Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
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: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(-0.206962 - 0.636964i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.w.729.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.541834 | − | 0.393666i | −0.383135 | − | 0.278364i | 0.379502 | − | 0.925191i | \(-0.376095\pi\) |
−0.762636 | + | 0.646827i | \(0.776095\pi\) | |||||||
\(3\) | 0.970243 | − | 2.98610i | 0.560170 | − | 1.72403i | −0.121713 | − | 0.992565i | \(-0.538839\pi\) |
0.681883 | − | 0.731461i | \(-0.261161\pi\) | |||||||
\(4\) | −0.479422 | − | 1.47551i | −0.239711 | − | 0.737755i | ||||
\(5\) | −1.73435 | + | 1.26008i | −0.775626 | + | 0.563526i | −0.903663 | − | 0.428244i | \(-0.859132\pi\) |
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(6\) | −1.70124 | + | 1.23602i | −0.694527 | + | 0.504603i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | −0.735015 | + | 2.26214i | −0.259867 | + | 0.799788i | ||||
\(9\) | −5.54838 | − | 4.03113i | −1.84946 | − | 1.34371i | ||||
\(10\) | 1.43578 | 0.454034 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −4.87118 | −1.40619 | ||||||||
\(13\) | −2.04541 | − | 1.48608i | −0.567294 | − | 0.412163i | 0.266827 | − | 0.963744i | \(-0.414025\pi\) |
−0.834121 | + | 0.551581i | \(0.814025\pi\) | |||||||
\(14\) | 0.206962 | − | 0.636964i | 0.0553130 | − | 0.170236i | ||||
\(15\) | 2.07999 | + | 6.40154i | 0.537050 | + | 1.65287i | ||||
\(16\) | −1.22150 | + | 0.887475i | −0.305376 | + | 0.221869i | ||||
\(17\) | 1.44888 | − | 1.05268i | 0.351406 | − | 0.255311i | −0.398053 | − | 0.917363i | \(-0.630314\pi\) |
0.749459 | + | 0.662051i | \(0.230314\pi\) | |||||||
\(18\) | 1.41938 | + | 4.36841i | 0.334552 | + | 1.02964i | ||||
\(19\) | −2.07888 | + | 6.39814i | −0.476928 | + | 1.46783i | 0.366412 | + | 0.930453i | \(0.380586\pi\) |
−0.843340 | + | 0.537381i | \(0.819414\pi\) | |||||||
\(20\) | 2.69075 | + | 1.95494i | 0.601670 | + | 0.437139i | ||||
\(21\) | 3.13977 | 0.685155 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.16429 | −0.659799 | −0.329900 | − | 0.944016i | \(-0.607015\pi\) | ||||
−0.329900 | + | 0.944016i | \(0.607015\pi\) | |||||||
\(24\) | 6.04184 | + | 4.38966i | 1.23329 | + | 0.896035i | ||||
\(25\) | −0.124909 | + | 0.384430i | −0.0249818 | + | 0.0768860i | ||||
\(26\) | 0.523255 | + | 1.61041i | 0.102619 | + | 0.315828i | ||||
\(27\) | −9.80027 | + | 7.12031i | −1.88606 | + | 1.37030i | ||||
\(28\) | 1.25514 | − | 0.911915i | 0.237200 | − | 0.172336i | ||||
\(29\) | −0.285584 | − | 0.878938i | −0.0530317 | − | 0.163215i | 0.921033 | − | 0.389485i | \(-0.127347\pi\) |
−0.974065 | + | 0.226270i | \(0.927347\pi\) | |||||||
\(30\) | 1.39306 | − | 4.28739i | 0.254337 | − | 0.782767i | ||||
\(31\) | −2.42849 | − | 1.76440i | −0.436170 | − | 0.316896i | 0.347941 | − | 0.937516i | \(-0.386881\pi\) |
−0.784111 | + | 0.620620i | \(0.786881\pi\) | |||||||
\(32\) | 5.76834 | 1.01971 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.19946 | −0.205705 | ||||||||
\(35\) | −1.73435 | − | 1.26008i | −0.293159 | − | 0.212993i | ||||
\(36\) | −3.28796 | + | 10.1193i | −0.547994 | + | 1.68655i | ||||
\(37\) | −0.465744 | − | 1.43341i | −0.0765678 | − | 0.235652i | 0.905446 | − | 0.424462i | \(-0.139537\pi\) |
−0.982014 | + | 0.188811i | \(0.939537\pi\) | |||||||
\(38\) | 3.64514 | − | 2.64835i | 0.591319 | − | 0.429618i | ||||
\(39\) | −6.42211 | + | 4.66594i | −1.02836 | + | 0.747148i | ||||
\(40\) | −1.57571 | − | 4.84953i | −0.249141 | − | 0.766778i | ||||
\(41\) | 1.71846 | − | 5.28886i | 0.268378 | − | 0.825981i | −0.722518 | − | 0.691352i | \(-0.757016\pi\) |
0.990896 | − | 0.134630i | \(-0.0429845\pi\) | |||||||
\(42\) | −1.70124 | − | 1.23602i | −0.262506 | − | 0.190722i | ||||
\(43\) | −8.42985 | −1.28554 | −0.642770 | − | 0.766059i | \(-0.722215\pi\) | ||||
−0.642770 | + | 0.766059i | \(0.722215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.7024 | 2.19171 | ||||||||
\(46\) | 1.71452 | + | 1.24567i | 0.252792 | + | 0.183664i | ||||
\(47\) | 1.35897 | − | 4.18247i | 0.198226 | − | 0.610076i | −0.801698 | − | 0.597729i | \(-0.796070\pi\) |
0.999924 | − | 0.0123466i | \(-0.00393014\pi\) | |||||||
\(48\) | 1.46493 | + | 4.50860i | 0.211445 | + | 0.650761i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0.219017 | − | 0.159125i | 0.0309737 | − | 0.0225037i | ||||
\(51\) | −1.73763 | − | 5.34787i | −0.243317 | − | 0.748851i | ||||
\(52\) | −1.21211 | + | 3.73048i | −0.168089 | + | 0.517324i | ||||
\(53\) | −0.539955 | − | 0.392300i | −0.0741685 | − | 0.0538866i | 0.550083 | − | 0.835110i | \(-0.314596\pi\) |
−0.624252 | + | 0.781223i | \(0.714596\pi\) | |||||||
\(54\) | 8.11314 | 1.10406 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.37856 | −0.317848 | ||||||||
\(57\) | 17.0885 | + | 12.4155i | 2.26342 | + | 1.64447i | ||||
\(58\) | −0.191268 | + | 0.588663i | −0.0251148 | + | 0.0772953i | ||||
\(59\) | −0.113830 | − | 0.350331i | −0.0148193 | − | 0.0456093i | 0.943373 | − | 0.331733i | \(-0.107633\pi\) |
−0.958193 | + | 0.286124i | \(0.907633\pi\) | |||||||
\(60\) | 8.44835 | − | 6.13808i | 1.09068 | − | 0.792423i | ||||
\(61\) | −4.05438 | + | 2.94568i | −0.519110 | + | 0.377155i | −0.816268 | − | 0.577673i | \(-0.803961\pi\) |
0.297159 | + | 0.954828i | \(0.403961\pi\) | |||||||
\(62\) | 0.621256 | + | 1.91203i | 0.0788996 | + | 0.242828i | ||||
\(63\) | 2.11929 | − | 6.52251i | 0.267006 | − | 0.821759i | ||||
\(64\) | −0.682474 | − | 0.495846i | −0.0853092 | − | 0.0619808i | ||||
\(65\) | 5.42003 | 0.672273 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.902129 | −0.110213 | −0.0551063 | − | 0.998480i | \(-0.517550\pi\) | ||||
−0.0551063 | + | 0.998480i | \(0.517550\pi\) | |||||||
\(68\) | −2.24786 | − | 1.63317i | −0.272593 | − | 0.198051i | ||||
\(69\) | −3.07013 | + | 9.44888i | −0.369600 | + | 1.13751i | ||||
\(70\) | 0.443681 | + | 1.36551i | 0.0530300 | + | 0.163210i | ||||
\(71\) | 12.0296 | − | 8.74000i | 1.42765 | − | 1.03725i | 0.437199 | − | 0.899365i | \(-0.355971\pi\) |
0.990449 | − | 0.137882i | \(-0.0440294\pi\) | |||||||
\(72\) | 13.1971 | − | 9.58828i | 1.55530 | − | 1.12999i | ||||
\(73\) | 2.48393 | + | 7.64474i | 0.290722 | + | 0.894750i | 0.984625 | + | 0.174681i | \(0.0558895\pi\) |
−0.693903 | + | 0.720068i | \(0.744110\pi\) | |||||||
\(74\) | −0.311929 | + | 0.960019i | −0.0362610 | + | 0.111600i | ||||
\(75\) | 1.02676 | + | 0.745981i | 0.118559 | + | 0.0861385i | ||||
\(76\) | 10.4372 | 1.19723 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.31654 | 0.601980 | ||||||||
\(79\) | −3.28192 | − | 2.38446i | −0.369245 | − | 0.268272i | 0.387653 | − | 0.921805i | \(-0.373286\pi\) |
−0.756898 | + | 0.653533i | \(0.773286\pi\) | |||||||
\(80\) | 1.00023 | − | 3.07839i | 0.111829 | − | 0.344174i | ||||
\(81\) | 5.39545 | + | 16.6055i | 0.599495 | + | 1.84505i | ||||
\(82\) | −3.01316 | + | 2.18919i | −0.332748 | + | 0.241756i | ||||
\(83\) | 3.27760 | − | 2.38132i | 0.359764 | − | 0.261384i | −0.393190 | − | 0.919457i | \(-0.628628\pi\) |
0.752954 | + | 0.658074i | \(0.228628\pi\) | |||||||
\(84\) | −1.50528 | − | 4.63277i | −0.164239 | − | 0.505476i | ||||
\(85\) | −1.18642 | + | 3.65142i | −0.128685 | + | 0.396053i | ||||
\(86\) | 4.56758 | + | 3.31854i | 0.492535 | + | 0.357847i | ||||
\(87\) | −2.90168 | −0.311093 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.30727 | −0.880569 | −0.440284 | − | 0.897858i | \(-0.645122\pi\) | ||||
−0.440284 | + | 0.897858i | \(0.645122\pi\) | |||||||
\(90\) | −7.96627 | − | 5.78783i | −0.839718 | − | 0.610091i | ||||
\(91\) | 0.781276 | − | 2.40452i | 0.0819000 | − | 0.252062i | ||||
\(92\) | 1.51703 | + | 4.66894i | 0.158161 | + | 0.486770i | ||||
\(93\) | −7.62492 | + | 5.53983i | −0.790667 | + | 0.574453i | ||||
\(94\) | −2.38283 | + | 1.73123i | −0.245770 | + | 0.178562i | ||||
\(95\) | −4.45666 | − | 13.7162i | −0.457244 | − | 1.40725i | ||||
\(96\) | 5.59669 | − | 17.2248i | 0.571210 | − | 1.75800i | ||||
\(97\) | −6.88945 | − | 5.00548i | −0.699518 | − | 0.508230i | 0.180257 | − | 0.983620i | \(-0.442307\pi\) |
−0.879775 | + | 0.475390i | \(0.842307\pi\) | |||||||
\(98\) | 0.669744 | 0.0676544 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.627115 | 0.0627115 | ||||||||
\(101\) | 3.25797 | + | 2.36705i | 0.324180 | + | 0.235530i | 0.737957 | − | 0.674848i | \(-0.235791\pi\) |
−0.413777 | + | 0.910378i | \(0.635791\pi\) | |||||||
\(102\) | −1.16377 | + | 3.58170i | −0.115230 | + | 0.354641i | ||||
\(103\) | −5.44668 | − | 16.7632i | −0.536678 | − | 1.65172i | −0.739996 | − | 0.672611i | \(-0.765173\pi\) |
0.203319 | − | 0.979113i | \(-0.434827\pi\) | |||||||
\(104\) | 4.86512 | − | 3.53472i | 0.477064 | − | 0.346607i | ||||
\(105\) | −5.44548 | + | 3.95637i | −0.531424 | + | 0.386102i | ||||
\(106\) | 0.138131 | + | 0.425123i | 0.0134165 | + | 0.0412916i | ||||
\(107\) | −4.76001 | + | 14.6498i | −0.460168 | + | 1.41625i | 0.404792 | + | 0.914409i | \(0.367344\pi\) |
−0.864959 | + | 0.501842i | \(0.832656\pi\) | |||||||
\(108\) | 15.2046 | + | 11.0468i | 1.46306 | + | 1.06297i | ||||
\(109\) | −18.9265 | −1.81283 | −0.906416 | − | 0.422386i | \(-0.861193\pi\) | ||||
−0.906416 | + | 0.422386i | \(0.861193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.73220 | −0.449161 | ||||||||
\(112\) | −1.22150 | − | 0.887475i | −0.115421 | − | 0.0838585i | ||||
\(113\) | 0.519340 | − | 1.59837i | 0.0488554 | − | 0.150362i | −0.923653 | − | 0.383231i | \(-0.874811\pi\) |
0.972508 | + | 0.232869i | \(0.0748114\pi\) | |||||||
\(114\) | −4.37156 | − | 13.4543i | −0.409434 | − | 1.26011i | ||||
\(115\) | 5.48799 | − | 3.98726i | 0.511758 | − | 0.371814i | ||||
\(116\) | −1.15997 | + | 0.842765i | −0.107700 | + | 0.0782487i | ||||
