Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1079,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1079");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.e (of order \(2\), degree \(1\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{12} - 10x^{10} + 4x^{8} - 40x^{6} + 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1079.13 | ||
Root | \(-1.13008 + 0.850247i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1079 |
Dual form | 1764.2.e.h.1079.14 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13008 | − | 0.850247i | 0.799087 | − | 0.601215i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.554161 | − | 1.92169i | 0.277081 | − | 0.960847i | ||||
\(5\) | − | 3.87147i | − | 1.73137i | −0.500586 | − | 0.865687i | \(-0.666882\pi\) | ||
0.500586 | − | 0.865687i | \(-0.333118\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00767 | − | 2.64284i | −0.356264 | − | 0.934385i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.29170 | − | 4.37507i | −1.04093 | − | 1.38352i | ||||
\(11\) | 3.46960 | 1.04612 | 0.523061 | − | 0.852295i | \(-0.324790\pi\) | ||||
0.523061 | + | 0.852295i | \(0.324790\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.296538 | 0.0822448 | 0.0411224 | − | 0.999154i | \(-0.486907\pi\) | ||||
0.0411224 | + | 0.999154i | \(0.486907\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.38581 | − | 2.12986i | −0.846453 | − | 0.532464i | ||||
\(17\) | 1.56741i | 0.380152i | 0.981769 | + | 0.190076i | \(0.0608734\pi\) | ||||
−0.981769 | + | 0.190076i | \(0.939127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.07478i | − | 1.62307i | −0.584307 | − | 0.811533i | \(-0.698633\pi\) | ||
0.584307 | − | 0.811533i | \(-0.301367\pi\) | |||||||
\(20\) | −7.43977 | − | 2.14542i | −1.66358 | − | 0.479730i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.92092 | − | 2.95001i | 0.835943 | − | 0.628945i | ||||
\(23\) | 5.43537 | 1.13335 | 0.566676 | − | 0.823940i | \(-0.308229\pi\) | ||||
0.566676 | + | 0.823940i | \(0.308229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.98827 | −1.99765 | ||||||||
\(26\) | 0.335112 | − | 0.252130i | 0.0657208 | − | 0.0494468i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.85309i | 1.27259i | 0.771447 | + | 0.636293i | \(0.219533\pi\) | ||||
−0.771447 | + | 0.636293i | \(0.780467\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.81507i | − | 0.505601i | −0.967518 | − | 0.252800i | \(-0.918648\pi\) | ||
0.967518 | − | 0.252800i | \(-0.0813516\pi\) | |||||||
\(32\) | −5.63714 | + | 0.471866i | −0.996515 | + | 0.0834149i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.33268 | + | 1.77129i | 0.228553 | + | 0.303774i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51318 | 0.413165 | 0.206582 | − | 0.978429i | \(-0.433766\pi\) | ||||
0.206582 | + | 0.978429i | \(0.433766\pi\) | |||||||
\(38\) | −6.01531 | − | 7.99507i | −0.975812 | − | 1.29697i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.2317 | + | 3.90115i | −1.61777 | + | 0.616826i | ||||
\(41\) | 3.55418i | 0.555069i | 0.960716 | + | 0.277535i | \(0.0895173\pi\) | ||||
−0.960716 | + | 0.277535i | \(0.910483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.682082i | 0.104017i | 0.998647 | + | 0.0520083i | \(0.0165622\pi\) | ||||
−0.998647 | + | 0.0520083i | \(0.983438\pi\) | |||||||
\(44\) | 1.92272 | − | 6.66750i | 0.289860 | − | 1.00516i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.14240 | − | 4.62140i | 0.905648 | − | 0.681389i | ||||
\(47\) | −2.36931 | −0.345600 | −0.172800 | − | 0.984957i | \(-0.555281\pi\) | ||||
−0.172800 | + | 0.984957i | \(0.555281\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −11.2875 | + | 8.49249i | −1.59630 | + | 1.20102i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.164330 | − | 0.569855i | 0.0227884 | − | 0.0790247i | ||||
\(53\) | 0.623673i | 0.0856681i | 0.999082 | + | 0.0428340i | \(0.0136387\pi\) | ||||
−0.999082 | + | 0.0428340i | \(0.986361\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 13.4324i | − | 1.81123i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.82681 | + | 7.74454i | 0.765098 | + | 1.01691i | ||||
\(59\) | −8.85541 | −1.15288 | −0.576438 | − | 0.817141i | \(-0.695558\pi\) | ||||
−0.576438 | + | 0.817141i | \(0.695558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.66536 | −0.341265 | −0.170632 | − | 0.985335i | \(-0.554581\pi\) | ||||
−0.170632 | + | 0.985335i | \(0.554581\pi\) | |||||||
\(62\) | −2.39350 | − | 3.18125i | −0.303975 | − | 0.404019i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.96922 | + | 5.32621i | −0.746152 | + | 0.665776i | ||||
\(65\) | − | 1.14804i | − | 0.142396i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6174i | 1.29712i | 0.761165 | + | 0.648559i | \(0.224628\pi\) | ||||
−0.761165 | + | 0.648559i | \(0.775372\pi\) | |||||||
\(68\) | 3.01207 | + | 0.868595i | 0.365267 | + | 0.105333i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.539214 | 0.0639929 | 0.0319964 | − | 0.999488i | \(-0.489813\pi\) | ||||
0.0319964 | + | 0.999488i | \(0.489813\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.39519 | −0.865542 | −0.432771 | − | 0.901504i | \(-0.642464\pi\) | ||||
−0.432771 | + | 0.901504i | \(0.642464\pi\) | |||||||
\(74\) | 2.84010 | − | 2.13683i | 0.330155 | − | 0.248401i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.5956 | − | 3.92057i | −1.55952 | − | 0.449720i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.16578i | 0.693705i | 0.937920 | + | 0.346852i | \(0.112749\pi\) | ||||
−0.937920 | + | 0.346852i | \(0.887251\pi\) | |||||||
\(80\) | −8.24567 | + | 13.1081i | −0.921894 | + | 1.46553i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.02193 | + | 4.01651i | 0.333716 | + | 0.443549i | ||||
\(83\) | 6.15982 | 0.676128 | 0.338064 | − | 0.941123i | \(-0.390228\pi\) | ||||
0.338064 | + | 0.941123i | \(0.390228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.06816 | 0.658184 | ||||||||
\(86\) | 0.579938 | + | 0.770808i | 0.0625363 | + | 0.0831183i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.49620 | − | 9.16959i | −0.372696 | − | 0.977482i | ||||
\(89\) | 11.7165i | 1.24194i | 0.783832 | + | 0.620972i | \(0.213262\pi\) | ||||
−0.783832 | + | 0.620972i | \(0.786738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.01207 | − | 10.4451i | 0.314030 | − | 1.08898i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.67751 | + | 2.01450i | −0.276164 | + | 0.207780i | ||||
\(95\) | −27.3898 | −2.81013 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.84782 | 0.695291 | 0.347645 | − | 0.937626i | \(-0.386981\pi\) | ||||
0.347645 | + | 0.937626i | \(0.386981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.53511 | + | 19.1944i | −0.553511 | + | 1.91944i | ||||
\(101\) | 3.55418i | 0.353654i | 0.984242 | + | 0.176827i | \(0.0565833\pi\) | ||||
−0.984242 | + | 0.176827i | \(0.943417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.09794i | − | 0.206716i | −0.994644 | − | 0.103358i | \(-0.967041\pi\) | ||
0.994644 | − | 0.103358i | \(-0.0329588\pi\) | |||||||
\(104\) | −0.298811 | − | 0.783703i | −0.0293009 | − | 0.0768484i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.530276 | + | 0.704801i | 0.0515050 | + | 0.0684563i | ||||
\(107\) | 11.0560 | 1.06882 | 0.534411 | − | 0.845225i | \(-0.320534\pi\) | ||||
0.534411 | + | 0.845225i | \(0.320534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.3190 | 1.27573 | 0.637864 | − | 0.770149i | \(-0.279818\pi\) | ||||
