Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [93,2,Mod(4,93)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(93, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("93.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 93 = 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 93.f (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.742608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 13 x^{14} - 28 x^{13} + 90 x^{12} - 119 x^{11} + 382 x^{10} - 356 x^{9} + 1869 x^{8} - 2812 x^{7} + 5846 x^{6} - 4987 x^{5} + 4006 x^{4} - 1014 x^{3} + 2493 x^{2} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 64.2 | ||
Root | \(0.968675 + 0.703784i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 93.64 |
Dual form | 93.2.f.b.16.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).
\(n\) | \(32\) | \(34\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.968675 | − | 0.703784i | −0.684957 | − | 0.497650i | 0.190042 | − | 0.981776i | \(-0.439138\pi\) |
−0.874998 | + | 0.484126i | \(0.839138\pi\) | |||||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −0.175014 | − | 0.538638i | −0.0875071 | − | 0.269319i | ||||
\(5\) | −2.70381 | −1.20918 | −0.604591 | − | 0.796536i | \(-0.706663\pi\) | ||||
−0.604591 | + | 0.796536i | \(0.706663\pi\) | |||||||
\(6\) | 1.19735 | 0.488815 | ||||||||
\(7\) | −1.33552 | − | 4.11032i | −0.504781 | − | 1.55356i | −0.801139 | − | 0.598479i | \(-0.795772\pi\) |
0.296358 | − | 0.955077i | \(-0.404228\pi\) | |||||||
\(8\) | −0.949555 | + | 2.92243i | −0.335718 | + | 1.03323i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 2.61912 | + | 1.90290i | 0.828237 | + | 0.601750i | ||||
\(11\) | −0.299148 | − | 0.920682i | −0.0901964 | − | 0.277596i | 0.895776 | − | 0.444506i | \(-0.146621\pi\) |
−0.985972 | + | 0.166910i | \(0.946621\pi\) | |||||||
\(12\) | 0.458193 | + | 0.332897i | 0.132269 | + | 0.0960990i | ||||
\(13\) | −2.55039 | + | 1.85297i | −0.707351 | + | 0.513920i | −0.882318 | − | 0.470654i | \(-0.844018\pi\) |
0.174967 | + | 0.984574i | \(0.444018\pi\) | |||||||
\(14\) | −1.59909 | + | 4.92149i | −0.427374 | + | 1.31532i | ||||
\(15\) | 2.18743 | − | 1.58926i | 0.564792 | − | 0.410346i | ||||
\(16\) | 2.06018 | − | 1.49681i | 0.515045 | − | 0.374202i | ||||
\(17\) | 1.52318 | − | 4.68787i | 0.369426 | − | 1.13697i | −0.577738 | − | 0.816223i | \(-0.696064\pi\) |
0.947163 | − | 0.320752i | \(-0.103936\pi\) | |||||||
\(18\) | −0.968675 | + | 0.703784i | −0.228319 | + | 0.165883i | ||||
\(19\) | 4.82213 | + | 3.50348i | 1.10627 | + | 0.803754i | 0.982073 | − | 0.188503i | \(-0.0603636\pi\) |
0.124200 | + | 0.992257i | \(0.460364\pi\) | |||||||
\(20\) | 0.473206 | + | 1.45638i | 0.105812 | + | 0.325656i | ||||
\(21\) | 3.49645 | + | 2.54032i | 0.762988 | + | 0.554343i | ||||
\(22\) | −0.358184 | + | 1.10238i | −0.0763651 | + | 0.235027i | ||||
\(23\) | 1.05276 | − | 3.24006i | 0.219515 | − | 0.675599i | −0.779287 | − | 0.626668i | \(-0.784418\pi\) |
0.998802 | − | 0.0489316i | \(-0.0155816\pi\) | |||||||
\(24\) | −0.949555 | − | 2.92243i | −0.193827 | − | 0.596538i | ||||
\(25\) | 2.31061 | 0.462122 | ||||||||
\(26\) | 3.77458 | 0.740257 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | −1.98024 | + | 1.43873i | −0.374230 | + | 0.271894i | ||||
\(29\) | −4.12478 | − | 2.99683i | −0.765953 | − | 0.556497i | 0.134778 | − | 0.990876i | \(-0.456968\pi\) |
−0.900730 | + | 0.434379i | \(0.856968\pi\) | |||||||
\(30\) | −3.23741 | −0.591067 | ||||||||
\(31\) | 5.08903 | − | 2.25872i | 0.914016 | − | 0.405678i | ||||
\(32\) | 3.09657 | 0.547402 | ||||||||
\(33\) | 0.783179 | + | 0.569013i | 0.136334 | + | 0.0990524i | ||||
\(34\) | −4.77471 | + | 3.46903i | −0.818856 | + | 0.594934i | ||||
\(35\) | 3.61101 | + | 11.1135i | 0.610372 | + | 1.87853i | ||||
\(36\) | −0.566358 | −0.0943929 | ||||||||
\(37\) | −8.13184 | −1.33687 | −0.668434 | − | 0.743772i | \(-0.733035\pi\) | ||||
−0.668434 | + | 0.743772i | \(0.733035\pi\) | |||||||
\(38\) | −2.20538 | − | 6.78747i | −0.357760 | − | 1.10107i | ||||
\(39\) | 0.974162 | − | 2.99816i | 0.155991 | − | 0.480090i | ||||
\(40\) | 2.56742 | − | 7.90170i | 0.405945 | − | 1.24937i | ||||
\(41\) | −2.61912 | − | 1.90290i | −0.409037 | − | 0.297183i | 0.364175 | − | 0.931331i | \(-0.381351\pi\) |
−0.773212 | + | 0.634148i | \(0.781351\pi\) | |||||||
\(42\) | −1.59909 | − | 4.92149i | −0.246745 | − | 0.759402i | ||||
\(43\) | −4.94934 | − | 3.59590i | −0.754767 | − | 0.548370i | 0.142534 | − | 0.989790i | \(-0.454475\pi\) |
−0.897301 | + | 0.441420i | \(0.854475\pi\) | |||||||
\(44\) | −0.443559 | + | 0.322265i | −0.0668691 | + | 0.0485832i | ||||
\(45\) | −0.835524 | + | 2.57148i | −0.124553 | + | 0.383334i | ||||
\(46\) | −3.30008 | + | 2.39765i | −0.486571 | + | 0.353514i | ||||
\(47\) | −6.41291 | + | 4.65925i | −0.935420 | + | 0.679622i | −0.947314 | − | 0.320307i | \(-0.896214\pi\) |
0.0118942 | + | 0.999929i | \(0.496214\pi\) | |||||||
\(48\) | −0.786919 | + | 2.42189i | −0.113582 | + | 0.349569i | ||||
\(49\) | −9.44800 | + | 6.86437i | −1.34971 | + | 0.980625i | ||||
\(50\) | −2.23823 | − | 1.62617i | −0.316533 | − | 0.229975i | ||||
\(51\) | 1.52318 | + | 4.68787i | 0.213288 | + | 0.656433i | ||||
\(52\) | 1.44443 | + | 1.04944i | 0.200307 | + | 0.145531i | ||||
\(53\) | 1.66138 | − | 5.11322i | 0.228209 | − | 0.702354i | −0.769741 | − | 0.638356i | \(-0.779615\pi\) |
0.997950 | − | 0.0639983i | \(-0.0203852\pi\) | |||||||
\(54\) | 0.370001 | − | 1.13875i | 0.0503507 | − | 0.154964i | ||||
\(55\) | 0.808840 | + | 2.48935i | 0.109064 | + | 0.335664i | ||||
\(56\) | 13.2803 | 1.77465 | ||||||||
\(57\) | −5.96048 | −0.789485 | ||||||||
\(58\) | 1.88645 | + | 5.80591i | 0.247703 | + | 0.762353i | ||||
\(59\) | 11.0224 | − | 8.00828i | 1.43500 | − | 1.04259i | 0.445942 | − | 0.895062i | \(-0.352869\pi\) |
0.989058 | − | 0.147527i | \(-0.0471314\pi\) | |||||||
\(60\) | −1.23887 | − | 0.900090i | −0.159937 | − | 0.116201i | ||||
\(61\) | 1.99991 | 0.256062 | 0.128031 | − | 0.991770i | \(-0.459134\pi\) | ||||
0.128031 | + | 0.991770i | \(0.459134\pi\) | |||||||
\(62\) | −6.51926 | − | 1.39361i | −0.827947 | − | 0.176988i | ||||
\(63\) | −4.32185 | −0.544502 | ||||||||
\(64\) | −7.11993 | − | 5.17293i | −0.889992 | − | 0.646617i | ||||
\(65\) | 6.89578 | − | 5.01007i | 0.855316 | − | 0.621423i | ||||
\(66\) | −0.358184 | − | 1.10238i | −0.0440894 | − | 0.135693i | ||||
\(67\) | 7.01351 | 0.856836 | 0.428418 | − | 0.903581i | \(-0.359071\pi\) | ||||
0.428418 | + | 0.903581i | \(0.359071\pi\) | |||||||
\(68\) | −2.79164 | −0.338536 | ||||||||
\(69\) | 1.05276 | + | 3.24006i | 0.126737 | + | 0.390057i | ||||
\(70\) | 4.32364 | − | 13.3068i | 0.516773 | − | 1.59046i | ||||
\(71\) | −1.95020 | + | 6.00211i | −0.231446 | + | 0.712319i | 0.766127 | + | 0.642690i | \(0.222182\pi\) |
−0.997573 | + | 0.0696291i | \(0.977818\pi\) | |||||||
\(72\) | 2.48597 | + | 1.80616i | 0.292974 | + | 0.212858i | ||||
\(73\) | 0.0487339 | + | 0.149988i | 0.00570387 | + | 0.0175547i | 0.953868 | − | 0.300226i | \(-0.0970623\pi\) |
−0.948164 | + | 0.317781i | \(0.897062\pi\) | |||||||
\(74\) | 7.87711 | + | 5.72306i | 0.915696 | + | 0.665292i | ||||
\(75\) | −1.86932 | + | 1.35814i | −0.215851 | + | 0.156825i | ||||
\(76\) | 1.04317 | − | 3.21054i | 0.119660 | − | 0.368274i | ||||
\(77\) | −3.38478 | + | 2.45919i | −0.385731 | + | 0.280250i | ||||
\(78\) | −3.05370 | + | 2.21865i | −0.345764 | + | 0.251212i | ||||
\(79\) | 5.17389 | − | 15.9236i | 0.582109 | − | 1.79155i | −0.0284757 | − | 0.999594i | \(-0.509065\pi\) |
0.610584 | − | 0.791951i | \(-0.290935\pi\) | |||||||
\(80\) | −5.57035 | + | 4.04709i | −0.622784 | + | 0.452479i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 1.19784 | + | 3.68658i | 0.132280 | + | 0.407115i | ||||
\(83\) | 5.63973 | + | 4.09750i | 0.619041 | + | 0.449759i | 0.852586 | − | 0.522587i | \(-0.175033\pi\) |
−0.233546 | + | 0.972346i | \(0.575033\pi\) | |||||||
\(84\) | 0.756384 | − | 2.32791i | 0.0825283 | − | 0.253996i | ||||
\(85\) | −4.11840 | + | 12.6751i | −0.446703 | + | 1.37481i | ||||
\(86\) | 2.26356 | + | 6.96652i | 0.244086 | + | 0.751220i | ||||
\(87\) | 5.09851 | 0.546618 | ||||||||
\(88\) | 2.97468 | 0.317102 | ||||||||
\(89\) | 2.78370 | + | 8.56735i | 0.295072 | + | 0.908137i | 0.983197 | + | 0.182546i | \(0.0584337\pi\) |
−0.688126 | + | 0.725591i | \(0.741566\pi\) | |||||||
\(90\) | 2.61912 | − | 1.90290i | 0.276079 | − | 0.200583i | ||||
\(91\) | 11.0224 | + | 8.00824i | 1.15546 | + | 0.839491i | ||||
\(92\) | −1.92947 | −0.201161 | ||||||||
\(93\) | −2.78947 | + | 4.81860i | −0.289254 | + | 0.499665i | ||||
\(94\) | 9.49114 | 0.978936 | ||||||||
\(95\) | −13.0381 | − | 9.47276i | −1.33768 | − | 0.971885i | ||||
\(96\) | −2.50518 | + | 1.82012i | −0.255684 | + | 0.185765i | ||||
\(97\) | 0.516238 | + | 1.58882i | 0.0524160 | + | 0.161320i | 0.973838 | − | 0.227244i | \(-0.0729714\pi\) |
−0.921422 | + | 0.388564i | \(0.872971\pi\) | |||||||
\(98\) | 13.9831 | 1.41250 | ||||||||
\(99\) | −0.968062 | −0.0972939 | ||||||||
\(100\) | −0.404389 | − | 1.24458i | −0.0404389 | − | 0.124458i | ||||
\(101\) | −1.17169 | + | 3.60608i | −0.116587 | + | 0.358819i | −0.992275 | − | 0.124060i | \(-0.960409\pi\) |
0.875688 | + | 0.482878i | \(0.160409\pi\) | |||||||
\(102\) | 1.82378 | − | 5.61301i | 0.180581 | − | 0.555771i | ||||
\(103\) | 2.95477 | + | 2.14676i | 0.291142 | + | 0.211527i | 0.723763 | − | 0.690049i | \(-0.242411\pi\) |
−0.432621 | + | 0.901576i | \(0.642411\pi\) | |||||||
\(104\) | −2.99343 | − | 9.21282i | −0.293530 | − | 0.903391i | ||||
\(105\) | −9.45375 | − | 6.86855i | −0.922591 | − | 0.670302i | ||||
\(106\) | −5.20794 | + | 3.78379i | −0.505840 | + | 0.367514i | ||||
\(107\) | 2.64239 | − | 8.13245i | 0.255450 | − | 0.786194i | −0.738291 | − | 0.674482i | \(-0.764367\pi\) |
0.993741 | − | 0.111711i | \(-0.0356332\pi\) | |||||||
\(108\) | 0.458193 | − | 0.332897i | 0.0440896 | − | 0.0320330i | ||||
\(109\) | −12.0046 | + | 8.72185i | −1.14983 | + | 0.835401i | −0.988458 | − | 0.151492i | \(-0.951592\pi\) |
