Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [875,2,Mod(82,875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(875, base_ring=CyclotomicField(60))
chi = DirichletCharacter(H, H._module([27, 50]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("875.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 875 = 5^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 875.bb (of order \(60\), degree \(16\), not 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: | \(6.98691017686\) |
Analytic rank: | \(0\) |
Dimension: | \(288\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{60})\) |
Twist minimal: | no (minimal twist has level 175) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{60}]$ |
Embedding invariants
Embedding label | 143.16 | ||
Character | \(\chi\) | \(=\) | 875.143 |
Dual form | 875.2.bb.b.257.16 |
$q$-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 \(\left(\mathbb{Z}/875\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(626\) |
\(\chi(n)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.109427 | + | 2.08800i | 0.0773768 | + | 1.47644i | 0.711216 | + | 0.702973i | \(0.248145\pi\) |
−0.633839 | + | 0.773465i | \(0.718522\pi\) | |||||||
\(3\) | −0.645540 | − | 0.522748i | −0.372703 | − | 0.301809i | 0.424609 | − | 0.905377i | \(-0.360412\pi\) |
−0.797311 | + | 0.603568i | \(0.793745\pi\) | |||||||
\(4\) | −2.35872 | + | 0.247911i | −1.17936 | + | 0.123956i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.02086 | − | 1.40509i | 0.416763 | − | 0.573625i | ||||
\(7\) | −2.15744 | + | 1.53148i | −0.815436 | + | 0.578847i | ||||
\(8\) | −0.121581 | − | 0.767632i | −0.0429853 | − | 0.271399i | ||||
\(9\) | −0.480279 | − | 2.25953i | −0.160093 | − | 0.753178i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.02734 | + | 0.218367i | 0.309753 | + | 0.0658401i | 0.360166 | − | 0.932888i | \(-0.382720\pi\) |
−0.0504122 | + | 0.998728i | \(0.516054\pi\) | |||||||
\(12\) | 1.65224 | + | 1.07298i | 0.476961 | + | 0.309742i | ||||
\(13\) | −2.08008 | − | 4.08239i | −0.576911 | − | 1.13225i | −0.976492 | − | 0.215554i | \(-0.930844\pi\) |
0.399580 | − | 0.916698i | \(-0.369156\pi\) | |||||||
\(14\) | −3.43382 | − | 4.33715i | −0.917727 | − | 1.15915i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.05026 | + | 0.648353i | −0.762565 | + | 0.162088i | ||||
\(17\) | 2.10566 | + | 0.808289i | 0.510699 | + | 0.196039i | 0.600052 | − | 0.799961i | \(-0.295147\pi\) |
−0.0893531 | + | 0.996000i | \(0.528480\pi\) | |||||||
\(18\) | 4.66535 | − | 1.25008i | 1.09963 | − | 0.294646i | ||||
\(19\) | 0.520869 | − | 4.95574i | 0.119496 | − | 1.13692i | −0.756294 | − | 0.654232i | \(-0.772992\pi\) |
0.875790 | − | 0.482693i | \(-0.160341\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.19329 | + | 0.139164i | 0.478616 | + | 0.0303680i | ||||
\(22\) | −0.343531 | + | 2.16897i | −0.0732411 | + | 0.462426i | ||||
\(23\) | −6.21536 | + | 0.325733i | −1.29599 | + | 0.0679201i | −0.687818 | − | 0.725884i | \(-0.741431\pi\) |
−0.608174 | + | 0.793804i | \(0.708098\pi\) | |||||||
\(24\) | −0.322792 | + | 0.559093i | −0.0658897 | + | 0.114124i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.29642 | − | 4.78994i | 1.62706 | − | 0.939384i | ||||
\(27\) | −2.00245 | + | 3.93004i | −0.385373 | + | 0.756336i | ||||
\(28\) | 4.70913 | − | 4.14720i | 0.889942 | − | 0.783747i | ||||
\(29\) | 0.743348 | + | 1.02313i | 0.138036 | + | 0.189991i | 0.872439 | − | 0.488724i | \(-0.162537\pi\) |
−0.734402 | + | 0.678714i | \(0.762537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.14336 | − | 9.30613i | −0.744169 | − | 1.67143i | −0.741063 | − | 0.671435i | \(-0.765678\pi\) |
−0.00310567 | − | 0.999995i | \(-0.500989\pi\) | |||||||
\(32\) | −2.08985 | − | 7.79943i | −0.369437 | − | 1.37876i | ||||
\(33\) | −0.549035 | − | 0.678002i | −0.0955748 | − | 0.118025i | ||||
\(34\) | −1.45729 | + | 4.48507i | −0.249923 | + | 0.769184i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.69301 | + | 5.21054i | 0.282168 | + | 0.868424i | ||||
\(37\) | 3.42368 | − | 5.27200i | 0.562849 | − | 0.866712i | −0.436608 | − | 0.899652i | \(-0.643820\pi\) |
0.999457 | + | 0.0329402i | \(0.0104871\pi\) | |||||||
\(38\) | 10.4046 | + | 0.545281i | 1.68785 | + | 0.0884562i | ||||
\(39\) | −0.791286 | + | 3.72271i | −0.126707 | + | 0.596110i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.32280 | + | 1.72948i | 0.831282 | + | 0.270100i | 0.693585 | − | 0.720374i | \(-0.256030\pi\) |
0.137697 | + | 0.990474i | \(0.456030\pi\) | |||||||
\(42\) | −0.0505673 | + | 4.59482i | −0.00780270 | + | 0.708997i | ||||
\(43\) | 4.80861 | + | 4.80861i | 0.733306 | + | 0.733306i | 0.971273 | − | 0.237968i | \(-0.0764812\pi\) |
−0.237968 | + | 0.971273i | \(0.576481\pi\) | |||||||
\(44\) | −2.47733 | − | 0.260378i | −0.373472 | − | 0.0392535i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.36026 | − | 12.9420i | −0.200559 | − | 1.90820i | ||||
\(47\) | −0.112172 | − | 0.292218i | −0.0163620 | − | 0.0426244i | 0.925156 | − | 0.379587i | \(-0.123934\pi\) |
−0.941518 | + | 0.336962i | \(0.890600\pi\) | |||||||
\(48\) | 2.30799 | + | 1.17598i | 0.333130 | + | 0.169738i | ||||
\(49\) | 2.30911 | − | 6.60818i | 0.329873 | − | 0.944025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.936759 | − | 1.62251i | −0.131172 | − | 0.227197i | ||||
\(52\) | 5.91841 | + | 9.11355i | 0.820736 | + | 1.26382i | ||||
\(53\) | 0.176281 | − | 0.217690i | 0.0242141 | − | 0.0299020i | −0.764895 | − | 0.644155i | \(-0.777209\pi\) |
0.789109 | + | 0.614253i | \(0.210543\pi\) | |||||||
\(54\) | −8.42504 | − | 3.75107i | −1.14650 | − | 0.510456i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.43792 | + | 1.46992i | 0.192150 | + | 0.196426i | ||||
\(57\) | −2.92684 | + | 2.92684i | −0.387670 | + | 0.387670i | ||||
\(58\) | −2.05495 | + | 1.66407i | −0.269829 | + | 0.218503i | ||||
\(59\) | −4.60084 | − | 5.10975i | −0.598978 | − | 0.665232i | 0.365064 | − | 0.930982i | \(-0.381047\pi\) |
−0.964042 | + | 0.265750i | \(0.914380\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.94111 | − | 3.54859i | −0.504607 | − | 0.454350i | 0.377083 | − | 0.926180i | \(-0.376927\pi\) |
−0.881690 | + | 0.471829i | \(0.843594\pi\) | |||||||
\(62\) | 18.9778 | − | 9.66967i | 2.41018 | − | 1.22805i | ||||
\(63\) | 4.49661 | + | 4.13927i | 0.566520 | + | 0.521499i | ||||
\(64\) | 10.1249 | − | 3.28979i | 1.26562 | − | 0.411224i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.35559 | − | 1.22058i | 0.166861 | − | 0.150243i | ||||
\(67\) | 4.40181 | − | 11.4671i | 0.537767 | − | 1.40093i | −0.348304 | − | 0.937382i | \(-0.613242\pi\) |
0.886071 | − | 0.463550i | \(-0.153425\pi\) | |||||||
\(68\) | −5.16706 | − | 1.38451i | −0.626598 | − | 0.167896i | ||||
\(69\) | 4.18254 | + | 3.03879i | 0.503518 | + | 0.365827i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.66579 | + | 1.21027i | −0.197693 | + | 0.143632i | −0.682228 | − | 0.731140i | \(-0.738989\pi\) |
0.484535 | + | 0.874772i | \(0.338989\pi\) | |||||||
\(72\) | −1.67610 | + | 0.643393i | −0.197530 | + | 0.0758246i | ||||
\(73\) | 1.08702 | − | 0.705919i | 0.127226 | − | 0.0826215i | −0.479457 | − | 0.877565i | \(-0.659166\pi\) |
0.606683 | + | 0.794944i | \(0.292500\pi\) | |||||||
\(74\) | 11.3826 | + | 6.57173i | 1.32320 | + | 0.763948i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.8183i | 1.35566i | ||||||||
\(77\) | −2.55084 | + | 1.10223i | −0.290696 | + | 0.125611i | ||||
\(78\) | −7.85959 | − | 1.24484i | −0.889924 | − | 0.140950i | ||||
\(79\) | −4.40735 | + | 9.89907i | −0.495865 | + | 1.11373i | 0.476267 | + | 0.879301i | \(0.341989\pi\) |
−0.972133 | + | 0.234431i | \(0.924677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.98382 | + | 1.32848i | −0.331536 | + | 0.147609i | ||||
\(82\) | −3.02870 | + | 11.3033i | −0.334464 | + | 1.24824i | ||||
\(83\) | −3.66064 | + | 0.579789i | −0.401808 | + | 0.0636401i | −0.354068 | − | 0.935220i | \(-0.615202\pi\) |
−0.0477399 | + | 0.998860i | \(0.515202\pi\) | |||||||
\(84\) | −5.20787 | + | 0.215495i | −0.568225 | + | 0.0235124i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.51417 | + | 10.5666i | −1.02594 | + | 1.13942i | ||||
\(87\) | 0.0549787 | − | 1.04906i | 0.00589433 | − | 0.112471i | ||||
\(88\) | 0.0427210 | − | 0.815165i | 0.00455407 | − | 0.0868968i | ||||
\(89\) | 7.09604 | − | 7.88095i | 0.752179 | − | 0.835379i | −0.238565 | − | 0.971127i | \(-0.576677\pi\) |
0.990743 | + | 0.135747i | \(0.0433435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.7398 | + | 5.62191i | 1.12584 | + | 0.589337i | ||||
\(92\) | 14.5795 | − | 2.30917i | 1.52002 | − | 0.240748i | ||||
\(93\) | −2.19006 | + | 8.17341i | −0.227098 | + | 0.847543i | ||||
\(94\) | 0.597877 | − | 0.266192i | 0.0616663 | − | 0.0274556i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.72805 | + | 6.12730i | −0.278431 | + | 0.625365i | ||||
\(97\) | −4.89604 | − | 0.775456i | −0.497117 | − | 0.0787356i | −0.0971587 | − | 0.995269i | \(-0.530975\pi\) |
−0.399958 | + | 0.916533i | \(0.630975\pi\) | |||||||
\(98\) | 14.0505 | + | 4.09830i | 1.41932 | + | 0.413991i | ||||
\(99\) | − | 2.42618i | − | 0.243840i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1637 | + | 7.60006i | 1.30984 | + | 0.756234i | 0.982069 | − | 0.188524i | \(-0.0603704\pi\) |
0.327767 | + | 0.944758i | \(0.393704\pi\) | |||||||
\(102\) | 3.28530 | − | 2.13350i | 0.325293 | − | 0.211248i | ||||
\(103\) | −6.33830 | + | 2.43305i | −0.624532 | + | 0.239735i | −0.649993 | − | 0.759941i | \(-0.725228\pi\) |
0.0254609 | + | 0.999676i | \(0.491895\pi\) | |||||||
\(104\) | −2.88088 | + | 2.09308i | −0.282493 | + | 0.205243i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.473825 | + | 0.344254i | 0.0460220 | + | 0.0334369i | ||||
\(107\) | −18.9985 | − | 5.09063i | −1.83665 | − | 0.492130i | −0.838081 | − | 0.545546i | \(-0.816322\pi\) |