0.637864 | + | 0.770149i | \(0.279818\pi\) | |||||||
\(110\) | −11.4209 | − | 15.1797i | −1.08894 | − | 1.44733i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.75101i | − | 0.635082i | −0.948245 | − | 0.317541i | \(-0.897143\pi\) | ||
0.948245 | − | 0.317541i | \(-0.102857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 21.0429i | − | 1.96226i | ||||||
\(116\) | 13.1695 | + | 3.79772i | 1.22276 | + | 0.352609i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.0073 | + | 7.52928i | −0.921248 | + | 0.693126i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.03810 | 0.0943728 | ||||||||
\(122\) | −3.01207 | + | 2.26621i | −0.272700 | + | 0.205173i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.40970 | − | 1.56000i | −0.485805 | − | 0.140092i | ||||
\(125\) | 19.3119i | 1.72731i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 20.3153i | − | 1.80270i | −0.433097 | − | 0.901348i | \(-0.642579\pi\) | ||
0.433097 | − | 0.901348i | \(-0.357421\pi\) | |||||||
\(128\) | −2.21710 | + | 11.0943i | −0.195966 | + | 0.980611i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.976115 | − | 1.29737i | −0.0856109 | − | 0.113787i | ||||
\(131\) | 17.2489 | 1.50704 | 0.753520 | − | 0.657425i | \(-0.228354\pi\) | ||||
0.753520 | + | 0.657425i | \(0.228354\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.02738 | + | 11.9985i | 0.779847 | + | 1.03651i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.14240 | − | 1.57942i | 0.355208 | − | 0.135434i | ||||
\(137\) | − | 16.6310i | − | 1.42088i | −0.703757 | − | 0.710441i | \(-0.748496\pi\) | ||
0.703757 | − | 0.710441i | \(-0.251504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.2475i | − | 1.37809i | −0.724716 | − | 0.689047i | \(-0.758029\pi\) | ||
0.724716 | − | 0.689047i | \(-0.241971\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.609354 | − | 0.458465i | 0.0511359 | − | 0.0384735i | ||||
\(143\) | 1.02887 | 0.0860382 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26.5315 | 2.20332 | ||||||||
\(146\) | −8.35716 | + | 6.28774i | −0.691643 | + | 0.520377i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.39271 | − | 4.82957i | 0.114480 | − | 0.396988i | ||||
\(149\) | 5.65685i | 0.463428i | 0.972784 | + | 0.231714i | \(0.0744333\pi\) | ||||
−0.972784 | + | 0.231714i | \(0.925567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.99775i | − | 0.325332i | −0.986681 | − | 0.162666i | \(-0.947991\pi\) | ||
0.986681 | − | 0.162666i | \(-0.0520094\pi\) | |||||||
\(152\) | −18.6975 | + | 7.12902i | −1.51657 | + | 0.578240i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.8984 | −0.875384 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9502 | 0.873918 | 0.436959 | − | 0.899481i | \(-0.356055\pi\) | ||||
0.436959 | + | 0.899481i | \(0.356055\pi\) | |||||||
\(158\) | 5.24244 | + | 6.96783i | 0.417066 | + | 0.554331i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.82681 | + | 21.8240i | 0.144422 | + | 1.72534i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.0429i | − | 1.64820i | −0.566441 | − | 0.824102i | \(-0.691680\pi\) | ||
0.566441 | − | 0.824102i | \(-0.308320\pi\) | |||||||
\(164\) | 6.83004 | + | 1.96959i | 0.533337 | + | 0.153799i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.96109 | − | 5.23736i | 0.540285 | − | 0.406498i | ||||
\(167\) | −8.39346 | −0.649505 | −0.324753 | − | 0.945799i | \(-0.605281\pi\) | ||||
−0.324753 | + | 0.945799i | \(0.605281\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9121 | −0.993236 | ||||||||
\(170\) | 6.85750 | − | 5.15943i | 0.525947 | − | 0.395710i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.31075 | + | 0.377984i | 0.0999440 | + | 0.0288210i | ||||
\(173\) | 15.0211i | 1.14203i | 0.820939 | + | 0.571016i | \(0.193450\pi\) | ||||
−0.820939 | + | 0.571016i | \(0.806550\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.7474 | − | 7.38974i | −0.885493 | − | 0.557023i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.96190 | + | 13.2406i | 0.746676 | + | 0.992422i | ||||
\(179\) | −2.57640 | −0.192569 | −0.0962847 | − | 0.995354i | \(-0.530696\pi\) | ||||
−0.0962847 | + | 0.995354i | \(0.530696\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.3412 | 1.66061 | 0.830305 | − | 0.557309i | \(-0.188166\pi\) | ||||
0.830305 | + | 0.557309i | \(0.188166\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.47704 | − | 14.3648i | −0.403773 | − | 1.05899i | ||||
\(185\) | − | 9.72971i | − | 0.715342i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.43826i | 0.397685i | ||||||||
\(188\) | −1.31298 | + | 4.55309i | −0.0957590 | + | 0.332068i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −30.9526 | + | 23.2881i | −2.24554 | + | 1.68949i | ||||
\(191\) | 8.29434 | 0.600157 | 0.300079 | − | 0.953914i | \(-0.402987\pi\) | ||||
0.300079 | + | 0.953914i | \(0.402987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.3530 | −1.53702 | −0.768510 | − | 0.639838i | \(-0.779002\pi\) | ||||
−0.768510 | + | 0.639838i | \(0.779002\pi\) | |||||||
\(194\) | 7.73859 | − | 5.82234i | 0.555598 | − | 0.418019i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.572559i | − | 0.0407932i | −0.999792 | − | 0.0203966i | \(-0.993507\pi\) | ||
0.999792 | − | 0.0203966i | \(-0.00649288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.5003i | 1.24056i | 0.784380 | + | 0.620281i | \(0.212981\pi\) | ||||
−0.784380 | + | 0.620281i | \(0.787019\pi\) | |||||||
\(200\) | 10.0648 | + | 26.3974i | 0.711692 | + | 1.86658i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.02193 | + | 4.01651i | 0.212622 | + | 0.282600i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.7599 | 0.961032 | ||||||||
\(206\) | −1.78377 | − | 2.37084i | −0.124281 | − | 0.165184i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00402 | − | 0.631583i | −0.0696163 | − | 0.0437924i | ||||
\(209\) | − | 24.5466i | − | 1.69793i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.94873i | − | 0.547213i | −0.961842 | − | 0.273607i | \(-0.911783\pi\) | ||
0.961842 | − | 0.273607i | \(-0.0882167\pi\) | |||||||
\(212\) | 1.19851 | + | 0.345616i | 0.0823139 | + | 0.0237370i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.4941 | − | 9.40030i | 0.854081 | − | 0.642592i | ||||
\(215\) | 2.64066 | 0.180092 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 15.0515 | − | 11.3244i | 1.01942 | − | 0.766987i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −25.8130 | − | 7.44374i | −1.74031 | − | 0.501857i | ||||
\(221\) | 0.464795i | 0.0312655i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.17855i | 0.0789216i | 0.999221 | + | 0.0394608i | \(0.0125640\pi\) | ||||
−0.999221 | + | 0.0394608i | \(0.987436\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.74002 | − | 7.62918i | −0.381821 | − | 0.507486i | ||||
\(227\) | −4.54802 | −0.301863 | −0.150931 | − | 0.988544i | \(-0.548227\pi\) | ||||
−0.150931 | + | 0.988544i | \(0.548227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1287 | −1.06582 | −0.532908 | − | 0.846173i | \(-0.678901\pi\) | ||||
−0.532908 | + | 0.846173i | \(0.678901\pi\) | |||||||
\(230\) | −17.8916 | − | 23.7801i | −1.17974 | − | 1.56801i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.1116 | − | 6.90563i | 1.18909 | − | 0.453377i | ||||
\(233\) | − | 8.27821i | − | 0.542323i | −0.962534 | − | 0.271162i | \(-0.912592\pi\) | ||
0.962534 | − | 0.271162i | \(-0.0874078\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.17272i | 0.598362i | ||||||||