\(117\) | 5.35813 | + | 16.4906i | 0.495359 | + | 1.52456i | ||||
\(118\) | −0.0762367 | + | 0.234632i | −0.00701815 | + | 0.0215997i | ||||
\(119\) | 1.44888 | + | 1.05268i | 0.132819 | + | 0.0964987i | ||||
\(120\) | −16.0100 | −1.46151 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.35641 | 0.303875 | ||||||||
\(123\) | −14.1258 | − | 10.2630i | −1.27368 | − | 0.925380i | ||||
\(124\) | −1.43912 | + | 4.42916i | −0.129237 | + | 0.397750i | ||||
\(125\) | −3.58010 | − | 11.0184i | −0.320214 | − | 0.985516i | ||||
\(126\) | −3.71599 | + | 2.69983i | −0.331047 | + | 0.240520i | ||||
\(127\) | −14.2119 | + | 10.3256i | −1.26111 | + | 0.916247i | −0.998811 | − | 0.0487414i | \(-0.984479\pi\) |
−0.262294 | + | 0.964988i | \(0.584479\pi\) | |||||||
\(128\) | −3.39044 | − | 10.4347i | −0.299675 | − | 0.922305i | ||||
\(129\) | −8.17900 | + | 25.1724i | −0.720121 | + | 2.21630i | ||||
\(130\) | −2.93676 | − | 2.13368i | −0.257571 | − | 0.187136i | ||||
\(131\) | 6.72557 | 0.587616 | 0.293808 | − | 0.955865i | \(-0.405077\pi\) | ||||
0.293808 | + | 0.955865i | \(0.405077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.72740 | −0.583340 | ||||||||
\(134\) | 0.488804 | + | 0.355137i | 0.0422263 | + | 0.0306792i | ||||
\(135\) | 8.02495 | − | 24.6983i | 0.690678 | − | 2.12569i | ||||
\(136\) | 1.31635 | + | 4.05132i | 0.112876 | + | 0.347397i | ||||
\(137\) | −11.2191 | + | 8.15119i | −0.958516 | + | 0.696403i | −0.952806 | − | 0.303581i | \(-0.901818\pi\) |
−0.00571070 | + | 0.999984i | \(0.501818\pi\) | |||||||
\(138\) | 5.38320 | − | 3.91112i | 0.458248 | − | 0.332937i | ||||
\(139\) | 4.40990 | + | 13.5723i | 0.374043 | + | 1.15118i | 0.944122 | + | 0.329595i | \(0.106912\pi\) |
−0.570080 | + | 0.821589i | \(0.693088\pi\) | |||||||
\(140\) | −1.02778 | + | 3.16317i | −0.0868629 | + | 0.267336i | ||||
\(141\) | −11.1707 | − | 8.11602i | −0.940747 | − | 0.683492i | ||||
\(142\) | −9.95867 | −0.835713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.3549 | 0.862908 | ||||||||
\(145\) | 1.60284 | + | 1.16453i | 0.133108 | + | 0.0967089i | ||||
\(146\) | 1.66360 | − | 5.12002i | 0.137680 | − | 0.423736i | ||||
\(147\) | 0.970243 | + | 2.98610i | 0.0800243 | + | 0.246290i | ||||
\(148\) | −1.89173 | + | 1.37442i | −0.155499 | + | 0.112977i | ||||
\(149\) | −2.12199 | + | 1.54171i | −0.173840 | + | 0.126302i | −0.671303 | − | 0.741183i | \(-0.734265\pi\) |
0.497463 | + | 0.867485i | \(0.334265\pi\) | |||||||
\(150\) | −0.262664 | − | 0.808396i | −0.0214464 | − | 0.0660053i | ||||
\(151\) | −0.923837 | + | 2.84328i | −0.0751808 | + | 0.231383i | −0.981584 | − | 0.191031i | \(-0.938817\pi\) |
0.906403 | + | 0.422413i | \(0.138817\pi\) | |||||||
\(152\) | −12.9455 | − | 9.40545i | −1.05002 | − | 0.762883i | ||||
\(153\) | −12.2824 | −0.992977 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.43516 | 0.516884 | ||||||||
\(156\) | 9.96355 | + | 7.23894i | 0.797722 | + | 0.579579i | ||||
\(157\) | 3.47789 | − | 10.7038i | 0.277566 | − | 0.854260i | −0.710963 | − | 0.703229i | \(-0.751741\pi\) |
0.988529 | − | 0.151031i | \(-0.0482593\pi\) | |||||||
\(158\) | 0.839579 | + | 2.58396i | 0.0667934 | + | 0.205569i | ||||
\(159\) | −1.69534 | + | 1.23173i | −0.134449 | + | 0.0976828i | ||||
\(160\) | −10.0043 | + | 7.26857i | −0.790912 | + | 0.574631i | ||||
\(161\) | −0.977818 | − | 3.00941i | −0.0770629 | − | 0.237175i | ||||
\(162\) | 3.61357 | − | 11.1214i | 0.283909 | − | 0.873782i | ||||
\(163\) | 14.7265 | + | 10.6994i | 1.15347 | + | 0.838044i | 0.988938 | − | 0.148328i | \(-0.0473892\pi\) |
0.164530 | + | 0.986372i | \(0.447389\pi\) | |||||||
\(164\) | −8.62763 | −0.673705 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.71336 | −0.210598 | ||||||||
\(167\) | −16.1247 | − | 11.7153i | −1.24777 | − | 0.906556i | −0.249677 | − | 0.968329i | \(-0.580325\pi\) |
−0.998090 | + | 0.0617729i | \(0.980325\pi\) | |||||||
\(168\) | −2.30778 | + | 7.10261i | −0.178049 | + | 0.547979i | ||||
\(169\) | −2.04195 | − | 6.28448i | −0.157073 | − | 0.483421i | ||||
\(170\) | 2.08028 | − | 1.51141i | 0.159550 | − | 0.115920i | ||||
\(171\) | 37.3262 | − | 27.1191i | 2.85440 | − | 2.07385i | ||||
\(172\) | 4.04146 | + | 12.4383i | 0.308158 | + | 0.948413i | ||||
\(173\) | 1.85104 | − | 5.69690i | 0.140732 | − | 0.433127i | −0.855706 | − | 0.517463i | \(-0.826877\pi\) |
0.996437 | + | 0.0843352i | \(0.0268766\pi\) | |||||||
\(174\) | 1.57223 | + | 1.14229i | 0.119191 | + | 0.0865970i | ||||
\(175\) | −0.404214 | −0.0305557 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.15657 | −0.0869329 | ||||||||
\(178\) | 4.50116 | + | 3.27029i | 0.337376 | + | 0.245118i | ||||
\(179\) | −0.500280 | + | 1.53970i | −0.0373927 | + | 0.115083i | −0.968011 | − | 0.250910i | \(-0.919270\pi\) |
0.930618 | + | 0.365992i | \(0.119270\pi\) | |||||||
\(180\) | −7.04866 | − | 21.6936i | −0.525376 | − | 1.61694i | ||||
\(181\) | −1.96334 | + | 1.42645i | −0.145934 | + | 0.106027i | −0.658357 | − | 0.752706i | \(-0.728748\pi\) |
0.512423 | + | 0.858733i | \(0.328748\pi\) | |||||||
\(182\) | −1.36990 | + | 0.995290i | −0.101544 | + | 0.0737758i | ||||
\(183\) | 4.86236 | + | 14.9648i | 0.359436 | + | 1.10623i | ||||
\(184\) | 2.32580 | − | 7.15806i | 0.171460 | − | 0.527700i | ||||
\(185\) | 2.61398 | + | 1.89917i | 0.192184 | + | 0.139630i | ||||
\(186\) | 6.31228 | 0.462839 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.82279 | −0.497603 | ||||||||
\(189\) | −9.80027 | − | 7.12031i | −0.712865 | − | 0.517926i | ||||
\(190\) | −2.98482 | + | 9.18634i | −0.216542 | + | 0.666447i | ||||
\(191\) | 3.92480 | + | 12.0793i | 0.283989 | + | 0.874027i | 0.986700 | + | 0.162552i | \(0.0519725\pi\) |
−0.702711 | + | 0.711475i | \(0.748027\pi\) | |||||||
\(192\) | −2.14281 | + | 1.55684i | −0.154644 | + | 0.112356i | ||||
\(193\) | 1.42331 | − | 1.03410i | 0.102452 | − | 0.0744359i | −0.535380 | − | 0.844612i | \(-0.679831\pi\) |
0.637832 | + | 0.770176i | \(0.279831\pi\) | |||||||
\(194\) | 1.76246 | + | 5.42428i | 0.126537 | + | 0.389441i | ||||
\(195\) | 5.25875 | − | 16.1848i | 0.376587 | − | 1.15902i | ||||
\(196\) | 1.25514 | + | 0.911915i | 0.0896531 | + | 0.0651368i | ||||
\(197\) | −0.903053 | −0.0643399 | −0.0321699 | − | 0.999482i | \(-0.510242\pi\) | ||||
−0.0321699 | + | 0.999482i | \(0.510242\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.6296 | −1.10795 | −0.553976 | − | 0.832533i | \(-0.686890\pi\) | ||||
−0.553976 | + | 0.832533i | \(0.686890\pi\) | |||||||
\(200\) | −0.777826 | − | 0.565123i | −0.0550006 | − | 0.0399603i | ||||
\(201\) | −0.875285 | + | 2.69385i | −0.0617378 | + | 0.190009i | ||||
\(202\) | −0.833451 | − | 2.56510i | −0.0586414 | − | 0.180480i | ||||
\(203\) | 0.747669 | − | 0.543213i | 0.0524761 | − | 0.0381261i | ||||
\(204\) | −7.05778 | + | 5.12777i | −0.494143 | + | 0.359016i | ||||
\(205\) | 3.68399 | + | 11.3381i | 0.257301 | + | 0.791891i | ||||
\(206\) | −3.64788 | + | 11.2270i | −0.254160 | + | 0.782224i | ||||
\(207\) | 17.5567 | + | 12.7557i | 1.22027 | + | 0.886580i | ||||
\(208\) | 3.81733 | 0.264684 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.50803 | 0.311084 | ||||||||
\(211\) | −11.9481 | − | 8.68083i | −0.822544 | − | 0.597613i | 0.0948964 | − | 0.995487i | \(-0.469748\pi\) |
−0.917440 | + | 0.397874i | \(0.869748\pi\) | |||||||
\(212\) | −0.319976 | + | 0.984786i | −0.0219761 | + | 0.0676354i | ||||
\(213\) | −14.4269 | − | 44.4014i | −0.988515 | − | 3.04234i | ||||
\(214\) | 8.34626 | − | 6.06392i | 0.570539 | − | 0.414521i | ||||
\(215\) | 14.6203 | − | 10.6223i | 0.997099 | − | 0.724434i | ||||
\(216\) | −8.90382 | − | 27.4031i | −0.605828 | − | 1.86455i | ||||
\(217\) | 0.927602 | − | 2.85487i | 0.0629697 | − | 0.193801i | ||||
\(218\) | 10.2550 | + | 7.45072i | 0.694559 | + | 0.504626i | ||||
\(219\) | 25.2380 | 1.70543 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.52791 | −0.304581 | ||||||||
\(222\) | 2.56407 | + | 1.86290i | 0.172089 | + | 0.125030i | ||||
\(223\) | −0.570250 | + | 1.75505i | −0.0381868 | + | 0.117527i | −0.968333 | − | 0.249663i | \(-0.919680\pi\) |
0.930146 | + | 0.367190i | \(0.119680\pi\) | |||||||
\(224\) | 1.78251 | + | 5.48601i | 0.119099 | + | 0.366550i | ||||
\(225\) | 2.24273 | − | 1.62944i | 0.149515 | − | 0.108629i | ||||
\(226\) | −0.910618 | + | 0.661603i | −0.0605734 | + | 0.0440092i | ||||
\(227\) | −6.77981 | − | 20.8661i | −0.449992 | − | 1.38493i | −0.876915 | − | 0.480645i | \(-0.840403\pi\) |
0.426923 | − | 0.904288i | \(-0.359597\pi\) | |||||||
\(228\) | 10.1266 | − | 31.1665i | 0.670651 | − | 2.06405i | ||||
\(229\) | 16.3840 | + | 11.9037i | 1.08269 | + | 0.786619i | 0.978150 | − | 0.207902i | \(-0.0666634\pi\) |
0.104539 | + | 0.994521i | \(0.466663\pi\) | |||||||
\(230\) | −4.54323 | −0.299571 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.19819 | 0.144318 | ||||||||
\(233\) | −17.0400 | − | 12.3803i | −1.11633 | − | 0.811059i | −0.132678 | − | 0.991159i | \(-0.542358\pi\) |
−0.983648 | + | 0.180100i | \(0.942358\pi\) | |||||||
\(234\) | 3.58857 | − | 11.0445i | 0.234592 | − | 0.722001i | ||||
\(235\) | 2.91332 | + | 8.96628i | 0.190044 | + | 0.584896i | ||||
\(236\) | −0.462345 | + | 0.335913i | −0.0300961 | + | 0.0218661i | ||||
\(237\) | −10.3045 | + | 7.48665i | −0.669349 | + | 0.486310i | ||||
\(238\) | −0.370653 | − | 1.14075i | −0.0240259 | − | 0.0739440i | ||||
\(239\) | 4.78869 | − | 14.7381i | 0.309755 | − | 0.953327i | −0.668105 | − | 0.744067i | \(-0.732894\pi\) |
0.977860 | − | 0.209260i | \(-0.0671055\pi\) | |||||||
\(240\) | −8.22192 | − | 5.97357i | −0.530722 | − | 0.385592i | ||||
\(241\) | 14.0848 | 0.907283 | 0.453641 | − | 0.891184i | \(-0.350125\pi\) | ||||
0.453641 | + | 0.891184i | \(0.350125\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.4792 | 1.18544 | ||||||||