−0.161373 | + | 0.986893i | \(0.551592\pi\) | |||||||
\(110\) | 0.968463 | − | 2.98062i | 0.0923393 | − | 0.284191i | ||||
\(111\) | 6.57880 | − | 4.77978i | 0.624432 | − | 0.453676i | ||||
\(112\) | −8.90379 | − | 6.46898i | −0.841329 | − | 0.611261i | ||||
\(113\) | −1.91147 | − | 5.88289i | −0.179816 | − | 0.553416i | 0.820005 | − | 0.572356i | \(-0.193971\pi\) |
−0.999821 | + | 0.0189408i | \(0.993971\pi\) | |||||||
\(114\) | 5.77377 | + | 4.19489i | 0.540763 | + | 0.392887i | ||||
\(115\) | −2.84647 | + | 8.76052i | −0.265434 | + | 0.816923i | ||||
\(116\) | −0.892311 | + | 2.74625i | −0.0828490 | + | 0.254983i | ||||
\(117\) | 0.974162 | + | 2.99816i | 0.0900613 | + | 0.277180i | ||||
\(118\) | −16.3133 | −1.50176 | ||||||||
\(119\) | −21.3029 | −1.95283 | ||||||||
\(120\) | 2.56742 | + | 7.90170i | 0.234372 | + | 0.721324i | ||||
\(121\) | 8.14102 | − | 5.91480i | 0.740093 | − | 0.537709i | ||||
\(122\) | −1.93726 | − | 1.40750i | −0.175391 | − | 0.127429i | ||||
\(123\) | 3.23741 | 0.291907 | ||||||||
\(124\) | −2.10728 | − | 2.34584i | −0.189240 | − | 0.210662i | ||||
\(125\) | 7.27161 | 0.650393 | ||||||||
\(126\) | 4.18647 | + | 3.04165i | 0.372960 | + | 0.270971i | ||||
\(127\) | 0.715575 | − | 0.519896i | 0.0634970 | − | 0.0461333i | −0.555584 | − | 0.831460i | \(-0.687505\pi\) |
0.619081 | + | 0.785327i | \(0.287505\pi\) | |||||||
\(128\) | 1.34249 | + | 4.13176i | 0.118660 | + | 0.365199i | ||||
\(129\) | 6.11772 | 0.538635 | ||||||||
\(130\) | −10.2058 | −0.895106 | ||||||||
\(131\) | −1.30131 | − | 4.00503i | −0.113696 | − | 0.349921i | 0.877977 | − | 0.478703i | \(-0.158893\pi\) |
−0.991673 | + | 0.128783i | \(0.958893\pi\) | |||||||
\(132\) | 0.169425 | − | 0.521435i | 0.0147465 | − | 0.0453851i | ||||
\(133\) | 7.96037 | − | 24.4995i | 0.690251 | − | 2.12438i | ||||
\(134\) | −6.79381 | − | 4.93599i | −0.586896 | − | 0.426405i | ||||
\(135\) | −0.835524 | − | 2.57148i | −0.0719105 | − | 0.221318i | ||||
\(136\) | 12.2536 | + | 8.90277i | 1.05074 | + | 0.763406i | ||||
\(137\) | −7.04271 | + | 5.11683i | −0.601699 | + | 0.437160i | −0.846482 | − | 0.532418i | \(-0.821283\pi\) |
0.244782 | + | 0.969578i | \(0.421283\pi\) | |||||||
\(138\) | 1.26052 | − | 3.87948i | 0.107303 | − | 0.330243i | ||||
\(139\) | −11.6557 | + | 8.46838i | −0.988626 | + | 0.718279i | −0.959620 | − | 0.281301i | \(-0.909234\pi\) |
−0.0290060 | + | 0.999579i | \(0.509234\pi\) | |||||||
\(140\) | 5.35420 | − | 3.89005i | 0.452512 | − | 0.328770i | ||||
\(141\) | 2.44951 | − | 7.53883i | 0.206286 | − | 0.634884i | ||||
\(142\) | 6.11330 | − | 4.44157i | 0.513016 | − | 0.372728i | ||||
\(143\) | 2.46893 | + | 1.79379i | 0.206463 | + | 0.150004i | ||||
\(144\) | −0.786919 | − | 2.42189i | −0.0655766 | − | 0.201824i | ||||
\(145\) | 11.1526 | + | 8.10287i | 0.926176 | + | 0.672907i | ||||
\(146\) | 0.0583514 | − | 0.179587i | 0.00482920 | − | 0.0148628i | ||||
\(147\) | 3.60881 | − | 11.1068i | 0.297650 | − | 0.916073i | ||||
\(148\) | 1.42319 | + | 4.38012i | 0.116985 | + | 0.360044i | ||||
\(149\) | 12.8277 | 1.05089 | 0.525443 | − | 0.850829i | \(-0.323900\pi\) | ||||
0.525443 | + | 0.850829i | \(0.323900\pi\) | |||||||
\(150\) | 2.76660 | 0.225892 | ||||||||
\(151\) | −1.79345 | − | 5.51967i | −0.145949 | − | 0.449184i | 0.851183 | − | 0.524869i | \(-0.175886\pi\) |
−0.997132 | + | 0.0756849i | \(0.975886\pi\) | |||||||
\(152\) | −14.8176 | + | 10.7656i | −1.20186 | + | 0.873204i | ||||
\(153\) | −3.98774 | − | 2.89726i | −0.322390 | − | 0.234230i | ||||
\(154\) | 5.00949 | 0.403676 | ||||||||
\(155\) | −13.7598 | + | 6.10716i | −1.10521 | + | 0.490539i | ||||
\(156\) | −1.78542 | −0.142948 | ||||||||
\(157\) | 1.11267 | + | 0.808402i | 0.0888007 | + | 0.0645175i | 0.631300 | − | 0.775539i | \(-0.282522\pi\) |
−0.542499 | + | 0.840056i | \(0.682522\pi\) | |||||||
\(158\) | −16.2186 | + | 11.7835i | −1.29028 | + | 0.937445i | ||||
\(159\) | 1.66138 | + | 5.11322i | 0.131756 | + | 0.405504i | ||||
\(160\) | −8.37255 | −0.661908 | ||||||||
\(161\) | −14.7237 | −1.16039 | ||||||||
\(162\) | 0.370001 | + | 1.13875i | 0.0290700 | + | 0.0894683i | ||||
\(163\) | −0.130095 | + | 0.400391i | −0.0101898 | + | 0.0313611i | −0.956022 | − | 0.293294i | \(-0.905248\pi\) |
0.945832 | + | 0.324656i | \(0.105248\pi\) | |||||||
\(164\) | −0.566592 | + | 1.74379i | −0.0442434 | + | 0.136167i | ||||
\(165\) | −2.11757 | − | 1.53850i | −0.164853 | − | 0.119772i | ||||
\(166\) | −2.57931 | − | 7.93830i | −0.200193 | − | 0.616131i | ||||
\(167\) | 9.30952 | + | 6.76376i | 0.720392 | + | 0.523396i | 0.886509 | − | 0.462710i | \(-0.153123\pi\) |
−0.166117 | + | 0.986106i | \(0.553123\pi\) | |||||||
\(168\) | −10.7440 | + | 7.80595i | −0.828915 | + | 0.602242i | ||||
\(169\) | −0.946221 | + | 2.91217i | −0.0727862 | + | 0.224013i | ||||
\(170\) | 12.9099 | − | 9.37961i | 0.990146 | − | 0.719384i | ||||
\(171\) | 4.82213 | − | 3.50348i | 0.368757 | − | 0.267918i | ||||
\(172\) | −1.07069 | + | 3.29524i | −0.0816391 | + | 0.251259i | ||||
\(173\) | −6.18435 | + | 4.49319i | −0.470187 | + | 0.341611i | −0.797514 | − | 0.603300i | \(-0.793852\pi\) |
0.327327 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(174\) | −4.93880 | − | 3.58825i | −0.374409 | − | 0.272024i | ||||
\(175\) | −3.08588 | − | 9.49735i | −0.233270 | − | 0.717932i | ||||
\(176\) | −1.99438 | − | 1.44900i | −0.150332 | − | 0.109223i | ||||
\(177\) | −4.21020 | + | 12.9577i | −0.316458 | + | 0.973958i | ||||
\(178\) | 3.33306 | − | 10.2581i | 0.249823 | − | 0.768877i | ||||
\(179\) | −3.88662 | − | 11.9618i | −0.290499 | − | 0.894065i | −0.984696 | − | 0.174280i | \(-0.944240\pi\) |
0.694197 | − | 0.719785i | \(-0.255760\pi\) | |||||||
\(180\) | 1.53133 | 0.114138 | ||||||||
\(181\) | 21.6662 | 1.61044 | 0.805218 | − | 0.592979i | \(-0.202048\pi\) | ||||
0.805218 | + | 0.592979i | \(0.202048\pi\) | |||||||
\(182\) | −5.04105 | − | 15.5148i | −0.373667 | − | 1.15003i | ||||
\(183\) | −1.61796 | + | 1.17551i | −0.119603 | + | 0.0868966i | ||||
\(184\) | 8.46919 | + | 6.15323i | 0.624357 | + | 0.453622i | ||||
\(185\) | 21.9870 | 1.61652 | ||||||||
\(186\) | 6.09334 | − | 2.70447i | 0.446785 | − | 0.198302i | ||||
\(187\) | −4.77169 | −0.348941 | ||||||||
\(188\) | 3.63200 | + | 2.63880i | 0.264891 | + | 0.192455i | ||||
\(189\) | 3.49645 | − | 2.54032i | 0.254329 | − | 0.184781i | ||||
\(190\) | 5.96294 | + | 18.3521i | 0.432597 | + | 1.33140i | ||||
\(191\) | −1.43435 | −0.103786 | −0.0518929 | − | 0.998653i | \(-0.516525\pi\) | ||||
−0.0518929 | + | 0.998653i | \(0.516525\pi\) | |||||||
\(192\) | 8.80072 | 0.635137 | ||||||||
\(193\) | −2.84063 | − | 8.74256i | −0.204473 | − | 0.629304i | −0.999735 | − | 0.0230370i | \(-0.992666\pi\) |
0.795261 | − | 0.606267i | \(-0.207334\pi\) | |||||||
\(194\) | 0.618116 | − | 1.90237i | 0.0443782 | − | 0.136582i | ||||
\(195\) | −2.63395 | + | 8.10647i | −0.188621 | + | 0.580516i | ||||
\(196\) | 5.35095 | + | 3.88769i | 0.382210 | + | 0.277692i | ||||
\(197\) | −2.32348 | − | 7.15092i | −0.165541 | − | 0.509482i | 0.833535 | − | 0.552467i | \(-0.186313\pi\) |
−0.999076 | + | 0.0429846i | \(0.986313\pi\) | |||||||
\(198\) | 0.937738 | + | 0.681306i | 0.0666421 | + | 0.0484183i | ||||
\(199\) | −0.714198 | + | 0.518895i | −0.0506282 | + | 0.0367835i | −0.612812 | − | 0.790229i | \(-0.709962\pi\) |
0.562183 | + | 0.827013i | \(0.309962\pi\) | |||||||
\(200\) | −2.19405 | + | 6.75259i | −0.155143 | + | 0.477480i | ||||
\(201\) | −5.67405 | + | 4.12244i | −0.400216 | + | 0.290774i | ||||
\(202\) | 3.67289 | − | 2.66851i | 0.258423 | − | 0.187756i | ||||
\(203\) | −6.80918 | + | 20.9565i | −0.477911 | + | 1.47086i | ||||
\(204\) | 2.25849 | − | 1.64089i | 0.158126 | − | 0.114885i | ||||
\(205\) | 7.08160 | + | 5.14509i | 0.494601 | + | 0.359348i | ||||
\(206\) | −1.35135 | − | 4.15903i | −0.0941531 | − | 0.289773i | ||||
\(207\) | −2.75616 | − | 2.00247i | −0.191566 | − | 0.139181i | ||||
\(208\) | −2.48073 | + | 7.63489i | −0.172007 | + | 0.529384i | ||||
\(209\) | 1.78306 | − | 5.48771i | 0.123337 | − | 0.379593i | ||||
\(210\) | 4.32364 | + | 13.3068i | 0.298359 | + | 0.918255i | ||||
\(211\) | 2.31905 | 0.159650 | 0.0798248 | − | 0.996809i | \(-0.474564\pi\) | ||||
0.0798248 | + | 0.996809i | \(0.474564\pi\) | |||||||
\(212\) | −3.04494 | −0.209127 | ||||||||
\(213\) | −1.95020 | − | 6.00211i | −0.133626 | − | 0.411257i | ||||
\(214\) | −8.28311 | + | 6.01803i | −0.566222 | + | 0.411384i | ||||
\(215\) | 13.3821 | + | 9.72266i | 0.912651 | + | 0.663080i | ||||
\(216\) | −3.07282 | −0.209079 | ||||||||
\(217\) | −16.0806 | − | 17.9010i | −1.09162 | − | 1.21520i | ||||
\(218\) | 17.7668 | 1.20332 | ||||||||
\(219\) | −0.127587 | − | 0.0926974i | −0.00862153 | − | 0.00626391i | ||||
\(220\) | 1.19930 | − | 0.871344i | 0.0808569 | − | 0.0587460i | ||||
\(221\) | 4.80176 | + | 14.7783i | 0.323001 | + | 0.994095i | ||||
\(222\) | −9.73665 | −0.653481 | ||||||||
\(223\) | −5.46955 | −0.366268 | −0.183134 | − | 0.983088i | \(-0.558624\pi\) | ||||
−0.183134 | + | 0.983088i | \(0.558624\pi\) | |||||||
\(224\) | −4.13555 | − | 12.7279i | −0.276318 | − | 0.850419i | ||||
\(225\) | 0.714018 | − | 2.19752i | 0.0476012 | − | 0.146501i | ||||
\(226\) | −2.28869 | + | 7.04387i | −0.152241 | + | 0.468551i | ||||
\(227\) | 20.2802 | + | 14.7344i | 1.34604 | + | 0.977957i | 0.999198 | + | 0.0400345i | \(0.0127468\pi\) |
0.346844 | + | 0.937923i | \(0.387253\pi\) | |||||||
\(228\) | 1.04317 | + | 3.21054i | 0.0690855 | + | 0.212623i | ||||
\(229\) | −20.4230 | − | 14.8382i | −1.34959 | − | 0.980533i | −0.999032 | − | 0.0439906i | \(-0.985993\pi\) |
−0.350555 | − | 0.936542i | \(-0.614007\pi\) | |||||||
\(230\) | 8.92281 | − | 6.48280i | 0.588353 | − | 0.427463i | ||||
\(231\) | 1.29287 | − | 3.97905i | 0.0850646 | − | 0.261802i | ||||
\(232\) | 12.6747 | − | 9.20873i | 0.832136 | − | 0.604582i | ||||
\(233\) | 18.1585 | − | 13.1929i | 1.18960 | − | 0.864296i | 0.196379 | − | 0.980528i | \(-0.437082\pi\) |
0.993222 | + | 0.116232i | \(0.0370816\pi\) | |||||||
\(234\) | 1.16641 | − | 3.58984i | 0.0762507 | − | 0.234675i | ||||