−0.998572 | + | 0.0534166i | \(0.982989\pi\) | |||||||
\(108\) | 3.74893 | − | 9.76629i | 0.360741 | − | 0.939762i | ||||
\(109\) | −14.2080 | + | 12.7930i | −1.36088 | + | 1.22535i | −0.411428 | + | 0.911442i | \(0.634970\pi\) |
−0.949455 | + | 0.313903i | \(0.898363\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.96605 | + | 1.61357i | −0.471356 | + | 0.153153i | ||||
\(112\) | 5.58782 | − | 6.07021i | 0.527999 | − | 0.573581i | ||||
\(113\) | −7.77652 | + | 3.96233i | −0.731553 | + | 0.372745i | −0.779748 | − | 0.626093i | \(-0.784653\pi\) |
0.0481952 | + | 0.998838i | \(0.484653\pi\) | |||||||
\(114\) | −6.43152 | − | 5.79097i | −0.602367 | − | 0.542374i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00700 | − | 2.22900i | −0.186345 | − | 0.206957i | ||||
\(117\) | −8.22529 | + | 6.66071i | −0.760428 | + | 0.615783i | ||||
\(118\) | 10.1657 | − | 10.1657i | 0.935827 | − | 0.935827i | ||||
\(119\) | −5.78073 | + | 1.48096i | −0.529919 | + | 0.135759i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.04127 | − | 4.02543i | −0.821933 | − | 0.365948i | ||||
\(122\) | 6.97819 | − | 8.61734i | 0.631775 | − | 0.780177i | ||||
\(123\) | −2.53200 | − | 3.89893i | −0.228303 | − | 0.351555i | ||||
\(124\) | 12.0801 | + | 20.9234i | 1.08483 | + | 1.87897i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.15074 | + | 9.84188i | −0.726126 | + | 0.876784i | ||||
\(127\) | −11.5760 | − | 5.89827i | −1.02720 | − | 0.523386i | −0.142625 | − | 0.989777i | \(-0.545554\pi\) |
−0.884579 | + | 0.466390i | \(0.845554\pi\) | |||||||
\(128\) | 2.18971 | + | 5.70438i | 0.193544 | + | 0.504201i | ||||
\(129\) | −0.590458 | − | 5.61783i | −0.0519869 | − | 0.494623i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.52330 | + | 0.370314i | 0.307832 | + | 0.0323545i | 0.257185 | − | 0.966362i | \(-0.417205\pi\) |
0.0506472 | + | 0.998717i | \(0.483872\pi\) | |||||||
\(132\) | 1.46310 | + | 1.46310i | 0.127347 | + | 0.127347i | ||||
\(133\) | 6.46590 | + | 11.4894i | 0.560664 | + | 0.996260i | ||||
\(134\) | 24.4250 | + | 7.93617i | 2.11000 | + | 0.685580i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.364459 | − | 1.71465i | 0.0312521 | − | 0.147030i | ||||
\(137\) | −7.56424 | − | 0.396425i | −0.646257 | − | 0.0338689i | −0.273608 | − | 0.961841i | \(-0.588217\pi\) |
−0.372649 | + | 0.927972i | \(0.621550\pi\) | |||||||
\(138\) | −5.88731 | + | 9.06566i | −0.501161 | + | 0.771720i | ||||
\(139\) | 2.73221 | + | 8.40888i | 0.231743 | + | 0.713232i | 0.997537 | + | 0.0701455i | \(0.0223463\pi\) |
−0.765794 | + | 0.643086i | \(0.777654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0803449 | + | 0.247276i | −0.00676626 | + | 0.0208244i | ||||
\(142\) | −2.70932 | − | 3.34573i | −0.227361 | − | 0.280767i | ||||
\(143\) | −1.24548 | − | 4.64821i | −0.104153 | − | 0.388703i | ||||
\(144\) | 2.92995 | + | 6.58078i | 0.244163 | + | 0.548398i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.59291 | + | 2.19245i | 0.131830 | + | 0.181448i | ||||
\(147\) | −4.94503 | + | 3.05876i | −0.407859 | + | 0.252282i | ||||
\(148\) | −6.76851 | + | 13.2839i | −0.556368 | + | 1.09193i | ||||
\(149\) | 1.52475 | − | 0.880317i | 0.124913 | − | 0.0721183i | −0.436242 | − | 0.899830i | \(-0.643691\pi\) |
0.561154 | + | 0.827711i | \(0.310357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.13479 | + | 5.42962i | −0.255106 | + | 0.441856i | −0.964924 | − | 0.262529i | \(-0.915444\pi\) |
0.709819 | + | 0.704385i | \(0.248777\pi\) | |||||||
\(152\) | −3.86751 | + | 0.202688i | −0.313697 | + | 0.0164401i | ||||
\(153\) | 0.815050 | − | 5.14602i | 0.0658929 | − | 0.416031i | ||||
\(154\) | −2.58060 | − | 5.20554i | −0.207950 | − | 0.419474i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.943520 | − | 8.97699i | 0.0755420 | − | 0.718735i | ||||
\(157\) | 10.4389 | − | 2.79709i | 0.833115 | − | 0.223232i | 0.183043 | − | 0.983105i | \(-0.441405\pi\) |
0.650072 | + | 0.759872i | \(0.274739\pi\) | |||||||
\(158\) | −21.1515 | − | 8.11931i | −1.68272 | − | 0.645937i | ||||
\(159\) | −0.227593 | + | 0.0483765i | −0.0180493 | + | 0.00383650i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9104 | − | 10.2215i | 1.01748 | − | 0.805565i | ||||
\(162\) | −3.10038 | − | 6.08485i | −0.243589 | − | 0.478071i | ||||
\(163\) | −4.67900 | − | 3.03858i | −0.366488 | − | 0.238000i | 0.348236 | − | 0.937407i | \(-0.386781\pi\) |
−0.714724 | + | 0.699407i | \(0.753448\pi\) | |||||||
\(164\) | −12.9838 | − | 2.75978i | −1.01386 | − | 0.215503i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.61117 | − | 7.57998i | −0.125051 | − | 0.588320i | ||||
\(167\) | 1.64024 | + | 10.3561i | 0.126926 | + | 0.801379i | 0.966223 | + | 0.257706i | \(0.0829667\pi\) |
−0.839297 | + | 0.543673i | \(0.817033\pi\) | |||||||
\(168\) | −0.159836 | − | 1.70056i | −0.0123316 | − | 0.131201i | ||||
\(169\) | −4.69799 | + | 6.46623i | −0.361384 | + | 0.497402i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.4478 | + | 1.20322i | −0.875437 | + | 0.0920122i | ||||
\(172\) | −12.5343 | − | 10.1500i | −0.955729 | − | 0.773934i | ||||
\(173\) | −0.718462 | − | 13.7091i | −0.0546236 | − | 1.04228i | −0.879177 | − | 0.476496i | \(-0.841907\pi\) |
0.824553 | − | 0.565785i | \(-0.191427\pi\) | |||||||
\(174\) | 2.19644 | 0.166512 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.27522 | −0.246879 | ||||||||
\(177\) | 0.298914 | + | 5.70362i | 0.0224678 | + | 0.428710i | ||||
\(178\) | 17.2319 | + | 13.9541i | 1.29159 | + | 1.04591i | ||||
\(179\) | −1.60078 | + | 0.168248i | −0.119648 | + | 0.0125755i | −0.164163 | − | 0.986433i | \(-0.552492\pi\) |
0.0445154 | + | 0.999009i | \(0.485826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.04450 | + | 2.81402i | −0.151967 | + | 0.209164i | −0.878212 | − | 0.478271i | \(-0.841264\pi\) |
0.726245 | + | 0.687436i | \(0.241264\pi\) | |||||||
\(182\) | −10.5633 | + | 23.0398i | −0.783005 | + | 1.70783i | ||||
\(183\) | 0.689125 | + | 4.35096i | 0.0509416 | + | 0.321632i | ||||
\(184\) | 1.00571 | + | 4.73150i | 0.0741421 | + | 0.348811i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −17.3057 | − | 3.67844i | −1.26892 | − | 0.269717i | ||||
\(187\) | 1.98672 | + | 1.29019i | 0.145283 | + | 0.0943481i | ||||
\(188\) | 0.337027 | + | 0.661452i | 0.0245802 | + | 0.0482414i | ||||
\(189\) | −1.69861 | − | 11.5456i | −0.123556 | − | 0.839816i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.89987 | − | 0.616386i | 0.209827 | − | 0.0446001i | −0.101799 | − | 0.994805i | \(-0.532460\pi\) |
0.311626 | + | 0.950205i | \(0.399126\pi\) | |||||||
\(192\) | −8.25579 | − | 3.16910i | −0.595810 | − | 0.228710i | ||||
\(193\) | −16.4661 | + | 4.41207i | −1.18525 | + | 0.317588i | −0.797009 | − | 0.603968i | \(-0.793586\pi\) |
−0.388246 | + | 0.921556i | \(0.626919\pi\) | |||||||
\(194\) | 1.08339 | − | 10.3078i | 0.0777829 | − | 0.740055i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.80830 | + | 16.1593i | −0.272022 | + | 1.15424i | ||||
\(197\) | 3.02785 | − | 19.1171i | 0.215725 | − | 1.36204i | −0.607499 | − | 0.794320i | \(-0.707827\pi\) |
0.823225 | − | 0.567716i | \(-0.192173\pi\) | |||||||
\(198\) | 5.06585 | − | 0.265490i | 0.360015 | − | 0.0188676i | ||||
\(199\) | 0.0959424 | − | 0.166177i | 0.00680118 | − | 0.0117800i | −0.862605 | − | 0.505878i | \(-0.831168\pi\) |
0.869406 | + | 0.494098i | \(0.164502\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.83596 | + | 5.10144i | −0.623240 | + | 0.359828i | ||||
\(202\) | −14.4284 | + | 28.3174i | −1.01518 | + | 1.99241i | ||||
\(203\) | −3.17064 | − | 1.06892i | −0.222535 | − | 0.0750234i | ||||
\(204\) | 2.61179 | + | 3.59482i | 0.182862 | + | 0.251688i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.77378 | − | 12.9681i | −0.402278 | − | 0.903532i | ||||
\(207\) | 3.72111 | + | 13.8874i | 0.258635 | + | 0.965239i | ||||
\(208\) | 8.99163 | + | 11.1037i | 0.623457 | + | 0.769906i | ||||
\(209\) | 1.61728 | − | 4.97747i | 0.111869 | − | 0.344299i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.96658 | + | 6.05250i | 0.135385 | + | 0.416671i | 0.995650 | − | 0.0931759i | \(-0.0297019\pi\) |
−0.860265 | + | 0.509847i | \(0.829702\pi\) | |||||||
\(212\) | −0.361831 | + | 0.557171i | −0.0248507 | + | 0.0382666i | ||||
\(213\) | 1.70800 | + | 0.0895123i | 0.117030 | + | 0.00613328i | ||||
\(214\) | 8.55027 | − | 40.2259i | 0.584485 | − | 2.74978i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.26028 | + | 1.05933i | 0.221834 | + | 0.0720783i | ||||
\(217\) | 23.1912 | + | 13.7319i | 1.57432 | + | 0.932185i | ||||
\(218\) | −28.2665 | − | 28.2665i | −1.91445 | − | 1.91445i | ||||
\(219\) | −1.07073 | − | 0.112538i | −0.0723533 | − | 0.00760464i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.08020 | − | 10.2775i | −0.0726624 | − | 0.691337i | ||||
\(222\) | −3.91254 | − | 10.1925i | −0.262593 | − | 0.684078i | ||||
\(223\) | −11.8807 | − | 6.05349i | −0.795587 | − | 0.405372i | 0.00843996 | − | 0.999964i | \(-0.497313\pi\) |
−0.804027 | + | 0.594592i | \(0.797313\pi\) | |||||||
\(224\) | 16.4534 | + | 13.6262i | 1.09934 | + | 0.910441i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.12431 | − | 15.8038i | −0.606940 | − | 1.05125i | ||||
\(227\) | 2.64274 | + | 4.06947i | 0.175405 | + | 0.270100i | 0.915428 | − | 0.402481i | \(-0.131852\pi\) |
−0.740023 | + | 0.672581i | \(0.765185\pi\) | |||||||
\(228\) | 6.17801 | − | 7.62920i | 0.409149 | − | 0.505256i | ||||
\(229\) | 6.10856 | + | 2.71971i | 0.403665 | + | 0.179723i | 0.598518 | − | 0.801109i | \(-0.295756\pi\) |
−0.194853 | + | 0.980832i | \(0.562423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.22286 | + | 0.621911i | 0.146254 | + | 0.0409187i | ||||
\(232\) | 0.695011 | − | 0.695011i | 0.0456297 | − | 0.0456297i | ||||
\(233\) | 6.71012 | − | 5.43374i | 0.439594 | − | 0.355976i | −0.383829 | − | 0.923404i | \(-0.625395\pi\) |
0.823423 | + | 0.567428i | \(0.192061\pi\) | |||||||