\(244\) | 6.29014 | + | 4.57005i | 0.402685 | + | 0.292568i | ||||
\(245\) | 0.662464 | − | 2.03885i | 0.0423233 | − | 0.130258i | ||||
\(246\) | 3.61364 | + | 11.1217i | 0.230397 | + | 0.709091i | ||||
\(247\) | 13.7603 | − | 9.99742i | 0.875545 | − | 0.636121i | ||||
\(248\) | 5.77631 | − | 4.19674i | 0.366796 | − | 0.266493i | ||||
\(249\) | −3.93079 | − | 12.0977i | −0.249103 | − | 0.766662i | ||||
\(250\) | −2.39775 | + | 7.37951i | −0.151647 | + | 0.466721i | ||||
\(251\) | 0.871529 | + | 0.633203i | 0.0550104 | + | 0.0399674i | 0.614951 | − | 0.788566i | \(-0.289176\pi\) |
−0.559940 | + | 0.828533i | \(0.689176\pi\) | |||||||
\(252\) | −10.6401 | −0.670261 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 11.7653 | 0.738223 | ||||||||
\(255\) | 9.75241 | + | 7.08554i | 0.610720 | + | 0.443714i | ||||
\(256\) | −2.79209 | + | 8.59316i | −0.174506 | + | 0.537073i | ||||
\(257\) | 4.04226 | + | 12.4408i | 0.252149 | + | 0.776035i | 0.994378 | + | 0.105889i | \(0.0337687\pi\) |
−0.742229 | + | 0.670146i | \(0.766231\pi\) | |||||||
\(258\) | 14.3412 | − | 10.4195i | 0.892842 | − | 0.648688i | ||||
\(259\) | 1.21933 | − | 0.885898i | 0.0757657 | − | 0.0550470i | ||||
\(260\) | −2.59849 | − | 7.99732i | −0.161151 | − | 0.495972i | ||||
\(261\) | −1.95859 | + | 6.02791i | −0.121233 | + | 0.373118i | ||||
\(262\) | −3.64414 | − | 2.64763i | −0.225136 | − | 0.163571i | ||||
\(263\) | −9.57216 | −0.590245 | −0.295122 | − | 0.955459i | \(-0.595360\pi\) | ||||
−0.295122 | + | 0.955459i | \(0.595360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.43080 | 0.0878935 | ||||||||
\(266\) | 3.64514 | + | 2.64835i | 0.223498 | + | 0.162381i | ||||
\(267\) | −8.06007 | + | 24.8064i | −0.493268 | + | 1.51812i | ||||
\(268\) | 0.432501 | + | 1.33110i | 0.0264192 | + | 0.0813099i | ||||
\(269\) | 3.85782 | − | 2.80287i | 0.235216 | − | 0.170894i | −0.463933 | − | 0.885870i | \(-0.653562\pi\) |
0.699149 | + | 0.714976i | \(0.253562\pi\) | |||||||
\(270\) | −14.0711 | + | 10.2232i | −0.856337 | + | 0.622165i | ||||
\(271\) | −6.19650 | − | 19.0709i | −0.376410 | − | 1.15847i | −0.942522 | − | 0.334144i | \(-0.891553\pi\) |
0.566112 | − | 0.824328i | \(-0.308447\pi\) | |||||||
\(272\) | −0.835595 | + | 2.57170i | −0.0506654 | + | 0.155932i | ||||
\(273\) | −6.42211 | − | 4.66594i | −0.388684 | − | 0.282395i | ||||
\(274\) | 9.28776 | 0.561094 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.4138 | 0.927802 | ||||||||
\(277\) | 9.38658 | + | 6.81975i | 0.563985 | + | 0.409759i | 0.832915 | − | 0.553401i | \(-0.186670\pi\) |
−0.268930 | + | 0.963160i | \(0.586670\pi\) | |||||||
\(278\) | 2.95350 | − | 9.08994i | 0.177139 | − | 0.545179i | ||||
\(279\) | 6.36166 | + | 19.5792i | 0.380862 | + | 1.17217i | ||||
\(280\) | 4.12526 | − | 2.99718i | 0.246531 | − | 0.179116i | ||||
\(281\) | −9.77197 | + | 7.09975i | −0.582947 | + | 0.423536i | −0.839785 | − | 0.542919i | \(-0.817319\pi\) |
0.256838 | + | 0.966454i | \(0.417319\pi\) | |||||||
\(282\) | 2.85769 | + | 8.79508i | 0.170173 | + | 0.523739i | ||||
\(283\) | 6.79628 | − | 20.9168i | 0.403997 | − | 1.24337i | −0.517733 | − | 0.855542i | \(-0.673224\pi\) |
0.921730 | − | 0.387832i | \(-0.126776\pi\) | |||||||
\(284\) | −18.6632 | − | 13.5596i | −1.10746 | − | 0.804615i | ||||
\(285\) | −45.2820 | −2.68227 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.56104 | 0.328258 | ||||||||
\(288\) | −32.0049 | − | 23.2529i | −1.88591 | − | 1.37019i | ||||
\(289\) | −4.26215 | + | 13.1175i | −0.250715 | + | 0.771620i | ||||
\(290\) | −0.410037 | − | 1.26196i | −0.0240782 | − | 0.0741051i | ||||
\(291\) | −21.6313 | + | 15.7161i | −1.26805 | + | 0.921293i | ||||
\(292\) | 10.0890 | − | 7.33012i | 0.590417 | − | 0.428963i | ||||
\(293\) | 0.437941 | + | 1.34784i | 0.0255848 | + | 0.0787419i | 0.963034 | − | 0.269381i | \(-0.0868191\pi\) |
−0.937449 | + | 0.348123i | \(0.886819\pi\) | |||||||
\(294\) | 0.649815 | − | 1.99992i | 0.0378980 | − | 0.116638i | ||||
\(295\) | 0.638867 | + | 0.464164i | 0.0371963 | + | 0.0270247i | ||||
\(296\) | 3.58491 | 0.208369 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.75669 | 0.101762 | ||||||||
\(299\) | 6.47225 | + | 4.70237i | 0.374300 | + | 0.271945i | ||||
\(300\) | 0.608454 | − | 1.87263i | 0.0351291 | − | 0.108116i | ||||
\(301\) | −2.60497 | − | 8.01726i | −0.150148 | − | 0.462107i | ||||
\(302\) | 1.61987 | − | 1.17690i | 0.0932129 | − | 0.0677231i | ||||
\(303\) | 10.2293 | − | 7.43200i | 0.587657 | − | 0.426957i | ||||
\(304\) | −3.13882 | − | 9.66031i | −0.180024 | − | 0.554057i | ||||
\(305\) | 3.31993 | − | 10.2177i | 0.190099 | − | 0.585063i | ||||
\(306\) | 6.65505 | + | 4.83517i | 0.380444 | + | 0.276409i | ||||
\(307\) | 29.4646 | 1.68163 | 0.840817 | − | 0.541319i | \(-0.182075\pi\) | ||||
0.840817 | + | 0.541319i | \(0.182075\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −55.3411 | −3.14825 | ||||||||
\(310\) | −3.48679 | − | 2.53330i | −0.198036 | − | 0.143882i | ||||
\(311\) | 8.30597 | − | 25.5631i | 0.470988 | − | 1.44955i | −0.380304 | − | 0.924862i | \(-0.624181\pi\) |
0.851292 | − | 0.524692i | \(-0.175819\pi\) | |||||||
\(312\) | −5.83467 | − | 17.9573i | −0.330323 | − | 1.01663i | ||||
\(313\) | 3.63467 | − | 2.64074i | 0.205444 | − | 0.149264i | −0.480306 | − | 0.877101i | \(-0.659474\pi\) |
0.685750 | + | 0.727837i | \(0.259474\pi\) | |||||||
\(314\) | −6.09818 | + | 4.43059i | −0.344140 | + | 0.250032i | ||||
\(315\) | 4.54329 | + | 13.9828i | 0.255986 | + | 0.787843i | ||||
\(316\) | −1.94486 | + | 5.98567i | −0.109407 | + | 0.336720i | ||||
\(317\) | 8.85879 | + | 6.43628i | 0.497559 | + | 0.361498i | 0.808084 | − | 0.589068i | \(-0.200505\pi\) |
−0.310525 | + | 0.950565i | \(0.600505\pi\) | |||||||
\(318\) | 1.40348 | 0.0787034 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.80846 | 0.101096 | ||||||||
\(321\) | 39.1275 | + | 28.4278i | 2.18388 | + | 1.58668i | ||||
\(322\) | −0.654888 | + | 2.01554i | −0.0364955 | + | 0.112321i | ||||
\(323\) | 3.72311 | + | 11.4586i | 0.207159 | + | 0.637571i | ||||
\(324\) | 21.9149 | − | 15.9221i | 1.21749 | − | 0.884560i | ||||
\(325\) | 0.826781 | − | 0.600692i | 0.0458616 | − | 0.0333204i | ||||
\(326\) | −3.76732 | − | 11.5946i | −0.208653 | − | 0.642167i | ||||
\(327\) | −18.3633 | + | 56.5165i | −1.01549 | + | 3.12537i | ||||
\(328\) | 10.7011 | + | 7.77478i | 0.590868 | + | 0.429290i | ||||
\(329\) | 4.39771 | 0.242453 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5226 | 0.908166 | 0.454083 | − | 0.890959i | \(-0.349967\pi\) | ||||
0.454083 | + | 0.890959i | \(0.349967\pi\) | |||||||
\(332\) | −5.08502 | − | 3.69448i | −0.279077 | − | 0.202761i | ||||
\(333\) | −3.19415 | + | 9.83060i | −0.175039 | + | 0.538713i | ||||
\(334\) | 4.12501 | + | 12.6955i | 0.225711 | + | 0.694666i | ||||
\(335\) | 1.56461 | − | 1.13676i | 0.0854838 | − | 0.0621076i | ||||
\(336\) | −3.83525 | + | 2.78647i | −0.209230 | + | 0.152014i | ||||
\(337\) | −3.74551 | − | 11.5275i | −0.204031 | − | 0.627943i | −0.999752 | − | 0.0222794i | \(-0.992908\pi\) |
0.795721 | − | 0.605664i | \(-0.207092\pi\) | |||||||
\(338\) | −1.36758 | + | 4.20899i | −0.0743868 | + | 0.228939i | ||||
\(339\) | −4.26900 | − | 3.10161i | −0.231860 | − | 0.168456i | ||||
\(340\) | 5.95651 | 0.323037 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −30.9004 | −1.67090 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | 6.19606 | − | 19.0695i | 0.334069 | − | 1.02816i | ||||
\(345\) | −6.58167 | − | 20.2563i | −0.354345 | − | 1.09056i | ||||
\(346\) | −3.24563 | + | 2.35809i | −0.174486 | + | 0.126772i | ||||
\(347\) | 19.6471 | − | 14.2744i | 1.05471 | − | 0.766292i | 0.0816081 | − | 0.996664i | \(-0.473994\pi\) |
0.973103 | + | 0.230372i | \(0.0739944\pi\) | |||||||
\(348\) | 1.39113 | + | 4.28146i | 0.0745725 | + | 0.229511i | ||||
\(349\) | −1.02557 | + | 3.15637i | −0.0548973 | + | 0.168957i | −0.974746 | − | 0.223317i | \(-0.928311\pi\) |
0.919849 | + | 0.392274i | \(0.128311\pi\) | |||||||
\(350\) | 0.219017 | + | 0.159125i | 0.0117069 | + | 0.00850559i | ||||
\(351\) | 30.6269 | 1.63474 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.3272 | 1.08191 | 0.540955 | − | 0.841051i | \(-0.318063\pi\) | ||||
0.540955 | + | 0.841051i | \(0.318063\pi\) | |||||||
\(354\) | 0.626668 | + | 0.455301i | 0.0333070 | + | 0.0241990i | ||||
\(355\) | −9.85042 | + | 30.3165i | −0.522806 | + | 1.60903i | ||||
\(356\) | 3.98269 | + | 12.2575i | 0.211082 | + | 0.649644i | ||||
\(357\) | 4.54917 | − | 3.30516i | 0.240768 | − | 0.174928i | ||||
\(358\) | 0.877196 | − | 0.637321i | 0.0463613 | − | 0.0336834i | ||||
\(359\) | 8.97423 | + | 27.6199i | 0.473642 | + | 1.45772i | 0.847780 | + | 0.530347i | \(0.177938\pi\) |
−0.374139 | + | 0.927373i | \(0.622062\pi\) | |||||||
\(360\) | −10.8065 | + | 33.2589i | −0.569552 | + | 1.75290i | ||||
\(361\) | −21.2431 | − | 15.4340i | −1.11806 | − | 0.812317i | ||||
\(362\) | 1.62535 | 0.0854264 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.92246 | −0.205593 | ||||||||
\(365\) | −13.9410 | − | 10.1287i | −0.729706 | − | 0.530162i | ||||
\(366\) | 3.25654 | − | 10.0226i | 0.170222 | − | 0.523889i | ||||
\(367\) | −7.03285 | − | 21.6449i | −0.367112 | − | 1.12985i | −0.948648 | − | 0.316333i | \(-0.897548\pi\) |
0.581536 | − | 0.813520i | \(-0.302452\pi\) | |||||||
\(368\) | 3.86519 | − | 2.80822i | 0.201487 | − | 0.146389i | ||||
\(369\) | −30.8548 | + | 22.4173i | −1.60623 | + | 1.16700i | ||||
\(370\) | −0.668707 | − | 2.05807i | −0.0347644 | − | 0.106994i | ||||
\(371\) | 0.206244 | − | 0.634755i | 0.0107077 | − | 0.0329548i | ||||
\(372\) | 11.8296 | + | 8.59473i | 0.613338 | + | 0.445616i | ||||
\(373\) | −22.2412 | −1.15160 | −0.575802 | − | 0.817589i | \(-0.695310\pi\) | ||||
−0.575802 | + | 0.817589i | \(0.695310\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −36.3756 | −1.87843 | ||||||||