\(235\) | 17.3393 | − | 12.5978i | 1.13109 | − | 0.821787i | ||||
\(236\) | −6.24265 | − | 4.53555i | −0.406362 | − | 0.295239i | ||||
\(237\) | 5.17389 | + | 15.9236i | 0.336081 | + | 1.03435i | ||||
\(238\) | 20.6356 | + | 14.9926i | 1.33761 | + | 0.971827i | ||||
\(239\) | 2.26408 | − | 6.96812i | 0.146451 | − | 0.450730i | −0.850744 | − | 0.525581i | \(-0.823848\pi\) |
0.997195 | + | 0.0748508i | \(0.0238481\pi\) | |||||||
\(240\) | 2.12768 | − | 6.54834i | 0.137341 | − | 0.422693i | ||||
\(241\) | −3.79880 | − | 11.6915i | −0.244702 | − | 0.753115i | −0.995685 | − | 0.0927940i | \(-0.970420\pi\) |
0.750983 | − | 0.660321i | \(-0.229580\pi\) | |||||||
\(242\) | −12.0487 | −0.774522 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.350012 | − | 1.07722i | −0.0224072 | − | 0.0689623i | ||||
\(245\) | 25.5456 | − | 18.5600i | 1.63205 | − | 1.18575i | ||||
\(246\) | −3.13599 | − | 2.27843i | −0.199944 | − | 0.145268i | ||||
\(247\) | −18.7901 | −1.19559 | ||||||||
\(248\) | 1.76864 | + | 17.0171i | 0.112309 | + | 1.08059i | ||||
\(249\) | −6.97109 | −0.441775 | ||||||||
\(250\) | −7.04383 | − | 5.11764i | −0.445491 | − | 0.323668i | ||||
\(251\) | −23.8106 | + | 17.2994i | −1.50291 | + | 1.09193i | −0.533708 | + | 0.845669i | \(0.679202\pi\) |
−0.969204 | + | 0.246260i | \(0.920798\pi\) | |||||||
\(252\) | 0.756384 | + | 2.32791i | 0.0476477 | + | 0.146645i | ||||
\(253\) | −3.29799 | −0.207343 | ||||||||
\(254\) | −1.05905 | −0.0664510 | ||||||||
\(255\) | −4.11840 | − | 12.6751i | −0.257904 | − | 0.793747i | ||||
\(256\) | −3.83172 | + | 11.7928i | −0.239482 | + | 0.737051i | ||||
\(257\) | −3.37890 | + | 10.3992i | −0.210770 | + | 0.648682i | 0.788657 | + | 0.614833i | \(0.210777\pi\) |
−0.999427 | + | 0.0338493i | \(0.989223\pi\) | |||||||
\(258\) | −5.92608 | − | 4.30555i | −0.368942 | − | 0.268052i | ||||
\(259\) | 10.8603 | + | 33.4245i | 0.674825 | + | 2.07690i | ||||
\(260\) | −3.90547 | − | 2.83749i | −0.242207 | − | 0.175974i | ||||
\(261\) | −4.12478 | + | 2.99683i | −0.255318 | + | 0.185499i | ||||
\(262\) | −1.55812 | + | 4.79541i | −0.0962612 | + | 0.296262i | ||||
\(263\) | 20.0899 | − | 14.5962i | 1.23880 | − | 0.900037i | 0.241278 | − | 0.970456i | \(-0.422434\pi\) |
0.997518 | + | 0.0704186i | \(0.0224335\pi\) | |||||||
\(264\) | −2.40657 | + | 1.74848i | −0.148114 | + | 0.107611i | ||||
\(265\) | −4.49208 | + | 13.8252i | −0.275946 | + | 0.849274i | ||||
\(266\) | −24.9533 | + | 18.1297i | −1.52999 | + | 1.11160i | ||||
\(267\) | −7.28782 | − | 5.29491i | −0.446007 | − | 0.324043i | ||||
\(268\) | −1.22746 | − | 3.77774i | −0.0749792 | − | 0.230762i | ||||
\(269\) | −20.2113 | − | 14.6844i | −1.23231 | − | 0.895324i | −0.235246 | − | 0.971936i | \(-0.575590\pi\) |
−0.997061 | + | 0.0766123i | \(0.975590\pi\) | |||||||
\(270\) | −1.00041 | + | 3.07896i | −0.0608832 | + | 0.187379i | ||||
\(271\) | 6.25946 | − | 19.2646i | 0.380235 | − | 1.17024i | −0.559644 | − | 0.828733i | \(-0.689062\pi\) |
0.939878 | − | 0.341509i | \(-0.110938\pi\) | |||||||
\(272\) | −3.87882 | − | 11.9378i | −0.235188 | − | 0.723834i | ||||
\(273\) | −13.6244 | −0.824588 | ||||||||
\(274\) | 10.4232 | 0.629691 | ||||||||
\(275\) | −0.691213 | − | 2.12734i | −0.0416817 | − | 0.128283i | ||||
\(276\) | 1.56097 | − | 1.13411i | 0.0939595 | − | 0.0682655i | ||||
\(277\) | −1.56206 | − | 1.13491i | −0.0938553 | − | 0.0681899i | 0.539868 | − | 0.841750i | \(-0.318474\pi\) |
−0.633723 | + | 0.773560i | \(0.718474\pi\) | |||||||
\(278\) | 17.2505 | 1.03462 | ||||||||
\(279\) | −0.575574 | − | 5.53793i | −0.0344587 | − | 0.331547i | ||||
\(280\) | −35.9074 | −2.14588 | ||||||||
\(281\) | −3.45068 | − | 2.50707i | −0.205850 | − | 0.149559i | 0.480084 | − | 0.877223i | \(-0.340606\pi\) |
−0.685934 | + | 0.727664i | \(0.740606\pi\) | |||||||
\(282\) | −7.67849 | + | 5.57875i | −0.457247 | + | 0.332210i | ||||
\(283\) | −8.93251 | − | 27.4914i | −0.530982 | − | 1.63420i | −0.752173 | − | 0.658965i | \(-0.770994\pi\) |
0.221191 | − | 0.975230i | \(-0.429006\pi\) | |||||||
\(284\) | 3.57428 | 0.212094 | ||||||||
\(285\) | 16.1160 | 0.954631 | ||||||||
\(286\) | −1.12916 | − | 3.47519i | −0.0667685 | − | 0.205492i | ||||
\(287\) | −4.32364 | + | 13.3068i | −0.255216 | + | 0.785474i | ||||
\(288\) | 0.956893 | − | 2.94501i | 0.0563855 | − | 0.173537i | ||||
\(289\) | −5.90274 | − | 4.28859i | −0.347220 | − | 0.252270i | ||||
\(290\) | −5.10062 | − | 15.6981i | −0.299519 | − | 0.921824i | ||||
\(291\) | −1.35153 | − | 0.981943i | −0.0792280 | − | 0.0575625i | ||||
\(292\) | 0.0722599 | − | 0.0524999i | 0.00422869 | − | 0.00307232i | ||||
\(293\) | 8.00748 | − | 24.6445i | 0.467802 | − | 1.43975i | −0.387623 | − | 0.921818i | \(-0.626704\pi\) |
0.855424 | − | 0.517928i | \(-0.173296\pi\) | |||||||
\(294\) | −11.3125 | + | 8.21904i | −0.659761 | + | 0.479344i | ||||
\(295\) | −29.8026 | + | 21.6529i | −1.73518 | + | 1.26068i | ||||
\(296\) | 7.72163 | − | 23.7647i | 0.448811 | − | 1.38130i | ||||
\(297\) | 0.783179 | − | 0.569013i | 0.0454446 | − | 0.0330175i | ||||
\(298\) | −12.4259 | − | 9.02793i | −0.719812 | − | 0.522974i | ||||
\(299\) | 3.31877 | + | 10.2141i | 0.191930 | + | 0.590699i | ||||
\(300\) | 1.05870 | + | 0.769194i | 0.0611243 | + | 0.0444094i | ||||
\(301\) | −8.17036 | + | 25.1458i | −0.470932 | + | 1.44938i | ||||
\(302\) | −2.14738 | + | 6.60896i | −0.123568 | + | 0.380303i | ||||
\(303\) | −1.17169 | − | 3.60608i | −0.0673117 | − | 0.207164i | ||||
\(304\) | 15.1785 | 0.870547 | ||||||||
\(305\) | −5.40737 | −0.309625 | ||||||||
\(306\) | 1.82378 | + | 5.61301i | 0.104258 | + | 0.320874i | ||||
\(307\) | 4.87499 | − | 3.54189i | 0.278230 | − | 0.202146i | −0.439915 | − | 0.898040i | \(-0.644991\pi\) |
0.718145 | + | 0.695893i | \(0.244991\pi\) | |||||||
\(308\) | 1.91700 | + | 1.39278i | 0.109231 | + | 0.0793609i | ||||
\(309\) | −3.65229 | −0.207772 | ||||||||
\(310\) | 17.6269 | + | 3.76806i | 1.00114 | + | 0.214011i | ||||
\(311\) | −21.4723 | −1.21758 | −0.608791 | − | 0.793331i | \(-0.708345\pi\) | ||||
−0.608791 | + | 0.793331i | \(0.708345\pi\) | |||||||
\(312\) | 7.83689 | + | 5.69384i | 0.443677 | + | 0.322350i | ||||
\(313\) | 1.05789 | − | 0.768601i | 0.0597954 | − | 0.0434439i | −0.557486 | − | 0.830186i | \(-0.688234\pi\) |
0.617281 | + | 0.786742i | \(0.288234\pi\) | |||||||
\(314\) | −0.508875 | − | 1.56616i | −0.0287175 | − | 0.0883834i | ||||
\(315\) | 11.6855 | 0.658402 | ||||||||
\(316\) | −9.48256 | −0.533436 | ||||||||
\(317\) | 6.59915 | + | 20.3101i | 0.370645 | + | 1.14073i | 0.946370 | + | 0.323085i | \(0.104720\pi\) |
−0.575725 | + | 0.817643i | \(0.695280\pi\) | |||||||
\(318\) | 1.98926 | − | 6.12230i | 0.111552 | − | 0.343322i | ||||
\(319\) | −1.52521 | + | 4.69411i | −0.0853952 | + | 0.262819i | ||||
\(320\) | 19.2510 | + | 13.9867i | 1.07616 | + | 0.781878i | ||||
\(321\) | 2.64239 | + | 8.13245i | 0.147484 | + | 0.453909i | ||||
\(322\) | 14.2625 | + | 10.3623i | 0.794815 | + | 0.577467i | ||||
\(323\) | 23.7688 | − | 17.2691i | 1.32253 | − | 0.960877i | ||||
\(324\) | −0.175014 | + | 0.538638i | −0.00972301 | + | 0.0299243i | ||||
\(325\) | −5.89295 | + | 4.28148i | −0.326882 | + | 0.237494i | ||||
\(326\) | 0.407808 | − | 0.296290i | 0.0225864 | − | 0.0164100i | ||||
\(327\) | 4.58535 | − | 14.1122i | 0.253570 | − | 0.780409i | ||||
\(328\) | 8.04808 | − | 5.84727i | 0.444381 | − | 0.322862i | ||||
\(329\) | 27.7156 | + | 20.1366i | 1.52801 | + | 1.11017i | ||||
\(330\) | 0.968463 | + | 2.98062i | 0.0533121 | + | 0.164078i | ||||
\(331\) | −18.3782 | − | 13.3525i | −1.01016 | − | 0.733921i | −0.0459137 | − | 0.998945i | \(-0.514620\pi\) |
−0.964242 | + | 0.265025i | \(0.914620\pi\) | |||||||
\(332\) | 1.22004 | − | 3.75489i | 0.0669583 | − | 0.206076i | ||||
\(333\) | −2.51288 | + | 7.73384i | −0.137705 | + | 0.423812i | ||||
\(334\) | −4.25767 | − | 13.1038i | −0.232970 | − | 0.717007i | ||||
\(335\) | −18.9632 | −1.03607 | ||||||||
\(336\) | 11.0057 | 0.600410 | ||||||||
\(337\) | 8.01397 | + | 24.6645i | 0.436549 | + | 1.34356i | 0.891491 | + | 0.453038i | \(0.149660\pi\) |
−0.454943 | + | 0.890521i | \(0.650340\pi\) | |||||||
\(338\) | 2.96612 | − | 2.15501i | 0.161336 | − | 0.117217i | ||||
\(339\) | 5.00428 | + | 3.63583i | 0.271795 | + | 0.197471i | ||||
\(340\) | 7.54808 | 0.409352 | ||||||||
\(341\) | −3.60193 | − | 4.00968i | −0.195056 | − | 0.217137i | ||||
\(342\) | −7.13677 | −0.385912 | ||||||||
\(343\) | 16.3577 | + | 11.8845i | 0.883231 | + | 0.641705i | ||||
\(344\) | 15.2084 | − | 11.0496i | 0.819984 | − | 0.595753i | ||||
\(345\) | −2.84647 | − | 8.76052i | −0.153249 | − | 0.471650i | ||||
\(346\) | 9.15286 | 0.492061 | ||||||||
\(347\) | 3.06248 | 0.164402 | 0.0822012 | − | 0.996616i | \(-0.473805\pi\) | ||||
0.0822012 | + | 0.996616i | \(0.473805\pi\) | |||||||
\(348\) | −0.892311 | − | 2.74625i | −0.0478329 | − | 0.147215i | ||||
\(349\) | −0.706484 | + | 2.17434i | −0.0378172 | + | 0.116390i | −0.968183 | − | 0.250243i | \(-0.919489\pi\) |
0.930366 | + | 0.366633i | \(0.119489\pi\) | |||||||
\(350\) | −3.69487 | + | 11.3716i | −0.197499 | + | 0.607839i | ||||
\(351\) | −2.55039 | − | 1.85297i | −0.136130 | − | 0.0989040i | ||||
\(352\) | −0.926332 | − | 2.85096i | −0.0493737 | − | 0.151956i | ||||
\(353\) | 10.3883 | + | 7.54752i | 0.552911 | + | 0.401714i | 0.828858 | − | 0.559459i | \(-0.188991\pi\) |
−0.275946 | + | 0.961173i | \(0.588991\pi\) | |||||||
\(354\) | 13.1977 | − | 9.58870i | 0.701450 | − | 0.509633i | ||||
\(355\) | 5.27298 | − | 16.2286i | 0.279861 | − | 0.861323i | ||||
\(356\) | 4.12751 | − | 2.99881i | 0.218758 | − | 0.158937i | ||||
\(357\) | 17.2344 | − | 12.5215i | 0.912141 | − | 0.662709i | ||||
\(358\) | −4.65363 | + | 14.3224i | −0.245952 | + | 0.756963i | ||||
\(359\) | −7.27240 | + | 5.28371i | −0.383823 | + | 0.278864i | −0.762919 | − | 0.646493i | \(-0.776235\pi\) |
0.379097 | + | 0.925357i | \(0.376235\pi\) | |||||||
\(360\) | −6.72159 | − | 4.88352i | −0.354259 | − | 0.257384i | ||||
\(361\) | 5.10722 | + | 15.7184i | 0.268801 | + | 0.827285i | ||||