\(234\) | −14.8076 | − | 16.4455i | −0.968004 | − | 1.07508i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.1189 | + | 10.9119i | 0.788870 | + | 0.710302i | ||||
\(237\) | 8.01983 | − | 4.08631i | 0.520944 | − | 0.265434i | ||||
\(238\) | −3.72480 | − | 11.9081i | −0.241443 | − | 0.771887i | ||||
\(239\) | 18.2461 | − | 5.92852i | 1.18024 | − | 0.383484i | 0.347785 | − | 0.937574i | \(-0.386934\pi\) |
0.832457 | + | 0.554090i | \(0.186934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.2863 | − | 17.3654i | 1.24234 | − | 1.11861i | 0.253861 | − | 0.967241i | \(-0.418300\pi\) |
0.988478 | − | 0.151366i | \(-0.0483671\pi\) | |||||||
\(242\) | 7.41573 | − | 19.3186i | 0.476701 | − | 1.24185i | ||||
\(243\) | 15.4021 | + | 4.12698i | 0.988046 | + | 0.264746i | ||||
\(244\) | 10.1757 | + | 7.39308i | 0.651433 | + | 0.473294i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.86390 | − | 5.71346i | 0.501384 | − | 0.364277i | ||||
\(247\) | −21.3147 | + | 8.18196i | −1.35622 | + | 0.520606i | ||||
\(248\) | −6.63993 | + | 4.31202i | −0.421636 | + | 0.273814i | ||||
\(249\) | 2.66617 | + | 1.53932i | 0.168962 | + | 0.0975502i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.4133i | − | 0.972880i | −0.873714 | − | 0.486440i | \(-0.838295\pi\) | ||
0.873714 | − | 0.486440i | \(-0.161705\pi\) | |||||||
\(252\) | −11.6324 | − | 8.64862i | −0.732774 | − | 0.544812i | ||||
\(253\) | −6.45639 | − | 1.02259i | −0.405910 | − | 0.0642898i | ||||
\(254\) | 11.0488 | − | 24.8161i | 0.693266 | − | 1.55710i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.78009 | − | 3.46392i | 0.486256 | − | 0.216495i | ||||
\(257\) | 7.91188 | − | 29.5275i | 0.493529 | − | 1.84188i | −0.0445856 | − | 0.999006i | \(-0.514197\pi\) |
0.538115 | − | 0.842871i | \(-0.319137\pi\) | |||||||
\(258\) | 11.6654 | − | 1.84762i | 0.726257 | − | 0.115028i | ||||
\(259\) | 0.687603 | + | 16.6173i | 0.0427256 | + | 1.03255i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.95479 | − | 2.17101i | 0.120998 | − | 0.134382i | ||||
\(262\) | −0.387670 | + | 7.39718i | −0.0239503 | + | 0.456999i | ||||
\(263\) | 0.0213379 | − | 0.407151i | 0.00131575 | − | 0.0251060i | −0.997893 | − | 0.0648848i | \(-0.979332\pi\) |
0.999209 | + | 0.0397788i | \(0.0126653\pi\) | |||||||
\(264\) | −0.453704 | + | 0.503889i | −0.0279235 | + | 0.0310122i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −23.2824 | + | 14.7580i | −1.42753 | + | 0.904873i | ||||
\(267\) | −8.70053 | + | 1.37803i | −0.532464 | + | 0.0843340i | ||||
\(268\) | −7.53982 | + | 28.1390i | −0.460568 | + | 1.71886i | ||||
\(269\) | −17.4978 | + | 7.79051i | −1.06686 | + | 0.474996i | −0.863625 | − | 0.504134i | \(-0.831812\pi\) |
−0.203233 | + | 0.979130i | \(0.565145\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.85265 | + | 17.6373i | −0.477015 | + | 1.07139i | 0.501489 | + | 0.865164i | \(0.332786\pi\) |
−0.978504 | + | 0.206228i | \(0.933881\pi\) | |||||||
\(272\) | −6.94688 | − | 1.10028i | −0.421216 | − | 0.0667141i | ||||
\(273\) | −3.99411 | − | 9.24337i | −0.241735 | − | 0.559434i | ||||
\(274\) | − | 15.8375i | − | 0.956779i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.6188 | − | 6.13076i | −0.639176 | − | 0.369028i | ||||
\(277\) | −6.41377 | + | 4.16515i | −0.385366 | + | 0.250260i | −0.722753 | − | 0.691106i | \(-0.757124\pi\) |
0.337387 | + | 0.941366i | \(0.390457\pi\) | |||||||
\(278\) | −17.2587 | + | 6.62501i | −1.03511 | + | 0.397342i | ||||
\(279\) | −19.0376 | + | 13.8316i | −1.13975 | + | 0.828076i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1432 | + | 11.0022i | 0.903367 | + | 0.656334i | 0.939329 | − | 0.343019i | \(-0.111449\pi\) |
−0.0359618 | + | 0.999353i | \(0.511449\pi\) | |||||||
\(282\) | −0.525104 | − | 0.140701i | −0.0312695 | − | 0.00837864i | ||||
\(283\) | −1.02124 | + | 2.66042i | −0.0607063 | + | 0.158145i | −0.960579 | − | 0.278008i | \(-0.910326\pi\) |
0.899873 | + | 0.436153i | \(0.143659\pi\) | |||||||
\(284\) | 3.62909 | − | 3.26765i | 0.215347 | − | 0.193899i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.56917 | − | 3.10921i | 0.565837 | − | 0.183852i | ||||
\(287\) | −14.1323 | + | 4.42053i | −0.834204 | + | 0.260936i | ||||
\(288\) | −16.6194 | + | 8.46799i | −0.979305 | + | 0.498981i | ||||
\(289\) | −8.85297 | − | 7.97125i | −0.520763 | − | 0.468897i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.75522 | + | 3.05998i | 0.161514 | + | 0.179379i | ||||
\(292\) | −2.38897 | + | 1.93455i | −0.139804 | + | 0.113211i | ||||
\(293\) | −0.584948 | + | 0.584948i | −0.0341730 | + | 0.0341730i | −0.723987 | − | 0.689814i | \(-0.757692\pi\) |
0.689814 | + | 0.723987i | \(0.257692\pi\) | |||||||
\(294\) | −6.92781 | − | 9.99051i | −0.404038 | − | 0.582658i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.46321 | − | 1.98715i | −0.259419 | − | 0.115501i | ||||
\(297\) | −2.91538 | + | 3.60020i | −0.169168 | + | 0.208905i | ||||
\(298\) | 2.00495 | + | 3.08735i | 0.116144 | + | 0.178845i | ||||
\(299\) | 14.2582 | + | 24.6960i | 0.824575 | + | 1.42821i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.7386 | − | 3.00998i | −1.02244 | − | 0.173492i | ||||
\(302\) | −11.6801 | − | 5.95129i | −0.672112 | − | 0.342458i | ||||
\(303\) | −4.52477 | − | 11.7874i | −0.259941 | − | 0.677170i | ||||
\(304\) | 1.62428 | + | 15.4540i | 0.0931589 | + | 0.886348i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.8341 | + | 1.13871i | 0.619343 | + | 0.0650956i | ||||
\(307\) | 10.4006 | + | 10.4006i | 0.593593 | + | 0.593593i | 0.938600 | − | 0.345007i | \(-0.112123\pi\) |
−0.345007 | + | 0.938600i | \(0.612123\pi\) | |||||||
\(308\) | 5.74347 | − | 3.23225i | 0.327264 | − | 0.184174i | ||||
\(309\) | 5.36350 | + | 1.74271i | 0.305119 | + | 0.0991391i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.47049 | + | 11.6228i | −0.140089 | + | 0.659066i | 0.850923 | + | 0.525291i | \(0.176043\pi\) |
−0.991012 | + | 0.133776i | \(0.957290\pi\) | |||||||
\(312\) | 2.95387 | + | 0.154806i | 0.167230 | + | 0.00876416i | ||||
\(313\) | 5.48632 | − | 8.44819i | 0.310105 | − | 0.477520i | −0.648914 | − | 0.760862i | \(-0.724777\pi\) |
0.959019 | + | 0.283342i | \(0.0914432\pi\) | |||||||
\(314\) | 6.98263 | + | 21.4903i | 0.394053 | + | 1.21277i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.94161 | − | 24.4418i | 0.446750 | − | 1.37496i | ||||
\(317\) | −11.8979 | − | 14.6927i | −0.668252 | − | 0.825223i | 0.324439 | − | 0.945907i | \(-0.394825\pi\) |
−0.992691 | + | 0.120684i | \(0.961491\pi\) | |||||||
\(318\) | −0.125915 | − | 0.469921i | −0.00706096 | − | 0.0263519i | ||||
\(319\) | 0.540250 | + | 1.21342i | 0.0302482 | + | 0.0679386i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.60316 | + | 13.2176i | 0.535996 | + | 0.737736i | ||||
\(322\) | 22.7552 | + | 25.8384i | 1.26810 | + | 1.43992i | ||||
\(323\) | 5.10245 | − | 10.0141i | 0.283908 | − | 0.557200i | ||||
\(324\) | 6.70866 | − | 3.87325i | 0.372703 | − | 0.215180i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.83254 | − | 10.1023i | 0.323035 | − | 0.559512i | ||||
\(327\) | 15.8594 | − | 0.831154i | 0.877024 | − | 0.0459629i | ||||
\(328\) | 0.680455 | − | 4.29622i | 0.0375719 | − | 0.237219i | ||||
\(329\) | 0.689532 | + | 0.458654i | 0.0380152 | + | 0.0252864i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.25235 | + | 30.9441i | −0.178766 | + | 1.70084i | 0.426232 | + | 0.904614i | \(0.359841\pi\) |
−0.604998 | + | 0.796227i | \(0.706826\pi\) | |||||||
\(332\) | 8.49070 | − | 2.27508i | 0.465988 | − | 0.124861i | ||||
\(333\) | −13.5566 | − | 5.20388i | −0.742896 | − | 0.285171i | ||||
\(334\) | −21.4440 | + | 4.55807i | −1.17336 | + | 0.249406i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.78035 | + | 0.997543i | −0.369898 | + | 0.0544204i | ||||
\(337\) | 15.8054 | + | 31.0198i | 0.860974 | + | 1.68976i | 0.713460 | + | 0.700696i | \(0.247127\pi\) |
0.147514 | + | 0.989060i | \(0.452873\pi\) | |||||||
\(338\) | −14.0156 | − | 9.10181i | −0.762346 | − | 0.495073i | ||||
\(339\) | 7.09135 | + | 1.50731i | 0.385149 | + | 0.0818660i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.22447 | − | 10.4653i | −0.120462 | − | 0.566727i | ||||
\(342\) | −3.76502 | − | 23.7714i | −0.203589 | − | 1.28541i | ||||
\(343\) | 5.13855 | + | 17.7931i | 0.277456 | + | 0.960738i | ||||
\(344\) | 3.10660 | − | 4.27587i | 0.167497 | − | 0.230540i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.5459 | − | 3.00029i | 1.53464 | − | 0.161297i | ||||
\(347\) | 20.9357 | + | 16.9534i | 1.12389 | + | 0.910107i | 0.996652 | − | 0.0817651i | \(-0.0260557\pi\) |
0.127237 | + | 0.991872i | \(0.459389\pi\) | |||||||
\(348\) | 0.130394 | + | 2.48806i | 0.00698983 | + | 0.133374i | ||||
\(349\) | −28.9278 | −1.54847 | −0.774236 | − | 0.632897i | \(-0.781866\pi\) | ||||
−0.774236 | + | 0.632897i | \(0.781866\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.2092 | 1.07869 | ||||||||
\(352\) | −0.443841 | − | 8.46898i | −0.0236568 | − | 0.451398i | ||||
\(353\) | −9.06748 | − | 7.34270i | −0.482613 | − | 0.390813i | 0.356908 | − | 0.934140i | \(-0.383831\pi\) |
−0.839521 | + | 0.543327i | \(0.817164\pi\) | |||||||
\(354\) | −11.8764 | + | 1.24826i | −0.631226 | + | 0.0663445i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.7838 | + | 20.3482i | −0.783540 | + | 1.07845i | ||||
\(357\) | 4.50586 | + | 2.06585i | 0.238475 | + | 0.109336i | ||||
\(358\) | −0.526471 | − | 3.32401i | −0.0278248 | − | 0.175679i | ||||
\(359\) | −0.925593 | − | 4.35457i | −0.0488509 | − | 0.229826i | 0.946949 | − | 0.321385i | \(-0.104148\pi\) |
−0.995800 | + | 0.0915592i | \(0.970815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.70326 | − | 1.21227i | −0.300172 | − | 0.0638034i | ||||
\(362\) | −6.09939 | − | 3.96099i | −0.320577 | − | 0.208185i | ||||
\(363\) | 3.73221 | + | 7.32488i | 0.195890 | + | 0.384456i | ||||