\(236\) | −4.90732 | + | 17.0174i | −0.319440 | + | 1.10774i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.1308 | 1.17279 | 0.586393 | − | 0.810027i | \(-0.300547\pi\) | ||||
0.586393 | + | 0.810027i | \(0.300547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4216 | 1.25105 | 0.625526 | − | 0.780203i | \(-0.284884\pi\) | ||||
0.625526 | + | 0.780203i | \(0.284884\pi\) | |||||||
\(242\) | 1.17314 | − | 0.882641i | 0.0754121 | − | 0.0567383i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.47704 | + | 5.12201i | −0.0945578 | + | 0.327903i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.09794i | − | 0.133489i | ||||||
\(248\) | −7.43977 | + | 2.83665i | −0.472426 | + | 0.180127i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.4199 | + | 21.8240i | 1.03849 | + | 1.38027i | ||||
\(251\) | 13.8654 | 0.875175 | 0.437587 | − | 0.899176i | \(-0.355833\pi\) | ||||
0.437587 | + | 0.899176i | \(0.355833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.8585 | 1.18563 | ||||||||
\(254\) | −17.2731 | − | 22.9580i | −1.08381 | − | 1.44051i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.92742 | + | 14.4226i | 0.432964 | + | 0.901411i | ||||
\(257\) | − | 7.69751i | − | 0.480157i | −0.970753 | − | 0.240079i | \(-0.922827\pi\) | ||
0.970753 | − | 0.240079i | \(-0.0771733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.20618 | − | 0.636198i | −0.136821 | − | 0.0394553i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.4926 | − | 14.6658i | 1.20426 | − | 0.906055i | ||||
\(263\) | 10.0548 | 0.620006 | 0.310003 | − | 0.950736i | \(-0.399670\pi\) | ||||
0.310003 | + | 0.950736i | \(0.399670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.41453 | 0.148323 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 20.4033 | + | 5.88373i | 1.24633 | + | 0.359406i | ||||
\(269\) | 28.1088i | 1.71382i | 0.515463 | + | 0.856912i | \(0.327620\pi\) | ||||
−0.515463 | + | 0.856912i | \(0.672380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 25.3026i | − | 1.53702i | −0.639837 | − | 0.768511i | \(-0.720998\pi\) | ||
0.639837 | − | 0.768511i | \(-0.279002\pi\) | |||||||
\(272\) | 3.33835 | − | 5.30694i | 0.202417 | − | 0.321780i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.1404 | − | 18.7944i | −0.854255 | − | 1.13541i | ||||
\(275\) | −34.6553 | −2.08979 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.52861 | 0.151929 | 0.0759647 | − | 0.997111i | \(-0.475796\pi\) | ||||
0.0759647 | + | 0.997111i | \(0.475796\pi\) | |||||||
\(278\) | −13.8144 | − | 18.3610i | −0.828532 | − | 1.10122i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.00911i | − | 0.477784i | −0.971046 | − | 0.238892i | \(-0.923216\pi\) | ||
0.971046 | − | 0.238892i | \(-0.0767841\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.07478i | 0.420552i | 0.977642 | + | 0.210276i | \(0.0674363\pi\) | ||||
−0.977642 | + | 0.210276i | \(0.932564\pi\) | |||||||
\(284\) | 0.298811 | − | 1.03620i | 0.0177312 | − | 0.0614873i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.16270 | − | 0.874791i | 0.0687520 | − | 0.0517275i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.5432 | 0.855485 | ||||||||
\(290\) | 29.9827 | − | 22.5583i | 1.76065 | − | 1.32467i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.09813 | + | 14.2113i | −0.239825 | + | 0.831653i | ||||
\(293\) | 19.9465i | 1.16529i | 0.812728 | + | 0.582643i | \(0.197982\pi\) | ||||
−0.812728 | + | 0.582643i | \(0.802018\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.2834i | 1.99606i | ||||||||
\(296\) | −2.53245 | − | 6.64194i | −0.147196 | − | 0.386055i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.80972 | + | 6.39270i | 0.278620 | + | 0.370319i | ||||
\(299\) | 1.61179 | 0.0932124 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.39908 | − | 4.51778i | −0.195595 | − | 0.259969i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.0683 | + | 23.9539i | −0.864224 | + | 1.37385i | ||||
\(305\) | 10.3189i | 0.590856i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.4255i | − | 0.595014i | −0.954720 | − | 0.297507i | \(-0.903845\pi\) | ||
0.954720 | − | 0.297507i | \(-0.0961552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.3161 | + | 9.26636i | −0.699508 | + | 0.526294i | ||||
\(311\) | 22.7061 | 1.28754 | 0.643772 | − | 0.765217i | \(-0.277368\pi\) | ||||
0.643772 | + | 0.765217i | \(0.277368\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.3835 | 1.26519 | 0.632594 | − | 0.774484i | \(-0.281990\pi\) | ||||
0.632594 | + | 0.774484i | \(0.281990\pi\) | |||||||
\(314\) | 12.3746 | − | 9.31034i | 0.698337 | − | 0.525413i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.8487 | + | 3.41684i | 0.666544 | + | 0.192212i | ||||
\(317\) | 29.1409i | 1.63672i | 0.574707 | + | 0.818359i | \(0.305116\pi\) | ||||
−0.574707 | + | 0.818359i | \(0.694884\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.7774i | 1.33128i | ||||||||
\(320\) | 20.6202 | + | 23.1096i | 1.15271 | + | 1.29187i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.0890 | 0.617011 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.96190 | −0.164297 | ||||||||
\(326\) | −17.8916 | − | 23.7801i | −0.990925 | − | 1.31706i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.39313 | − | 3.58143i | 0.518649 | − | 0.197751i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.4309i | 1.12298i | 0.827483 | + | 0.561491i | \(0.189772\pi\) | ||||
−0.827483 | + | 0.561491i | \(0.810228\pi\) | |||||||
\(332\) | 3.41353 | − | 11.8373i | 0.187342 | − | 0.649655i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.48528 | + | 7.13651i | −0.519011 | + | 0.390492i | ||||
\(335\) | 41.1048 | 2.24579 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.16681 | −0.335928 | −0.167964 | − | 0.985793i | \(-0.553719\pi\) | ||||
−0.167964 | + | 0.985793i | \(0.553719\pi\) | |||||||
\(338\) | −14.5917 | + | 10.9784i | −0.793682 | + | 0.597148i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.36274 | − | 11.6611i | 0.182370 | − | 0.632414i | ||||
\(341\) | − | 9.76715i | − | 0.528921i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.80264 | − | 0.687312i | 0.0971916 | − | 0.0370574i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.7716 | + | 16.9750i | 0.686607 | + | 0.912583i | ||||
\(347\) | 15.1197 | 0.811669 | 0.405834 | − | 0.913947i | \(-0.366981\pi\) | ||||
0.405834 | + | 0.913947i | \(0.366981\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.8933 | −1.01134 | −0.505668 | − | 0.862728i | \(-0.668754\pi\) | ||||
−0.505668 | + | 0.862728i | \(0.668754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.5586 | + | 1.63718i | −1.04248 | + | 0.0872622i | ||||
\(353\) | − | 10.6282i | − | 0.565680i | −0.959167 | − | 0.282840i | \(-0.908723\pi\) | ||
0.959167 | − | 0.282840i | \(-0.0912766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.08755i | − | 0.110796i | ||||||
\(356\) | 22.5155 | + | 6.49282i | 1.19332 | + | 0.344119i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.91154 | + | 2.19058i | −0.153880 | + | 0.115776i | ||||
\(359\) | −2.80941 | −0.148275 | −0.0741374 | − | 0.997248i | \(-0.523620\pi\) | ||||
−0.0741374 | + | 0.997248i | \(0.523620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.0525 | −1.63434 | ||||||||
\(362\) | 25.2474 | − | 18.9956i | 1.32697 | − | 0.998384i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.6302i | 1.49858i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.8811i | 0.985585i | 0.870147 | + | 0.492792i | \(0.164024\pi\) | ||||
