Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.n (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 10 x^{10} - 15 x^{9} + 61 x^{8} - 25 x^{7} + 316 x^{6} + 50 x^{5} + 1336 x^{4} + \cdots + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 481.1 | ||
Root | \(0.472164 + 0.343047i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.481 |
Dual form | 930.2.n.f.901.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.31116 | + | 4.03534i | −0.495572 | + | 1.52521i | 0.320491 | + | 0.947252i | \(0.396152\pi\) |
−0.816063 | + | 0.577963i | \(0.803848\pi\) | |||||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0.809017 | − | 0.587785i | 0.255834 | − | 0.185874i | ||||
\(11\) | 0.399170 | − | 1.22852i | 0.120354 | − | 0.370412i | −0.872672 | − | 0.488307i | \(-0.837615\pi\) |
0.993026 | + | 0.117895i | \(0.0376146\pi\) | |||||||
\(12\) | 0.809017 | − | 0.587785i | 0.233543 | − | 0.169679i | ||||
\(13\) | 0.763978 | + | 0.555062i | 0.211889 | + | 0.153947i | 0.688668 | − | 0.725077i | \(-0.258196\pi\) |
−0.476779 | + | 0.879023i | \(0.658196\pi\) | |||||||
\(14\) | 1.31116 | + | 4.03534i | 0.350423 | + | 1.07849i | ||||
\(15\) | 0.809017 | + | 0.587785i | 0.208887 | + | 0.151765i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 1.37094 | + | 4.21932i | 0.332502 | + | 1.02334i | 0.967940 | + | 0.251183i | \(0.0808196\pi\) |
−0.635438 | + | 0.772152i | \(0.719180\pi\) | |||||||
\(18\) | 0.809017 | + | 0.587785i | 0.190687 | + | 0.138542i | ||||
\(19\) | 5.50566 | − | 4.00010i | 1.26308 | − | 0.917685i | 0.264180 | − | 0.964473i | \(-0.414899\pi\) |
0.998905 | + | 0.0467886i | \(0.0148987\pi\) | |||||||
\(20\) | 0.309017 | − | 0.951057i | 0.0690983 | − | 0.212663i | ||||
\(21\) | −3.43266 | + | 2.49398i | −0.749069 | + | 0.544230i | ||||
\(22\) | −0.399170 | − | 1.22852i | −0.0851032 | − | 0.261921i | ||||
\(23\) | 1.49726 | + | 4.60810i | 0.312201 | + | 0.960856i | 0.976891 | + | 0.213737i | \(0.0685636\pi\) |
−0.664690 | + | 0.747119i | \(0.731436\pi\) | |||||||
\(24\) | 0.309017 | − | 0.951057i | 0.0630778 | − | 0.194134i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.944328 | 0.185198 | ||||||||
\(27\) | −0.309017 | + | 0.951057i | −0.0594703 | + | 0.183031i | ||||
\(28\) | 3.43266 | + | 2.49398i | 0.648713 | + | 0.471317i | ||||
\(29\) | −6.88755 | + | 5.00410i | −1.27899 | + | 0.929238i | −0.999522 | − | 0.0309183i | \(-0.990157\pi\) |
−0.279464 | + | 0.960156i | \(0.590157\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 2.91834 | − | 4.74166i | 0.524149 | − | 0.851627i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.04504 | − | 0.759266i | 0.181918 | − | 0.132171i | ||||
\(34\) | 3.58917 | + | 2.60768i | 0.615537 | + | 0.447214i | ||||
\(35\) | −1.31116 | + | 4.03534i | −0.221627 | + | 0.682097i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 11.2154 | 1.84380 | 0.921899 | − | 0.387429i | \(-0.126637\pi\) | ||||
0.921899 | + | 0.387429i | \(0.126637\pi\) | |||||||
\(38\) | 2.10297 | − | 6.47229i | 0.341148 | − | 1.04994i | ||||
\(39\) | 0.291813 | + | 0.898110i | 0.0467276 | + | 0.143813i | ||||
\(40\) | −0.309017 | − | 0.951057i | −0.0488599 | − | 0.150375i | ||||
\(41\) | 3.23164 | − | 2.34792i | 0.504698 | − | 0.366684i | −0.306111 | − | 0.951996i | \(-0.599028\pi\) |
0.810808 | + | 0.585312i | \(0.199028\pi\) | |||||||
\(42\) | −1.31116 | + | 4.03534i | −0.202317 | + | 0.622666i | ||||
\(43\) | −10.3176 | + | 7.49614i | −1.57341 | + | 1.14315i | −0.649618 | + | 0.760260i | \(0.725071\pi\) |
−0.923794 | + | 0.382890i | \(0.874929\pi\) | |||||||
\(44\) | −1.04504 | − | 0.759266i | −0.157546 | − | 0.114464i | ||||
\(45\) | 0.309017 | + | 0.951057i | 0.0460655 | + | 0.141775i | ||||
\(46\) | 3.91989 | + | 2.84797i | 0.577956 | + | 0.419910i | ||||
\(47\) | 2.42609 | + | 1.76266i | 0.353882 | + | 0.257110i | 0.750496 | − | 0.660875i | \(-0.229815\pi\) |
−0.396614 | + | 0.917986i | \(0.629815\pi\) | |||||||
\(48\) | −0.309017 | − | 0.951057i | −0.0446028 | − | 0.137273i | ||||
\(49\) | −8.90170 | − | 6.46746i | −1.27167 | − | 0.923923i | ||||
\(50\) | 0.809017 | − | 0.587785i | 0.114412 | − | 0.0831254i | ||||
\(51\) | −1.37094 | + | 4.21932i | −0.191970 | + | 0.590823i | ||||
\(52\) | 0.763978 | − | 0.555062i | 0.105945 | − | 0.0769733i | ||||
\(53\) | −4.17533 | − | 12.8503i | −0.573526 | − | 1.76513i | −0.641145 | − | 0.767420i | \(-0.721540\pi\) |
0.0676187 | − | 0.997711i | \(-0.478460\pi\) | |||||||
\(54\) | 0.309017 | + | 0.951057i | 0.0420519 | + | 0.129422i | ||||
\(55\) | 0.399170 | − | 1.22852i | 0.0538240 | − | 0.165653i | ||||
\(56\) | 4.24301 | 0.566996 | ||||||||
\(57\) | 6.80537 | 0.901393 | ||||||||
\(58\) | −2.63081 | + | 8.09680i | −0.345442 | + | 1.06316i | ||||
\(59\) | −8.27968 | − | 6.01554i | −1.07792 | − | 0.783156i | −0.100603 | − | 0.994927i | \(-0.532077\pi\) |
−0.977319 | + | 0.211770i | \(0.932077\pi\) | |||||||
\(60\) | 0.809017 | − | 0.587785i | 0.104444 | − | 0.0758827i | ||||
\(61\) | 1.47470 | 0.188815 | 0.0944077 | − | 0.995534i | \(-0.469904\pi\) | ||||
0.0944077 | + | 0.995534i | \(0.469904\pi\) | |||||||
\(62\) | −0.426093 | − | 5.55144i | −0.0541139 | − | 0.705033i | ||||
\(63\) | −4.24301 | −0.534569 | ||||||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0.763978 | + | 0.555062i | 0.0947598 | + | 0.0688470i | ||||
\(66\) | 0.399170 | − | 1.22852i | 0.0491344 | − | 0.151220i | ||||
\(67\) | −3.14457 | −0.384170 | −0.192085 | − | 0.981378i | \(-0.561525\pi\) | ||||
−0.192085 | + | 0.981378i | \(0.561525\pi\) | |||||||
\(68\) | 4.43645 | 0.537999 | ||||||||
\(69\) | −1.49726 | + | 4.60810i | −0.180249 | + | 0.554751i | ||||
\(70\) | 1.31116 | + | 4.03534i | 0.156714 | + | 0.482315i | ||||
\(71\) | 0.155251 | + | 0.477813i | 0.0184249 | + | 0.0567060i | 0.959846 | − | 0.280527i | \(-0.0905091\pi\) |
−0.941421 | + | 0.337233i | \(0.890509\pi\) | |||||||
\(72\) | 0.809017 | − | 0.587785i | 0.0953436 | − | 0.0692712i | ||||
\(73\) | 1.63084 | − | 5.01921i | 0.190875 | − | 0.587454i | −0.809125 | − | 0.587637i | \(-0.800058\pi\) |
1.00000 | 0.000183359i | \(5.83649e-5\pi\) | ||||||||
\(74\) | 9.07344 | − | 6.59224i | 1.05477 | − | 0.766332i | ||||
\(75\) | 0.809017 | + | 0.587785i | 0.0934172 | + | 0.0678716i | ||||
\(76\) | −2.10297 | − | 6.47229i | −0.241228 | − | 0.742423i | ||||
\(77\) | 4.43411 | + | 3.22157i | 0.505314 | + | 0.367132i | ||||
\(78\) | 0.763978 | + | 0.555062i | 0.0865034 | + | 0.0628484i | ||||
\(79\) | −0.331101 | − | 1.01902i | −0.0372517 | − | 0.114649i | 0.930701 | − | 0.365780i | \(-0.119198\pi\) |
−0.967953 | + | 0.251131i | \(0.919198\pi\) | |||||||
\(80\) | −0.809017 | − | 0.587785i | −0.0904508 | − | 0.0657164i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 1.23438 | − | 3.79902i | 0.136314 | − | 0.419532i | ||||
\(83\) | −3.66105 | + | 2.65991i | −0.401852 | + | 0.291963i | −0.770295 | − | 0.637688i | \(-0.779891\pi\) |
0.368443 | + | 0.929650i | \(0.379891\pi\) | |||||||
\(84\) | 1.31116 | + | 4.03534i | 0.143059 | + | 0.440292i | ||||
\(85\) | 1.37094 | + | 4.21932i | 0.148699 | + | 0.457649i | ||||
\(86\) | −3.94095 | + | 12.1290i | −0.424964 | + | 1.30790i | ||||
\(87\) | −8.51348 | −0.912741 | ||||||||
\(88\) | −1.29174 | −0.137700 | ||||||||
\(89\) | 5.55143 | − | 17.0855i | 0.588451 | − | 1.81106i | 0.00350254 | − | 0.999994i | \(-0.498885\pi\) |
0.584948 | − | 0.811071i | \(-0.301115\pi\) | |||||||
\(90\) | 0.809017 | + | 0.587785i | 0.0852779 | + | 0.0619580i | ||||
\(91\) | −3.24156 | + | 2.35513i | −0.339808 | + | 0.246885i | ||||
\(92\) | 4.84525 | 0.505152 | ||||||||
\(93\) | 5.14806 | − | 2.12073i | 0.533829 | − | 0.219909i | ||||
\(94\) | 2.99882 | 0.309304 | ||||||||
\(95\) | 5.50566 | − | 4.00010i | 0.564869 | − | 0.410401i | ||||
\(96\) | −0.809017 | − | 0.587785i | −0.0825700 | − | 0.0599906i | ||||
\(97\) | 4.11658 | − | 12.6695i | 0.417975 | − | 1.28640i | −0.491587 | − | 0.870828i | \(-0.663583\pi\) |
0.909563 | − | 0.415567i | \(-0.136417\pi\) | |||||||
\(98\) | −11.0031 | −1.11148 | ||||||||
\(99\) | 1.29174 | 0.129825 | ||||||||
\(100\) | 0.309017 | − | 0.951057i | 0.0309017 | − | 0.0951057i | ||||
\(101\) | −2.06555 | − | 6.35711i | −0.205530 | − | 0.632556i | −0.999691 | − | 0.0248492i | \(-0.992089\pi\) |
0.794161 | − | 0.607707i | \(-0.207911\pi\) | |||||||
\(102\) | 1.37094 | + | 4.21932i | 0.135743 | + | 0.417775i | ||||
\(103\) | −15.0867 | + | 10.9611i | −1.48653 | + | 1.08003i | −0.511157 | + | 0.859487i | \(0.670783\pi\) |
−0.975377 | + | 0.220543i | \(0.929217\pi\) | |||||||
\(104\) | 0.291813 | − | 0.898110i | 0.0286147 | − | 0.0880669i | ||||
\(105\) | −3.43266 | + | 2.49398i | −0.334994 | + | 0.243387i | ||||
\(106\) | −10.9312 | − | 7.94195i | −1.06173 | − | 0.771391i | ||||
\(107\) | −2.51418 | − | 7.73784i | −0.243055 | − | 0.748045i | −0.995950 | − | 0.0899052i | \(-0.971344\pi\) |
0.752896 | − | 0.658140i | \(-0.228656\pi\) | |||||||
\(108\) | 0.809017 | + | 0.587785i | 0.0778477 | + | 0.0565597i | ||||
\(109\) | 10.2609 | + | 7.45494i | 0.982811 | + | 0.714054i | 0.958335 | − | 0.285646i | \(-0.0922082\pi\) |
0.0244761 | + | 0.999700i | \(0.492208\pi\) | |||||||
\(110\) | −0.399170 | − | 1.22852i | −0.0380593 | − | 0.117135i | ||||
\(111\) | 9.07344 | + | 6.59224i | 0.861213 | + | 0.625708i | ||||
\(112\) | 3.43266 | − | 2.49398i | 0.324356 | − | 0.235659i | ||||
\(113\) | 1.78699 | − | 5.49980i | 0.168106 | − | 0.517377i | −0.831146 | − | 0.556055i | \(-0.812314\pi\) |
0.999252 | + | 0.0386774i | \(0.0123145\pi\) | |||||||
\(114\) | 5.50566 | − | 4.00010i | 0.515652 | − | 0.374643i | ||||
\(115\) | 1.49726 | + | 4.60810i | 0.139621 | + | 0.429708i | ||||
\(116\) | 2.63081 | + | 8.09680i | 0.244265 | + | 0.751769i | ||||
\(117\) | −0.291813 | + | 0.898110i | −0.0269782 | + | 0.0830303i | ||||
\(118\) | −10.2342 | −0.942138 | ||||||||
\(119\) | −18.8239 | −1.72558 | ||||||||
