Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.6 | ||
Character | \(\chi\) | \(=\) | 1110.529 |
Dual form | 1110.2.ba.b.619.6 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.18223 | − | 0.487744i | 0.975921 | − | 0.218126i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −2.13280 | − | 1.23137i | −0.806122 | − | 0.465415i | 0.0394853 | − | 0.999220i | \(-0.487428\pi\) |
−0.845607 | + | 0.533805i | \(0.820761\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 1.51351 | + | 1.64599i | 0.478614 | + | 0.520508i | ||||
\(11\) | −0.452075 | −0.136306 | −0.0681529 | − | 0.997675i | \(-0.521711\pi\) | ||||
−0.0681529 | + | 0.997675i | \(0.521711\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | 1.54402 | − | 2.67433i | 0.428235 | − | 0.741724i | −0.568482 | − | 0.822696i | \(-0.692469\pi\) |
0.996716 | + | 0.0809716i | \(0.0258023\pi\) | |||||||
\(14\) | − | 2.46274i | − | 0.658196i | ||||||
\(15\) | −2.13373 | − | 0.668714i | −0.550928 | − | 0.172661i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.05737 | − | 1.83142i | −0.256450 | − | 0.444185i | 0.708838 | − | 0.705371i | \(-0.249220\pi\) |
−0.965288 | + | 0.261186i | \(0.915886\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 2.58246 | + | 1.49098i | 0.592457 | + | 0.342055i | 0.766068 | − | 0.642759i | \(-0.222210\pi\) |
−0.173611 | + | 0.984814i | \(0.555544\pi\) | |||||||
\(20\) | −0.668714 | + | 2.13373i | −0.149529 | + | 0.477117i | ||||
\(21\) | 1.23137 | + | 2.13280i | 0.268707 | + | 0.465415i | ||||
\(22\) | −0.226038 | − | 0.391509i | −0.0481914 | − | 0.0834699i | ||||
\(23\) | 1.77585 | 0.370290 | 0.185145 | − | 0.982711i | \(-0.440725\pi\) | ||||
0.185145 | + | 0.982711i | \(0.440725\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 4.52421 | − | 2.12873i | 0.904843 | − | 0.425746i | ||||
\(26\) | 3.08804 | 0.605615 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.13280 | − | 1.23137i | 0.403061 | − | 0.232707i | ||||
\(29\) | − | 8.36900i | − | 1.55408i | −0.629448 | − | 0.777042i | \(-0.716719\pi\) | ||
0.629448 | − | 0.777042i | \(-0.283281\pi\) | |||||||
\(30\) | −0.487744 | − | 2.18223i | −0.0890494 | − | 0.398418i | ||||
\(31\) | − | 2.55531i | − | 0.458947i | −0.973315 | − | 0.229473i | \(-0.926300\pi\) | ||
0.973315 | − | 0.229473i | \(-0.0737004\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0.391509 | + | 0.226038i | 0.0681529 | + | 0.0393481i | ||||
\(34\) | 1.05737 | − | 1.83142i | 0.181338 | − | 0.314086i | ||||
\(35\) | −5.25484 | − | 1.64687i | −0.888230 | − | 0.278372i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −0.0294493 | − | 6.08269i | −0.00484144 | − | 0.999988i | ||||
\(38\) | 2.98197i | 0.483739i | ||||||||
\(39\) | −2.67433 | + | 1.54402i | −0.428235 | + | 0.247241i | ||||
\(40\) | −2.18223 | + | 0.487744i | −0.345040 | + | 0.0771190i | ||||
\(41\) | −1.18271 | + | 2.04852i | −0.184709 | + | 0.319925i | −0.943478 | − | 0.331434i | \(-0.892468\pi\) |
0.758769 | + | 0.651359i | \(0.225801\pi\) | |||||||
\(42\) | −1.23137 | + | 2.13280i | −0.190005 | + | 0.329098i | ||||
\(43\) | 3.94663 | 0.601856 | 0.300928 | − | 0.953647i | \(-0.402704\pi\) | ||||
0.300928 | + | 0.953647i | \(0.402704\pi\) | |||||||
\(44\) | 0.226038 | − | 0.391509i | 0.0340765 | − | 0.0590222i | ||||
\(45\) | 1.51351 | + | 1.64599i | 0.225621 | + | 0.245370i | ||||
\(46\) | 0.887924 | + | 1.53793i | 0.130917 | + | 0.226755i | ||||
\(47\) | 2.64363i | 0.385613i | 0.981237 | + | 0.192807i | \(0.0617590\pi\) | ||||
−0.981237 | + | 0.192807i | \(0.938241\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −0.467447 | − | 0.809642i | −0.0667782 | − | 0.115663i | ||||
\(50\) | 4.10564 | + | 2.85372i | 0.580626 | + | 0.403577i | ||||
\(51\) | 2.11474i | 0.296123i | ||||||||
\(52\) | 1.54402 | + | 2.67433i | 0.214117 | + | 0.370862i | ||||
\(53\) | 8.26490 | − | 4.77175i | 1.13527 | − | 0.655450i | 0.190017 | − | 0.981781i | \(-0.439146\pi\) |
0.945255 | + | 0.326331i | \(0.105813\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | −0.986530 | + | 0.220497i | −0.133024 | + | 0.0297318i | ||||
\(56\) | 2.13280 | + | 1.23137i | 0.285007 | + | 0.164549i | ||||
\(57\) | −1.49098 | − | 2.58246i | −0.197486 | − | 0.342055i | ||||
\(58\) | 7.24777 | − | 4.18450i | 0.951679 | − | 0.549452i | ||||
\(59\) | −2.78387 | + | 1.60727i | −0.362429 | + | 0.209248i | −0.670146 | − | 0.742230i | \(-0.733768\pi\) |
0.307717 | + | 0.951478i | \(0.400435\pi\) | |||||||
\(60\) | 1.64599 | − | 1.51351i | 0.212496 | − | 0.195393i | ||||
\(61\) | 7.10381 | + | 4.10139i | 0.909550 | + | 0.525129i | 0.880286 | − | 0.474443i | \(-0.157350\pi\) |
0.0292637 | + | 0.999572i | \(0.490684\pi\) | |||||||
\(62\) | 2.21296 | − | 1.27765i | 0.281046 | − | 0.162262i | ||||
\(63\) | − | 2.46274i | − | 0.310277i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.06502 | − | 6.58907i | 0.256134 | − | 0.817273i | ||||
\(66\) | 0.452075i | 0.0556466i | ||||||||
\(67\) | −8.26563 | − | 4.77217i | −1.00981 | − | 0.583013i | −0.0986725 | − | 0.995120i | \(-0.531460\pi\) |
−0.911135 | + | 0.412107i | \(0.864793\pi\) | |||||||
\(68\) | 2.11474 | 0.256450 | ||||||||
\(69\) | −1.53793 | − | 0.887924i | −0.185145 | − | 0.106893i | ||||
\(70\) | −1.20119 | − | 5.37426i | −0.143569 | − | 0.642347i | ||||
\(71\) | 0.00323694 | − | 0.00560655i | 0.000384154 | − | 0.000665375i | −0.865833 | − | 0.500333i | \(-0.833211\pi\) |
0.866217 | + | 0.499667i | \(0.166544\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | − | 9.13122i | − | 1.06873i | −0.845254 | − | 0.534364i | \(-0.820551\pi\) | ||
0.845254 | − | 0.534364i | \(-0.179449\pi\) | |||||||
\(74\) | 5.25304 | − | 3.06685i | 0.610654 | − | 0.356514i | ||||
\(75\) | −4.98245 | − | 0.418570i | −0.575324 | − | 0.0483323i | ||||
\(76\) | −2.58246 | + | 1.49098i | −0.296228 | + | 0.171028i | ||||
\(77\) | 0.964186 | + | 0.556673i | 0.109879 | + | 0.0634388i | ||||
\(78\) | −2.67433 | − | 1.54402i | −0.302808 | − | 0.174826i | ||||
\(79\) | 10.9751 | + | 6.33650i | 1.23480 | + | 0.712912i | 0.968027 | − | 0.250848i | \(-0.0807093\pi\) |
0.266773 | + | 0.963759i | \(0.414043\pi\) | |||||||
\(80\) | −1.51351 | − | 1.64599i | −0.169216 | − | 0.184027i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.36543 | −0.261218 | ||||||||
\(83\) | −6.55955 | + | 3.78716i | −0.720005 | + | 0.415695i | −0.814754 | − | 0.579806i | \(-0.803128\pi\) |
0.0947497 | + | 0.995501i | \(0.469795\pi\) | |||||||
\(84\) | −2.46274 | −0.268707 | ||||||||
\(85\) | −3.20068 | − | 3.48085i | −0.347163 | − | 0.377551i | ||||
\(86\) | 1.97332 | + | 3.41789i | 0.212788 | + | 0.368560i | ||||
\(87\) | −4.18450 | + | 7.24777i | −0.448626 | + | 0.777042i | ||||
\(88\) | 0.452075 | 0.0481914 | ||||||||
\(89\) | 9.02573 | − | 5.21101i | 0.956726 | − | 0.552366i | 0.0615619 | − | 0.998103i | \(-0.480392\pi\) |
0.895164 | + | 0.445737i | \(0.147059\pi\) | |||||||
\(90\) | −0.668714 | + | 2.13373i | −0.0704887 | + | 0.224915i | ||||
\(91\) | −6.58618 | + | 3.80253i | −0.690419 | + | 0.398614i | ||||
\(92\) | −0.887924 | + | 1.53793i | −0.0925725 | + | 0.160340i | ||||
\(93\) | −1.27765 | + | 2.21296i | −0.132487 | + | 0.229473i | ||||
\(94\) | −2.28945 | + | 1.32182i | −0.236139 | + | 0.136335i | ||||
\(95\) | 6.36273 | + | 1.99408i | 0.652802 | + | 0.204589i | ||||
\(96\) | −0.866025 | + | 0.500000i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | −5.64069 | −0.572725 | −0.286363 | − | 0.958121i | \(-0.592446\pi\) | ||||
−0.286363 | + | 0.958121i | \(0.592446\pi\) | |||||||
\(98\) | 0.467447 | − | 0.809642i | 0.0472193 | − | 0.0817862i | ||||
\(99\) | −0.226038 | − | 0.391509i | −0.0227176 | − | 0.0393481i | ||||
\(100\) | −0.418570 | + | 4.98245i | −0.0418570 | + | 0.498245i | ||||
\(101\) | 6.59186 | 0.655914 | 0.327957 | − | 0.944693i | \(-0.393640\pi\) | ||||
0.327957 | + | 0.944693i | \(0.393640\pi\) | |||||||
\(102\) | −1.83142 | + | 1.05737i | −0.181338 | + | 0.104695i | ||||
\(103\) | 0.706172 | 0.0695812 | 0.0347906 | − | 0.999395i | \(-0.488924\pi\) | ||||
0.0347906 | + | 0.999395i | \(0.488924\pi\) | |||||||
\(104\) | −1.54402 | + | 2.67433i | −0.151404 | + | 0.262239i | ||||
\(105\) | 3.72739 | + | 4.05365i | 0.363756 | + | 0.395596i | ||||
\(106\) | 8.26490 | + | 4.77175i | 0.802759 | + | 0.463473i | ||||
\(107\) | 4.58807 | + | 2.64892i | 0.443545 | + | 0.256081i | 0.705100 | − | 0.709108i | \(-0.250902\pi\) |
−0.261555 | + | 0.965189i | \(0.584235\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 5.76779 | − | 3.33004i | 0.552454 | − | 0.318960i | −0.197657 | − | 0.980271i | \(-0.563333\pi\) |
0.750111 | + | 0.661312i | \(0.230000\pi\) | |||||||
\(110\) | −0.684221 | − | 0.744112i | −0.0652379 | − | 0.0709483i | ||||
\(111\) | −3.01584 | + | 5.28249i | −0.286251 | + | 0.501392i | ||||
\(112\) | 2.46274i | 0.232707i | ||||||||
\(113\) | 6.58655 | + | 11.4082i | 0.619611 | + | 1.07320i | 0.989557 | + | 0.144144i | \(0.0460429\pi\) |
−0.369946 | + | 0.929053i | \(0.620624\pi\) | |||||||
\(114\) | 1.49098 | − | 2.58246i | 0.139643 | − | 0.241870i | ||||
\(115\) | 3.87530 | − | 0.866158i | 0.361374 | − | 0.0807697i | ||||
\(116\) | 7.24777 | + | 4.18450i | 0.672938 | + | 0.388521i | ||||
\(117\) | 3.08804 | 0.285490 | ||||||||
\(118\) | −2.78387 | − | 1.60727i | −0.256276 | − | 0.147961i | ||||
\(119\) | 5.20807i | 0.477423i | ||||||||
\(120\) | 2.13373 | + | 0.668714i | 0.194782 | + | 0.0610450i | ||||
\(121\) | −10.7956 | −0.981421 | ||||||||
\(122\) | 8.20278i | 0.742644i | ||||||||
\(123\) | 2.04852 | − | 1.18271i | 0.184709 | − | 0.106642i | ||||
\(124\) | 2.21296 | + | 1.27765i | 0.198730 | + | 0.114737i | ||||
\(125\) | 8.83457 | − | 6.85203i | 0.790188 | − | 0.612864i | ||||