\(376\) | 8.46248 | + | 6.14835i | 0.436419 | + | 0.317077i | ||||
\(377\) | −0.722032 | + | 2.22219i | −0.0371865 | + | 0.114448i | ||||
\(378\) | 2.50710 | + | 7.71606i | 0.128951 | + | 0.396871i | ||||
\(379\) | −27.0784 | + | 19.6736i | −1.39092 | + | 1.01056i | −0.395158 | + | 0.918613i | \(0.629310\pi\) |
−0.995764 | + | 0.0919503i | \(0.970690\pi\) | |||||||
\(380\) | −18.1018 | + | 13.1517i | −0.928601 | + | 0.674668i | ||||
\(381\) | 17.0442 | + | 52.4566i | 0.873200 | + | 2.68743i | ||||
\(382\) | 2.62861 | − | 8.09003i | 0.134491 | − | 0.413922i | ||||
\(383\) | 4.97216 | + | 3.61248i | 0.254065 | + | 0.184589i | 0.707527 | − | 0.706687i | \(-0.249811\pi\) |
−0.453461 | + | 0.891276i | \(0.649811\pi\) | |||||||
\(384\) | −34.4486 | −1.75795 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.17829 | −0.0599733 | ||||||||
\(387\) | 46.7720 | + | 33.9819i | 2.37755 | + | 1.72739i | ||||
\(388\) | −4.08268 | + | 12.5652i | −0.207267 | + | 0.637901i | ||||
\(389\) | 2.28785 | + | 7.04128i | 0.115999 | + | 0.357007i | 0.992154 | − | 0.125022i | \(-0.0399000\pi\) |
−0.876155 | + | 0.482029i | \(0.839900\pi\) | |||||||
\(390\) | −9.22076 | + | 6.69927i | −0.466911 | + | 0.339231i | ||||
\(391\) | −4.58468 | + | 3.33097i | −0.231857 | + | 0.168454i | ||||
\(392\) | −0.735015 | − | 2.26214i | −0.0371238 | − | 0.114255i | ||||
\(393\) | 6.52544 | − | 20.0832i | 0.329165 | − | 1.01307i | ||||
\(394\) | 0.489305 | + | 0.355501i | 0.0246508 | + | 0.0179099i | ||||
\(395\) | 8.69662 | 0.437575 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.8079 | 0.893752 | 0.446876 | − | 0.894596i | \(-0.352537\pi\) | ||||
0.446876 | + | 0.894596i | \(0.352537\pi\) | |||||||
\(398\) | 8.46865 | + | 6.15283i | 0.424495 | + | 0.308414i | ||||
\(399\) | −6.52722 | + | 20.0887i | −0.326769 | + | 1.00569i | ||||
\(400\) | −0.188595 | − | 0.580436i | −0.00942976 | − | 0.0290218i | ||||
\(401\) | −20.7746 | + | 15.0937i | −1.03744 | + | 0.753741i | −0.969783 | − | 0.243968i | \(-0.921551\pi\) |
−0.0676523 | + | 0.997709i | \(0.521551\pi\) | |||||||
\(402\) | 1.53474 | − | 1.11505i | 0.0765456 | − | 0.0556137i | ||||
\(403\) | 2.34522 | + | 7.21785i | 0.116824 | + | 0.359547i | ||||
\(404\) | 1.93067 | − | 5.94198i | 0.0960542 | − | 0.295625i | ||||
\(405\) | −30.2819 | − | 22.0011i | −1.50472 | − | 1.09324i | ||||
\(406\) | −0.618957 | −0.0307183 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 13.3748 | 0.662152 | ||||||||
\(409\) | −1.08210 | − | 0.786189i | −0.0535062 | − | 0.0388746i | 0.560711 | − | 0.828012i | \(-0.310528\pi\) |
−0.614217 | + | 0.789137i | \(0.710528\pi\) | |||||||
\(410\) | 2.46733 | − | 7.59366i | 0.121853 | − | 0.375024i | ||||
\(411\) | 13.4550 | + | 41.4101i | 0.663685 | + | 2.04261i | ||||
\(412\) | −22.1230 | + | 16.0733i | −1.08992 | + | 0.791873i | ||||
\(413\) | 0.298010 | − | 0.216517i | 0.0146641 | − | 0.0106541i | ||||
\(414\) | −4.49133 | − | 13.8229i | −0.220737 | − | 0.679359i | ||||
\(415\) | −2.68387 | + | 8.26010i | −0.131746 | + | 0.405472i | ||||
\(416\) | −11.7986 | − | 8.57218i | −0.578474 | − | 0.420286i | ||||
\(417\) | 44.8068 | 2.19420 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.4618 | 1.83013 | 0.915064 | − | 0.403310i | \(-0.132140\pi\) | ||||
0.915064 | + | 0.403310i | \(0.132140\pi\) | |||||||
\(420\) | 8.44835 | + | 6.13808i | 0.412237 | + | 0.299508i | ||||
\(421\) | 2.55296 | − | 7.85721i | 0.124424 | − | 0.382937i | −0.869372 | − | 0.494158i | \(-0.835476\pi\) |
0.993796 | + | 0.111221i | \(0.0354763\pi\) | |||||||
\(422\) | 3.05656 | + | 9.40714i | 0.148791 | + | 0.457932i | ||||
\(423\) | −24.4002 | + | 17.7277i | −1.18638 | + | 0.861953i | ||||
\(424\) | 1.28431 | − | 0.933108i | 0.0623718 | − | 0.0453158i | ||||
\(425\) | 0.223702 | + | 0.688483i | 0.0108511 | + | 0.0333963i | ||||
\(426\) | −9.66233 | + | 29.7376i | −0.468141 | + | 1.44079i | ||||
\(427\) | −4.05438 | − | 2.94568i | −0.196205 | − | 0.142551i | ||||
\(428\) | 23.8980 | 1.15515 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.1034 | −0.583679 | ||||||||
\(431\) | −26.4196 | − | 19.1950i | −1.27259 | − | 0.924590i | −0.273286 | − | 0.961933i | \(-0.588110\pi\) |
−0.999302 | + | 0.0373433i | \(0.988110\pi\) | |||||||
\(432\) | 5.65197 | − | 17.3950i | 0.271931 | − | 0.836916i | ||||
\(433\) | 4.88100 | + | 15.0222i | 0.234566 | + | 0.721920i | 0.997179 | + | 0.0750647i | \(0.0239163\pi\) |
−0.762613 | + | 0.646856i | \(0.776084\pi\) | |||||||
\(434\) | −1.62647 | + | 1.18170i | −0.0780730 | + | 0.0567234i | ||||
\(435\) | 5.03254 | − | 3.65636i | 0.241292 | − | 0.175309i | ||||
\(436\) | 9.07380 | + | 27.9263i | 0.434556 | + | 1.33743i | ||||
\(437\) | 6.57817 | − | 20.2455i | 0.314677 | − | 0.968475i | ||||
\(438\) | −13.6748 | − | 9.93533i | −0.653408 | − | 0.474728i | ||||
\(439\) | −20.6942 | −0.987678 | −0.493839 | − | 0.869553i | \(-0.664407\pi\) | ||||
−0.493839 | + | 0.869553i | \(0.664407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.85818 | 0.326580 | ||||||||
\(442\) | 2.45338 | + | 1.78248i | 0.116695 | + | 0.0847841i | ||||
\(443\) | 9.30001 | − | 28.6225i | 0.441857 | − | 1.35990i | −0.444037 | − | 0.896008i | \(-0.646454\pi\) |
0.885894 | − | 0.463887i | \(-0.153546\pi\) | |||||||
\(444\) | 2.26872 | + | 6.98241i | 0.107669 | + | 0.331371i | ||||
\(445\) | 14.4077 | − | 10.4678i | 0.682992 | − | 0.496223i | ||||
\(446\) | 0.999883 | − | 0.726458i | 0.0473459 | − | 0.0343988i | ||||
\(447\) | 2.54487 | + | 7.83231i | 0.120368 | + | 0.370456i | ||||
\(448\) | 0.260682 | − | 0.802296i | 0.0123161 | − | 0.0379049i | ||||
\(449\) | −29.4437 | − | 21.3921i | −1.38953 | − | 1.00956i | −0.995916 | − | 0.0902818i | \(-0.971223\pi\) |
−0.393618 | − | 0.919274i | \(-0.628777\pi\) | |||||||
\(450\) | −1.85664 | −0.0875230 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −2.60739 | −0.122641 | ||||||||
\(453\) | 7.59397 | + | 5.51734i | 0.356796 | + | 0.259227i | ||||
\(454\) | −4.54074 | + | 13.9750i | −0.213107 | + | 0.655877i | ||||
\(455\) | 1.67488 | + | 5.15476i | 0.0785197 | + | 0.241659i | ||||
\(456\) | −40.6459 | + | 29.5310i | −1.90342 | + | 1.38291i | ||||
\(457\) | 7.92352 | − | 5.75678i | 0.370647 | − | 0.269291i | −0.386832 | − | 0.922150i | \(-0.626431\pi\) |
0.757479 | + | 0.652859i | \(0.226431\pi\) | |||||||
\(458\) | −4.19136 | − | 12.8997i | −0.195849 | − | 0.602762i | ||||
\(459\) | −6.70407 | + | 20.6330i | −0.312919 | + | 0.963067i | ||||
\(460\) | −8.51430 | − | 6.18600i | −0.396981 | − | 0.288424i | ||||
\(461\) | −21.8596 | −1.01810 | −0.509052 | − | 0.860736i | \(-0.670004\pi\) | ||||
−0.509052 | + | 0.860736i | \(0.670004\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.75889 | 0.314112 | 0.157056 | − | 0.987590i | \(-0.449800\pi\) | ||||
0.157056 | + | 0.987590i | \(0.449800\pi\) | |||||||
\(464\) | 1.12888 | + | 0.820177i | 0.0524068 | + | 0.0380758i | ||||
\(465\) | 6.24367 | − | 19.2160i | 0.289543 | − | 0.891122i | ||||
\(466\) | 4.35916 | + | 13.4161i | 0.201934 | + | 0.621489i | ||||
\(467\) | 24.2893 | − | 17.6472i | 1.12397 | − | 0.816615i | 0.139167 | − | 0.990269i | \(-0.455558\pi\) |
0.984807 | + | 0.173654i | \(0.0555575\pi\) | |||||||
\(468\) | 21.7633 | − | 15.8119i | 1.00601 | − | 0.730907i | ||||
\(469\) | −0.278773 | − | 0.857976i | −0.0128726 | − | 0.0396176i | ||||
\(470\) | 1.95118 | − | 6.00511i | 0.0900012 | − | 0.276995i | ||||
\(471\) | −28.5884 | − | 20.7707i | −1.31728 | − | 0.957062i | ||||
\(472\) | 0.876166 | 0.0403288 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.53056 | 0.391822 | ||||||||
\(475\) | −2.19997 | − | 1.59837i | −0.100941 | − | 0.0733382i | ||||
\(476\) | 0.858607 | − | 2.64252i | 0.0393542 | − | 0.121120i | ||||
\(477\) | 1.41446 | + | 4.35326i | 0.0647637 | + | 0.199322i | ||||
\(478\) | −8.39655 | + | 6.10045i | −0.384049 | + | 0.279028i | ||||
\(479\) | 4.85696 | − | 3.52879i | 0.221920 | − | 0.161234i | −0.471270 | − | 0.881989i | \(-0.656204\pi\) |
0.693191 | + | 0.720754i | \(0.256204\pi\) | |||||||
\(480\) | 11.9981 | + | 36.9262i | 0.547634 | + | 1.68544i | ||||
\(481\) | −1.17752 | + | 3.62404i | −0.0536904 | + | 0.165242i | ||||
\(482\) | −7.63164 | − | 5.54471i | −0.347612 | − | 0.252555i | ||||
\(483\) | −9.93514 | −0.452064 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.2561 | 0.828965 | ||||||||
\(486\) | −10.0127 | − | 7.27462i | −0.454184 | − | 0.329984i | ||||
\(487\) | 1.96758 | − | 6.05559i | 0.0891596 | − | 0.274405i | −0.896528 | − | 0.442987i | \(-0.853919\pi\) |
0.985688 | + | 0.168582i | \(0.0539188\pi\) | |||||||
\(488\) | −3.68352 | − | 11.3367i | −0.166745 | − | 0.513188i | ||||
\(489\) | 46.2379 | − | 33.5938i | 2.09095 | − | 1.51916i | ||||
\(490\) | −1.16157 | + | 0.843932i | −0.0524745 | + | 0.0381250i | ||||
\(491\) | 3.82467 | + | 11.7711i | 0.172605 | + | 0.531223i | 0.999516 | − | 0.0311093i | \(-0.00990401\pi\) |
−0.826911 | + | 0.562333i | \(0.809904\pi\) | |||||||
\(492\) | −8.37090 | + | 25.7630i | −0.377390 | + | 1.16149i | ||||
\(493\) | −1.33902 | − | 0.972852i | −0.0603062 | − | 0.0438150i | ||||
\(494\) | −11.3914 | −0.512525 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.53228 | 0.203505 | ||||||||
\(497\) | 12.0296 | + | 8.74000i | 0.539600 | + | 0.392042i | ||||
\(498\) | −2.63262 | + | 8.10237i | −0.117971 | + | 0.363076i | ||||
\(499\) | −4.41266 | − | 13.5808i | −0.197538 | − | 0.607958i | −0.999938 | − | 0.0111716i | \(-0.996444\pi\) |
0.802400 | − | 0.596787i | \(-0.203556\pi\) | |||||||
\(500\) | −14.5414 | + | 10.5649i | −0.650311 | + | 0.472478i | ||||
\(501\) | −50.6279 | + | 36.7833i | −2.26189 | + | 1.64336i | ||||
\(502\) | −0.222954 | − | 0.686182i | −0.00995092 | − | 0.0306258i | ||||