\(120\) | 0.309017 | − | 0.951057i | 0.0282093 | − | 0.0868192i | ||||
\(121\) | 7.54927 | + | 5.48486i | 0.686297 | + | 0.498624i | ||||
\(122\) | 1.19305 | − | 0.866804i | 0.108014 | − | 0.0784767i | ||||
\(123\) | 3.99453 | 0.360174 | ||||||||
\(124\) | −3.60777 | − | 4.24075i | −0.323987 | − | 0.380831i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.43266 | + | 2.49398i | −0.305806 | + | 0.222181i | ||||
\(127\) | 10.9227 | + | 7.93580i | 0.969232 | + | 0.704188i | 0.955276 | − | 0.295714i | \(-0.0955576\pi\) |
0.0139557 | + | 0.999903i | \(0.495558\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | −12.7532 | −1.12286 | ||||||||
\(130\) | 0.944328 | 0.0828231 | ||||||||
\(131\) | −5.28516 | + | 16.2660i | −0.461766 | + | 1.42117i | 0.401238 | + | 0.915974i | \(0.368580\pi\) |
−0.863004 | + | 0.505197i | \(0.831420\pi\) | |||||||
\(132\) | −0.399170 | − | 1.22852i | −0.0347432 | − | 0.106929i | ||||
\(133\) | 8.92293 | + | 27.4620i | 0.773717 | + | 2.38125i | ||||
\(134\) | −2.54401 | + | 1.84833i | −0.219769 | + | 0.159671i | ||||
\(135\) | −0.309017 | + | 0.951057i | −0.0265959 | + | 0.0818539i | ||||
\(136\) | 3.58917 | − | 2.60768i | 0.307768 | − | 0.223607i | ||||
\(137\) | −14.4427 | − | 10.4932i | −1.23392 | − | 0.896496i | −0.236743 | − | 0.971572i | \(-0.576080\pi\) |
−0.997178 | + | 0.0750760i | \(0.976080\pi\) | |||||||
\(138\) | 1.49726 | + | 4.60810i | 0.127456 | + | 0.392268i | ||||
\(139\) | 1.78724 | + | 1.29851i | 0.151592 | + | 0.110138i | 0.660996 | − | 0.750390i | \(-0.270134\pi\) |
−0.509404 | + | 0.860527i | \(0.670134\pi\) | |||||||
\(140\) | 3.43266 | + | 2.49398i | 0.290113 | + | 0.210779i | ||||
\(141\) | 0.926685 | + | 2.85204i | 0.0780410 | + | 0.240185i | ||||
\(142\) | 0.406452 | + | 0.295305i | 0.0341087 | + | 0.0247814i | ||||
\(143\) | 0.986860 | − | 0.716996i | 0.0825254 | − | 0.0599582i | ||||
\(144\) | 0.309017 | − | 0.951057i | 0.0257514 | − | 0.0792547i | ||||
\(145\) | −6.88755 | + | 5.00410i | −0.571980 | + | 0.415568i | ||||
\(146\) | −1.63084 | − | 5.01921i | −0.134969 | − | 0.415392i | ||||
\(147\) | −3.40015 | − | 10.4646i | −0.280439 | − | 0.863104i | ||||
\(148\) | 3.46575 | − | 10.6665i | 0.284883 | − | 0.876778i | ||||
\(149\) | −16.6896 | −1.36726 | −0.683632 | − | 0.729827i | \(-0.739601\pi\) | ||||
−0.683632 | + | 0.729827i | \(0.739601\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 4.00793 | − | 12.3351i | 0.326160 | − | 1.00382i | −0.644754 | − | 0.764391i | \(-0.723040\pi\) |
0.970914 | − | 0.239428i | \(-0.0769600\pi\) | |||||||
\(152\) | −5.50566 | − | 4.00010i | −0.446568 | − | 0.324451i | ||||
\(153\) | −3.58917 | + | 2.60768i | −0.290167 | + | 0.210819i | ||||
\(154\) | 5.48086 | 0.441660 | ||||||||
\(155\) | 2.91834 | − | 4.74166i | 0.234406 | − | 0.380859i | ||||
\(156\) | 0.944328 | 0.0756068 | ||||||||
\(157\) | −9.15205 | + | 6.64935i | −0.730413 | + | 0.530676i | −0.889694 | − | 0.456557i | \(-0.849082\pi\) |
0.159281 | + | 0.987233i | \(0.449082\pi\) | |||||||
\(158\) | −0.866833 | − | 0.629791i | −0.0689615 | − | 0.0501035i | ||||
\(159\) | 4.17533 | − | 12.8503i | 0.331125 | − | 1.01910i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −20.5584 | −1.62023 | ||||||||
\(162\) | −0.309017 | + | 0.951057i | −0.0242787 | + | 0.0747221i | ||||
\(163\) | −3.23835 | − | 9.96662i | −0.253647 | − | 0.780646i | −0.994093 | − | 0.108530i | \(-0.965386\pi\) |
0.740446 | − | 0.672116i | \(-0.234614\pi\) | |||||||
\(164\) | −1.23438 | − | 3.79902i | −0.0963887 | − | 0.296654i | ||||
\(165\) | 1.04504 | − | 0.759266i | 0.0813562 | − | 0.0591087i | ||||
\(166\) | −1.39840 | + | 4.30382i | −0.108537 | + | 0.334041i | ||||
\(167\) | 15.1098 | − | 10.9779i | 1.16923 | − | 0.849497i | 0.178316 | − | 0.983973i | \(-0.442935\pi\) |
0.990917 | + | 0.134476i | \(0.0429352\pi\) | |||||||
\(168\) | 3.43266 | + | 2.49398i | 0.264836 | + | 0.192414i | ||||
\(169\) | −3.74165 | − | 11.5156i | −0.287819 | − | 0.885817i | ||||
\(170\) | 3.58917 | + | 2.60768i | 0.275277 | + | 0.200000i | ||||
\(171\) | 5.50566 | + | 4.00010i | 0.421028 | + | 0.305895i | ||||
\(172\) | 3.94095 | + | 12.1290i | 0.300495 | + | 0.924828i | ||||
\(173\) | −2.14742 | − | 1.56019i | −0.163265 | − | 0.118619i | 0.503153 | − | 0.864198i | \(-0.332173\pi\) |
−0.666418 | + | 0.745578i | \(0.732173\pi\) | |||||||
\(174\) | −6.88755 | + | 5.00410i | −0.522144 | + | 0.379360i | ||||
\(175\) | −1.31116 | + | 4.03534i | −0.0991145 | + | 0.305043i | ||||
\(176\) | −1.04504 | + | 0.759266i | −0.0787728 | + | 0.0572318i | ||||
\(177\) | −3.16256 | − | 9.73334i | −0.237712 | − | 0.731603i | ||||
\(178\) | −5.55143 | − | 17.0855i | −0.416097 | − | 1.28062i | ||||
\(179\) | −5.99171 | + | 18.4406i | −0.447841 | + | 1.37831i | 0.431496 | + | 0.902115i | \(0.357986\pi\) |
−0.879337 | + | 0.476199i | \(0.842014\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 8.29722 | 0.616727 | 0.308364 | − | 0.951269i | \(-0.400219\pi\) | ||||
0.308364 | + | 0.951269i | \(0.400219\pi\) | |||||||
\(182\) | −1.23817 | + | 3.81068i | −0.0917790 | + | 0.282467i | ||||
\(183\) | 1.19305 | + | 0.866804i | 0.0881930 | + | 0.0640760i | ||||
\(184\) | 3.91989 | − | 2.84797i | 0.288978 | − | 0.209955i | ||||
\(185\) | 11.2154 | 0.824572 | ||||||||
\(186\) | 2.91834 | − | 4.74166i | 0.213983 | − | 0.347675i | ||||
\(187\) | 5.73074 | 0.419073 | ||||||||
\(188\) | 2.42609 | − | 1.76266i | 0.176941 | − | 0.128555i | ||||
\(189\) | −3.43266 | − | 2.49398i | −0.249690 | − | 0.181410i | ||||
\(190\) | 2.10297 | − | 6.47229i | 0.152566 | − | 0.469549i | ||||
\(191\) | 5.24124 | 0.379242 | 0.189621 | − | 0.981857i | \(-0.439274\pi\) | ||||
0.189621 | + | 0.981857i | \(0.439274\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 7.96515 | − | 24.5142i | 0.573344 | − | 1.76457i | −0.0684046 | − | 0.997658i | \(-0.521791\pi\) |
0.641749 | − | 0.766915i | \(-0.278209\pi\) | |||||||
\(194\) | −4.11658 | − | 12.6695i | −0.295553 | − | 0.909619i | ||||
\(195\) | 0.291813 | + | 0.898110i | 0.0208972 | + | 0.0643150i | ||||
\(196\) | −8.90170 | + | 6.46746i | −0.635836 | + | 0.461962i | ||||
\(197\) | −2.93308 | + | 9.02708i | −0.208973 | + | 0.643153i | 0.790554 | + | 0.612393i | \(0.209793\pi\) |
−0.999527 | + | 0.0307602i | \(0.990207\pi\) | |||||||
\(198\) | 1.04504 | − | 0.759266i | 0.0742677 | − | 0.0539587i | ||||
\(199\) | −12.2061 | − | 8.86822i | −0.865265 | − | 0.628652i | 0.0640473 | − | 0.997947i | \(-0.479599\pi\) |
−0.929312 | + | 0.369295i | \(0.879599\pi\) | |||||||
\(200\) | −0.309017 | − | 0.951057i | −0.0218508 | − | 0.0672499i | ||||
\(201\) | −2.54401 | − | 1.84833i | −0.179440 | − | 0.130371i | ||||
\(202\) | −5.40768 | − | 3.92891i | −0.380483 | − | 0.276437i | ||||
\(203\) | −11.1625 | − | 34.3548i | −0.783457 | − | 2.41123i | ||||
\(204\) | 3.58917 | + | 2.60768i | 0.251292 | + | 0.182574i | ||||
\(205\) | 3.23164 | − | 2.34792i | 0.225708 | − | 0.163986i | ||||
\(206\) | −5.76260 | + | 17.7355i | −0.401499 | + | 1.23569i | ||||
\(207\) | −3.91989 | + | 2.84797i | −0.272451 | + | 0.197947i | ||||
\(208\) | −0.291813 | − | 0.898110i | −0.0202336 | − | 0.0622727i | ||||
\(209\) | −2.71650 | − | 8.36051i | −0.187904 | − | 0.578309i | ||||
\(210\) | −1.31116 | + | 4.03534i | −0.0904787 | + | 0.278465i | ||||
\(211\) | 0.341792 | 0.0235299 | 0.0117650 | − | 0.999931i | \(-0.496255\pi\) | ||||
0.0117650 | + | 0.999931i | \(0.496255\pi\) | |||||||
\(212\) | −13.5117 | −0.927984 | ||||||||
\(213\) | −0.155251 | + | 0.477813i | −0.0106376 | + | 0.0327392i | ||||
\(214\) | −6.58220 | − | 4.78225i | −0.449950 | − | 0.326908i | ||||
\(215\) | −10.3176 | + | 7.49614i | −0.703651 | + | 0.511233i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 15.3078 | + | 17.9936i | 1.03916 | + | 1.22148i | ||||
\(218\) | 12.6831 | 0.859008 | ||||||||
\(219\) | 4.26959 | − | 3.10204i | 0.288512 | − | 0.209616i | ||||
\(220\) | −1.04504 | − | 0.759266i | −0.0704565 | − | 0.0511897i | ||||
\(221\) | −1.29462 | + | 3.98442i | −0.0870854 | + | 0.268021i | ||||
\(222\) | 11.2154 | 0.752728 | ||||||||
\(223\) | 7.68709 | 0.514765 | 0.257383 | − | 0.966310i | \(-0.417140\pi\) | ||||
0.257383 | + | 0.966310i | \(0.417140\pi\) | |||||||
\(224\) | 1.31116 | − | 4.03534i | 0.0876056 | − | 0.269622i | ||||
\(225\) | 0.309017 | + | 0.951057i | 0.0206011 | + | 0.0634038i | ||||
\(226\) | −1.78699 | − | 5.49980i | −0.118869 | − | 0.365841i | ||||
\(227\) | −1.24953 | + | 0.907838i | −0.0829344 | + | 0.0602553i | −0.628480 | − | 0.777826i | \(-0.716323\pi\) |
0.545545 | + | 0.838081i | \(0.316323\pi\) | |||||||
\(228\) | 2.10297 | − | 6.47229i | 0.139273 | − | 0.428638i | ||||
\(229\) | −6.00598 | + | 4.36360i | −0.396887 | + | 0.288355i | −0.768272 | − | 0.640124i | \(-0.778883\pi\) |
0.371385 | + | 0.928479i | \(0.378883\pi\) | |||||||
\(230\) | 3.91989 | + | 2.84797i | 0.258470 | + | 0.187789i | ||||
\(231\) | 1.69368 | + | 5.21261i | 0.111436 | + | 0.342964i | ||||
\(232\) | 6.88755 | + | 5.00410i | 0.452190 | + | 0.328535i | ||||
\(233\) | −17.4684 | − | 12.6915i | −1.14439 | − | 0.831451i | −0.156668 | − | 0.987651i | \(-0.550075\pi\) |
−0.987725 | + | 0.156200i | \(0.950075\pi\) | |||||||
\(234\) | 0.291813 | + | 0.898110i | 0.0190764 | + | 0.0587113i | ||||
\(235\) | 2.42609 | + | 1.76266i | 0.158261 | + | 0.114983i | ||||
\(236\) | −8.27968 | + | 6.01554i | −0.538961 | + | 0.391578i | ||||
\(237\) | 0.331101 | − | 1.01902i | 0.0215073 | − | 0.0661927i | ||||
\(238\) | −15.2289 | + | 11.0644i | −0.987140 | + | 0.717199i | ||||
\(239\) | −1.36603 | − | 4.20422i | −0.0883614 | − | 0.271949i | 0.897105 | − | 0.441817i | \(-0.145666\pi\) |
−0.985467 | + | 0.169868i | \(0.945666\pi\) | |||||||
\(240\) | −0.309017 | − | 0.951057i | −0.0199470 | − | 0.0613904i | ||||
\(241\) | −5.15747 | + | 15.8731i | −0.332222 | + | 1.02247i | 0.635852 | + | 0.771811i | \(0.280649\pi\) |