−0.870147 | + | 0.492792i | \(0.835976\pi\) | |||||||
\(368\) | −18.4031 | − | 11.5766i | −0.959329 | − | 0.603470i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.27265 | − | 10.9953i | −0.430075 | − | 0.571621i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.5884 | −1.73914 | −0.869570 | − | 0.493810i | \(-0.835604\pi\) | ||||
−0.869570 | + | 0.493810i | \(0.835604\pi\) | |||||||
\(374\) | 4.62386 | + | 6.14567i | 0.239094 | + | 0.317785i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.38748 | + | 6.26172i | 0.123125 | + | 0.322923i | ||||
\(377\) | 2.03220i | 0.104664i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.57538i | − | 0.389121i | −0.980890 | − | 0.194561i | \(-0.937672\pi\) | ||
0.980890 | − | 0.194561i | \(-0.0623281\pi\) | |||||||
\(380\) | −15.1784 | + | 52.6348i | −0.778633 | + | 2.70011i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.37326 | − | 7.05223i | 0.479578 | − | 0.360824i | ||||
\(383\) | −36.3809 | −1.85898 | −0.929488 | − | 0.368853i | \(-0.879751\pi\) | ||||
−0.929488 | + | 0.368853i | \(0.879751\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.1306 | + | 18.1553i | −1.22821 | + | 0.924080i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.79480 | − | 13.1594i | 0.192652 | − | 0.668068i | ||||
\(389\) | − | 3.41758i | − | 0.173278i | −0.996240 | − | 0.0866391i | \(-0.972387\pi\) | ||
0.996240 | − | 0.0866391i | \(-0.0276127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.51943i | 0.430846i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.486817 | − | 0.647038i | −0.0245255 | − | 0.0325973i | ||||
\(395\) | 23.8706 | 1.20106 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.7716 | −0.992309 | −0.496155 | − | 0.868234i | \(-0.665255\pi\) | ||||
−0.496155 | + | 0.868234i | \(0.665255\pi\) | |||||||
\(398\) | 14.8795 | + | 19.7767i | 0.745844 | + | 0.991317i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 33.8184 | + | 21.2736i | 1.69092 | + | 1.06368i | ||||
\(401\) | 3.80960i | 0.190242i | 0.995466 | + | 0.0951211i | \(0.0303238\pi\) | ||||
−0.995466 | + | 0.0951211i | \(0.969676\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.834774i | − | 0.0415831i | ||||||
\(404\) | 6.83004 | + | 1.96959i | 0.339807 | + | 0.0979907i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.71973 | 0.432221 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.4934 | −1.45836 | −0.729178 | − | 0.684325i | \(-0.760097\pi\) | ||||
−0.729178 | + | 0.684325i | \(0.760097\pi\) | |||||||
\(410\) | 15.5498 | − | 11.6993i | 0.767949 | − | 0.577787i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.03160 | − | 1.16260i | −0.198623 | − | 0.0572771i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 23.8475i | − | 1.17063i | ||||||
\(416\) | −1.67163 | + | 0.139926i | −0.0819582 | + | 0.00686044i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.8707 | − | 27.7397i | −1.02082 | − | 1.35679i | ||||
\(419\) | 4.99528 | 0.244035 | 0.122018 | − | 0.992528i | \(-0.461064\pi\) | ||||
0.122018 | + | 0.992528i | \(0.461064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.51318 | −0.219959 | −0.109980 | − | 0.993934i | \(-0.535079\pi\) | ||||
−0.109980 | + | 0.993934i | \(0.535079\pi\) | |||||||
\(422\) | −6.75838 | − | 8.98270i | −0.328993 | − | 0.437271i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.64827 | − | 0.628455i | 0.0800470 | − | 0.0305205i | ||||
\(425\) | − | 15.6557i | − | 0.759411i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.12679 | − | 21.2462i | 0.296150 | − | 1.02697i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.98416 | − | 2.24521i | 0.143909 | − | 0.108274i | ||||
\(431\) | 20.2872 | 0.977201 | 0.488600 | − | 0.872508i | \(-0.337508\pi\) | ||||
0.488600 | + | 0.872508i | \(0.337508\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.34123 | −0.400854 | −0.200427 | − | 0.979709i | \(-0.564233\pi\) | ||||
−0.200427 | + | 0.979709i | \(0.564233\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.38087 | − | 25.5950i | 0.353480 | − | 1.22578i | ||||
\(437\) | − | 38.4540i | − | 1.83951i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8683i | 1.13917i | 0.821931 | + | 0.569586i | \(0.192897\pi\) | ||||
−0.821931 | + | 0.569586i | \(0.807103\pi\) | |||||||
\(440\) | −35.4998 | + | 13.5354i | −1.69239 | + | 0.645276i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.395190 | + | 0.525256i | 0.0187973 | + | 0.0249839i | ||||
\(443\) | 6.00229 | 0.285177 | 0.142589 | − | 0.989782i | \(-0.454457\pi\) | ||||
0.142589 | + | 0.989782i | \(0.454457\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45.3600 | 2.15027 | ||||||||
\(446\) | 1.00206 | + | 1.33186i | 0.0474488 | + | 0.0630652i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.92296i | − | 0.232329i | −0.993230 | − | 0.116165i | \(-0.962940\pi\) | ||
0.993230 | − | 0.116165i | \(-0.0370600\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.3316i | 0.580671i | ||||||||
\(452\) | −12.9734 | − | 3.74115i | −0.610216 | − | 0.175969i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.13963 | + | 3.86694i | −0.241215 | + | 0.181485i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.4436 | −1.23698 | −0.618489 | − | 0.785793i | \(-0.712255\pi\) | ||||
−0.618489 | + | 0.785793i | \(0.712255\pi\) | |||||||
\(458\) | −18.2267 | + | 13.7134i | −0.851679 | + | 0.640784i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −40.4379 | − | 11.6611i | −1.88543 | − | 0.543703i | ||||
\(461\) | 8.92124i | 0.415504i | 0.978182 | + | 0.207752i | \(0.0666147\pi\) | ||||
−0.978182 | + | 0.207752i | \(0.933385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.3310i | 0.666020i | 0.942923 | + | 0.333010i | \(0.108064\pi\) | ||||
−0.942923 | + | 0.333010i | \(0.891936\pi\) | |||||||
\(464\) | 14.5961 | − | 23.2033i | 0.677606 | − | 1.07718i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.03852 | − | 9.35504i | −0.326053 | − | 0.433364i | ||||
\(467\) | 21.3656 | 0.988684 | 0.494342 | − | 0.869268i | \(-0.335409\pi\) | ||||
0.494342 | + | 0.869268i | \(0.335409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.79907 | + | 10.3659i | 0.359744 | + | 0.478144i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.92330 | + | 23.4034i | 0.410728 | + | 1.07723i | ||||
\(473\) | 2.36655i | 0.108814i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 70.6648i | 3.24232i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.4893 | − | 15.4157i | 0.937159 | − | 0.705097i | ||||
\(479\) | 32.3851 | 1.47971 | 0.739856 | − | 0.672766i | \(-0.234894\pi\) | ||||
0.739856 | + | 0.672766i | \(0.234894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.745254 | 0.0339807 | ||||||||
\(482\) | 21.9479 | − | 16.5131i | 0.999700 | − | 0.752152i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.575275 | − | 1.99491i | 0.0261489 | − | 0.0906778i | ||||
\(485\) | − | 26.5111i | − | 1.20381i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.88516i | − | 0.130739i | −0.997861 | − | 0.0653695i | \(-0.979177\pi\) | ||
0.997861 | − | 0.0653695i | \(-0.0208226\pi\) | |||||||
\(488\) | 2.68580 | + | 7.04413i | 0.121580 | + | 0.318873i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.6547 | 0.751617 | 0.375808 | − | 0.926697i | \(-0.377365\pi\) | ||||
0.375808 | + | 0.926697i | \(0.377365\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.7416 | −0.483776 | ||||||||