\(362\) | −20.9875 | − | 15.2483i | −1.10308 | − | 0.801433i | ||||
\(363\) | −3.10959 | + | 9.57034i | −0.163211 | + | 0.502313i | ||||
\(364\) | 2.38447 | − | 7.33863i | 0.124980 | − | 0.384649i | ||||
\(365\) | −0.131767 | − | 0.405538i | −0.00689702 | − | 0.0212268i | ||||
\(366\) | 2.39458 | 0.125167 | ||||||||
\(367\) | 18.2920 | 0.954833 | 0.477416 | − | 0.878677i | \(-0.341573\pi\) | ||||
0.477416 | + | 0.878677i | \(0.341573\pi\) | |||||||
\(368\) | −2.68088 | − | 8.25089i | −0.139750 | − | 0.430107i | ||||
\(369\) | −2.61912 | + | 1.90290i | −0.136346 | + | 0.0990610i | ||||
\(370\) | −21.2983 | − | 15.4741i | −1.10724 | − | 0.804459i | ||||
\(371\) | −23.2358 | −1.20634 | ||||||||
\(372\) | 3.08368 | + | 0.659191i | 0.159881 | + | 0.0341774i | ||||
\(373\) | 34.6042 | 1.79174 | 0.895868 | − | 0.444321i | \(-0.146555\pi\) | ||||
0.895868 | + | 0.444321i | \(0.146555\pi\) | |||||||
\(374\) | 4.62222 | + | 3.35824i | 0.239009 | + | 0.173650i | ||||
\(375\) | −5.88286 | + | 4.27415i | −0.303789 | + | 0.220716i | ||||
\(376\) | −7.52693 | − | 23.1655i | −0.388172 | − | 1.19467i | ||||
\(377\) | 16.0728 | 0.827792 | ||||||||
\(378\) | −5.17476 | −0.266161 | ||||||||
\(379\) | 3.28910 | + | 10.1228i | 0.168950 | + | 0.519974i | 0.999306 | − | 0.0372596i | \(-0.0118629\pi\) |
−0.830356 | + | 0.557233i | \(0.811863\pi\) | |||||||
\(380\) | −2.82053 | + | 8.68071i | −0.144690 | + | 0.445311i | ||||
\(381\) | −0.273325 | + | 0.841209i | −0.0140029 | + | 0.0430965i | ||||
\(382\) | 1.38942 | + | 1.00947i | 0.0710888 | + | 0.0516490i | ||||
\(383\) | 4.69200 | + | 14.4405i | 0.239750 | + | 0.737874i | 0.996456 | + | 0.0841187i | \(0.0268075\pi\) |
−0.756706 | + | 0.653755i | \(0.773193\pi\) | |||||||
\(384\) | −3.51468 | − | 2.55357i | −0.179358 | − | 0.130311i | ||||
\(385\) | 9.15181 | − | 6.64918i | 0.466420 | − | 0.338874i | ||||
\(386\) | −3.40122 | + | 10.4679i | −0.173118 | + | 0.532802i | ||||
\(387\) | −4.94934 | + | 3.59590i | −0.251589 | + | 0.182790i | ||||
\(388\) | 0.765448 | − | 0.556131i | 0.0388597 | − | 0.0282333i | ||||
\(389\) | −10.5433 | + | 32.4488i | −0.534564 | + | 1.64522i | 0.210025 | + | 0.977696i | \(0.432646\pi\) |
−0.744589 | + | 0.667523i | \(0.767354\pi\) | |||||||
\(390\) | 8.25664 | − | 5.99880i | 0.418091 | − | 0.303761i | ||||
\(391\) | −13.5854 | − | 9.87039i | −0.687045 | − | 0.499167i | ||||
\(392\) | −11.0892 | − | 34.1292i | −0.560092 | − | 1.72378i | ||||
\(393\) | 3.40688 | + | 2.47524i | 0.171854 | + | 0.124860i | ||||
\(394\) | −2.78201 | + | 8.56214i | −0.140156 | + | 0.431355i | ||||
\(395\) | −13.9892 | + | 43.0545i | −0.703875 | + | 2.16631i | ||||
\(396\) | 0.169425 | + | 0.521435i | 0.00851390 | + | 0.0262031i | ||||
\(397\) | 18.0947 | 0.908146 | 0.454073 | − | 0.890965i | \(-0.349971\pi\) | ||||
0.454073 | + | 0.890965i | \(0.349971\pi\) | |||||||
\(398\) | 1.05702 | 0.0529834 | ||||||||
\(399\) | 7.96037 | + | 24.4995i | 0.398517 | + | 1.22651i | ||||
\(400\) | 4.76027 | − | 3.45854i | 0.238014 | − | 0.172927i | ||||
\(401\) | −15.7130 | − | 11.4162i | −0.784672 | − | 0.570097i | 0.121706 | − | 0.992566i | \(-0.461164\pi\) |
−0.906377 | + | 0.422469i | \(0.861164\pi\) | |||||||
\(402\) | 8.39761 | 0.418835 | ||||||||
\(403\) | −8.79367 | + | 15.1904i | −0.438044 | + | 0.756688i | ||||
\(404\) | 2.14743 | 0.106839 | ||||||||
\(405\) | 2.18743 | + | 1.58926i | 0.108694 | + | 0.0789711i | ||||
\(406\) | 21.3447 | − | 15.5079i | 1.05932 | − | 0.769642i | ||||
\(407\) | 2.43262 | + | 7.48684i | 0.120581 | + | 0.371109i | ||||
\(408\) | −15.1463 | −0.749854 | ||||||||
\(409\) | 15.4039 | 0.761673 | 0.380836 | − | 0.924642i | \(-0.375636\pi\) | ||||
0.380836 | + | 0.924642i | \(0.375636\pi\) | |||||||
\(410\) | −3.23875 | − | 9.96783i | −0.159950 | − | 0.492276i | ||||
\(411\) | 2.69008 | − | 8.27920i | 0.132692 | − | 0.408383i | ||||
\(412\) | 0.639202 | − | 1.96726i | 0.0314912 | − | 0.0969201i | ||||
\(413\) | −47.6373 | − | 34.6106i | −2.34408 | − | 1.70307i | ||||
\(414\) | 1.26052 | + | 3.87948i | 0.0619511 | + | 0.190666i | ||||
\(415\) | −15.2488 | − | 11.0789i | −0.748533 | − | 0.543841i | ||||
\(416\) | −7.89746 | + | 5.73784i | −0.387205 | + | 0.281321i | ||||
\(417\) | 4.45209 | − | 13.7021i | 0.218020 | − | 0.670996i | ||||
\(418\) | −5.58937 | + | 4.06091i | −0.273385 | + | 0.198626i | ||||
\(419\) | −6.28375 | + | 4.56541i | −0.306981 | + | 0.223035i | −0.730600 | − | 0.682805i | \(-0.760760\pi\) |
0.423619 | + | 0.905841i | \(0.360760\pi\) | |||||||
\(420\) | −2.04512 | + | 6.29424i | −0.0997918 | + | 0.307127i | ||||
\(421\) | −4.30613 | + | 3.12859i | −0.209868 | + | 0.152478i | −0.687754 | − | 0.725944i | \(-0.741403\pi\) |
0.477886 | + | 0.878422i | \(0.341403\pi\) | |||||||
\(422\) | −2.24640 | − | 1.63211i | −0.109353 | − | 0.0794497i | ||||
\(423\) | 2.44951 | + | 7.53883i | 0.119099 | + | 0.366551i | ||||
\(424\) | 13.3654 | + | 9.71056i | 0.649083 | + | 0.471586i | ||||
\(425\) | 3.51948 | − | 10.8318i | 0.170720 | − | 0.525421i | ||||
\(426\) | −2.33507 | + | 7.18661i | −0.113135 | + | 0.348192i | ||||
\(427\) | −2.67092 | − | 8.22025i | −0.129255 | − | 0.397806i | ||||
\(428\) | −4.84290 | −0.234091 | ||||||||
\(429\) | −3.05177 | −0.147341 | ||||||||
\(430\) | −6.12025 | − | 18.8362i | −0.295145 | − | 0.908362i | ||||
\(431\) | 7.83383 | − | 5.69161i | 0.377342 | − | 0.274155i | −0.382907 | − | 0.923787i | \(-0.625077\pi\) |
0.760249 | + | 0.649632i | \(0.225077\pi\) | |||||||
\(432\) | 2.06018 | + | 1.49681i | 0.0991205 | + | 0.0720153i | ||||
\(433\) | 11.3906 | 0.547398 | 0.273699 | − | 0.961815i | \(-0.411753\pi\) | ||||
0.273699 | + | 0.961815i | \(0.411753\pi\) | |||||||
\(434\) | 2.97845 | + | 28.6575i | 0.142970 | + | 1.37560i | ||||
\(435\) | −13.7854 | −0.660960 | ||||||||
\(436\) | 6.79889 | + | 4.93968i | 0.325608 | + | 0.236568i | ||||
\(437\) | 16.4280 | − | 11.9357i | 0.785859 | − | 0.570960i | ||||
\(438\) | 0.0583514 | + | 0.179587i | 0.00278814 | + | 0.00858101i | ||||
\(439\) | 16.4255 | 0.783946 | 0.391973 | − | 0.919977i | \(-0.371793\pi\) | ||||
0.391973 | + | 0.919977i | \(0.371793\pi\) | |||||||
\(440\) | −8.04299 | −0.383435 | ||||||||
\(441\) | 3.60881 | + | 11.1068i | 0.171848 | + | 0.528895i | ||||
\(442\) | 5.74937 | − | 17.6948i | 0.273470 | − | 0.841654i | ||||
\(443\) | −2.93757 | + | 9.04092i | −0.139568 | + | 0.429547i | −0.996273 | − | 0.0862607i | \(-0.972508\pi\) |
0.856704 | + | 0.515808i | \(0.172508\pi\) | |||||||
\(444\) | −3.72595 | − | 2.70706i | −0.176826 | − | 0.128472i | ||||
\(445\) | −7.52661 | − | 23.1645i | −0.356795 | − | 1.09810i | ||||
\(446\) | 5.29822 | + | 3.84938i | 0.250878 | + | 0.182274i | ||||
\(447\) | −10.3778 | + | 7.53993i | −0.490854 | + | 0.356627i | ||||
\(448\) | −11.7536 | + | 36.1738i | −0.555304 | + | 1.70905i | ||||
\(449\) | 3.57166 | − | 2.59496i | 0.168557 | − | 0.122464i | −0.500309 | − | 0.865847i | \(-0.666780\pi\) |
0.668866 | + | 0.743383i | \(0.266780\pi\) | |||||||
\(450\) | −2.23823 | + | 1.62617i | −0.105511 | + | 0.0766583i | ||||
\(451\) | −0.968463 | + | 2.98062i | −0.0456031 | + | 0.140352i | ||||
\(452\) | −2.83421 | + | 2.05918i | −0.133310 | + | 0.0968555i | ||||
\(453\) | 4.69531 | + | 3.41134i | 0.220605 | + | 0.160279i | ||||
\(454\) | −9.27506 | − | 28.5457i | −0.435300 | − | 1.33972i | ||||
\(455\) | −29.8025 | − | 21.6528i | −1.39716 | − | 1.01510i | ||||
\(456\) | 5.65980 | − | 17.4191i | 0.265044 | − | 0.815723i | ||||
\(457\) | −8.19600 | + | 25.2247i | −0.383393 | + | 1.17996i | 0.554247 | + | 0.832353i | \(0.313006\pi\) |
−0.937639 | + | 0.347609i | \(0.886994\pi\) | |||||||
\(458\) | 9.34037 | + | 28.7467i | 0.436447 | + | 1.34324i | ||||
\(459\) | 4.92912 | 0.230071 | ||||||||
\(460\) | 5.21692 | 0.243240 | ||||||||
\(461\) | −6.60062 | − | 20.3146i | −0.307422 | − | 0.946146i | −0.978762 | − | 0.204998i | \(-0.934281\pi\) |
0.671341 | − | 0.741149i | \(-0.265719\pi\) | |||||||
\(462\) | −4.05276 | + | 2.94450i | −0.188551 | + | 0.136991i | ||||
\(463\) | −12.1130 | − | 8.80062i | −0.562940 | − | 0.409000i | 0.269594 | − | 0.962974i | \(-0.413111\pi\) |
−0.832534 | + | 0.553974i | \(0.813111\pi\) | |||||||
\(464\) | −12.9835 | −0.602743 | ||||||||
\(465\) | 7.54220 | − | 13.0286i | 0.349761 | − | 0.604186i | ||||
\(466\) | −26.8746 | −1.24494 | ||||||||
\(467\) | −6.89119 | − | 5.00674i | −0.318886 | − | 0.231684i | 0.416814 | − | 0.908992i | \(-0.363147\pi\) |
−0.735700 | + | 0.677307i | \(0.763147\pi\) | |||||||
\(468\) | 1.44443 | − | 1.04944i | 0.0667689 | − | 0.0485104i | ||||
\(469\) | −9.36671 | − | 28.8278i | −0.432514 | − | 1.33114i | ||||
\(470\) | −25.6623 | −1.18371 | ||||||||
\(471\) | −1.37534 | −0.0633721 | ||||||||
\(472\) | 12.9372 | + | 39.8166i | 0.595483 | + | 1.83271i | ||||
\(473\) | −1.83010 | + | 5.63247i | −0.0841481 | + | 0.258981i | ||||
\(474\) | 6.19495 | − | 19.0661i | 0.284544 | − | 0.875735i | ||||
\(475\) | 11.1421 | + | 8.09518i | 0.511233 | + | 0.371432i | ||||
\(476\) | 3.72831 | + | 11.4745i | 0.170887 | + | 0.525935i | ||||
\(477\) | −4.34956 | − | 3.16014i | −0.199153 | − | 0.144693i | ||||
\(478\) | −7.09720 | + | 5.15642i | −0.324618 | + | 0.235849i | ||||
\(479\) | 4.44665 | − | 13.6854i | 0.203173 | − | 0.625301i | −0.796611 | − | 0.604492i | \(-0.793376\pi\) |
0.999783 | − | 0.0208085i | \(-0.00662403\pi\) | |||||||
\(480\) | 6.77354 | − | 4.92126i | 0.309168 | − | 0.224624i | ||||
\(481\) | 20.7394 | − | 15.0680i | 0.945634 | − | 0.687043i | ||||
\(482\) | −4.54848 | + | 13.9988i | −0.207178 | + | 0.637627i | ||||
\(483\) | 11.9117 | − | 8.65436i | 0.542001 | − | 0.393787i | ||||
\(484\) | −4.61073 | − | 3.34989i | −0.209579 | − | 0.152268i | ||||
\(485\) | −1.39581 | − | 4.29586i | −0.0633805 | − | 0.195065i | ||||
\(486\) | −0.968675 | − | 0.703784i | −0.0439400 | − | 0.0319243i | ||||
\(487\) | 8.07893 | − | 24.8644i | 0.366091 | − | 1.12671i | −0.583203 | − | 0.812326i | \(-0.698201\pi\) |
0.949295 | − | 0.314387i | \(-0.101799\pi\) | |||||||
\(488\) | −1.89902 | + | 5.84458i | −0.0859646 | + | 0.264572i | ||||