\(503\) | 1.83115 | − | 5.63571i | 0.0816470 | − | 0.251284i | −0.901897 | − | 0.431950i | \(-0.857826\pi\) |
0.983544 | + | 0.180667i | \(0.0578255\pi\) | |||||||
\(504\) | 13.1971 | + | 9.58828i | 0.587847 | + | 0.427096i | ||||
\(505\) | −8.63314 | −0.384170 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.7473 | −0.921419 | ||||||||
\(508\) | 22.0490 | + | 16.0195i | 0.978267 | + | 0.710752i | ||||
\(509\) | 9.54043 | − | 29.3624i | 0.422872 | − | 1.30147i | −0.482145 | − | 0.876092i | \(-0.660142\pi\) |
0.905017 | − | 0.425376i | \(-0.139858\pi\) | |||||||
\(510\) | −2.49486 | − | 7.67838i | −0.110474 | − | 0.340004i | ||||
\(511\) | −6.50301 | + | 4.72471i | −0.287676 | + | 0.209009i | ||||
\(512\) | −12.8569 | + | 9.34107i | −0.568199 | + | 0.412821i | ||||
\(513\) | −25.1831 | − | 77.5057i | −1.11186 | − | 3.42196i | ||||
\(514\) | 2.70728 | − | 8.33214i | 0.119413 | − | 0.367515i | ||||
\(515\) | 30.5694 | + | 22.2100i | 1.34705 | + | 0.978689i | ||||
\(516\) | 41.0633 | 1.80771 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.00942 | −0.0443516 | ||||||||
\(519\) | −15.2156 | − | 11.0548i | −0.667890 | − | 0.485250i | ||||
\(520\) | −3.98380 | + | 12.2609i | −0.174701 | + | 0.537676i | ||||
\(521\) | 5.83639 | + | 17.9626i | 0.255697 | + | 0.786954i | 0.993692 | + | 0.112148i | \(0.0357730\pi\) |
−0.737995 | + | 0.674807i | \(0.764227\pi\) | |||||||
\(522\) | 3.43421 | − | 2.49510i | 0.150311 | − | 0.109208i | ||||
\(523\) | 6.42528 | − | 4.66824i | 0.280958 | − | 0.204128i | −0.438377 | − | 0.898791i | \(-0.644447\pi\) |
0.719335 | + | 0.694663i | \(0.244447\pi\) | |||||||
\(524\) | −3.22439 | − | 9.92365i | −0.140858 | − | 0.433516i | ||||
\(525\) | −0.392186 | + | 1.20702i | −0.0171164 | + | 0.0526788i | ||||
\(526\) | 5.18652 | + | 3.76823i | 0.226143 | + | 0.164303i | ||||
\(527\) | −5.37595 | −0.234180 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9873 | −0.564665 | ||||||||
\(530\) | −0.775258 | − | 0.563258i | −0.0336750 | − | 0.0244664i | ||||
\(531\) | −0.780663 | + | 2.40263i | −0.0338779 | + | 0.104265i | ||||
\(532\) | 3.22527 | + | 9.92635i | 0.139833 | + | 0.430362i | ||||
\(533\) | −11.3746 | + | 8.26412i | −0.492688 | + | 0.357959i | ||||
\(534\) | 14.1326 | − | 10.2680i | 0.611579 | − | 0.444338i | ||||
\(535\) | −10.2044 | − | 31.4060i | −0.441175 | − | 1.35780i | ||||
\(536\) | 0.663078 | − | 2.04074i | 0.0286406 | − | 0.0881467i | ||||
\(537\) | 4.11231 | + | 2.98777i | 0.177459 | + | 0.128932i | ||||
\(538\) | −3.19370 | −0.137690 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −40.2899 | −1.73380 | ||||||||
\(541\) | −6.14986 | − | 4.46814i | −0.264403 | − | 0.192100i | 0.447683 | − | 0.894192i | \(-0.352249\pi\) |
−0.712086 | + | 0.702092i | \(0.752249\pi\) | |||||||
\(542\) | −4.15007 | + | 12.7726i | −0.178261 | + | 0.548630i | ||||
\(543\) | 2.35461 | + | 7.24673i | 0.101046 | + | 0.310987i | ||||
\(544\) | 8.35765 | − | 6.07219i | 0.358331 | − | 0.260343i | ||||
\(545\) | 32.8253 | − | 23.8490i | 1.40608 | − | 1.02158i | ||||
\(546\) | 1.64290 | + | 5.05633i | 0.0703097 | + | 0.216391i | ||||
\(547\) | 6.70534 | − | 20.6369i | 0.286700 | − | 0.882371i | −0.699184 | − | 0.714942i | \(-0.746453\pi\) |
0.985884 | − | 0.167430i | \(-0.0535467\pi\) | |||||||
\(548\) | 17.4059 | + | 12.6461i | 0.743542 | + | 0.540215i | ||||
\(549\) | 34.3697 | 1.46686 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.21726 | 0.264864 | ||||||||
\(552\) | −19.1181 | − | 13.8901i | −0.813721 | − | 0.591203i | ||||
\(553\) | 1.25358 | − | 3.85813i | 0.0533078 | − | 0.164064i | ||||
\(554\) | −2.40127 | − | 7.39035i | −0.102020 | − | 0.313986i | ||||
\(555\) | 8.20731 | − | 5.96296i | 0.348381 | − | 0.253114i | ||||
\(556\) | 17.9118 | − | 13.0137i | 0.759630 | − | 0.551904i | ||||
\(557\) | −12.5502 | − | 38.6256i | −0.531770 | − | 1.63662i | −0.750527 | − | 0.660840i | \(-0.770200\pi\) |
0.218757 | − | 0.975779i | \(-0.429800\pi\) | |||||||
\(558\) | 4.26068 | − | 13.1130i | 0.180369 | − | 0.555119i | ||||
\(559\) | 17.2425 | + | 12.5274i | 0.729279 | + | 0.529852i | ||||
\(560\) | 3.23681 | 0.136780 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.08972 | 0.341244 | ||||||||
\(563\) | 18.9547 | + | 13.7714i | 0.798844 | + | 0.580394i | 0.910575 | − | 0.413344i | \(-0.135639\pi\) |
−0.111731 | + | 0.993739i | \(0.535639\pi\) | |||||||
\(564\) | −6.61977 | + | 20.3736i | −0.278743 | + | 0.857881i | ||||
\(565\) | 1.11335 | + | 3.42654i | 0.0468390 | + | 0.144156i | ||||
\(566\) | −11.9167 | + | 8.65797i | −0.500895 | + | 0.363922i | ||||
\(567\) | −14.1255 | + | 10.2628i | −0.593214 | + | 0.430995i | ||||
\(568\) | 10.9292 | + | 33.6366i | 0.458579 | + | 1.41136i | ||||
\(569\) | −3.44410 | + | 10.5999i | −0.144384 | + | 0.444369i | −0.996931 | − | 0.0782814i | \(-0.975057\pi\) |
0.852547 | + | 0.522650i | \(0.175057\pi\) | |||||||
\(570\) | 24.5353 | + | 17.8260i | 1.02767 | + | 0.746647i | ||||
\(571\) | −6.15846 | −0.257724 | −0.128862 | − | 0.991663i | \(-0.541132\pi\) | ||||
−0.128862 | + | 0.991663i | \(0.541132\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.8780 | 1.66593 | ||||||||
\(574\) | −3.01316 | − | 2.18919i | −0.125767 | − | 0.0913750i | ||||
\(575\) | 0.395247 | − | 1.21645i | 0.0164830 | − | 0.0507293i | ||||
\(576\) | 1.78780 | + | 5.50229i | 0.0744917 | + | 0.229262i | ||||
\(577\) | 11.7179 | − | 8.51357i | 0.487824 | − | 0.354425i | −0.316523 | − | 0.948585i | \(-0.602515\pi\) |
0.804347 | + | 0.594160i | \(0.202515\pi\) | |||||||
\(578\) | 7.47331 | − | 5.42967i | 0.310849 | − | 0.225845i | ||||
\(579\) | −1.70696 | − | 5.25348i | −0.0709388 | − | 0.218327i | ||||
\(580\) | 0.949839 | − | 2.92330i | 0.0394399 | − | 0.121384i | ||||
\(581\) | 3.27760 | + | 2.38132i | 0.135978 | + | 0.0987937i | ||||
\(582\) | 17.9075 | 0.742288 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −19.1192 | −0.791159 | ||||||||
\(585\) | −30.0724 | − | 21.8489i | −1.24334 | − | 0.903340i | ||||
\(586\) | 0.293308 | − | 0.902710i | 0.0121165 | − | 0.0372906i | ||||
\(587\) | 4.90007 | + | 15.0809i | 0.202247 | + | 0.622454i | 0.999815 | + | 0.0192243i | \(0.00611967\pi\) |
−0.797568 | + | 0.603229i | \(0.793880\pi\) | |||||||
\(588\) | 3.94087 | − | 2.86321i | 0.162519 | − | 0.118077i | ||||
\(589\) | 16.3374 | − | 11.8699i | 0.673173 | − | 0.489089i | ||||
\(590\) | −0.163435 | − | 0.503000i | −0.00672849 | − | 0.0207082i | ||||
\(591\) | −0.876181 | + | 2.69661i | −0.0360413 | + | 0.110924i | ||||
\(592\) | 1.84103 | + | 1.33758i | 0.0756657 | + | 0.0549743i | ||||
\(593\) | 22.9285 | 0.941560 | 0.470780 | − | 0.882251i | \(-0.343973\pi\) | ||||
0.470780 | + | 0.882251i | \(0.343973\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.83934 | −0.157397 | ||||||||
\(596\) | 3.29214 | + | 2.39188i | 0.134851 | + | 0.0979753i | ||||
\(597\) | −15.1645 | + | 46.6715i | −0.620642 | + | 1.91014i | ||||
\(598\) | −1.65573 | − | 5.09581i | −0.0677077 | − | 0.208383i | ||||
\(599\) | −10.6395 | + | 7.73008i | −0.434720 | + | 0.315843i | −0.783533 | − | 0.621350i | \(-0.786585\pi\) |
0.348813 | + | 0.937192i | \(0.386585\pi\) | |||||||
\(600\) | −2.44220 | + | 1.77436i | −0.0997022 | + | 0.0724379i | ||||
\(601\) | 8.45237 | + | 26.0137i | 0.344780 | + | 1.06112i | 0.961702 | + | 0.274098i | \(0.0883793\pi\) |
−0.616922 | + | 0.787024i | \(0.711621\pi\) | |||||||
\(602\) | −1.74466 | + | 5.36951i | −0.0711070 | + | 0.218845i | ||||
\(603\) | 5.00536 | + | 3.63660i | 0.203834 | + | 0.148094i | ||||
\(604\) | 4.63819 | 0.188725 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.46830 | −0.344001 | ||||||||
\(607\) | 37.9221 | + | 27.5520i | 1.53921 | + | 1.11830i | 0.950827 | + | 0.309721i | \(0.100236\pi\) |
0.588384 | + | 0.808582i | \(0.299764\pi\) | |||||||
\(608\) | −11.9917 | + | 36.9066i | −0.486327 | + | 1.49676i | ||||
\(609\) | −0.896670 | − | 2.75967i | −0.0363349 | − | 0.111827i | ||||
\(610\) | −5.82120 | + | 4.22935i | −0.235694 | + | 0.171241i | ||||
\(611\) | −8.99510 | + | 6.53532i | −0.363903 | + | 0.264391i | ||||
\(612\) | 5.88848 | + | 18.1229i | 0.238028 | + | 0.732573i | ||||
\(613\) | −6.32540 | + | 19.4676i | −0.255481 | + | 0.786288i | 0.738254 | + | 0.674523i | \(0.235651\pi\) |
−0.993735 | + | 0.111765i | \(0.964349\pi\) | |||||||
\(614\) | −15.9649 | − | 11.5992i | −0.644292 | − | 0.468106i | ||||
\(615\) | 37.4312 | 1.50937 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.1691 | 1.77818 | 0.889090 | − | 0.457733i | \(-0.151338\pi\) | ||||
0.889090 | + | 0.457733i | \(0.151338\pi\) | |||||||
\(618\) | 29.9857 | + | 21.7859i | 1.20620 | + | 0.876357i | ||||
\(619\) | 0.210621 | − | 0.648225i | 0.00846557 | − | 0.0260544i | −0.946735 | − | 0.322015i | \(-0.895640\pi\) |
0.955200 | + | 0.295961i | \(0.0956398\pi\) | |||||||
\(620\) | −3.08516 | − | 9.49514i | −0.123903 | − | 0.381334i | ||||
\(621\) | 31.0108 | − | 22.5307i | 1.24442 | − | 0.904126i | ||||
\(622\) | −14.5638 | + | 10.5812i | −0.583955 | + | 0.424268i | ||||
\(623\) | −2.56709 | − | 7.90068i | −0.102848 | − | 0.316534i | ||||
\(624\) | 3.70374 | − | 11.3989i | 0.148268 | − | 0.456322i | ||||
\(625\) | 18.4582 | + | 13.4106i | 0.738326 | + | 0.536426i | ||||
\(626\) | −3.00896 | −0.120262 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.4610 | −0.696770 | ||||||||
\(629\) | −2.18373 | − | 1.58657i | −0.0870710 | − | 0.0632608i | ||||
\(630\) | 3.04284 | − | 9.36491i | 0.121230 | − | 0.373107i | ||||
\(631\) | −11.3940 | − | 35.0672i | −0.453588 | − | 1.39600i | −0.872784 | − | 0.488106i | \(-0.837688\pi\) |
0.419196 | − | 0.907896i | \(-0.362312\pi\) | |||||||
\(632\) | 7.80624 | − | 5.67157i | 0.310516 | − | 0.225603i | ||||
\(633\) | −37.5144 | + | 27.2558i | −1.49106 | + | 1.08332i | ||||
\(634\) | −2.26625 | − | 6.97480i | −0.0900043 | − | 0.277005i | ||||