−0.968074 | + | 0.250664i | \(0.919351\pi\) | |||||||
\(242\) | 9.33141 | 0.599846 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.455706 | − | 1.40252i | 0.0291736 | − | 0.0897870i | ||||
\(245\) | −8.90170 | − | 6.46746i | −0.568709 | − | 0.413191i | ||||
\(246\) | 3.23164 | − | 2.34792i | 0.206042 | − | 0.149698i | ||||
\(247\) | 6.42650 | 0.408909 | ||||||||
\(248\) | −5.41140 | − | 1.31025i | −0.343624 | − | 0.0832009i | ||||
\(249\) | −4.52530 | −0.286780 | ||||||||
\(250\) | 0.809017 | − | 0.587785i | 0.0511667 | − | 0.0371748i | ||||
\(251\) | −1.75153 | − | 1.27256i | −0.110555 | − | 0.0803231i | 0.531134 | − | 0.847288i | \(-0.321766\pi\) |
−0.641689 | + | 0.766965i | \(0.721766\pi\) | |||||||
\(252\) | −1.31116 | + | 4.03534i | −0.0825954 | + | 0.254202i | ||||
\(253\) | 6.25880 | 0.393487 | ||||||||
\(254\) | 13.5012 | 0.847140 | ||||||||
\(255\) | −1.37094 | + | 4.21932i | −0.0858516 | + | 0.264224i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 4.74579 | + | 14.6060i | 0.296034 | + | 0.911099i | 0.982872 | + | 0.184289i | \(0.0589982\pi\) |
−0.686838 | + | 0.726811i | \(0.741002\pi\) | |||||||
\(258\) | −10.3176 | + | 7.49614i | −0.642343 | + | 0.466689i | ||||
\(259\) | −14.7052 | + | 45.2579i | −0.913736 | + | 2.81219i | ||||
\(260\) | 0.763978 | − | 0.555062i | 0.0473799 | − | 0.0344235i | ||||
\(261\) | −6.88755 | − | 5.00410i | −0.426329 | − | 0.309746i | ||||
\(262\) | 5.28516 | + | 16.2660i | 0.326518 | + | 1.00492i | ||||
\(263\) | 0.255339 | + | 0.185514i | 0.0157449 | + | 0.0114393i | 0.595630 | − | 0.803259i | \(-0.296903\pi\) |
−0.579885 | + | 0.814698i | \(0.696903\pi\) | |||||||
\(264\) | −1.04504 | − | 0.759266i | −0.0643177 | − | 0.0467296i | ||||
\(265\) | −4.17533 | − | 12.8503i | −0.256489 | − | 0.789391i | ||||
\(266\) | 23.3605 | + | 16.9724i | 1.43233 | + | 1.04065i | ||||
\(267\) | 14.5338 | − | 10.5595i | 0.889456 | − | 0.646228i | ||||
\(268\) | −0.971725 | + | 2.99066i | −0.0593575 | + | 0.182684i | ||||
\(269\) | 7.45208 | − | 5.41425i | 0.454361 | − | 0.330113i | −0.336954 | − | 0.941521i | \(-0.609397\pi\) |
0.791315 | + | 0.611408i | \(0.209397\pi\) | |||||||
\(270\) | 0.309017 | + | 0.951057i | 0.0188062 | + | 0.0578795i | ||||
\(271\) | −0.585301 | − | 1.80137i | −0.0355545 | − | 0.109425i | 0.931704 | − | 0.363218i | \(-0.118322\pi\) |
−0.967259 | + | 0.253793i | \(0.918322\pi\) | |||||||
\(272\) | 1.37094 | − | 4.21932i | 0.0831254 | − | 0.255834i | ||||
\(273\) | −4.00679 | −0.242502 | ||||||||
\(274\) | −17.8521 | −1.07849 | ||||||||
\(275\) | 0.399170 | − | 1.22852i | 0.0240708 | − | 0.0740824i | ||||
\(276\) | 3.91989 | + | 2.84797i | 0.235950 | + | 0.171427i | ||||
\(277\) | 9.54764 | − | 6.93677i | 0.573662 | − | 0.416790i | −0.262772 | − | 0.964858i | \(-0.584637\pi\) |
0.836434 | + | 0.548068i | \(0.184637\pi\) | |||||||
\(278\) | 2.20915 | 0.132496 | ||||||||
\(279\) | 5.41140 | + | 1.31025i | 0.323972 | + | 0.0784426i | ||||
\(280\) | 4.24301 | 0.253568 | ||||||||
\(281\) | 3.65705 | − | 2.65700i | 0.218161 | − | 0.158504i | −0.473337 | − | 0.880881i | \(-0.656951\pi\) |
0.691499 | + | 0.722378i | \(0.256951\pi\) | |||||||
\(282\) | 2.42609 | + | 1.76266i | 0.144472 | + | 0.104965i | ||||
\(283\) | −8.52089 | + | 26.2246i | −0.506514 | + | 1.55889i | 0.291696 | + | 0.956511i | \(0.405781\pi\) |
−0.798210 | + | 0.602379i | \(0.794219\pi\) | |||||||
\(284\) | 0.502402 | 0.0298121 | ||||||||
\(285\) | 6.80537 | 0.403115 | ||||||||
\(286\) | 0.376947 | − | 1.16012i | 0.0222893 | − | 0.0685996i | ||||
\(287\) | 5.23747 | + | 16.1193i | 0.309158 | + | 0.951491i | ||||
\(288\) | −0.309017 | − | 0.951057i | −0.0182090 | − | 0.0560415i | ||||
\(289\) | −2.16988 | + | 1.57651i | −0.127640 | + | 0.0927360i | ||||
\(290\) | −2.63081 | + | 8.09680i | −0.154487 | + | 0.475461i | ||||
\(291\) | 10.7773 | − | 7.83020i | 0.631779 | − | 0.459014i | ||||
\(292\) | −4.26959 | − | 3.10204i | −0.249859 | − | 0.181533i | ||||
\(293\) | −1.27656 | − | 3.92883i | −0.0745772 | − | 0.229525i | 0.906818 | − | 0.421521i | \(-0.138504\pi\) |
−0.981396 | + | 0.191997i | \(0.938504\pi\) | |||||||
\(294\) | −8.90170 | − | 6.46746i | −0.519158 | − | 0.377190i | ||||
\(295\) | −8.27968 | − | 6.01554i | −0.482061 | − | 0.350238i | ||||
\(296\) | −3.46575 | − | 10.6665i | −0.201442 | − | 0.619976i | ||||
\(297\) | 1.04504 | + | 0.759266i | 0.0606393 | + | 0.0440571i | ||||
\(298\) | −13.5022 | + | 9.80989i | −0.782159 | + | 0.568272i | ||||
\(299\) | −1.41391 | + | 4.35156i | −0.0817684 | + | 0.251657i | ||||
\(300\) | 0.809017 | − | 0.587785i | 0.0467086 | − | 0.0339358i | ||||
\(301\) | −16.7215 | − | 51.4635i | −0.963811 | − | 2.96631i | ||||
\(302\) | −4.00793 | − | 12.3351i | −0.230630 | − | 0.709807i | ||||
\(303\) | 2.06555 | − | 6.35711i | 0.118663 | − | 0.365207i | ||||
\(304\) | −6.80537 | −0.390315 | ||||||||
\(305\) | 1.47470 | 0.0844408 | ||||||||
\(306\) | −1.37094 | + | 4.21932i | −0.0783714 | + | 0.241202i | ||||
\(307\) | 3.78146 | + | 2.74739i | 0.215819 | + | 0.156802i | 0.690443 | − | 0.723387i | \(-0.257416\pi\) |
−0.474624 | + | 0.880189i | \(0.657416\pi\) | |||||||
\(308\) | 4.43411 | − | 3.22157i | 0.252657 | − | 0.183566i | ||||
\(309\) | −18.6482 | −1.06086 | ||||||||
\(310\) | −0.426093 | − | 5.55144i | −0.0242005 | − | 0.315300i | ||||
\(311\) | −3.36080 | −0.190573 | −0.0952866 | − | 0.995450i | \(-0.530377\pi\) | ||||
−0.0952866 | + | 0.995450i | \(0.530377\pi\) | |||||||
\(312\) | 0.763978 | − | 0.555062i | 0.0432517 | − | 0.0314242i | ||||
\(313\) | 20.3115 | + | 14.7572i | 1.14807 | + | 0.834125i | 0.988224 | − | 0.153016i | \(-0.0488986\pi\) |
0.159851 | + | 0.987141i | \(0.448899\pi\) | |||||||
\(314\) | −3.49577 | + | 10.7589i | −0.197278 | + | 0.607159i | ||||
\(315\) | −4.24301 | −0.239066 | ||||||||
\(316\) | −1.07146 | −0.0602746 | ||||||||
\(317\) | −1.54899 | + | 4.76730i | −0.0869999 | + | 0.267758i | −0.985086 | − | 0.172061i | \(-0.944957\pi\) |
0.898086 | + | 0.439819i | \(0.144957\pi\) | |||||||
\(318\) | −4.17533 | − | 12.8503i | −0.234141 | − | 0.720612i | ||||
\(319\) | 3.39832 | + | 10.4590i | 0.190270 | + | 0.585589i | ||||
\(320\) | −0.809017 | + | 0.587785i | −0.0452254 | + | 0.0328582i | ||||
\(321\) | 2.51418 | − | 7.73784i | 0.140328 | − | 0.431884i | ||||
\(322\) | −16.6321 | + | 12.0839i | −0.926871 | + | 0.673411i | ||||
\(323\) | 24.4256 | + | 17.7462i | 1.35908 | + | 0.987427i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | 0.763978 | + | 0.555062i | 0.0423779 | + | 0.0307893i | ||||
\(326\) | −8.47812 | − | 6.15971i | −0.469559 | − | 0.341155i | ||||
\(327\) | 3.91930 | + | 12.0624i | 0.216738 | + | 0.667050i | ||||
\(328\) | −3.23164 | − | 2.34792i | −0.178438 | − | 0.129642i | ||||
\(329\) | −10.2939 | + | 7.47898i | −0.567523 | + | 0.412329i | ||||
\(330\) | 0.399170 | − | 1.22852i | 0.0219736 | − | 0.0676277i | ||||
\(331\) | −19.1667 | + | 13.9254i | −1.05350 | + | 0.765412i | −0.972875 | − | 0.231333i | \(-0.925691\pi\) |
−0.0806243 | + | 0.996745i | \(0.525691\pi\) | |||||||
\(332\) | 1.39840 | + | 4.30382i | 0.0767470 | + | 0.236203i | ||||
\(333\) | 3.46575 | + | 10.6665i | 0.189922 | + | 0.584519i | ||||
\(334\) | 5.77144 | − | 17.7627i | 0.315799 | − | 0.971929i | ||||
\(335\) | −3.14457 | −0.171806 | ||||||||
\(336\) | 4.24301 | 0.231475 | ||||||||
\(337\) | −6.24132 | + | 19.2088i | −0.339986 | + | 1.04637i | 0.624227 | + | 0.781243i | \(0.285414\pi\) |
−0.964214 | + | 0.265127i | \(0.914586\pi\) | |||||||
\(338\) | −9.79578 | − | 7.11705i | −0.532820 | − | 0.387116i | ||||
\(339\) | 4.67841 | − | 3.39906i | 0.254096 | − | 0.184612i | ||||
\(340\) | 4.43645 | 0.240600 | ||||||||
\(341\) | −4.66030 | − | 5.47795i | −0.252369 | − | 0.296648i | ||||
\(342\) | 6.80537 | 0.367992 | ||||||||
\(343\) | 13.7413 | − | 9.98365i | 0.741961 | − | 0.539066i | ||||
\(344\) | 10.3176 | + | 7.49614i | 0.556285 | + | 0.404165i | ||||
\(345\) | −1.49726 | + | 4.60810i | −0.0806100 | + | 0.248092i | ||||
\(346\) | −2.65436 | −0.142699 | ||||||||
\(347\) | 15.4353 | 0.828608 | 0.414304 | − | 0.910138i | \(-0.364025\pi\) | ||||
0.414304 | + | 0.910138i | \(0.364025\pi\) | |||||||
\(348\) | −2.63081 | + | 8.09680i | −0.141026 | + | 0.434034i | ||||
\(349\) | −5.52006 | − | 16.9890i | −0.295482 | − | 0.909401i | −0.983059 | − | 0.183289i | \(-0.941326\pi\) |
0.687577 | − | 0.726112i | \(-0.258674\pi\) | |||||||
\(350\) | 1.31116 | + | 4.03534i | 0.0700845 | + | 0.215698i | ||||
\(351\) | −0.763978 | + | 0.555062i | −0.0407781 | + | 0.0296270i | ||||
\(352\) | −0.399170 | + | 1.22852i | −0.0212758 | + | 0.0654802i | ||||
\(353\) | 0.195464 | − | 0.142013i | 0.0104035 | − | 0.00755860i | −0.582571 | − | 0.812780i | \(-0.697953\pi\) |
0.592975 | + | 0.805221i | \(0.297953\pi\) | |||||||
\(354\) | −8.27968 | − | 6.01554i | −0.440060 | − | 0.319722i | ||||
\(355\) | 0.155251 | + | 0.477813i | 0.00823986 | + | 0.0253597i | ||||
\(356\) | −14.5338 | − | 10.5595i | −0.770292 | − | 0.559650i | ||||
\(357\) | −15.2289 | − | 11.0644i | −0.805997 | − | 0.585591i | ||||
\(358\) | 5.99171 | + | 18.4406i | 0.316672 | + | 0.974615i | ||||
\(359\) | −14.3716 | − | 10.4415i | −0.758502 | − | 0.551084i | 0.139949 | − | 0.990159i | \(-0.455306\pi\) |
−0.898450 | + | 0.439075i | \(0.855306\pi\) | |||||||
\(360\) | 0.809017 | − | 0.587785i | 0.0426389 | − | 0.0309790i | ||||
\(361\) | 8.44019 | − | 25.9762i | 0.444221 | − | 1.36717i | ||||
\(362\) | 6.71259 | − | 4.87698i | 0.352806 | − | 0.256328i | ||||
\(363\) | 2.88356 | + | 8.87470i | 0.151348 | + | 0.465801i | ||||
\(364\) | 1.23817 | + | 3.81068i | 0.0648976 | + | 0.199734i | ||||
\(365\) | 1.63084 | − | 5.01921i | 0.0853620 | − | 0.262717i | ||||
\(366\) | 1.47470 | 0.0770835 | ||||||||
\(367\) | 11.9833 | 0.625522 | 0.312761 | − | 0.949832i | \(-0.398746\pi\) | ||||
0.312761 | + | 0.949832i | \(0.398746\pi\) | |||||||