\(489\) | −0.130095 | − | 0.400391i | −0.00588310 | − | 0.0181063i | ||||
\(490\) | −37.8076 | −1.70797 | ||||||||
\(491\) | 16.3293 | 0.736931 | 0.368466 | − | 0.929641i | \(-0.379883\pi\) | ||||
0.368466 | + | 0.929641i | \(0.379883\pi\) | |||||||
\(492\) | −0.566592 | − | 1.74379i | −0.0255439 | − | 0.0786161i | ||||
\(493\) | −20.3315 | + | 14.7717i | −0.915686 | + | 0.665285i | ||||
\(494\) | 18.2015 | + | 13.2242i | 0.818926 | + | 0.594984i | ||||
\(495\) | 2.61746 | 0.117646 | ||||||||
\(496\) | 7.10345 | − | 12.2707i | 0.318954 | − | 0.550969i | ||||
\(497\) | 27.2751 | 1.22346 | ||||||||
\(498\) | 6.75272 | + | 4.90614i | 0.302597 | + | 0.219849i | ||||
\(499\) | −18.8884 | + | 13.7232i | −0.845559 | + | 0.614335i | −0.923918 | − | 0.382590i | \(-0.875032\pi\) |
0.0783587 | + | 0.996925i | \(0.475032\pi\) | |||||||
\(500\) | −1.27263 | − | 3.91677i | −0.0569139 | − | 0.175163i | ||||
\(501\) | −11.5072 | −0.514104 | ||||||||
\(502\) | 35.2398 | 1.57283 | ||||||||
\(503\) | 0.402009 | + | 1.23726i | 0.0179247 | + | 0.0551665i | 0.959619 | − | 0.281304i | \(-0.0907668\pi\) |
−0.941694 | + | 0.336470i | \(0.890767\pi\) | |||||||
\(504\) | 4.10383 | − | 12.6303i | 0.182799 | − | 0.562598i | ||||
\(505\) | 3.16802 | − | 9.75018i | 0.140975 | − | 0.433877i | ||||
\(506\) | 3.19469 | + | 2.32107i | 0.142021 | + | 0.103184i | ||||
\(507\) | −0.946221 | − | 2.91217i | −0.0420232 | − | 0.129334i | ||||
\(508\) | −0.405271 | − | 0.294447i | −0.0179810 | − | 0.0130640i | ||||
\(509\) | −22.9756 | + | 16.6927i | −1.01838 | + | 0.739893i | −0.965949 | − | 0.258732i | \(-0.916695\pi\) |
−0.0524261 | + | 0.998625i | \(0.516695\pi\) | |||||||
\(510\) | −4.93115 | + | 15.1765i | −0.218355 | + | 0.672028i | ||||
\(511\) | 0.551412 | − | 0.400624i | 0.0243930 | − | 0.0177226i | ||||
\(512\) | 19.0406 | − | 13.8338i | 0.841485 | − | 0.611375i | ||||
\(513\) | −1.84189 | + | 5.66875i | −0.0813214 | + | 0.250282i | ||||
\(514\) | 10.5918 | − | 7.69541i | 0.467185 | − | 0.339430i | ||||
\(515\) | −7.98914 | − | 5.80445i | −0.352043 | − | 0.255774i | ||||
\(516\) | −1.07069 | − | 3.29524i | −0.0471344 | − | 0.145065i | ||||
\(517\) | 6.20810 | + | 4.51045i | 0.273032 | + | 0.198369i | ||||
\(518\) | 13.0035 | − | 40.0208i | 0.571342 | − | 1.75841i | ||||
\(519\) | 2.36221 | − | 7.27014i | 0.103690 | − | 0.319124i | ||||
\(520\) | 8.09367 | + | 24.9098i | 0.354931 | + | 1.09236i | ||||
\(521\) | 31.4473 | 1.37773 | 0.688866 | − | 0.724889i | \(-0.258109\pi\) | ||||
0.688866 | + | 0.724889i | \(0.258109\pi\) | |||||||
\(522\) | 6.10469 | 0.267195 | ||||||||
\(523\) | −0.397623 | − | 1.22376i | −0.0173868 | − | 0.0535112i | 0.941987 | − | 0.335650i | \(-0.108956\pi\) |
−0.959374 | + | 0.282139i | \(0.908956\pi\) | |||||||
\(524\) | −1.92951 | + | 1.40187i | −0.0842911 | + | 0.0612411i | ||||
\(525\) | 8.07893 | + | 5.86968i | 0.352593 | + | 0.256174i | ||||
\(526\) | −29.7331 | −1.29642 | ||||||||
\(527\) | −2.83707 | − | 27.2971i | −0.123585 | − | 1.18908i | ||||
\(528\) | 2.46519 | 0.107284 | ||||||||
\(529\) | 9.21770 | + | 6.69705i | 0.400770 | + | 0.291176i | ||||
\(530\) | 14.0813 | − | 10.2307i | 0.611653 | − | 0.444392i | ||||
\(531\) | −4.21020 | − | 12.9577i | −0.182707 | − | 0.562315i | ||||
\(532\) | −14.5895 | −0.632536 | ||||||||
\(533\) | 10.2058 | 0.442061 | ||||||||
\(534\) | 3.33306 | + | 10.2581i | 0.144236 | + | 0.443911i | ||||
\(535\) | −7.14454 | + | 21.9886i | −0.308885 | + | 0.950652i | ||||
\(536\) | −6.65971 | + | 20.4965i | −0.287656 | + | 0.885313i | ||||
\(537\) | 10.1753 | + | 7.39279i | 0.439096 | + | 0.319022i | ||||
\(538\) | 9.24358 | + | 28.4488i | 0.398519 | + | 1.22652i | ||||
\(539\) | 9.14625 | + | 6.64514i | 0.393957 | + | 0.286226i | ||||
\(540\) | −1.23887 | + | 0.900090i | −0.0533124 | + | 0.0387337i | ||||
\(541\) | −4.18567 | + | 12.8822i | −0.179956 | + | 0.553848i | −0.999825 | − | 0.0187031i | \(-0.994046\pi\) |
0.819869 | + | 0.572551i | \(0.194046\pi\) | |||||||
\(542\) | −19.6215 | + | 14.2559i | −0.842816 | + | 0.612341i | ||||
\(543\) | −17.5283 | + | 12.7351i | −0.752212 | + | 0.546514i | ||||
\(544\) | 4.71664 | − | 14.5163i | 0.202224 | − | 0.622382i | ||||
\(545\) | 32.4582 | − | 23.5823i | 1.39036 | − | 1.01015i | ||||
\(546\) | 13.1976 | + | 9.58865i | 0.564807 | + | 0.410356i | ||||
\(547\) | 4.89483 | + | 15.0648i | 0.209288 | + | 0.644122i | 0.999510 | + | 0.0313015i | \(0.00996521\pi\) |
−0.790222 | + | 0.612821i | \(0.790035\pi\) | |||||||
\(548\) | 3.98869 | + | 2.89795i | 0.170388 | + | 0.123794i | ||||
\(549\) | 0.618005 | − | 1.90202i | 0.0263758 | − | 0.0811764i | ||||
\(550\) | −0.827623 | + | 2.54716i | −0.0352900 | + | 0.108611i | ||||
\(551\) | −9.39089 | − | 28.9022i | −0.400065 | − | 1.23127i | ||||
\(552\) | −10.4685 | −0.445569 | ||||||||
\(553\) | −72.3610 | −3.07710 | ||||||||
\(554\) | 0.714404 | + | 2.19871i | 0.0303521 | + | 0.0934142i | ||||
\(555\) | −17.7879 | + | 12.9236i | −0.755052 | + | 0.548578i | ||||
\(556\) | 6.60131 | + | 4.79613i | 0.279958 | + | 0.203401i | ||||
\(557\) | −10.3809 | −0.439855 | −0.219927 | − | 0.975516i | \(-0.570582\pi\) | ||||
−0.219927 | + | 0.975516i | \(0.570582\pi\) | |||||||
\(558\) | −3.33996 | + | 5.76954i | −0.141392 | + | 0.244244i | ||||
\(559\) | 19.2858 | 0.815703 | ||||||||
\(560\) | 24.0742 | + | 17.4909i | 1.01732 | + | 0.739126i | ||||
\(561\) | 3.86038 | − | 2.80473i | 0.162985 | − | 0.118416i | ||||
\(562\) | 1.57816 | + | 4.85707i | 0.0665705 | + | 0.204883i | ||||
\(563\) | −11.0602 | −0.466133 | −0.233067 | − | 0.972461i | \(-0.574876\pi\) | ||||
−0.233067 | + | 0.972461i | \(0.574876\pi\) | |||||||
\(564\) | −4.48940 | −0.189038 | ||||||||
\(565\) | 5.16825 | + | 15.9062i | 0.217430 | + | 0.669180i | ||||
\(566\) | −10.6953 | + | 32.9168i | −0.449558 | + | 1.38360i | ||||
\(567\) | −1.33552 | + | 4.11032i | −0.0560868 | + | 0.172617i | ||||
\(568\) | −15.6889 | − | 11.3987i | −0.658292 | − | 0.478277i | ||||
\(569\) | −0.408127 | − | 1.25609i | −0.0171096 | − | 0.0526579i | 0.942137 | − | 0.335227i | \(-0.108813\pi\) |
−0.959247 | + | 0.282570i | \(0.908813\pi\) | |||||||
\(570\) | −15.6112 | − | 11.3422i | −0.653881 | − | 0.475072i | ||||
\(571\) | 24.1749 | − | 17.5641i | 1.01169 | − | 0.735035i | 0.0471262 | − | 0.998889i | \(-0.484994\pi\) |
0.964563 | + | 0.263854i | \(0.0849937\pi\) | |||||||
\(572\) | 0.534103 | − | 1.64380i | 0.0223320 | − | 0.0687307i | ||||
\(573\) | 1.16041 | − | 0.843089i | 0.0484769 | − | 0.0352205i | ||||
\(574\) | 13.5533 | − | 9.84704i | 0.565703 | − | 0.411008i | ||||
\(575\) | 2.43252 | − | 7.48651i | 0.101443 | − | 0.312209i | ||||
\(576\) | −7.11993 | + | 5.17293i | −0.296664 | + | 0.215539i | ||||
\(577\) | −7.60522 | − | 5.52552i | −0.316610 | − | 0.230030i | 0.418118 | − | 0.908393i | \(-0.362690\pi\) |
−0.734727 | + | 0.678362i | \(0.762690\pi\) | |||||||
\(578\) | 2.69959 | + | 8.30850i | 0.112288 | + | 0.345588i | ||||
\(579\) | 7.43687 | + | 5.40320i | 0.309066 | + | 0.224549i | ||||
\(580\) | 2.41264 | − | 7.42535i | 0.100180 | − | 0.308321i | ||||
\(581\) | 9.31006 | − | 28.6534i | 0.386246 | − | 1.18874i | ||||
\(582\) | 0.618116 | + | 1.90237i | 0.0256217 | + | 0.0788556i | ||||
\(583\) | −5.20465 | −0.215554 | ||||||||
\(584\) | −0.484603 | −0.0200530 | ||||||||
\(585\) | −2.63395 | − | 8.10647i | −0.108901 | − | 0.335161i | ||||
\(586\) | −25.1010 | + | 18.2370i | −1.03691 | + | 0.753362i | ||||
\(587\) | 16.0801 | + | 11.6828i | 0.663695 | + | 0.482202i | 0.867909 | − | 0.496724i | \(-0.165464\pi\) |
−0.204214 | + | 0.978926i | \(0.565464\pi\) | |||||||
\(588\) | −6.61413 | −0.272762 | ||||||||
\(589\) | 32.4533 | + | 6.93748i | 1.33722 | + | 0.285854i | ||||
\(590\) | 44.1080 | 1.81590 | ||||||||
\(591\) | 6.08294 | + | 4.41951i | 0.250219 | + | 0.181794i | ||||
\(592\) | −16.7531 | + | 12.1718i | −0.688547 | + | 0.500259i | ||||
\(593\) | 4.56842 | + | 14.0602i | 0.187603 | + | 0.577382i | 0.999983 | − | 0.00574559i | \(-0.00182889\pi\) |
−0.812381 | + | 0.583127i | \(0.801829\pi\) | |||||||
\(594\) | −1.15911 | −0.0475588 | ||||||||
\(595\) | 57.5990 | 2.36133 | ||||||||
\(596\) | −2.24503 | − | 6.90949i | −0.0919600 | − | 0.283024i | ||||
\(597\) | 0.272799 | − | 0.839591i | 0.0111649 | − | 0.0343622i | ||||
\(598\) | 3.97373 | − | 12.2299i | 0.162498 | − | 0.500117i | ||||
\(599\) | −6.91709 | − | 5.02556i | −0.282624 | − | 0.205339i | 0.437437 | − | 0.899249i | \(-0.355886\pi\) |
−0.720061 | + | 0.693910i | \(0.755886\pi\) | |||||||
\(600\) | −2.19405 | − | 6.75259i | −0.0895717 | − | 0.275673i | ||||
\(601\) | −16.7106 | − | 12.1409i | −0.681638 | − | 0.495239i | 0.192262 | − | 0.981344i | \(-0.438418\pi\) |
−0.873901 | + | 0.486104i | \(0.838418\pi\) | |||||||
\(602\) | 25.6116 | − | 18.6079i | 1.04385 | − | 0.758403i | ||||
\(603\) | 2.16729 | − | 6.67024i | 0.0882590 | − | 0.271633i | ||||
\(604\) | −2.65922 | + | 1.93204i | −0.108202 | + | 0.0786136i | ||||
\(605\) | −22.0118 | + | 15.9925i | −0.894907 | + | 0.650188i | ||||
\(606\) | −1.40292 | + | 4.31774i | −0.0569896 | + | 0.175396i | ||||
\(607\) | −1.13379 | + | 0.823745i | −0.0460190 | + | 0.0334348i | −0.610557 | − | 0.791972i | \(-0.709054\pi\) |
0.564538 | + | 0.825407i | \(0.309054\pi\) | |||||||
\(608\) | 14.9321 | + | 10.8488i | 0.605575 | + | 0.439976i | ||||
\(609\) | −6.80918 | − | 20.9565i | −0.275922 | − | 0.849201i | ||||
\(610\) | 5.23799 | + | 3.80562i | 0.212080 | + | 0.154085i | ||||
\(611\) | 7.72198 | − | 23.7658i | 0.312398 | − | 0.961462i | ||||
\(612\) | −0.862665 | + | 2.65501i | −0.0348712 | + | 0.107322i | ||||
\(613\) | 3.44465 | + | 10.6015i | 0.139128 | + | 0.428192i | 0.996209 | − | 0.0869891i | \(-0.0277245\pi\) |
−0.857081 | + | 0.515181i | \(0.827725\pi\) | |||||||
\(614\) | −7.21500 | −0.291174 | ||||||||
\(615\) | −8.75334 | −0.352969 | ||||||||
\(616\) | −3.97276 | − | 12.2269i | −0.160067 | − | 0.492636i | ||||
\(617\) | −34.5460 | + | 25.0992i | −1.39077 | + | 1.01045i | −0.394990 | + | 0.918685i | \(0.629252\pi\) |