\(635\) | 11.6375 | − | 35.8164i | 0.461818 | − | 1.42133i | ||||
\(636\) | 2.63022 | + | 1.91096i | 0.104295 | + | 0.0757747i | ||||
\(637\) | 2.52826 | 0.100173 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −101.977 | −4.03414 | ||||||||
\(640\) | 19.0288 | + | 13.8252i | 0.752179 | + | 0.546490i | ||||
\(641\) | −6.33875 | + | 19.5087i | −0.250366 | + | 0.770546i | 0.744342 | + | 0.667799i | \(0.232763\pi\) |
−0.994707 | + | 0.102748i | \(0.967237\pi\) | |||||||
\(642\) | −10.0096 | − | 30.8063i | −0.395046 | − | 1.21583i | ||||
\(643\) | 6.17814 | − | 4.48868i | 0.243642 | − | 0.177016i | −0.459262 | − | 0.888301i | \(-0.651886\pi\) |
0.702904 | + | 0.711284i | \(0.251886\pi\) | |||||||
\(644\) | −3.97163 | + | 2.88556i | −0.156504 | + | 0.113707i | ||||
\(645\) | −17.5340 | − | 53.9640i | −0.690399 | − | 2.12483i | ||||
\(646\) | 2.49353 | − | 7.67430i | 0.0981066 | − | 0.301941i | ||||
\(647\) | −11.8787 | − | 8.63035i | −0.466998 | − | 0.339294i | 0.329272 | − | 0.944235i | \(-0.393197\pi\) |
−0.796270 | + | 0.604941i | \(0.793197\pi\) | |||||||
\(648\) | −41.5297 | −1.63144 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.684450 | −0.0268463 | ||||||||
\(651\) | −7.62492 | − | 5.53983i | −0.298844 | − | 0.217123i | ||||
\(652\) | 8.72690 | − | 26.8586i | 0.341772 | − | 1.05187i | ||||
\(653\) | 0.348273 | + | 1.07187i | 0.0136290 | + | 0.0419457i | 0.957640 | − | 0.287969i | \(-0.0929800\pi\) |
−0.944011 | + | 0.329915i | \(0.892980\pi\) | |||||||
\(654\) | 32.1985 | − | 23.3936i | 1.25906 | − | 0.914761i | ||||
\(655\) | −11.6645 | + | 8.47476i | −0.455770 | + | 0.331136i | ||||
\(656\) | 2.59463 | + | 7.98545i | 0.101303 | + | 0.311779i | ||||
\(657\) | 17.0352 | − | 52.4290i | 0.664607 | − | 2.04545i | ||||
\(658\) | −2.38283 | − | 1.73123i | −0.0928923 | − | 0.0674902i | ||||
\(659\) | 10.0215 | 0.390384 | 0.195192 | − | 0.980765i | \(-0.437467\pi\) | ||||
0.195192 | + | 0.980765i | \(0.437467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.7371 | 0.612101 | 0.306050 | − | 0.952015i | \(-0.400992\pi\) | ||||
0.306050 | + | 0.952015i | \(0.400992\pi\) | |||||||
\(662\) | −8.95253 | − | 6.50439i | −0.347950 | − | 0.252800i | ||||
\(663\) | −4.39318 | + | 13.5208i | −0.170617 | + | 0.525105i | ||||
\(664\) | 2.97780 | + | 9.16471i | 0.115561 | + | 0.355660i | ||||
\(665\) | 11.6677 | − | 8.47707i | 0.452454 | − | 0.328727i | ||||
\(666\) | 5.60067 | − | 4.06912i | 0.217022 | − | 0.157675i | ||||
\(667\) | 0.903670 | + | 2.78121i | 0.0349902 | + | 0.107689i | ||||
\(668\) | −9.55548 | + | 29.4087i | −0.369713 | + | 1.13786i | ||||
\(669\) | 4.68747 | + | 3.40565i | 0.181228 | + | 0.131670i | ||||
\(670\) | −1.29526 | −0.0500403 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 18.1113 | 0.698657 | ||||||||
\(673\) | −25.8983 | − | 18.8162i | −0.998305 | − | 0.725311i | −0.0365810 | − | 0.999331i | \(-0.511647\pi\) |
−0.961724 | + | 0.274020i | \(0.911647\pi\) | |||||||
\(674\) | −2.50853 | + | 7.72048i | −0.0966251 | + | 0.297382i | ||||
\(675\) | −1.51312 | − | 4.65691i | −0.0582401 | − | 0.179244i | ||||
\(676\) | −8.29385 | + | 6.02584i | −0.318994 | + | 0.231763i | ||||
\(677\) | 12.4104 | − | 9.01665i | 0.476969 | − | 0.346538i | −0.323182 | − | 0.946337i | \(-0.604753\pi\) |
0.800151 | + | 0.599799i | \(0.204753\pi\) | |||||||
\(678\) | 1.09209 | + | 3.36111i | 0.0419415 | + | 0.129083i | ||||
\(679\) | 2.63154 | − | 8.09904i | 0.100989 | − | 0.310813i | ||||
\(680\) | −7.38801 | − | 5.36770i | −0.283317 | − | 0.205842i | ||||
\(681\) | −68.8864 | −2.63973 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.04764 | 0.0400868 | 0.0200434 | − | 0.999799i | \(-0.493620\pi\) | ||||
0.0200434 | + | 0.999799i | \(0.493620\pi\) | |||||||
\(684\) | −57.9094 | − | 42.0737i | −2.21422 | − | 1.60873i | ||||
\(685\) | 9.18680 | − | 28.2741i | 0.351010 | − | 1.08030i | ||||
\(686\) | 0.206962 | + | 0.636964i | 0.00790186 | + | 0.0243194i | ||||
\(687\) | 51.4422 | − | 37.3749i | 1.96264 | − | 1.42594i | ||||
\(688\) | 10.2971 | − | 7.48128i | 0.392573 | − | 0.285221i | ||||
\(689\) | 0.521440 | + | 1.60483i | 0.0198653 | + | 0.0611390i | ||||
\(690\) | −4.40803 | + | 13.5665i | −0.167811 | + | 0.516469i | ||||
\(691\) | −23.6138 | − | 17.1565i | −0.898313 | − | 0.652663i | 0.0397191 | − | 0.999211i | \(-0.487354\pi\) |
−0.938032 | + | 0.346548i | \(0.887354\pi\) | |||||||
\(692\) | −9.29326 | −0.353277 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.2648 | −0.617404 | ||||||||
\(695\) | −24.7505 | − | 17.9823i | −0.938839 | − | 0.682107i | ||||
\(696\) | 2.13278 | − | 6.56402i | 0.0808428 | − | 0.248809i | ||||
\(697\) | −3.07762 | − | 9.47193i | −0.116573 | − | 0.358775i | ||||
\(698\) | 1.79824 | − | 1.30650i | 0.0680644 | − | 0.0494517i | ||||
\(699\) | −53.5017 | + | 38.8713i | −2.02362 | + | 1.47025i | ||||
\(700\) | 0.193789 | + | 0.596421i | 0.00732454 | + | 0.0225426i | ||||
\(701\) | 3.94877 | − | 12.1531i | 0.149143 | − | 0.459015i | −0.848378 | − | 0.529392i | \(-0.822420\pi\) |
0.997520 | + | 0.0703770i | \(0.0224202\pi\) | |||||||
\(702\) | −16.5947 | − | 12.0567i | −0.626326 | − | 0.455052i | ||||
\(703\) | 10.1394 | 0.382415 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.6009 | 1.11483 | ||||||||
\(706\) | −11.0140 | − | 8.00214i | −0.414517 | − | 0.301164i | ||||
\(707\) | −1.24443 | + | 3.82997i | −0.0468017 | + | 0.144041i | ||||
\(708\) | 0.554484 | + | 1.70653i | 0.0208388 | + | 0.0641352i | ||||
\(709\) | −30.8001 | + | 22.3775i | −1.15672 | + | 0.840406i | −0.989360 | − | 0.145489i | \(-0.953524\pi\) |
−0.167360 | + | 0.985896i | \(0.553524\pi\) | |||||||
\(710\) | 17.2718 | − | 12.5487i | 0.648201 | − | 0.470946i | ||||
\(711\) | 8.59729 | + | 26.4597i | 0.322424 | + | 0.992318i | ||||
\(712\) | 6.10596 | − | 18.7922i | 0.228831 | − | 0.704269i | ||||
\(713\) | 7.68445 | + | 5.58308i | 0.287785 | + | 0.209088i | ||||
\(714\) | −3.76602 | −0.140940 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.51169 | 0.0938663 | ||||||||
\(717\) | −39.3632 | − | 28.5990i | −1.47005 | − | 1.06805i | ||||
\(718\) | 6.01044 | − | 18.4982i | 0.224308 | − | 0.690348i | ||||
\(719\) | −12.1349 | − | 37.3474i | −0.452555 | − | 1.39282i | −0.873981 | − | 0.485959i | \(-0.838470\pi\) |
0.421426 | − | 0.906863i | \(-0.361530\pi\) | |||||||
\(720\) | −17.9591 | + | 13.0480i | −0.669294 | + | 0.486271i | ||||
\(721\) | 14.2596 | − | 10.3602i | 0.531055 | − | 0.385834i | ||||
\(722\) | 5.43440 | + | 16.7254i | 0.202247 | + | 0.622453i | ||||
\(723\) | 13.6657 | − | 42.0587i | 0.508233 | − | 1.56418i | ||||
\(724\) | 3.04601 | + | 2.21305i | 0.113204 | + | 0.0822475i | ||||
\(725\) | 0.373562 | 0.0138737 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.4699 | −1.05589 | −0.527946 | − | 0.849278i | \(-0.677037\pi\) | ||||
−0.527946 | + | 0.849278i | \(0.677037\pi\) | |||||||
\(728\) | 4.86512 | + | 3.53472i | 0.180313 | + | 0.131005i | ||||
\(729\) | 1.74296 | − | 5.36429i | 0.0645542 | − | 0.198677i | ||||
\(730\) | 3.56638 | + | 10.9762i | 0.131998 | + | 0.406247i | ||||
\(731\) | −12.2139 | + | 8.87390i | −0.451747 | + | 0.328213i | ||||
\(732\) | 19.7496 | − | 14.3489i | 0.729966 | − | 0.530352i | ||||
\(733\) | −0.925001 | − | 2.84686i | −0.0341657 | − | 0.105151i | 0.932519 | − | 0.361120i | \(-0.117606\pi\) |
−0.966685 | + | 0.255969i | \(0.917606\pi\) | |||||||
\(734\) | −4.71021 | + | 14.4965i | −0.173857 | + | 0.535077i | ||||
\(735\) | −5.44548 | − | 3.95637i | −0.200859 | − | 0.145933i | ||||
\(736\) | −18.2527 | −0.672802 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 25.5431 | 0.940254 | ||||||||
\(739\) | 41.0438 | + | 29.8200i | 1.50982 | + | 1.09695i | 0.966257 | + | 0.257579i | \(0.0829247\pi\) |
0.543562 | + | 0.839369i | \(0.317075\pi\) | |||||||
\(740\) | 1.54904 | − | 4.76746i | 0.0569439 | − | 0.175255i | ||||
\(741\) | −16.5025 | − | 50.7895i | −0.606235 | − | 1.86580i | ||||
\(742\) | −0.361631 | + | 0.262741i | −0.0132759 | + | 0.00964551i | ||||
\(743\) | 0.310563 | − | 0.225637i | 0.0113935 | − | 0.00827783i | −0.582074 | − | 0.813136i | \(-0.697759\pi\) |
0.593467 | + | 0.804858i | \(0.297759\pi\) | |||||||
\(744\) | −6.92745 | − | 21.3205i | −0.253973 | − | 0.781648i | ||||
\(745\) | 1.73759 | − | 5.34776i | 0.0636604 | − | 0.195927i | ||||
\(746\) | 12.0510 | + | 8.75559i | 0.441220 | + | 0.320565i | ||||
\(747\) | −27.7848 | −1.01659 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.4037 | −0.562840 | ||||||||
\(750\) | 19.7096 | + | 14.3198i | 0.719692 | + | 0.522887i | ||||
\(751\) | −12.1620 | + | 37.4307i | −0.443797 | + | 1.36587i | 0.440002 | + | 0.897997i | \(0.354978\pi\) |
−0.883798 | + | 0.467868i | \(0.845022\pi\) | |||||||
\(752\) | 2.05185 | + | 6.31495i | 0.0748233 | + | 0.230282i | ||||
\(753\) | 2.73640 | − | 1.98811i | 0.0997200 | − | 0.0724509i | ||||
\(754\) | 1.26602 | − | 0.919817i | 0.0461057 | − | 0.0334978i | ||||
\(755\) | −1.98050 | − | 6.09536i | −0.0720778 | − | 0.221833i | ||||
\(756\) | −5.80762 | + | 17.8740i | −0.211221 | + | 0.650072i | ||||
\(757\) | −9.21202 | − | 6.69292i | −0.334817 | − | 0.243258i | 0.407655 | − | 0.913136i | \(-0.366347\pi\) |
−0.742472 | + | 0.669878i | \(0.766347\pi\) | |||||||
\(758\) | 22.4168 | 0.814214 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 34.3037 | 1.24433 | ||||||||
\(761\) | 6.05278 | + | 4.39760i | 0.219413 | + | 0.159413i | 0.692062 | − | 0.721838i | \(-0.256702\pi\) |
−0.472649 | + | 0.881251i | \(0.656702\pi\) | |||||||
\(762\) | 11.4152 | − | 35.1325i | 0.413530 | − | 1.27272i | ||||
\(763\) | −5.84862 | − | 18.0002i | −0.211734 | − | 0.651651i | ||||
\(764\) | 15.9415 | − | 11.5822i | 0.576743 | − | 0.419028i | ||||
\(765\) | 21.3021 | − | 15.4769i | 0.770179 | − | 0.559568i | ||||
\(766\) | −1.27197 | − | 3.91473i | −0.0459583 | − | 0.141445i | ||||
