1.65432 | + | 0.685243i | −0.0733988 | + | 0.0304028i | ||||
\(509\) | 36.2754 | 1.60788 | 0.803939 | − | 0.594711i | \(-0.202734\pi\) | ||||
0.803939 | + | 0.594711i | \(0.202734\pi\) | |||||||
\(510\) | −2.69465 | + | 10.4314i | −0.119321 | + | 0.461911i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.94712 | + | 14.3576i | 0.262828 | + | 0.634523i | ||||
\(513\) | −13.7463 | + | 9.18501i | −0.606916 | + | 0.405528i | ||||
\(514\) | 28.2712 | + | 28.2712i | 1.24699 | + | 1.24699i | ||||
\(515\) | −16.8560 | − | 3.35287i | −0.742765 | − | 0.147745i | ||||
\(516\) | −0.376860 | + | 0.564011i | −0.0165903 | + | 0.0248292i | ||||
\(517\) | −8.39907 | − | 42.2250i | −0.369391 | − | 1.85705i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.739659 | + | 1.78570i | −0.0324674 | + | 0.0783834i | ||||
\(520\) | −4.99295 | − | 25.1013i | −0.218955 | − | 1.10076i | ||||
\(521\) | −22.0440 | − | 14.7294i | −0.965767 | − | 0.645305i | −0.0306076 | − | 0.999531i | \(-0.509744\pi\) |
−0.935160 | + | 0.354226i | \(0.884744\pi\) | |||||||
\(522\) | −9.18814 | + | 46.1919i | −0.402154 | + | 2.02177i | ||||
\(523\) | 14.7577 | − | 14.7577i | 0.645308 | − | 0.645308i | −0.306547 | − | 0.951856i | \(-0.599174\pi\) |
0.951856 | + | 0.306547i | \(0.0991737\pi\) | |||||||
\(524\) | −3.57500 | + | 2.38874i | −0.156174 | + | 0.104352i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.5848i | 0.548721i | ||||||||
\(527\) | 2.85361 | + | 1.37544i | 0.124305 | + | 0.0599151i | ||||
\(528\) | − | 13.5586i | − | 0.590062i | ||||||
\(529\) | −2.39865 | − | 5.79085i | −0.104289 | − | 0.251776i | ||||
\(530\) | 4.87364 | + | 7.29392i | 0.211698 | + | 0.316828i | ||||
\(531\) | 11.4115 | + | 11.4115i | 0.495215 | + | 0.495215i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.44837 | − | 0.967768i | −0.0627358 | − | 0.0419187i | ||||
\(534\) | −1.87297 | + | 0.372558i | −0.0810515 | + | 0.0161221i | ||||
\(535\) | 5.55878 | − | 13.4201i | 0.240327 | − | 0.580201i | ||||
\(536\) | −6.78995 | + | 16.3924i | −0.293281 | + | 0.708044i | ||||
\(537\) | −4.58309 | + | 0.911634i | −0.197775 | + | 0.0393399i | ||||
\(538\) | 6.25061 | + | 4.17652i | 0.269483 | + | 0.180063i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.05770 | + | 7.05770i | 0.303715 | + | 0.303715i | ||||
\(541\) | 19.3927 | + | 29.0232i | 0.833757 | + | 1.24780i | 0.966503 | + | 0.256655i | \(0.0826204\pi\) |
−0.132746 | + | 0.991150i | \(0.542380\pi\) | |||||||
\(542\) | −2.93982 | − | 7.09736i | −0.126276 | − | 0.304858i | ||||
\(543\) | 2.77532i | 0.119100i | ||||||||
\(544\) | −19.7675 | − | 14.8873i | −0.847526 | − | 0.638287i | ||||
\(545\) | − | 6.26581i | − | 0.268398i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.70359 | − | 2.47466i | 0.158354 | − | 0.105809i | −0.473869 | − | 0.880596i | \(-0.657143\pi\) |
0.632223 | + | 0.774787i | \(0.282143\pi\) | |||||||
\(548\) | −4.13394 | + | 4.13394i | −0.176593 | + | 0.176593i | ||||
\(549\) | 0.799399 | − | 4.01885i | 0.0341175 | − | 0.171520i | ||||
\(550\) | −16.3040 | − | 10.8940i | −0.695206 | − | 0.464522i | ||||
\(551\) | 10.1104 | + | 50.8284i | 0.430718 | + | 2.16536i | ||||
\(552\) | −1.22409 | + | 2.95521i | −0.0521007 | + | 0.125782i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.35492 | + | 21.8937i | 0.185023 | + | 0.930172i | ||||
\(555\) | 4.81696 | − | 7.20908i | 0.204468 | − | 0.306009i | ||||
\(556\) | 6.27011 | + | 1.24720i | 0.265912 | + | 0.0528932i | ||||
\(557\) | −5.88222 | − | 5.88222i | −0.249238 | − | 0.249238i | 0.571420 | − | 0.820658i | \(-0.306393\pi\) |
−0.820658 | + | 0.571420i | \(0.806393\pi\) | |||||||
\(558\) | 3.08765 | − | 2.06310i | 0.130711 | − | 0.0873381i | ||||
\(559\) | 2.64591 | + | 6.38780i | 0.111910 | + | 0.270175i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.72206 | + | 9.70795i | 0.241585 | + | 0.409870i | ||||
\(562\) | 13.6430 | 0.575497 | ||||||||
\(563\) | 33.3865 | − | 13.8291i | 1.40707 | − | 0.582829i | 0.455496 | − | 0.890238i | \(-0.349462\pi\) |
0.951577 | + | 0.307409i | \(0.0994621\pi\) | |||||||
\(564\) | 4.66074 | − | 3.11421i | 0.196253 | − | 0.131132i | ||||
\(565\) | −35.1989 | − | 35.1989i | −1.48083 | − | 1.48083i | ||||
\(566\) | −2.50068 | + | 12.5718i | −0.105111 | + | 0.528430i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.69154 | − | 1.33103i | 0.280771 | − | 0.0558488i | ||||
\(569\) | 7.83649 | + | 3.24598i | 0.328523 | + | 0.136079i | 0.540848 | − | 0.841120i | \(-0.318103\pi\) |
−0.212325 | + | 0.977199i | \(0.568103\pi\) | |||||||
\(570\) | 12.8396 | + | 5.31834i | 0.537792 | + | 0.222761i | ||||
\(571\) | 3.94479 | + | 19.8318i | 0.165084 | + | 0.829935i | 0.971216 | + | 0.238199i | \(0.0765572\pi\) |
−0.806132 | + | 0.591736i | \(0.798443\pi\) | |||||||