\(368\) | 1.49726 | − | 4.60810i | 0.0780503 | − | 0.240214i | ||||
\(369\) | 3.23164 | + | 2.34792i | 0.168233 | + | 0.122228i | ||||
\(370\) | 9.07344 | − | 6.59224i | 0.471706 | − | 0.342714i | ||||
\(371\) | 57.3300 | 2.97643 | ||||||||
\(372\) | −0.426093 | − | 5.55144i | −0.0220919 | − | 0.287829i | ||||
\(373\) | 21.2595 | 1.10078 | 0.550388 | − | 0.834909i | \(-0.314480\pi\) | ||||
0.550388 | + | 0.834909i | \(0.314480\pi\) | |||||||
\(374\) | 4.63627 | − | 3.36845i | 0.239736 | − | 0.174178i | ||||
\(375\) | 0.809017 | + | 0.587785i | 0.0417775 | + | 0.0303531i | ||||
\(376\) | 0.926685 | − | 2.85204i | 0.0477901 | − | 0.147083i | ||||
\(377\) | −8.03952 | −0.414056 | ||||||||
\(378\) | −4.24301 | −0.218237 | ||||||||
\(379\) | −2.80451 | + | 8.63139i | −0.144058 | + | 0.443365i | −0.996889 | − | 0.0788228i | \(-0.974884\pi\) |
0.852831 | + | 0.522188i | \(0.174884\pi\) | |||||||
\(380\) | −2.10297 | − | 6.47229i | −0.107880 | − | 0.332021i | ||||
\(381\) | 4.17210 | + | 12.8404i | 0.213743 | + | 0.657833i | ||||
\(382\) | 4.24025 | − | 3.08072i | 0.216950 | − | 0.157623i | ||||
\(383\) | −1.82277 | + | 5.60990i | −0.0931390 | + | 0.286652i | −0.986764 | − | 0.162162i | \(-0.948153\pi\) |
0.893625 | + | 0.448814i | \(0.148153\pi\) | |||||||
\(384\) | −0.809017 | + | 0.587785i | −0.0412850 | + | 0.0299953i | ||||
\(385\) | 4.43411 | + | 3.22157i | 0.225983 | + | 0.164186i | ||||
\(386\) | −7.96515 | − | 24.5142i | −0.405416 | − | 1.24774i | ||||
\(387\) | −10.3176 | − | 7.49614i | −0.524471 | − | 0.381050i | ||||
\(388\) | −10.7773 | − | 7.83020i | −0.547137 | − | 0.397518i | ||||
\(389\) | 8.12724 | + | 25.0131i | 0.412067 | + | 1.26821i | 0.914848 | + | 0.403799i | \(0.132310\pi\) |
−0.502780 | + | 0.864414i | \(0.667690\pi\) | |||||||
\(390\) | 0.763978 | + | 0.555062i | 0.0386855 | + | 0.0281067i | ||||
\(391\) | −17.3904 | + | 12.6349i | −0.879470 | + | 0.638973i | ||||
\(392\) | −3.40015 | + | 10.4646i | −0.171733 | + | 0.528541i | ||||
\(393\) | −13.8367 | + | 10.0530i | −0.697970 | + | 0.507105i | ||||
\(394\) | 2.93308 | + | 9.02708i | 0.147766 | + | 0.454778i | ||||
\(395\) | −0.331101 | − | 1.01902i | −0.0166595 | − | 0.0512726i | ||||
\(396\) | 0.399170 | − | 1.22852i | 0.0200590 | − | 0.0617353i | ||||
\(397\) | 10.3759 | 0.520750 | 0.260375 | − | 0.965508i | \(-0.416154\pi\) | ||||
0.260375 | + | 0.965508i | \(0.416154\pi\) | |||||||
\(398\) | −15.0875 | −0.756269 | ||||||||
\(399\) | −8.92293 | + | 27.4620i | −0.446705 | + | 1.37482i | ||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | 26.9651 | − | 19.5913i | 1.34658 | − | 0.978344i | 0.347401 | − | 0.937717i | \(-0.387064\pi\) |
0.999174 | − | 0.0406274i | \(-0.0129357\pi\) | |||||||
\(402\) | −3.14457 | −0.156837 | ||||||||
\(403\) | 4.86146 | − | 2.00266i | 0.242166 | − | 0.0997597i | ||||
\(404\) | −6.68426 | −0.332555 | ||||||||
\(405\) | −0.809017 | + | 0.587785i | −0.0402004 | + | 0.0292073i | ||||
\(406\) | −29.2239 | − | 21.2324i | −1.45036 | − | 1.05375i | ||||
\(407\) | 4.47684 | − | 13.7783i | 0.221909 | − | 0.682965i | ||||
\(408\) | 4.43645 | 0.219637 | ||||||||
\(409\) | −7.28358 | −0.360150 | −0.180075 | − | 0.983653i | \(-0.557634\pi\) | ||||
−0.180075 | + | 0.983653i | \(0.557634\pi\) | |||||||
\(410\) | 1.23438 | − | 3.79902i | 0.0609615 | − | 0.187620i | ||||
\(411\) | −5.51661 | − | 16.9784i | −0.272114 | − | 0.837482i | ||||
\(412\) | 5.76260 | + | 17.7355i | 0.283903 | + | 0.873763i | ||||
\(413\) | 35.1307 | − | 25.5240i | 1.72867 | − | 1.25595i | ||||
\(414\) | −1.49726 | + | 4.60810i | −0.0735865 | + | 0.226476i | ||||
\(415\) | −3.66105 | + | 2.65991i | −0.179714 | + | 0.130570i | ||||
\(416\) | −0.763978 | − | 0.555062i | −0.0374571 | − | 0.0272142i | ||||
\(417\) | 0.682665 | + | 2.10103i | 0.0334302 | + | 0.102888i | ||||
\(418\) | −7.11188 | − | 5.16708i | −0.347853 | − | 0.252730i | ||||
\(419\) | −30.8733 | − | 22.4308i | −1.50826 | − | 1.09582i | −0.966942 | − | 0.254998i | \(-0.917925\pi\) |
−0.541319 | − | 0.840817i | \(-0.682075\pi\) | |||||||
\(420\) | 1.31116 | + | 4.03534i | 0.0639781 | + | 0.196904i | ||||
\(421\) | −4.94986 | − | 3.59629i | −0.241242 | − | 0.175272i | 0.460595 | − | 0.887611i | \(-0.347636\pi\) |
−0.701836 | + | 0.712338i | \(0.747636\pi\) | |||||||
\(422\) | 0.276515 | − | 0.200900i | 0.0134606 | − | 0.00977967i | ||||
\(423\) | −0.926685 | + | 2.85204i | −0.0450570 | + | 0.138671i | ||||
\(424\) | −10.9312 | + | 7.94195i | −0.530864 | + | 0.385695i | ||||
\(425\) | 1.37094 | + | 4.21932i | 0.0665003 | + | 0.204667i | ||||
\(426\) | 0.155251 | + | 0.477813i | 0.00752193 | + | 0.0231501i | ||||
\(427\) | −1.93356 | + | 5.95089i | −0.0935717 | + | 0.287984i | ||||
\(428\) | −8.13604 | −0.393270 | ||||||||
\(429\) | 1.21983 | 0.0588938 | ||||||||
\(430\) | −3.94095 | + | 12.1290i | −0.190050 | + | 0.584913i | ||||
\(431\) | 22.8066 | + | 16.5700i | 1.09856 | + | 0.798149i | 0.980824 | − | 0.194896i | \(-0.0624371\pi\) |
0.117734 | + | 0.993045i | \(0.462437\pi\) | |||||||
\(432\) | 0.809017 | − | 0.587785i | 0.0389238 | − | 0.0282798i | ||||
\(433\) | 17.1380 | 0.823600 | 0.411800 | − | 0.911274i | \(-0.364900\pi\) | ||||
0.411800 | + | 0.911274i | \(0.364900\pi\) | |||||||
\(434\) | 22.9606 | + | 5.55940i | 1.10214 | + | 0.266860i | ||||
\(435\) | −8.51348 | −0.408190 | ||||||||
\(436\) | 10.2609 | − | 7.45494i | 0.491406 | − | 0.357027i | ||||
\(437\) | 26.6763 | + | 19.3815i | 1.27610 | + | 0.927141i | ||||
\(438\) | 1.63084 | − | 5.01921i | 0.0779245 | − | 0.239827i | ||||
\(439\) | 28.2634 | 1.34894 | 0.674470 | − | 0.738302i | \(-0.264372\pi\) | ||||
0.674470 | + | 0.738302i | \(0.264372\pi\) | |||||||
\(440\) | −1.29174 | −0.0615813 | ||||||||
\(441\) | 3.40015 | − | 10.4646i | 0.161912 | − | 0.498313i | ||||
\(442\) | 1.29462 | + | 3.98442i | 0.0615787 | + | 0.189520i | ||||
\(443\) | −8.12699 | − | 25.0123i | −0.386125 | − | 1.18837i | −0.935661 | − | 0.352901i | \(-0.885195\pi\) |
0.549536 | − | 0.835470i | \(-0.314805\pi\) | |||||||
\(444\) | 9.07344 | − | 6.59224i | 0.430606 | − | 0.312854i | ||||
\(445\) | 5.55143 | − | 17.0855i | 0.263163 | − | 0.809933i | ||||
\(446\) | 6.21898 | − | 4.51836i | 0.294477 | − | 0.213950i | ||||
\(447\) | −13.5022 | − | 9.80989i | −0.638630 | − | 0.463992i | ||||
\(448\) | −1.31116 | − | 4.03534i | −0.0619465 | − | 0.190652i | ||||
\(449\) | −4.82567 | − | 3.50605i | −0.227737 | − | 0.165461i | 0.468065 | − | 0.883694i | \(-0.344951\pi\) |
−0.695803 | + | 0.718233i | \(0.744951\pi\) | |||||||
\(450\) | 0.809017 | + | 0.587785i | 0.0381374 | + | 0.0277085i | ||||
\(451\) | −1.59449 | − | 4.90735i | −0.0750818 | − | 0.231078i | ||||
\(452\) | −4.67841 | − | 3.39906i | −0.220054 | − | 0.159878i | ||||
\(453\) | 10.4929 | − | 7.62353i | 0.492999 | − | 0.358185i | ||||
\(454\) | −0.477279 | + | 1.46891i | −0.0223998 | + | 0.0689395i | ||||
\(455\) | −3.24156 | + | 2.35513i | −0.151967 | + | 0.110410i | ||||
\(456\) | −2.10297 | − | 6.47229i | −0.0984808 | − | 0.303093i | ||||
\(457\) | 5.78202 | + | 17.7952i | 0.270471 | + | 0.832426i | 0.990382 | + | 0.138359i | \(0.0441827\pi\) |
−0.719911 | + | 0.694067i | \(0.755817\pi\) | |||||||
\(458\) | −2.29408 | + | 7.06046i | −0.107195 | + | 0.329914i | ||||
\(459\) | −4.43645 | −0.207076 | ||||||||
\(460\) | 4.84525 | 0.225911 | ||||||||
\(461\) | −3.96850 | + | 12.2138i | −0.184832 | + | 0.568853i | −0.999945 | − | 0.0104478i | \(-0.996674\pi\) |
0.815114 | + | 0.579301i | \(0.196674\pi\) | |||||||
\(462\) | 4.43411 | + | 3.22157i | 0.206293 | + | 0.149881i | ||||
\(463\) | 30.1357 | − | 21.8949i | 1.40053 | − | 1.01754i | 0.405911 | − | 0.913913i | \(-0.366954\pi\) |
0.994616 | − | 0.103630i | \(-0.0330457\pi\) | |||||||
\(464\) | 8.51348 | 0.395228 | ||||||||
\(465\) | 5.14806 | − | 2.12073i | 0.238736 | − | 0.0983464i | ||||
\(466\) | −21.5921 | −1.00024 | ||||||||
\(467\) | 8.97851 | − | 6.52327i | 0.415476 | − | 0.301861i | −0.360339 | − | 0.932821i | \(-0.617339\pi\) |
0.775815 | + | 0.630960i | \(0.217339\pi\) | |||||||
\(468\) | 0.763978 | + | 0.555062i | 0.0353149 | + | 0.0256578i | ||||
\(469\) | 4.12303 | − | 12.6894i | 0.190384 | − | 0.585942i | ||||
\(470\) | 2.99882 | 0.138325 | ||||||||
\(471\) | −11.3126 | −0.521255 | ||||||||
\(472\) | −3.16256 | + | 9.73334i | −0.145568 | + | 0.448013i | ||||
\(473\) | 5.09069 | + | 15.6675i | 0.234070 | + | 0.720394i | ||||
\(474\) | −0.331101 | − | 1.01902i | −0.0152080 | − | 0.0468053i | ||||
\(475\) | 5.50566 | − | 4.00010i | 0.252617 | − | 0.183537i | ||||
\(476\) | −5.81691 | + | 17.9026i | −0.266617 | + | 0.820564i | ||||
\(477\) | 10.9312 | − | 7.94195i | 0.500503 | − | 0.363637i | ||||
\(478\) | −3.57633 | − | 2.59835i | −0.163577 | − | 0.118846i | ||||
\(479\) | −5.08012 | − | 15.6350i | −0.232117 | − | 0.714382i | −0.997491 | − | 0.0707962i | \(-0.977446\pi\) |
0.765374 | − | 0.643586i | \(-0.222554\pi\) | |||||||
\(480\) | −0.809017 | − | 0.587785i | −0.0369264 | − | 0.0268286i | ||||
\(481\) | 8.56831 | + | 6.22524i | 0.390681 | + | 0.283846i | ||||
\(482\) | 5.15747 | + | 15.8731i | 0.234917 | + | 0.722999i | ||||
\(483\) | −16.6321 | − | 12.0839i | −0.756787 | − | 0.549838i | ||||
\(484\) | 7.54927 | − | 5.48486i | 0.343149 | − | 0.249312i | ||||
\(485\) | 4.11658 | − | 12.6695i | 0.186924 | − | 0.575293i | ||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | 8.89343 | + | 27.3712i | 0.403000 | + | 1.24031i | 0.922554 | + | 0.385868i | \(0.126098\pi\) |
−0.519554 | + | 0.854438i | \(0.673902\pi\) | |||||||
\(488\) | −0.455706 | − | 1.40252i | −0.0206288 | − | 0.0634890i | ||||
\(489\) | 3.23835 | − | 9.96662i | 0.146443 | − | 0.450706i | ||||
\(490\) | −11.0031 | −0.497070 | ||||||||
\(491\) | 12.6411 | 0.570485 | 0.285242 | − | 0.958455i | \(-0.407926\pi\) | ||||
0.285242 | + | 0.958455i | \(0.407926\pi\) | |||||||
\(492\) | 1.23438 | − | 3.79902i | 0.0556500 | − | 0.171273i | ||||