\(767\) | −0.287791 | + | 0.885730i | −0.0103915 | + | 0.0319818i | ||||
\(768\) | 22.9511 | + | 16.6749i | 0.828175 | + | 0.601704i | ||||
\(769\) | −26.8378 | −0.967798 | −0.483899 | − | 0.875124i | \(-0.660780\pi\) | ||||
−0.483899 | + | 0.875124i | \(0.660780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.0714 | 1.47915 | ||||||||
\(772\) | −2.20819 | − | 1.60434i | −0.0794745 | − | 0.0577416i | ||||
\(773\) | 1.38063 | − | 4.24914i | 0.0496577 | − | 0.152831i | −0.923153 | − | 0.384433i | \(-0.874397\pi\) |
0.972811 | + | 0.231602i | \(0.0743969\pi\) | |||||||
\(774\) | −11.9652 | − | 36.8251i | −0.430080 | − | 1.32365i | ||||
\(775\) | 0.981630 | − | 0.713196i | 0.0352612 | − | 0.0256188i | ||||
\(776\) | 16.3870 | − | 11.9058i | 0.588258 | − | 0.427394i | ||||
\(777\) | −1.46233 | − | 4.50059i | −0.0524608 | − | 0.161458i | ||||
\(778\) | 1.53227 | − | 4.71586i | 0.0549347 | − | 0.169072i | ||||
\(779\) | 30.2664 | + | 21.9898i | 1.08441 | + | 0.787867i | ||||
\(780\) | −26.4020 | −0.945342 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.79543 | 0.135724 | ||||||||
\(783\) | 9.05711 | + | 6.58038i | 0.323675 | + | 0.235163i | ||||
\(784\) | 0.466573 | − | 1.43596i | 0.0166633 | − | 0.0512844i | ||||
\(785\) | 7.45583 | + | 22.9467i | 0.266110 | + | 0.819002i | ||||
\(786\) | −11.4418 | + | 8.31294i | −0.408115 | + | 0.296513i | ||||
\(787\) | 10.9103 | − | 7.92683i | 0.388912 | − | 0.282561i | −0.376098 | − | 0.926580i | \(-0.622734\pi\) |
0.765009 | + | 0.644019i | \(0.222734\pi\) | |||||||
\(788\) | 0.432944 | + | 1.33246i | 0.0154230 | + | 0.0474671i | ||||
\(789\) | −9.28732 | + | 28.5834i | −0.330638 | + | 1.01760i | ||||
\(790\) | −4.71213 | − | 3.42356i | −0.167650 | − | 0.121805i | ||||
\(791\) | 1.68062 | 0.0597560 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.6704 | 0.449937 | ||||||||
\(794\) | −9.64892 | − | 7.01035i | −0.342427 | − | 0.248788i | ||||
\(795\) | 1.38823 | − | 4.27252i | 0.0492353 | − | 0.151531i | ||||
\(796\) | 7.49317 | + | 23.0616i | 0.265588 | + | 0.817397i | ||||
\(797\) | −42.4776 | + | 30.8618i | −1.50463 | + | 1.09318i | −0.536144 | + | 0.844127i | \(0.680120\pi\) |
−0.968490 | + | 0.249054i | \(0.919880\pi\) | |||||||
\(798\) | 11.4449 | − | 8.31521i | 0.405145 | − | 0.294355i | ||||
\(799\) | −2.43380 | − | 7.49046i | −0.0861016 | − | 0.264994i | ||||
\(800\) | −0.720516 | + | 2.21752i | −0.0254741 | + | 0.0784012i | ||||
\(801\) | 46.0919 | + | 33.4877i | 1.62858 | + | 1.18323i | ||||
\(802\) | 17.1983 | 0.607292 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.39443 | 0.154980 | ||||||||
\(805\) | 5.48799 | + | 3.98726i | 0.193426 | + | 0.140532i | ||||
\(806\) | 1.57070 | − | 4.83411i | 0.0553255 | − | 0.170274i | ||||
\(807\) | −4.62664 | − | 14.2393i | −0.162865 | − | 0.501248i | ||||
\(808\) | −7.74926 | + | 5.63017i | −0.272618 | + | 0.198069i | ||||
\(809\) | 1.04350 | − | 0.758150i | 0.0366877 | − | 0.0266551i | −0.569290 | − | 0.822137i | \(-0.692782\pi\) |
0.605978 | + | 0.795481i | \(0.292782\pi\) | |||||||
\(810\) | 7.74669 | + | 23.8419i | 0.272191 | + | 0.837718i | ||||
\(811\) | −10.5646 | + | 32.5145i | −0.370973 | + | 1.14174i | 0.575182 | + | 0.818025i | \(0.304931\pi\) |
−0.946155 | + | 0.323713i | \(0.895069\pi\) | |||||||
\(812\) | −1.15997 | − | 0.842765i | −0.0407068 | − | 0.0295752i | ||||
\(813\) | −62.9596 | −2.20809 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.0231 | −1.36692 | ||||||||
\(816\) | 6.86862 | + | 4.99034i | 0.240450 | + | 0.174697i | ||||
\(817\) | 17.5247 | − | 53.9353i | 0.613110 | − | 1.88696i | ||||
\(818\) | 0.276821 | + | 0.851968i | 0.00967883 | + | 0.0297884i | ||||
\(819\) | −14.0278 | + | 10.1918i | −0.490170 | + | 0.356129i | ||||
\(820\) | 14.9634 | − | 10.8715i | 0.522543 | − | 0.379650i | ||||
\(821\) | 12.2556 | + | 37.7188i | 0.427723 | + | 1.31640i | 0.900363 | + | 0.435141i | \(0.143301\pi\) |
−0.472639 | + | 0.881256i | \(0.656699\pi\) | |||||||
\(822\) | 9.01139 | − | 27.7342i | 0.314308 | − | 0.967341i | ||||
\(823\) | 7.46492 | + | 5.42358i | 0.260211 | + | 0.189054i | 0.710240 | − | 0.703960i | \(-0.248586\pi\) |
−0.450029 | + | 0.893014i | \(0.648586\pi\) | |||||||
\(824\) | 41.9241 | 1.46049 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.246707 | −0.00858403 | ||||||||
\(827\) | 20.7883 | + | 15.1036i | 0.722881 | + | 0.525204i | 0.887303 | − | 0.461186i | \(-0.152576\pi\) |
−0.164423 | + | 0.986390i | \(0.552576\pi\) | |||||||
\(828\) | 10.4041 | − | 32.0204i | 0.361566 | − | 1.11279i | ||||
\(829\) | 3.38019 | + | 10.4032i | 0.117399 | + | 0.361316i | 0.992440 | − | 0.122732i | \(-0.0391657\pi\) |
−0.875041 | + | 0.484049i | \(0.839166\pi\) | |||||||
\(830\) | 4.70593 | − | 3.41906i | 0.163345 | − | 0.118677i | ||||
\(831\) | 29.4717 | − | 21.4125i | 1.02236 | − | 0.742790i | ||||
\(832\) | 0.659072 | + | 2.02841i | 0.0228492 | + | 0.0703226i | ||||
\(833\) | −0.553425 | + | 1.70327i | −0.0191750 | + | 0.0590147i | ||||
\(834\) | −24.2779 | − | 17.6389i | −0.840674 | − | 0.610786i | ||||
\(835\) | 42.7282 | 1.47867 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.3630 | 1.25689 | ||||||||
\(838\) | −20.2981 | − | 14.7474i | −0.701185 | − | 0.509441i | ||||
\(839\) | −10.7344 | + | 33.0372i | −0.370594 | + | 1.14057i | 0.575809 | + | 0.817584i | \(0.304687\pi\) |
−0.946403 | + | 0.322987i | \(0.895313\pi\) | |||||||
\(840\) | −4.94737 | − | 15.2264i | −0.170700 | − | 0.525362i | ||||
\(841\) | 22.7705 | − | 16.5438i | 0.785190 | − | 0.570474i | ||||
\(842\) | −4.47640 | + | 3.25229i | −0.154267 | + | 0.112081i | ||||
\(843\) | 11.7194 | + | 36.0686i | 0.403637 | + | 1.24227i | ||||
\(844\) | −7.08045 | + | 21.7914i | −0.243719 | + | 0.750090i | ||||
\(845\) | 11.4604 | + | 8.32648i | 0.394250 | + | 0.286440i | ||||
\(846\) | 20.1996 | 0.694478 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.00771 | 0.0346050 | ||||||||
\(849\) | −55.8656 | − | 40.5888i | −1.91730 | − | 1.39300i | ||||
\(850\) | 0.149823 | − | 0.461108i | 0.00513888 | − | 0.0158159i | ||||
\(851\) | 1.47375 | + | 4.53573i | 0.0505194 | + | 0.155483i | ||||
\(852\) | −58.5982 | + | 42.5741i | −2.00754 | + | 1.45856i | ||||
\(853\) | 16.6999 | − | 12.1332i | 0.571795 | − | 0.415433i | −0.263962 | − | 0.964533i | \(-0.585029\pi\) |
0.835757 | + | 0.549100i | \(0.185029\pi\) | |||||||
\(854\) | 1.03719 | + | 3.19214i | 0.0354919 | + | 0.109233i | ||||
\(855\) | −30.5646 | + | 94.0681i | −1.04529 | + | 3.21706i | ||||
\(856\) | −29.6413 | − | 21.5357i | −1.01312 | − | 0.736073i | ||||
\(857\) | −34.1512 | −1.16658 | −0.583291 | − | 0.812263i | \(-0.698235\pi\) | ||||
−0.583291 | + | 0.812263i | \(0.698235\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.4493 | −1.14127 | −0.570637 | − | 0.821202i | \(-0.693304\pi\) | ||||
−0.570637 | + | 0.821202i | \(0.693304\pi\) | |||||||
\(860\) | −22.6826 | − | 16.4799i | −0.773471 | − | 0.561959i | ||||
\(861\) | 5.39556 | − | 16.6058i | 0.183880 | − | 0.565925i | ||||
\(862\) | 6.75865 | + | 20.8010i | 0.230201 | + | 0.708485i | ||||
\(863\) | 27.5341 | − | 20.0047i | 0.937271 | − | 0.680967i | −0.0104912 | − | 0.999945i | \(-0.503340\pi\) |
0.947762 | + | 0.318978i | \(0.103340\pi\) | |||||||
\(864\) | −56.5312 | + | 41.0723i | −1.92323 | + | 1.39731i | ||||
\(865\) | 3.96821 | + | 12.2129i | 0.134923 | + | 0.415251i | ||||
\(866\) | 3.26902 | − | 10.0610i | 0.111086 | − | 0.341887i | ||||
\(867\) | 35.0350 | + | 25.4544i | 1.18985 | + | 0.864478i | ||||
\(868\) | −4.65710 | −0.158072 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4.16619 | −0.141247 | ||||||||
\(871\) | 1.84522 | + | 1.34063i | 0.0625229 | + | 0.0454256i | ||||
\(872\) | 13.9113 | − | 42.8145i | 0.471095 | − | 1.44988i | ||||
\(873\) | 18.0475 | + | 55.5446i | 0.610817 | + | 1.87990i | ||||
\(874\) | −11.5343 | + | 8.38012i | −0.390152 | + | 0.283462i | ||||
\(875\) | 9.37282 | − | 6.80975i | 0.316859 | − | 0.230212i | ||||
\(876\) | −12.0997 | − | 37.2389i | −0.408810 | − | 1.25819i | ||||
\(877\) | 2.43106 | − | 7.48202i | 0.0820909 | − | 0.252650i | −0.901584 | − | 0.432604i | \(-0.857595\pi\) |
0.983675 | + | 0.179954i | \(0.0575949\pi\) | |||||||
\(878\) | 11.2128 | + | 8.14658i | 0.378414 | + | 0.274934i | ||||
\(879\) | 4.44971 | 0.150085 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.3289 | 0.449063 | 0.224531 | − | 0.974467i | \(-0.427915\pi\) | ||||
0.224531 | + | 0.974467i | \(0.427915\pi\) | |||||||
\(882\) | −3.71599 | − | 2.69983i | −0.125124 | − | 0.0909079i | ||||
\(883\) | −5.28413 | + | 16.2629i | −0.177825 | + | 0.547289i | −0.999751 | − | 0.0223048i | \(-0.992900\pi\) |
0.821926 | + | 0.569594i | \(0.192900\pi\) | |||||||
\(884\) | 2.17078 | + | 6.68098i | 0.0730113 | + | 0.224706i | ||||
\(885\) | 2.00590 | − | 1.45737i | 0.0674275 | − | 0.0489889i | ||||
\(886\) | −16.3068 | + | 11.8475i | −0.547836 | + | 0.398026i | ||||
\(887\) | −8.19466 | − | 25.2206i | −0.275150 | − | 0.846823i | −0.989180 | − | 0.146709i | \(-0.953132\pi\) |
0.714030 | − | 0.700115i | \(-0.246868\pi\) | |||||||
\(888\) | 3.47824 | − | 10.7049i | 0.116722 | − | 0.359233i | ||||
\(889\) | −14.2119 | − | 10.3256i | −0.476653 | − | 0.346309i | ||||
\(890\) | −11.9274 | −0.399808 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.86298 | 0.0958598 | ||||||||
\(893\) | 23.9349 | + | 17.3897i | 0.800950 | + | 0.581924i | ||||
\(894\) | 1.70441 | − | 5.24564i | 0.0570041 | − | 0.175441i | ||||
\(895\) | −1.07249 | − | 3.30078i | −0.0358493 | − | 0.110333i | ||||
\(896\) | 8.87628 | − | 6.44900i | 0.296536 | − | 0.215446i | ||||
\(897\) | 20.3214 | − | 14.7644i | 0.678512 | − | 0.492968i | ||||
\(898\) | 7.53227 | + | 23.1819i | 0.251355 | + | 0.773592i | ||||
\(899\) | −0.857262 | + | 2.63838i | −0.0285913 | + | 0.0879949i | ||||