\(572\) | 33.2284 | + | 22.2025i | 1.38935 | + | 0.928333i | ||||
\(573\) | 13.1862 | + | 2.62289i | 0.550860 | + | 0.109573i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.96984 | + | 7.43789i | 0.207257 | + | 0.310181i | ||||
\(576\) | −2.02490 | + | 0.838742i | −0.0843710 | + | 0.0349476i | ||||
\(577\) | −36.0093 | −1.49909 | −0.749543 | − | 0.661956i | \(-0.769727\pi\) | ||||
−0.749543 | + | 0.661956i | \(0.769727\pi\) | |||||||
\(578\) | 30.2062 | + | 3.42455i | 1.25641 | + | 0.142442i | ||||
\(579\) | − | 11.1307i | − | 0.462575i | ||||||
\(580\) | 28.9058 | − | 11.9732i | 1.20025 | − | 0.497159i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.92063 | + | 6.92063i | −0.286869 | + | 0.286869i | ||||
\(583\) | 8.99904 | + | 1.79002i | 0.372702 | + | 0.0741351i | ||||
\(584\) | 0.903699 | − | 1.35248i | 0.0373953 | − | 0.0559661i | ||||
\(585\) | 47.2913 | − | 9.40681i | 1.95525 | − | 0.388924i | ||||
\(586\) | 4.01734 | − | 9.69871i | 0.165955 | − | 0.400650i | ||||
\(587\) | −18.6945 | − | 7.74352i | −0.771605 | − | 0.319609i | −0.0380824 | − | 0.999275i | \(-0.512125\pi\) |
−0.733522 | + | 0.679666i | \(0.762125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.27019 | − | 3.39757i | 0.0935414 | − | 0.139995i | ||||
\(590\) | 5.58411 | − | 28.0732i | 0.229894 | − | 1.15576i | ||||
\(591\) | −3.29401 | + | 3.29401i | −0.135497 | + | 0.135497i | ||||
\(592\) | 16.3534 | + | 24.4746i | 0.672120 | + | 1.00590i | ||||
\(593\) | −9.53650 | − | 23.0231i | −0.391617 | − | 0.945447i | −0.989588 | − | 0.143929i | \(-0.954026\pi\) |
0.597971 | − | 0.801518i | \(-0.295974\pi\) | |||||||
\(594\) | 27.8721 | 1.14361 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.99580 | −0.368482 | ||||||||
\(597\) | −3.39013 | − | 8.18449i | −0.138749 | − | 0.334969i | ||||
\(598\) | −27.0421 | − | 40.4714i | −1.10583 | − | 1.65500i | ||||
\(599\) | −8.05216 | + | 8.05216i | −0.329002 | + | 0.329002i | −0.852207 | − | 0.523205i | \(-0.824736\pi\) |
0.523205 | + | 0.852207i | \(0.324736\pi\) | |||||||
\(600\) | −0.333629 | + | 1.67727i | −0.0136203 | + | 0.0684741i | ||||
\(601\) | 10.4548 | − | 15.6467i | 0.426460 | − | 0.638243i | −0.554561 | − | 0.832143i | \(-0.687114\pi\) |
0.981021 | + | 0.193900i | \(0.0621138\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.8836 | − | 12.7924i | −1.25768 | − | 0.520947i | ||||
\(604\) | 2.63616 | − | 6.36425i | 0.107264 | − | 0.258958i | ||||
\(605\) | −37.1837 | + | 7.39629i | −1.51173 | + | 0.300702i | ||||
\(606\) | 2.82072 | − | 4.22150i | 0.114584 | − | 0.171487i | ||||
\(607\) | 35.7964 | + | 7.12034i | 1.45293 | + | 0.289006i | 0.857535 | − | 0.514426i | \(-0.171995\pi\) |
0.595396 | + | 0.803432i | \(0.296995\pi\) | |||||||
\(608\) | −22.5717 | + | 22.5717i | −0.915402 | + | 0.915402i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.71437 | + | 2.78118i | −0.271857 | + | 0.112607i | ||||
\(611\) | − | 57.1352i | − | 2.31144i | ||||||
\(612\) | 8.02996 | − | 10.6623i | 0.324592 | − | 0.430997i | ||||
\(613\) | −3.48685 | −0.140832 | −0.0704162 | − | 0.997518i | \(-0.522433\pi\) | ||||
−0.0704162 | + | 0.997518i | \(0.522433\pi\) | |||||||
\(614\) | −39.7899 | + | 16.4815i | −1.60579 | + | 0.665139i | ||||
\(615\) | 0.212515 | + | 0.318052i | 0.00856944 | + | 0.0128251i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.2155 | + | 9.19283i | 1.86057 | + | 0.370089i | 0.992078 | − | 0.125622i | \(-0.0400928\pi\) |
0.868487 | + | 0.495712i | \(0.165093\pi\) | |||||||
\(618\) | −5.19555 | − | 3.47156i | −0.208996 | − | 0.139647i | ||||
\(619\) | −0.779629 | − | 3.91946i | −0.0313359 | − | 0.157536i | 0.961949 | − | 0.273228i | \(-0.0880915\pi\) |
−0.993285 | + | 0.115692i | \(0.963091\pi\) | |||||||
\(620\) | −2.27916 | − | 0.944060i | −0.0915334 | − | 0.0379144i | ||||
\(621\) | −11.7473 | − | 4.86591i | −0.471405 | − | 0.195262i | ||||
\(622\) | −5.67381 | + | 1.12859i | −0.227499 | + | 0.0452524i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.51041 | − | 17.6480i | 0.140529 | − | 0.706487i | ||||
\(625\) | −22.0278 | − | 22.0278i | −0.881111 | − | 0.881111i | ||||
\(626\) | −9.85477 | + | 6.58475i | −0.393876 | + | 0.263179i | ||||
\(627\) | 13.4295 | − | 5.56268i | 0.536322 | − | 0.222152i | ||||
\(628\) | 8.29548 | 0.331026 | ||||||||
\(629\) | −22.0379 | − | 10.6223i | −0.878708 | − | 0.423537i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.89828 | − | 4.58286i | −0.0755694 | − | 0.182441i | 0.881580 | − | 0.472034i | \(-0.156480\pi\) |
−0.957150 | + | 0.289593i | \(0.906480\pi\) | |||||||
\(632\) | 14.4344 | − | 9.64473i | 0.574168 | − | 0.383647i | ||||
\(633\) | −3.82937 | − | 3.82937i | −0.152204 | − | 0.152204i | ||||
\(634\) | −19.9019 | − | 3.95873i | −0.790404 | − | 0.157221i | ||||