\(364\) | −26.7259 | − | 10.5980i | −1.40082 | − | 0.555486i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.00939 | + | 1.91501i | −0.470928 | + | 0.100099i | ||||
\(367\) | −23.9770 | − | 9.20390i | −1.25159 | − | 0.480440i | −0.359858 | − | 0.933007i | \(-0.617175\pi\) |
−0.891730 | + | 0.452567i | \(0.850508\pi\) | |||||||
\(368\) | 18.7473 | − | 5.02332i | 0.977269 | − | 0.261858i | ||||
\(369\) | 1.35140 | − | 12.8577i | 0.0703510 | − | 0.669345i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0469289 | + | 0.739625i | −0.00243643 | + | 0.0383994i | ||||
\(372\) | 3.13945 | − | 19.8217i | 0.162773 | − | 1.02771i | ||||
\(373\) | 35.7641 | − | 1.87432i | 1.85180 | − | 0.0970485i | 0.906291 | − | 0.422655i | \(-0.138902\pi\) |
0.945506 | + | 0.325606i | \(0.105568\pi\) | |||||||
\(374\) | −2.47652 | + | 4.28945i | −0.128058 | + | 0.221802i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.210678 | + | 0.121635i | −0.0108649 | + | 0.00627285i | ||||
\(377\) | 2.63060 | − | 5.16284i | 0.135483 | − | 0.265900i | ||||
\(378\) | 23.9212 | − | 4.81010i | 1.23038 | − | 0.247405i | ||||
\(379\) | 13.3436 | + | 18.3659i | 0.685416 | + | 0.943394i | 0.999983 | − | 0.00584095i | \(-0.00185924\pi\) |
−0.314567 | + | 0.949235i | \(0.601859\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.38946 | + | 9.85889i | 0.224879 | + | 0.505086i | ||||
\(382\) | 1.60434 | + | 5.98747i | 0.0820850 | + | 0.306346i | ||||
\(383\) | 13.6894 | + | 16.9050i | 0.699496 | + | 0.863806i | 0.995825 | − | 0.0912802i | \(-0.0290959\pi\) |
−0.296329 | + | 0.955086i | \(0.595763\pi\) | |||||||
\(384\) | 1.56841 | − | 4.82707i | 0.0800375 | − | 0.246330i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.0142 | − | 33.8984i | −0.560610 | − | 1.72538i | ||||
\(387\) | 8.55574 | − | 13.1747i | 0.434913 | − | 0.669707i | ||||
\(388\) | 11.7406 | + | 0.615300i | 0.596040 | + | 0.0312371i | ||||
\(389\) | −2.70252 | + | 12.7143i | −0.137023 | + | 0.644643i | 0.855004 | + | 0.518621i | \(0.173554\pi\) |
−0.992027 | + | 0.126022i | \(0.959779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.3507 | − | 4.33792i | −0.675176 | − | 0.219378i | ||||
\(392\) | −5.35339 | − | 0.969118i | −0.270387 | − | 0.0489478i | ||||
\(393\) | −2.08085 | − | 2.08085i | −0.104965 | − | 0.104965i | ||||
\(394\) | 40.2478 | + | 4.23021i | 2.02765 | + | 0.213115i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.601477 | + | 5.72267i | 0.0302254 | + | 0.287575i | ||||
\(397\) | 1.71242 | + | 4.46102i | 0.0859441 | + | 0.223892i | 0.969816 | − | 0.243836i | \(-0.0784059\pi\) |
−0.883872 | + | 0.467728i | \(0.845073\pi\) | |||||||
\(398\) | 0.357476 | + | 0.182143i | 0.0179187 | + | 0.00913002i | ||||
\(399\) | 1.83208 | − | 10.7969i | 0.0917187 | − | 0.540522i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.58351 | + | 13.1350i | 0.378702 | + | 0.655932i | 0.990874 | − | 0.134793i | \(-0.0430370\pi\) |
−0.612171 | + | 0.790725i | \(0.709704\pi\) | |||||||
\(402\) | −11.6187 | − | 17.8912i | −0.579488 | − | 0.892333i | ||||
\(403\) | −29.3728 | + | 36.2724i | −1.46316 | + | 1.80685i | ||||
\(404\) | −32.9336 | − | 14.6630i | −1.63851 | − | 0.729511i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.88495 | − | 6.73726i | 0.0935484 | − | 0.334365i | ||||
\(407\) | 4.66850 | − | 4.66850i | 0.231409 | − | 0.231409i | ||||
\(408\) | −1.13160 | + | 0.916352i | −0.0560226 | + | 0.0453662i | ||||
\(409\) | −6.87712 | − | 7.63781i | −0.340052 | − | 0.377666i | 0.548728 | − | 0.836001i | \(-0.315112\pi\) |
−0.888779 | + | 0.458336i | \(0.848446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.67579 | + | 4.21010i | 0.230640 | + | 0.207669i | ||||
\(412\) | 14.3471 | − | 7.31021i | 0.706831 | − | 0.360148i | ||||
\(413\) | 17.7515 | + | 3.97787i | 0.873496 | + | 0.195738i | ||||
\(414\) | −28.5896 | + | 9.28933i | −1.40510 | + | 0.456546i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −27.4933 | + | 24.7551i | −1.34797 | + | 1.21372i | ||||
\(417\) | 2.63197 | − | 6.85652i | 0.128888 | − | 0.335765i | ||||
\(418\) | 10.5699 | + | 2.83220i | 0.516992 | + | 0.138528i | ||||
\(419\) | 14.4852 | + | 10.5241i | 0.707648 | + | 0.514137i | 0.882414 | − | 0.470473i | \(-0.155917\pi\) |
−0.174766 | + | 0.984610i | \(0.555917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.5865 | − | 9.87120i | 0.662168 | − | 0.481093i | −0.205227 | − | 0.978714i | \(-0.565793\pi\) |
0.867394 | + | 0.497621i | \(0.165793\pi\) | |||||||
\(422\) | −12.4224 | + | 4.76852i | −0.604714 | + | 0.232128i | ||||
\(423\) | −0.606403 | + | 0.393803i | −0.0294843 | + | 0.0191473i | ||||
\(424\) | −0.188538 | − | 0.108852i | −0.00915621 | − | 0.00528634i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.57609i | 0.173262i | ||||||||
\(427\) | 13.9373 | + | 1.62013i | 0.674474 | + | 0.0784036i | ||||
\(428\) | 46.0741 | + | 7.29743i | 2.22708 | + | 0.352734i | ||||
\(429\) | −1.62583 | + | 3.65168i | −0.0784959 | + | 0.176305i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.17166 | + | 3.63826i | −0.393615 | + | 0.175249i | −0.593993 | − | 0.804470i | \(-0.702449\pi\) |
0.200378 | + | 0.979719i | \(0.435783\pi\) | |||||||
\(432\) | 3.55996 | − | 13.2859i | 0.171278 | − | 0.639220i | ||||
\(433\) | 17.4040 | − | 2.75652i | 0.836382 | − | 0.132470i | 0.276471 | − | 0.961022i | \(-0.410835\pi\) |
0.559912 | + | 0.828552i | \(0.310835\pi\) | |||||||
\(434\) | −26.1345 | + | 49.9259i | −1.25450 | + | 2.39652i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.3413 | − | 33.6974i | 1.45308 | − | 1.61381i | ||||
\(437\) | −1.62314 | + | 30.9714i | −0.0776454 | + | 1.48156i | ||||
\(438\) | 0.117813 | − | 2.24800i | 0.00562931 | − | 0.107414i | ||||
\(439\) | 18.3365 | − | 20.3647i | 0.875151 | − | 0.971954i | −0.124644 | − | 0.992202i | \(-0.539779\pi\) |
0.999795 | + | 0.0202474i | \(0.00644540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.0404 | − | 2.04375i | −0.763829 | − | 0.0973212i | ||||
\(442\) | 21.3411 | − | 3.38010i | 1.01509 | − | 0.160775i | ||||
\(443\) | 2.86872 | − | 10.7062i | 0.136297 | − | 0.508667i | −0.863692 | − | 0.504019i | \(-0.831854\pi\) |
0.999989 | − | 0.00464732i | \(-0.00147929\pi\) | |||||||
\(444\) | 11.3135 | − | 5.03709i | 0.536914 | − | 0.239050i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.3396 | − | 25.4692i | 0.536947 | − | 1.20600i | ||||
\(447\) | −1.44447 | − | 0.228782i | −0.0683212 | − | 0.0108210i | ||||
\(448\) | −16.8057 | + | 22.6037i | −0.793995 | + | 1.06793i | ||||
\(449\) | − | 40.1154i | − | 1.89316i | −0.322465 | − | 0.946581i | \(-0.604511\pi\) | ||
0.322465 | − | 0.946581i | \(-0.395489\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.09064 | + | 2.93909i | 0.239709 | + | 0.138396i | ||||
\(452\) | 17.3603 | − | 11.2739i | 0.816561 | − | 0.530281i | ||||
\(453\) | 4.86195 | − | 1.86633i | 0.228434 | − | 0.0876878i | ||||
\(454\) | −8.20786 | + | 5.96336i | −0.385214 | + | 0.279874i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.60259 | + | 1.89089i | 0.121877 | + | 0.0885490i | ||||
\(457\) | 32.8230 | + | 8.79489i | 1.53539 | + | 0.411408i | 0.924774 | − | 0.380516i | \(-0.124254\pi\) |
0.610620 | + | 0.791924i | \(0.290920\pi\) | |||||||
\(458\) | −5.01030 | + | 13.0523i | −0.234116 | + | 0.609893i | ||||
\(459\) | −7.39310 | + | 6.65678i | −0.345081 | + | 0.310712i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0506 | − | 9.76402i | 1.39959 | − | 0.454756i | 0.490535 | − | 0.871422i | \(-0.336802\pi\) |
0.909060 | + | 0.416666i | \(0.136802\pi\) | |||||||
\(462\) | −1.05531 | + | 4.70938i | −0.0490973 | + | 0.219100i | ||||
\(463\) | 16.9684 | − | 8.64582i | 0.788587 | − | 0.401805i | −0.0128250 | − | 0.999918i | \(-0.504082\pi\) |
0.801412 | + | 0.598113i | \(0.204082\pi\) | |||||||
\(464\) | −2.93076 | − | 2.63886i | −0.136057 | − | 0.122506i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0799 | + | 13.4161i | 0.559592 | + | 0.621489i | ||||
\(467\) | 4.63073 | − | 3.74989i | 0.214285 | − | 0.173524i | −0.516169 | − | 0.856487i | \(-0.672642\pi\) |
0.730453 | + | 0.682963i | \(0.239309\pi\) | |||||||
\(468\) | 17.7499 | − | 17.7499i | 0.820489 | − | 0.820489i | ||||
\(469\) | 8.06506 | + | 31.4810i | 0.372410 | + | 1.45366i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.20090 | − | 3.65128i | −0.377877 | − | 0.168242i | ||||
\(472\) | −3.36303 | + | 4.15300i | −0.154796 | + | 0.191157i | ||||
\(473\) | 3.89001 | + | 5.99009i | 0.178863 | + | 0.275425i | ||||
\(474\) | 9.40980 | + | 16.2982i | 0.432206 | + | 0.748603i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.2680 | − | 4.92627i | 0.608137 | − | 0.225795i | ||||
\(477\) | −0.576541 | − | 0.293762i | −0.0263980 | − | 0.0134505i | ||||
\(478\) | 14.3754 | + | 37.4491i | 0.657513 | + | 1.71288i | ||||
\(479\) | −2.17952 | − | 20.7367i | −0.0995846 | − | 0.947484i | −0.924231 | − | 0.381835i | \(-0.875292\pi\) |
0.824646 | − | 0.565649i | \(-0.191374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.6439 | − | 3.01060i | −1.30605 | − | 0.137271i | ||||
\(482\) | 38.3695 | + | 38.3695i | 1.74768 | + | 1.74768i | ||||
\(483\) | −13.6774 | − | 0.150524i | −0.622345 | − | 0.00684907i | ||||
\(484\) | 22.3238 | + | 7.25343i | 1.01472 | + | 0.329701i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.93172 | + | 32.6112i | −0.314429 | + | 1.47927i | ||||
\(487\) | −29.3101 | − | 1.53608i | −1.32817 | − | 0.0696064i | −0.624997 | − | 0.780627i | \(-0.714900\pi\) |
−0.703171 | + | 0.711021i | \(0.748233\pi\) | |||||||
\(488\) | −2.24485 | + | 3.45676i | −0.101619 | + | 0.156480i | ||||
\(489\) | 1.43207 | + | 4.40746i | 0.0647605 | + | 0.199312i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.56395 | + | 17.1241i | −0.251097 | + | 0.772798i | 0.743476 | + | 0.668762i | \(0.233176\pi\) |
−0.994574 | + | 0.104036i | \(0.966824\pi\) | |||||||
\(492\) | 6.93886 | + | 8.56878i | 0.312828 | + | 0.386311i | ||||