−0.995780 | + | 0.0917689i | \(0.970748\pi\) | |||||||
\(618\) | 3.53788 | + | 2.57042i | 0.142315 | + | 0.103398i | ||||
\(619\) | 0.248366 | 0.00998268 | 0.00499134 | − | 0.999988i | \(-0.498411\pi\) | ||||
0.00499134 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(620\) | 5.69770 | + | 6.34270i | 0.228825 | + | 0.254729i | ||||
\(621\) | 3.40680 | 0.136710 | ||||||||
\(622\) | 20.7997 | + | 15.1118i | 0.833991 | + | 0.605930i | ||||
\(623\) | 31.4969 | − | 22.8838i | 1.26189 | − | 0.916820i | ||||
\(624\) | −2.48073 | − | 7.63489i | −0.0993085 | − | 0.305640i | ||||
\(625\) | −31.2141 | −1.24857 | ||||||||
\(626\) | −1.56568 | −0.0625771 | ||||||||
\(627\) | 1.78306 | + | 5.48771i | 0.0712087 | + | 0.219158i | ||||
\(628\) | 0.240703 | − | 0.740808i | 0.00960510 | − | 0.0295615i | ||||
\(629\) | −12.3863 | + | 38.1210i | −0.493873 | + | 1.51998i | ||||
\(630\) | −11.3194 | − | 8.22404i | −0.450977 | − | 0.327654i | ||||
\(631\) | 3.21031 | + | 9.88032i | 0.127800 | + | 0.393329i | 0.994401 | − | 0.105673i | \(-0.0336998\pi\) |
−0.866601 | + | 0.499003i | \(0.833700\pi\) | |||||||
\(632\) | 41.6227 | + | 30.2407i | 1.65566 | + | 1.20291i | ||||
\(633\) | −1.87615 | + | 1.36310i | −0.0745702 | + | 0.0541784i | ||||
\(634\) | 7.90148 | − | 24.3182i | 0.313808 | − | 0.965801i | ||||
\(635\) | −1.93478 | + | 1.40570i | −0.0767795 | + | 0.0557836i | ||||
\(636\) | 2.46341 | − | 1.78977i | 0.0976805 | − | 0.0709690i | ||||
\(637\) | 11.3766 | − | 35.0136i | 0.450758 | − | 1.38729i | ||||
\(638\) | 4.78106 | − | 3.47365i | 0.189284 | − | 0.137523i | ||||
\(639\) | 5.10570 | + | 3.70951i | 0.201978 | + | 0.146746i | ||||
\(640\) | −3.62984 | − | 11.1715i | −0.143482 | − | 0.441592i | ||||
\(641\) | −13.7387 | − | 9.98175i | −0.542646 | − | 0.394256i | 0.282421 | − | 0.959291i | \(-0.408863\pi\) |
−0.825067 | + | 0.565035i | \(0.808863\pi\) | |||||||
\(642\) | 3.16387 | − | 9.73738i | 0.124868 | − | 0.384304i | ||||
\(643\) | 0.544835 | − | 1.67683i | 0.0214862 | − | 0.0661278i | −0.939738 | − | 0.341894i | \(-0.888932\pi\) |
0.961225 | + | 0.275766i | \(0.0889316\pi\) | |||||||
\(644\) | 2.57685 | + | 7.93073i | 0.101542 | + | 0.312515i | ||||
\(645\) | −16.5412 | −0.651308 | ||||||||
\(646\) | −35.1780 | −1.38406 | ||||||||
\(647\) | −9.45832 | − | 29.1097i | −0.371845 | − | 1.14442i | −0.945583 | − | 0.325382i | \(-0.894507\pi\) |
0.573738 | − | 0.819039i | \(-0.305493\pi\) | |||||||
\(648\) | 2.48597 | − | 1.80616i | 0.0976580 | − | 0.0709527i | ||||
\(649\) | −10.6704 | − | 7.75251i | −0.418850 | − | 0.304313i | ||||
\(650\) | 8.72159 | 0.342089 | ||||||||
\(651\) | 23.5314 | + | 5.03025i | 0.922268 | + | 0.197151i | ||||
\(652\) | 0.238434 | 0.00933781 | ||||||||
\(653\) | −32.0256 | − | 23.2680i | −1.25326 | − | 0.910546i | −0.254853 | − | 0.966980i | \(-0.582027\pi\) |
−0.998406 | + | 0.0564338i | \(0.982027\pi\) | |||||||
\(654\) | −14.3737 | + | 10.4431i | −0.562055 | + | 0.408357i | ||||
\(655\) | 3.51851 | + | 10.8288i | 0.137479 | + | 0.423118i | ||||
\(656\) | −8.24413 | −0.321879 | ||||||||
\(657\) | 0.157706 | 0.00615271 | ||||||||
\(658\) | −12.6756 | − | 39.0116i | −0.494148 | − | 1.52083i | ||||
\(659\) | 13.5645 | − | 41.7473i | 0.528399 | − | 1.62624i | −0.229096 | − | 0.973404i | \(-0.573577\pi\) |
0.757495 | − | 0.652841i | \(-0.226423\pi\) | |||||||
\(660\) | −0.458092 | + | 1.40986i | −0.0178312 | + | 0.0548789i | ||||
\(661\) | 20.4550 | + | 14.8615i | 0.795609 | + | 0.578044i | 0.909623 | − | 0.415436i | \(-0.136371\pi\) |
−0.114014 | + | 0.993479i | \(0.536371\pi\) | |||||||
\(662\) | 8.40519 | + | 25.8685i | 0.326677 | + | 1.00541i | ||||
\(663\) | −12.5712 | − | 9.13348i | −0.488223 | − | 0.354715i | ||||
\(664\) | −17.3299 | + | 12.5909i | −0.672530 | + | 0.488622i | ||||
\(665\) | −21.5233 | + | 66.2421i | −0.834640 | + | 2.56876i | ||||
\(666\) | 7.87711 | − | 5.72306i | 0.305232 | − | 0.221764i | ||||
\(667\) | −14.0523 | + | 10.2096i | −0.544108 | + | 0.395317i | ||||
\(668\) | 2.01392 | − | 6.19821i | 0.0779210 | − | 0.239816i | ||||
\(669\) | 4.42496 | − | 3.21492i | 0.171079 | − | 0.124296i | ||||
\(670\) | 18.3692 | + | 13.3460i | 0.709664 | + | 0.515601i | ||||
\(671\) | −0.598267 | − | 1.84128i | −0.0230958 | − | 0.0710817i | ||||
\(672\) | 10.8270 | + | 7.86628i | 0.417661 | + | 0.303448i | ||||
\(673\) | −0.0484325 | + | 0.149060i | −0.00186693 | + | 0.00574583i | −0.951986 | − | 0.306143i | \(-0.900962\pi\) |
0.950119 | + | 0.311889i | \(0.100962\pi\) | |||||||
\(674\) | 9.59551 | − | 29.5319i | 0.369605 | − | 1.13753i | ||||
\(675\) | 0.714018 | + | 2.19752i | 0.0274826 | + | 0.0845826i | ||||
\(676\) | 1.73421 | 0.0667003 | ||||||||
\(677\) | −18.7088 | −0.719037 | −0.359519 | − | 0.933138i | \(-0.617059\pi\) | ||||
−0.359519 | + | 0.933138i | \(0.617059\pi\) | |||||||
\(678\) | −2.28869 | − | 7.04387i | −0.0878966 | − | 0.270518i | ||||
\(679\) | 5.84110 | − | 4.24381i | 0.224161 | − | 0.162862i | ||||
\(680\) | −33.1315 | − | 24.0714i | −1.27053 | − | 0.923098i | ||||
\(681\) | −25.0677 | −0.960596 | ||||||||
\(682\) | 0.667152 | + | 6.41906i | 0.0255466 | + | 0.245799i | ||||
\(683\) | 3.94761 | 0.151051 | 0.0755256 | − | 0.997144i | \(-0.475937\pi\) | ||||
0.0755256 | + | 0.997144i | \(0.475937\pi\) | |||||||
\(684\) | −2.73105 | − | 1.98422i | −0.104424 | − | 0.0758687i | ||||
\(685\) | 19.0422 | − | 13.8350i | 0.727564 | − | 0.528606i | ||||
\(686\) | −7.48112 | − | 23.0245i | −0.285631 | − | 0.879080i | ||||
\(687\) | 25.2442 | 0.963125 | ||||||||
\(688\) | −15.5789 | −0.593941 | ||||||||
\(689\) | 5.23744 | + | 16.1192i | 0.199531 | + | 0.614092i | ||||
\(690\) | −3.40821 | + | 10.4894i | −0.129748 | + | 0.399324i | ||||
\(691\) | −5.76359 | + | 17.7385i | −0.219257 | + | 0.674805i | 0.779567 | + | 0.626319i | \(0.215439\pi\) |
−0.998824 | + | 0.0484853i | \(0.984561\pi\) | |||||||
\(692\) | 3.50255 | + | 2.54475i | 0.133147 | + | 0.0967370i | ||||
\(693\) | 1.29287 | + | 3.97905i | 0.0491121 | + | 0.151151i | ||||
\(694\) | −2.96654 | − | 2.15532i | −0.112608 | − | 0.0818148i | ||||
\(695\) | 31.5149 | − | 22.8969i | 1.19543 | − | 0.868530i | ||||
\(696\) | −4.84131 | + | 14.9000i | −0.183510 | + | 0.564784i | ||||
\(697\) | −12.9099 | + | 9.37961i | −0.488998 | + | 0.355278i | ||||
\(698\) | 2.21462 | − | 1.60901i | 0.0838244 | − | 0.0609020i | ||||
\(699\) | −6.93592 | + | 21.3466i | −0.262341 | + | 0.807401i | ||||
\(700\) | −4.57556 | + | 3.32434i | −0.172940 | + | 0.125648i | ||||
\(701\) | 25.0433 | + | 18.1950i | 0.945873 | + | 0.687217i | 0.949827 | − | 0.312776i | \(-0.101259\pi\) |
−0.00395455 | + | 0.999992i | \(0.501259\pi\) | |||||||
\(702\) | 1.16641 | + | 3.58984i | 0.0440233 | + | 0.135490i | ||||
\(703\) | −39.2128 | − | 28.4898i | −1.47894 | − | 1.07451i | ||||
\(704\) | −2.63272 | + | 8.10266i | −0.0992242 | + | 0.305381i | ||||
\(705\) | −6.62303 | + | 20.3836i | −0.249438 | + | 0.767691i | ||||
\(706\) | −4.75103 | − | 14.6222i | −0.178808 | − | 0.550313i | ||||
\(707\) | 16.3870 | 0.616296 | ||||||||
\(708\) | 7.71634 | 0.289998 | ||||||||
\(709\) | −2.34524 | − | 7.21791i | −0.0880773 | − | 0.271074i | 0.897310 | − | 0.441400i | \(-0.145518\pi\) |
−0.985388 | + | 0.170326i | \(0.945518\pi\) | |||||||
\(710\) | −16.5292 | + | 12.0092i | −0.620330 | + | 0.450696i | ||||
\(711\) | −13.5454 | − | 9.84133i | −0.507993 | − | 0.369079i | ||||
\(712\) | −27.6807 | −1.03738 | ||||||||
\(713\) | −1.96086 | − | 18.8666i | −0.0734350 | − | 0.706561i | ||||
\(714\) | −25.5070 | −0.954575 | ||||||||
\(715\) | −6.67554 | − | 4.85006i | −0.249651 | − | 0.181382i | ||||
\(716\) | −5.76286 | + | 4.18696i | −0.215368 | + | 0.156474i | ||||
\(717\) | 2.26408 | + | 6.96812i | 0.0845535 | + | 0.260229i | ||||
\(718\) | 10.7632 | 0.401678 | ||||||||
\(719\) | 17.5841 | 0.655777 | 0.327888 | − | 0.944716i | \(-0.393663\pi\) | ||||
0.327888 | + | 0.944716i | \(0.393663\pi\) | |||||||
\(720\) | 2.12768 | + | 6.54834i | 0.0792941 | + | 0.244042i | ||||
\(721\) | 4.87772 | − | 15.0121i | 0.181656 | − | 0.559079i | ||||
\(722\) | 6.11512 | − | 18.8204i | 0.227581 | − | 0.700423i | ||||
\(723\) | 9.94537 | + | 7.22574i | 0.369872 | + | 0.268728i | ||||
\(724\) | −3.79189 | − | 11.6702i | −0.140924 | − | 0.433721i | ||||
\(725\) | −9.53076 | − | 6.92450i | −0.353963 | − | 0.257170i | ||||
\(726\) | 9.74764 | − | 7.08207i | 0.361769 | − | 0.262840i | ||||
\(727\) | 5.84819 | − | 17.9989i | 0.216897 | − | 0.667541i | −0.782116 | − | 0.623133i | \(-0.785860\pi\) |
0.999013 | − | 0.0444085i | \(-0.0141403\pi\) | |||||||
\(728\) | −33.8699 | + | 24.6079i | −1.25530 | + | 0.912029i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | −0.157771 | + | 0.485571i | −0.00583938 | + | 0.0179718i | ||||
\(731\) | −24.3959 | + | 17.7246i | −0.902313 | + | 0.655569i | ||||
\(732\) | 0.916342 | + | 0.665762i | 0.0338690 | + | 0.0246073i | ||||
\(733\) | 11.1233 | + | 34.2339i | 0.410847 | + | 1.26446i | 0.915913 | + | 0.401377i | \(0.131468\pi\) |
−0.505066 | + | 0.863081i | \(0.668532\pi\) | |||||||
\(734\) | −17.7190 | − | 12.8736i | −0.654019 | − | 0.475173i | ||||
\(735\) | −9.75756 | + | 30.0307i | −0.359913 | + | 1.10770i | ||||
\(736\) | 3.25994 | − | 10.0331i | 0.120163 | − | 0.369824i | ||||
\(737\) | −2.09807 | − | 6.45721i | −0.0772835 | − | 0.237854i | ||||
\(738\) | 3.87630 | 0.142689 | ||||||||
\(739\) | 15.7132 | 0.578021 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(740\) | −3.84803 | − | 11.8430i | −0.141457 | − | 0.435358i | ||||
\(741\) | 15.2015 | − | 11.0446i | 0.558443 | − | 0.405732i | ||||
\(742\) | 22.5079 | + | 16.3530i | 0.826292 | + | 0.600336i | ||||
\(743\) | 39.6677 | 1.45527 | 0.727634 | − | 0.685965i | \(-0.240620\pi\) | ||||
0.727634 | + | 0.685965i | \(0.240620\pi\) | |||||||
\(744\) | −11.4333 | − | 12.7275i | −0.419163 | − | 0.466614i | ||||
\(745\) | −34.6837 | −1.27071 | ||||||||
\(746\) | −33.5202 | − | 24.3538i | −1.22726 | − | 0.891657i | ||||
\(747\) | 5.63973 | − | 4.09750i | 0.206347 | − | 0.149920i | ||||
\(748\) | 0.835113 | + | 2.57021i | 0.0305348 | + | 0.0939763i | ||||