\(493\) | −30.5563 | − | 22.2005i | −1.37619 | − | 0.999858i | ||||
\(494\) | 5.19915 | − | 3.77740i | 0.233921 | − | 0.169953i | ||||
\(495\) | 1.29174 | 0.0580594 | ||||||||
\(496\) | −5.14806 | + | 2.12073i | −0.231155 | + | 0.0952234i | ||||
\(497\) | −2.13170 | −0.0956196 | ||||||||
\(498\) | −3.66105 | + | 2.65991i | −0.164056 | + | 0.119193i | ||||
\(499\) | 26.0963 | + | 18.9601i | 1.16823 | + | 0.848769i | 0.990796 | − | 0.135364i | \(-0.0432204\pi\) |
0.177434 | + | 0.984133i | \(0.443220\pi\) | |||||||
\(500\) | 0.309017 | − | 0.951057i | 0.0138197 | − | 0.0425325i | ||||
\(501\) | 18.6768 | 0.834416 | ||||||||
\(502\) | −2.16500 | −0.0966289 | ||||||||
\(503\) | −11.4666 | + | 35.2906i | −0.511271 | + | 1.57353i | 0.278694 | + | 0.960380i | \(0.410098\pi\) |
−0.789965 | + | 0.613151i | \(0.789902\pi\) | |||||||
\(504\) | 1.31116 | + | 4.03534i | 0.0584038 | + | 0.179748i | ||||
\(505\) | −2.06555 | − | 6.35711i | −0.0919158 | − | 0.282888i | ||||
\(506\) | 5.06347 | − | 3.67883i | 0.225099 | − | 0.163544i | ||||
\(507\) | 3.74165 | − | 11.5156i | 0.166173 | − | 0.511427i | ||||
\(508\) | 10.9227 | − | 7.93580i | 0.484616 | − | 0.352094i | ||||
\(509\) | 5.81886 | + | 4.22765i | 0.257916 | + | 0.187387i | 0.709228 | − | 0.704979i | \(-0.249044\pi\) |
−0.451312 | + | 0.892366i | \(0.649044\pi\) | |||||||
\(510\) | 1.37094 | + | 4.21932i | 0.0607062 | + | 0.186835i | ||||
\(511\) | 18.1159 | + | 13.1620i | 0.801400 | + | 0.582251i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | 2.10297 | + | 6.47229i | 0.0928486 | + | 0.285759i | ||||
\(514\) | 12.4246 | + | 9.02703i | 0.548027 | + | 0.398165i | ||||
\(515\) | −15.0867 | + | 10.9611i | −0.664798 | + | 0.483004i | ||||
\(516\) | −3.94095 | + | 12.1290i | −0.173491 | + | 0.533950i | ||||
\(517\) | 3.13388 | − | 2.27690i | 0.137828 | − | 0.100138i | ||||
\(518\) | 14.7052 | + | 45.2579i | 0.646109 | + | 1.98852i | ||||
\(519\) | −0.820241 | − | 2.52444i | −0.0360046 | − | 0.110811i | ||||
\(520\) | 0.291813 | − | 0.898110i | 0.0127969 | − | 0.0393847i | ||||
\(521\) | 3.74655 | 0.164140 | 0.0820698 | − | 0.996627i | \(-0.473847\pi\) | ||||
0.0820698 | + | 0.996627i | \(0.473847\pi\) | |||||||
\(522\) | −8.51348 | −0.372625 | ||||||||
\(523\) | −1.50795 | + | 4.64098i | −0.0659379 | + | 0.202936i | −0.978597 | − | 0.205785i | \(-0.934025\pi\) |
0.912659 | + | 0.408721i | \(0.134025\pi\) | |||||||
\(524\) | 13.8367 | + | 10.0530i | 0.604460 | + | 0.439166i | ||||
\(525\) | −3.43266 | + | 2.49398i | −0.149814 | + | 0.108846i | ||||
\(526\) | 0.315616 | 0.0137615 | ||||||||
\(527\) | 24.0074 | + | 5.81286i | 1.04578 | + | 0.253212i | ||||
\(528\) | −1.29174 | −0.0562158 | ||||||||
\(529\) | −0.385438 | + | 0.280037i | −0.0167582 | + | 0.0121755i | ||||
\(530\) | −10.9312 | − | 7.94195i | −0.474819 | − | 0.344976i | ||||
\(531\) | 3.16256 | − | 9.73334i | 0.137243 | − | 0.422391i | ||||
\(532\) | 28.8752 | 1.25190 | ||||||||
\(533\) | 3.77215 | 0.163390 | ||||||||
\(534\) | 5.55143 | − | 17.0855i | 0.240234 | − | 0.739364i | ||||
\(535\) | −2.51418 | − | 7.73784i | −0.108697 | − | 0.334536i | ||||
\(536\) | 0.971725 | + | 2.99066i | 0.0419721 | + | 0.129177i | ||||
\(537\) | −15.6865 | + | 11.3969i | −0.676922 | + | 0.491813i | ||||
\(538\) | 2.84644 | − | 8.76045i | 0.122719 | − | 0.377690i | ||||
\(539\) | −11.4987 | + | 8.35428i | −0.495283 | + | 0.359844i | ||||
\(540\) | 0.809017 | + | 0.587785i | 0.0348145 | + | 0.0252942i | ||||
\(541\) | −5.56171 | − | 17.1172i | −0.239116 | − | 0.735925i | −0.996549 | − | 0.0830108i | \(-0.973546\pi\) |
0.757432 | − | 0.652914i | \(-0.226454\pi\) | |||||||
\(542\) | −1.53234 | − | 1.11331i | −0.0658195 | − | 0.0478207i | ||||
\(543\) | 6.71259 | + | 4.87698i | 0.288065 | + | 0.209291i | ||||
\(544\) | −1.37094 | − | 4.21932i | −0.0587786 | − | 0.180902i | ||||
\(545\) | 10.2609 | + | 7.45494i | 0.439527 | + | 0.319335i | ||||
\(546\) | −3.24156 | + | 2.35513i | −0.138726 | + | 0.100790i | ||||
\(547\) | 4.72713 | − | 14.5486i | 0.202117 | − | 0.622053i | −0.797702 | − | 0.603052i | \(-0.793951\pi\) |
0.999819 | − | 0.0190016i | \(-0.00604877\pi\) | |||||||
\(548\) | −14.4427 | + | 10.4932i | −0.616961 | + | 0.448248i | ||||
\(549\) | 0.455706 | + | 1.40252i | 0.0194491 | + | 0.0598580i | ||||
\(550\) | −0.399170 | − | 1.22852i | −0.0170206 | − | 0.0523842i | ||||
\(551\) | −17.9036 | + | 55.1017i | −0.762721 | + | 2.34741i | ||||
\(552\) | 4.84525 | 0.206227 | ||||||||
\(553\) | 4.54623 | 0.193325 | ||||||||
\(554\) | 3.64687 | − | 11.2239i | 0.154941 | − | 0.476859i | ||||
\(555\) | 9.07344 | + | 6.59224i | 0.385146 | + | 0.279825i | ||||
\(556\) | 1.78724 | − | 1.29851i | 0.0757958 | − | 0.0550689i | ||||
\(557\) | 35.0608 | 1.48557 | 0.742787 | − | 0.669528i | \(-0.233504\pi\) | ||||
0.742787 | + | 0.669528i | \(0.233504\pi\) | |||||||
\(558\) | 5.14806 | − | 2.12073i | 0.217935 | − | 0.0897775i | ||||
\(559\) | −12.0432 | −0.509373 | ||||||||
\(560\) | 3.43266 | − | 2.49398i | 0.145057 | − | 0.105390i | ||||
\(561\) | 4.63627 | + | 3.36845i | 0.195743 | + | 0.142216i | ||||
\(562\) | 1.39687 | − | 4.29912i | 0.0589234 | − | 0.181347i | ||||
\(563\) | −9.28442 | −0.391292 | −0.195646 | − | 0.980675i | \(-0.562680\pi\) | ||||
−0.195646 | + | 0.980675i | \(0.562680\pi\) | |||||||
\(564\) | 2.99882 | 0.126273 | ||||||||
\(565\) | 1.78699 | − | 5.49980i | 0.0751793 | − | 0.231378i | ||||
\(566\) | 8.52089 | + | 26.2246i | 0.358160 | + | 1.10230i | ||||
\(567\) | −1.31116 | − | 4.03534i | −0.0550636 | − | 0.169468i | ||||
\(568\) | 0.406452 | − | 0.295305i | 0.0170543 | − | 0.0123907i | ||||
\(569\) | −2.01986 | + | 6.21647i | −0.0846767 | + | 0.260608i | −0.984426 | − | 0.175799i | \(-0.943749\pi\) |
0.899749 | + | 0.436407i | \(0.143749\pi\) | |||||||
\(570\) | 5.50566 | − | 4.00010i | 0.230607 | − | 0.167546i | ||||
\(571\) | −11.6761 | − | 8.48321i | −0.488631 | − | 0.355011i | 0.316027 | − | 0.948750i | \(-0.397651\pi\) |
−0.804658 | + | 0.593739i | \(0.797651\pi\) | |||||||
\(572\) | −0.376947 | − | 1.16012i | −0.0157609 | − | 0.0485072i | ||||
\(573\) | 4.24025 | + | 3.08072i | 0.177139 | + | 0.128699i | ||||
\(574\) | 13.7119 | + | 9.96226i | 0.572323 | + | 0.415817i | ||||
\(575\) | 1.49726 | + | 4.60810i | 0.0624402 | + | 0.192171i | ||||
\(576\) | −0.809017 | − | 0.587785i | −0.0337090 | − | 0.0244911i | ||||
\(577\) | 10.0211 | − | 7.28073i | 0.417182 | − | 0.303101i | −0.359321 | − | 0.933214i | \(-0.616992\pi\) |
0.776503 | + | 0.630113i | \(0.216992\pi\) | |||||||
\(578\) | −0.828822 | + | 2.55085i | −0.0344744 | + | 0.106101i | ||||
\(579\) | 20.8530 | − | 15.1506i | 0.866623 | − | 0.629638i | ||||
\(580\) | 2.63081 | + | 8.09680i | 0.109238 | + | 0.336201i | ||||
\(581\) | −5.93340 | − | 18.2611i | −0.246159 | − | 0.757600i | ||||
\(582\) | 4.11658 | − | 12.6695i | 0.170638 | − | 0.525169i | ||||
\(583\) | −17.4535 | −0.722852 | ||||||||
\(584\) | −5.27750 | −0.218385 | ||||||||
\(585\) | −0.291813 | + | 0.898110i | −0.0120650 | + | 0.0371323i | ||||
\(586\) | −3.34206 | − | 2.42815i | −0.138059 | − | 0.100306i | ||||
\(587\) | −30.4316 | + | 22.1098i | −1.25604 | + | 0.912570i | −0.998556 | − | 0.0537117i | \(-0.982895\pi\) |
−0.257488 | + | 0.966281i | \(0.582895\pi\) | |||||||
\(588\) | −11.0031 | −0.453760 | ||||||||
\(589\) | −2.89972 | − | 37.7796i | −0.119481 | − | 1.55668i | ||||
\(590\) | −10.2342 | −0.421337 | ||||||||
\(591\) | −7.67889 | + | 5.57904i | −0.315867 | + | 0.229491i | ||||
\(592\) | −9.07344 | − | 6.59224i | −0.372916 | − | 0.270939i | ||||
\(593\) | 10.8035 | − | 33.2496i | 0.443645 | − | 1.36540i | −0.440319 | − | 0.897842i | \(-0.645134\pi\) |
0.883963 | − | 0.467556i | \(-0.154866\pi\) | |||||||
\(594\) | 1.29174 | 0.0530007 | ||||||||
\(595\) | −18.8239 | −0.771705 | ||||||||
\(596\) | −5.15737 | + | 15.8727i | −0.211254 | + | 0.650173i | ||||
\(597\) | −4.66230 | − | 14.3491i | −0.190815 | − | 0.587269i | ||||
\(598\) | 1.41391 | + | 4.35156i | 0.0578190 | + | 0.177949i | ||||
\(599\) | 7.53991 | − | 5.47806i | 0.308072 | − | 0.223828i | −0.422997 | − | 0.906131i | \(-0.639022\pi\) |
0.731069 | + | 0.682304i | \(0.239022\pi\) | |||||||
\(600\) | 0.309017 | − | 0.951057i | 0.0126156 | − | 0.0388267i | ||||
\(601\) | −27.4705 | + | 19.9585i | −1.12054 | + | 0.814123i | −0.984292 | − | 0.176551i | \(-0.943506\pi\) |
−0.136253 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(602\) | −43.7774 | − | 31.8062i | −1.78424 | − | 1.29632i | ||||
\(603\) | −0.971725 | − | 2.99066i | −0.0395717 | − | 0.121789i | ||||
\(604\) | −10.4929 | − | 7.62353i | −0.426950 | − | 0.310197i | ||||
\(605\) | 7.54927 | + | 5.48486i | 0.306921 | + | 0.222991i | ||||
\(606\) | −2.06555 | − | 6.35711i | −0.0839073 | − | 0.258240i | ||||
\(607\) | −9.68860 | − | 7.03918i | −0.393248 | − | 0.285712i | 0.373537 | − | 0.927615i | \(-0.378145\pi\) |
−0.766785 | + | 0.641904i | \(0.778145\pi\) | |||||||
\(608\) | −5.50566 | + | 4.00010i | −0.223284 | + | 0.162225i | ||||
\(609\) | 11.1625 | − | 34.3548i | 0.452329 | − | 1.39213i | ||||
\(610\) | 1.19305 | − | 0.866804i | 0.0483053 | − | 0.0350959i | ||||
\(611\) | 0.875095 | + | 2.69327i | 0.0354026 | + | 0.108958i | ||||
\(612\) | 1.37094 | + | 4.21932i | 0.0554170 | + | 0.170556i | ||||
\(613\) | 3.22699 | − | 9.93164i | 0.130337 | − | 0.401135i | −0.864499 | − | 0.502635i | \(-0.832364\pi\) |
0.994836 | + | 0.101500i | \(0.0323640\pi\) | |||||||
\(614\) | 4.67414 | 0.188633 | ||||||||
\(615\) | 3.99453 | 0.161075 | ||||||||
\(616\) | 1.69368 | − | 5.21261i | 0.0682403 | − | 0.210022i | ||||
\(617\) | −34.7069 | − | 25.2161i | −1.39725 | − | 1.01516i | −0.995026 | − | 0.0996180i | \(-0.968238\pi\) |
−0.402222 | − | 0.915542i | \(-0.631762\pi\) | |||||||
\(618\) | −15.0867 | + | 10.9611i | −0.606875 | + | 0.440921i | ||||
\(619\) | −15.9291 | −0.640243 | −0.320122 | − | 0.947376i | \(-0.603724\pi\) | ||||