\(126\) | 2.13280 | − | 1.23137i | 0.190005 | − | 0.109699i | ||||
\(127\) | −15.7823 | + | 9.11192i | −1.40045 | + | 0.808552i | −0.994439 | − | 0.105315i | \(-0.966415\pi\) |
−0.406014 | + | 0.913867i | \(0.633082\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −3.41789 | − | 1.97332i | −0.300928 | − | 0.173741i | ||||
\(130\) | 6.73881 | − | 1.50617i | 0.591033 | − | 0.132100i | ||||
\(131\) | 9.09771 | − | 5.25257i | 0.794871 | − | 0.458919i | −0.0468037 | − | 0.998904i | \(-0.514904\pi\) |
0.841674 | + | 0.539985i | \(0.181570\pi\) | |||||||
\(132\) | −0.391509 | + | 0.226038i | −0.0340765 | + | 0.0196741i | ||||
\(133\) | −3.67191 | − | 6.35994i | −0.318395 | − | 0.551476i | ||||
\(134\) | − | 9.54433i | − | 0.824505i | ||||||
\(135\) | −0.487744 | − | 2.18223i | −0.0419783 | − | 0.187816i | ||||
\(136\) | 1.05737 | + | 1.83142i | 0.0906688 | + | 0.157043i | ||||
\(137\) | 15.4821i | 1.32272i | 0.750068 | + | 0.661361i | \(0.230021\pi\) | ||||
−0.750068 | + | 0.661361i | \(0.769979\pi\) | |||||||
\(138\) | − | 1.77585i | − | 0.151170i | ||||||
\(139\) | −6.46352 | − | 11.1951i | −0.548228 | − | 0.949560i | −0.998396 | − | 0.0566155i | \(-0.981969\pi\) |
0.450168 | − | 0.892944i | \(-0.351364\pi\) | |||||||
\(140\) | 4.05365 | − | 3.72739i | 0.342596 | − | 0.315022i | ||||
\(141\) | 1.32182 | − | 2.28945i | 0.111317 | − | 0.192807i | ||||
\(142\) | 0.00647388 | 0.000543276 | ||||||||
\(143\) | −0.698014 | + | 1.20900i | −0.0583709 | + | 0.101101i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | −4.08193 | − | 18.2630i | −0.338986 | − | 1.51666i | ||||
\(146\) | 7.90787 | − | 4.56561i | 0.654460 | − | 0.377853i | ||||
\(147\) | 0.934894i | 0.0771088i | ||||||||
\(148\) | 5.28249 | + | 3.01584i | 0.434218 | + | 0.247901i | ||||
\(149\) | 0.922279 | 0.0755560 | 0.0377780 | − | 0.999286i | \(-0.487972\pi\) | ||||
0.0377780 | + | 0.999286i | \(0.487972\pi\) | |||||||
\(150\) | −2.12873 | − | 4.52421i | −0.173810 | − | 0.369400i | ||||
\(151\) | −9.43397 | + | 16.3401i | −0.767726 | + | 1.32974i | 0.171067 | + | 0.985259i | \(0.445278\pi\) |
−0.938793 | + | 0.344481i | \(0.888055\pi\) | |||||||
\(152\) | −2.58246 | − | 1.49098i | −0.209465 | − | 0.120935i | ||||
\(153\) | 1.05737 | − | 1.83142i | 0.0854834 | − | 0.148062i | ||||
\(154\) | 1.11335i | 0.0897159i | ||||||||
\(155\) | −1.24634 | − | 5.57626i | −0.100108 | − | 0.447896i | ||||
\(156\) | − | 3.08804i | − | 0.247241i | ||||||
\(157\) | −13.0389 | + | 7.52798i | −1.04061 | + | 0.600799i | −0.920007 | − | 0.391902i | \(-0.871817\pi\) |
−0.120607 | + | 0.992700i | \(0.538484\pi\) | |||||||
\(158\) | 12.6730i | 1.00821i | ||||||||
\(159\) | −9.54349 | −0.756848 | ||||||||
\(160\) | 0.668714 | − | 2.13373i | 0.0528665 | − | 0.168686i | ||||
\(161\) | −3.78753 | − | 2.18673i | −0.298499 | − | 0.172338i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.68670 | − | 15.0458i | −0.680395 | − | 1.17848i | −0.974860 | − | 0.222817i | \(-0.928475\pi\) |
0.294465 | − | 0.955662i | \(-0.404859\pi\) | |||||||
\(164\) | −1.18271 | − | 2.04852i | −0.0923545 | − | 0.159963i | ||||
\(165\) | 0.964609 | + | 0.302309i | 0.0750947 | + | 0.0235347i | ||||
\(166\) | −6.55955 | − | 3.78716i | −0.509120 | − | 0.293941i | ||||
\(167\) | 1.65702 | − | 2.87004i | 0.128224 | − | 0.222090i | −0.794765 | − | 0.606918i | \(-0.792406\pi\) |
0.922988 | + | 0.384828i | \(0.125739\pi\) | |||||||
\(168\) | −1.23137 | − | 2.13280i | −0.0950024 | − | 0.164549i | ||||
\(169\) | 1.73199 | + | 2.99990i | 0.133230 | + | 0.230761i | ||||
\(170\) | 1.41416 | − | 4.51230i | 0.108461 | − | 0.346077i | ||||
\(171\) | 2.98197i | 0.228037i | ||||||||
\(172\) | −1.97332 | + | 3.41789i | −0.150464 | + | 0.260611i | ||||
\(173\) | 0.977227 | − | 0.564202i | 0.0742972 | − | 0.0428955i | −0.462391 | − | 0.886676i | \(-0.653008\pi\) |
0.536688 | + | 0.843781i | \(0.319675\pi\) | |||||||
\(174\) | −8.36900 | −0.634452 | ||||||||
\(175\) | −12.2705 | − | 1.03083i | −0.927562 | − | 0.0779235i | ||||
\(176\) | 0.226038 | + | 0.391509i | 0.0170382 | + | 0.0295111i | ||||
\(177\) | 3.21453 | 0.241619 | ||||||||
\(178\) | 9.02573 | + | 5.21101i | 0.676507 | + | 0.390582i | ||||
\(179\) | 9.79245i | 0.731922i | 0.930630 | + | 0.365961i | \(0.119260\pi\) | ||||
−0.930630 | + | 0.365961i | \(0.880740\pi\) | |||||||
\(180\) | −2.18223 | + | 0.487744i | −0.162653 | + | 0.0363543i | ||||
\(181\) | −6.70130 | + | 11.6070i | −0.498103 | + | 0.862740i | −0.999998 | − | 0.00218861i | \(-0.999303\pi\) |
0.501894 | + | 0.864929i | \(0.332637\pi\) | |||||||
\(182\) | −6.58618 | − | 3.80253i | −0.488200 | − | 0.281862i | ||||
\(183\) | −4.10139 | − | 7.10381i | −0.303183 | − | 0.525129i | ||||
\(184\) | −1.77585 | −0.130917 | ||||||||
\(185\) | −3.03106 | − | 13.2594i | −0.222848 | − | 0.974853i | ||||
\(186\) | −2.55531 | −0.187364 | ||||||||
\(187\) | 0.478011 | + | 0.827940i | 0.0349556 | + | 0.0605450i | ||||
\(188\) | −2.28945 | − | 1.32182i | −0.166975 | − | 0.0964033i | ||||
\(189\) | −1.23137 | + | 2.13280i | −0.0895691 | + | 0.155138i | ||||
\(190\) | 1.45444 | + | 6.50733i | 0.105516 | + | 0.472091i | ||||
\(191\) | 9.38260i | 0.678901i | 0.940624 | + | 0.339451i | \(0.110241\pi\) | ||||
−0.940624 | + | 0.339451i | \(0.889759\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | −12.5017 | −0.899890 | −0.449945 | − | 0.893056i | \(-0.648556\pi\) | ||||
−0.449945 | + | 0.893056i | \(0.648556\pi\) | |||||||
\(194\) | −2.82034 | − | 4.88498i | −0.202489 | − | 0.350721i | ||||
\(195\) | −5.08289 | + | 4.67379i | −0.363993 | + | 0.334697i | ||||
\(196\) | 0.934894 | 0.0667782 | ||||||||
\(197\) | 1.70221 | − | 0.982774i | 0.121278 | − | 0.0700197i | −0.438134 | − | 0.898910i | \(-0.644360\pi\) |
0.559412 | + | 0.828890i | \(0.311027\pi\) | |||||||
\(198\) | 0.226038 | − | 0.391509i | 0.0160638 | − | 0.0278233i | ||||
\(199\) | − | 12.7088i | − | 0.900900i | −0.892802 | − | 0.450450i | \(-0.851263\pi\) | ||
0.892802 | − | 0.450450i | \(-0.148737\pi\) | |||||||
\(200\) | −4.52421 | + | 2.12873i | −0.319910 | + | 0.150524i | ||||
\(201\) | 4.77217 | + | 8.26563i | 0.336603 | + | 0.583013i | ||||
\(202\) | 3.29593 | + | 5.70872i | 0.231901 | + | 0.401664i | ||||
\(203\) | −10.3054 | + | 17.8494i | −0.723294 | + | 1.25278i | ||||
\(204\) | −1.83142 | − | 1.05737i | −0.128225 | − | 0.0740308i | ||||
\(205\) | −1.58180 | + | 5.04720i | −0.110477 | + | 0.352512i | ||||
\(206\) | 0.353086 | + | 0.611563i | 0.0246007 | + | 0.0426096i | ||||
\(207\) | 0.887924 | + | 1.53793i | 0.0617150 | + | 0.106893i | ||||
\(208\) | −3.08804 | −0.214117 | ||||||||
\(209\) | −1.16747 | − | 0.674037i | −0.0807554 | − | 0.0466241i | ||||
\(210\) | −1.64687 | + | 5.25484i | −0.113645 | + | 0.362618i | ||||
\(211\) | −11.2817 | −0.776662 | −0.388331 | − | 0.921520i | \(-0.626948\pi\) | ||||
−0.388331 | + | 0.921520i | \(0.626948\pi\) | |||||||
\(212\) | 9.54349i | 0.655450i | ||||||||
\(213\) | −0.00560655 | + | 0.00323694i | −0.000384154 | + | 0.000221792i | ||||
\(214\) | 5.29785i | 0.362153i | ||||||||
\(215\) | 8.61245 | − | 1.92495i | 0.587364 | − | 0.131280i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −3.14653 | + | 5.44996i | −0.213601 | + | 0.369967i | ||||
\(218\) | 5.76779 | + | 3.33004i | 0.390644 | + | 0.225539i | ||||
\(219\) | −4.56561 | + | 7.90787i | −0.308515 | + | 0.534364i | ||||
\(220\) | 0.302309 | − | 0.964609i | 0.0203817 | − | 0.0650339i | ||||
\(221\) | −6.53042 | −0.439283 | ||||||||
\(222\) | −6.08269 | + | 0.0294493i | −0.408244 | + | 0.00197651i | ||||
\(223\) | − | 13.9818i | − | 0.936293i | −0.883651 | − | 0.468146i | \(-0.844922\pi\) | ||
0.883651 | − | 0.468146i | \(-0.155078\pi\) | |||||||
\(224\) | −2.13280 | + | 1.23137i | −0.142504 | + | 0.0822745i | ||||
\(225\) | 4.10564 | + | 2.85372i | 0.273709 | + | 0.190248i | ||||
\(226\) | −6.58655 | + | 11.4082i | −0.438131 | + | 0.758865i | ||||
\(227\) | −10.0487 | + | 17.4048i | −0.666953 | + | 1.15520i | 0.311799 | + | 0.950148i | \(0.399068\pi\) |
−0.978752 | + | 0.205048i | \(0.934265\pi\) | |||||||
\(228\) | 2.98197 | 0.197486 | ||||||||
\(229\) | 2.81341 | − | 4.87296i | 0.185915 | − | 0.322014i | −0.757969 | − | 0.652290i | \(-0.773808\pi\) |
0.943885 | + | 0.330276i | \(0.107142\pi\) | |||||||
\(230\) | 2.68777 | + | 2.92303i | 0.177226 | + | 0.192739i | ||||
\(231\) | −0.556673 | − | 0.964186i | −0.0366264 | − | 0.0634388i | ||||
\(232\) | 8.36900i | 0.549452i | ||||||||
\(233\) | 16.2683i | 1.06577i | 0.846187 | + | 0.532887i | \(0.178893\pi\) | ||||
−0.846187 | + | 0.532887i | \(0.821107\pi\) | |||||||
\(234\) | 1.54402 | + | 2.67433i | 0.100936 | + | 0.174826i | ||||
\(235\) | 1.28941 | + | 5.76900i | 0.0841121 | + | 0.376328i | ||||
\(236\) | − | 3.21453i | − | 0.209248i | ||||||
\(237\) | −6.33650 | − | 10.9751i | −0.411600 | − | 0.712912i | ||||
\(238\) | −4.51032 | + | 2.60403i | −0.292360 | + | 0.168794i | ||||
\(239\) | 4.52658 | − | 2.61342i | 0.292800 | − | 0.169048i | −0.346404 | − | 0.938085i | \(-0.612597\pi\) |
0.639204 | + | 0.769037i | \(0.279264\pi\) | |||||||
\(240\) | 0.487744 | + | 2.18223i | 0.0314837 | + | 0.140862i | ||||
\(241\) | −21.8978 | − | 12.6427i | −1.41056 | − | 0.814387i | −0.415119 | − | 0.909767i | \(-0.636260\pi\) |
−0.995441 | + | 0.0953804i | \(0.969593\pi\) | |||||||
\(242\) | −5.39781 | − | 9.34929i | −0.346985 | − | 0.600995i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −7.10381 | + | 4.10139i | −0.454775 | + | 0.262564i | ||||
\(245\) | −1.41497 | − | 1.53883i | −0.0903993 | − | 0.0983121i | ||||
\(246\) | 2.04852 | + | 1.18271i | 0.130609 | + | 0.0754071i | ||||
\(247\) | 7.97475 | − | 4.60423i | 0.507421 | − | 0.292960i | ||||
\(248\) | 2.55531i | 0.162262i | ||||||||