\(493\) | 0.738256 | + | 2.75521i | 0.0332494 | + | 0.124088i | ||||
\(494\) | −19.4163 | − | 43.6098i | −0.873583 | − | 1.96210i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.6720 | + | 25.6998i | 0.838396 | + | 1.15395i | ||||
\(497\) | 1.74034 | − | 5.16221i | 0.0780648 | − | 0.231557i | ||||
\(498\) | −2.92234 | + | 5.73541i | −0.130953 | + | 0.257010i | ||||
\(499\) | −4.60639 | + | 2.65950i | −0.206210 | + | 0.119056i | −0.599549 | − | 0.800338i | \(-0.704653\pi\) |
0.393339 | + | 0.919394i | \(0.371320\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.35478 | − | 7.54270i | 0.194557 | − | 0.336983i | ||||
\(502\) | 32.1830 | − | 1.68664i | 1.43640 | − | 0.0752784i | ||||
\(503\) | 4.13001 | − | 26.0759i | 0.184148 | − | 1.16267i | −0.706412 | − | 0.707801i | \(-0.749687\pi\) |
0.890560 | − | 0.454865i | \(-0.150313\pi\) | |||||||
\(504\) | 2.63073 | − | 3.95500i | 0.117182 | − | 0.176170i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.42866 | − | 13.5928i | 0.0635119 | − | 0.604275i | ||||
\(507\) | 6.41294 | − | 1.71834i | 0.284809 | − | 0.0763143i | ||||
\(508\) | 28.7668 | + | 11.0425i | 1.27632 | + | 0.489933i | ||||
\(509\) | −4.37813 | + | 0.930600i | −0.194057 | + | 0.0412481i | −0.303915 | − | 0.952699i | \(-0.598294\pi\) |
0.109858 | + | 0.993947i | \(0.464960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.26408 | + | 3.18773i | −0.0559195 | + | 0.141017i | ||||
\(512\) | 13.6320 | + | 26.7543i | 0.602454 | + | 1.18238i | ||||
\(513\) | 18.4332 | + | 11.9707i | 0.813847 | + | 0.528519i | ||||
\(514\) | 62.5192 | + | 13.2889i | 2.75760 | + | 0.586147i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.78545 | + | 13.1045i | 0.122623 | + | 0.576894i | ||||
\(517\) | −0.0514276 | − | 0.324701i | −0.00226178 | − | 0.0142803i | ||||
\(518\) | −34.6217 | + | 3.25411i | −1.52119 | + | 0.142977i | ||||
\(519\) | −6.70259 | + | 9.22532i | −0.294211 | + | 0.404947i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.5618 | + | 2.68665i | −1.11988 | + | 0.117704i | −0.646327 | − | 0.763060i | \(-0.723696\pi\) |
−0.473554 | + | 0.880765i | \(0.657029\pi\) | |||||||
\(522\) | 4.74697 | + | 3.84402i | 0.207769 | + | 0.168248i | ||||
\(523\) | −1.15135 | − | 21.9690i | −0.0503450 | − | 0.960639i | −0.900703 | − | 0.434435i | \(-0.856948\pi\) |
0.850358 | − | 0.526204i | \(-0.176385\pi\) | |||||||
\(524\) | −8.40229 | −0.367056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.852467 | 0.0371693 | ||||||||
\(527\) | −1.20248 | − | 22.9446i | −0.0523807 | − | 0.999483i | ||||
\(528\) | 2.11428 | + | 1.71211i | 0.0920124 | + | 0.0745102i | ||||
\(529\) | 15.6506 | − | 1.64494i | 0.680460 | − | 0.0715192i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.33596 | + | 12.8499i | −0.405146 | + | 0.557636i | ||||
\(532\) | −18.0996 | − | 25.4974i | −0.784717 | − | 1.10545i | ||||
\(533\) | −4.01144 | − | 25.3273i | −0.173755 | − | 1.09705i | ||||
\(534\) | −3.82940 | − | 18.0159i | −0.165714 | − | 0.779624i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.33770 | − | 1.98479i | −0.403327 | − | 0.0857299i | ||||
\(537\) | 1.12132 | + | 0.728191i | 0.0483883 | + | 0.0314238i | ||||
\(538\) | −18.1813 | − | 35.6828i | −0.783852 | − | 1.53840i | ||||
\(539\) | 3.81524 | − | 6.28458i | 0.164334 | − | 0.270696i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.92633 | + | 1.68479i | −0.340780 | + | 0.0724349i | −0.375123 | − | 0.926975i | \(-0.622399\pi\) |
0.0343432 | + | 0.999410i | \(0.489066\pi\) | |||||||
\(542\) | −37.6860 | − | 14.4663i | −1.61875 | − | 0.621381i | ||||
\(543\) | 2.79083 | − | 0.747801i | 0.119766 | − | 0.0320912i | ||||
\(544\) | 1.90367 | − | 18.1122i | 0.0816190 | − | 0.776553i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 18.8631 | − | 9.35118i | 0.807265 | − | 0.400194i | ||||
\(547\) | 3.02255 | − | 19.0836i | 0.129235 | − | 0.815958i | −0.834872 | − | 0.550444i | \(-0.814458\pi\) |
0.964107 | − | 0.265514i | \(-0.0855416\pi\) | |||||||
\(548\) | 17.9402 | − | 0.940206i | 0.766368 | − | 0.0401636i | ||||
\(549\) | −6.12533 | + | 10.6094i | −0.261423 | + | 0.452797i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.45756 | − | 3.15092i | 0.232500 | − | 0.134234i | ||||
\(552\) | 1.82416 | − | 3.58011i | 0.0776412 | − | 0.152379i | ||||
\(553\) | −5.65167 | − | 28.1064i | −0.240333 | − | 1.19521i | ||||
\(554\) | −9.39867 | − | 12.9362i | −0.399311 | − | 0.549605i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.52918 | − | 19.1568i | −0.361718 | − | 0.812431i | ||||
\(557\) | 4.82211 | + | 17.9964i | 0.204320 | + | 0.762531i | 0.989656 | + | 0.143462i | \(0.0458234\pi\) |
−0.785336 | + | 0.619069i | \(0.787510\pi\) | |||||||
\(558\) | −30.9636 | − | 38.2368i | −1.31079 | − | 1.61869i | ||||
\(559\) | 9.62832 | − | 29.6329i | 0.407235 | − | 1.25334i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.608062 | − | 1.87142i | −0.0256724 | − | 0.0790116i | ||||
\(562\) | −21.3154 | + | 32.8229i | −0.899137 | + | 1.38455i | ||||
\(563\) | −21.5909 | − | 1.13153i | −0.909947 | − | 0.0476883i | −0.408385 | − | 0.912810i | \(-0.633908\pi\) |
−0.501562 | + | 0.865122i | \(0.667241\pi\) | |||||||
\(564\) | 0.128209 | − | 0.603174i | 0.00539855 | − | 0.0253982i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.66670 | − | 1.84122i | −0.238189 | − | 0.0773923i | ||||
\(567\) | 4.40287 | − | 7.43581i | 0.184903 | − | 0.312275i | ||||
\(568\) | 1.13157 | + | 1.13157i | 0.0474795 | + | 0.0474795i | ||||
\(569\) | −39.9222 | − | 4.19599i | −1.67362 | − | 0.175905i | −0.780327 | − | 0.625371i | \(-0.784947\pi\) |
−0.893297 | + | 0.449466i | \(0.851614\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.48054 | − | 33.1151i | −0.145656 | − | 1.38582i | −0.786233 | − | 0.617930i | \(-0.787971\pi\) |
0.640577 | − | 0.767894i | \(-0.278695\pi\) | |||||||
\(572\) | 4.09009 | + | 10.6551i | 0.171015 | + | 0.445510i | ||||
\(573\) | −2.19419 | − | 1.11800i | −0.0916638 | − | 0.0467050i | ||||
\(574\) | −10.7765 | − | 29.0245i | −0.449803 | − | 1.21146i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.2962 | − | 21.2976i | −0.512342 | − | 0.887402i | ||||
\(577\) | −3.12235 | − | 4.80800i | −0.129985 | − | 0.200160i | 0.767685 | − | 0.640827i | \(-0.221408\pi\) |
−0.897670 | + | 0.440667i | \(0.854742\pi\) | |||||||
\(578\) | 15.6752 | − | 19.3573i | 0.652002 | − | 0.805156i | ||||
\(579\) | 12.9359 | + | 5.75944i | 0.537598 | + | 0.239354i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.00969 | − | 6.85708i | 0.290811 | − | 0.284480i | ||||
\(582\) | −6.08774 | + | 6.08774i | −0.252345 | + | 0.252345i | ||||
\(583\) | 0.228636 | − | 0.185146i | 0.00946915 | − | 0.00766797i | ||||
\(584\) | −0.674046 | − | 0.748604i | −0.0278922 | − | 0.0309775i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.28538 | − | 1.15736i | −0.0530985 | − | 0.0478101i | ||||
\(587\) | 10.7577 | − | 5.48135i | 0.444020 | − | 0.226239i | −0.217662 | − | 0.976024i | \(-0.569843\pi\) |
0.661682 | + | 0.749785i | \(0.269843\pi\) | |||||||
\(588\) | 10.9056 | − | 8.44069i | 0.449741 | − | 0.348088i | ||||
\(589\) | −48.2769 | + | 15.6861i | −1.98922 | + | 0.646335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.9480 | + | 10.7580i | −0.491475 | + | 0.442526i | ||||
\(592\) | −7.02499 | + | 18.3007i | −0.288725 | + | 0.752155i | ||||
\(593\) | 41.9372 | + | 11.2370i | 1.72215 | + | 0.461449i | 0.978351 | − | 0.206951i | \(-0.0663541\pi\) |
0.743802 | + | 0.668401i | \(0.233021\pi\) | |||||||
\(594\) | −7.83623 | − | 5.69336i | −0.321525 | − | 0.233601i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.37823 | + | 2.45442i | −0.138377 | + | 0.100537i | ||||
\(597\) | −0.148803 | + | 0.0571202i | −0.00609011 | + | 0.00233778i | ||||
\(598\) | −50.0050 | + | 32.4736i | −2.04485 | + | 1.32794i | ||||
\(599\) | 0.677665 | + | 0.391250i | 0.0276887 | + | 0.0159860i | 0.513780 | − | 0.857922i | \(-0.328245\pi\) |
−0.486092 | + | 0.873908i | \(0.661578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.23002i | − | 0.294919i | −0.989068 | − | 0.147459i | \(-0.952890\pi\) | ||
0.989068 | − | 0.147459i | \(-0.0471095\pi\) | |||||||
\(602\) | 4.34375 | − | 37.3675i | 0.177038 | − | 1.52299i | ||||
\(603\) | −28.0244 | − | 4.43864i | −1.14124 | − | 0.180755i | ||||
\(604\) | 6.04803 | − | 13.5841i | 0.246091 | − | 0.552729i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 24.1170 | − | 10.7376i | 0.979686 | − | 0.436184i | ||||
\(607\) | −0.459640 | + | 1.71540i | −0.0186562 | + | 0.0696260i | −0.974626 | − | 0.223838i | \(-0.928141\pi\) |
0.955970 | + | 0.293464i | \(0.0948080\pi\) | |||||||
\(608\) | −39.7405 | + | 6.29427i | −1.61169 | + | 0.255267i | ||||
\(609\) | 1.48800 | + | 2.34747i | 0.0602968 | + | 0.0951245i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.959623 | + | 1.06577i | −0.0388222 | + | 0.0431164i | ||||
\(612\) | −0.646717 | + | 12.3401i | −0.0261420 | + | 0.498819i | ||||
\(613\) | 0.0573433 | − | 1.09418i | 0.00231608 | − | 0.0441934i | −0.997227 | − | 0.0744198i | \(-0.976290\pi\) |
0.999543 | + | 0.0302265i | \(0.00962285\pi\) | |||||||
\(614\) | −20.5783 | + | 22.8545i | −0.830473 | + | 0.922334i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.15624 | + | 1.82410i | 0.0465864 | + | 0.0734950i | ||||
\(617\) | 31.8056 | − | 5.03752i | 1.28045 | − | 0.202803i | 0.521103 | − | 0.853494i | \(-0.325521\pi\) |
0.759343 | + | 0.650691i | \(0.225521\pi\) | |||||||
\(618\) | −3.05185 | + | 11.3897i | −0.122764 | + | 0.458160i | ||||
\(619\) | 16.9052 | − | 7.52667i | 0.679476 | − | 0.302522i | −0.0378261 | − | 0.999284i | \(-0.512043\pi\) |
0.717302 | + | 0.696762i | \(0.245377\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.1658 | − | 25.0789i | 0.448069 | − | 1.00638i | ||||
\(622\) | −24.5386 | − | 3.88654i | −0.983910 | − | 0.155836i | ||||
\(623\) | −3.23974 | + | 27.8702i | −0.129797 | + | 1.11660i | ||||