\(635\) | 2.22668 | − | 3.33246i | 0.0883632 | − | 0.132245i | ||||
\(636\) | 0.233062 | + | 1.17168i | 0.00924150 | + | 0.0464602i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 33.4350 | − | 80.7193i | 1.32370 | − | 3.19571i | ||||
\(639\) | 2.50769 | + | 12.6070i | 0.0992025 | + | 0.498725i | ||||
\(640\) | −23.5247 | − | 15.7187i | −0.929895 | − | 0.621336i | ||||
\(641\) | −6.50339 | + | 32.6948i | −0.256869 | + | 1.29137i | 0.609830 | + | 0.792533i | \(0.291238\pi\) |
−0.866698 | + | 0.498833i | \(0.833762\pi\) | |||||||
\(642\) | 3.73448 | − | 3.73448i | 0.147388 | − | 0.147388i | ||||
\(643\) | 27.9715 | − | 18.6900i | 1.10309 | − | 0.737061i | 0.135800 | − | 0.990736i | \(-0.456639\pi\) |
0.967289 | + | 0.253675i | \(0.0816394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.51829i | − | 0.0597826i | ||||||
\(646\) | 9.80772 | − | 37.9672i | 0.385879 | − | 1.49380i | ||||
\(647\) | − | 34.7391i | − | 1.36574i | −0.730542 | − | 0.682868i | \(-0.760732\pi\) | ||
0.730542 | − | 0.682868i | \(-0.239268\pi\) | |||||||
\(648\) | 3.52156 | + | 8.50179i | 0.138340 | + | 0.333982i | ||||
\(649\) | −16.6328 | − | 24.8927i | −0.652893 | − | 0.977124i | ||||
\(650\) | −18.4010 | − | 18.4010i | −0.721747 | − | 0.721747i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.5631 | − | 8.39441i | −0.492010 | − | 0.328750i | ||||
\(653\) | 35.1878 | − | 6.99928i | 1.37700 | − | 0.273903i | 0.549561 | − | 0.835454i | \(-0.314795\pi\) |
0.827442 | + | 0.561551i | \(0.189795\pi\) | |||||||
\(654\) | 0.871809 | − | 2.10473i | 0.0340904 | − | 0.0823016i | ||||
\(655\) | 3.68284 | − | 8.89116i | 0.143900 | − | 0.347406i | ||||
\(656\) | −1.27368 | + | 0.253351i | −0.0497289 | + | 0.00989168i | ||||
\(657\) | 2.54810 | + | 1.70259i | 0.0994109 | + | 0.0664242i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.30369 | − | 4.30369i | −0.167648 | − | 0.167648i | 0.618297 | − | 0.785945i | \(-0.287823\pi\) |
−0.785945 | + | 0.618297i | \(0.787823\pi\) | |||||||
\(660\) | −4.87552 | − | 7.29673i | −0.189779 | − | 0.284025i | ||||
\(661\) | 12.6534 | + | 30.5481i | 0.492161 | + | 1.18818i | 0.953618 | + | 0.301019i | \(0.0973269\pi\) |
−0.461457 | + | 0.887163i | \(0.652673\pi\) | |||||||
\(662\) | − | 43.9337i | − | 1.70753i | ||||||
\(663\) | 4.93445 | + | 14.1175i | 0.191638 | + | 0.548277i | ||||
\(664\) | 19.1595i | 0.743533i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.8454 | + | 15.9330i | −0.923990 | + | 0.617390i | ||||
\(667\) | −28.1839 | + | 28.1839i | −1.09129 | + | 1.09129i | ||||
\(668\) | 3.12448 | − | 15.7078i | 0.120890 | − | 0.607753i | ||||
\(669\) | −0.922617 | − | 0.616473i | −0.0356704 | − | 0.0238342i | ||||
\(670\) | 11.5667 | + | 58.1498i | 0.446861 | + | 2.24652i | ||||
\(671\) | −2.90896 | + | 7.02284i | −0.112299 | + | 0.271114i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.94208 | − | 19.8182i | −0.151956 | − | 0.763934i | −0.979328 | − | 0.202279i | \(-0.935165\pi\) |
0.827372 | − | 0.561654i | \(-0.189835\pi\) | |||||||
\(674\) | 5.07834 | − | 7.60028i | 0.195611 | − | 0.292752i | ||||
\(675\) | −6.66735 | − | 1.32622i | −0.256626 | − | 0.0510462i | ||||
\(676\) | 26.4922 | + | 26.4922i | 1.01893 | + | 1.01893i | ||||
\(677\) | −21.3826 | + | 14.2874i | −0.821798 | + | 0.549108i | −0.893888 | − | 0.448290i | \(-0.852033\pi\) |
0.0720898 | + | 0.997398i | \(0.477033\pi\) | |||||||
\(678\) | −6.92610 | − | 16.7211i | −0.265995 | − | 0.642170i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.8324 | + | 0.894614i | 0.607145 | + | 0.0343069i | ||||
\(681\) | 0.778817 | 0.0298443 | ||||||||
\(682\) | −6.36454 | + | 2.63628i | −0.243711 | + | 0.100948i | ||||
\(683\) | 21.7925 | − | 14.5613i | 0.833866 | − | 0.557171i | −0.0637421 | − | 0.997966i | \(-0.520304\pi\) |
0.897608 | + | 0.440795i | \(0.145304\pi\) | |||||||
\(684\) | −12.1748 | − | 12.1748i | −0.465515 | − | 0.465515i | ||||
\(685\) | 2.55287 | − | 12.8341i | 0.0975401 | − | 0.490367i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.83118 | − | 0.960982i | 0.184321 | − | 0.0366637i | ||||
\(688\) | 4.76217 | + | 1.97256i | 0.181556 | + | 0.0752030i | ||||
\(689\) | 11.2498 | + | 4.65983i | 0.428584 | + | 0.177525i | ||||
\(690\) | 2.08524 | + | 10.4832i | 0.0793838 | + | 0.399089i | ||||
\(691\) | 33.0199 | + | 22.0632i | 1.25614 | + | 0.839324i | 0.992132 | − | 0.125198i | \(-0.0399565\pi\) |
0.264005 | + | 0.964521i | \(0.414956\pi\) | |||||||
\(692\) | −4.16551 | − | 0.828572i | −0.158349 | − | 0.0314976i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.8901 | + | 31.2642i | 0.792975 | + | 1.18677i | ||||
\(695\) | −13.2200 | + | 5.47589i | −0.501462 | + | 0.207712i | ||||
\(696\) | −7.61976 | −0.288826 | ||||||||