\(249\) | 7.57432 | 0.480003 | ||||||||
\(250\) | 10.3513 | + | 4.22495i | 0.654675 | + | 0.267209i | ||||
\(251\) | − | 2.27414i | − | 0.143542i | −0.997421 | − | 0.0717712i | \(-0.977135\pi\) | ||
0.997421 | − | 0.0717712i | \(-0.0228652\pi\) | |||||||
\(252\) | 2.13280 | + | 1.23137i | 0.134354 | + | 0.0775691i | ||||
\(253\) | −0.802817 | −0.0504727 | ||||||||
\(254\) | −15.7823 | − | 9.11192i | −0.990270 | − | 0.571733i | ||||
\(255\) | 1.03145 | + | 4.61484i | 0.0645920 | + | 0.288993i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.8758 | + | 18.8374i | 0.678413 | + | 1.17505i | 0.975459 | + | 0.220182i | \(0.0706652\pi\) |
−0.297046 | + | 0.954863i | \(0.596001\pi\) | |||||||
\(258\) | − | 3.94663i | − | 0.245707i | ||||||
\(259\) | −7.42724 | + | 13.0094i | −0.461507 | + | 0.808366i | ||||
\(260\) | 4.67379 | + | 5.08289i | 0.289856 | + | 0.315228i | ||||
\(261\) | 7.24777 | − | 4.18450i | 0.448626 | − | 0.259014i | ||||
\(262\) | 9.09771 | + | 5.25257i | 0.562059 | + | 0.324505i | ||||
\(263\) | −5.41619 | − | 3.12704i | −0.333977 | − | 0.192822i | 0.323629 | − | 0.946184i | \(-0.395097\pi\) |
−0.657605 | + | 0.753363i | \(0.728431\pi\) | |||||||
\(264\) | −0.391509 | − | 0.226038i | −0.0240957 | − | 0.0139117i | ||||
\(265\) | 15.7085 | − | 14.4442i | 0.964965 | − | 0.887299i | ||||
\(266\) | 3.67191 | − | 6.35994i | 0.225139 | − | 0.389953i | ||||
\(267\) | −10.4220 | −0.637817 | ||||||||
\(268\) | 8.26563 | − | 4.77217i | 0.504904 | − | 0.291506i | ||||
\(269\) | −7.07555 | −0.431404 | −0.215702 | − | 0.976459i | \(-0.569204\pi\) | ||||
−0.215702 | + | 0.976459i | \(0.569204\pi\) | |||||||
\(270\) | 1.64599 | − | 1.51351i | 0.100172 | − | 0.0921093i | ||||
\(271\) | −2.51174 | − | 4.35046i | −0.152577 | − | 0.264272i | 0.779597 | − | 0.626282i | \(-0.215424\pi\) |
−0.932174 | + | 0.362010i | \(0.882091\pi\) | |||||||
\(272\) | −1.05737 | + | 1.83142i | −0.0641125 | + | 0.111046i | ||||
\(273\) | 7.60506 | 0.460279 | ||||||||
\(274\) | −13.4079 | + | 7.74103i | −0.809999 | + | 0.467653i | ||||
\(275\) | −2.04528 | + | 0.962347i | −0.123335 | + | 0.0580317i | ||||
\(276\) | 1.53793 | − | 0.887924i | 0.0925725 | − | 0.0534467i | ||||
\(277\) | −14.3006 | + | 24.7694i | −0.859242 | + | 1.48825i | 0.0134110 | + | 0.999910i | \(0.495731\pi\) |
−0.872653 | + | 0.488341i | \(0.837602\pi\) | |||||||
\(278\) | 6.46352 | − | 11.1951i | 0.387656 | − | 0.671440i | ||||
\(279\) | 2.21296 | − | 1.27765i | 0.132487 | − | 0.0764912i | ||||
\(280\) | 5.25484 | + | 1.64687i | 0.314037 | + | 0.0984194i | ||||
\(281\) | −11.1812 | + | 6.45549i | −0.667017 | + | 0.385102i | −0.794945 | − | 0.606681i | \(-0.792500\pi\) |
0.127929 | + | 0.991783i | \(0.459167\pi\) | |||||||
\(282\) | 2.64363 | 0.157426 | ||||||||
\(283\) | 10.3736 | − | 17.9677i | 0.616648 | − | 1.06807i | −0.373444 | − | 0.927653i | \(-0.621823\pi\) |
0.990093 | − | 0.140414i | \(-0.0448433\pi\) | |||||||
\(284\) | 0.00323694 | + | 0.00560655i | 0.000192077 | + | 0.000332687i | ||||
\(285\) | −4.51324 | − | 4.90829i | −0.267341 | − | 0.290742i | ||||
\(286\) | −1.39603 | −0.0825489 | ||||||||
\(287\) | 5.04498 | − | 2.91272i | 0.297796 | − | 0.171933i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 6.26393 | − | 10.8495i | 0.368467 | − | 0.638203i | ||||
\(290\) | 13.7753 | − | 12.6666i | 0.808913 | − | 0.743807i | ||||
\(291\) | 4.88498 | + | 2.82034i | 0.286363 | + | 0.165332i | ||||
\(292\) | 7.90787 | + | 4.56561i | 0.462773 | + | 0.267182i | ||||
\(293\) | −8.12951 | − | 4.69358i | −0.474931 | − | 0.274202i | 0.243371 | − | 0.969933i | \(-0.421747\pi\) |
−0.718302 | + | 0.695732i | \(0.755080\pi\) | |||||||
\(294\) | −0.809642 | + | 0.467447i | −0.0472193 | + | 0.0272621i | ||||
\(295\) | −5.29109 | + | 4.86523i | −0.308059 | + | 0.283265i | ||||
\(296\) | 0.0294493 | + | 6.08269i | 0.00171171 | + | 0.353549i | ||||
\(297\) | 0.452075i | 0.0262321i | ||||||||
\(298\) | 0.461139 | + | 0.798717i | 0.0267131 | + | 0.0462684i | ||||
\(299\) | 2.74195 | − | 4.74919i | 0.158571 | − | 0.274653i | ||||
\(300\) | 2.85372 | − | 4.10564i | 0.164759 | − | 0.237039i | ||||
\(301\) | −8.41738 | − | 4.85977i | −0.485170 | − | 0.280113i | ||||
\(302\) | −18.8679 | −1.08573 | ||||||||
\(303\) | −5.70872 | − | 3.29593i | −0.327957 | − | 0.189346i | ||||
\(304\) | − | 2.98197i | − | 0.171028i | ||||||
\(305\) | 17.5025 | + | 5.48531i | 1.00219 | + | 0.314088i | ||||
\(306\) | 2.11474 | 0.120892 | ||||||||
\(307\) | − | 2.11341i | − | 0.120619i | −0.998180 | − | 0.0603095i | \(-0.980791\pi\) | ||
0.998180 | − | 0.0603095i | \(-0.0192088\pi\) | |||||||
\(308\) | −0.964186 | + | 0.556673i | −0.0549396 | + | 0.0317194i | ||||
\(309\) | −0.611563 | − | 0.353086i | −0.0347906 | − | 0.0200864i | ||||
\(310\) | 4.20601 | − | 3.86749i | 0.238886 | − | 0.219658i | ||||
\(311\) | 19.2848 | − | 11.1341i | 1.09354 | − | 0.631355i | 0.159023 | − | 0.987275i | \(-0.449166\pi\) |
0.934517 | + | 0.355920i | \(0.115832\pi\) | |||||||
\(312\) | 2.67433 | − | 1.54402i | 0.151404 | − | 0.0874130i | ||||
\(313\) | 8.32368 | + | 14.4170i | 0.470482 | + | 0.814899i | 0.999430 | − | 0.0337549i | \(-0.0107466\pi\) |
−0.528948 | + | 0.848654i | \(0.677413\pi\) | |||||||
\(314\) | −13.0389 | − | 7.52798i | −0.735825 | − | 0.424829i | ||||
\(315\) | −1.20119 | − | 5.37426i | −0.0676792 | − | 0.302805i | ||||
\(316\) | −10.9751 | + | 6.33650i | −0.617400 | + | 0.356456i | ||||
\(317\) | 2.95498 | − | 1.70606i | 0.165968 | − | 0.0958219i | −0.414715 | − | 0.909951i | \(-0.636119\pi\) |
0.580683 | + | 0.814129i | \(0.302785\pi\) | |||||||
\(318\) | −4.77175 | − | 8.26490i | −0.267586 | − | 0.463473i | ||||
\(319\) | 3.78342i | 0.211831i | ||||||||
\(320\) | 2.18223 | − | 0.487744i | 0.121990 | − | 0.0272657i | ||||
\(321\) | −2.64892 | − | 4.58807i | −0.147848 | − | 0.256081i | ||||
\(322\) | − | 4.37346i | − | 0.243723i | ||||||
\(323\) | − | 6.30609i | − | 0.350880i | ||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 1.29256 | − | 15.3860i | 0.0716985 | − | 0.853463i | ||||
\(326\) | 8.68670 | − | 15.0458i | 0.481112 | − | 0.833311i | ||||
\(327\) | −6.66007 | −0.368303 | ||||||||
\(328\) | 1.18271 | − | 2.04852i | 0.0653045 | − | 0.113111i | ||||
\(329\) | 3.25529 | − | 5.63833i | 0.179470 | − | 0.310851i | ||||
\(330\) | 0.220497 | + | 0.986530i | 0.0121380 | + | 0.0543067i | ||||
\(331\) | 23.5466 | − | 13.5946i | 1.29424 | − | 0.747229i | 0.314835 | − | 0.949146i | \(-0.398051\pi\) |
0.979403 | + | 0.201918i | \(0.0647173\pi\) | |||||||
\(332\) | − | 7.57432i | − | 0.415695i | ||||||
\(333\) | 5.25304 | − | 3.06685i | 0.287865 | − | 0.168062i | ||||
\(334\) | 3.31403 | 0.181336 | ||||||||
\(335\) | −20.3651 | − | 6.38243i | −1.11266 | − | 0.348709i | ||||
\(336\) | 1.23137 | − | 2.13280i | 0.0671768 | − | 0.116354i | ||||
\(337\) | 10.0266 | + | 5.78887i | 0.546185 | + | 0.315340i | 0.747582 | − | 0.664170i | \(-0.231215\pi\) |
−0.201397 | + | 0.979510i | \(0.564548\pi\) | |||||||
\(338\) | −1.73199 | + | 2.99990i | −0.0942079 | + | 0.163173i | ||||
\(339\) | − | 13.1731i | − | 0.715465i | ||||||
\(340\) | 4.61484 | − | 1.03145i | 0.250275 | − | 0.0559383i | ||||
\(341\) | 1.15519i | 0.0625571i | ||||||||
\(342\) | −2.58246 | + | 1.49098i | −0.139643 | + | 0.0806232i | ||||
\(343\) | 19.5416i | 1.05515i | ||||||||
\(344\) | −3.94663 | −0.212788 | ||||||||
\(345\) | −3.78919 | − | 1.18753i | −0.204003 | − | 0.0639347i | ||||
\(346\) | 0.977227 | + | 0.564202i | 0.0525360 | + | 0.0303317i | ||||
\(347\) | 18.7028 | 1.00402 | 0.502010 | − | 0.864862i | \(-0.332594\pi\) | ||||
0.502010 | + | 0.864862i | \(0.332594\pi\) | |||||||
\(348\) | −4.18450 | − | 7.24777i | −0.224313 | − | 0.388521i | ||||
\(349\) | 9.61263 | + | 16.6496i | 0.514552 | + | 0.891231i | 0.999857 | + | 0.0168860i | \(0.00537524\pi\) |
−0.485305 | + | 0.874345i | \(0.661291\pi\) | |||||||
\(350\) | −5.24252 | − | 11.1420i | −0.280225 | − | 0.595564i | ||||
\(351\) | −2.67433 | − | 1.54402i | −0.142745 | − | 0.0824138i | ||||
\(352\) | −0.226038 | + | 0.391509i | −0.0120478 | + | 0.0208675i | ||||
\(353\) | 5.24212 | + | 9.07961i | 0.279010 | + | 0.483259i | 0.971139 | − | 0.238515i | \(-0.0766605\pi\) |
−0.692129 | + | 0.721774i | \(0.743327\pi\) | |||||||
\(354\) | 1.60727 | + | 2.78387i | 0.0854253 | + | 0.147961i | ||||
\(355\) | 0.00432918 | − | 0.0138135i | 0.000229769 | − | 0.000733147i | ||||
\(356\) | 10.4220i | 0.552366i | ||||||||
\(357\) | 2.60403 | − | 4.51032i | 0.137820 | − | 0.238711i | ||||
\(358\) | −8.48051 | + | 4.89623i | −0.448209 | + | 0.258774i | ||||
\(359\) | −6.92393 | −0.365431 | −0.182716 | − | 0.983166i | \(-0.558489\pi\) | ||||
−0.182716 | + | 0.983166i | \(0.558489\pi\) | |||||||
\(360\) | −1.51351 | − | 1.64599i | −0.0797690 | − | 0.0867513i | ||||
\(361\) | −5.05393 | − | 8.75367i | −0.265996 | − | 0.460719i | ||||
\(362\) | −13.4026 | −0.704425 | ||||||||
\(363\) | 9.34929 | + | 5.39781i | 0.490710 | + | 0.283312i | ||||
\(364\) | − | 7.60506i | − | 0.398614i | ||||||
\(365\) | −4.45369 | − | 19.9264i | −0.233117 | − | 1.04299i | ||||
\(366\) | 4.10139 | − | 7.10381i | 0.214383 | − | 0.371322i | ||||
\(367\) | 9.18534 | + | 5.30316i | 0.479471 | + | 0.276823i | 0.720196 | − | 0.693771i | \(-0.244052\pi\) |
−0.240725 | + | 0.970593i | \(0.577385\pi\) | |||||||
\(368\) | −0.887924 | − | 1.53793i | −0.0462862 | − | 0.0801701i | ||||
\(369\) | −2.36543 | −0.123139 | ||||||||
\(370\) | 9.96748 | − | 9.25469i | 0.518185 | − | 0.481129i | ||||
\(371\) | −23.5032 | −1.22022 | ||||||||
\(372\) | −1.27765 | − | 2.21296i | −0.0662433 | − | 0.114737i | ||||
\(373\) | 14.0490 | + | 8.11120i | 0.727430 | + | 0.419982i | 0.817481 | − | 0.575955i | \(-0.195370\pi\) |