−0.320122 | + | 0.947376i | \(0.603724\pi\) | |||||||
\(620\) | −3.60777 | − | 4.24075i | −0.144891 | − | 0.170313i | ||||
\(621\) | −4.84525 | −0.194433 | ||||||||
\(622\) | −2.71894 | + | 1.97543i | −0.109020 | + | 0.0792074i | ||||
\(623\) | 61.6672 | + | 44.8038i | 2.47064 | + | 1.79503i | ||||
\(624\) | 0.291813 | − | 0.898110i | 0.0116819 | − | 0.0359532i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 25.1064 | 1.00345 | ||||||||
\(627\) | 2.71650 | − | 8.36051i | 0.108486 | − | 0.333887i | ||||
\(628\) | 3.49577 | + | 10.7589i | 0.139496 | + | 0.429326i | ||||
\(629\) | 15.3756 | + | 47.3213i | 0.613066 | + | 1.88682i | ||||
\(630\) | −3.43266 | + | 2.49398i | −0.136761 | + | 0.0993624i | ||||
\(631\) | 3.85773 | − | 11.8729i | 0.153574 | − | 0.472652i | −0.844440 | − | 0.535651i | \(-0.820066\pi\) |
0.998014 | + | 0.0629988i | \(0.0200664\pi\) | |||||||
\(632\) | −0.866833 | + | 0.629791i | −0.0344808 | + | 0.0250517i | ||||
\(633\) | 0.276515 | + | 0.200900i | 0.0109905 | + | 0.00798507i | ||||
\(634\) | 1.54899 | + | 4.76730i | 0.0615183 | + | 0.189334i | ||||
\(635\) | 10.9227 | + | 7.93580i | 0.433454 | + | 0.314923i | ||||
\(636\) | −10.9312 | − | 7.94195i | −0.433449 | − | 0.314919i | ||||
\(637\) | −3.21085 | − | 9.88199i | −0.127219 | − | 0.391539i | ||||
\(638\) | 8.89692 | + | 6.46399i | 0.352233 | + | 0.255912i | ||||
\(639\) | −0.406452 | + | 0.295305i | −0.0160790 | + | 0.0116821i | ||||
\(640\) | −0.309017 | + | 0.951057i | −0.0122150 | + | 0.0375938i | ||||
\(641\) | −32.4368 | + | 23.5667i | −1.28118 | + | 0.930829i | −0.999588 | − | 0.0287065i | \(-0.990861\pi\) |
−0.281588 | + | 0.959535i | \(0.590861\pi\) | |||||||
\(642\) | −2.51418 | − | 7.73784i | −0.0992266 | − | 0.305388i | ||||
\(643\) | 8.10447 | + | 24.9430i | 0.319609 | + | 0.983656i | 0.973816 | + | 0.227340i | \(0.0730027\pi\) |
−0.654206 | + | 0.756316i | \(0.726997\pi\) | |||||||
\(644\) | −6.35290 | + | 19.5522i | −0.250339 | + | 0.770465i | ||||
\(645\) | −12.7532 | −0.502157 | ||||||||
\(646\) | 30.1917 | 1.18788 | ||||||||
\(647\) | 1.78951 | − | 5.50755i | 0.0703529 | − | 0.216524i | −0.909698 | − | 0.415270i | \(-0.863687\pi\) |
0.980051 | + | 0.198746i | \(0.0636870\pi\) | |||||||
\(648\) | 0.809017 | + | 0.587785i | 0.0317812 | + | 0.0230904i | ||||
\(649\) | −10.6952 | + | 7.77051i | −0.419823 | + | 0.305019i | ||||
\(650\) | 0.944328 | 0.0370396 | ||||||||
\(651\) | 1.80792 | + | 23.5548i | 0.0708578 | + | 0.923185i | ||||
\(652\) | −10.4795 | −0.410410 | ||||||||
\(653\) | −25.8810 | + | 18.8037i | −1.01280 | + | 0.735844i | −0.964795 | − | 0.263003i | \(-0.915287\pi\) |
−0.0480074 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(654\) | 10.2609 | + | 7.45494i | 0.401231 | + | 0.291511i | ||||
\(655\) | −5.28516 | + | 16.2660i | −0.206508 | + | 0.635567i | ||||
\(656\) | −3.99453 | −0.155960 | ||||||||
\(657\) | 5.27750 | 0.205895 | ||||||||
\(658\) | −3.93193 | + | 12.1012i | −0.153283 | + | 0.471755i | ||||
\(659\) | 0.297208 | + | 0.914713i | 0.0115776 | + | 0.0356322i | 0.956678 | − | 0.291147i | \(-0.0940368\pi\) |
−0.945101 | + | 0.326779i | \(0.894037\pi\) | |||||||
\(660\) | −0.399170 | − | 1.22852i | −0.0155377 | − | 0.0478200i | ||||
\(661\) | 32.7971 | − | 23.8285i | 1.27566 | − | 0.926820i | 0.276246 | − | 0.961087i | \(-0.410910\pi\) |
0.999413 | + | 0.0342668i | \(0.0109096\pi\) | |||||||
\(662\) | −7.32104 | + | 22.5318i | −0.284540 | + | 0.875725i | ||||
\(663\) | −3.38935 | + | 2.46251i | −0.131632 | + | 0.0956359i | ||||
\(664\) | 3.66105 | + | 2.65991i | 0.142076 | + | 0.103224i | ||||
\(665\) | 8.92293 | + | 27.4620i | 0.346017 | + | 1.06493i | ||||
\(666\) | 9.07344 | + | 6.59224i | 0.351589 | + | 0.255444i | ||||
\(667\) | −33.3719 | − | 24.2461i | −1.29216 | − | 0.938813i | ||||
\(668\) | −5.77144 | − | 17.7627i | −0.223304 | − | 0.687258i | ||||
\(669\) | 6.21898 | + | 4.51836i | 0.240440 | + | 0.174690i | ||||
\(670\) | −2.54401 | + | 1.84833i | −0.0982836 | + | 0.0714072i | ||||
\(671\) | 0.588653 | − | 1.81169i | 0.0227247 | − | 0.0699395i | ||||
\(672\) | 3.43266 | − | 2.49398i | 0.132418 | − | 0.0962072i | ||||
\(673\) | −4.71354 | − | 14.5068i | −0.181694 | − | 0.559195i | 0.818182 | − | 0.574959i | \(-0.194982\pi\) |
−0.999876 | + | 0.0157639i | \(0.994982\pi\) | |||||||
\(674\) | 6.24132 | + | 19.2088i | 0.240406 | + | 0.739895i | ||||
\(675\) | −0.309017 | + | 0.951057i | −0.0118941 | + | 0.0366062i | ||||
\(676\) | −12.1082 | −0.465702 | ||||||||
\(677\) | 3.64072 | 0.139924 | 0.0699622 | − | 0.997550i | \(-0.477712\pi\) | ||||
0.0699622 | + | 0.997550i | \(0.477712\pi\) | |||||||
\(678\) | 1.78699 | − | 5.49980i | 0.0686290 | − | 0.211218i | ||||
\(679\) | 45.7283 | + | 33.2236i | 1.75489 | + | 1.27500i | ||||
\(680\) | 3.58917 | − | 2.60768i | 0.137638 | − | 0.100000i | ||||
\(681\) | −1.54451 | −0.0591856 | ||||||||
\(682\) | −6.99012 | − | 1.69250i | −0.267666 | − | 0.0648092i | ||||
\(683\) | −27.1103 | −1.03735 | −0.518674 | − | 0.854972i | \(-0.673574\pi\) | ||||
−0.518674 | + | 0.854972i | \(0.673574\pi\) | |||||||
\(684\) | 5.50566 | − | 4.00010i | 0.210514 | − | 0.152947i | ||||
\(685\) | −14.4427 | − | 10.4932i | −0.551826 | − | 0.400925i | ||||
\(686\) | 5.24871 | − | 16.1539i | 0.200397 | − | 0.616758i | ||||
\(687\) | −7.42380 | −0.283236 | ||||||||
\(688\) | 12.7532 | 0.486211 | ||||||||
\(689\) | 3.94288 | − | 12.1349i | 0.150212 | − | 0.462305i | ||||
\(690\) | 1.49726 | + | 4.60810i | 0.0569999 | + | 0.175428i | ||||
\(691\) | −3.75966 | − | 11.5710i | −0.143024 | − | 0.440183i | 0.853728 | − | 0.520720i | \(-0.174336\pi\) |
−0.996752 | + | 0.0805372i | \(0.974336\pi\) | |||||||
\(692\) | −2.14742 | + | 1.56019i | −0.0816326 | + | 0.0593096i | ||||
\(693\) | −1.69368 | + | 5.21261i | −0.0643375 | + | 0.198011i | ||||
\(694\) | 12.4874 | − | 9.07262i | 0.474015 | − | 0.344392i | ||||
\(695\) | 1.78724 | + | 1.29851i | 0.0677938 | + | 0.0492551i | ||||
\(696\) | 2.63081 | + | 8.09680i | 0.0997206 | + | 0.306908i | ||||
\(697\) | 14.3370 | + | 10.4165i | 0.543054 | + | 0.394552i | ||||
\(698\) | −14.4517 | − | 10.4998i | −0.547005 | − | 0.397423i | ||||
\(699\) | −6.67234 | − | 20.5354i | −0.252371 | − | 0.776718i | ||||
\(700\) | 3.43266 | + | 2.49398i | 0.129743 | + | 0.0942635i | ||||
\(701\) | −31.6523 | + | 22.9967i | −1.19549 | + | 0.868574i | −0.993834 | − | 0.110882i | \(-0.964632\pi\) |
−0.201656 | + | 0.979456i | \(0.564632\pi\) | |||||||
\(702\) | −0.291813 | + | 0.898110i | −0.0110138 | + | 0.0338970i | ||||
\(703\) | 61.7481 | − | 44.8626i | 2.32887 | − | 1.69203i | ||||
\(704\) | 0.399170 | + | 1.22852i | 0.0150443 | + | 0.0463015i | ||||
\(705\) | 0.926685 | + | 2.85204i | 0.0349010 | + | 0.107414i | ||||
\(706\) | 0.0746608 | − | 0.229782i | 0.00280989 | − | 0.00864797i | ||||
\(707\) | 28.3614 | 1.06664 | ||||||||
\(708\) | −10.2342 | −0.384626 | ||||||||
\(709\) | −10.2047 | + | 31.4067i | −0.383244 | + | 1.17950i | 0.554503 | + | 0.832182i | \(0.312909\pi\) |
−0.937746 | + | 0.347321i | \(0.887091\pi\) | |||||||
\(710\) | 0.406452 | + | 0.295305i | 0.0152539 | + | 0.0110826i | ||||
\(711\) | 0.866833 | − | 0.629791i | 0.0325088 | − | 0.0236190i | ||||
\(712\) | −17.9648 | −0.673260 | ||||||||
\(713\) | 26.2196 | + | 6.34848i | 0.981931 | + | 0.237753i | ||||
\(714\) | −18.8239 | −0.704467 | ||||||||
\(715\) | 0.986860 | − | 0.716996i | 0.0369065 | − | 0.0268141i | ||||
\(716\) | 15.6865 | + | 11.3969i | 0.586232 | + | 0.425922i | ||||
\(717\) | 1.36603 | − | 4.20422i | 0.0510155 | − | 0.157010i | ||||
\(718\) | −17.7642 | −0.662955 | ||||||||
\(719\) | −16.9972 | −0.633889 | −0.316944 | − | 0.948444i | \(-0.602657\pi\) | ||||
−0.316944 | + | 0.948444i | \(0.602657\pi\) | |||||||
\(720\) | 0.309017 | − | 0.951057i | 0.0115164 | − | 0.0354438i | ||||
\(721\) | −24.4507 | − | 75.2516i | −0.910593 | − | 2.80252i | ||||
\(722\) | −8.44019 | − | 25.9762i | −0.314112 | − | 0.966736i | ||||
\(723\) | −13.5024 | + | 9.81010i | −0.502161 | + | 0.364842i | ||||
\(724\) | 2.56398 | − | 7.89112i | 0.0952896 | − | 0.293271i | ||||
\(725\) | −6.88755 | + | 5.00410i | −0.255797 | + | 0.185848i | ||||
\(726\) | 7.54927 | + | 5.48486i | 0.280180 | + | 0.203562i | ||||
\(727\) | −7.24989 | − | 22.3129i | −0.268883 | − | 0.827538i | −0.990773 | − | 0.135530i | \(-0.956726\pi\) |
0.721890 | − | 0.692008i | \(-0.243274\pi\) | |||||||
\(728\) | 3.24156 | + | 2.35513i | 0.120140 | + | 0.0872870i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | −1.63084 | − | 5.01921i | −0.0603600 | − | 0.185769i | ||||
\(731\) | −45.7733 | − | 33.2563i | −1.69299 | − | 1.23003i | ||||
\(732\) | 1.19305 | − | 0.866804i | 0.0440965 | − | 0.0320380i | ||||
\(733\) | −6.81258 | + | 20.9670i | −0.251629 | + | 0.774433i | 0.742847 | + | 0.669462i | \(0.233475\pi\) |
−0.994475 | + | 0.104971i | \(0.966525\pi\) | |||||||
\(734\) | 9.69467 | − | 7.04359i | 0.357837 | − | 0.259984i | ||||
\(735\) | −3.40015 | − | 10.4646i | −0.125416 | − | 0.385992i | ||||
\(736\) | −1.49726 | − | 4.60810i | −0.0551899 | − | 0.169857i | ||||
\(737\) | −1.25522 | + | 3.86316i | −0.0462364 | + | 0.142301i | ||||
\(738\) | 3.99453 | 0.147041 | ||||||||
\(739\) | 12.4433 | 0.457733 | 0.228867 | − | 0.973458i | \(-0.426498\pi\) | ||||
0.228867 | + | 0.973458i | \(0.426498\pi\) | |||||||
\(740\) | 3.46575 | − | 10.6665i | 0.127403 | − | 0.392107i | ||||
\(741\) | 5.19915 | + | 3.77740i | 0.190996 | + | 0.138766i | ||||
\(742\) | 46.3810 | − | 33.6978i | 1.70270 | − | 1.23708i | ||||
\(743\) | −4.40377 | −0.161559 | −0.0807793 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807793 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(744\) | −3.60777 | − | 4.24075i | −0.132267 | − | 0.155474i | ||||
\(745\) | −16.6896 | −0.611459 | ||||||||
\(746\) | 17.1993 | − | 12.4960i | 0.629711 | − | 0.457512i | ||||