\(697\) | 0.805034 | − | 0.718923i | 0.0304929 | − | 0.0272311i | ||||
\(698\) | − | 50.6557i | − | 1.91735i | ||||||
\(699\) | −0.915246 | + | 0.379107i | −0.0346178 | + | 0.0143392i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.39878 | − | 9.39878i | 0.354987 | − | 0.354987i | −0.506974 | − | 0.861961i | \(-0.669236\pi\) |
0.861961 | + | 0.506974i | \(0.169236\pi\) | |||||||
\(702\) | 36.2787 | + | 7.21628i | 1.36925 | + | 0.272361i | ||||
\(703\) | −17.5322 | + | 26.2389i | −0.661241 | + | 0.989617i | ||||
\(704\) | 3.98779 | − | 0.793221i | 0.150296 | − | 0.0298957i | ||||
\(705\) | −4.80133 | + | 11.5914i | −0.180829 | + | 0.436559i | ||||
\(706\) | −9.45764 | − | 3.91748i | −0.355943 | − | 0.147436i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.16560 | − | 3.24104i | 0.0813881 | − | 0.121806i | ||||
\(709\) | −8.28893 | + | 41.6713i | −0.311297 | + | 1.56500i | 0.435651 | + | 0.900115i | \(0.356518\pi\) |
−0.746949 | + | 0.664882i | \(0.768482\pi\) | |||||||
\(710\) | 16.1207 | − | 16.1207i | 0.605000 | − | 0.605000i | ||||
\(711\) | 18.1708 | + | 27.1946i | 0.681460 | + | 1.01988i | ||||
\(712\) | 1.07564 | + | 2.59682i | 0.0403112 | + | 0.0973199i | ||||
\(713\) | 3.14273 | 0.117696 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −89.4492 | −3.34521 | ||||||||
\(716\) | −3.92940 | − | 9.48641i | −0.146849 | − | 0.354524i | ||||
\(717\) | −1.44544 | − | 2.16325i | −0.0539809 | − | 0.0807881i | ||||
\(718\) | −28.0202 | + | 28.0202i | −1.04571 | + | 1.04571i | ||||
\(719\) | −3.92972 | + | 19.7560i | −0.146554 | + | 0.736775i | 0.835695 | + | 0.549193i | \(0.185065\pi\) |
−0.982249 | + | 0.187582i | \(0.939935\pi\) | |||||||
\(720\) | 19.9710 | − | 29.8887i | 0.744275 | − | 1.11389i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.3424 | − | 6.35503i | −0.570985 | − | 0.236510i | ||||
\(723\) | −3.01675 | + | 7.28307i | −0.112194 | + | 0.270860i | ||||
\(724\) | −5.98121 | + | 1.18974i | −0.222290 | + | 0.0442162i | ||||
\(725\) | −11.8389 | + | 17.7181i | −0.439685 | + | 0.658035i | ||||
\(726\) | −13.5194 | − | 2.68917i | −0.501751 | − | 0.0998046i | ||||
\(727\) | −15.6585 | + | 15.6585i | −0.580743 | + | 0.580743i | −0.935107 | − | 0.354364i | \(-0.884697\pi\) |
0.354364 | + | 0.935107i | \(0.384697\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.3214 | + | 4.68947i | −0.419311 | + | 0.173684i | ||||
\(730\) | − | 5.43541i | − | 0.201174i | ||||||
\(731\) | −4.24218 | + | 0.597403i | −0.156903 | + | 0.0220957i | ||||
\(732\) | −0.989716 | −0.0365809 | ||||||||
\(733\) | −30.4919 | + | 12.6302i | −1.12624 | + | 0.466505i | −0.866502 | − | 0.499173i | \(-0.833637\pi\) |
−0.259741 | + | 0.965678i | \(0.583637\pi\) | |||||||
\(734\) | −27.5000 | − | 41.1567i | −1.01505 | − | 1.51912i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0789 | − | 4.78959i | −0.887560 | − | 0.176547i | ||||
\(737\) | 51.5618 | + | 34.4525i | 1.89930 | + | 1.26907i | ||||
\(738\) | −0.246837 | − | 1.24094i | −0.00908621 | − | 0.0456795i | ||||
\(739\) | 21.3775 | + | 8.85484i | 0.786383 | + | 0.325731i | 0.739488 | − | 0.673169i | \(-0.235067\pi\) |
0.0468947 | + | 0.998900i | \(0.485067\pi\) | |||||||
\(740\) | 17.6016 | + | 7.29081i | 0.647046 | + | 0.268015i | ||||
\(741\) | 18.9202 | − | 3.76346i | 0.695051 | − | 0.138254i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.30776 | + | 21.6566i | −0.158037 | + | 0.794503i | 0.817715 | + | 0.575623i | \(0.195240\pi\) |
−0.975752 | + | 0.218880i | \(0.929760\pi\) | |||||||
\(744\) | 0.424831 | + | 0.424831i | 0.0155751 | + | 0.0155751i | ||||
\(745\) | 16.7417 | − | 11.1865i | 0.613369 | − | 0.409840i | ||||
\(746\) | 43.1322 | − | 17.8660i | 1.57918 | − | 0.654119i | ||||
\(747\) | −36.0969 | −1.32071 | ||||||||
\(748\) | −18.4691 | + | 16.4935i | −0.675296 | + | 0.603062i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.81301 | − | 6.79120i | −0.102717 | − | 0.247980i | ||||
\(751\) | −2.11608 | + | 1.41392i | −0.0772170 | + | 0.0515947i | −0.593579 | − | 0.804775i | \(-0.702286\pi\) |
0.516362 | + | 0.856370i | \(0.327286\pi\) | |||||||
\(752\) | −30.1191 | − | 30.1191i | −1.09833 | − | 1.09833i | ||||
\(753\) | 16.7047 | + | 3.32277i | 0.608753 | + | 0.121089i | ||||
\(754\) | 64.4182 | − | 96.4087i | 2.34597 | − | 3.51100i | ||||
\(755\) | 3.00803 | + | 15.1224i | 0.109473 | + | 0.550360i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.2277 | + | 34.3488i | −0.517115 | + | 1.24843i | 0.422552 | + | 0.906339i | \(0.361134\pi\) |
−0.939668 | + | 0.342089i | \(0.888866\pi\) | |||||||
\(758\) | −2.33319 | − | 11.7297i | −0.0847453 | − | 0.426043i | ||||
\(759\) | 9.29554 | + | 6.21108i | 0.337407 | + | 0.225448i | ||||
\(760\) | 3.99063 | − | 20.0622i | 0.144755 | − | 0.727734i | ||||