−0.0900510 | + | 0.995937i | \(0.528703\pi\) | |||||||
\(374\) | −0.478011 | + | 0.827940i | −0.0247174 | + | 0.0428118i | ||||
\(375\) | −11.0770 | + | 1.51674i | −0.572013 | + | 0.0783243i | ||||
\(376\) | − | 2.64363i | − | 0.136335i | ||||||
\(377\) | −22.3814 | − | 12.9219i | −1.15270 | − | 0.665513i | ||||
\(378\) | −2.46274 | −0.126670 | ||||||||
\(379\) | 1.83877 | + | 3.18484i | 0.0944511 | + | 0.163594i | 0.909379 | − | 0.415968i | \(-0.136557\pi\) |
−0.814928 | + | 0.579562i | \(0.803224\pi\) | |||||||
\(380\) | −4.90829 | + | 4.51324i | −0.251790 | + | 0.231524i | ||||
\(381\) | 18.2238 | 0.933635 | ||||||||
\(382\) | −8.12557 | + | 4.69130i | −0.415740 | + | 0.240028i | ||||
\(383\) | 2.74370 | − | 4.75222i | 0.140196 | − | 0.242827i | −0.787374 | − | 0.616475i | \(-0.788560\pi\) |
0.927570 | + | 0.373648i | \(0.121893\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 2.37558 | + | 0.744510i | 0.121071 | + | 0.0379437i | ||||
\(386\) | −6.25084 | − | 10.8268i | −0.318159 | − | 0.551068i | ||||
\(387\) | 1.97332 | + | 3.41789i | 0.100309 | + | 0.173741i | ||||
\(388\) | 2.82034 | − | 4.88498i | 0.143181 | − | 0.247997i | ||||
\(389\) | 24.9890 | + | 14.4274i | 1.26699 | + | 0.731497i | 0.974417 | − | 0.224746i | \(-0.0721551\pi\) |
0.292573 | + | 0.956243i | \(0.405488\pi\) | |||||||
\(390\) | −6.58907 | − | 2.06502i | −0.333650 | − | 0.104566i | ||||
\(391\) | −1.87773 | − | 3.25232i | −0.0949609 | − | 0.164477i | ||||
\(392\) | 0.467447 | + | 0.809642i | 0.0236096 | + | 0.0408931i | ||||
\(393\) | −10.5051 | −0.529914 | ||||||||
\(394\) | 1.70221 | + | 0.982774i | 0.0857563 | + | 0.0495114i | ||||
\(395\) | 27.0408 | + | 8.47461i | 1.36057 | + | 0.426404i | ||||
\(396\) | 0.452075 | 0.0227176 | ||||||||
\(397\) | 13.9468i | 0.699970i | 0.936755 | + | 0.349985i | \(0.113813\pi\) | ||||
−0.936755 | + | 0.349985i | \(0.886187\pi\) | |||||||
\(398\) | 11.0061 | − | 6.35438i | 0.551687 | − | 0.318516i | ||||
\(399\) | 7.34382i | 0.367651i | ||||||||
\(400\) | −4.10564 | − | 2.85372i | −0.205282 | − | 0.142686i | ||||
\(401\) | − | 20.0498i | − | 1.00124i | −0.865667 | − | 0.500620i | \(-0.833105\pi\) | ||
0.865667 | − | 0.500620i | \(-0.166895\pi\) | |||||||
\(402\) | −4.77217 | + | 8.26563i | −0.238014 | + | 0.412252i | ||||
\(403\) | −6.83373 | − | 3.94545i | −0.340412 | − | 0.196537i | ||||
\(404\) | −3.29593 | + | 5.70872i | −0.163979 | + | 0.284019i | ||||
\(405\) | −0.668714 | + | 2.13373i | −0.0332287 | + | 0.106026i | ||||
\(406\) | −20.6107 | −1.02289 | ||||||||
\(407\) | 0.0133133 | + | 2.74983i | 0.000659916 | + | 0.136304i | ||||
\(408\) | − | 2.11474i | − | 0.104695i | ||||||
\(409\) | 16.0291 | − | 9.25441i | 0.792588 | − | 0.457601i | −0.0482847 | − | 0.998834i | \(-0.515375\pi\) |
0.840873 | + | 0.541233i | \(0.182042\pi\) | |||||||
\(410\) | −5.16190 | + | 1.15372i | −0.254928 | + | 0.0569783i | ||||
\(411\) | 7.74103 | − | 13.4079i | 0.381837 | − | 0.661361i | ||||
\(412\) | −0.353086 | + | 0.611563i | −0.0173953 | + | 0.0301295i | ||||
\(413\) | 7.91658 | 0.389549 | ||||||||
\(414\) | −0.887924 | + | 1.53793i | −0.0436391 | + | 0.0755851i | ||||
\(415\) | −12.4673 | + | 11.4638i | −0.611994 | + | 0.562737i | ||||
\(416\) | −1.54402 | − | 2.67433i | −0.0757019 | − | 0.131120i | ||||
\(417\) | 12.9270i | 0.633040i | ||||||||
\(418\) | − | 1.34807i | − | 0.0659365i | ||||||
\(419\) | 14.5978 | + | 25.2842i | 0.713150 | + | 1.23521i | 0.963669 | + | 0.267100i | \(0.0860654\pi\) |
−0.250519 | + | 0.968112i | \(0.580601\pi\) | |||||||
\(420\) | −5.37426 | + | 1.20119i | −0.262237 | + | 0.0586119i | ||||
\(421\) | − | 26.4129i | − | 1.28728i | −0.765327 | − | 0.643642i | \(-0.777423\pi\) | ||
0.765327 | − | 0.643642i | \(-0.222577\pi\) | |||||||
\(422\) | −5.64084 | − | 9.77021i | −0.274592 | − | 0.475607i | ||||
\(423\) | −2.28945 | + | 1.32182i | −0.111317 | + | 0.0642689i | ||||
\(424\) | −8.26490 | + | 4.77175i | −0.401379 | + | 0.231736i | ||||
\(425\) | −8.68237 | − | 6.03487i | −0.421157 | − | 0.292734i | ||||
\(426\) | −0.00560655 | − | 0.00323694i | −0.000271638 | − | 0.000156830i | ||||
\(427\) | −10.1007 | − | 17.4949i | −0.488806 | − | 0.846636i | ||||
\(428\) | −4.58807 | + | 2.64892i | −0.221773 | + | 0.128041i | ||||
\(429\) | 1.20900 | − | 0.698014i | 0.0583709 | − | 0.0337005i | ||||
\(430\) | 5.97327 | + | 6.49612i | 0.288057 | + | 0.313271i | ||||
\(431\) | 17.6376 | + | 10.1831i | 0.849571 | + | 0.490500i | 0.860506 | − | 0.509440i | \(-0.170147\pi\) |
−0.0109348 | + | 0.999940i | \(0.503481\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 33.1108i | 1.59120i | 0.605820 | + | 0.795602i | \(0.292845\pi\) | ||||
−0.605820 | + | 0.795602i | \(0.707155\pi\) | |||||||
\(434\) | −6.29307 | −0.302077 | ||||||||
\(435\) | −5.59647 | + | 17.8572i | −0.268330 | + | 0.856188i | ||||
\(436\) | 6.66007i | 0.318960i | ||||||||
\(437\) | 4.58606 | + | 2.64776i | 0.219381 | + | 0.126660i | ||||
\(438\) | −9.13122 | −0.436307 | ||||||||
\(439\) | 9.84542 | + | 5.68426i | 0.469896 | + | 0.271295i | 0.716196 | − | 0.697899i | \(-0.245882\pi\) |
−0.246300 | + | 0.969194i | \(0.579215\pi\) | |||||||
\(440\) | 0.986530 | − | 0.220497i | 0.0470310 | − | 0.0105118i | ||||
\(441\) | 0.467447 | − | 0.809642i | 0.0222594 | − | 0.0385544i | ||||
\(442\) | −3.26521 | − | 5.65551i | −0.155310 | − | 0.269005i | ||||
\(443\) | − | 3.67208i | − | 0.174466i | −0.996188 | − | 0.0872328i | \(-0.972198\pi\) | ||
0.996188 | − | 0.0872328i | \(-0.0278024\pi\) | |||||||
\(444\) | −3.06685 | − | 5.25304i | −0.145546 | − | 0.249298i | ||||
\(445\) | 17.1545 | − | 15.7738i | 0.813203 | − | 0.747752i | ||||
\(446\) | 12.1086 | − | 6.99092i | 0.573360 | − | 0.331029i | ||||
\(447\) | −0.798717 | − | 0.461139i | −0.0377780 | − | 0.0218111i | ||||
\(448\) | −2.13280 | − | 1.23137i | −0.100765 | − | 0.0581768i | ||||
\(449\) | 13.3926 | + | 7.73221i | 0.632035 | + | 0.364906i | 0.781540 | − | 0.623855i | \(-0.214435\pi\) |
−0.149505 | + | 0.988761i | \(0.547768\pi\) | |||||||
\(450\) | −0.418570 | + | 4.98245i | −0.0197316 | + | 0.234875i | ||||
\(451\) | 0.534676 | − | 0.926086i | 0.0251769 | − | 0.0436077i | ||||
\(452\) | −13.1731 | −0.619611 | ||||||||
\(453\) | 16.3401 | − | 9.43397i | 0.767726 | − | 0.443247i | ||||
\(454\) | −20.0973 | −0.943214 | ||||||||
\(455\) | −12.5179 | + | 11.5103i | −0.586846 | + | 0.539613i | ||||
\(456\) | 1.49098 | + | 2.58246i | 0.0698217 | + | 0.120935i | ||||
\(457\) | −1.63400 | + | 2.83018i | −0.0764355 | + | 0.132390i | −0.901710 | − | 0.432342i | \(-0.857687\pi\) |
0.825274 | + | 0.564732i | \(0.191021\pi\) | |||||||
\(458\) | 5.62681 | 0.262924 | ||||||||
\(459\) | −1.83142 | + | 1.05737i | −0.0854834 | + | 0.0493538i | ||||
\(460\) | −1.18753 | + | 3.78919i | −0.0553691 | + | 0.176672i | ||||
\(461\) | 27.4011 | − | 15.8201i | 1.27620 | − | 0.736813i | 0.300051 | − | 0.953923i | \(-0.402996\pi\) |
0.976147 | + | 0.217110i | \(0.0696629\pi\) | |||||||
\(462\) | 0.556673 | − | 0.964186i | 0.0258988 | − | 0.0448580i | ||||
\(463\) | 2.72366 | − | 4.71752i | 0.126579 | − | 0.219242i | −0.795770 | − | 0.605599i | \(-0.792933\pi\) |
0.922349 | + | 0.386357i | \(0.126267\pi\) | |||||||
\(464\) | −7.24777 | + | 4.18450i | −0.336469 | + | 0.194261i | ||||
\(465\) | −1.70877 | + | 5.45235i | −0.0792424 | + | 0.252847i | ||||
\(466\) | −14.0888 | + | 8.13416i | −0.652650 | + | 0.376808i | ||||
\(467\) | −32.5303 | −1.50532 | −0.752662 | − | 0.658407i | \(-0.771230\pi\) | ||||
−0.752662 | + | 0.658407i | \(0.771230\pi\) | |||||||
\(468\) | −1.54402 | + | 2.67433i | −0.0713725 | + | 0.123621i | ||||
\(469\) | 11.7526 | + | 20.3561i | 0.542686 | + | 0.939959i | ||||
\(470\) | −4.35139 | + | 4.00116i | −0.200715 | + | 0.184560i | ||||
\(471\) | 15.0560 | 0.693742 | ||||||||
\(472\) | 2.78387 | − | 1.60727i | 0.128138 | − | 0.0739805i | ||||
\(473\) | −1.78418 | −0.0820365 | ||||||||
\(474\) | 6.33650 | − | 10.9751i | 0.291045 | − | 0.504105i | ||||
\(475\) | 14.8575 | + | 1.24816i | 0.681709 | + | 0.0572696i | ||||
\(476\) | −4.51032 | − | 2.60403i | −0.206730 | − | 0.119356i | ||||
\(477\) | 8.26490 | + | 4.77175i | 0.378424 | + | 0.218483i | ||||
\(478\) | 4.52658 | + | 2.61342i | 0.207041 | + | 0.119535i | ||||
\(479\) | −2.08893 | + | 1.20604i | −0.0954456 | + | 0.0551055i | −0.546963 | − | 0.837157i | \(-0.684216\pi\) |
0.451517 | + | 0.892262i | \(0.350883\pi\) | |||||||
\(480\) | −1.64599 | + | 1.51351i | −0.0751288 | + | 0.0690820i | ||||
\(481\) | −16.3126 | − | 9.31305i | −0.743789 | − | 0.424639i | ||||
\(482\) | − | 25.2854i | − | 1.15172i | ||||||
\(483\) | 2.18673 | + | 3.78753i | 0.0994996 | + | 0.172338i | ||||
\(484\) | 5.39781 | − | 9.34929i | 0.245355 | − | 0.424968i | ||||
\(485\) | −12.3093 | + | 2.75121i | −0.558934 | + | 0.124926i | ||||
\(486\) | 0.866025 | + | 0.500000i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | 15.6442 | 0.708907 | 0.354453 | − | 0.935074i | \(-0.384667\pi\) | ||||
0.354453 | + | 0.935074i | \(0.384667\pi\) | |||||||
\(488\) | −7.10381 | − | 4.10139i | −0.321574 | − | 0.185661i | ||||
\(489\) | 17.3734i | 0.785653i | ||||||||
\(490\) | 0.625177 | − | 1.99482i | 0.0282426 | − | 0.0901166i | ||||
\(491\) | −20.4625 | −0.923459 | −0.461730 | − | 0.887021i | \(-0.652771\pi\) | ||||
−0.461730 | + | 0.887021i | \(0.652771\pi\) | |||||||
\(492\) | 2.36543i | 0.106642i | ||||||||
\(493\) | −15.3272 | + | 8.84914i | −0.690301 | + | 0.398545i | ||||
\(494\) | 7.97475 | + | 4.60423i | 0.358801 | + | 0.207154i | ||||
\(495\) | −0.684221 | − | 0.744112i | −0.0307534 | − | 0.0334453i | ||||
\(496\) | −2.21296 | + | 1.27765i | −0.0993649 | + | 0.0573684i | ||||
\(497\) | −0.0138075 | + | 0.00797176i | −0.000619351 | + | 0.000357582i | ||||