\(494\) | −1.78377 | − | 2.37084i | −0.0802555 | − | 0.106669i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.99569 | + | 9.53128i | −0.269214 | + | 0.427967i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 26.0610i | − | 1.16665i | −0.812239 | − | 0.583325i | \(-0.801751\pi\) | ||
0.812239 | − | 0.583325i | \(-0.198249\pi\) | |||||||
\(500\) | 37.1116 | + | 10.7019i | 1.65968 | + | 0.478604i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.6690 | − | 11.7890i | 0.699341 | − | 0.526168i | ||||
\(503\) | −28.7302 | −1.28102 | −0.640509 | − | 0.767951i | \(-0.721277\pi\) | ||||
−0.640509 | + | 0.767951i | \(0.721277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.7599 | 0.612307 | ||||||||
\(506\) | 21.3117 | − | 16.0344i | 0.947419 | − | 0.712816i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −39.0399 | − | 11.2580i | −1.73211 | − | 0.499492i | ||||
\(509\) | − | 15.7921i | − | 0.699973i | −0.936755 | − | 0.349986i | \(-0.886186\pi\) | ||
0.936755 | − | 0.349986i | \(-0.113814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.0913 | + | 10.4086i | 0.887918 | + | 0.460002i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.54478 | − | 8.69880i | −0.288678 | − | 0.383688i | ||||
\(515\) | −8.12211 | −0.357903 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.22056 | −0.361540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.03408 | + | 1.15684i | −0.133053 | + | 0.0507307i | ||||
\(521\) | 3.41466i | 0.149599i | 0.997199 | + | 0.0747995i | \(0.0238317\pi\) | ||||
−0.997199 | + | 0.0747995i | \(0.976168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.61336i | 0.289182i | 0.989492 | + | 0.144591i | \(0.0461866\pi\) | ||||
−0.989492 | + | 0.144591i | \(0.953813\pi\) | |||||||
\(524\) | 9.55865 | − | 33.1470i | 0.417572 | − | 1.44803i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.3627 | − | 8.54907i | 0.495439 | − | 0.372757i | ||||
\(527\) | 4.41235 | 0.192205 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.54324 | 0.284489 | ||||||||
\(530\) | 2.72861 | − | 2.05295i | 0.118523 | − | 0.0891743i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.05395i | 0.0456516i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 42.8028i | − | 1.85053i | ||||||
\(536\) | 28.0600 | − | 10.6988i | 1.21201 | − | 0.462116i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23.8994 | + | 31.7652i | 1.03038 | + | 1.36949i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.39128 | 0.403762 | 0.201881 | − | 0.979410i | \(-0.435295\pi\) | ||||
0.201881 | + | 0.979410i | \(0.435295\pi\) | |||||||
\(542\) | −21.5134 | − | 28.5939i | −0.924081 | − | 1.22821i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.739605 | − | 8.83568i | −0.0317103 | − | 0.378827i | ||||
\(545\) | − | 51.5640i | − | 2.20876i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8029i | 0.632924i | 0.948605 | + | 0.316462i | \(0.102495\pi\) | ||||
−0.948605 | + | 0.316462i | \(0.897505\pi\) | |||||||
\(548\) | −31.9597 | − | 9.21625i | −1.36525 | − | 0.393699i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −39.1632 | + | 29.4655i | −1.66992 | + | 1.25641i | ||||
\(551\) | 48.4841 | 2.06549 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.85753 | − | 2.14994i | 0.121405 | − | 0.0913422i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −31.2227 | − | 9.00374i | −1.32414 | − | 0.381843i | ||||
\(557\) | 3.59946i | 0.152514i | 0.997088 | + | 0.0762569i | \(0.0242969\pi\) | ||||
−0.997088 | + | 0.0762569i | \(0.975703\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.202263i | 0.00855482i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.80972 | − | 9.05094i | −0.287251 | − | 0.381791i | ||||
\(563\) | −19.1320 | −0.806318 | −0.403159 | − | 0.915130i | \(-0.632088\pi\) | ||||
−0.403159 | + | 0.915130i | \(0.632088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.1363 | −1.09956 | ||||||||
\(566\) | 6.01531 | + | 7.99507i | 0.252842 | + | 0.336058i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.543348 | − | 1.42506i | −0.0227984 | − | 0.0597940i | ||||
\(569\) | − | 31.8810i | − | 1.33652i | −0.743928 | − | 0.668260i | \(-0.767040\pi\) | ||
0.743928 | − | 0.668260i | \(-0.232960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 22.6794i | − | 0.949102i | −0.880228 | − | 0.474551i | \(-0.842610\pi\) | ||
0.880228 | − | 0.474551i | \(-0.157390\pi\) | |||||||
\(572\) | 0.570158 | − | 1.97717i | 0.0238395 | − | 0.0826695i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −54.2899 | −2.26405 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.38056 | 0.0574734 | 0.0287367 | − | 0.999587i | \(-0.490852\pi\) | ||||
0.0287367 | + | 0.999587i | \(0.490852\pi\) | |||||||
\(578\) | 16.4350 | − | 12.3653i | 0.683607 | − | 0.514330i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.7027 | − | 50.9854i | 0.610498 | − | 2.11705i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.16389i | 0.0896193i | ||||||||
\(584\) | 7.45189 | + | 19.5443i | 0.308361 | + | 0.808749i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.9594 | + | 22.5411i | 0.700588 | + | 0.931166i | ||||
\(587\) | −39.5737 | −1.63338 | −0.816692 | − | 0.577074i | \(-0.804194\pi\) | ||||
−0.816692 | + | 0.577074i | \(0.804194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.9160 | −0.820624 | ||||||||
\(590\) | 29.1494 | + | 38.7430i | 1.20006 | + | 1.59502i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.50916 | − | 5.35272i | −0.349724 | − | 0.219995i | ||||
\(593\) | 22.7337i | 0.933563i | 0.884373 | + | 0.466781i | \(0.154587\pi\) | ||||
−0.884373 | + | 0.466781i | \(0.845413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.8707 | + | 3.13481i | 0.445283 | + | 0.128407i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.82146 | − | 1.37042i | 0.0744848 | − | 0.0560407i | ||||
\(599\) | 13.0276 | 0.532293 | 0.266147 | − | 0.963933i | \(-0.414249\pi\) | ||||
0.266147 | + | 0.963933i | \(0.414249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.6907 | 1.78218 | 0.891091 | − | 0.453825i | \(-0.149941\pi\) | ||||
0.891091 | + | 0.453825i | \(0.149941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.68245 | − | 2.21540i | −0.312595 | − | 0.0901433i | ||||
\(605\) | − | 4.01897i | − | 0.163394i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.05507i | − | 0.367534i | −0.982970 | − | 0.183767i | \(-0.941171\pi\) | ||
0.982970 | − | 0.183767i | \(-0.0588292\pi\) | |||||||
\(608\) | 3.33835 | + | 39.8815i | 0.135388 | + | 1.61741i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.77358 | + | 11.6611i | 0.355232 | + | 0.472146i | ||||
\(611\) | −0.702591 | −0.0284238 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.6275 | 0.469630 | 0.234815 | − | 0.972040i | \(-0.424552\pi\) | ||||
0.234815 | + | 0.972040i | \(0.424552\pi\) | |||||||
\(614\) | −8.86424 | − | 11.7816i | −0.357732 | − | 0.475468i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.3734i | − | 0.739685i | −0.929094 | − | 0.369843i | \(-0.879412\pi\) | ||
0.929094 | − | 0.369843i | \(-0.120588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.6794i | 0.911561i | 0.890092 | + | 0.455781i | \(0.150640\pi\) | ||||
−0.890092 | + | 0.455781i | \(0.849360\pi\) | |||||||
\(620\) | −6.03950 | + | 20.9435i | −0.242552 | + | 0.841110i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.6597 | − | 19.3058i | 1.02886 | − | 0.774091i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8241 | 0.992965 | ||||||||
\(626\) | 25.2951 | − | 19.0315i | 1.01100 | − | 0.760650i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.06816 | − | 21.0429i | 0.242146 | − | 0.839702i | ||||