\(761\) | 2.05410 | − | 2.05410i | 0.0744609 | − | 0.0744609i | −0.668896 | − | 0.743356i | \(-0.733233\pi\) |
0.743356 | + | 0.668896i | \(0.233233\pi\) | |||||||
\(762\) | 1.21163 | − | 0.809585i | 0.0438927 | − | 0.0293282i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 29.5425i | 1.06881i | ||||||||
\(765\) | −1.68547 | + | 29.8286i | −0.0609383 | + | 1.07845i | ||||
\(766\) | 26.1143i | 0.943546i | ||||||||
\(767\) | −15.2045 | − | 36.7070i | −0.549004 | − | 1.32541i | ||||
\(768\) | −6.20618 | − | 9.28820i | −0.223946 | − | 0.335159i | ||||
\(769\) | −22.1893 | − | 22.1893i | −0.800166 | − | 0.800166i | 0.182955 | − | 0.983121i | \(-0.441434\pi\) |
−0.983121 | + | 0.182955i | \(0.941434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.1330 | − | 6.77069i | −0.364933 | − | 0.243840i | ||||
\(772\) | 23.9882 | − | 4.77155i | 0.863354 | − | 0.171732i | ||||
\(773\) | 1.36515 | − | 3.29576i | 0.0491010 | − | 0.118540i | −0.897426 | − | 0.441165i | \(-0.854565\pi\) |
0.946527 | + | 0.322625i | \(0.104565\pi\) | |||||||
\(774\) | −1.92185 | + | 4.63975i | −0.0690793 | + | 0.166772i | ||||
\(775\) | 1.64792 | − | 0.327791i | 0.0591949 | − | 0.0117746i | ||||
\(776\) | 11.9778 | + | 8.00328i | 0.429976 | + | 0.287301i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.9696 | + | 15.9696i | 0.572538 | + | 0.572538i | ||||
\(779\) | −0.773490 | − | 1.15761i | −0.0277132 | − | 0.0414757i | ||||
\(780\) | −4.45686 | − | 10.7598i | −0.159581 | − | 0.385263i | ||||
\(781\) | − | 23.8455i | − | 0.853261i | ||||||
\(782\) | 28.4702 | − | 9.95111i | 1.01809 | − | 0.355851i | ||||
\(783\) | − | 30.2895i | − | 1.08246i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.4384 | + | 10.3156i | −0.551019 | + | 0.368179i | ||||
\(786\) | 2.47419 | − | 2.47419i | 0.0882514 | − | 0.0882514i | ||||
\(787\) | −8.39050 | + | 42.1819i | −0.299089 | + | 1.50362i | 0.480312 | + | 0.877098i | \(0.340523\pi\) |
−0.779401 | + | 0.626525i | \(0.784477\pi\) | |||||||
\(788\) | −8.51115 | − | 5.68697i | −0.303197 | − | 0.202590i | ||||
\(789\) | −0.748367 | − | 3.76230i | −0.0266426 | − | 0.133941i | ||||
\(790\) | 22.1992 | − | 53.5937i | 0.789813 | − | 1.90678i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.79322 | − | 19.0698i | −0.134786 | − | 0.677616i | ||||
\(793\) | −5.60460 | + | 8.38787i | −0.199025 | + | 0.297862i | ||||
\(794\) | −6.71413 | − | 1.33552i | −0.238276 | − | 0.0473960i | ||||
\(795\) | −1.89075 | − | 1.89075i | −0.0670580 | − | 0.0670580i | ||||
\(796\) | 16.1855 | − | 10.8148i | 0.573678 | − | 0.383320i | ||||
\(797\) | −4.78470 | − | 11.5513i | −0.169483 | − | 0.409168i | 0.816202 | − | 0.577767i | \(-0.196076\pi\) |
−0.985685 | + | 0.168599i | \(0.946076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.2763 | + | 8.85429i | 1.21261 | + | 0.313242i | ||||
\(800\) | −13.1255 | −0.464058 | ||||||||
\(801\) | −4.89246 | + | 2.02652i | −0.172866 | + | 0.0716036i | ||||
\(802\) | 17.6629 | − | 11.8020i | 0.623698 | − | 0.416742i | ||||
\(803\) | −4.01999 | − | 4.01999i | −0.141862 | − | 0.141862i | ||||
\(804\) | −1.57518 | + | 7.91897i | −0.0555524 | + | 0.279281i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.96672 | + | 1.78359i | −0.315839 | + | 0.0628243i | ||||
\(807\) | −2.11702 | − | 0.876899i | −0.0745227 | − | 0.0308683i | ||||
\(808\) | −6.90406 | − | 2.85976i | −0.242884 | − | 0.100606i | ||||
\(809\) | −8.88319 | − | 44.6588i | −0.312316 | − | 1.57012i | −0.744053 | − | 0.668120i | \(-0.767099\pi\) |
0.431737 | − | 0.902000i | \(-0.357901\pi\) | |||||||
\(810\) | 25.5675 | + | 17.0837i | 0.898352 | + | 0.600259i | ||||
\(811\) | 22.1324 | + | 4.40241i | 0.777174 | + | 0.154590i | 0.567712 | − | 0.823227i | \(-0.307829\pi\) |
0.209462 | + | 0.977817i | \(0.432829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.30093 | + | 1.94698i | 0.0456257 | + | 0.0682836i | ||||
\(814\) | 49.1522 | − | 20.3595i | 1.72278 | − | 0.713600i | ||||
\(815\) | 33.8193 | 1.18464 | ||||||||
\(816\) | 10.0433 | + | 4.84089i | 0.351587 | + | 0.169465i | ||||
\(817\) | 5.52611i | 0.193334i | ||||||||
\(818\) | −4.05755 | + | 1.68069i | −0.141869 | + | 0.0587641i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.594345 | + | 0.594345i | −0.0207554 | + | 0.0207554i | ||||
\(821\) | −41.4807 | − | 8.25103i | −1.44769 | − | 0.287963i | −0.592202 | − | 0.805790i | \(-0.701741\pi\) |
−0.855485 | + | 0.517827i | \(0.826741\pi\) | |||||||
\(822\) | 2.64324 | − | 3.95589i | 0.0921935 | − | 0.137977i | ||||
\(823\) | −27.9541 | + | 5.56042i | −0.974419 | + | 0.193824i | −0.656526 | − | 0.754303i | \(-0.727975\pi\) |
−0.317892 | + | 0.948127i | \(0.602975\pi\) | |||||||
\(824\) | −3.51960 | + | 8.49707i | −0.122611 | + | 0.296010i | ||||