\(900\) | −3.47947 | − | 2.52798i | −0.115982 | − | 0.0842661i | ||||
\(901\) | −1.19530 | −0.0398211 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.4678 | −0.880794 | ||||||||
\(904\) | 3.23401 | + | 2.34964i | 0.107561 | + | 0.0781480i | ||||
\(905\) | 1.60768 | − | 4.94793i | 0.0534411 | − | 0.164475i | ||||
\(906\) | −1.94268 | − | 5.97897i | −0.0645414 | − | 0.198638i | ||||
\(907\) | −7.16187 | + | 5.20340i | −0.237806 | + | 0.172776i | −0.700305 | − | 0.713844i | \(-0.746953\pi\) |
0.462499 | + | 0.886620i | \(0.346953\pi\) | |||||||
\(908\) | −27.5378 | + | 20.0074i | −0.913873 | + | 0.663968i | ||||
\(909\) | −8.53454 | − | 26.2666i | −0.283073 | − | 0.871208i | ||||
\(910\) | 1.12174 | − | 3.45237i | 0.0371854 | − | 0.114445i | ||||
\(911\) | 45.2239 | + | 32.8571i | 1.49834 | + | 1.08860i | 0.971039 | + | 0.238923i | \(0.0767944\pi\) |
0.527297 | + | 0.849681i | \(0.323206\pi\) | |||||||
\(912\) | −31.8921 | −1.05605 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6.55948 | −0.216968 | ||||||||
\(915\) | −27.2899 | − | 19.8273i | −0.902177 | − | 0.655470i | ||||
\(916\) | 9.70916 | − | 29.8817i | 0.320800 | − | 0.987320i | ||||
\(917\) | 2.07832 | + | 6.39640i | 0.0686320 | + | 0.211228i | ||||
\(918\) | 11.7550 | − | 8.54051i | 0.387973 | − | 0.281879i | ||||
\(919\) | −39.1383 | + | 28.4356i | −1.29105 | + | 0.938005i | −0.999826 | − | 0.0186486i | \(-0.994064\pi\) |
−0.291227 | + | 0.956654i | \(0.594064\pi\) | |||||||
\(920\) | 4.98599 | + | 15.3453i | 0.164383 | + | 0.505920i | ||||
\(921\) | 28.5878 | − | 87.9843i | 0.942001 | − | 2.89918i | ||||
\(922\) | 11.8443 | + | 8.60539i | 0.390071 | + | 0.283403i | ||||
\(923\) | −37.5937 | −1.23741 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.609223 | 0.0200311 | ||||||||
\(926\) | −3.66220 | − | 2.66074i | −0.120347 | − | 0.0874374i | ||||
\(927\) | −37.3543 | + | 114.965i | −1.22688 | + | 3.77594i | ||||
\(928\) | −1.64735 | − | 5.07001i | −0.0540768 | − | 0.166431i | ||||
\(929\) | −0.699229 | + | 0.508020i | −0.0229410 | + | 0.0166676i | −0.599197 | − | 0.800602i | \(-0.704513\pi\) |
0.576256 | + | 0.817269i | \(0.304513\pi\) | |||||||
\(930\) | −10.9477 | + | 7.95399i | −0.358990 | + | 0.260822i | ||||
\(931\) | −2.07888 | − | 6.39814i | −0.0681326 | − | 0.209691i | ||||
\(932\) | −10.0979 | + | 31.0781i | −0.330767 | + | 1.01800i | ||||
\(933\) | −68.2753 | − | 49.6049i | −2.23523 | − | 1.62399i | ||||
\(934\) | −20.1079 | −0.657949 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −41.2424 | −1.34805 | ||||||||
\(937\) | −43.2485 | − | 31.4218i | −1.41287 | − | 1.02651i | −0.992898 | − | 0.118967i | \(-0.962042\pi\) |
−0.419967 | − | 0.907539i | \(-0.637958\pi\) | |||||||
\(938\) | −0.186707 | + | 0.574624i | −0.00609619 | + | 0.0187621i | ||||
\(939\) | −4.35901 | − | 13.4157i | −0.142251 | − | 0.437804i | ||||
\(940\) | 11.8331 | − | 8.59727i | 0.385954 | − | 0.280412i | ||||
\(941\) | −11.0835 | + | 8.05265i | −0.361313 | + | 0.262509i | −0.753599 | − | 0.657334i | \(-0.771684\pi\) |
0.392287 | + | 0.919843i | \(0.371684\pi\) | |||||||
\(942\) | 7.31346 | + | 22.5085i | 0.238286 | + | 0.733367i | ||||
\(943\) | −5.43768 | + | 16.7355i | −0.177075 | + | 0.544982i | ||||
\(944\) | 0.449953 | + | 0.326910i | 0.0146447 | + | 0.0106400i | ||||
\(945\) | 25.9693 | 0.844781 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.6444 | 1.02830 | 0.514152 | − | 0.857699i | \(-0.328107\pi\) | ||||
0.514152 | + | 0.857699i | \(0.328107\pi\) | |||||||
\(948\) | 15.9868 | + | 11.6151i | 0.519228 | + | 0.377241i | ||||
\(949\) | 6.28002 | − | 19.3279i | 0.203858 | − | 0.627411i | ||||
\(950\) | 0.562794 | + | 1.73210i | 0.0182594 | + | 0.0561968i | ||||
\(951\) | 27.8146 | − | 20.2085i | 0.901949 | − | 0.655305i | ||||
\(952\) | −3.44625 | + | 2.50385i | −0.111694 | + | 0.0811503i | ||||
\(953\) | 10.1166 | + | 31.1356i | 0.327708 | + | 1.00858i | 0.970203 | + | 0.242292i | \(0.0778993\pi\) |
−0.642495 | + | 0.766290i | \(0.722101\pi\) | |||||||
\(954\) | 0.947326 | − | 2.91557i | 0.0306708 | − | 0.0943951i | ||||
\(955\) | −22.0279 | − | 16.0042i | −0.712806 | − | 0.517884i | ||||
\(956\) | −24.0420 | −0.777573 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.02083 | −0.129907 | ||||||||
\(959\) | −11.2191 | − | 8.15119i | −0.362285 | − | 0.263216i | ||||
\(960\) | 1.75464 | − | 5.40024i | 0.0566309 | − | 0.174292i | ||||
\(961\) | −6.79507 | − | 20.9131i | −0.219196 | − | 0.674615i | ||||
\(962\) | 2.06468 | − | 1.50008i | 0.0665681 | − | 0.0483645i | ||||
\(963\) | 85.4657 | − | 62.0945i | 2.75409 | − | 2.00097i | ||||
\(964\) | −6.75258 | − | 20.7823i | −0.217486 | − | 0.669353i | ||||
\(965\) | −1.16548 | + | 3.58698i | −0.0375181 | + | 0.115469i | ||||
\(966\) | 5.38320 | + | 3.91112i | 0.173202 | + | 0.125838i | ||||
\(967\) | −32.3487 | −1.04026 | −0.520132 | − | 0.854086i | \(-0.674117\pi\) | ||||
−0.520132 | + | 0.854086i | \(0.674117\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.8287 | 1.21523 | ||||||||
\(970\) | −9.89176 | − | 7.18678i | −0.317605 | − | 0.230754i | ||||
\(971\) | −9.09344 | + | 27.9867i | −0.291823 | + | 0.898137i | 0.692448 | + | 0.721468i | \(0.256532\pi\) |
−0.984270 | + | 0.176669i | \(0.943468\pi\) | |||||||
\(972\) | −8.85934 | − | 27.2662i | −0.284163 | − | 0.874565i | ||||
\(973\) | −11.5453 | + | 8.38812i | −0.370124 | + | 0.268911i | ||||
\(974\) | −3.44998 | + | 2.50656i | −0.110545 | + | 0.0803153i | ||||
\(975\) | −0.991548 | − | 3.05167i | −0.0317550 | − | 0.0977317i | ||||
\(976\) | 2.33822 | − | 7.19631i | 0.0748447 | − | 0.230348i | ||||
\(977\) | −11.0790 | − | 8.04939i | −0.354450 | − | 0.257523i | 0.396284 | − | 0.918128i | \(-0.370300\pi\) |
−0.750733 | + | 0.660605i | \(0.770300\pi\) | |||||||
\(978\) | −38.2780 | −1.22399 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.32595 | −0.106244 | ||||||||
\(981\) | 105.012 | + | 76.2954i | 3.35276 | + | 2.43592i | ||||
\(982\) | 2.56155 | − | 7.88364i | 0.0817423 | − | 0.251577i | ||||
\(983\) | 5.26316 | + | 16.1983i | 0.167869 | + | 0.516647i | 0.999236 | − | 0.0390763i | \(-0.0124415\pi\) |
−0.831368 | + | 0.555723i | \(0.812442\pi\) | |||||||
\(984\) | 33.5989 | − | 24.4111i | 1.07109 | − | 0.778196i | ||||
\(985\) | 1.56621 | − | 1.13792i | 0.0499037 | − | 0.0362572i | ||||
\(986\) | 0.342546 | + | 1.05425i | 0.0109089 | + | 0.0335741i | ||||
\(987\) | 4.26685 | − | 13.1320i | 0.135815 | − | 0.417996i | ||||
\(988\) | −21.3483 | − | 15.5104i | −0.679179 | − | 0.493453i | ||||
\(989\) | 26.6744 | 0.848198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.2202 | 0.737614 | 0.368807 | − | 0.929506i | \(-0.379766\pi\) | ||||
0.368807 | + | 0.929506i | \(0.379766\pi\) | |||||||
\(992\) | −14.0084 | − | 10.1777i | −0.444766 | − | 0.323141i | ||||
\(993\) | 16.0310 | − | 49.3383i | 0.508728 | − | 1.56570i | ||||
\(994\) | −3.07740 | − | 9.47126i | −0.0976091 | − | 0.300410i | ||||
\(995\) | 27.1072 | − | 19.6946i | 0.859357 | − | 0.624359i | ||||
\(996\) | −15.9658 | + | 11.5998i | −0.505896 | + | 0.367555i | ||||
\(997\) | −5.67899 | − | 17.4781i | −0.179855 | − | 0.553538i | 0.819966 | − | 0.572412i | \(-0.193992\pi\) |
−0.999822 | + | 0.0188734i | \(0.993992\pi\) | |||||||
\(998\) | −2.95535 | + | 9.09563i | −0.0935499 | + | 0.287917i | ||||
\(999\) | 14.7708 | + | 10.7316i | 0.467326 | + | 0.339532i |
(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 | 847.2.f.w.323.2 | 16 | ||
11.2 | odd | 10 | 847.2.f.x.148.2 | 16 | |||
11.3 | even | 5 | inner | 847.2.f.w.729.2 | 16 | ||
11.4 | even | 5 | 77.2.f.b.64.3 | ✓ | 16 | ||
11.5 | even | 5 | 847.2.a.p.1.5 | 8 | |||
11.6 | odd | 10 | 847.2.a.o.1.4 | 8 | |||
11.7 | odd | 10 | 847.2.f.x.372.2 | 16 | |||
11.8 | odd | 10 | 847.2.f.v.729.3 | 16 | |||
11.9 | even | 5 | 77.2.f.b.71.3 | yes | 16 | ||
11.10 | odd | 2 | 847.2.f.v.323.3 | 16 | |||
33.5 | odd | 10 | 7623.2.a.ct.1.4 | 8 | |||
33.17 | even | 10 | 7623.2.a.cw.1.5 | 8 | |||
33.20 | odd | 10 | 693.2.m.i.379.2 | 16 | |||
33.26 | odd | 10 | 693.2.m.i.64.2 | 16 | |||
77.4 | even | 15 | 539.2.q.g.471.3 | 32 | |||
77.6 | even | 10 | 5929.2.a.bs.1.4 | 8 | |||
77.9 | even | 15 | 539.2.q.g.214.3 | 32 | |||
77.20 | odd | 10 | 539.2.f.e.148.3 | 16 | |||
77.26 | odd | 30 | 539.2.q.f.361.2 | 32 | |||
77.27 | odd | 10 | 5929.2.a.bt.1.5 | 8 | |||
77.31 | odd | 30 | 539.2.q.f.324.2 | 32 | |||
77.37 | even | 15 | 539.2.q.g.361.2 | 32 | |||
77.48 | odd | 10 | 539.2.f.e.295.3 | 16 | |||
77.53 | even | 15 | 539.2.q.g.324.2 | 32 | |||
77.59 | odd | 30 | 539.2.q.f.471.3 | 32 | |||
77.75 | odd | 30 | 539.2.q.f.214.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.64.3 | ✓ | 16 | 11.4 | even | 5 | ||
77.2.f.b.71.3 | yes | 16 | 11.9 | even | 5 | ||
539.2.f.e.148.3 | 16 | 77.20 | odd | 10 | |||
539.2.f.e.295.3 | 16 | 77.48 | odd | 10 | |||
539.2.q.f.214.3 | 32 | 77.75 | odd | 30 | |||
539.2.q.f.324.2 | 32 | 77.31 | odd | 30 | |||
539.2.q.f.361.2 | 32 | 77.26 | odd | 30 | |||
539.2.q.f.471.3 | 32 | 77.59 | odd | 30 | |||
539.2.q.g.214.3 | 32 | 77.9 | even | 15 | |||
539.2.q.g.324.2 | 32 | 77.53 | even | 15 | |||
539.2.q.g.361.2 | 32 | 77.37 | even | 15 | |||
539.2.q.g.471.3 | 32 | 77.4 | even | 15 | |||
693.2.m.i.64.2 | 16 | 33.26 | odd | 10 | |||
693.2.m.i.379.2 | 16 | 33.20 | odd | 10 | |||
847.2.a.o.1.4 | 8 | 11.6 | odd | 10 | |||
847.2.a.p.1.5 | 8 | 11.5 | even | 5 | |||
847.2.f.v.323.3 | 16 | 11.10 | odd | 2 | |||
847.2.f.v.729.3 | 16 | 11.8 | odd | 10 | |||
847.2.f.w.323.2 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.w.729.2 | 16 | 11.3 | even | 5 | inner | ||
847.2.f.x.148.2 | 16 | 11.2 | odd | 10 | |||
847.2.f.x.372.2 | 16 | 11.7 | odd | 10 | |||
5929.2.a.bs.1.4 | 8 | 77.6 | even | 10 | |||
5929.2.a.bt.1.5 | 8 | 77.27 | odd | 10 | |||
7623.2.a.ct.1.4 | 8 | 33.5 | odd | 10 | |||
7623.2.a.cw.1.5 | 8 | 33.17 | even | 10 |