\(498\) | 3.78716 | + | 6.55955i | 0.169707 | + | 0.293941i | ||||
\(499\) | 26.3043 | + | 15.1868i | 1.17754 | + | 0.679854i | 0.955444 | − | 0.295171i | \(-0.0953766\pi\) |
0.222097 | + | 0.975025i | \(0.428710\pi\) | |||||||
\(500\) | 1.51674 | + | 11.0770i | 0.0678308 | + | 0.495378i | ||||
\(501\) | −2.87004 | + | 1.65702i | −0.128224 | + | 0.0740300i | ||||
\(502\) | 1.96946 | − | 1.13707i | 0.0879015 | − | 0.0507499i | ||||
\(503\) | −10.7612 | − | 18.6389i | −0.479817 | − | 0.831068i | 0.519915 | − | 0.854218i | \(-0.325964\pi\) |
−0.999732 | + | 0.0231501i | \(0.992630\pi\) | |||||||
\(504\) | 2.46274i | 0.109699i | ||||||||
\(505\) | 14.3849 | − | 3.21514i | 0.640120 | − | 0.143072i | ||||
\(506\) | −0.401409 | − | 0.695260i | −0.0178448 | − | 0.0309081i | ||||
\(507\) | − | 3.46398i | − | 0.153841i | ||||||
\(508\) | − | 18.2238i | − | 0.808552i | ||||||
\(509\) | 7.88620 | + | 13.6593i | 0.349550 | + | 0.605438i | 0.986169 | − | 0.165740i | \(-0.0530013\pi\) |
−0.636620 | + | 0.771178i | \(0.719668\pi\) | |||||||
\(510\) | −3.48085 | + | 3.20068i | −0.154134 | + | 0.141729i | ||||
\(511\) | −11.2439 | + | 19.4751i | −0.497402 | + | 0.861526i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.49098 | − | 2.58246i | 0.0658286 | − | 0.114018i | ||||
\(514\) | −10.8758 | + | 18.8374i | −0.479710 | + | 0.830883i | ||||
\(515\) | 1.54103 | − | 0.344431i | 0.0679057 | − | 0.0151774i | ||||
\(516\) | 3.41789 | − | 1.97332i | 0.150464 | − | 0.0868705i | ||||
\(517\) | − | 1.19512i | − | 0.0525613i | ||||||
\(518\) | −14.9801 | + | 0.0725261i | −0.658188 | + | 0.00318661i | ||||
\(519\) | −1.12840 | −0.0495314 | ||||||||
\(520\) | −2.06502 | + | 6.58907i | −0.0905571 | + | 0.288950i | ||||
\(521\) | −10.0002 | + | 17.3208i | −0.438115 | + | 0.758837i | −0.997544 | − | 0.0700410i | \(-0.977687\pi\) |
0.559429 | + | 0.828878i | \(0.311020\pi\) | |||||||
\(522\) | 7.24777 | + | 4.18450i | 0.317226 | + | 0.183151i | ||||
\(523\) | −12.9129 | + | 22.3658i | −0.564643 | + | 0.977990i | 0.432440 | + | 0.901663i | \(0.357653\pi\) |
−0.997083 | + | 0.0763270i | \(0.975681\pi\) | |||||||
\(524\) | 10.5051i | 0.458919i | ||||||||
\(525\) | 10.1111 | + | 7.02797i | 0.441287 | + | 0.306726i | ||||
\(526\) | − | 6.25408i | − | 0.272691i | ||||||
\(527\) | −4.67984 | + | 2.70191i | −0.203857 | + | 0.117697i | ||||
\(528\) | − | 0.452075i | − | 0.0196741i | ||||||
\(529\) | −19.8464 | −0.862885 | ||||||||
\(530\) | 20.3633 | + | 6.38187i | 0.884524 | + | 0.277211i | ||||
\(531\) | −2.78387 | − | 1.60727i | −0.120810 | − | 0.0697495i | ||||
\(532\) | 7.34382 | 0.318395 | ||||||||
\(533\) | 3.65228 | + | 6.32593i | 0.158198 | + | 0.274006i | ||||
\(534\) | −5.21101 | − | 9.02573i | −0.225502 | − | 0.390582i | ||||
\(535\) | 11.3042 | + | 3.54275i | 0.488723 | + | 0.153166i | ||||
\(536\) | 8.26563 | + | 4.77217i | 0.357021 | + | 0.206126i | ||||
\(537\) | 4.89623 | − | 8.48051i | 0.211288 | − | 0.365961i | ||||
\(538\) | −3.53778 | − | 6.12761i | −0.152524 | − | 0.264180i | ||||
\(539\) | 0.211321 | + | 0.366019i | 0.00910225 | + | 0.0157656i | ||||
\(540\) | 2.13373 | + | 0.668714i | 0.0918213 | + | 0.0287769i | ||||
\(541\) | 18.3497i | 0.788917i | 0.918914 | + | 0.394459i | \(0.129068\pi\) | ||||
−0.918914 | + | 0.394459i | \(0.870932\pi\) | |||||||
\(542\) | 2.51174 | − | 4.35046i | 0.107888 | − | 0.186868i | ||||
\(543\) | 11.6070 | − | 6.70130i | 0.498103 | − | 0.287580i | ||||
\(544\) | −2.11474 | −0.0906688 | ||||||||
\(545\) | 10.9624 | − | 10.0801i | 0.469578 | − | 0.431784i | ||||
\(546\) | 3.80253 | + | 6.58618i | 0.162733 | + | 0.281862i | ||||
\(547\) | −19.3385 | −0.826856 | −0.413428 | − | 0.910537i | \(-0.635669\pi\) | ||||
−0.413428 | + | 0.910537i | \(0.635669\pi\) | |||||||
\(548\) | −13.4079 | − | 7.74103i | −0.572755 | − | 0.330681i | ||||
\(549\) | 8.20278i | 0.350086i | ||||||||
\(550\) | −1.85606 | − | 1.29010i | −0.0791427 | − | 0.0550098i | ||||
\(551\) | 12.4780 | − | 21.6126i | 0.531583 | − | 0.920728i | ||||
\(552\) | 1.53793 | + | 0.887924i | 0.0654586 | + | 0.0377926i | ||||
\(553\) | −15.6052 | − | 27.0290i | −0.663599 | − | 1.14939i | ||||
\(554\) | −28.6013 | −1.21515 | ||||||||
\(555\) | −4.00475 | + | 12.9985i | −0.169992 | + | 0.551757i | ||||
\(556\) | 12.9270 | 0.548228 | ||||||||
\(557\) | 2.23202 | + | 3.86597i | 0.0945736 | + | 0.163806i | 0.909431 | − | 0.415856i | \(-0.136518\pi\) |
−0.814857 | + | 0.579662i | \(0.803185\pi\) | |||||||
\(558\) | 2.21296 | + | 1.27765i | 0.0936821 | + | 0.0540874i | ||||
\(559\) | 6.09369 | − | 10.5546i | 0.257736 | − | 0.446411i | ||||
\(560\) | 1.20119 | + | 5.37426i | 0.0507594 | + | 0.227104i | ||||
\(561\) | − | 0.956023i | − | 0.0403633i | ||||||
\(562\) | −11.1812 | − | 6.45549i | −0.471652 | − | 0.272308i | ||||
\(563\) | 36.4158 | 1.53474 | 0.767371 | − | 0.641203i | \(-0.221564\pi\) | ||||
0.767371 | + | 0.641203i | \(0.221564\pi\) | |||||||
\(564\) | 1.32182 | + | 2.28945i | 0.0556585 | + | 0.0964033i | ||||
\(565\) | 19.9376 | + | 21.6828i | 0.838783 | + | 0.912203i | ||||
\(566\) | 20.7473 | 0.872073 | ||||||||
\(567\) | 2.13280 | − | 1.23137i | 0.0895691 | − | 0.0517128i | ||||
\(568\) | −0.00323694 | + | 0.00560655i | −0.000135819 | + | 0.000235246i | ||||
\(569\) | − | 19.5165i | − | 0.818175i | −0.912495 | − | 0.409087i | \(-0.865847\pi\) | ||
0.912495 | − | 0.409087i | \(-0.134153\pi\) | |||||||
\(570\) | 1.99408 | − | 6.36273i | 0.0835230 | − | 0.266505i | ||||
\(571\) | 11.5820 | + | 20.0607i | 0.484693 | + | 0.839512i | 0.999845 | − | 0.0175863i | \(-0.00559817\pi\) |
−0.515153 | + | 0.857098i | \(0.672265\pi\) | |||||||
\(572\) | −0.698014 | − | 1.20900i | −0.0291854 | − | 0.0505507i | ||||
\(573\) | 4.69130 | − | 8.12557i | 0.195982 | − | 0.339451i | ||||
\(574\) | 5.04498 | + | 2.91272i | 0.210574 | + | 0.121575i | ||||
\(575\) | 8.03431 | − | 3.78030i | 0.335054 | − | 0.157650i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −1.50983 | − | 2.61511i | −0.0628552 | − | 0.108868i | 0.832885 | − | 0.553446i | \(-0.186687\pi\) |
−0.895741 | + | 0.444577i | \(0.853354\pi\) | |||||||
\(578\) | 12.5279 | 0.521091 | ||||||||
\(579\) | 10.8268 | + | 6.25084i | 0.449945 | + | 0.259776i | ||||
\(580\) | 17.8572 | + | 5.59647i | 0.741481 | + | 0.232381i | ||||
\(581\) | 18.6536 | 0.773882 | ||||||||
\(582\) | 5.64069i | 0.233814i | ||||||||
\(583\) | −3.73636 | + | 2.15719i | −0.154744 | + | 0.0893416i | ||||
\(584\) | 9.13122i | 0.377853i | ||||||||
\(585\) | 6.73881 | − | 1.50617i | 0.278615 | − | 0.0622726i | ||||
\(586\) | − | 9.38715i | − | 0.387780i | ||||||
\(587\) | 14.4633 | − | 25.0511i | 0.596963 | − | 1.03397i | −0.396303 | − | 0.918120i | \(-0.629707\pi\) |
0.993267 | − | 0.115851i | \(-0.0369596\pi\) | |||||||
\(588\) | −0.809642 | − | 0.467447i | −0.0333891 | − | 0.0192772i | ||||
\(589\) | 3.80992 | − | 6.59898i | 0.156985 | − | 0.271906i | ||||
\(590\) | −6.85896 | − | 2.14961i | −0.282379 | − | 0.0884979i | ||||
\(591\) | −1.96555 | −0.0808518 | ||||||||
\(592\) | −5.25304 | + | 3.06685i | −0.215899 | + | 0.126047i | ||||
\(593\) | − | 45.1760i | − | 1.85516i | −0.373630 | − | 0.927578i | \(-0.621887\pi\) | ||
0.373630 | − | 0.927578i | \(-0.378113\pi\) | |||||||
\(594\) | −0.391509 | + | 0.226038i | −0.0160638 | + | 0.00927444i | ||||
\(595\) | 2.54020 | + | 11.3652i | 0.104138 | + | 0.465927i | ||||
\(596\) | −0.461139 | + | 0.798717i | −0.0188890 | + | 0.0327167i | ||||
\(597\) | −6.35438 | + | 11.0061i | −0.260068 | + | 0.450450i | ||||
\(598\) | 5.48390 | 0.224253 | ||||||||
\(599\) | −3.30328 | + | 5.72145i | −0.134968 | + | 0.233772i | −0.925585 | − | 0.378539i | \(-0.876427\pi\) |
0.790617 | + | 0.612311i | \(0.209760\pi\) | |||||||
\(600\) | 4.98245 | + | 0.418570i | 0.203408 | + | 0.0170881i | ||||
\(601\) | −7.30388 | − | 12.6507i | −0.297932 | − | 0.516033i | 0.677731 | − | 0.735310i | \(-0.262963\pi\) |
−0.975663 | + | 0.219277i | \(0.929630\pi\) | |||||||
\(602\) | − | 9.71955i | − | 0.396139i | ||||||
\(603\) | − | 9.54433i | − | 0.388675i | ||||||
\(604\) | −9.43397 | − | 16.3401i | −0.383863 | − | 0.664870i | ||||
\(605\) | −23.5585 | + | 5.26550i | −0.957789 | + | 0.214073i | ||||
\(606\) | − | 6.59186i | − | 0.267776i | ||||||
\(607\) | −13.5413 | − | 23.4542i | −0.549624 | − | 0.951976i | −0.998300 | − | 0.0582820i | \(-0.981438\pi\) |
0.448676 | − | 0.893694i | \(-0.351896\pi\) | |||||||
\(608\) | 2.58246 | − | 1.49098i | 0.104733 | − | 0.0604674i | ||||
\(609\) | 17.8494 | − | 10.3054i | 0.723294 | − | 0.417594i | ||||
\(610\) | 4.00085 | + | 17.9003i | 0.161990 | + | 0.724762i | ||||
\(611\) | 7.06993 | + | 4.08183i | 0.286019 | + | 0.165133i | ||||
\(612\) | 1.05737 | + | 1.83142i | 0.0427417 | + | 0.0740308i | ||||
\(613\) | −5.04052 | + | 2.91015i | −0.203585 | + | 0.117540i | −0.598326 | − | 0.801252i | \(-0.704167\pi\) |
0.394742 | + | 0.918792i | \(0.370834\pi\) | |||||||
\(614\) | 1.83027 | − | 1.05671i | 0.0738637 | − | 0.0426452i | ||||
\(615\) | 3.89347 | − | 3.58010i | 0.157000 | − | 0.144364i | ||||
\(616\) | −0.964186 | − | 0.556673i | −0.0388481 | − | 0.0224290i | ||||
\(617\) | 25.8535 | − | 14.9265i | 1.04082 | − | 0.600920i | 0.120758 | − | 0.992682i | \(-0.461468\pi\) |
0.920067 | + | 0.391762i | \(0.128134\pi\) | |||||||
\(618\) | − | 0.706172i | − | 0.0284064i | ||||||
\(619\) | 36.9652 | 1.48576 | 0.742878 | − | 0.669427i | \(-0.233460\pi\) | ||||
0.742878 | + | 0.669427i | \(0.233460\pi\) | |||||||
\(620\) | 5.45235 | + | 1.70877i | 0.218972 | + | 0.0686259i | ||||
\(621\) | − | 1.77585i | − | 0.0712623i | ||||||
\(622\) | 19.2848 | + | 11.1341i | 0.773249 | + | 0.446436i | ||||