\(825\) | 5.52202 | + | 2.28730i | 0.192252 | + | 0.0796335i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.50470 | + | 8.23837i | −0.191417 | + | 0.286476i | −0.914747 | − | 0.404026i | \(-0.867610\pi\) |
0.723330 | + | 0.690502i | \(0.242610\pi\) | |||||||
\(828\) | 2.58343 | − | 12.9878i | 0.0897803 | − | 0.451356i | ||||
\(829\) | 28.5355 | − | 28.5355i | 0.991079 | − | 0.991079i | −0.00888175 | − | 0.999961i | \(-0.502827\pi\) |
0.999961 | + | 0.00888175i | \(0.00282719\pi\) | |||||||
\(830\) | 35.5689 | + | 53.2326i | 1.23461 | + | 1.84773i | ||||
\(831\) | −2.60386 | − | 6.28628i | −0.0903270 | − | 0.218069i | ||||
\(832\) | 5.39593 | 0.187070 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.20259 | −0.180151 | ||||||||
\(835\) | 13.7181 | + | 33.1185i | 0.474736 | + | 1.14611i | ||||
\(836\) | 17.7454 | + | 26.5578i | 0.613737 | + | 0.918522i | ||||
\(837\) | −1.68876 | + | 1.68876i | −0.0583720 | + | 0.0583720i | ||||
\(838\) | 11.8858 | − | 59.7542i | 0.410590 | − | 2.06417i | ||||
\(839\) | −26.4350 | + | 39.5628i | −0.912637 | + | 1.36586i | 0.0179698 | + | 0.999839i | \(0.494280\pi\) |
−0.930607 | + | 0.366020i | \(0.880720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −60.9278 | − | 25.2371i | −2.10096 | − | 0.870245i | ||||
\(842\) | −0.485817 | + | 1.17287i | −0.0167424 | + | 0.0404196i | ||||
\(843\) | −4.07868 | + | 0.811300i | −0.140477 | + | 0.0279427i | ||||
\(844\) | 6.61124 | − | 9.89442i | 0.227568 | − | 0.340580i | ||||
\(845\) | −82.2470 | − | 16.3599i | −2.82938 | − | 0.562799i | ||||
\(846\) | 29.3448 | − | 29.3448i | 1.00890 | − | 1.00890i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.38687 | − | 3.47395i | 0.288006 | − | 0.119296i | ||||
\(849\) | − | 3.90711i | − | 0.134092i | ||||||
\(850\) | 13.8907 | − | 8.18743i | 0.476446 | − | 0.280827i | ||||
\(851\) | −24.2707 | −0.831989 | ||||||||
\(852\) | 2.86837 | − | 1.18812i | 0.0982688 | − | 0.0407043i | ||||
\(853\) | 2.30560 | + | 3.45057i | 0.0789422 | + | 0.118145i | 0.868840 | − | 0.495094i | \(-0.164866\pi\) |
−0.789897 | + | 0.613239i | \(0.789866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 37.7976 | + | 7.51841i | 1.29265 | + | 0.257124i | ||||
\(856\) | −6.46338 | − | 4.31869i | −0.220914 | − | 0.147610i | ||||
\(857\) | 4.07401 | + | 20.4814i | 0.139165 | + | 0.699632i | 0.985862 | + | 0.167557i | \(0.0535877\pi\) |
−0.846697 | + | 0.532075i | \(0.821412\pi\) | |||||||
\(858\) | −30.0467 | − | 12.4457i | −1.02578 | − | 0.424891i | ||||
\(859\) | 12.4145 | + | 5.14224i | 0.423576 | + | 0.175451i | 0.584281 | − | 0.811552i | \(-0.301377\pi\) |
−0.160705 | + | 0.987003i | \(0.551377\pi\) | |||||||
\(860\) | 3.27213 | − | 0.650867i | 0.111579 | − | 0.0221944i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.92361 | + | 19.7253i | −0.133639 | + | 0.671846i | ||||
\(863\) | 18.3763 | + | 18.3763i | 0.625537 | + | 0.625537i | 0.946942 | − | 0.321405i | \(-0.104155\pi\) |
−0.321405 | + | 0.946942i | \(0.604155\pi\) | |||||||
\(864\) | 15.5126 | − | 10.3652i | 0.527750 | − | 0.352631i | ||||
\(865\) | 8.78261 | − | 3.63788i | 0.298618 | − | 0.123691i | ||||
\(866\) | −11.5740 | −0.393300 | ||||||||
\(867\) | −9.23399 | + | 0.772456i | −0.313603 | + | 0.0262340i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.2191 | − | 56.0559i | −0.787654 | − | 1.90157i | ||||
\(870\) | −21.1707 | + | 14.1458i | −0.717753 | + | 0.479587i | ||||
\(871\) | 58.1936 | + | 58.1936i | 1.97181 | + | 1.97181i | ||||
\(872\) | −3.28870 | − | 0.654163i | −0.111369 | − | 0.0221528i | ||||
\(873\) | −15.0783 | + | 22.5663i | −0.510324 | + | 0.763754i | ||||
\(874\) | −7.58964 | − | 38.1557i | −0.256723 | − | 1.29064i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.283265 | − | 0.683861i | 0.00957063 | − | 0.0231055i | ||||
\(877\) | 5.54597 | + | 27.8815i | 0.187274 | + | 0.941490i | 0.954067 | + | 0.299595i | \(0.0968515\pi\) |
−0.766793 | + | 0.641895i | \(0.778148\pi\) | |||||||
\(878\) | 32.0144 | + | 21.3914i | 1.08044 | + | 0.721924i | ||||
\(879\) | −0.624265 | + | 3.13839i | −0.0210559 | + | 0.105855i | ||||
\(880\) | −47.1537 | + | 47.1537i | −1.58955 | + | 1.58955i | ||||
\(881\) | 2.44242 | − | 1.63198i | 0.0822873 | − | 0.0549826i | −0.513746 | − | 0.857942i | \(-0.671743\pi\) |
0.596033 | + | 0.802960i | \(0.296743\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 17.1609i | − | 0.577509i | −0.957403 | − | 0.288755i | \(-0.906759\pi\) | ||
0.957403 | − | 0.288755i | \(-0.0932411\pi\) | |||||||
\(884\) | −28.3098 | + | 16.6864i | −0.952163 | + | 0.561224i | ||||
\(885\) | 8.72474i | 0.293279i | ||||||||
\(886\) | 22.1202 | + | 53.4028i | 0.743142 | + | 1.79410i | ||||
\(887\) | 4.24508 | + | 6.35321i | 0.142536 | + | 0.213320i | 0.895868 | − | 0.444320i | \(-0.146555\pi\) |