\(629\) | 3.93918i | 0.157065i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 27.5820i | − | 1.09802i | −0.835815 | − | 0.549011i | \(-0.815005\pi\) | ||
0.835815 | − | 0.549011i | \(-0.184995\pi\) | |||||||
\(632\) | 16.2952 | − | 6.21305i | 0.648187 | − | 0.247142i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.7770 | + | 32.9316i | 0.984020 | + | 1.30788i | ||||
\(635\) | −78.6502 | −3.12114 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.2167 | + | 26.8704i | 0.800387 | + | 1.06381i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 42.9514 | + | 8.58345i | 1.69780 | + | 0.339290i | ||||
\(641\) | 28.7971i | 1.13742i | 0.822539 | + | 0.568709i | \(0.192557\pi\) | ||||
−0.822539 | + | 0.568709i | \(0.807443\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 38.1698i | − | 1.50527i | −0.658438 | − | 0.752635i | \(-0.728783\pi\) | ||
0.658438 | − | 0.752635i | \(-0.271217\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.5315 | − | 9.42842i | 0.493046 | − | 0.370956i | ||||
\(647\) | −45.7885 | −1.80013 | −0.900066 | − | 0.435754i | \(-0.856482\pi\) | ||||
−0.900066 | + | 0.435754i | \(0.856482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.7247 | −1.20605 | ||||||||
\(650\) | −3.34718 | + | 2.51835i | −0.131287 | + | 0.0987776i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −40.4379 | − | 11.6611i | −1.58367 | − | 0.456685i | ||||
\(653\) | 6.01957i | 0.235564i | 0.993039 | + | 0.117782i | \(0.0375784\pi\) | ||||
−0.993039 | + | 0.117782i | \(0.962422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 66.7784i | − | 2.60925i | ||||||
\(656\) | 7.56989 | − | 12.0338i | 0.295554 | − | 0.469840i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.45187 | −0.329238 | −0.164619 | − | 0.986357i | \(-0.552639\pi\) | ||||
−0.164619 | + | 0.986357i | \(0.552639\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.3229 | 0.751574 | 0.375787 | − | 0.926706i | \(-0.377372\pi\) | ||||
0.375787 | + | 0.926706i | \(0.377372\pi\) | |||||||
\(662\) | 17.3713 | + | 23.0885i | 0.675154 | + | 0.897361i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.20704 | − | 16.2794i | −0.240880 | − | 0.631764i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.2491i | 1.44229i | ||||||||
\(668\) | −4.65133 | + | 16.1296i | −0.179965 | + | 0.624075i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 46.4517 | − | 34.9492i | 1.79459 | − | 1.35021i | ||||
\(671\) | −9.24773 | −0.357005 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.5239 | 1.17661 | 0.588305 | − | 0.808639i | \(-0.299795\pi\) | ||||
0.588305 | + | 0.808639i | \(0.299795\pi\) | |||||||
\(674\) | −6.96899 | + | 5.24331i | −0.268435 | + | 0.201965i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.15537 | + | 24.8130i | −0.275206 | + | 0.954347i | ||||
\(677\) | 19.9465i | 0.766606i | 0.923623 | + | 0.383303i | \(0.125214\pi\) | ||||
−0.923623 | + | 0.383303i | \(0.874786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.11468 | − | 16.0372i | −0.234487 | − | 0.614998i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.30448 | − | 11.0377i | −0.317995 | − | 0.422654i | ||||
\(683\) | −27.3733 | −1.04741 | −0.523705 | − | 0.851900i | \(-0.675451\pi\) | ||||
−0.523705 | + | 0.851900i | \(0.675451\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −64.3864 | −2.46008 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.45274 | − | 2.30940i | 0.0553851 | − | 0.0880451i | ||||
\(689\) | 0.184943i | 0.00704576i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.3588i | 1.83965i | 0.392324 | + | 0.919827i | \(0.371671\pi\) | ||||
−0.392324 | + | 0.919827i | \(0.628329\pi\) | |||||||
\(692\) | 28.8659 | + | 8.32410i | 1.09732 | + | 0.316435i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.0865 | − | 12.8555i | 0.648594 | − | 0.487987i | ||||
\(695\) | −62.9017 | −2.38600 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.57084 | −0.211010 | ||||||||
\(698\) | −21.3509 | + | 16.0640i | −0.808145 | + | 0.608030i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 17.0447i | − | 0.643768i | −0.946779 | − | 0.321884i | \(-0.895684\pi\) | ||
0.946779 | − | 0.321884i | \(-0.104316\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 17.7802i | − | 0.670594i | ||||||
\(704\) | −20.7108 | + | 18.4798i | −0.780567 | + | 0.696483i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.03656 | − | 12.0107i | −0.340095 | − | 0.452028i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.4407 | −0.993000 | −0.496500 | − | 0.868037i | \(-0.665382\pi\) | ||||
−0.496500 | + | 0.868037i | \(0.665382\pi\) | |||||||
\(710\) | −1.77493 | − | 2.35910i | −0.0666120 | − | 0.0885353i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30.9648 | − | 11.8063i | 1.16045 | − | 0.442460i | ||||
\(713\) | − | 15.3009i | − | 0.573024i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3.98323i | − | 0.148964i | ||||||
\(716\) | −1.42774 | + | 4.95106i | −0.0533573 | + | 0.185030i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.17485 | + | 2.38869i | −0.118484 | + | 0.0891450i | ||||
\(719\) | 34.7544 | 1.29612 | 0.648060 | − | 0.761590i | \(-0.275581\pi\) | ||||
0.648060 | + | 0.761590i | \(0.275581\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −35.0918 | + | 26.4023i | −1.30598 | + | 0.982592i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.3806 | − | 42.9330i | 0.460123 | − | 1.59559i | ||||
\(725\) | − | 68.4505i | − | 2.54219i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.9785i | 0.852226i | 0.904670 | + | 0.426113i | \(0.140117\pi\) | ||||
−0.904670 | + | 0.426113i | \(0.859883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 24.3428 | + | 32.3545i | 0.900966 | + | 1.19749i | ||||
\(731\) | −1.06910 | −0.0395421 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.8777 | 0.771134 | 0.385567 | − | 0.922680i | \(-0.374006\pi\) | ||||
0.385567 | + | 0.922680i | \(0.374006\pi\) | |||||||
\(734\) | 16.0536 | + | 21.3371i | 0.592548 | + | 0.787568i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.6399 | + | 2.56477i | −1.12940 | + | 0.0945385i | ||||
\(737\) | 36.8380i | 1.35694i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.90369i | − | 0.253956i | −0.991906 | − | 0.126978i | \(-0.959472\pi\) | ||
0.991906 | − | 0.126978i | \(-0.0405278\pi\) | |||||||
\(740\) | −18.6975 | − | 5.39183i | −0.687334 | − | 0.198208i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.7592 | 0.468091 | 0.234046 | − | 0.972226i | \(-0.424803\pi\) | ||||
0.234046 | + | 0.972226i | \(0.424803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.9003 | 0.802366 | ||||||||
\(746\) | −37.9575 | + | 28.5584i | −1.38972 | + | 1.04560i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.4507 | + | 3.01368i | 0.382114 | + | 0.110191i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.7473i | 1.88829i | 0.329535 | + | 0.944143i | \(0.393108\pi\) | ||||
−0.329535 | + | 0.944143i | \(0.606892\pi\) | |||||||
\(752\) | 8.02204 | + | 5.04630i | 0.292534 | + | 0.184019i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.72787 | + | 2.29655i | 0.0629254 | + | 0.0836354i | ||||
\(755\) | −15.4772 | −0.563272 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.2613 | −0.881793 | −0.440897 | − | 0.897558i | \(-0.645339\pi\) | ||||
−0.440897 | + | 0.897558i | \(0.645339\pi\) | |||||||
\(758\) | −6.44094 | − | 8.56079i | −0.233946 | − | 0.310942i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.5998 | + | 72.3868i | 1.00115 | + | 2.62575i | ||||