\(624\) | − | 11.8683i | − | 0.475111i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.2402 | + | 10.5310i | 0.729023 | + | 0.420902i | ||||
\(627\) | −3.64598 | + | 2.36773i | −0.145606 | + | 0.0945578i | ||||
\(628\) | −23.9290 | + | 9.18549i | −0.954871 | + | 0.366541i | ||||
\(629\) | 11.4704 | − | 8.33374i | 0.457355 | − | 0.332288i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.5730 | + | 14.9472i | 0.818998 | + | 0.595037i | 0.916425 | − | 0.400206i | \(-0.131061\pi\) |
−0.0974273 | + | 0.995243i | \(0.531061\pi\) | |||||||
\(632\) | 8.13469 | + | 2.17968i | 0.323580 | + | 0.0867031i | ||||
\(633\) | 1.89443 | − | 4.93515i | 0.0752968 | − | 0.196155i | ||||
\(634\) | 29.3763 | − | 26.4506i | 1.16668 | − | 1.05049i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.524836 | − | 0.170530i | 0.0208111 | − | 0.00676194i | ||||
\(637\) | −31.7803 | + | 4.31887i | −1.25918 | + | 0.171120i | ||||
\(638\) | −2.47450 | + | 1.26082i | −0.0979666 | + | 0.0499165i | ||||
\(639\) | 3.53468 | + | 3.18264i | 0.139830 | + | 0.125903i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.0351 | + | 27.8043i | 0.988828 | + | 1.09820i | 0.995164 | + | 0.0982243i | \(0.0313163\pi\) |
−0.00633676 | + | 0.999980i | \(0.502017\pi\) | |||||||
\(642\) | −26.5475 | + | 21.4978i | −1.04775 | + | 0.848449i | ||||
\(643\) | −14.7951 | + | 14.7951i | −0.583460 | + | 0.583460i | −0.935852 | − | 0.352392i | \(-0.885368\pi\) |
0.352392 | + | 0.935852i | \(0.385368\pi\) | |||||||
\(644\) | −27.9180 | + | 27.3102i | −1.10012 | + | 1.07617i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.4678 | + | 9.55808i | 0.844639 | + | 0.376058i | ||||
\(647\) | −16.2665 | + | 20.0874i | −0.639502 | + | 0.789719i | −0.989110 | − | 0.147177i | \(-0.952981\pi\) |
0.349608 | + | 0.936896i | \(0.386315\pi\) | |||||||
\(648\) | 1.38256 | + | 2.12896i | 0.0543122 | + | 0.0836334i | ||||
\(649\) | −3.61080 | − | 6.25410i | −0.141736 | − | 0.245495i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.79252 | − | 20.9877i | −0.305413 | − | 0.822572i | ||||
\(652\) | 11.7898 | + | 6.00718i | 0.461723 | + | 0.235259i | ||||
\(653\) | −9.42440 | − | 24.5514i | −0.368805 | − | 0.960770i | −0.984904 | − | 0.173101i | \(-0.944621\pi\) |
0.616099 | − | 0.787669i | \(-0.288712\pi\) | |||||||
\(654\) | 3.47089 | + | 33.0234i | 0.135723 | + | 1.29132i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.3573 | − | 1.82432i | −0.677687 | − | 0.0712278i | ||||
\(657\) | −2.11712 | − | 2.11712i | −0.0825967 | − | 0.0825967i | ||||
\(658\) | −0.882215 | + | 1.48993i | −0.0343923 | + | 0.0580836i | ||||
\(659\) | 5.69893 | + | 1.85169i | 0.221999 | + | 0.0721317i | 0.417904 | − | 0.908491i | \(-0.362765\pi\) |
−0.195906 | + | 0.980623i | \(0.562765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.56586 | − | 45.0038i | 0.372069 | − | 1.75045i | −0.250723 | − | 0.968059i | \(-0.580668\pi\) |
0.622792 | − | 0.782387i | \(-0.285998\pi\) | |||||||
\(662\) | −64.9671 | − | 3.40478i | −2.52502 | − | 0.132331i | ||||
\(663\) | −4.67520 | + | 7.19918i | −0.181570 | + | 0.279593i | ||||
\(664\) | 0.890129 | + | 2.73954i | 0.0345437 | + | 0.106315i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.38224 | − | 28.8756i | 0.363555 | − | 1.11891i | ||||
\(667\) | −4.95344 | − | 6.11699i | −0.191798 | − | 0.236851i | ||||
\(668\) | −6.43627 | − | 24.0205i | −0.249027 | − | 0.929381i | ||||
\(669\) | 4.50498 | + | 10.1184i | 0.174173 | + | 0.391198i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.27395 | − | 4.50620i | −0.126389 | − | 0.173960i | ||||
\(672\) | −3.49826 | − | 17.3973i | −0.134948 | − | 0.671114i | ||||
\(673\) | 7.94108 | − | 15.5853i | 0.306106 | − | 0.600767i | −0.685793 | − | 0.727797i | \(-0.740544\pi\) |
0.991899 | + | 0.127030i | \(0.0405443\pi\) | |||||||
\(674\) | −63.0398 | + | 36.3960i | −2.42820 | + | 1.40192i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.47819 | − | 16.4167i | 0.364546 | − | 0.631412i | ||||
\(677\) | −34.8733 | + | 1.82763i | −1.34029 | + | 0.0702417i | −0.708947 | − | 0.705262i | \(-0.750830\pi\) |
−0.631344 | + | 0.775503i | \(0.717496\pi\) | |||||||
\(678\) | −2.37128 | + | 14.9717i | −0.0910685 | + | 0.574984i | ||||
\(679\) | 11.7505 | − | 5.82520i | 0.450943 | − | 0.223551i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.421309 | − | 4.00849i | 0.0161446 | − | 0.153606i | ||||
\(682\) | 21.6081 | − | 5.78987i | 0.827417 | − | 0.221706i | ||||
\(683\) | 37.9867 | + | 14.5817i | 1.45352 | + | 0.557954i | 0.951703 | − | 0.307020i | \(-0.0993318\pi\) |
0.501817 | + | 0.864974i | \(0.332665\pi\) | |||||||
\(684\) | 26.7039 | − | 5.67610i | 1.02105 | − | 0.217031i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −36.5897 | + | 12.6763i | −1.39700 | + | 0.483985i | ||||
\(687\) | −2.52160 | − | 4.94891i | −0.0962049 | − | 0.188813i | ||||
\(688\) | −17.7852 | − | 11.5498i | −0.678053 | − | 0.440333i | ||||
\(689\) | −1.25537 | − | 0.266838i | −0.0478260 | − | 0.0101657i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.69969 | − | 17.4057i | −0.140743 | − | 0.662144i | −0.990787 | − | 0.135432i | \(-0.956758\pi\) |
0.850044 | − | 0.526712i | \(-0.176575\pi\) | |||||||
\(692\) | 5.09328 | + | 32.1577i | 0.193618 | + | 1.22245i | ||||
\(693\) | 3.71565 | + | 5.23434i | 0.141146 | + | 0.198836i | ||||
\(694\) | −33.1078 | + | 45.5689i | −1.25675 | + | 1.72977i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.811972 | + | 0.0853417i | −0.0307777 | + | 0.00323487i | ||||
\(697\) | 9.81012 | + | 7.94408i | 0.371585 | + | 0.300903i | ||||
\(698\) | −3.16550 | − | 60.4013i | −0.119816 | − | 2.28622i | ||||
\(699\) | −7.17212 | −0.271275 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.8675 | −0.788156 | −0.394078 | − | 0.919077i | \(-0.628936\pi\) | ||||
−0.394078 | + | 0.919077i | \(0.628936\pi\) | |||||||
\(702\) | 2.21144 | + | 42.1969i | 0.0834656 | + | 1.59262i | ||||
\(703\) | −24.3434 | − | 19.7129i | −0.918128 | − | 0.743485i | ||||
\(704\) | 11.1201 | − | 1.16877i | 0.419105 | − | 0.0440497i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.3393 | − | 19.7364i | 0.539667 | − | 0.742788i | ||||
\(707\) | −40.0393 | + | 3.76330i | −1.50583 | + | 0.141533i | ||||
\(708\) | −2.11905 | − | 13.3791i | −0.0796387 | − | 0.502819i | ||||
\(709\) | −0.161305 | − | 0.758882i | −0.00605795 | − | 0.0285004i | 0.975015 | − | 0.222140i | \(-0.0713041\pi\) |
−0.981073 | + | 0.193639i | \(0.937971\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.4840 | + | 5.20424i | 0.918223 | + | 0.195174i | ||||
\(712\) | −6.91241 | − | 4.48897i | −0.259054 | − | 0.168231i | ||||
\(713\) | 28.7838 | + | 56.4913i | 1.07796 | + | 2.11562i | ||||
\(714\) | −3.82042 | + | 9.63428i | −0.142976 | + | 0.360554i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.73407 | − | 0.793701i | 0.139549 | − | 0.0296620i | ||||
\(717\) | −14.8777 | − | 5.71101i | −0.555618 | − | 0.213282i | ||||
\(718\) | 8.99106 | − | 2.40915i | 0.335543 | − | 0.0899086i | ||||
\(719\) | 3.85474 | − | 36.6754i | 0.143757 | − | 1.36776i | −0.650189 | − | 0.759773i | \(-0.725310\pi\) |
0.793946 | − | 0.607988i | \(-0.208023\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.94835 | − | 14.9562i | 0.370496 | − | 0.556997i | ||||
\(722\) | 1.90712 | − | 12.0411i | 0.0709755 | − | 0.448122i | ||||
\(723\) | −21.5278 | + | 1.12822i | −0.800628 | + | 0.0419591i | ||||
\(724\) | 4.12478 | − | 7.14434i | 0.153296 | − | 0.265517i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.8859 | + | 8.59439i | −0.552468 | + | 0.318968i | ||||
\(727\) | 9.04006 | − | 17.7421i | 0.335277 | − | 0.658019i | −0.660398 | − | 0.750915i | \(-0.729613\pi\) |
0.995676 | + | 0.0928967i | \(0.0296126\pi\) | |||||||
\(728\) | 3.00980 | − | 8.92772i | 0.111551 | − | 0.330883i | ||||
\(729\) | −2.02583 | − | 2.78831i | −0.0750307 | − | 0.103271i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.23857 | + | 14.0121i | 0.230742 | + | 0.518254i | ||||
\(732\) | −2.70410 | − | 10.0919i | −0.0999466 | − | 0.373006i | ||||
\(733\) | −0.0252173 | − | 0.0311408i | −0.000931422 | − | 0.00115021i | 0.776680 | − | 0.629895i | \(-0.216902\pi\) |
−0.777611 | + | 0.628745i | \(0.783569\pi\) | |||||||
\(734\) | 16.5940 | − | 51.0711i | 0.612496 | − | 1.88507i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.5297 | + | 47.7955i | 0.572432 | + | 1.76177i | ||||
\(737\) | 7.02618 | − | 10.8194i | 0.258813 | − | 0.398537i | ||||
\(738\) | 26.9947 | + | 1.41473i | 0.993689 | + | 0.0520771i | ||||
\(739\) | 4.01685 | − | 18.8978i | 0.147762 | − | 0.695167i | −0.840427 | − | 0.541925i | \(-0.817696\pi\) |
0.988189 | − | 0.153241i | \(-0.0489712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.0366 | + | 5.86045i | 0.662592 | + | 0.215289i | ||||
\(742\) | −1.54947 | − | 0.0170523i | −0.0568829 | − | 0.000626011i | ||||
\(743\) | 16.7789 | + | 16.7789i | 0.615557 | + | 0.615557i | 0.944389 | − | 0.328831i | \(-0.106655\pi\) |
−0.328831 | + | 0.944389i | \(0.606655\pi\) | |||||||
\(744\) | 6.54044 | + | 0.687427i | 0.239784 | + | 0.0252023i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.82715 | + | 74.4703i | 0.286572 | + | 2.72655i | ||||
\(747\) | 3.06818 | + | 7.99289i | 0.112259 | + | 0.292445i | ||||
\(748\) | −5.00597 | − | 2.55067i | −0.183036 | − | 0.0932617i | ||||
\(749\) | 48.7843 | − | 18.1132i | 1.78254 | − | 0.661840i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.63402 | − | 11.4905i | −0.242079 | − | 0.419293i | 0.719227 | − | 0.694775i | \(-0.244496\pi\) |
−0.961306 | + | 0.275482i | \(0.911163\pi\) | |||||||
\(752\) | 0.531615 | + | 0.818615i | 0.0193860 | + | 0.0298518i | ||||
\(753\) | −8.05728 | + | 9.94991i | −0.293623 | + | 0.362595i | ||||
\(754\) | 11.0679 | + | 4.92773i | 0.403068 | + | 0.179457i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.86883 | + | 26.8116i | 0.249817 | + | 0.975130i | ||||