−0.753332 | + | 0.657640i | \(0.771555\pi\) | |||||||
\(888\) | −3.28089 | − | 3.28089i | −0.110100 | − | 0.110100i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.80944 | + | 5.21810i | 0.261773 | + | 0.174911i | ||||
\(891\) | 31.5445 | − | 6.27460i | 1.05678 | − | 0.210207i | ||||
\(892\) | 0.933075 | − | 2.25264i | 0.0312417 | − | 0.0754241i | ||||
\(893\) | 17.4754 | − | 42.1893i | 0.584791 | − | 1.41181i | ||||
\(894\) | 7.18013 | − | 1.42822i | 0.240139 | − | 0.0477667i | ||||
\(895\) | 19.1094 | + | 12.7685i | 0.638757 | + | 0.426804i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.4911 | + | 10.4911i | 0.350288 | + | 0.350288i | ||||
\(898\) | 21.4039 | + | 32.0331i | 0.714256 | + | 1.06896i | ||||
\(899\) | 2.86493 | + | 6.91655i | 0.0955508 | + | 0.230680i | ||||
\(900\) | − | 7.07971i | − | 0.235990i | ||||||
\(901\) | −4.53890 | + | 6.02681i | −0.151213 | + | 0.200782i | ||||
\(902\) | 2.34717i | 0.0781523i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.1495 | + | 14.7998i | −0.736682 | + | 0.492235i | ||||
\(905\) | 9.65193 | − | 9.65193i | 0.320841 | − | 0.320841i | ||||
\(906\) | −1.09367 | + | 5.49825i | −0.0363348 | + | 0.182667i | ||||
\(907\) | 25.1433 | + | 16.8002i | 0.834869 | + | 0.557842i | 0.897915 | − | 0.440169i | \(-0.145081\pi\) |
−0.0630460 | + | 0.998011i | \(0.520081\pi\) | |||||||
\(908\) | 0.333867 | + | 1.67846i | 0.0110798 | + | 0.0557017i | ||||
\(909\) | 5.38783 | − | 13.0074i | 0.178703 | − | 0.431428i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.758034 | + | 3.81090i | 0.0251148 | + | 0.126261i | 0.991309 | − | 0.131555i | \(-0.0419971\pi\) |
−0.966194 | + | 0.257816i | \(0.916997\pi\) | |||||||
\(912\) | 7.98997 | − | 11.9578i | 0.264574 | − | 0.395964i | ||||
\(913\) | 65.6770 | + | 13.0640i | 2.17359 | + | 0.432354i | ||||
\(914\) | −5.35141 | − | 5.35141i | −0.177009 | − | 0.177009i | ||||
\(915\) | 1.84192 | − | 1.23073i | 0.0608920 | − | 0.0406867i | ||||
\(916\) | 4.14211 | + | 9.99993i | 0.136859 | + | 0.330407i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −9.95130 | + | 20.6458i | −0.328442 | + | 0.681415i | ||||
\(919\) | 2.67414 | 0.0882118 | 0.0441059 | − | 0.999027i | \(-0.485956\pi\) | ||||
0.0441059 | + | 0.999027i | \(0.485956\pi\) | |||||||
\(920\) | 14.5346 | − | 6.02045i | 0.479193 | − | 0.198488i | ||||
\(921\) | 10.9154 | − | 7.29341i | 0.359673 | − | 0.240326i | ||||
\(922\) | 45.8685 | + | 45.8685i | 1.51060 | + | 1.51060i | ||||
\(923\) | 6.17377 | − | 31.0377i | 0.203212 | − | 1.02162i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.7266 | + | 2.53147i | −0.418447 | + | 0.0832342i | ||||
\(926\) | −22.9386 | − | 9.50146i | −0.753808 | − | 0.312237i | ||||
\(927\) | −16.0086 | − | 6.63100i | −0.525793 | − | 0.217791i | ||||
\(928\) | −11.4095 | − | 57.3594i | −0.374535 | − | 1.88291i | ||||
\(929\) | 6.15442 | + | 4.11225i | 0.201920 | + | 0.134919i | 0.652420 | − | 0.757858i | \(-0.273754\pi\) |
−0.450499 | + | 0.892777i | \(0.648754\pi\) | |||||||
\(930\) | 1.96903 | + | 0.391664i | 0.0645670 | + | 0.0128432i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.20938 | − | 1.80997i | −0.0396146 | − | 0.0592875i | ||||
\(933\) | 1.62911 | − | 0.674800i | 0.0533347 | − | 0.0220920i | ||||
\(934\) | −63.4061 | −2.07471 | ||||||||
\(935\) | 13.8620 | − | 53.6620i | 0.453337 | − | 1.75494i | ||||
\(936\) | − | 25.8036i | − | 0.843417i | ||||||
\(937\) | −8.20064 | + | 3.39682i | −0.267903 | + | 0.110969i | −0.512591 | − | 0.858633i | \(-0.671314\pi\) |
0.244688 | + | 0.969602i | \(0.421314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.55458 | − | 2.55458i | 0.0833655 | − | 0.0833655i | ||||
\(940\) | −27.0395 | − | 5.37849i | −0.881931 | − | 0.175427i | ||||
\(941\) | −19.8675 | + | 29.7338i | −0.647662 | + | 0.969294i | 0.351787 | + | 0.936080i | \(0.385574\pi\) |
−0.999448 | + | 0.0332140i | \(0.989426\pi\) | |||||||
\(942\) | −6.62115 | + | 1.31703i | −0.215729 | + | 0.0429111i | ||||
\(943\) | 0.409769 | − | 0.989271i | 0.0133439 | − | 0.0322151i | ||||
\(944\) | −27.3655 | − | 11.3351i | −0.890670 | − | 0.368928i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.17592 | − | 7.74631i | 0.168284 | − | 0.251854i | ||||
\(947\) | 3.99355 | − | 20.0769i | 0.129773 | − | 0.652413i | −0.860062 | − | 0.510190i | \(-0.829575\pi\) |
0.989835 | − | 0.142223i | \(-0.0454249\pi\) | |||||||
\(948\) | 5.58604 | − | 5.58604i | 0.181426 | − | 0.181426i | ||||
\(949\) | −4.19167 | − | 6.27327i | −0.136067 | − | 0.203639i | ||||
\(950\) | −7.95939 | − | 19.2157i | −0.258237 | − | 0.623438i | ||||
\(951\) | 6.18521 | 0.200569 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.8889 | 0.838625 | 0.419312 | − | 0.907842i | \(-0.362271\pi\) | ||||