\(761\) | − | 48.1383i | − | 1.74501i | −0.488603 | − | 0.872506i | \(-0.662493\pi\) | ||
0.488603 | − | 0.872506i | \(-0.337507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.59640 | − | 15.9392i | 0.166292 | − | 0.576659i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.1133 | + | 30.9327i | −1.48548 | + | 1.11764i | ||||
\(767\) | −2.62596 | −0.0948180 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.1961 | −1.16102 | −0.580510 | − | 0.814253i | \(-0.697147\pi\) | ||||
−0.580510 | + | 0.814253i | \(0.697147\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.8330 | + | 41.0338i | −0.425879 | + | 1.47684i | ||||
\(773\) | 40.1610i | 1.44449i | 0.691638 | + | 0.722245i | \(0.256890\pi\) | ||||
−0.691638 | + | 0.722245i | \(0.743110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.1176i | 1.01002i | ||||||||
\(776\) | −6.90032 | − | 18.0977i | −0.247707 | − | 0.649670i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.90579 | − | 3.86214i | −0.104177 | − | 0.138464i | ||||
\(779\) | 25.1450 | 0.900914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.87085 | 0.0669444 | ||||||||
\(782\) | 7.24361 | + | 9.62763i | 0.259031 | + | 0.344283i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 42.3932i | − | 1.51308i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.1924i | 1.25447i | 0.778828 | + | 0.627237i | \(0.215814\pi\) | ||||
−0.778828 | + | 0.627237i | \(0.784186\pi\) | |||||||
\(788\) | −1.10028 | − | 0.317290i | −0.0391960 | − | 0.0113030i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.9757 | − | 20.2959i | 0.959753 | − | 0.722096i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.790381 | −0.0280672 | ||||||||
\(794\) | −22.3435 | + | 16.8108i | −0.792942 | + | 0.596591i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.6302 | + | 9.69798i | 1.19199 | + | 0.343736i | ||||
\(797\) | − | 18.8026i | − | 0.666021i | −0.942923 | − | 0.333010i | \(-0.891936\pi\) | ||
0.942923 | − | 0.333010i | \(-0.108064\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.71367i | − | 0.131380i | ||||||
\(800\) | 56.3053 | − | 4.71312i | 1.99069 | − | 0.166634i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.23910 | + | 4.30515i | 0.114376 | + | 0.152020i | ||||
\(803\) | −25.6583 | −0.905463 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.709764 | − | 0.943361i | −0.0250004 | − | 0.0332285i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.39313 | − | 3.58143i | 0.330449 | − | 0.125994i | ||||
\(809\) | 54.3925i | 1.91234i | 0.292816 | + | 0.956169i | \(0.405408\pi\) | ||||
−0.292816 | + | 0.956169i | \(0.594592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.91646i | − | 0.0672961i | −0.999434 | − | 0.0336480i | \(-0.989287\pi\) | ||
0.999434 | − | 0.0336480i | \(-0.0107125\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.85399 | − | 7.41392i | 0.345382 | − | 0.259858i | ||||
\(815\) | −81.4668 | −2.85366 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.82558 | 0.168826 | ||||||||
\(818\) | −33.3299 | + | 25.0767i | −1.16535 | + | 0.876785i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.62520 | − | 26.4423i | 0.266283 | − | 0.923405i | ||||
\(821\) | 25.3538i | 0.884853i | 0.896805 | + | 0.442426i | \(0.145882\pi\) | ||||
−0.896805 | + | 0.442426i | \(0.854118\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.26718i | 0.183602i | 0.995777 | + | 0.0918011i | \(0.0292624\pi\) | ||||
−0.995777 | + | 0.0918011i | \(0.970738\pi\) | |||||||
\(824\) | −5.54452 | + | 2.11402i | −0.193153 | + | 0.0736455i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.4115 | −1.50957 | −0.754784 | − | 0.655974i | \(-0.772258\pi\) | ||||
−0.754784 | + | 0.655974i | \(0.772258\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.96581 | −0.311396 | −0.155698 | − | 0.987805i | \(-0.549763\pi\) | ||||
−0.155698 | + | 0.987805i | \(0.549763\pi\) | |||||||
\(830\) | −20.2763 | − | 26.9496i | −0.703800 | − | 0.935435i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.77010 | + | 1.57942i | −0.0613671 | + | 0.0547566i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.4950i | 1.12454i | ||||||||
\(836\) | −47.1711 | − | 13.6028i | −1.63145 | − | 0.470462i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.64506 | − | 4.24722i | 0.195005 | − | 0.146718i | ||||
\(839\) | −36.4358 | −1.25790 | −0.628952 | − | 0.777444i | \(-0.716516\pi\) | ||||
−0.628952 | + | 0.777444i | \(0.716516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9648 | −0.619476 | ||||||||
\(842\) | −5.10026 | + | 3.83732i | −0.175766 | + | 0.132243i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.2750 | − | 4.40488i | −0.525788 | − | 0.151622i | ||||
\(845\) | 49.9887i | 1.71966i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.32833 | − | 2.11164i | 0.0456152 | − | 0.0725140i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.3112 | − | 17.6921i | −0.456569 | − | 0.606836i | ||||
\(851\) | 13.6601 | 0.468262 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.08381 | −0.139827 | −0.0699135 | − | 0.997553i | \(-0.522272\pi\) | ||||
−0.0699135 | + | 0.997553i | \(0.522272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.1407 | − | 29.2192i | −0.380782 | − | 0.998691i | ||||
\(857\) | 11.7762i | 0.402267i | 0.979564 | + | 0.201134i | \(0.0644626\pi\) | ||||
−0.979564 | + | 0.201134i | \(0.935537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 33.3744i | − | 1.13872i | −0.822088 | − | 0.569360i | \(-0.807191\pi\) | ||
0.822088 | − | 0.569360i | \(-0.192809\pi\) | |||||||
\(860\) | 1.46335 | − | 5.07454i | 0.0498999 | − | 0.173040i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.9262 | − | 17.2491i | 0.780869 | − | 0.587508i | ||||
\(863\) | 24.8629 | 0.846344 | 0.423172 | − | 0.906049i | \(-0.360917\pi\) | ||||
0.423172 | + | 0.906049i | \(0.360917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.1536 | 1.97728 | ||||||||
\(866\) | −9.42626 | + | 7.09210i | −0.320317 | + | 0.240999i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.3928i | 0.725700i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.14845i | 0.106681i | ||||||||
\(872\) | −13.4211 | − | 35.2000i | −0.454496 | − | 1.19202i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32.6954 | − | 43.4561i | −1.10594 | − | 1.46993i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.0935 | 1.55647 | 0.778234 | − | 0.627975i | \(-0.216116\pi\) | ||||
0.778234 | + | 0.627975i | \(0.216116\pi\) | |||||||
\(878\) | 20.2940 | + | 26.9731i | 0.684888 | + | 0.910298i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −28.6092 | + | 45.4797i | −0.964414 | + | 1.53312i | ||||
\(881\) | − | 15.9952i | − | 0.538893i | −0.963015 | − | 0.269446i | \(-0.913159\pi\) | ||
0.963015 | − | 0.269446i | \(-0.0868407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.9597i | 1.44571i | 0.691001 | + | 0.722854i | \(0.257170\pi\) | ||||
−0.691001 | + | 0.722854i | \(0.742830\pi\) | |||||||
\(884\) | 0.893193 | + | 0.257571i | 0.0300413 | + | 0.00866306i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.78306 | − | 5.10342i | 0.227882 | − | 0.171453i | ||||
\(887\) | −19.5243 | −0.655563 | −0.327781 | − | 0.944754i | \(-0.606301\pi\) | ||||
−0.327781 | + | 0.944754i | \(0.606301\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 51.2604 | − | 38.5672i | 1.71825 | − | 1.29277i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.26481 | + | 0.653107i | 0.0758315 | + | 0.0218676i | ||||