\(749\) | −36.9560 | −1.35034 | ||||||||
\(750\) | 8.70665 | 0.317922 | ||||||||
\(751\) | 14.7071 | + | 45.2637i | 0.536668 | + | 1.65169i | 0.740017 | + | 0.672588i | \(0.234817\pi\) |
−0.203349 | + | 0.979106i | \(0.565183\pi\) | |||||||
\(752\) | −6.23775 | + | 19.1978i | −0.227467 | + | 0.700072i | ||||
\(753\) | 9.09484 | − | 27.9910i | 0.331434 | − | 1.02005i | ||||
\(754\) | −15.5693 | − | 11.3118i | −0.567002 | − | 0.411951i | ||||
\(755\) | 4.84915 | + | 14.9242i | 0.176479 | + | 0.543145i | ||||
\(756\) | −1.98024 | − | 1.43873i | −0.0720206 | − | 0.0523260i | ||||
\(757\) | 1.10661 | − | 0.804001i | 0.0402205 | − | 0.0292219i | −0.567493 | − | 0.823378i | \(-0.692087\pi\) |
0.607714 | + | 0.794156i | \(0.292087\pi\) | |||||||
\(758\) | 3.93820 | − | 12.1205i | 0.143042 | − | 0.440237i | ||||
\(759\) | 2.66813 | − | 1.93851i | 0.0968471 | − | 0.0703636i | ||||
\(760\) | 40.0639 | − | 29.1081i | 1.45327 | − | 1.05586i | ||||
\(761\) | −9.74431 | + | 29.9899i | −0.353231 | + | 1.08713i | 0.603797 | + | 0.797138i | \(0.293654\pi\) |
−0.957028 | + | 0.289995i | \(0.906346\pi\) | |||||||
\(762\) | 0.856793 | − | 0.622496i | 0.0310383 | − | 0.0225507i | ||||
\(763\) | 51.8820 | + | 37.6945i | 1.87826 | + | 1.36463i | ||||
\(764\) | 0.251031 | + | 0.772595i | 0.00908199 | + | 0.0279515i | ||||
\(765\) | 10.7821 | + | 7.83366i | 0.389828 | + | 0.283226i | ||||
\(766\) | 5.61795 | − | 17.2903i | 0.202985 | − | 0.624723i | ||||
\(767\) | −13.2725 | + | 40.8484i | −0.479241 | + | 1.47495i | ||||
\(768\) | −3.83172 | − | 11.7928i | −0.138265 | − | 0.425537i | ||||
\(769\) | −12.7303 | −0.459065 | −0.229533 | − | 0.973301i | \(-0.573720\pi\) | ||||
−0.229533 | + | 0.973301i | \(0.573720\pi\) | |||||||
\(770\) | −13.5447 | −0.488118 | ||||||||
\(771\) | −3.37890 | − | 10.3992i | −0.121688 | − | 0.374517i | ||||
\(772\) | −4.21193 | + | 3.06014i | −0.151591 | + | 0.110137i | ||||
\(773\) | −27.5626 | − | 20.0254i | −0.991358 | − | 0.720264i | −0.0311401 | − | 0.999515i | \(-0.509914\pi\) |
−0.960218 | + | 0.279251i | \(0.909914\pi\) | |||||||
\(774\) | 7.32504 | 0.263293 | ||||||||
\(775\) | 11.7588 | − | 5.21902i | 0.422387 | − | 0.187473i | ||||
\(776\) | −5.13340 | −0.184278 | ||||||||
\(777\) | −28.4326 | − | 20.6575i | −1.02001 | − | 0.741083i | ||||
\(778\) | 33.0499 | − | 24.0122i | 1.18490 | − | 0.860878i | ||||
\(779\) | −5.96294 | − | 18.3521i | −0.213645 | − | 0.657531i | ||||
\(780\) | 4.82743 | 0.172850 | ||||||||
\(781\) | 6.10943 | 0.218613 | ||||||||
\(782\) | 6.21325 | + | 19.1224i | 0.222185 | + | 0.683816i | ||||
\(783\) | 1.57553 | − | 4.84897i | 0.0563047 | − | 0.173288i | ||||
\(784\) | −9.18993 | + | 28.2837i | −0.328212 | + | 1.01013i | ||||
\(785\) | −3.00845 | − | 2.18577i | −0.107376 | − | 0.0780134i | ||||
\(786\) | −1.55812 | − | 4.79541i | −0.0555764 | − | 0.171047i | ||||
\(787\) | −34.1974 | − | 24.8459i | −1.21901 | − | 0.885660i | −0.222989 | − | 0.974821i | \(-0.571581\pi\) |
−0.996017 | + | 0.0891609i | \(0.971581\pi\) | |||||||
\(788\) | −3.44512 | + | 2.50302i | −0.122727 | + | 0.0891666i | ||||
\(789\) | −7.67365 | + | 23.6171i | −0.273189 | + | 0.840790i | ||||
\(790\) | 43.8521 | − | 31.8604i | 1.56019 | − | 1.13354i | ||||
\(791\) | −21.6278 | + | 15.7135i | −0.768994 | + | 0.558707i | ||||
\(792\) | 0.919228 | − | 2.82909i | 0.0326633 | − | 0.100527i | ||||
\(793\) | −5.10054 | + | 3.70576i | −0.181125 | + | 0.131595i | ||||
\(794\) | −17.5279 | − | 12.7347i | −0.622041 | − | 0.451939i | ||||
\(795\) | −4.49208 | − | 13.8252i | −0.159318 | − | 0.490329i | ||||
\(796\) | 0.404492 | + | 0.293880i | 0.0143368 | + | 0.0104163i | ||||
\(797\) | −2.29403 | + | 7.06029i | −0.0812586 | + | 0.250088i | −0.983430 | − | 0.181290i | \(-0.941973\pi\) |
0.902171 | + | 0.431379i | \(0.141973\pi\) | |||||||
\(798\) | 9.53133 | − | 29.3344i | 0.337405 | − | 1.03843i | ||||
\(799\) | 12.0739 | + | 37.1598i | 0.427145 | + | 1.31462i | ||||
\(800\) | 7.15497 | 0.252966 | ||||||||
\(801\) | 9.00824 | 0.318291 | ||||||||
\(802\) | 7.18630 | + | 22.1172i | 0.253757 | + | 0.780984i | ||||
\(803\) | 0.123512 | − | 0.0897368i | 0.00435865 | − | 0.00316674i | ||||
\(804\) | 3.21354 | + | 2.33477i | 0.113333 | + | 0.0823411i | ||||
\(805\) | 39.8101 | 1.40312 | ||||||||
\(806\) | 19.2090 | − | 8.52573i | 0.676607 | − | 0.300306i | ||||
\(807\) | 24.9826 | 0.879429 | ||||||||
\(808\) | −9.42594 | − | 6.84834i | −0.331603 | − | 0.240924i | ||||
\(809\) | 39.4021 | − | 28.6273i | 1.38530 | − | 1.00648i | 0.388943 | − | 0.921262i | \(-0.372840\pi\) |
0.996362 | − | 0.0852207i | \(-0.0271595\pi\) | |||||||
\(810\) | −1.00041 | − | 3.07896i | −0.0351510 | − | 0.108184i | ||||
\(811\) | −10.2486 | −0.359875 | −0.179938 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179938 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(812\) | 12.4797 | 0.437951 | ||||||||
\(813\) | 6.25946 | + | 19.2646i | 0.219529 | + | 0.675640i | ||||
\(814\) | 2.91270 | − | 8.96436i | 0.102090 | − | 0.314201i | ||||
\(815\) | 0.351753 | − | 1.08258i | 0.0123214 | − | 0.0379212i | ||||
\(816\) | 10.1549 | + | 7.37795i | 0.355492 | + | 0.258280i | ||||
\(817\) | −11.2682 | − | 34.6798i | −0.394223 | − | 1.21329i | ||||
\(818\) | −14.9213 | − | 10.8410i | −0.521713 | − | 0.379047i | ||||
\(819\) | 11.0224 | − | 8.00824i | 0.385154 | − | 0.279830i | ||||
\(820\) | 1.53196 | − | 4.71488i | 0.0534983 | − | 0.164651i | ||||
\(821\) | 24.2631 | − | 17.6281i | 0.846786 | − | 0.615226i | −0.0774717 | − | 0.996995i | \(-0.524685\pi\) |
0.924258 | + | 0.381768i | \(0.124685\pi\) | |||||||
\(822\) | −8.43258 | + | 6.12662i | −0.294120 | + | 0.213691i | ||||
\(823\) | −7.97269 | + | 24.5374i | −0.277911 | + | 0.855321i | 0.710524 | + | 0.703673i | \(0.248458\pi\) |
−0.988435 | + | 0.151648i | \(0.951542\pi\) | |||||||
\(824\) | −9.07947 | + | 6.59662i | −0.316298 | + | 0.229804i | ||||
\(825\) | 1.80962 | + | 1.31477i | 0.0630029 | + | 0.0457743i | ||||
\(826\) | 21.7868 | + | 67.0528i | 0.758058 | + | 2.33306i | ||||
\(827\) | 31.3230 | + | 22.7575i | 1.08921 | + | 0.791355i | 0.979265 | − | 0.202583i | \(-0.0649337\pi\) |
0.109941 | + | 0.993938i | \(0.464934\pi\) | |||||||
\(828\) | −0.596238 | + | 1.83503i | −0.0207207 | + | 0.0637718i | ||||
\(829\) | −1.11055 | + | 3.41793i | −0.0385711 | + | 0.118710i | −0.968488 | − | 0.249060i | \(-0.919878\pi\) |
0.929917 | + | 0.367769i | \(0.119878\pi\) | |||||||
\(830\) | 6.97397 | + | 21.4637i | 0.242070 | + | 0.745015i | ||||
\(831\) | 1.93082 | 0.0669793 | ||||||||
\(832\) | 27.7439 | 0.961846 | ||||||||
\(833\) | 17.7883 | + | 54.7467i | 0.616327 | + | 1.89686i | ||||
\(834\) | −13.9560 | + | 10.1396i | −0.483255 | + | 0.351106i | ||||
\(835\) | −25.1712 | − | 18.2880i | −0.871085 | − | 0.632881i | ||||
\(836\) | −3.26795 | −0.113024 | ||||||||
\(837\) | 3.72076 | + | 4.14197i | 0.128608 | + | 0.143167i | ||||
\(838\) | 9.29998 | 0.321262 | ||||||||
\(839\) | 40.7291 | + | 29.5914i | 1.40612 | + | 1.02161i | 0.993872 | + | 0.110540i | \(0.0352579\pi\) |
0.412253 | + | 0.911070i | \(0.364742\pi\) | |||||||
\(840\) | 29.0497 | − | 21.1058i | 1.00231 | − | 0.728220i | ||||
\(841\) | −0.928656 | − | 2.85811i | −0.0320226 | − | 0.0985555i | ||||
\(842\) | 6.37309 | 0.219631 | ||||||||
\(843\) | 4.26528 | 0.146904 | ||||||||
\(844\) | −0.405866 | − | 1.24913i | −0.0139705 | − | 0.0429967i | ||||
\(845\) | 2.55841 | − | 7.87396i | 0.0880118 | − | 0.270873i | ||||
\(846\) | 2.93292 | − | 9.02661i | 0.100836 | − | 0.310341i | ||||
\(847\) | −35.1843 | − | 25.5629i | −1.20895 | − | 0.878350i | ||||
\(848\) | −4.23076 | − | 13.0209i | −0.145285 | − | 0.447141i | ||||
\(849\) | 23.3856 | + | 16.9906i | 0.802592 | + | 0.583117i | ||||
\(850\) | −11.0325 | + | 8.01558i | −0.378411 | + | 0.274932i | ||||
\(851\) | −8.56088 | + | 26.3477i | −0.293463 | + | 0.903186i | ||||
\(852\) | −2.89165 | + | 2.10091i | −0.0990663 | + | 0.0719759i | ||||
\(853\) | 6.60658 | − | 4.79996i | 0.226205 | − | 0.164348i | −0.468910 | − | 0.883246i | \(-0.655353\pi\) |
0.695115 | + | 0.718898i | \(0.255353\pi\) | |||||||
\(854\) | −3.19802 | + | 9.84250i | −0.109434 | + | 0.336804i | ||||
\(855\) | −13.0381 | + | 9.47276i | −0.445895 | + | 0.323962i | ||||
\(856\) | 21.2574 | + | 15.4444i | 0.726563 | + | 0.527879i | ||||
\(857\) | 9.86493 | + | 30.3611i | 0.336980 | + | 1.03712i | 0.965739 | + | 0.259517i | \(0.0835633\pi\) |
−0.628759 | + | 0.777600i | \(0.716437\pi\) | |||||||
\(858\) | 2.95617 | + | 2.14779i | 0.100922 | + | 0.0733242i | ||||
\(859\) | 2.99613 | − | 9.22115i | 0.102227 | − | 0.314622i | −0.886843 | − | 0.462071i | \(-0.847106\pi\) |
0.989070 | + | 0.147450i | \(0.0471064\pi\) | |||||||
\(860\) | 2.89494 | − | 8.90970i | 0.0987166 | − | 0.303818i | ||||
\(861\) | −4.32364 | − | 13.3068i | −0.147349 | − | 0.453494i | ||||
\(862\) | −11.5941 | −0.394896 | ||||||||
\(863\) | 18.2464 | 0.621115 | 0.310558 | − | 0.950555i | \(-0.399484\pi\) | ||||
0.310558 | + | 0.950555i | \(0.399484\pi\) | |||||||
\(864\) | 0.956893 | + | 2.94501i | 0.0325542 | + | 0.100191i | ||||
\(865\) | 16.7213 | − | 12.1488i | 0.568542 | − | 0.413070i | ||||
\(866\) | −11.0338 | − | 8.01653i | −0.374944 | − | 0.272413i | ||||
\(867\) | 7.29618 | 0.247791 | ||||||||
\(868\) | −6.82781 | + | 11.7945i | −0.231751 | + | 0.400333i | ||||
\(869\) | −16.2083 | −0.549830 | ||||||||
\(870\) | 13.3536 | + | 9.70195i | 0.452729 | + | 0.328927i | ||||
\(871\) | −17.8872 | + | 12.9958i | −0.606083 | + | 0.440345i | ||||
\(872\) | −14.0900 | − | 43.3644i | −0.477146 | − | 1.46851i | ||||
\(873\) | 1.67058 | 0.0565406 | ||||||||
\(874\) | −24.3135 | −0.822418 | ||||||||
\(875\) | −9.71141 | − | 29.8887i | −0.328306 | − | 1.01042i | ||||
\(876\) | −0.0276008 | + | 0.0849466i | −0.000932545 | + | 0.00287008i | ||||
\(877\) | −1.37370 | + | 4.22780i | −0.0463864 | + | 0.142763i | −0.971567 | − | 0.236764i | \(-0.923913\pi\) |
0.925181 | + | 0.379527i | \(0.123913\pi\) | |||||||
\(878\) | −15.9110 | − | 11.5600i | −0.536969 | − | 0.390131i | ||||
\(879\) | 8.00748 | + | 24.6445i | 0.270086 | + | 0.831238i | ||||