0.419312 | + | 0.907842i | \(0.362271\pi\) | |||||||
\(954\) | 3.38464 | + | 8.17125i | 0.109582 | + | 0.264554i | ||||
\(955\) | −36.7366 | − | 54.9803i | −1.18877 | − | 1.77912i | ||||
\(956\) | 4.04248 | − | 4.04248i | 0.130743 | − | 0.130743i | ||||
\(957\) | −5.19555 | + | 26.1198i | −0.167948 | + | 0.844334i | ||||
\(958\) | 11.4952 | − | 17.2038i | 0.371394 | − | 0.555830i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.09471 | − | 0.453445i | −0.0353317 | − | 0.0146349i | ||||
\(961\) | −11.6373 | + | 28.0949i | −0.375397 | + | 0.906287i | ||||
\(962\) | 69.2483 | − | 13.7744i | 2.23266 | − | 0.444103i | ||||
\(963\) | 8.13650 | − | 12.1771i | 0.262195 | − | 0.392402i | ||||
\(964\) | −16.9893 | − | 3.37938i | −0.547188 | − | 0.108842i | ||||
\(965\) | −38.7099 | + | 38.7099i | −1.24612 | + | 1.24612i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.4678 | − | 11.7917i | 0.915462 | − | 0.379197i | 0.125317 | − | 0.992117i | \(-0.460005\pi\) |
0.790145 | + | 0.612920i | \(0.210005\pi\) | |||||||
\(968\) | 20.2886i | 0.652100i | ||||||||
\(969\) | −0.674320 | + | 11.9338i | −0.0216623 | + | 0.383368i | ||||
\(970\) | 48.1367 | 1.54558 | ||||||||
\(971\) | 55.0899 | − | 22.8190i | 1.76792 | − | 0.732296i | 0.772685 | − | 0.634790i | \(-0.218913\pi\) |
0.995235 | − | 0.0975065i | \(-0.0310867\pi\) | |||||||
\(972\) | 8.53186 | + | 12.7688i | 0.273660 | + | 0.409560i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −47.3564 | − | 9.41978i | −1.51740 | − | 0.301829i | ||||
\(975\) | 6.59534 | + | 4.40686i | 0.211220 | + | 0.141133i | ||||
\(976\) | 1.46722 | + | 7.37621i | 0.0469646 | + | 0.236107i | ||||
\(977\) | −50.1000 | − | 20.7521i | −1.60284 | − | 0.663919i | −0.611028 | − | 0.791609i | \(-0.709244\pi\) |
−0.991814 | + | 0.127691i | \(0.959244\pi\) | |||||||
\(978\) | 11.3602 | + | 4.70554i | 0.363258 | + | 0.150467i | ||||
\(979\) | 9.63508 | − | 1.91654i | 0.307939 | − | 0.0612528i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.23246 | − | 6.19597i | 0.0393493 | − | 0.197822i | ||||
\(982\) | 8.16069 | + | 8.16069i | 0.260418 | + | 0.260418i | ||||
\(983\) | −30.4564 | + | 20.3503i | −0.971408 | + | 0.649074i | −0.936630 | − | 0.350321i | \(-0.886072\pi\) |
−0.0347783 | + | 0.999395i | \(0.511072\pi\) | |||||||
\(984\) | 0.189121 | − | 0.0783365i | 0.00602896 | − | 0.00249728i | ||||
\(985\) | 22.9116 | 0.730025 | ||||||||
\(986\) | 47.8541 | + | 53.5860i | 1.52399 | + | 1.70653i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.2216 | + | 39.1624i | 0.516078 | + | 1.24592i | ||||
\(989\) | −3.53386 | + | 2.36125i | −0.112370 | + | 0.0750834i | ||||
\(990\) | −45.9414 | − | 45.9414i | −1.46011 | − | 1.46011i | ||||
\(991\) | 42.4220 | + | 8.43825i | 1.34758 | + | 0.268050i | 0.815555 | − | 0.578680i | \(-0.196432\pi\) |
0.532023 | + | 0.846730i | \(0.321432\pi\) | |||||||
\(992\) | −2.56188 | + | 3.83413i | −0.0813399 | + | 0.121734i | ||||
\(993\) | 2.61257 | + | 13.1343i | 0.0829074 | + | 0.416803i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.6737 | + | 40.2539i | −0.528592 | + | 1.27613i | ||||
\(996\) | 1.70093 | + | 8.55118i | 0.0538962 | + | 0.270954i | ||||
\(997\) | −30.4788 | − | 20.3653i | −0.965272 | − | 0.644974i | −0.0302423 | − | 0.999543i | \(-0.509628\pi\) |
−0.935030 | + | 0.354568i | \(0.884628\pi\) | |||||||
\(998\) | −11.3273 | + | 56.9463i | −0.358560 | + | 1.80260i | ||||
\(999\) | 13.0420 | − | 13.0420i | 0.412630 | − | 0.412630i |
(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 | 833.2.t.d.97.2 | yes | 72 | |
7.2 | even | 3 | 833.2.bc.a.80.2 | 144 | |||
7.3 | odd | 6 | 833.2.bc.d.607.8 | 144 | |||
7.4 | even | 3 | 833.2.bc.a.607.8 | 144 | |||
7.5 | odd | 6 | 833.2.bc.d.80.2 | 144 | |||
7.6 | odd | 2 | 833.2.t.a.97.2 | ✓ | 72 | ||
17.10 | odd | 16 | 833.2.t.a.146.2 | yes | 72 | ||
119.10 | even | 48 | 833.2.bc.a.656.2 | 144 | |||
119.27 | even | 16 | inner | 833.2.t.d.146.2 | yes | 72 | |
119.44 | odd | 48 | 833.2.bc.d.129.8 | 144 | |||
119.61 | even | 48 | 833.2.bc.a.129.8 | 144 | |||
119.95 | odd | 48 | 833.2.bc.d.656.2 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
833.2.t.a.97.2 | ✓ | 72 | 7.6 | odd | 2 | ||
833.2.t.a.146.2 | yes | 72 | 17.10 | odd | 16 | ||
833.2.t.d.97.2 | yes | 72 | 1.1 | even | 1 | trivial | |
833.2.t.d.146.2 | yes | 72 | 119.27 | even | 16 | inner | |
833.2.bc.a.80.2 | 144 | 7.2 | even | 3 | |||
833.2.bc.a.129.8 | 144 | 119.61 | even | 48 | |||
833.2.bc.a.607.8 | 144 | 7.4 | even | 3 | |||
833.2.bc.a.656.2 | 144 | 119.10 | even | 48 | |||
833.2.bc.d.80.2 | 144 | 7.5 | odd | 6 | |||
833.2.bc.d.129.8 | 144 | 119.44 | odd | 48 | |||
833.2.bc.d.607.8 | 144 | 7.3 | odd | 6 | |||
833.2.bc.d.656.2 | 144 | 119.95 | odd | 48 |