\(623\) | −25.6668 | −1.02832 | ||||||||
\(624\) | 2.67433 | + | 1.54402i | 0.107059 | + | 0.0618104i | ||||
\(625\) | 15.9370 | − | 19.2617i | 0.637480 | − | 0.770467i | ||||
\(626\) | −8.32368 | + | 14.4170i | −0.332681 | + | 0.576221i | ||||
\(627\) | 0.674037 | + | 1.16747i | 0.0269185 | + | 0.0466241i | ||||
\(628\) | − | 15.0560i | − | 0.600799i | ||||||
\(629\) | −11.1088 | + | 6.48559i | −0.442938 | + | 0.258598i | ||||
\(630\) | 4.05365 | − | 3.72739i | 0.161501 | − | 0.148503i | ||||
\(631\) | 34.1186 | − | 19.6984i | 1.35824 | − | 0.784179i | 0.368852 | − | 0.929488i | \(-0.379751\pi\) |
0.989386 | + | 0.145309i | \(0.0464175\pi\) | |||||||
\(632\) | −10.9751 | − | 6.33650i | −0.436568 | − | 0.252052i | ||||
\(633\) | 9.77021 | + | 5.64084i | 0.388331 | + | 0.224203i | ||||
\(634\) | 2.95498 | + | 1.70606i | 0.117357 | + | 0.0677563i | ||||
\(635\) | −29.9963 | + | 27.5820i | −1.19037 | + | 1.09456i | ||||
\(636\) | 4.77175 | − | 8.26490i | 0.189212 | − | 0.327725i | ||||
\(637\) | −2.88699 | −0.114387 | ||||||||
\(638\) | −3.27654 | + | 1.89171i | −0.129719 | + | 0.0748935i | ||||
\(639\) | 0.00647388 | 0.000256103 | ||||||||
\(640\) | 1.51351 | + | 1.64599i | 0.0598268 | + | 0.0650635i | ||||
\(641\) | 14.7278 | + | 25.5093i | 0.581714 | + | 1.00756i | 0.995276 | + | 0.0970827i | \(0.0309511\pi\) |
−0.413562 | + | 0.910476i | \(0.635716\pi\) | |||||||
\(642\) | 2.64892 | − | 4.58807i | 0.104545 | − | 0.181077i | ||||
\(643\) | 22.3938 | 0.883124 | 0.441562 | − | 0.897231i | \(-0.354425\pi\) | ||||
0.441562 | + | 0.897231i | \(0.354425\pi\) | |||||||
\(644\) | 3.78753 | − | 2.18673i | 0.149249 | − | 0.0861692i | ||||
\(645\) | −8.42107 | − | 2.63917i | −0.331579 | − | 0.103917i | ||||
\(646\) | 5.46124 | − | 3.15305i | 0.214869 | − | 0.124055i | ||||
\(647\) | −10.8449 | + | 18.7839i | −0.426356 | + | 0.738471i | −0.996546 | − | 0.0830421i | \(-0.973536\pi\) |
0.570190 | + | 0.821513i | \(0.306870\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 1.25852 | − | 0.726606i | 0.0494012 | − | 0.0285218i | ||||
\(650\) | 13.9710 | − | 6.57362i | 0.547987 | − | 0.257839i | ||||
\(651\) | 5.44996 | − | 3.14653i | 0.213601 | − | 0.123322i | ||||
\(652\) | 17.3734 | 0.680395 | ||||||||
\(653\) | 0.510467 | − | 0.884155i | 0.0199761 | − | 0.0345996i | −0.855865 | − | 0.517200i | \(-0.826974\pi\) |
0.875841 | + | 0.482600i | \(0.160308\pi\) | |||||||
\(654\) | −3.33004 | − | 5.76779i | −0.130215 | − | 0.225539i | ||||
\(655\) | 17.2914 | − | 15.8996i | 0.675629 | − | 0.621250i | ||||
\(656\) | 2.36543 | 0.0923545 | ||||||||
\(657\) | 7.90787 | − | 4.56561i | 0.308515 | − | 0.178121i | ||||
\(658\) | 6.51059 | 0.253809 | ||||||||
\(659\) | −18.9266 | + | 32.7818i | −0.737274 | + | 1.27700i | 0.216444 | + | 0.976295i | \(0.430554\pi\) |
−0.953718 | + | 0.300701i | \(0.902779\pi\) | |||||||
\(660\) | −0.744112 | + | 0.684221i | −0.0289645 | + | 0.0266333i | ||||
\(661\) | −23.1502 | − | 13.3658i | −0.900437 | − | 0.519868i | −0.0230953 | − | 0.999733i | \(-0.507352\pi\) |
−0.877342 | + | 0.479866i | \(0.840685\pi\) | |||||||
\(662\) | 23.5466 | + | 13.5946i | 0.915164 | + | 0.528370i | ||||
\(663\) | 5.65551 | + | 3.26521i | 0.219642 | + | 0.126810i | ||||
\(664\) | 6.55955 | − | 3.78716i | 0.254560 | − | 0.146970i | ||||
\(665\) | −11.1150 | − | 12.0879i | −0.431019 | − | 0.468747i | ||||
\(666\) | 5.28249 | + | 3.01584i | 0.204692 | + | 0.116861i | ||||
\(667\) | − | 14.8621i | − | 0.575462i | ||||||
\(668\) | 1.65702 | + | 2.87004i | 0.0641119 | + | 0.111045i | ||||
\(669\) | −6.99092 | + | 12.1086i | −0.270284 | + | 0.468146i | ||||
\(670\) | −4.65519 | − | 20.8279i | −0.179846 | − | 0.804651i | ||||
\(671\) | −3.21146 | − | 1.85414i | −0.123977 | − | 0.0715781i | ||||
\(672\) | 2.46274 | 0.0950024 | ||||||||
\(673\) | −5.95454 | − | 3.43786i | −0.229531 | − | 0.132520i | 0.380825 | − | 0.924647i | \(-0.375640\pi\) |
−0.610356 | + | 0.792128i | \(0.708973\pi\) | |||||||
\(674\) | 11.5777i | 0.445958i | ||||||||
\(675\) | −2.12873 | − | 4.52421i | −0.0819349 | − | 0.174137i | ||||
\(676\) | −3.46398 | −0.133230 | ||||||||
\(677\) | 32.9788i | 1.26748i | 0.773547 | + | 0.633739i | \(0.218481\pi\) | ||||
−0.773547 | + | 0.633739i | \(0.781519\pi\) | |||||||
\(678\) | 11.4082 | − | 6.58655i | 0.438131 | − | 0.252955i | ||||
\(679\) | 12.0305 | + | 6.94578i | 0.461686 | + | 0.266555i | ||||
\(680\) | 3.20068 | + | 3.48085i | 0.122741 | + | 0.133484i | ||||
\(681\) | 17.4048 | − | 10.0487i | 0.666953 | − | 0.385065i | ||||
\(682\) | −1.00043 | + | 0.577596i | −0.0383083 | + | 0.0221173i | ||||
\(683\) | 19.1756 | + | 33.2131i | 0.733733 | + | 1.27086i | 0.955277 | + | 0.295713i | \(0.0955571\pi\) |
−0.221544 | + | 0.975150i | \(0.571110\pi\) | |||||||
\(684\) | −2.58246 | − | 1.49098i | −0.0987428 | − | 0.0570092i | ||||
\(685\) | 7.55128 | + | 33.7853i | 0.288519 | + | 1.29087i | ||||
\(686\) | −16.9235 | + | 9.77080i | −0.646143 | + | 0.373051i | ||||
\(687\) | −4.87296 | + | 2.81341i | −0.185915 | + | 0.107338i | ||||
\(688\) | −1.97332 | − | 3.41789i | −0.0752320 | − | 0.130306i | ||||
\(689\) | − | 29.4707i | − | 1.12275i | ||||||
\(690\) | −0.866158 | − | 3.87530i | −0.0329741 | − | 0.147530i | ||||
\(691\) | 2.58576 | + | 4.47867i | 0.0983669 | + | 0.170376i | 0.911009 | − | 0.412387i | \(-0.135305\pi\) |
−0.812642 | + | 0.582763i | \(0.801971\pi\) | |||||||
\(692\) | 1.12840i | 0.0428955i | ||||||||
\(693\) | 1.11335i | 0.0422925i | ||||||||
\(694\) | 9.35142 | + | 16.1971i | 0.354975 | + | 0.614835i | ||||
\(695\) | −19.5652 | − | 21.2778i | −0.742151 | − | 0.807112i | ||||
\(696\) | 4.18450 | − | 7.24777i | 0.158613 | − | 0.274726i | ||||
\(697\) | 5.00227 | 0.189475 | ||||||||
\(698\) | −9.61263 | + | 16.6496i | −0.363844 | + | 0.630195i | ||||
\(699\) | 8.13416 | − | 14.0888i | 0.307662 | − | 0.532887i | ||||
\(700\) | 7.02797 | − | 10.1111i | 0.265632 | − | 0.382165i | ||||
\(701\) | −9.82218 | + | 5.67084i | −0.370979 | + | 0.214185i | −0.673886 | − | 0.738835i | \(-0.735376\pi\) |
0.302907 | + | 0.953020i | \(0.402043\pi\) | |||||||
\(702\) | − | 3.08804i | − | 0.116551i | ||||||
\(703\) | 8.99314 | − | 15.7522i | 0.339183 | − | 0.594106i | ||||
\(704\) | −0.452075 | −0.0170382 | ||||||||
\(705\) | 1.76783 | − | 5.64081i | 0.0665805 | − | 0.212445i | ||||
\(706\) | −5.24212 | + | 9.07961i | −0.197290 | + | 0.341716i | ||||
\(707\) | −14.0591 | − | 8.11703i | −0.528747 | − | 0.305272i | ||||
\(708\) | −1.60727 | + | 2.78387i | −0.0604048 | + | 0.104624i | ||||
\(709\) | − | 19.5292i | − | 0.733434i | −0.930332 | − | 0.366717i | \(-0.880482\pi\) | ||
0.930332 | − | 0.366717i | \(-0.119518\pi\) | |||||||
\(710\) | 0.0141275 | − | 0.00315760i | 0.000530195 | − | 0.000118502i | ||||
\(711\) | 12.6730i | 0.475275i | ||||||||
\(712\) | −9.02573 | + | 5.21101i | −0.338254 | + | 0.195291i | ||||
\(713\) | − | 4.53784i | − | 0.169943i | ||||||
\(714\) | 5.20807 | 0.194907 | ||||||||
\(715\) | −0.933544 | + | 2.97875i | −0.0349126 | + | 0.111399i | ||||
\(716\) | −8.48051 | − | 4.89623i | −0.316932 | − | 0.182981i | ||||
\(717\) | −5.22684 | −0.195200 | ||||||||
\(718\) | −3.46197 | − | 5.99630i | −0.129199 | − | 0.223780i | ||||
\(719\) | −0.612617 | − | 1.06108i | −0.0228468 | − | 0.0395718i | 0.854376 | − | 0.519655i | \(-0.173940\pi\) |
−0.877223 | + | 0.480084i | \(0.840606\pi\) | |||||||
\(720\) | 0.668714 | − | 2.13373i | 0.0249215 | − | 0.0795196i | ||||
\(721\) | −1.50612 | − | 0.869560i | −0.0560909 | − | 0.0323841i | ||||
\(722\) | 5.05393 | − | 8.75367i | 0.188088 | − | 0.325778i | ||||
\(723\) | 12.6427 | + | 21.8978i | 0.470187 | + | 0.814387i | ||||
\(724\) | −6.70130 | − | 11.6070i | −0.249052 | − | 0.431370i | ||||
\(725\) | −17.8154 | − | 37.8631i | −0.661646 | − | 1.40620i | ||||
\(726\) | 10.7956i | 0.400663i | ||||||||
\(727\) | −3.71182 | + | 6.42905i | −0.137664 | + | 0.238440i | −0.926612 | − | 0.376019i | \(-0.877293\pi\) |
0.788948 | + | 0.614460i | \(0.210626\pi\) | |||||||
\(728\) | 6.58618 | − | 3.80253i | 0.244100 | − | 0.140931i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 15.0299 | − | 13.8202i | 0.556282 | − | 0.511509i | ||||
\(731\) | −4.17306 | − | 7.22795i | −0.154346 | − | 0.267335i | ||||
\(732\) | 8.20278 | 0.303183 | ||||||||
\(733\) | 12.8570 | + | 7.42300i | 0.474885 | + | 0.274175i | 0.718282 | − | 0.695752i | \(-0.244929\pi\) |
−0.243398 | + | 0.969927i | \(0.578262\pi\) | |||||||
\(734\) | 10.6063i | 0.391486i | ||||||||
\(735\) | 0.455989 | + | 2.04015i | 0.0168194 | + | 0.0752520i | ||||
\(736\) | 0.887924 | − | 1.53793i | 0.0327293 | − | 0.0566888i | ||||
\(737\) | 3.73669 | + | 2.15738i | 0.137643 | + | 0.0794681i | ||||
\(738\) | −1.18271 | − | 2.04852i | −0.0435363 | − | 0.0754071i | ||||
\(739\) | −10.3995 | −0.382552 | −0.191276 | − | 0.981536i | \(-0.561263\pi\) | ||||
−0.191276 | + | 0.981536i | \(0.561263\pi\) | |||||||
\(740\) | 12.9985 | + | 4.00475i | 0.477836 | + | 0.147217i | ||||
\(741\) | −9.20845 | −0.338281 | ||||||||
\(742\) | −11.7516 | − | 20.3543i | −0.431414 | − | 0.747231i | ||||
\(743\) | −44.2189 | − | 25.5298i | −1.62223 | − | 0.936597i | −0.986321 | − | 0.164836i | \(-0.947290\pi\) |
−0.635913 | − | 0.771761i | \(-0.719376\pi\) | |||||||
\(744\) | 1.27765 | − | 2.21296i | 0.0468411 | − | 0.0811311i | ||||
\(745\) | 2.01262 | − | 0.449835i | 0.0737367 | − | 0.0164807i | ||||
\(746\) | 16.2224i | 0.593944i | ||||||||
\(747\) | −6.55955 | − | 3.78716i | −0.240002 | − | 0.138565i | ||||
\(748\) | −0.956023 | −0.0349556 | ||||||||
\(749\) | −6.52362 | − | 11.2992i | −0.238368 | − | 0.412865i | ||||
\(750\) | −6.85203 | − | 8.83457i | −0.250201 | − | 0.322593i | ||||
\(751\) | −51.8267 | −1.89118 | −0.945591 | − | 0.325357i | \(-0.894516\pi\) | ||||