\(880\) | 5.39244 | + | 3.91784i | 0.181779 | + | 0.132070i | ||||
\(881\) | 44.9353 | − | 32.6474i | 1.51391 | − | 1.09992i | 0.549503 | − | 0.835492i | \(-0.314817\pi\) |
0.964406 | − | 0.264427i | \(-0.0851829\pi\) | |||||||
\(882\) | 4.32101 | − | 13.2987i | 0.145496 | − | 0.447790i | ||||
\(883\) | −17.4061 | + | 12.6463i | −0.585762 | + | 0.425581i | −0.840797 | − | 0.541351i | \(-0.817913\pi\) |
0.255035 | + | 0.966932i | \(0.417913\pi\) | |||||||
\(884\) | 7.11977 | − | 5.17282i | 0.239464 | − | 0.173981i | ||||
\(885\) | 11.3836 | − | 35.0351i | 0.382655 | − | 1.17769i | ||||
\(886\) | 9.20841 | − | 6.69030i | 0.309362 | − | 0.224765i | ||||
\(887\) | −7.23033 | − | 5.25314i | −0.242771 | − | 0.176383i | 0.459746 | − | 0.888050i | \(-0.347940\pi\) |
−0.702517 | + | 0.711667i | \(0.747940\pi\) | |||||||
\(888\) | 7.72163 | + | 23.7647i | 0.259121 | + | 0.797492i | ||||
\(889\) | −3.09261 | − | 2.24691i | −0.103723 | − | 0.0753590i | ||||
\(890\) | −9.01197 | + | 27.7360i | −0.302082 | + | 0.929712i | ||||
\(891\) | −0.299148 | + | 0.920682i | −0.0100218 | + | 0.0308440i | ||||
\(892\) | 0.957249 | + | 2.94611i | 0.0320511 | + | 0.0986430i | ||||
\(893\) | −47.2475 | −1.58108 | ||||||||
\(894\) | 15.3592 | 0.513689 | ||||||||
\(895\) | 10.5087 | + | 32.3424i | 0.351267 | + | 1.08109i | ||||
\(896\) | 15.1899 | − | 11.0361i | 0.507460 | − | 0.368691i | ||||
\(897\) | −8.68867 | − | 6.31268i | −0.290106 | − | 0.210774i | ||||
\(898\) | −5.28606 | −0.176398 | ||||||||
\(899\) | −27.7601 | − | 5.93422i | −0.925852 | − | 0.197917i | ||||
\(900\) | −1.30863 | −0.0436210 | ||||||||
\(901\) | −21.4395 | − | 15.5767i | −0.714253 | − | 0.518935i | ||||
\(902\) | 3.03584 | − | 2.20567i | 0.101082 | − | 0.0734406i | ||||
\(903\) | −8.17036 | − | 25.1458i | −0.271893 | − | 0.836799i | ||||
\(904\) | 19.0074 | 0.632176 | ||||||||
\(905\) | −58.5813 | −1.94731 | ||||||||
\(906\) | −2.14738 | − | 6.60896i | −0.0713420 | − | 0.219568i | ||||
\(907\) | 9.92049 | − | 30.5321i | 0.329404 | − | 1.01380i | −0.640009 | − | 0.768368i | \(-0.721069\pi\) |
0.969413 | − | 0.245435i | \(-0.0789307\pi\) | |||||||
\(908\) | 4.38720 | − | 13.5024i | 0.145594 | − | 0.448093i | ||||
\(909\) | 3.06752 | + | 2.22868i | 0.101743 | + | 0.0739207i | ||||
\(910\) | 13.6301 | + | 41.9490i | 0.451832 | + | 1.39060i | ||||
\(911\) | 15.5663 | + | 11.3095i | 0.515733 | + | 0.374702i | 0.814994 | − | 0.579469i | \(-0.196740\pi\) |
−0.299261 | + | 0.954171i | \(0.596740\pi\) | |||||||
\(912\) | −12.2797 | + | 8.92170i | −0.406620 | + | 0.295427i | ||||
\(913\) | 2.08538 | − | 6.41815i | 0.0690162 | − | 0.212410i | ||||
\(914\) | 25.6920 | − | 18.6663i | 0.849816 | − | 0.617427i | ||||
\(915\) | 4.37466 | − | 3.17837i | 0.144622 | − | 0.105074i | ||||
\(916\) | −4.41809 | + | 13.5975i | −0.145978 | + | 0.449273i | ||||
\(917\) | −14.7240 | + | 10.6976i | −0.486230 | + | 0.353267i | ||||
\(918\) | −4.77471 | − | 3.46903i | −0.157589 | − | 0.114495i | ||||
\(919\) | −2.20906 | − | 6.79877i | −0.0728700 | − | 0.224271i | 0.907988 | − | 0.418997i | \(-0.137618\pi\) |
−0.980858 | + | 0.194726i | \(0.937618\pi\) | |||||||
\(920\) | −22.8991 | − | 16.6372i | −0.754962 | − | 0.548512i | ||||
\(921\) | −1.86208 | + | 5.73089i | −0.0613576 | + | 0.188839i | ||||
\(922\) | −7.90324 | + | 24.3237i | −0.260279 | + | 0.801057i | ||||
\(923\) | −6.14792 | − | 18.9214i | −0.202361 | − | 0.622804i | ||||
\(924\) | −2.36954 | −0.0779520 | ||||||||
\(925\) | −18.7895 | −0.617796 | ||||||||
\(926\) | 5.53984 | + | 17.0499i | 0.182051 | + | 0.560294i | ||||
\(927\) | 2.95477 | − | 2.14676i | 0.0970472 | − | 0.0705089i | ||||
\(928\) | −12.7727 | − | 9.27989i | −0.419284 | − | 0.304627i | ||||
\(929\) | −38.1829 | −1.25274 | −0.626369 | − | 0.779526i | \(-0.715460\pi\) | ||||
−0.626369 | + | 0.779526i | \(0.715460\pi\) | |||||||
\(930\) | −16.4752 | + | 7.31239i | −0.540245 | + | 0.239783i | ||||
\(931\) | −69.6087 | −2.28133 | ||||||||
\(932\) | −10.2842 | − | 7.47190i | −0.336870 | − | 0.244750i | ||||
\(933\) | 17.3714 | − | 12.6211i | 0.568715 | − | 0.413196i | ||||
\(934\) | 3.15166 | + | 9.69981i | 0.103125 | + | 0.317388i | ||||
\(935\) | 12.9018 | 0.421933 | ||||||||
\(936\) | −9.68693 | −0.316627 | ||||||||
\(937\) | −6.72531 | − | 20.6984i | −0.219706 | − | 0.676186i | −0.998786 | − | 0.0492613i | \(-0.984313\pi\) |
0.779080 | − | 0.626925i | \(-0.215687\pi\) | |||||||
\(938\) | −11.2152 | + | 34.5169i | −0.366190 | + | 1.12702i | ||||
\(939\) | −0.404077 | + | 1.24362i | −0.0131866 | + | 0.0405841i | ||||
\(940\) | −9.82026 | − | 7.13483i | −0.320301 | − | 0.232713i | ||||
\(941\) | −13.1981 | − | 40.6195i | −0.430245 | − | 1.32416i | −0.897882 | − | 0.440237i | \(-0.854894\pi\) |
0.467637 | − | 0.883921i | \(-0.345106\pi\) | |||||||
\(942\) | 1.33225 | + | 0.967938i | 0.0434071 | + | 0.0315371i | ||||
\(943\) | −8.92281 | + | 6.48280i | −0.290567 | + | 0.211109i | ||||
\(944\) | 10.7214 | − | 32.9970i | 0.348951 | − | 1.07396i | ||||
\(945\) | −9.45375 | + | 6.86855i | −0.307530 | + | 0.223434i | ||||
\(946\) | 5.73681 | − | 4.16804i | 0.186520 | − | 0.135515i | ||||
\(947\) | 10.2862 | − | 31.6577i | 0.334257 | − | 1.02874i | −0.632830 | − | 0.774291i | \(-0.718107\pi\) |
0.967087 | − | 0.254447i | \(-0.0818933\pi\) | |||||||
\(948\) | 7.67156 | − | 5.57371i | 0.249161 | − | 0.181026i | ||||
\(949\) | −0.402212 | − | 0.292224i | −0.0130564 | − | 0.00948600i | ||||
\(950\) | −5.09578 | − | 15.6832i | −0.165329 | − | 0.508830i | ||||
\(951\) | −17.2768 | − | 12.5523i | −0.560238 | − | 0.407037i | ||||
\(952\) | 20.2283 | − | 62.2562i | 0.655602 | − | 2.01773i | ||||
\(953\) | −9.10198 | + | 28.0130i | −0.294842 | + | 0.907431i | 0.688432 | + | 0.725301i | \(0.258299\pi\) |
−0.983274 | + | 0.182130i | \(0.941701\pi\) | |||||||
\(954\) | 1.98926 | + | 6.12230i | 0.0644045 | + | 0.198217i | ||||
\(955\) | 3.87821 | 0.125496 | ||||||||
\(956\) | −4.14954 | −0.134206 | ||||||||
\(957\) | −1.52521 | − | 4.69411i | −0.0493030 | − | 0.151739i | ||||
\(958\) | −13.9389 | + | 10.1272i | −0.450345 | + | 0.327195i | ||||
\(959\) | 30.4375 | + | 22.1142i | 0.982879 | + | 0.714103i | ||||
\(960\) | −23.7955 | −0.767997 | ||||||||
\(961\) | 20.7964 | − | 22.9894i | 0.670851 | − | 0.741592i | ||||
\(962\) | −30.6943 | −0.989625 | ||||||||
\(963\) | −6.91788 | − | 5.02613i | −0.222925 | − | 0.161965i | ||||
\(964\) | −5.63264 | + | 4.09235i | −0.181415 | + | 0.131806i | ||||
\(965\) | 7.68054 | + | 23.6383i | 0.247245 | + | 0.760943i | ||||
\(966\) | −17.6294 | −0.567215 | ||||||||
\(967\) | −11.9582 | −0.384548 | −0.192274 | − | 0.981341i | \(-0.561586\pi\) | ||||
−0.192274 | + | 0.981341i | \(0.561586\pi\) | |||||||
\(968\) | 9.55523 | + | 29.4080i | 0.307117 | + | 0.945208i | ||||
\(969\) | −9.07889 | + | 27.9419i | −0.291656 | + | 0.897624i | ||||
\(970\) | −1.67127 | + | 5.14364i | −0.0536613 | + | 0.165152i | ||||
\(971\) | 33.5237 | + | 24.3564i | 1.07583 | + | 0.781633i | 0.976950 | − | 0.213467i | \(-0.0684756\pi\) |
0.0988750 | + | 0.995100i | \(0.468476\pi\) | |||||||
\(972\) | −0.175014 | − | 0.538638i | −0.00561358 | − | 0.0172768i | ||||
\(973\) | 50.3743 | + | 36.5991i | 1.61493 | + | 1.17331i | ||||
\(974\) | −25.3250 | + | 18.3997i | −0.811466 | + | 0.589564i | ||||
\(975\) | 2.25091 | − | 6.92758i | 0.0720867 | − | 0.221860i | ||||
\(976\) | 4.12017 | − | 2.99348i | 0.131883 | − | 0.0958189i | ||||
\(977\) | −18.0922 | + | 13.1447i | −0.578820 | + | 0.420537i | −0.838299 | − | 0.545212i | \(-0.816449\pi\) |
0.259478 | + | 0.965749i | \(0.416449\pi\) | |||||||
\(978\) | −0.155769 | + | 0.479408i | −0.00498094 | + | 0.0153298i | ||||
\(979\) | 7.05506 | − | 5.12580i | 0.225481 | − | 0.163821i | ||||
\(980\) | −14.4680 | − | 10.5116i | −0.462162 | − | 0.335780i | ||||
\(981\) | 4.58535 | + | 14.1122i | 0.146399 | + | 0.450569i | ||||
\(982\) | −15.8178 | − | 11.4923i | −0.504766 | − | 0.366734i | ||||
\(983\) | −12.8655 | + | 39.5959i | −0.410346 | + | 1.26291i | 0.506003 | + | 0.862532i | \(0.331123\pi\) |
−0.916348 | + | 0.400382i | \(0.868877\pi\) | |||||||
\(984\) | −3.07409 | + | 9.46109i | −0.0979985 | + | 0.301609i | ||||
\(985\) | 6.28225 | + | 19.3348i | 0.200169 | + | 0.616057i | ||||
\(986\) | 30.0907 | 0.958284 | ||||||||
\(987\) | −34.2584 | −1.09046 | ||||||||
\(988\) | 3.28854 | + | 10.1211i | 0.104622 | + | 0.321995i | ||||
\(989\) | −16.8614 | + | 12.2505i | −0.536162 | + | 0.389544i | ||||
\(990\) | −2.53547 | − | 1.84213i | −0.0805825 | − | 0.0585466i | ||||
\(991\) | 14.9553 | 0.475071 | 0.237535 | − | 0.971379i | \(-0.423660\pi\) | ||||
0.237535 | + | 0.971379i | \(0.423660\pi\) | |||||||
\(992\) | 15.7585 | − | 6.99428i | 0.500334 | − | 0.222069i | ||||
\(993\) | 22.7167 | 0.720891 | ||||||||
\(994\) | −26.4207 | − | 19.1958i | −0.838015 | − | 0.608853i | ||||
\(995\) | 1.93106 | − | 1.40300i | 0.0612187 | − | 0.0444780i | ||||
\(996\) | 1.22004 | + | 3.75489i | 0.0386584 | + | 0.118978i | ||||
\(997\) | −14.1531 | −0.448235 | −0.224117 | − | 0.974562i | \(-0.571950\pi\) | ||||
−0.224117 | + | 0.974562i | \(0.571950\pi\) | |||||||
\(998\) | 27.9548 | 0.884895 | ||||||||
\(999\) | −2.51288 | − | 7.73384i | −0.0795040 | − | 0.244688i |
(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 | 93.2.f.b.64.2 | yes | 16 | |
3.2 | odd | 2 | 279.2.i.c.64.3 | 16 | |||
31.4 | even | 5 | 2883.2.a.p.1.6 | 8 | |||
31.16 | even | 5 | inner | 93.2.f.b.16.2 | ✓ | 16 | |
31.27 | odd | 10 | 2883.2.a.o.1.6 | 8 | |||
93.35 | odd | 10 | 8649.2.a.bh.1.3 | 8 | |||
93.47 | odd | 10 | 279.2.i.c.109.3 | 16 | |||
93.89 | even | 10 | 8649.2.a.bg.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
93.2.f.b.16.2 | ✓ | 16 | 31.16 | even | 5 | inner | |
93.2.f.b.64.2 | yes | 16 | 1.1 | even | 1 | trivial | |
279.2.i.c.64.3 | 16 | 3.2 | odd | 2 | |||
279.2.i.c.109.3 | 16 | 93.47 | odd | 10 | |||
2883.2.a.o.1.6 | 8 | 31.27 | odd | 10 | |||
2883.2.a.p.1.6 | 8 | 31.4 | even | 5 | |||
8649.2.a.bg.1.3 | 8 | 93.89 | even | 10 | |||
8649.2.a.bh.1.3 | 8 | 93.35 | odd | 10 |