\(757\) | 1.13591 | − | 1.13591i | 0.0412853 | − | 0.0412853i | −0.686163 | − | 0.727448i | \(-0.740706\pi\) |
0.727448 | + | 0.686163i | \(0.240706\pi\) | |||||||
\(758\) | −36.8879 | + | 29.8712i | −1.33983 | + | 1.08497i | ||||
\(759\) | 3.63330 | + | 4.03519i | 0.131880 | + | 0.146468i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.6079 | − | 21.2567i | −0.855787 | − | 0.770554i | 0.119187 | − | 0.992872i | \(-0.461971\pi\) |
−0.974974 | + | 0.222318i | \(0.928638\pi\) | |||||||
\(762\) | −20.1050 | + | 10.2440i | −0.728328 | + | 0.371102i | ||||
\(763\) | 11.0608 | − | 49.3595i | 0.400427 | − | 1.78693i | ||||
\(764\) | −6.68717 | + | 2.17279i | −0.241933 | + | 0.0786089i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.7996 | + | 30.4333i | −1.22123 | + | 1.09960i | ||||
\(767\) | −11.2899 | + | 29.4111i | −0.407654 | + | 1.06197i | ||||
\(768\) | −6.83311 | − | 1.83093i | −0.246569 | − | 0.0660679i | ||||
\(769\) | 11.1412 | + | 8.09458i | 0.401763 | + | 0.291898i | 0.770259 | − | 0.637731i | \(-0.220127\pi\) |
−0.368495 | + | 0.929630i | \(0.620127\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.5429 | + | 14.9253i | −0.739834 | + | 0.537521i | ||||
\(772\) | 37.7451 | − | 14.4890i | 1.35848 | − | 0.521470i | ||||
\(773\) | −8.42289 | + | 5.46989i | −0.302950 | + | 0.196738i | −0.687157 | − | 0.726509i | \(-0.741142\pi\) |
0.384207 | + | 0.923247i | \(0.374475\pi\) | |||||||
\(774\) | 28.4449 | + | 16.4227i | 1.02243 | + | 0.590302i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.85263i | 0.138301i | ||||||||
\(777\) | 8.24280 | − | 11.0866i | 0.295709 | − | 0.397729i | ||||
\(778\) | −26.8433 | − | 4.25155i | −0.962377 | − | 0.152426i | ||||
\(779\) | 11.3434 | − | 25.4776i | 0.406418 | − | 0.912830i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.97561 | + | 0.879597i | −0.0706928 | + | 0.0314745i | ||||
\(782\) | 7.59663 | − | 28.3510i | 0.271655 | − | 1.01383i | ||||
\(783\) | −5.50947 | + | 0.872614i | −0.196892 | + | 0.0311847i | ||||
\(784\) | −2.75896 | + | 21.6538i | −0.0985341 | + | 0.773349i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.11711 | − | 4.57252i | 0.146853 | − | 0.163096i | ||||
\(787\) | 1.12669 | − | 21.4984i | 0.0401620 | − | 0.766337i | −0.902114 | − | 0.431499i | \(-0.857985\pi\) |
0.942276 | − | 0.334838i | \(-0.108682\pi\) | |||||||
\(788\) | −2.40250 | + | 45.8425i | −0.0855856 | + | 1.63307i | ||||
\(789\) | −0.226612 | + | 0.251678i | −0.00806760 | + | 0.00895998i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7091 | − | 20.4581i | 0.380773 | − | 0.727407i | ||||
\(792\) | −1.86241 | + | 0.294977i | −0.0661779 | + | 0.0104815i | ||||
\(793\) | −6.28891 | + | 23.4705i | −0.223326 | + | 0.833463i | ||||
\(794\) | −9.12721 | + | 4.06369i | −0.323912 | + | 0.144215i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.185104 | + | 0.415750i | −0.00656084 | + | 0.0147359i | ||||
\(797\) | 5.20937 | + | 0.825084i | 0.184526 | + | 0.0292260i | 0.248013 | − | 0.968757i | \(-0.420222\pi\) |
−0.0634877 | + | 0.997983i | \(0.520222\pi\) | |||||||
\(798\) | 22.7444 | + | 2.64390i | 0.805144 | + | 0.0935931i | ||||
\(799\) | − | 0.705981i | − | 0.0249758i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.2154 | − | 12.2487i | −0.749608 | − | 0.432786i | ||||
\(802\) | −26.5961 | + | 17.2717i | −0.939140 | + | 0.609885i | ||||
\(803\) | 1.27088 | − | 0.487846i | 0.0448485 | − | 0.0172157i | ||||
\(804\) | 19.5768 | − | 14.2234i | 0.690422 | − | 0.501621i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −78.9508 | − | 57.3611i | −2.78092 | − | 2.02046i | ||||
\(807\) | 15.3680 | + | 4.11784i | 0.540979 | + | 0.144955i | ||||
\(808\) | 4.23359 | − | 11.0289i | 0.148937 | − | 0.387995i | ||||
\(809\) | 6.16004 | − | 5.54653i | 0.216575 | − | 0.195005i | −0.553701 | − | 0.832716i | \(-0.686785\pi\) |
0.770276 | + | 0.637710i | \(0.220118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.9445 | + | 7.45511i | −0.805689 | + | 0.261784i | −0.682771 | − | 0.730632i | \(-0.739225\pi\) |
−0.122918 | + | 0.992417i | \(0.539225\pi\) | |||||||
\(812\) | 7.74365 | + | 1.73524i | 0.271749 | + | 0.0608951i | ||||
\(813\) | 14.2891 | − | 7.28065i | 0.501140 | − | 0.255343i | ||||
\(814\) | 10.2587 | + | 9.23695i | 0.359566 | + | 0.323755i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.90932 | + | 4.34174i | 0.136854 | + | 0.151991i | ||||
\(817\) | 26.3349 | − | 21.3255i | 0.921340 | − | 0.746087i | ||||
\(818\) | 15.1952 | − | 15.1952i | 0.531288 | − | 0.531288i | ||||
\(819\) | 7.54481 | − | 26.9670i | 0.263637 | − | 0.942303i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.2681 | + | 4.57166i | 0.358359 | + | 0.159552i | 0.578016 | − | 0.816025i | \(-0.303827\pi\) |
−0.219657 | + | 0.975577i | \(0.570494\pi\) | |||||||
\(822\) | −8.27902 | + | 10.2237i | −0.288764 | + | 0.356594i | ||||
\(823\) | 9.34851 | + | 14.3955i | 0.325869 | + | 0.501794i | 0.963196 | − | 0.268799i | \(-0.0866268\pi\) |
−0.637327 | + | 0.770593i | \(0.719960\pi\) | |||||||
\(824\) | 2.63830 | + | 4.56967i | 0.0919096 | + | 0.159192i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.36329 | + | 37.5005i | −0.221407 | + | 1.30481i | ||||
\(827\) | −20.7397 | − | 10.5674i | −0.721190 | − | 0.367465i | 0.0545555 | − | 0.998511i | \(-0.482626\pi\) |
−0.775745 | + | 0.631046i | \(0.782626\pi\) | |||||||
\(828\) | −12.2199 | − | 31.8339i | −0.424671 | − | 1.10630i | ||||
\(829\) | 2.64740 | + | 25.1883i | 0.0919480 | + | 0.874827i | 0.939139 | + | 0.343538i | \(0.111625\pi\) |
−0.847191 | + | 0.531289i | \(0.821708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.31767 | + | 0.664014i | 0.219157 | + | 0.0230344i | ||||
\(832\) | −34.4910 | − | 34.4910i | −1.19576 | − | 1.19576i | ||||
\(833\) | 10.2035 | − | 12.0482i | 0.353531 | − | 0.417445i | ||||
\(834\) | 14.6044 | + | 4.74526i | 0.505710 | + | 0.164315i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.58073 | + | 12.1414i | −0.0892565 | + | 0.419919i | ||||
\(837\) | 44.8703 | + | 2.35155i | 1.55095 | + | 0.0812816i | ||||
\(838\) | −20.3893 | + | 31.3967i | −0.704335 | + | 1.08458i | ||||
\(839\) | 17.1783 | + | 52.8695i | 0.593062 | + | 1.82526i | 0.564144 | + | 0.825677i | \(0.309206\pi\) |
0.0289189 | + | 0.999582i | \(0.490794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.46726 | − | 26.0596i | 0.291975 | − | 0.898605i | ||||
\(842\) | 22.0978 | + | 27.2885i | 0.761540 | + | 0.940424i | ||||
\(843\) | −4.02417 | − | 15.0184i | −0.138600 | − | 0.517261i | ||||
\(844\) | −6.13909 | − | 13.7886i | −0.211316 | − | 0.474624i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.888617 | − | 1.22308i | −0.0305513 | − | 0.0420502i | ||||
\(847\) | 25.6709 | − | 5.16193i | 0.882062 | − | 0.177366i | ||||
\(848\) | −0.396565 | + | 0.778302i | −0.0136181 | + | 0.0267270i | ||||
\(849\) | 2.04998 | − | 1.18355i | 0.0703550 | − | 0.0406195i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.5621 | + | 33.8826i | −0.670581 | + | 1.16148i | ||||
\(852\) | −4.05088 | + | 0.212298i | −0.138781 | + | 0.00727319i | ||||
\(853\) | −6.62710 | + | 41.8419i | −0.226908 | + | 1.43264i | 0.566557 | + | 0.824023i | \(0.308275\pi\) |
−0.793465 | + | 0.608616i | \(0.791725\pi\) | |||||||
\(854\) | −1.85770 | + | 29.2784i | −0.0635693 | + | 1.00189i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.59787 | + | 15.2028i | −0.0546142 | + | 0.519620i | ||||
\(857\) | −36.7601 | + | 9.84983i | −1.25570 | + | 0.336464i | −0.824536 | − | 0.565810i | \(-0.808564\pi\) |
−0.431164 | + | 0.902274i | \(0.641897\pi\) | |||||||
\(858\) | −7.80261 | − | 2.99514i | −0.266377 | − | 0.102252i | ||||
\(859\) | −50.1863 | + | 10.6674i | −1.71233 | + | 0.363968i | −0.956711 | − | 0.291040i | \(-0.905999\pi\) |
−0.755622 | + | 0.655008i | \(0.772665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4338 | + | 4.53401i | 0.389663 | + | 0.154519i | ||||
\(862\) | −8.49088 | − | 16.6643i | −0.289200 | − | 0.567588i | ||||
\(863\) | −18.3280 | − | 11.9023i | −0.623893 | − | 0.405161i | 0.193616 | − | 0.981077i | \(-0.437979\pi\) |
−0.817508 | + | 0.575917i | \(0.804645\pi\) | |||||||
\(864\) | 34.8369 | + | 7.40481i | 1.18517 | + | 0.251917i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.66009 | + | 36.0379i | 0.260300 | + | 1.22462i | ||||
\(867\) | 1.54799 | + | 9.77363i | 0.0525725 | + | 0.331930i | ||||
\(868\) | −58.1060 | − | 26.6404i | −1.97224 | − | 0.904236i | ||||
\(869\) | −6.68946 | + | 9.20725i | −0.226924 | + | 0.312334i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −55.9695 | + | 5.88263i | −1.89645 | + | 0.199325i | ||||
\(872\) | 11.5477 | + | 9.35116i | 0.391055 | + | 0.316670i | ||||
\(873\) | 0.599293 | + | 11.4352i | 0.0202830 | + | 0.387023i | ||||
\(874\) | −64.8458 | −2.19344 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.55345 | 0.0862732 | ||||||||
\(877\) | 0.0741129 | + | 1.41416i | 0.00250261 | + | 0.0477527i | 0.999595 | − | 0.0284446i | \(-0.00905543\pi\) |
−0.997093 | + | 0.0761974i | \(0.975722\pi\) | |||||||
\(878\) | 44.5280 | + | 36.0580i | 1.50275 | + | 1.21690i | ||||
\(879\) | 0.683387 | − | 0.0718269i | 0.0230501 | − | 0.00242266i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.05676 | − | 6.96003i | 0.170367 | − | 0.234489i | −0.715293 | − | 0.698825i | \(-0.753707\pi\) |
0.885659 | + | 0.464335i | \(0.153707\pi\) | |||||||
\(882\) | 2.51208 | − | 33.7160i | 0.0845860 | − | 1.13528i | ||||
\(883\) | 6.37108 | + | 40.2254i | 0.214404 | + | 1.35369i | 0.826512 | + | 0.562919i | \(0.190322\pi\) |
−0.612108 | + | 0.790774i | \(0.709678\pi\) | |||||||
\(884\) | 5.09580 | + | 23.9739i | 0.171390 | + | 0.806328i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.6684 | + | 4.81832i | 0.761561 | + | 0.161875i | ||||
\(887\) | −20.8067 | − | 13.5120i | −0.698619 | − | 0.453689i | 0.145840 | − | 0.989308i | \(-0.453411\pi\) |