\(893\) | 16.7624i | 0.560931i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.97446i | 0.333410i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.18573 | − | 5.56334i | −0.139680 | − | 0.185651i | ||||
\(899\) | 19.2919 | 0.643421 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.977548 | −0.0325669 | ||||||||
\(902\) | 10.4849 | + | 13.9357i | 0.349108 | + | 0.464006i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.8418 | + | 6.80277i | −0.593411 | + | 0.226257i | ||||
\(905\) | − | 86.4934i | − | 2.87514i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 30.2961i | − | 1.00596i | −0.864297 | − | 0.502982i | \(-0.832236\pi\) | ||
0.864297 | − | 0.502982i | \(-0.167764\pi\) | |||||||
\(908\) | −2.52034 | + | 8.73991i | −0.0836404 | + | 0.290044i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1485 | −0.833207 | −0.416604 | − | 0.909088i | \(-0.636780\pi\) | ||||
−0.416604 | + | 0.909088i | \(0.636780\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.3721 | 0.707313 | ||||||||
\(914\) | −29.8834 | + | 22.4836i | −0.988453 | + | 0.743690i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.93791 | + | 30.9944i | −0.295317 | + | 1.02408i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.15458i | − | 0.137047i | −0.997650 | − | 0.0685235i | \(-0.978171\pi\) | ||
0.997650 | − | 0.0685235i | \(-0.0218288\pi\) | |||||||
\(920\) | −55.6129 | + | 21.2042i | −1.83350 | + | 0.699081i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.58526 | + | 10.0817i | 0.249807 | + | 0.332024i | ||||
\(923\) | 0.159897 | 0.00526308 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.1023 | −0.825360 | ||||||||
\(926\) | 12.1849 | + | 16.1952i | 0.400421 | + | 0.532208i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.23374 | − | 38.6318i | −0.106153 | − | 1.26815i | ||||
\(929\) | − | 43.3371i | − | 1.42184i | −0.703271 | − | 0.710922i | \(-0.748278\pi\) | ||
0.703271 | − | 0.710922i | \(-0.251722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.9082 | − | 4.58746i | −0.521090 | − | 0.150267i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.1449 | − | 18.1661i | 0.790045 | − | 0.594412i | ||||
\(935\) | 21.0541 | 0.688541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.6116 | 0.934701 | 0.467350 | − | 0.884072i | \(-0.345209\pi\) | ||||
0.467350 | + | 0.884072i | \(0.345209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17.6272 | + | 5.08317i | 0.574934 | + | 0.165795i | ||||
\(941\) | 23.2511i | 0.757964i | 0.925404 | + | 0.378982i | \(0.123726\pi\) | ||||
−0.925404 | + | 0.378982i | \(0.876274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.3183i | 0.629089i | ||||||||
\(944\) | 29.9827 | + | 18.8607i | 0.975855 | + | 0.613865i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.01215 | + | 2.67439i | 0.0654207 | + | 0.0869520i | ||||
\(947\) | 49.6558 | 1.61360 | 0.806798 | − | 0.590827i | \(-0.201199\pi\) | ||||
0.806798 | + | 0.590827i | \(0.201199\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.19295 | −0.0711863 | ||||||||
\(950\) | 60.0825 | + | 79.8569i | 1.94933 | + | 2.59090i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.7824i | 1.45065i | 0.688409 | + | 0.725323i | \(0.258310\pi\) | ||||
−0.688409 | + | 0.725323i | \(0.741690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 32.1113i | − | 1.03910i | ||||||
\(956\) | 10.0474 | − | 34.8419i | 0.324956 | − | 1.12687i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.5977 | − | 27.5353i | 1.18242 | − | 0.889625i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0754 | 0.744368 | ||||||||
\(962\) | 0.842197 | − | 0.633650i | 0.0271535 | − | 0.0204297i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.7627 | − | 37.3223i | 0.346642 | − | 1.20207i | ||||
\(965\) | 82.6673i | 2.66116i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13.2510i | − | 0.426122i | −0.977039 | − | 0.213061i | \(-0.931657\pi\) | ||
0.977039 | − | 0.213061i | \(-0.0683433\pi\) | |||||||
\(968\) | −1.04606 | − | 2.74353i | −0.0336216 | − | 0.0881805i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.5410 | − | 29.9597i | −0.723748 | − | 0.961948i | ||||
\(971\) | 4.38813 | 0.140822 | 0.0704108 | − | 0.997518i | \(-0.477569\pi\) | ||||
0.0704108 | + | 0.997518i | \(0.477569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.45309 | − | 3.26046i | −0.0786022 | − | 0.104472i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.02441 | + | 5.67684i | 0.288864 | + | 0.181711i | ||||
\(977\) | 35.5266i | 1.13660i | 0.822823 | + | 0.568298i | \(0.192398\pi\) | ||||
−0.822823 | + | 0.568298i | \(0.807602\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.6515i | 1.29923i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.8212 | − | 14.1606i | 0.600608 | − | 0.451884i | ||||
\(983\) | −12.2843 | −0.391808 | −0.195904 | − | 0.980623i | \(-0.562764\pi\) | ||||
−0.195904 | + | 0.980623i | \(0.562764\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.21665 | −0.0706282 | ||||||||
\(986\) | −12.1388 | + | 9.13298i | −0.386579 | + | 0.290853i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.03160 | − | 1.16260i | −0.128262 | − | 0.0369872i | ||||
\(989\) | 3.70737i | 0.117887i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.4376i | 0.966881i | 0.875377 | + | 0.483441i | \(0.160613\pi\) | ||||
−0.875377 | + | 0.483441i | \(0.839387\pi\) | |||||||
\(992\) | 1.32833 | + | 15.8689i | 0.0421747 | + | 0.503839i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 67.7518 | 2.14788 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.4846 | −1.63053 | −0.815266 | − | 0.579086i | \(-0.803409\pi\) | ||||
−0.815266 | + | 0.579086i | \(0.803409\pi\) | |||||||
\(998\) | −22.1583 | − | 29.4510i | −0.701408 | − | 0.932256i | ||||
\(999\) | 0 | 0 |
(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 | 1764.2.e.h.1079.13 | 16 | ||
3.2 | odd | 2 | inner | 1764.2.e.h.1079.4 | 16 | ||
4.3 | odd | 2 | inner | 1764.2.e.h.1079.3 | 16 | ||
7.3 | odd | 6 | 252.2.be.a.107.9 | yes | 32 | ||
7.5 | odd | 6 | 252.2.be.a.179.3 | yes | 32 | ||
7.6 | odd | 2 | 1764.2.e.i.1079.13 | 16 | |||
12.11 | even | 2 | inner | 1764.2.e.h.1079.14 | 16 | ||
21.5 | even | 6 | 252.2.be.a.179.14 | yes | 32 | ||
21.17 | even | 6 | 252.2.be.a.107.8 | yes | 32 | ||
21.20 | even | 2 | 1764.2.e.i.1079.4 | 16 | |||
28.3 | even | 6 | 252.2.be.a.107.14 | yes | 32 | ||
28.19 | even | 6 | 252.2.be.a.179.8 | yes | 32 | ||
28.27 | even | 2 | 1764.2.e.i.1079.3 | 16 | |||
84.47 | odd | 6 | 252.2.be.a.179.9 | yes | 32 | ||
84.59 | odd | 6 | 252.2.be.a.107.3 | ✓ | 32 | ||
84.83 | odd | 2 | 1764.2.e.i.1079.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.be.a.107.3 | ✓ | 32 | 84.59 | odd | 6 | ||
252.2.be.a.107.8 | yes | 32 | 21.17 | even | 6 | ||
252.2.be.a.107.9 | yes | 32 | 7.3 | odd | 6 | ||
252.2.be.a.107.14 | yes | 32 | 28.3 | even | 6 | ||
252.2.be.a.179.3 | yes | 32 | 7.5 | odd | 6 | ||
252.2.be.a.179.8 | yes | 32 | 28.19 | even | 6 | ||
252.2.be.a.179.9 | yes | 32 | 84.47 | odd | 6 | ||
252.2.be.a.179.14 | yes | 32 | 21.5 | even | 6 | ||
1764.2.e.h.1079.3 | 16 | 4.3 | odd | 2 | inner | ||
1764.2.e.h.1079.4 | 16 | 3.2 | odd | 2 | inner | ||
1764.2.e.h.1079.13 | 16 | 1.1 | even | 1 | trivial | ||
1764.2.e.h.1079.14 | 16 | 12.11 | even | 2 | inner | ||
1764.2.e.i.1079.3 | 16 | 28.27 | even | 2 | |||
1764.2.e.i.1079.4 | 16 | 21.20 | even | 2 | |||
1764.2.e.i.1079.13 | 16 | 7.6 | odd | 2 | |||
1764.2.e.i.1079.14 | 16 | 84.83 | odd | 2 |