\(747\) | −3.66105 | − | 2.65991i | −0.133951 | − | 0.0973209i | ||||
\(748\) | 1.77090 | − | 5.45026i | 0.0647504 | − | 0.199281i | ||||
\(749\) | 34.5213 | 1.26138 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −6.12241 | + | 18.8429i | −0.223410 | + | 0.687585i | 0.775039 | + | 0.631913i | \(0.217730\pi\) |
−0.998449 | + | 0.0556721i | \(0.982270\pi\) | |||||||
\(752\) | −0.926685 | − | 2.85204i | −0.0337927 | − | 0.104003i | ||||
\(753\) | −0.669023 | − | 2.05904i | −0.0243806 | − | 0.0750357i | ||||
\(754\) | −6.50411 | + | 4.72551i | −0.236866 | + | 0.172093i | ||||
\(755\) | 4.00793 | − | 12.3351i | 0.145863 | − | 0.448921i | ||||
\(756\) | −3.43266 | + | 2.49398i | −0.124845 | + | 0.0907051i | ||||
\(757\) | 8.43346 | + | 6.12727i | 0.306519 | + | 0.222699i | 0.730402 | − | 0.683018i | \(-0.239333\pi\) |
−0.423882 | + | 0.905717i | \(0.639333\pi\) | |||||||
\(758\) | 2.80451 | + | 8.63139i | 0.101864 | + | 0.313506i | ||||
\(759\) | 5.06347 | + | 3.67883i | 0.183792 | + | 0.133533i | ||||
\(760\) | −5.50566 | − | 4.00010i | −0.199711 | − | 0.145099i | ||||
\(761\) | 0.899635 | + | 2.76879i | 0.0326117 | + | 0.100369i | 0.966037 | − | 0.258402i | \(-0.0831960\pi\) |
−0.933426 | + | 0.358771i | \(0.883196\pi\) | |||||||
\(762\) | 10.9227 | + | 7.93580i | 0.395687 | + | 0.287484i | ||||
\(763\) | −43.5369 | + | 31.6314i | −1.57614 | + | 1.14513i | ||||
\(764\) | 1.61963 | − | 4.98471i | 0.0585962 | − | 0.180341i | ||||
\(765\) | −3.58917 | + | 2.60768i | −0.129767 | + | 0.0942809i | ||||
\(766\) | 1.82277 | + | 5.60990i | 0.0658592 | + | 0.202694i | ||||
\(767\) | −2.98649 | − | 9.19147i | −0.107836 | − | 0.331885i | ||||
\(768\) | −0.309017 | + | 0.951057i | −0.0111507 | + | 0.0343183i | ||||
\(769\) | 36.0845 | 1.30124 | 0.650621 | − | 0.759403i | \(-0.274509\pi\) | ||||
0.650621 | + | 0.759403i | \(0.274509\pi\) | |||||||
\(770\) | 5.48086 | 0.197516 | ||||||||
\(771\) | −4.74579 | + | 14.6060i | −0.170915 | + | 0.526023i | ||||
\(772\) | −20.8530 | − | 15.1506i | −0.750518 | − | 0.545283i | ||||
\(773\) | −15.5432 | + | 11.2928i | −0.559050 | + | 0.406174i | −0.831111 | − | 0.556106i | \(-0.812295\pi\) |
0.272061 | + | 0.962280i | \(0.412295\pi\) | |||||||
\(774\) | −12.7532 | −0.458404 | ||||||||
\(775\) | 2.91834 | − | 4.74166i | 0.104830 | − | 0.170325i | ||||
\(776\) | −13.3215 | −0.478215 | ||||||||
\(777\) | −38.4987 | + | 27.9709i | −1.38113 | + | 1.00345i | ||||
\(778\) | 21.2774 | + | 15.4589i | 0.762831 | + | 0.554229i | ||||
\(779\) | 8.40039 | − | 25.8537i | 0.300975 | − | 0.926307i | ||||
\(780\) | 0.944328 | 0.0338124 | ||||||||
\(781\) | 0.648973 | 0.0232221 | ||||||||
\(782\) | −6.64254 | + | 20.4436i | −0.237537 | + | 0.731063i | ||||
\(783\) | −2.63081 | − | 8.09680i | −0.0940175 | − | 0.289356i | ||||
\(784\) | 3.40015 | + | 10.4646i | 0.121434 | + | 0.373735i | ||||
\(785\) | −9.15205 | + | 6.64935i | −0.326651 | + | 0.237326i | ||||
\(786\) | −5.28516 | + | 16.2660i | −0.188515 | + | 0.580190i | ||||
\(787\) | −40.3521 | + | 29.3175i | −1.43840 | + | 1.04506i | −0.450021 | + | 0.893018i | \(0.648584\pi\) |
−0.988375 | + | 0.152038i | \(0.951416\pi\) | |||||||
\(788\) | 7.67889 | + | 5.57904i | 0.273549 | + | 0.198745i | ||||
\(789\) | 0.0975307 | + | 0.300169i | 0.00347218 | + | 0.0106863i | ||||
\(790\) | −0.866833 | − | 0.629791i | −0.0308405 | − | 0.0224070i | ||||
\(791\) | 19.8505 | + | 14.4222i | 0.705803 | + | 0.512796i | ||||
\(792\) | −0.399170 | − | 1.22852i | −0.0141839 | − | 0.0436535i | ||||
\(793\) | 1.12663 | + | 0.818548i | 0.0400079 | + | 0.0290675i | ||||
\(794\) | 8.39425 | − | 6.09878i | 0.297901 | − | 0.216438i | ||||
\(795\) | 4.17533 | − | 12.8503i | 0.148084 | − | 0.455755i | ||||
\(796\) | −12.2061 | + | 8.86822i | −0.432632 | + | 0.314326i | ||||
\(797\) | 12.5681 | + | 38.6805i | 0.445183 | + | 1.37013i | 0.882283 | + | 0.470720i | \(0.156006\pi\) |
−0.437099 | + | 0.899413i | \(0.643994\pi\) | |||||||
\(798\) | 8.92293 | + | 27.4620i | 0.315868 | + | 0.972143i | ||||
\(799\) | −4.11120 | + | 12.6530i | −0.145444 | + | 0.447630i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 17.9648 | 0.634755 | ||||||||
\(802\) | 10.2998 | − | 31.6994i | 0.363698 | − | 1.11935i | ||||
\(803\) | −5.51520 | − | 4.00703i | −0.194627 | − | 0.141405i | ||||
\(804\) | −2.54401 | + | 1.84833i | −0.0897202 | + | 0.0651856i | ||||
\(805\) | −20.5584 | −0.724589 | ||||||||
\(806\) | 2.75587 | − | 4.47768i | 0.0970713 | − | 0.157720i | ||||
\(807\) | 9.21128 | 0.324252 | ||||||||
\(808\) | −5.40768 | + | 3.92891i | −0.190242 | + | 0.138219i | ||||
\(809\) | −38.9051 | − | 28.2662i | −1.36783 | − | 0.993786i | −0.997903 | − | 0.0647253i | \(-0.979383\pi\) |
−0.369926 | − | 0.929061i | \(-0.620617\pi\) | |||||||
\(810\) | −0.309017 | + | 0.951057i | −0.0108578 | + | 0.0334167i | ||||
\(811\) | −26.2511 | −0.921800 | −0.460900 | − | 0.887452i | \(-0.652473\pi\) | ||||
−0.460900 | + | 0.887452i | \(0.652473\pi\) | |||||||
\(812\) | −36.1228 | −1.26766 | ||||||||
\(813\) | 0.585301 | − | 1.80137i | 0.0205274 | − | 0.0631768i | ||||
\(814\) | −4.47684 | − | 13.7783i | −0.156913 | − | 0.482929i | ||||
\(815\) | −3.23835 | − | 9.96662i | −0.113435 | − | 0.349116i | ||||
\(816\) | 3.58917 | − | 2.60768i | 0.125646 | − | 0.0912871i | ||||
\(817\) | −26.8197 | + | 82.5424i | −0.938301 | + | 2.88779i | ||||
\(818\) | −5.89254 | + | 4.28118i | −0.206028 | + | 0.149688i | ||||
\(819\) | −3.24156 | − | 2.35513i | −0.113269 | − | 0.0822950i | ||||
\(820\) | −1.23438 | − | 3.79902i | −0.0431063 | − | 0.132668i | ||||
\(821\) | 16.8227 | + | 12.2224i | 0.587116 | + | 0.426565i | 0.841283 | − | 0.540596i | \(-0.181801\pi\) |
−0.254166 | + | 0.967160i | \(0.581801\pi\) | |||||||
\(822\) | −14.4427 | − | 10.4932i | −0.503746 | − | 0.365993i | ||||
\(823\) | 2.94900 | + | 9.07610i | 0.102796 | + | 0.316373i | 0.989207 | − | 0.146526i | \(-0.0468092\pi\) |
−0.886411 | + | 0.462899i | \(0.846809\pi\) | |||||||
\(824\) | 15.0867 | + | 10.9611i | 0.525569 | + | 0.381848i | ||||
\(825\) | 1.04504 | − | 0.759266i | 0.0363836 | − | 0.0264342i | ||||
\(826\) | 13.4187 | − | 41.2986i | 0.466898 | − | 1.43696i | ||||
\(827\) | −13.8030 | + | 10.0284i | −0.479976 | + | 0.348723i | −0.801316 | − | 0.598241i | \(-0.795867\pi\) |
0.321341 | + | 0.946964i | \(0.395867\pi\) | |||||||
\(828\) | 1.49726 | + | 4.60810i | 0.0520335 | + | 0.160143i | ||||
\(829\) | −2.31124 | − | 7.11326i | −0.0802726 | − | 0.247054i | 0.902864 | − | 0.429926i | \(-0.141460\pi\) |
−0.983137 | + | 0.182873i | \(0.941460\pi\) | |||||||
\(830\) | −1.39840 | + | 4.30382i | −0.0485390 | + | 0.149388i | ||||
\(831\) | 11.8015 | 0.409391 | ||||||||
\(832\) | −0.944328 | −0.0327387 | ||||||||
\(833\) | 15.0846 | − | 46.4256i | 0.522650 | − | 1.60855i | ||||
\(834\) | 1.78724 | + | 1.29851i | 0.0618870 | + | 0.0449636i | ||||
\(835\) | 15.1098 | − | 10.9779i | 0.522897 | − | 0.379907i | ||||
\(836\) | −8.79077 | −0.304035 | ||||||||
\(837\) | 3.60777 | + | 4.24075i | 0.124703 | + | 0.146582i | ||||
\(838\) | −38.1615 | −1.31827 | ||||||||
\(839\) | 4.44777 | − | 3.23149i | 0.153554 | − | 0.111563i | −0.508355 | − | 0.861147i | \(-0.669746\pi\) |
0.661909 | + | 0.749584i | \(0.269746\pi\) | |||||||
\(840\) | 3.43266 | + | 2.49398i | 0.118438 | + | 0.0860504i | ||||
\(841\) | 13.4359 | − | 41.3513i | 0.463306 | − | 1.42591i | ||||
\(842\) | −6.11837 | −0.210853 | ||||||||
\(843\) | 4.52036 | 0.155690 | ||||||||
\(844\) | 0.105619 | − | 0.325063i | 0.00363557 | − | 0.0111891i | ||||
\(845\) | −3.74165 | − | 11.5156i | −0.128717 | − | 0.396150i | ||||
\(846\) | 0.926685 | + | 2.85204i | 0.0318601 | + | 0.0980553i | ||||
\(847\) | −32.0316 | + | 23.2723i | −1.10062 | + | 0.799646i | ||||
\(848\) | −4.17533 | + | 12.8503i | −0.143381 | + | 0.441283i | ||||
\(849\) | −22.3080 | + | 16.2077i | −0.765608 | + | 0.556247i | ||||
\(850\) | 3.58917 | + | 2.60768i | 0.123107 | + | 0.0894428i | ||||
\(851\) | 16.7924 | + | 51.6817i | 0.575636 | + | 1.77163i | ||||
\(852\) | 0.406452 | + | 0.295305i | 0.0139248 | + | 0.0101170i | ||||
\(853\) | −38.0785 | − | 27.6656i | −1.30378 | − | 0.947253i | −0.303797 | − | 0.952737i | \(-0.598255\pi\) |
−0.999985 | + | 0.00548328i | \(0.998255\pi\) | |||||||
\(854\) | 1.93356 | + | 5.95089i | 0.0661652 | + | 0.203635i | ||||
\(855\) | 5.50566 | + | 4.00010i | 0.188290 | + | 0.136800i | ||||
\(856\) | −6.58220 | + | 4.78225i | −0.224975 | + | 0.163454i | ||||
\(857\) | −6.35706 | + | 19.5650i | −0.217153 | + | 0.668328i | 0.781841 | + | 0.623478i | \(0.214281\pi\) |
−0.998994 | + | 0.0448498i | \(0.985719\pi\) | |||||||
\(858\) | 0.986860 | − | 0.716996i | 0.0336909 | − | 0.0244778i | ||||
\(859\) | 0.849216 | + | 2.61362i | 0.0289749 | + | 0.0891755i | 0.964498 | − | 0.264089i | \(-0.0850714\pi\) |
−0.935523 | + | 0.353265i | \(0.885071\pi\) | |||||||
\(860\) | 3.94095 | + | 12.1290i | 0.134385 | + | 0.413596i | ||||
\(861\) | −5.23747 | + | 16.1193i | −0.178492 | + | 0.549343i | ||||
\(862\) | 28.1906 | 0.960175 | ||||||||
\(863\) | −7.91434 | −0.269407 | −0.134704 | − | 0.990886i | \(-0.543008\pi\) | ||||
−0.134704 | + | 0.990886i | \(0.543008\pi\) | |||||||
\(864\) | 0.309017 | − | 0.951057i | 0.0105130 | − | 0.0323556i | ||||
\(865\) | −2.14742 | − | 1.56019i | −0.0730145 | − | 0.0530481i | ||||
\(866\) | 13.8649 | − | 10.0735i | 0.471150 | − | 0.342310i | ||||
\(867\) | −2.68212 | −0.0910897 | ||||||||
\(868\) | 21.8433 | − | 8.99826i | 0.741408 | − | 0.305421i | ||||
\(869\) | −1.38405 | −0.0469508 | ||||||||
\(870\) | −6.88755 | + | 5.00410i | −0.233510 | + | 0.169655i | ||||
\(871\) | −2.40238 | − | 1.74543i | −0.0814015 | − | 0.0591416i | ||||
\(872\) | 3.91930 | − | 12.0624i | 0.132724 | − | 0.408483i | ||||
\(873\) | 13.3215 | 0.450865 | ||||||||
\(874\) | 32.9737 | 1.11535 | ||||||||
\(875\) | −1.31116 | + | 4.03534i | −0.0443253 | + | 0.136419i | ||||