−0.945591 | + | 0.325357i | \(0.894516\pi\) | |||||||
\(752\) | 2.28945 | − | 1.32182i | 0.0834877 | − | 0.0482017i | ||||
\(753\) | −1.13707 | + | 1.96946i | −0.0414371 | + | 0.0717712i | ||||
\(754\) | − | 25.8439i | − | 0.941178i | ||||||
\(755\) | −12.6173 | + | 40.2592i | −0.459189 | + | 1.46518i | ||||
\(756\) | −1.23137 | − | 2.13280i | −0.0447846 | − | 0.0775691i | ||||
\(757\) | −15.0203 | − | 26.0160i | −0.545924 | − | 0.945567i | −0.998548 | − | 0.0538661i | \(-0.982846\pi\) |
0.452625 | − | 0.891701i | \(-0.350488\pi\) | |||||||
\(758\) | −1.83877 | + | 3.18484i | −0.0667870 | + | 0.115679i | ||||
\(759\) | 0.695260 | + | 0.401409i | 0.0252363 | + | 0.0145702i | ||||
\(760\) | −6.36273 | − | 1.99408i | −0.230800 | − | 0.0723331i | ||||
\(761\) | −4.46887 | − | 7.74032i | −0.161997 | − | 0.280586i | 0.773588 | − | 0.633689i | \(-0.218460\pi\) |
−0.935585 | + | 0.353103i | \(0.885127\pi\) | |||||||
\(762\) | 9.11192 | + | 15.7823i | 0.330090 | + | 0.571733i | ||||
\(763\) | −16.4021 | −0.593794 | ||||||||
\(764\) | −8.12557 | − | 4.69130i | −0.293973 | − | 0.169725i | ||||
\(765\) | 1.41416 | − | 4.51230i | 0.0511290 | − | 0.163142i | ||||
\(766\) | 5.48739 | 0.198267 | ||||||||
\(767\) | 9.92663i | 0.358430i | ||||||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | − | 24.4645i | − | 0.882214i | −0.897455 | − | 0.441107i | \(-0.854586\pi\) | ||
0.897455 | − | 0.441107i | \(-0.145414\pi\) | |||||||
\(770\) | 0.543027 | + | 2.42957i | 0.0195693 | + | 0.0875557i | ||||
\(771\) | − | 21.7516i | − | 0.783364i | ||||||
\(772\) | 6.25084 | − | 10.8268i | 0.224973 | − | 0.389664i | ||||
\(773\) | 30.1761 | + | 17.4222i | 1.08536 | + | 0.626633i | 0.932337 | − | 0.361590i | \(-0.117766\pi\) |
0.153023 | + | 0.988223i | \(0.451099\pi\) | |||||||
\(774\) | −1.97332 | + | 3.41789i | −0.0709294 | + | 0.122853i | ||||
\(775\) | −5.43957 | − | 11.5608i | −0.195395 | − | 0.415275i | ||||
\(776\) | 5.64069 | 0.202489 | ||||||||
\(777\) | 12.9369 | − | 7.55286i | 0.464108 | − | 0.270957i | ||||
\(778\) | 28.8548i | 1.03449i | ||||||||
\(779\) | −6.10863 | + | 3.52682i | −0.218864 | + | 0.126361i | ||||
\(780\) | −1.50617 | − | 6.73881i | −0.0539297 | − | 0.241288i | ||||
\(781\) | −0.00146334 | + | 0.00253458i | −5.23625e−5 | + | 9.06945e-5i | ||||
\(782\) | 1.87773 | − | 3.25232i | 0.0671475 | − | 0.116303i | ||||
\(783\) | −8.36900 | −0.299084 | ||||||||
\(784\) | −0.467447 | + | 0.809642i | −0.0166945 | + | 0.0289158i | ||||
\(785\) | −24.7820 | + | 22.7874i | −0.884507 | + | 0.813316i | ||||
\(786\) | −5.25257 | − | 9.09771i | −0.187353 | − | 0.324505i | ||||
\(787\) | − | 35.5191i | − | 1.26612i | −0.774103 | − | 0.633059i | \(-0.781799\pi\) | ||
0.774103 | − | 0.633059i | \(-0.218201\pi\) | |||||||
\(788\) | 1.96555i | 0.0700197i | ||||||||
\(789\) | 3.12704 | + | 5.41619i | 0.111326 | + | 0.192822i | ||||
\(790\) | 6.18117 | + | 27.6553i | 0.219916 | + | 0.983933i | ||||
\(791\) | − | 32.4420i | − | 1.15350i | ||||||
\(792\) | 0.226038 | + | 0.391509i | 0.00803190 | + | 0.0139117i | ||||
\(793\) | 21.9369 | − | 12.6653i | 0.779002 | − | 0.449757i | ||||
\(794\) | −12.0783 | + | 6.97341i | −0.428643 | + | 0.247477i | ||||
\(795\) | −20.8260 | + | 4.65478i | −0.738624 | + | 0.165088i | ||||
\(796\) | 11.0061 | + | 6.35438i | 0.390101 | + | 0.225225i | ||||
\(797\) | 9.39958 | + | 16.2806i | 0.332950 | + | 0.576687i | 0.983089 | − | 0.183129i | \(-0.0586225\pi\) |
−0.650139 | + | 0.759816i | \(0.725289\pi\) | |||||||
\(798\) | −6.35994 | + | 3.67191i | −0.225139 | + | 0.129984i | ||||
\(799\) | 4.84160 | − | 2.79530i | 0.171283 | − | 0.0988906i | ||||
\(800\) | 0.418570 | − | 4.98245i | 0.0147987 | − | 0.176156i | ||||
\(801\) | 9.02573 | + | 5.21101i | 0.318909 | + | 0.184122i | ||||
\(802\) | 17.3636 | − | 10.0249i | 0.613132 | − | 0.353992i | ||||
\(803\) | 4.12800i | 0.145674i | ||||||||
\(804\) | −9.54433 | −0.336603 | ||||||||
\(805\) | −9.33180 | − | 2.92459i | −0.328903 | − | 0.103078i | ||||
\(806\) | − | 7.89091i | − | 0.277945i | ||||||
\(807\) | 6.12761 | + | 3.53778i | 0.215702 | + | 0.124536i | ||||
\(808\) | −6.59186 | −0.231901 | ||||||||
\(809\) | −17.4303 | − | 10.0634i | −0.612815 | − | 0.353809i | 0.161251 | − | 0.986913i | \(-0.448447\pi\) |
−0.774066 | + | 0.633104i | \(0.781780\pi\) | |||||||
\(810\) | −2.18223 | + | 0.487744i | −0.0766756 | + | 0.0171376i | ||||
\(811\) | −5.19642 | + | 9.00046i | −0.182471 | + | 0.316049i | −0.942721 | − | 0.333581i | \(-0.891743\pi\) |
0.760251 | + | 0.649630i | \(0.225076\pi\) | |||||||
\(812\) | −10.3054 | − | 17.8494i | −0.361647 | − | 0.626391i | ||||
\(813\) | 5.02348i | 0.176181i | ||||||||
\(814\) | −2.37477 | + | 1.38645i | −0.0832356 | + | 0.0485949i | ||||
\(815\) | −26.2948 | − | 28.5965i | −0.921068 | − | 1.00169i | ||||
\(816\) | 1.83142 | − | 1.05737i | 0.0641125 | − | 0.0370154i | ||||
\(817\) | 10.1920 | + | 5.88437i | 0.356574 | + | 0.205868i | ||||
\(818\) | 16.0291 | + | 9.25441i | 0.560445 | + | 0.323573i | ||||
\(819\) | −6.58618 | − | 3.80253i | −0.230140 | − | 0.132871i | ||||
\(820\) | −3.58010 | − | 3.89347i | −0.125023 | − | 0.135966i | ||||
\(821\) | −22.3405 | + | 38.6948i | −0.779688 | + | 1.35046i | 0.152433 | + | 0.988314i | \(0.451289\pi\) |
−0.932122 | + | 0.362146i | \(0.882044\pi\) | |||||||
\(822\) | 15.4821 | 0.539999 | ||||||||
\(823\) | 26.1020 | − | 15.0700i | 0.909858 | − | 0.525307i | 0.0294727 | − | 0.999566i | \(-0.490617\pi\) |
0.880386 | + | 0.474259i | \(0.157284\pi\) | |||||||
\(824\) | −0.706172 | −0.0246007 | ||||||||
\(825\) | 2.25244 | + | 0.189225i | 0.0784200 | + | 0.00658798i | ||||
\(826\) | 3.95829 | + | 6.85596i | 0.137726 | + | 0.238549i | ||||
\(827\) | 13.9643 | − | 24.1869i | 0.485586 | − | 0.841060i | −0.514276 | − | 0.857625i | \(-0.671939\pi\) |
0.999863 | + | 0.0165641i | \(0.00527277\pi\) | |||||||
\(828\) | −1.77585 | −0.0617150 | ||||||||
\(829\) | 32.1434 | − | 18.5580i | 1.11639 | − | 0.644546i | 0.175910 | − | 0.984406i | \(-0.443713\pi\) |
0.940476 | + | 0.339861i | \(0.110380\pi\) | |||||||
\(830\) | −16.1616 | − | 5.06506i | −0.560977 | − | 0.175811i | ||||
\(831\) | 24.7694 | − | 14.3006i | 0.859242 | − | 0.496084i | ||||
\(832\) | 1.54402 | − | 2.67433i | 0.0535293 | − | 0.0927155i | ||||
\(833\) | −0.988530 | + | 1.71218i | −0.0342505 | + | 0.0593237i | ||||
\(834\) | −11.1951 | + | 6.46352i | −0.387656 | + | 0.223813i | ||||
\(835\) | 2.21614 | − | 7.07126i | 0.0766927 | − | 0.244711i | ||||
\(836\) | 1.16747 | − | 0.674037i | 0.0403777 | − | 0.0233121i | ||||
\(837\) | −2.55531 | −0.0883244 | ||||||||
\(838\) | −14.5978 | + | 25.2842i | −0.504273 | + | 0.873427i | ||||
\(839\) | 4.22147 | + | 7.31179i | 0.145741 | + | 0.252431i | 0.929649 | − | 0.368446i | \(-0.120110\pi\) |
−0.783908 | + | 0.620877i | \(0.786777\pi\) | |||||||
\(840\) | −3.72739 | − | 4.05365i | −0.128607 | − | 0.139864i | ||||
\(841\) | −41.0402 | −1.41518 | ||||||||
\(842\) | 22.8742 | − | 13.2064i | 0.788297 | − | 0.455124i | ||||
\(843\) | 12.9110 | 0.444678 | ||||||||
\(844\) | 5.64084 | − | 9.77021i | 0.194166 | − | 0.336305i | ||||
\(845\) | 5.24277 | + | 5.70168i | 0.180357 | + | 0.196144i | ||||
\(846\) | −2.28945 | − | 1.32182i | −0.0787130 | − | 0.0454450i | ||||
\(847\) | 23.0249 | + | 13.2934i | 0.791145 | + | 0.456768i | ||||
\(848\) | −8.26490 | − | 4.77175i | −0.283818 | − | 0.163862i | ||||
\(849\) | −17.9677 | + | 10.3736i | −0.616648 | + | 0.356022i | ||||
\(850\) | 0.885168 | − | 10.5366i | 0.0303610 | − | 0.361402i | ||||
\(851\) | −0.0522975 | − | 10.8019i | −0.00179274 | − | 0.370286i | ||||
\(852\) | − | 0.00647388i | − | 0.000221792i | ||||||
\(853\) | 6.10114 | + | 10.5675i | 0.208899 | + | 0.361824i | 0.951368 | − | 0.308057i | \(-0.0996787\pi\) |
−0.742469 | + | 0.669880i | \(0.766345\pi\) | |||||||
\(854\) | 10.1007 | − | 17.4949i | 0.345638 | − | 0.598662i | ||||
\(855\) | 1.45444 | + | 6.50733i | 0.0497406 | + | 0.222546i | ||||
\(856\) | −4.58807 | − | 2.64892i | −0.156817 | − | 0.0905383i | ||||
\(857\) | 28.1230 | 0.960663 | 0.480331 | − | 0.877087i | \(-0.340516\pi\) | ||||
0.480331 | + | 0.877087i | \(0.340516\pi\) | |||||||
\(858\) | 1.20900 | + | 0.698014i | 0.0412745 | + | 0.0238298i | ||||
\(859\) | 3.92512i | 0.133923i | 0.997756 | + | 0.0669616i | \(0.0213305\pi\) | ||||
−0.997756 | + | 0.0669616i | \(0.978669\pi\) | |||||||
\(860\) | −2.63917 | + | 8.42107i | −0.0899950 | + | 0.287156i | ||||
\(861\) | −5.82545 | −0.198531 | ||||||||
\(862\) | 20.3661i | 0.693672i | ||||||||
\(863\) | −49.8149 | + | 28.7607i | −1.69572 | + | 0.979025i | −0.745989 | + | 0.665958i | \(0.768023\pi\) |
−0.949731 | + | 0.313067i | \(0.898644\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 1.85734 | − | 1.70785i | 0.0631515 | − | 0.0580687i | ||||
\(866\) | −28.6748 | + | 16.5554i | −0.974410 | + | 0.562576i | ||||
\(867\) | −10.8495 | + | 6.26393i | −0.368467 | + | 0.212734i | ||||
\(868\) | −3.14653 | − | 5.44996i | −0.106800 | − | 0.184984i | ||||
\(869\) | −4.96159 | − | 2.86457i | −0.168310 | − | 0.0971740i | ||||
\(870\) | −18.2630 | + | 4.08193i | −0.619175 | + | 0.138390i | ||||
\(871\) | −25.5246 | + | 14.7367i | −0.864870 | + | 0.499333i | ||||
\(872\) | −5.76779 | + | 3.33004i | −0.195322 | + | 0.112769i | ||||
\(873\) | −2.82034 | − | 4.88498i | −0.0954542 | − | 0.165332i | ||||
\(874\) | 5.29552i | 0.179124i | ||||||||
\(875\) | −27.2798 | + | 3.73535i | −0.922224 | + | 0.126278i | ||||
\(876\) | −4.56561 | − | 7.90787i | −0.154258 | − | 0.267182i | ||||
\(877\) | − | 15.1386i | − | 0.511194i | −0.966783 | − | 0.255597i | \(-0.917728\pi\) | ||
0.966783 | − | 0.255597i | \(-0.0822720\pi\) | |||||||