−0.844459 | + | 0.535619i | \(0.820078\pi\) | |||||||
\(888\) | 1.84240 | + | 3.61591i | 0.0618269 | + | 0.121342i | ||||
\(889\) | 34.0076 | − | 5.00330i | 1.14058 | − | 0.167805i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.35549 | + | 0.713231i | −0.112413 | + | 0.0238941i | ||||
\(892\) | 29.5239 | + | 11.3331i | 0.988532 | + | 0.379462i | ||||
\(893\) | −1.50658 | + | 0.403688i | −0.0504159 | + | 0.0135089i | ||||
\(894\) | 0.319632 | − | 3.04109i | 0.0106901 | − | 0.101709i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.4603 | − | 8.95336i | −0.449678 | − | 0.299111i | ||||
\(897\) | 3.70552 | − | 23.3957i | 0.123724 | − | 0.781160i | ||||
\(898\) | 83.7609 | − | 4.38972i | 2.79514 | − | 0.146487i | ||||
\(899\) | 6.44144 | − | 11.1569i | 0.214834 | − | 0.372103i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.547146 | − | 0.315895i | 0.0182281 | − | 0.0105240i | ||||
\(902\) | −5.57975 | + | 10.9509i | −0.185785 | + | 0.364624i | ||||
\(903\) | 9.87750 | + | 11.2159i | 0.328703 | + | 0.373241i | ||||
\(904\) | 3.98709 | + | 5.48776i | 0.132609 | + | 0.182520i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.42892 | + | 9.94752i | 0.147141 | + | 0.330484i | ||||
\(907\) | −8.07670 | − | 30.1426i | −0.268182 | − | 1.00087i | −0.960274 | − | 0.279060i | \(-0.909977\pi\) |
0.692091 | − | 0.721810i | \(-0.256690\pi\) | |||||||
\(908\) | −7.24236 | − | 8.94357i | −0.240346 | − | 0.296803i | ||||
\(909\) | 10.8504 | − | 33.3940i | 0.359883 | − | 1.10761i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.4702 | − | 35.3017i | −0.380025 | − | 1.16960i | −0.940025 | − | 0.341105i | \(-0.889199\pi\) |
0.560000 | − | 0.828492i | \(-0.310801\pi\) | |||||||
\(912\) | 7.03001 | − | 10.8253i | 0.232787 | − | 0.358460i | ||||
\(913\) | −3.88732 | − | 0.203726i | −0.128651 | − | 0.00674234i | ||||
\(914\) | −14.7720 | + | 69.4967i | −0.488614 | + | 2.29875i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.0826 | − | 4.90064i | −0.498344 | − | 0.161922i | ||||
\(917\) | −8.16845 | + | 4.59695i | −0.269746 | + | 0.151805i | ||||
\(918\) | −14.7084 | − | 14.7084i | −0.485448 | − | 0.485448i | ||||
\(919\) | 42.2670 | + | 4.44244i | 1.39426 | + | 0.146543i | 0.771678 | − | 0.636013i | \(-0.219417\pi\) |
0.622581 | + | 0.782555i | \(0.286084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.27711 | − | 12.1509i | −0.0420822 | − | 0.400385i | ||||
\(922\) | 23.6756 | + | 61.6771i | 0.779715 | + | 2.03123i | ||||
\(923\) | 8.40577 | + | 4.28295i | 0.276679 | + | 0.140975i | ||||
\(924\) | −5.39729 | − | 0.915841i | −0.177558 | − | 0.0301290i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19.9093 | + | 34.4838i | 0.654259 | + | 1.13321i | ||||
\(927\) | 8.54171 | + | 13.1531i | 0.280546 | + | 0.432004i | ||||
\(928\) | 6.42635 | − | 7.93588i | 0.210955 | − | 0.260508i | ||||
\(929\) | −13.8640 | − | 6.17267i | −0.454864 | − | 0.202519i | 0.166498 | − | 0.986042i | \(-0.446754\pi\) |
−0.621363 | + | 0.783523i | \(0.713421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.5457 | − | 14.8853i | −1.03387 | − | 0.487848i | ||||
\(932\) | −14.4802 | + | 14.4802i | −0.474315 | + | 0.474315i | ||||
\(933\) | 7.67057 | − | 6.21151i | 0.251123 | − | 0.203356i | ||||
\(934\) | 8.33650 | + | 9.25862i | 0.272778 | + | 0.302951i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.11301 | + | 5.50418i | 0.199810 | + | 0.179910i | ||||
\(937\) | 22.2665 | − | 11.3453i | 0.727415 | − | 0.370636i | −0.0507375 | − | 0.998712i | \(-0.516157\pi\) |
0.778152 | + | 0.628076i | \(0.216157\pi\) | |||||||
\(938\) | −64.8497 | + | 20.2847i | −2.11742 | + | 0.662319i | ||||
\(939\) | −7.95790 | + | 2.58568i | −0.259696 | + | 0.0843805i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3945 | − | 11.1600i | 0.404049 | − | 0.363807i | −0.441906 | − | 0.897061i | \(-0.645698\pi\) |
0.845955 | + | 0.533254i | \(0.179031\pi\) | |||||||
\(942\) | 6.72646 | − | 17.5230i | 0.219160 | − | 0.570931i | ||||
\(943\) | −33.6465 | − | 9.01555i | −1.09568 | − | 0.293587i | ||||
\(944\) | 17.3467 | + | 12.6031i | 0.564586 | + | 0.410196i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0816 | + | 8.77782i | −0.392808 | + | 0.285392i | ||||
\(947\) | 22.3303 | − | 8.57180i | 0.725637 | − | 0.278546i | 0.0326209 | − | 0.999468i | \(-0.489615\pi\) |
0.693017 | + | 0.720922i | \(0.256281\pi\) | |||||||
\(948\) | −17.9035 | + | 11.6267i | −0.581478 | + | 0.377617i | ||||
\(949\) | −5.14293 | − | 2.96927i | −0.166947 | − | 0.0963866i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.7043i | 0.509247i | ||||||||
\(952\) | 1.83966 | + | 4.25742i | 0.0596236 | + | 0.137984i | ||||
\(953\) | 52.6232 | + | 8.33470i | 1.70463 | + | 0.269987i | 0.931364 | − | 0.364090i | \(-0.118620\pi\) |
0.773270 | + | 0.634077i | \(0.218620\pi\) | |||||||
\(954\) | 0.550286 | − | 1.23596i | 0.0178162 | − | 0.0400158i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −41.5677 | + | 18.5071i | −1.34440 | + | 0.598563i | ||||
\(957\) | 0.285561 | − | 1.06573i | 0.00923086 | − | 0.0344500i | ||||
\(958\) | 43.0597 | − | 6.81999i | 1.39120 | − | 0.220344i | ||||
\(959\) | 16.9265 | − | 10.7293i | 0.546586 | − | 0.346466i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −48.6936 | + | 54.0798i | −1.57076 | + | 1.74451i | ||||
\(962\) | 3.15169 | − | 60.1379i | 0.101615 | − | 1.93892i | ||||
\(963\) | −2.37788 | + | 45.3726i | −0.0766261 | + | 1.46211i | ||||
\(964\) | −41.1858 | + | 45.7415i | −1.32651 | + | 1.47323i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.18239 | − | 28.5749i | −0.0380429 | − | 0.919384i | ||||
\(967\) | −31.4763 | + | 4.98535i | −1.01221 | + | 0.160318i | −0.640441 | − | 0.768008i | \(-0.721248\pi\) |
−0.371768 | + | 0.928326i | \(0.621248\pi\) | |||||||
\(968\) | −1.99080 | + | 7.42978i | −0.0639868 | + | 0.238802i | ||||
\(969\) | −8.52869 | + | 3.79722i | −0.273981 | + | 0.121984i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.7478 | + | 35.3701i | −0.505370 | + | 1.13508i | 0.463180 | + | 0.886264i | \(0.346708\pi\) |
−0.968551 | + | 0.248816i | \(0.919958\pi\) | |||||||
\(972\) | −37.3524 | − | 5.91604i | −1.19808 | − | 0.189757i | ||||
\(973\) | −18.7727 | − | 13.9573i | −0.601824 | − | 0.447451i | ||||
\(974\) | − | 61.3676i | − | 1.96634i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.3221 | + | 8.26889i | 0.458441 | + | 0.264681i | ||||
\(977\) | 24.2449 | − | 15.7448i | 0.775663 | − | 0.503721i | −0.0950743 | − | 0.995470i | \(-0.530309\pi\) |
0.870737 | + | 0.491749i | \(0.163642\pi\) | |||||||
\(978\) | −9.04607 | + | 3.47246i | −0.289261 | + | 0.111037i | ||||
\(979\) | 9.01096 | − | 6.54684i | 0.287991 | − | 0.209238i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.7300 | + | 25.9594i | 1.14077 | + | 0.828818i | ||||
\(982\) | −36.3639 | − | 9.74367i | −1.16042 | − | 0.310933i | ||||
\(983\) | −3.50625 | + | 9.13410i | −0.111832 | + | 0.291332i | −0.978062 | − | 0.208313i | \(-0.933203\pi\) |
0.866230 | + | 0.499645i | \(0.166536\pi\) | |||||||
\(984\) | −2.68510 | + | 2.41768i | −0.0855979 | + | 0.0770727i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.67209 | + | 1.84297i | −0.180636 | + | 0.0586922i | ||||
\(987\) | −0.205360 | − | 0.656531i | −0.00653669 | − | 0.0208976i | ||||
\(988\) | 48.2471 | − | 24.5831i | 1.53494 | − | 0.782093i | ||||
\(989\) | −31.4535 | − | 28.3209i | −1.00016 | − | 0.900552i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.3474 | − | 18.1556i | −0.519291 | − | 0.576732i | 0.425270 | − | 0.905067i | \(-0.360179\pi\) |
−0.944561 | + | 0.328335i | \(0.893513\pi\) | |||||||
\(992\) | −63.9235 | + | 51.7642i | −2.02957 | + | 1.64352i | ||||
\(993\) | 18.2755 | − | 18.2755i | 0.579955 | − | 0.579955i | ||||
\(994\) | 10.9691 | + | 3.06894i | 0.347920 | + | 0.0973408i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.67037 | − | 2.96984i | −0.211359 | − | 0.0941030i | ||||
\(997\) | 13.7449 | − | 16.9735i | 0.435305 | − | 0.537556i | −0.511535 | − | 0.859262i | \(-0.670923\pi\) |
0.946840 | + | 0.321706i | \(0.104256\pi\) | |||||||
\(998\) | −6.05710 | − | 9.32712i | −0.191734 | − | 0.295245i | ||||
\(999\) | 13.8634 | + | 24.0121i | 0.438619 | + | 0.759710i |
(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 | 875.2.bb.b.143.16 | 288 | ||
5.2 | odd | 4 | 175.2.x.a.17.3 | yes | 288 | ||
5.3 | odd | 4 | 875.2.bb.c.857.16 | 288 | |||
5.4 | even | 2 | 875.2.bb.a.143.3 | 288 | |||
7.5 | odd | 6 | inner | 875.2.bb.b.768.16 | 288 | ||
25.3 | odd | 20 | 875.2.bb.a.507.3 | 288 | |||
25.4 | even | 10 | 875.2.bb.c.493.3 | 288 | |||
25.21 | even | 5 | 175.2.x.a.3.16 | ✓ | 288 | ||
25.22 | odd | 20 | inner | 875.2.bb.b.507.16 | 288 | ||
35.12 | even | 12 | 175.2.x.a.117.16 | yes | 288 | ||
35.19 | odd | 6 | 875.2.bb.a.768.3 | 288 | |||
35.33 | even | 12 | 875.2.bb.c.607.3 | 288 | |||
175.47 | even | 60 | inner | 875.2.bb.b.257.16 | 288 | ||
175.54 | odd | 30 | 875.2.bb.c.243.16 | 288 | |||
175.96 | odd | 30 | 175.2.x.a.103.3 | yes | 288 | ||
175.103 | even | 60 | 875.2.bb.a.257.3 | 288 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.x.a.3.16 | ✓ | 288 | 25.21 | even | 5 | ||
175.2.x.a.17.3 | yes | 288 | 5.2 | odd | 4 | ||
175.2.x.a.103.3 | yes | 288 | 175.96 | odd | 30 | ||
175.2.x.a.117.16 | yes | 288 | 35.12 | even | 12 | ||
875.2.bb.a.143.3 | 288 | 5.4 | even | 2 | |||
875.2.bb.a.257.3 | 288 | 175.103 | even | 60 | |||
875.2.bb.a.507.3 | 288 | 25.3 | odd | 20 | |||
875.2.bb.a.768.3 | 288 | 35.19 | odd | 6 | |||
875.2.bb.b.143.16 | 288 | 1.1 | even | 1 | trivial | ||
875.2.bb.b.257.16 | 288 | 175.47 | even | 60 | inner | ||
875.2.bb.b.507.16 | 288 | 25.22 | odd | 20 | inner | ||
875.2.bb.b.768.16 | 288 | 7.5 | odd | 6 | inner | ||
875.2.bb.c.243.16 | 288 | 175.54 | odd | 30 | |||
875.2.bb.c.493.3 | 288 | 25.4 | even | 10 | |||
875.2.bb.c.607.3 | 288 | 35.33 | even | 12 | |||
875.2.bb.c.857.16 | 288 | 5.3 | odd | 4 |