\(876\) | −1.63084 | − | 5.01921i | −0.0551009 | − | 0.169583i | ||||
\(877\) | −10.8196 | − | 33.2993i | −0.365352 | − | 1.12444i | −0.949761 | − | 0.312977i | \(-0.898674\pi\) |
0.584409 | − | 0.811459i | \(-0.301326\pi\) | |||||||
\(878\) | 22.8656 | − | 16.6128i | 0.771676 | − | 0.560656i | ||||
\(879\) | 1.27656 | − | 3.92883i | 0.0430571 | − | 0.132516i | ||||
\(880\) | −1.04504 | + | 0.759266i | −0.0352283 | + | 0.0255948i | ||||
\(881\) | 12.6171 | + | 9.16682i | 0.425079 | + | 0.308838i | 0.779678 | − | 0.626180i | \(-0.215383\pi\) |
−0.354599 | + | 0.935018i | \(0.615383\pi\) | |||||||
\(882\) | −3.40015 | − | 10.4646i | −0.114489 | − | 0.352361i | ||||
\(883\) | −20.1616 | − | 14.6483i | −0.678492 | − | 0.492953i | 0.194365 | − | 0.980929i | \(-0.437735\pi\) |
−0.872857 | + | 0.487976i | \(0.837735\pi\) | |||||||
\(884\) | 3.38935 | + | 2.46251i | 0.113996 | + | 0.0828231i | ||||
\(885\) | −3.16256 | − | 9.73334i | −0.106308 | − | 0.327183i | ||||
\(886\) | −21.2767 | − | 15.4585i | −0.714806 | − | 0.519337i | ||||
\(887\) | 20.9910 | − | 15.2509i | 0.704809 | − | 0.512074i | −0.176686 | − | 0.984267i | \(-0.556538\pi\) |
0.881495 | + | 0.472193i | \(0.156538\pi\) | |||||||
\(888\) | 3.46575 | − | 10.6665i | 0.116303 | − | 0.357943i | ||||
\(889\) | −46.3451 | + | 33.6717i | −1.55436 | + | 1.12931i | ||||
\(890\) | −5.55143 | − | 17.0855i | −0.186084 | − | 0.572709i | ||||
\(891\) | 0.399170 | + | 1.22852i | 0.0133727 | + | 0.0411569i | ||||
\(892\) | 2.37544 | − | 7.31085i | 0.0795356 | − | 0.244785i | ||||
\(893\) | 20.4080 | 0.682929 | ||||||||
\(894\) | −16.6896 | −0.558183 | ||||||||
\(895\) | −5.99171 | + | 18.4406i | −0.200281 | + | 0.616401i | ||||
\(896\) | −3.43266 | − | 2.49398i | −0.114677 | − | 0.0833179i | ||||
\(897\) | −3.70166 | + | 2.68941i | −0.123595 | + | 0.0897969i | ||||
\(898\) | −5.96485 | −0.199050 | ||||||||
\(899\) | 3.62754 | + | 47.2621i | 0.120985 | + | 1.57628i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 48.4956 | − | 35.2341i | 1.61562 | − | 1.17382i | ||||
\(902\) | −4.17444 | − | 3.03291i | −0.138994 | − | 0.100985i | ||||
\(903\) | 16.7215 | − | 51.4635i | 0.556457 | − | 1.71260i | ||||
\(904\) | −5.78283 | −0.192334 | ||||||||
\(905\) | 8.29722 | 0.275809 | ||||||||
\(906\) | 4.00793 | − | 12.3351i | 0.133154 | − | 0.409807i | ||||
\(907\) | −2.06741 | − | 6.36284i | −0.0686473 | − | 0.211275i | 0.910848 | − | 0.412742i | \(-0.135429\pi\) |
−0.979495 | + | 0.201468i | \(0.935429\pi\) | |||||||
\(908\) | 0.477279 | + | 1.46891i | 0.0158391 | + | 0.0487476i | ||||
\(909\) | 5.40768 | − | 3.92891i | 0.179362 | − | 0.130314i | ||||
\(910\) | −1.23817 | + | 3.81068i | −0.0410448 | + | 0.126323i | ||||
\(911\) | −9.21531 | + | 6.69532i | −0.305317 | + | 0.221826i | −0.729884 | − | 0.683571i | \(-0.760426\pi\) |
0.424567 | + | 0.905396i | \(0.360426\pi\) | |||||||
\(912\) | −5.50566 | − | 4.00010i | −0.182311 | − | 0.132456i | ||||
\(913\) | 1.80636 | + | 5.55942i | 0.0597819 | + | 0.183990i | ||||
\(914\) | 15.1375 | + | 10.9981i | 0.500705 | + | 0.363783i | ||||
\(915\) | 1.19305 | + | 0.866804i | 0.0394411 | + | 0.0286557i | ||||
\(916\) | 2.29408 | + | 7.06046i | 0.0757986 | + | 0.233284i | ||||
\(917\) | −58.7093 | − | 42.6548i | −1.93875 | − | 1.40859i | ||||
\(918\) | −3.58917 | + | 2.60768i | −0.118460 | + | 0.0860663i | ||||
\(919\) | −9.08105 | + | 27.9486i | −0.299556 | + | 0.921939i | 0.682097 | + | 0.731262i | \(0.261068\pi\) |
−0.981653 | + | 0.190677i | \(0.938932\pi\) | |||||||
\(920\) | 3.91989 | − | 2.84797i | 0.129235 | − | 0.0938946i | ||||
\(921\) | 1.44439 | + | 4.44537i | 0.0475942 | + | 0.146480i | ||||
\(922\) | 3.96850 | + | 12.2138i | 0.130696 | + | 0.402240i | ||||
\(923\) | −0.146608 | + | 0.451212i | −0.00482565 | + | 0.0148518i | ||||
\(924\) | 5.48086 | 0.180307 | ||||||||
\(925\) | 11.2154 | 0.368760 | ||||||||
\(926\) | 11.5108 | − | 35.4267i | 0.378269 | − | 1.16419i | ||||
\(927\) | −15.0867 | − | 10.9611i | −0.495511 | − | 0.360010i | ||||
\(928\) | 6.88755 | − | 5.00410i | 0.226095 | − | 0.164268i | ||||
\(929\) | 28.9130 | 0.948606 | 0.474303 | − | 0.880362i | \(-0.342700\pi\) | ||||
0.474303 | + | 0.880362i | \(0.342700\pi\) | |||||||
\(930\) | 2.91834 | − | 4.74166i | 0.0956960 | − | 0.155485i | ||||
\(931\) | −74.8802 | −2.45410 | ||||||||
\(932\) | −17.4684 | + | 12.6915i | −0.572197 | + | 0.415725i | ||||
\(933\) | −2.71894 | − | 1.97543i | −0.0890141 | − | 0.0646725i | ||||
\(934\) | 3.42949 | − | 10.5549i | 0.112216 | − | 0.345366i | ||||
\(935\) | 5.73074 | 0.187415 | ||||||||
\(936\) | 0.944328 | 0.0308663 | ||||||||
\(937\) | 18.3035 | − | 56.3323i | 0.597948 | − | 1.84029i | 0.0584801 | − | 0.998289i | \(-0.481375\pi\) |
0.539468 | − | 0.842006i | \(-0.318625\pi\) | |||||||
\(938\) | −4.12303 | − | 12.6894i | −0.134622 | − | 0.414323i | ||||
\(939\) | 7.75831 | + | 23.8776i | 0.253183 | + | 0.779217i | ||||
\(940\) | 2.42609 | − | 1.76266i | 0.0791304 | − | 0.0574916i | ||||
\(941\) | 6.27172 | − | 19.3024i | 0.204452 | − | 0.629239i | −0.795283 | − | 0.606238i | \(-0.792678\pi\) |
0.999735 | − | 0.0230012i | \(-0.00732216\pi\) | |||||||
\(942\) | −9.15205 | + | 6.64935i | −0.298190 | + | 0.216648i | ||||
\(943\) | 15.6581 | + | 11.3763i | 0.509898 | + | 0.370463i | ||||
\(944\) | 3.16256 | + | 9.73334i | 0.102932 | + | 0.316793i | ||||
\(945\) | −3.43266 | − | 2.49398i | −0.111665 | − | 0.0811291i | ||||
\(946\) | 13.3276 | + | 9.68306i | 0.433317 | + | 0.314824i | ||||
\(947\) | −12.2601 | − | 37.7326i | −0.398398 | − | 1.22614i | −0.926283 | − | 0.376828i | \(-0.877015\pi\) |
0.527885 | − | 0.849316i | \(-0.322985\pi\) | |||||||
\(948\) | −0.866833 | − | 0.629791i | −0.0281534 | − | 0.0204547i | ||||
\(949\) | 4.03190 | − | 2.92934i | 0.130881 | − | 0.0950905i | ||||
\(950\) | 2.10297 | − | 6.47229i | 0.0682295 | − | 0.209989i | ||||
\(951\) | −4.05531 | + | 2.94635i | −0.131502 | + | 0.0955421i | ||||
\(952\) | 5.81691 | + | 17.9026i | 0.188527 | + | 0.580226i | ||||
\(953\) | −8.78836 | − | 27.0478i | −0.284683 | − | 0.876164i | −0.986493 | − | 0.163801i | \(-0.947625\pi\) |
0.701810 | − | 0.712364i | \(-0.252375\pi\) | |||||||
\(954\) | 4.17533 | − | 12.8503i | 0.135181 | − | 0.416045i | ||||
\(955\) | 5.24124 | 0.169602 | ||||||||
\(956\) | −4.42058 | −0.142972 | ||||||||
\(957\) | −3.39832 | + | 10.4590i | −0.109852 | + | 0.338090i | ||||
\(958\) | −13.2999 | − | 9.66297i | −0.429701 | − | 0.312196i | ||||
\(959\) | 61.2804 | − | 44.5228i | 1.97885 | − | 1.43772i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −13.9666 | − | 27.6755i | −0.450537 | − | 0.892758i | ||||
\(962\) | 10.5910 | 0.341468 | ||||||||
\(963\) | 6.58220 | − | 4.78225i | 0.212108 | − | 0.154106i | ||||
\(964\) | 13.5024 | + | 9.81010i | 0.434884 | + | 0.315962i | ||||
\(965\) | 7.96515 | − | 24.5142i | 0.256407 | − | 0.789141i | ||||
\(966\) | −20.5584 | −0.661456 | ||||||||
\(967\) | −19.6437 | −0.631700 | −0.315850 | − | 0.948809i | \(-0.602290\pi\) | ||||
−0.315850 | + | 0.948809i | \(0.602290\pi\) | |||||||
\(968\) | 2.88356 | − | 8.87470i | 0.0926813 | − | 0.285244i | ||||
\(969\) | 9.32975 | + | 28.7140i | 0.299715 | + | 0.922427i | ||||
\(970\) | −4.11658 | − | 12.6695i | −0.132175 | − | 0.406794i | ||||
\(971\) | 19.3661 | − | 14.0703i | 0.621488 | − | 0.451538i | −0.231953 | − | 0.972727i | \(-0.574511\pi\) |
0.853441 | + | 0.521189i | \(0.174511\pi\) | |||||||
\(972\) | −0.309017 | + | 0.951057i | −0.00991172 | + | 0.0305052i | ||||
\(973\) | −7.58327 | + | 5.50957i | −0.243108 | + | 0.176629i | ||||
\(974\) | 23.2833 | + | 16.9163i | 0.746045 | + | 0.542034i | ||||
\(975\) | 0.291813 | + | 0.898110i | 0.00934551 | + | 0.0287625i | ||||
\(976\) | −1.19305 | − | 0.866804i | −0.0381887 | − | 0.0277457i | ||||
\(977\) | 8.50836 | + | 6.18168i | 0.272206 | + | 0.197770i | 0.715511 | − | 0.698602i | \(-0.246194\pi\) |
−0.443304 | + | 0.896371i | \(0.646194\pi\) | |||||||
\(978\) | −3.23835 | − | 9.96662i | −0.103551 | − | 0.318697i | ||||
\(979\) | −18.7739 | − | 13.6401i | −0.600018 | − | 0.435938i | ||||
\(980\) | −8.90170 | + | 6.46746i | −0.284354 | + | 0.206596i | ||||
\(981\) | −3.91930 | + | 12.0624i | −0.125133 | + | 0.385121i | ||||
\(982\) | 10.2269 | − | 7.43025i | 0.326352 | − | 0.237109i | ||||
\(983\) | 4.66371 | + | 14.3534i | 0.148749 | + | 0.457803i | 0.997474 | − | 0.0710317i | \(-0.0226291\pi\) |
−0.848725 | + | 0.528835i | \(0.822629\pi\) | |||||||
\(984\) | −1.23438 | − | 3.79902i | −0.0393505 | − | 0.121108i | ||||
\(985\) | −2.93308 | + | 9.02708i | −0.0934556 | + | 0.287627i | ||||
\(986\) | −37.7697 | −1.20283 | ||||||||
\(987\) | −12.7240 | −0.405009 | ||||||||
\(988\) | 1.98590 | − | 6.11197i | 0.0631798 | − | 0.194448i | ||||
\(989\) | −49.9911 | − | 36.3207i | −1.58962 | − | 1.15493i | ||||
\(990\) | 1.04504 | − | 0.759266i | 0.0332135 | − | 0.0241310i | ||||
\(991\) | 7.75806 | 0.246443 | 0.123221 | − | 0.992379i | \(-0.460677\pi\) | ||||
0.123221 | + | 0.992379i | \(0.460677\pi\) | |||||||
\(992\) | −2.91834 | + | 4.74166i | −0.0926573 | + | 0.150548i | ||||
\(993\) | −23.6914 | −0.751823 | ||||||||
\(994\) | −1.72458 | + | 1.25298i | −0.0547003 | + | 0.0397421i | ||||
\(995\) | −12.2061 | − | 8.86822i | −0.386958 | − | 0.281142i | ||||
\(996\) | −1.39840 | + | 4.30382i | −0.0443099 | + | 0.136372i | ||||
\(997\) | −25.5242 | −0.808359 | −0.404180 | − | 0.914680i | \(-0.632443\pi\) | ||||
−0.404180 | + | 0.914680i | \(0.632443\pi\) | |||||||
\(998\) | 32.2568 | 1.02107 | ||||||||
\(999\) | −3.46575 | + | 10.6665i | −0.109651 | + | 0.337472i |
(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 | 930.2.n.f.481.1 | ✓ | 12 | |
31.2 | even | 5 | inner | 930.2.n.f.901.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.f.481.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
930.2.n.f.901.1 | yes | 12 | 31.2 | even | 5 | inner |