\(878\) | 11.3685i | 0.383669i | ||||||||
\(879\) | 4.69358 | + | 8.12951i | 0.158310 | + | 0.274202i | ||||
\(880\) | 0.684221 | + | 0.744112i | 0.0230651 | + | 0.0250840i | ||||
\(881\) | −4.71995 | + | 8.17519i | −0.159019 | + | 0.275429i | −0.934515 | − | 0.355923i | \(-0.884166\pi\) |
0.775496 | + | 0.631352i | \(0.217500\pi\) | |||||||
\(882\) | 0.934894 | 0.0314795 | ||||||||
\(883\) | 14.3072 | − | 24.7808i | 0.481476 | − | 0.833940i | −0.518298 | − | 0.855200i | \(-0.673434\pi\) |
0.999774 | + | 0.0212597i | \(0.00676768\pi\) | |||||||
\(884\) | 3.26521 | − | 5.65551i | 0.109821 | − | 0.190215i | ||||
\(885\) | 7.01484 | − | 1.56787i | 0.235801 | − | 0.0527033i | ||||
\(886\) | 3.18011 | − | 1.83604i | 0.106838 | − | 0.0616829i | ||||
\(887\) | − | 17.5826i | − | 0.590365i | −0.955441 | − | 0.295182i | \(-0.904620\pi\) | ||
0.955441 | − | 0.295182i | \(-0.0953804\pi\) | |||||||
\(888\) | 3.01584 | − | 5.28249i | 0.101205 | − | 0.177269i | ||||
\(889\) | 44.8806 | 1.50525 | ||||||||
\(890\) | 22.2378 | + | 6.96935i | 0.745413 | + | 0.233613i | ||||
\(891\) | 0.226038 | − | 0.391509i | 0.00757255 | − | 0.0131160i | ||||
\(892\) | 12.1086 | + | 6.99092i | 0.405427 | + | 0.234073i | ||||
\(893\) | −3.94161 | + | 6.82707i | −0.131901 | + | 0.228459i | ||||
\(894\) | − | 0.922279i | − | 0.0308456i | ||||||
\(895\) | 4.77621 | + | 21.3693i | 0.159651 | + | 0.714298i | ||||
\(896\) | − | 2.46274i | − | 0.0822745i | ||||||
\(897\) | −4.74919 | + | 2.74195i | −0.158571 | + | 0.0915510i | ||||
\(898\) | 15.4644i | 0.516054i | ||||||||
\(899\) | −21.3854 | −0.713242 | ||||||||
\(900\) | −4.52421 | + | 2.12873i | −0.150807 | + | 0.0709577i | ||||
\(901\) | −17.4781 | − | 10.0910i | −0.582281 | − | 0.336180i | ||||
\(902\) | 1.06935 | 0.0356055 | ||||||||
\(903\) | 4.85977 | + | 8.41738i | 0.161723 | + | 0.280113i | ||||
\(904\) | −6.58655 | − | 11.4082i | −0.219066 | − | 0.379433i | ||||
\(905\) | −8.96250 | + | 28.5976i | −0.297924 | + | 0.950615i | ||||
\(906\) | 16.3401 | + | 9.43397i | 0.542864 | + | 0.313423i | ||||
\(907\) | −9.16742 | + | 15.8784i | −0.304399 | + | 0.527235i | −0.977127 | − | 0.212655i | \(-0.931789\pi\) |
0.672728 | + | 0.739890i | \(0.265122\pi\) | |||||||
\(908\) | −10.0487 | − | 17.4048i | −0.333476 | − | 0.577598i | ||||
\(909\) | 3.29593 | + | 5.70872i | 0.109319 | + | 0.189346i | ||||
\(910\) | −16.2272 | − | 5.08561i | −0.537926 | − | 0.168586i | ||||
\(911\) | − | 31.0919i | − | 1.03012i | −0.857154 | − | 0.515060i | \(-0.827770\pi\) | ||
0.857154 | − | 0.515060i | \(-0.172230\pi\) | |||||||
\(912\) | −1.49098 | + | 2.58246i | −0.0493714 | + | 0.0855138i | ||||
\(913\) | 2.96541 | − | 1.71208i | 0.0981408 | − | 0.0566616i | ||||
\(914\) | −3.26801 | −0.108096 | ||||||||
\(915\) | −12.4150 | − | 13.5017i | −0.410427 | − | 0.446352i | ||||
\(916\) | 2.81341 | + | 4.87296i | 0.0929576 | + | 0.161007i | ||||
\(917\) | −25.8714 | −0.854351 | ||||||||
\(918\) | −1.83142 | − | 1.05737i | −0.0604459 | − | 0.0348984i | ||||
\(919\) | 4.65598i | 0.153587i | 0.997047 | + | 0.0767934i | \(0.0244682\pi\) | ||||
−0.997047 | + | 0.0767934i | \(0.975532\pi\) | |||||||
\(920\) | −3.87530 | + | 0.866158i | −0.127765 | + | 0.0285564i | ||||
\(921\) | −1.05671 | + | 1.83027i | −0.0348197 | + | 0.0603095i | ||||
\(922\) | 27.4011 | + | 15.8201i | 0.902408 | + | 0.521006i | ||||
\(923\) | −0.00999582 | − | 0.0173133i | −0.000329016 | − | 0.000569873i | ||||
\(924\) | 1.11335 | 0.0366264 | ||||||||
\(925\) | −13.0817 | − | 27.4567i | −0.430122 | − | 0.902771i | ||||
\(926\) | 5.44733 | 0.179010 | ||||||||
\(927\) | 0.353086 | + | 0.611563i | 0.0115969 | + | 0.0200864i | ||||
\(928\) | −7.24777 | − | 4.18450i | −0.237920 | − | 0.137363i | ||||
\(929\) | 12.7005 | − | 21.9980i | 0.416691 | − | 0.721731i | −0.578913 | − | 0.815389i | \(-0.696523\pi\) |
0.995604 | + | 0.0936586i | \(0.0298562\pi\) | |||||||
\(930\) | −5.57626 | + | 1.24634i | −0.182853 | + | 0.0408689i | ||||
\(931\) | − | 2.78782i | − | 0.0913673i | ||||||
\(932\) | −14.0888 | − | 8.13416i | −0.461493 | − | 0.266443i | ||||
\(933\) | −22.2681 | −0.729026 | ||||||||
\(934\) | −16.2652 | − | 28.1721i | −0.532212 | − | 0.921819i | ||||
\(935\) | 1.44695 | + | 1.57360i | 0.0473203 | + | 0.0514624i | ||||
\(936\) | −3.08804 | −0.100936 | ||||||||
\(937\) | 17.8365 | − | 10.2979i | 0.582692 | − | 0.336417i | −0.179511 | − | 0.983756i | \(-0.557451\pi\) |
0.762202 | + | 0.647339i | \(0.224118\pi\) | |||||||
\(938\) | −11.7526 | + | 20.3561i | −0.383737 | + | 0.664651i | ||||
\(939\) | − | 16.6474i | − | 0.543266i | ||||||
\(940\) | −5.64081 | − | 1.76783i | −0.183983 | − | 0.0576604i | ||||
\(941\) | 2.99808 | + | 5.19283i | 0.0977348 | + | 0.169282i | 0.910747 | − | 0.412965i | \(-0.135507\pi\) |
−0.813012 | + | 0.582247i | \(0.802174\pi\) | |||||||
\(942\) | 7.52798 | + | 13.0389i | 0.245275 | + | 0.424829i | ||||
\(943\) | −2.10032 | + | 3.63786i | −0.0683959 | + | 0.118465i | ||||
\(944\) | 2.78387 | + | 1.60727i | 0.0906072 | + | 0.0523121i | ||||
\(945\) | −1.64687 | + | 5.25484i | −0.0535727 | + | 0.170940i | ||||
\(946\) | −0.892088 | − | 1.54514i | −0.0290043 | − | 0.0502369i | ||||
\(947\) | −0.385031 | − | 0.666893i | −0.0125118 | − | 0.0216711i | 0.859702 | − | 0.510796i | \(-0.170649\pi\) |
−0.872214 | + | 0.489125i | \(0.837316\pi\) | |||||||
\(948\) | 12.6730 | 0.411600 | ||||||||
\(949\) | −24.4199 | − | 14.0988i | −0.792702 | − | 0.457667i | ||||
\(950\) | 6.34781 | + | 13.4911i | 0.205950 | + | 0.437708i | ||||
\(951\) | −3.41212 | −0.110646 | ||||||||
\(952\) | − | 5.20807i | − | 0.168794i | ||||||
\(953\) | 41.0658 | − | 23.7093i | 1.33025 | − | 0.768021i | 0.344913 | − | 0.938635i | \(-0.387908\pi\) |
0.985338 | + | 0.170614i | \(0.0545752\pi\) | |||||||
\(954\) | 9.54349i | 0.308982i | ||||||||
\(955\) | 4.57630 | + | 20.4750i | 0.148086 | + | 0.662554i | ||||
\(956\) | 5.22684i | 0.169048i | ||||||||
\(957\) | 1.89171 | − | 3.27654i | 0.0611503 | − | 0.105915i | ||||
\(958\) | −2.08893 | − | 1.20604i | −0.0674902 | − | 0.0389655i | ||||
\(959\) | 19.0642 | − | 33.0201i | 0.615614 | − | 1.06628i | ||||
\(960\) | −2.13373 | − | 0.668714i | −0.0688660 | − | 0.0215827i | ||||
\(961\) | 24.4704 | 0.789368 | ||||||||
\(962\) | −0.0909408 | − | 18.7836i | −0.00293205 | − | 0.605608i | ||||
\(963\) | 5.29785i | 0.170721i | ||||||||
\(964\) | 21.8978 | − | 12.6427i | 0.705280 | − | 0.407193i | ||||
\(965\) | −27.2815 | + | 6.09761i | −0.878222 | + | 0.196289i | ||||
\(966\) | −2.18673 | + | 3.78753i | −0.0703569 | + | 0.121862i | ||||
\(967\) | −13.9911 | + | 24.2333i | −0.449923 | + | 0.779290i | −0.998381 | − | 0.0568884i | \(-0.981882\pi\) |
0.548457 | + | 0.836179i | \(0.315215\pi\) | |||||||
\(968\) | 10.7956 | 0.346985 | ||||||||
\(969\) | −3.15305 | + | 5.46124i | −0.101290 | + | 0.175440i | ||||
\(970\) | −8.53724 | − | 9.28452i | −0.274114 | − | 0.298108i | ||||
\(971\) | −2.43501 | − | 4.21757i | −0.0781433 | − | 0.135348i | 0.824306 | − | 0.566145i | \(-0.191566\pi\) |
−0.902449 | + | 0.430797i | \(0.858233\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 31.8360i | 1.02061i | ||||||||
\(974\) | 7.82210 | + | 13.5483i | 0.250636 | + | 0.434115i | ||||
\(975\) | −8.81240 | + | 12.6784i | −0.282223 | + | 0.406034i | ||||
\(976\) | − | 8.20278i | − | 0.262564i | ||||||
\(977\) | 4.47908 | + | 7.75800i | 0.143299 | + | 0.248200i | 0.928737 | − | 0.370740i | \(-0.120896\pi\) |
−0.785438 | + | 0.618940i | \(0.787562\pi\) | |||||||
\(978\) | −15.0458 | + | 8.68670i | −0.481112 | + | 0.277770i | ||||
\(979\) | −4.08031 | + | 2.35577i | −0.130407 | + | 0.0752907i | ||||
\(980\) | 2.04015 | − | 0.455989i | 0.0651702 | − | 0.0145660i | ||||
\(981\) | 5.76779 | + | 3.33004i | 0.184151 | + | 0.106320i | ||||
\(982\) | −10.2312 | − | 17.7210i | −0.326492 | − | 0.565501i | ||||
\(983\) | 6.93809 | − | 4.00571i | 0.221291 | − | 0.127762i | −0.385257 | − | 0.922809i | \(-0.625887\pi\) |
0.606548 | + | 0.795047i | \(0.292554\pi\) | |||||||
\(984\) | −2.04852 | + | 1.18271i | −0.0653045 | + | 0.0377036i | ||||
\(985\) | 3.23527 | − | 2.97488i | 0.103084 | − | 0.0947875i | ||||
\(986\) | −15.3272 | − | 8.84914i | −0.488116 | − | 0.281814i | ||||
\(987\) | −5.63833 | + | 3.25529i | −0.179470 | + | 0.103617i | ||||
\(988\) | 9.20845i | 0.292960i | ||||||||
\(989\) | 7.00862 | 0.222861 | ||||||||
\(990\) | 0.302309 | − | 0.964609i | 0.00960802 | − | 0.0306573i | ||||
\(991\) | − | 13.7352i | − | 0.436312i | −0.975914 | − | 0.218156i | \(-0.929996\pi\) | ||
0.975914 | − | 0.218156i | \(-0.0700041\pi\) | |||||||
\(992\) | −2.21296 | − | 1.27765i | −0.0702616 | − | 0.0405656i | ||||
\(993\) | −27.1893 | −0.862825 | ||||||||
\(994\) | −0.0138075 | − | 0.00797176i | −0.000437947 | − | 0.000252849i | ||||
\(995\) | −6.19862 | − | 27.7334i | −0.196509 | − | 0.879207i | ||||
\(996\) | −3.78716 | + | 6.55955i | −0.120001 | + | 0.207847i | ||||
\(997\) | 14.1059 | + | 24.4321i | 0.446738 | + | 0.773774i | 0.998172 | − | 0.0604454i | \(-0.0192521\pi\) |
−0.551433 | + | 0.834219i | \(0.685919\pi\) | |||||||
\(998\) | 30.3736i | 0.961458i | ||||||||
\(999\) | −6.08269 | + | 0.0294493i | −0.192448 | + | 0.000931735i |
(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 | 1110.2.ba.b.529.6 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.a.529.13 | ✓ | 36 | ||
37.27 | even | 6 | 1110.2.ba.a.619.13 | yes | 36 | ||
185.64 | even | 6 | inner | 1110.2.ba.b.619.6 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.13 | ✓ | 36 | 5.4 | even | 2 | ||
1110.2.ba.a.619.13 | yes | 36 | 37.27 | even | 6 | ||
1110.2.ba.b.529.6 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.619.6 | yes | 36 | 185.64 | even | 6 | inner |